MMSE Journal Vol.1 2015 by MMSE Journal

Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

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Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

Sankt Lorenzen 36, 8715, Sankt Lorenzen, Austria

Mechanics, Materials Science & Engineering Journal

October 2015 MMSE Journal. Open Access www.mmse.xyz 2

Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

Mechanics, Materials Sciences & Engineering Journal, Austria, Sankt Lorenzen, 2015

Mechanics, Materials Science & Engineering Journal (MMSE Journal) is journal that deals in peerreviewed, open access publishing, focusing on wide range of subject areas, including economics, business, social sciences, engineering etc.

MMSE Journal is dedicated to knowledge-based products and services for the academic, scientific, professional, research and student communities worldwide. Open Access model of the publications promotes research by allowing unrestricted availability of high quality articles.

All authors bear the personal responsibility for the material they published in the Journal. The Journal Policy declares the acceptance of the scientific papers worldwide, if they passed the peer-review procedure.

Editor-in-Chief Mr. Peter Zisser

ISSN 2412-5954 e-ISSN xxxx-xxxx

Design and layout: Mechanics, Materials

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Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

CONTENT I. MATERIALS SCIENCE ....................................................................................................................... 6 METAL MATRIX COMPOSITES REINFORCED WITH NANOPARTICLES FOR THE NEEDS OF SPACE EXPLORATION ....................................................................................................................................... 6 PRODUCING A615/A615M HIGH STRENGTH CONSTRUCTION RE-BARS WITHOUT USE OF MICROALLOYS: PART 2 ....................................................................................................................... 11 THERMAL CONDUCTIVITY OF ZINCBLENDE CRYSTALS ....................................................................... 28 PHOTO DEGRADATION IN DYE-SENSITIZED SOLAR CELLS .................................................................. 36 II. MECHANICAL ENGINEERING ....................................................................................................... 48 ANALYTICAL DESCRIPTION OF PLASTIC DEFORMATION DISTRIBUTION IN THE NECK OF A FLAT TENSILE SPECIMEN ............................................................................................................................. 48 COMPUTER AIDED ANALYSIS AND PROTOTYPE TESTING OF AN IMPROVED BIOGAS REACTOR FOR BIOMASS SYSTEM ............................................................................................................................... 59 ON THE EVOLUTION THEORY OF IDENTIFICATION OF MATHEMATICAL MODELS OF CORROSION DESTRUCTION AT THE OPTIMUM DESIGN OF STRUCTURES ................................................................. 66 PROPOSED DESIGN PROCEDURE OF A HELICAL COIL HEAT EXCHANGER FOR AN ORC ENERGY RECOVERY SYSTEM FOR VEHICULAR APPLICATION ........................................................................... 72 MELTING HEAT TRANSFER IN MHD BOUNDARY LAYER STAGNATION-POINT FLOW TOWARDS A STRETCHING SHEET WITH THERMAL RADIATION ................................................................................ 97 DYNAMIC DESIGN OF GROUND TRANSPORT WITH THE HELP OF COMPUTATIONAL EXPERIMENT .... 105 KINEMATICS AND LOAD FORMULATION OF ENGINE CRANK MECHANISM ........................................ 112 SAFE SIMULATION OF THE MANIPULATOR IN THE PRESENCE OF STATIC AND DYNAMIC OBSTACLES BY USING FUZZY SYSTEM ...................................................................................................................... 124 III. MACHINE BUILDING ................................................................................................................. 133 FEASIBLE WAYS TO IMPROVE THE DURABILITY OF THE PUMPS’ PARTS OPERATING WITH HYDROABRASIVE MIXTURES ............................................................................................................ 133 IX. ECONOMICS & MANAGEMENT ................................................................................................. 138 ON RELATIONS BETWEEN DUMP TRUCK EFFICIENCY AND SERVICE FACILITIES STRUCTURE ........... 138

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Preface

Our company, being a classical industrial enterprise, understands that production of the high-quality product or service must meet scientific background. Only in this case, the end product will be competitive on the growing international market. Therefore, innovation projects have to be market-targeted from idea to production. The company's management has always clearly understood and understands that it is impossible to demand from academicians fast, immediate, commercial return. Thus, we want to offer an easy to access service, which allows scientists expressing scientific thoughts and achievements. Our Journal is intended to expand the horizons of thought, setup the dialogue between science and industry. This will allow receiving information about new theoretical and applied research, consolidate the efforts of specialists and disseminate expertise in the field of mechanics, materials science, engineering, information technology, industrial and social processes. We hope for bilateral beneficial cooperation, authorsâ&#x20AC;&#x2122; support and success.

Magnolithe GmbH, Editor-in-Cheif

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Mr. Peter Zisser

Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

I. Materials Science Metal Matrix Composites Reinforced With Nanoparticles for the Needs of Space Exploration L.E. Agureev1a, V.I. Kostikov2, Zh.V. Eremeeva3, A.A. Barmin4, R.N. Rizakhanov5, B.S. Ivanov6 1 – Researcher, Department of Nanotechnology, Keldysh Research Center, Russia 2 – Doctor of Science, Associate Professor, Moscow State University of Steel and Alloys, Russia 3 – Doctor of Science, Associate Professor, Moscow State University of Steel and Alloys, Russia 4 – Ph.D., Leading Researcher, Department of Nanotechnology, Keldysh Research Center, Russia 5 – Ph.D., Head of Department, Department of Nanotechnology, Keldysh Research Center, Russia 6 – Engineer, Department of Nanotechnology, Keldysh Research Center, Russia a – trynano@gmail.com

Keywords: nanometric particles, aluminum composites, PM method ABSTRACT. Aluminum (Al) matrix composite materials reinforced with small amounts (0,01 – 0,15 % vol.) of aluminum or zirconium oxides nanoparticles were fabricated by tradition powder metallurgy (PM) techniques with cold pressing and vacuum sintering. Nanoparticles and their clusters were located on grain boundaries of a matrix. The microhardness of the produced composites was dramatically increased than bulk pure Al, by increasing the amount of nanoparticles. The tensile strength of the produced composites was dramatically increased (more than 2 times) than bulk pure Al, by increasing the amount of nanoparticles. This powder metallurgical approach could also be applied to other nanoreinforced composites, such as ceramics or complex matrix materials.

Introduction. For the development of space techniques we need lung and durable materials. As you know, reduction of weight payload per 1 kg reduces the cost of flying to 100 thousand rubles [1]. From this standpoint, aluminum based composites reinforced with nanoparticles of different refractory materials are promising materials. However, aware of the high activity of nanoparticles associated with an increased number of atoms on the surface and thus uncompensated surface energy, it is advisable to create aluminum composites with small concentrations of nano-additives (order of tenths and hundredths of a mass). In addition, according to the works of the school of Academician I.F.Obraztsov and results of empirical research under the supervision of a member-correspondent of RAS V.I.Kostikov, small additions of nanoparticles can contribute a substantial modification of the properties of interfacial layer [2, 3]. These factors can increase the mechanical properties of the composite with a metal matrix two or more times. Use of nanoparticles to reinforce metallic materials lead to the development of novel composites with unique mechanical and physical properties. In order to achieve desired mechanical properties of composites, reinforcing nanoparticles must be distributed uniformly within metal matrix of the composites. Various impact on characteristics of the baked composites is made by nanoparticles depending on the arrangement (on borders of grains or in grains) [4, 5]. Results of such influence are given in table 1, without specifying concentration. Composites on a basis "aluminum – ceramic particles" have lower density, than bronze, possess an optimum ratio MMSE Journal. Open Access www.mmse.xyz 6

Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

of durability and plasticity and sufficient corrosion resistance in combination with high operational mechanical characteristics. 1. Experimental procedure. At least five measurements were made per sample. The microstructure of the composites was observed by optical microscopy (Zeiss Axiovert 40 MAT light microscope), high resolution cold-field emission scanning electron microscopy (FEI Quanta 600 FEG) and transmission electron microscopy (JEOL, JEM-2100). The micro-Vickers hardnesses of the composites were measured according to EN ISO 6507-1 with a load of 20 and 0.02 kg for 15 s (Micromet 5114 microhardness tester). Determination of the compressive strength, bending and stretching performed on a universal servo-hydraulic machine for mechanical testing «LF-100KN» production «Walter + Bai» (Switzerland) with maximum force in static 100kN with an external digital controller (EDC) and a universal machine for mechanical tests VakEto-TestSystems.

Table 1. Influence of an arrangement of nanoparticles on properties of composites Nanoparticles in grain.

Nanoparticles on grain border

Reduce subgrains in grain

Reduce grain, without allowing to grow borders, increasing durability

Brake diffusive creep through grain volume

Brake creep on borders of grains, being pressed into a matrix and on turning at the movement

Interfere with distribution of cracks

Interfere with origin and promote annihilation of vacancies, increasing creep resistance on borders of grains

Increase crack resistance at the expense of a hitch of the dispersing crack passing through a nanoparticle

Nanopowders of Al2O3 and ZrO2 (Keldysh Research Center, purity 99.5%, d = 50-60 nm) and aluminum powder ASD-4 (SUAL, TU (Technical Specifications) 48_5_226–87, S = 0.34–0.38 m2/g, d = 2–10 μm) as a matrix were used as starting materials. The Al2O3 and ZrO2 nanoparticles were produced in an electro arc plasma reactor (the process is described in detail elsewhere [6,7]), producing an average particle size between 50 and 60 nm. Mixing. To achieve a homogeneous material structure and mechanical properties necessary that the distribution of the components in the powder batch was uniform. As to achieve this nanosized additives is very difficult, a method of mixing the charge in several steps: 1. Deagglomeration of the matrix powder ASD-4 in the ultrasonic treatment in ethanol. 2. Preparation of nanoparticle suspension in ethanol with their deagglomeration simultaneously exposed to ultrasound. 3. Mixing ethanol aluminum nanoparticles under the action of ultrasound. 4. Drying of the slurry. 5. Averaging dried charge in the mill with cylinders of ZrO2 in the mode of transition from slide to roll. 6. Request repeated charge and its mixing in a tumbling mixer. Pressing. Compression was performed in a batch cylindrical steel molds in a press 50T "Mekamak" at pressures of 100, 200, 300, 400, 500 MPa. Sintering. Sintering is carried out in an automatic vacuum furnace VMS-22-10,5. The sintering temperature was varied from 550 to 670oC in forevacuum (5·10-2 mm Hg. V.), The sintering time is MMSE Journal. Open Access www.mmse.xyz 7

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from 60 to 150 minutes. The resulting samples had a 15 mm diameter and a thickness of approximately 18 mm. 2. Results and discussions. Fig. 1 shows the microstructure of the samples with additives nanoparticles of zirconium oxide. Visible small bit elongated grains. The size of grains of pure aluminum was 7 microns. The average diameter of the grains of material with nanoparticles was 4-5 microns.

Fig. 1. Microstructure of aluminum composites with ZrO2 nanoparticles, SEM

In fig. 2 the composite microstructure removed from the transmission electronic microscope is shown. The cluster of nanoparticles of oxide of aluminum located on borders of grains of a matrix is visible. Besides, on borders of grains the set of nanodimensional films of oxide of aluminum is located.

Fig. 2. Microstructure of aluminum composites with Al2O3 nanoparticles, TEM

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The introduction of small amounts of nanoparticles of aluminum oxide prevents the recrystallization of aluminum grains during sintering and stores grain size in the sintered material at the particle size of the starting powder.

Nanoparticles content, % vol.

In fig. 3, the mechanical properties of the Al-Al2O3/ZrO2 composites resulted from microhardness test of specimens, is graphically represented.

0,15 0,1 AVPP 0,05

ZrO2 Al2O3

0,01

Al 0 0

0,1

0,2

0,3

0,4

0,5

Vickers microhardness, GPa

Fig. 3. Vickers microhardness of aluminum composites

Nanoparticles content, % vol.

In fig. 4 the mechanical properties of the Al- Al2O3/ZrO2 composites resulted from tensile test of specimens, is graphically represented in compare with the mechanical properties of the Al AVPP (Russian analogue of 6xxx (Mg+ Si)-alloys) which is a precipitation hardening aluminum alloy, containing magnesium and silicon as its major alloying elements. This alloy is widely used for construction of aerospace structures [8].

0,15 0,1 AVPP 0,05

ZrO2 Al2O3

0,01

Al 0 0

100

150

Tensile strength, MPa

Fig. 4. Tensile strength of aluminum composites MMSE Journal. Open Access www.mmse.xyz 9

200

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Summary. A homogeneous distribution of the Al2O3/ZrO2 nanoparticles and clusters reinforcement phase in the Al matrix was obtained by combination of wet and dry mixing. Characterization of the mechanically milled powders confirmed uniform distribution of the reinforcement phase. Low concentration additions of nanoparticles in Al powder leads the composite towards steady-state condition in which, all microstructure properties such as powder size, powder shape and distribution of Al2O3 within Al matrix remain fixed. An optimum concentration of nanopowders (0,1 %vol.), is established for the processing of the Al-Al2O3/ZrO2 composites, that assures mechanical strength close to those of the Al AVPP alloy. References [1] The piloted expedition to Mars / Under the editorship of A.S. Koroteyev, The Russian academy of astronautics of K. E. Tsiolkovsky, 2006, 320 p. [In Russian] [2] Obrazcov I.F., Lur'e S.A., Belov P.A. “Osnovy teorii mezhfaznogo sloja”, Mehanika kompozicionnyh materialov i konstrukcij, 2004, T. 10, №3, pp. 596-612. - Obraztsov I.F., Lur'e S.A., Belov P.A., “Bases of the theory of an interphase layer”, Mechanics of composite materials and designs. 2004, T. 10, №3, pp. 596-612. [In Russian] [3] Anisimov O.V., Kostikov V.I., Shtankin Ju.V. Sozdanie metallokompozitov na osnove aljuminija putem kristallizacii zhidkogo metalla v pole centrifug. Perspektivnye materialy. 2010, № 2, pp. 5-10. - Anisimov O. V., Kostikov V. I., Shtankin Yu.V. Creation of Metalcomposites on The Basis of Aluminium by Crystallization of Liquid Metal in the Field of Centrifuges. Perspective materials, 2010, №. 2, pp. 5-10. [In Russian] [4] T. Ohji, Y.-K. Jeong, Y.-H. Choa, K. Niihara, “Strengtheing and toughening mechanisms of ceramic nanocomposites”, Journal of American Ceramic Society, 1998, №81, pp. 1453-1460. [5] Chuvil'deev V.N. Neravnovesnye granicy zjoren v metallah. Teorija i prilozhenija/ V.N. Chuvil'deev –M.: FIZMATLIT, 2004. -304 s. - Chuvildeev V. N. Nonequilibrium borders of grains in metals. The theory and appendices / V. N. Chuvildeev – M.: FIZMATLIT, 2004, 304 p. [6] Polyanskiy M.N., Savishkina S.V. “Lateral layer-by-layer nanostructuring of thermal barrier coatings of zirconium dioxide during plasma spraying”, 2014, Т. 8, № 1, pp. 144-148. [7] Sirotinkin V.P., Shamrai V.F., Samokhin A.V., Alekseev N.V., Sinaiskii M.A. “Phase composition of Al2O3 nanopowders prepared by plasma synthesis and heat-treated. Inorganic Materials”, 2012, Т. 48, № 4, pp. 342-349. [8] Metal:Matrix Composites. Custom-made Materials for Automotive and, Aerospace Engineering. /Ed: Karl U. Kainer. -WILEY-VCH Verlag GmbH and Go. KGaA, Weinheim. - 2006.

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Producing A615/A615M High Strength Construction Re-bars Without Use Of Microalloys: Part 2 Ignatius C. Okafor1a, Kaushal R. Prayakarao2a, Heshmat A. Aglan2b 1 – Chief Metallurgist, Nucor Steel Corporation, Marion OH 43302, USA a – Ignatius.okafor@nucor.com 2 – Department of Mechanical Engineering, Tuskegee University, Tuskegee, Alabama, USA a – Kprayakarao2649@mytu.tuskegee.edu b – Aglanh@mytu.tuskegee.edu

Keywords: A615 high strength steel, re-bar steel (grade 60), rolling process, superheat, metallurgy, grain refinement, microalloys, economical steel.

ABSTRACT. The metallurgy of ASTM A615/A615M Gr. 60 steels made from three different chemistries was studied to suggest an economically advantageous route to produce a steel grade that saves the extra cost of alloying elements. Metallographic examinations, along with microhardness and XRD studies, were performed to rate the steel chemistries based on their superheats. This study of Theoretical calculations and experimental data allow to obtain parameters of interatomic potential which are used in theoretical evaluation of scattering matrices [16]. Lattice thermal conductivity is then obtained in the framework of the iterative approach, introducing anharmonic parameters  and ’ in the three-phonon scattering probabilities. Parameters ,’, estimated through anharmonic Grüneisen constants, are the coupling factors in the three-phonon scattering processes that we have to consider when we are evaluate the thermal resistance to phononic transport [16]. In a three-phonon scattering process, two phonons disappear to give an emerging phonon or a phonon decays in two others. Theoretical approach [16] to three-phonon processes, assumes a phonon wave-vector q belonging to a true lattice Brillouin Zone. Momentum conservation is then rigorously treated, in normal and umklapp processes. the steel grades revealed that producing steel for requisite standards like ASTM 615/A615M Grade 60 may not be dependent on starting superheat but on the chemistry and rolling process. Study of the three chemistries A, B and C indicated that the standards were met in all 3 chemistries; however, sample A had the lowest cost chemistry and therefore is a suggested route for this product.

1. Introduction. ASTM A615/A615M Grade 60 standard calls for a minimum 60 Ksi (420MPa) yield strength with no upper limit even on tensile strength. The standard only specifies that phosphorus (P) be no more than 0.06%. The resulting plain carbon steel is expected to have basic ferrite – pearlite microstructure with minimum grain size ASTM 5. Because every steel mill is different and processes vary, some steel mills use some microalloying to achieve fine grain size in pursuit of the aim microstructure. This process of compositional and process variations can produce yield strengths typically in the range of 350 to 700 Mpa (50 – 100 Ksi). Microalloying, which enhances physical properties through ferritic grain refinement, is often supplemented by precipitation and or dislocation strengthening. Hall-Petch type of strengthening is determined to suggest that a decrease of ferritic grain size from ASTM 6 – 8 to ASTM 12 – 13 is accompanied by an increase of 30 Ksi (210 Mpa) in yield strength. Admittedly the other good effect of fine grains besides strengthening is good ductility or toughness. Two common microalloying elements V and Nb are used in industry to achieve this goal and several authors [1-6] have studied their use. It is known that the behavior of individual micro alloying elements classifies them as mildly carbide forming or strongly carbide forming. The two micro alloying elements (V and Nb) used in this study do qualify as strong carbide formers. They therefore stabilize the α phase. This essentially means that they reduce the γ phase field. Any of the elements MMSE Journal. Open Access www.mmse.xyz 11

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in solid solution in α strengthen the ferrite matrix in steel. These elements differ in their contribution to hardening and the extent to which they reduce plasticity as they add a certain increment to strength. Furthermore, compared to other microalloying elements like Nb and Ti, vanadium exhibits essential differences. The Swedish Institute of Metals Research [6] found that the solubility of vanadium carbonitrides, in particular, is much larger and the solubility of vanadium’s nitride is about two orders of magnitude smaller than its carbide, contrary to Nb but similar to Ti. Vanadium has higher solubility in austenite than niobium, and its carbonitrides [V(C,N)] dissolve more easily prior to hot rolling than NbC. Consequently, vanadium is an excellent choice for strong and easily controllable precipitation strengthening, but it is expensive. Thermodynamically it is known that pure ferrite dissolves more N than C. Thus the total N-content of the steel is normally dissolved in the ferrite before V (C,N) precipitation, whereas only a fraction of the C-content is dissolved in ferrite. Hence the precipitation strengthening would and does increase with total C-content, an effect [6] not previously recognized. Regarding the Nb containing steel in this study, niobium is known to have three-fold influence on the mechanical properties of steel. It facilitates grain size refinement; lowers the gamma (γ) to alpha (α) transition temperature (Ar3), and enhances precipitation hardening. Grain refinement is the only mechanism that increases strength, toughness, and ductility all simultaneously. This makes niobium the most effective microalloying element even when small quantities are added to the steel. The mechanism for grain refinement is mainly due to delaying or preventing recrystallization in the last hot-forming (rolling) steps. Flattened grains associated with the process and the attendant dislocation density of the austenite enhance ferrite nucleation. By lowering the gamma (γ) to alpha (α) transformation temperature, niobium enhances ferrite nucleation and simultaneously reduces grain growth rate. The combined effect yields a very fine grain structure. This is, however, obtainable only when niobium is in solid solution. To achieve niobium in solid solution, an adequate furnace re-heating temperature is essential. At an elevated temperature, Nb(C,N) precipitates before rolling. More Nb(C,N) can precipitate quite easily in austenite under deformation. This is due to the well understood strain induced precipitation. The resulting particles from this process inhibit grain growth and even austenite grain recrystallization during the intermittent deformation at lower temperatures. Deformed austenite structure transforms to fine ferritic structure upon cooling, giving rise to high strength and toughness. Since the Nb carbonitrides are stable at low temperatures, more strength is accomplished as remaining niobium bearing particles precipitate during cooling. The third steel grade in this study (Fe-Mn-C) does not contain any intentionally added alloying element. Carbon content and elements like Mn and Ni do also stabilize and lower the Ar3 temperature. Ni content in the steels studied while not purposely added are appreciably high residuals (0.15 – 0.21Ni). Suppression of gamma to ferrite transformation temperatures is known to enhance refinement of the final structure by decreasing the growth rate of the ferrite grains. Traditionally the major difference in the steels for plate and long products lies in the higher carbon contents of the latter. Pearlite formation in long products is thus greater and does tend to develop bainitic or other acicular microstructures. Besides, the processing of long products necessitates relatively higher finishing temperatures; hence recrystallization controlled rolling (RCR, process 3 in Fig. 1 below) is used in order to obtain a most homogenous fine grain size and high strength in final product. The purpose of this work is to study the metallurgy of ASTM A615/A615M Gr. 60 steels made from three chemistries and so suggest an economically advantageous route that saves the extra cost of alloying elements. The study is in two parts. The first (Part 1, yet to be submitted) discusses MMSE Journal. Open Access www.mmse.xyz 12

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microstructure and the effect of cooling rates on the said chemistries while the second (Part 2; this paper) discusses microstructure, physical properties and centerline segregation.

Fig. 1 Thermo-mechanical controlled processes (TMCP): 1) recrystallization controlled rolling and accelerated cooling, 2) controlled rolling and accelerated cooling, and 3) recrystallization controlled rolling with air-cooling [6].

2. EXPERIMENTAL PROCEDURE 2.1. Processing of Steels The steels (A, B, and C) used in this work were melted by an electric-arc-furnace tapped into 60 ton ladles, cast into billets, and rolled into #6 (19 mm) re-bars. The compositions are shown in Table 1. All three steels had identical carbon, manganese, and silicon contents and all other elements besides vanadium and niobium were residuals. Steel A was specifically made without an intentional addition of vanadium or niobium. The 0.005 V in the chemistry is typical of residual vanadium content in scrap. Steel B was made with an intentional addition of 0.025 V and steel C was made with an intentional addition of 0.012 Nb. For the purpose of this work the effect of other elements (typically residuals) were not considered. All steels were air cooled on a hot bed at production conditions. 2.2. Tensile Strength Prediction Based on Chemistry: (Fe-C-Mn, Fe-C-Mn-Nb, and Fe-C-Mn-V) Tensile strength for each chemistry studied was calculated using the prediction models available in the literature. The relationship of these chemistries to strength has been made by several authors [7, 8]. In his work, Pickering [1] suggested the following formula for alloys where carbon content is less than 0.25%C. TS (MPa) = 243 + 1900C + 228(Cr+Mn) + 228Mo + 91W + 22Ni + 61Cu + 380(Ti + V) Pickering did not suggest any contribution from silicon. De Boer [2], however, basing his work on a carbon content of approximately 0.4%C and 1.5%Si, suggested a contribution for silicon as indicated in the following equation. TS (MPa) = 430 + 688 +81 Si + 196Mn + 202Cr + 80Mo + 400V MMSE Journal. Open Access www.mmse.xyz 13

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Table 1. Chemical composition of the three alloys used in the study No Vanadium added (A)

Vanadium Added (B)

Niobium Added (C)

Cast Temp- 2788â&#x201E;&#x2030;

Cast Temp- 2865â&#x201E;&#x2030;

Cast Temp- 2812â&#x201E;&#x2030;

Superheat- đ?&#x;&#x2022;đ?&#x;?â&#x201E;&#x2030;

Superheat- đ?&#x;?đ?&#x;&#x2019;đ?&#x;?â&#x201E;&#x2030;

Superheat- đ?&#x;&#x2013;đ?&#x;?â&#x201E;&#x2030;

Element

Wt%

Element

Wt%

Element

Wt%

0.40

0.37

0.30

1.06

0.99

1.10

0.033

0.029

0.037

0.017

0.024

0.012

0.18

0.24

0.48

0.31

0.36

0.22

0.23

0.16

0.06

0.08

0.05

0.013

0.011

0.018

0.21

0.17

0.15

0.000

0.012

0.005

0.025

0.003

0.000

0.004

De Boer also tested the influence of Mn (0.70 to 1.3 wt. %), Cr (0.15 to 1.5 wt. %), Mo (0.20 to 0.8 wt. %), and V (0.0 to 0.10 wt. %). Mesplont [3] and his team, starting from De Boerâ&#x20AC;&#x2122;s work, modified the equation with the use of more elements and developed the following equation. TS (MPa) = 288 + 803C + 83Mn + 178Si + 122Cr + 320Mo + 60Cu + 180Ti + 1326P + 2500Nb + +360000B. The authors applied this equation to 164 steels; the results are shown in Fig. 2. Because the elemental chemical analysis of our three alloys falls into the chemistry ranges used by Mesplont and co-workers [3], we have used their equation to â&#x20AC;&#x153;predictâ&#x20AC;? or verify the tensile strengths of the alloys studied. Steel A TS (MPa) = 288+803(0.402) +83(1.06) +178(0.18) +122(0.22) +320(0.056) +60(0.482) +180(0) +1326(0.017) + 2500(0.000) +36000(0.0). This gives an empirical tensile strength of 120 Ksi. The actual mill measurement for this heat was 110 Ksi; the difference of between 8% and 9% is certainly understandable and of no obvious concern. MMSE Journal. Open Access www.mmse.xyz 14

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Steel B Sample B calculated tensile strength is 116.6 Ksi while the actual mill result is 112.3 Ksi. As for alloy A, the difference between the theoretical value predicted by Mesplont’s’s equation and the actual is between 3.7% and 3.8%.

Fig. 2. Calculated TS (MPa) versus measured TS (MP a) [3]

Steel C Sample C in this study has a calculated tensile strength of 106.67 Ksi while the measured (mill) tensile strength was reported as 96.4 Ksi. The difference is between 9.63 % and 10.68%. The objective of this exercise is not to verify the accuracy or lack thereof of Mesplont’s equation but to have a common verifiable frame of reference other than mill reports to compare the tensile strengths. The maximum difference of 10 percentage points between calculated and measured values irrespective of the use of alloying elements (which we all know in metallurgy as grain refiners) is truly instructive. It is this closeness that further drove this work where we seek to minimize the use of expensive alloying elements in making some basic grades of carbon steel needed in the construction industry. 2.3. Metallography of Samples Three sets of samples, each from all three different steels, were mounted using Buehler Simplimet 1000 with Bakelite and polished for light optical metallography, microhardness studies, and SEM work. All samples were polished to the usual mirror image and etched using 2% Nital. Metallographic pictures obtained from the optical microscopy were then studied for microstructural variations and grain sizes were estimated from the microstructures for each steel grade. 2.4. Microhardness Tests Microhardness measurements were made on samples that had been polished and etched to reveal microstructure. Hardness was taken for each of the phases identified in the metallography. Microhardness data were obtained from around the center line of the three steel grade studies. Particular attention was paid to the center line to determine if any differences arose from the MMSE Journal. Open Access www.mmse.xyz 15

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difference in the superheat experience of the steels during casting. The microhardness data were also calculated using equations (obtained from literature) based on chemistry variations. Calculated and measured results were later compared. Microhardness measurements were made in both rolling (horizontal along the length of the bar) directions and transverse directions (vertically above and below the center line at about ±5mm above the center line). Effort was made to measure the contribution (microhardness) of each phase type found in the microstructure. Average hardness of the phases was then found and used for this study. 2.5. Solute Element Distribution Samples from each steel type studied (A, B and C) were sectioned along the center of the rolled piece, polished but not etched, and then studied in the SEM to find distribution of specific solute elements (C, P, S, and Mn). As in the case of the microhardness studies, the SEM element distribution was also done in two directions, longitudinal and transverse. Element distribution as identified in the SEM were color coded in each case, as discussed in the results. 2.6. Tensile and Yield Strength Measurements Tensile and yield strengths of the steels were obtained from the mill where they were rolled. All three results met the requirements for ASTM 615/615M specifications for tensile, yield, and elongation. 3. RESULTS AND DISCUSSION 3.1. Microstructural Analysis Steel A: Figs. 3 – 5 show the microstructures along the center line of the three different alloys (A, B and C) produced with different superheats (72 deg. F, 142 deg. F and 82 deg. F), respectively. Three microstructural phases, namely ferrite, pearlite (with small amounts of bainite) and grain boundary ferrite (GBF), are seen in all the samples.

(a)

(b)

Fig. 3. Optical micrographs of alloy A,72 deg. F superheat, at (a) 20X and (b) 50X magnification

Fig. 3 is the microstructure of the steel sample A, which was made without the addition of any microalloys. It shows mostly ferrite (whitish portions) and pearlite (dark areas) microstructure with little patches of bainitic structure. The average grain diameter meets a minimum of 32 μm (ASTM 7) grain size. Fine grain microstructure is typically defined as meeting ASTM 5 grain size. MMSE Journal. Open Access www.mmse.xyz 16

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Steel B: Fig. 4 shows the microstructure of Sample B, which was made with addition of 0.025V wt %. It shows evidence of pearlitic and ferritic microstructure with more patches of bainitic microstructure. Grain boundary allotriomorphs are evident growing off the prior austenite grain boundaries. This is more noticeable in Fig. 4 (b), which has a larger magnification. Grain size diameter here is about 16 Îźm (ASTM 9), which does meet the fine grain microstructure. This result is expected for vanadium addition to steel.

(a)

(b)

Fig. 4. Optical micrographs of alloy B, 142 deg. F superheat, at (a) 20X and (b) 50X magnification

Steel C: Sample C was made with small addition of niobium; the microstructure shows greater a amount of bainitic structure than the microstructures for samples A and b. Sample C has much lower level of carbon (0.3 wt %) compared to samples A and B, which had carbon around 0.4 wt%. The lower carbon levels take away from the strength but niobium, or microalloying for that matter, compensates for the strength and improves toughness. It is known that addition of Nb gives about twice as much boost in strength as vanadium of the same quantity. Combination of both Nb and V do provide a significant boost in strength [9].

(a)

(b)

Fig. 5. Optical micrographs of alloy C, 82 deg. F superheat, at (a) 20X and (b) 50X magnification MMSE Journal. Open Access www.mmse.xyz 17

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The volume fractions of ferrite and pearlite in the three steels studied are shown in Table 2.

Table 2. Volume fractions of the microstructural phases in different steels Vol. Fraction %

C (Nb)

B (V)

(No Microalloy)

Avg. Ferrite

11.48%

6.81%

9.17%

Avg. Pearlite

88.52%

93.20%

90.83%

Average bainite is assumed to be no more than 5% in A and B but about 10% in C. 3.2. Microhardness Results Microhardness of each steel sample (A, B and C) was measured at points indicated in Fig. 6. The dark points represent where the hardness measurements were made. The three horizontal lines represent (from top to bottom) +5mm above the center line; center line, and -5mm below the center line, respectively. Positive and negative signs are used to emphasize top and below the center line, which is presumed to be zero.

Fig. 6. Schematic representation of the locations on the sample surface where microhardness data was obtained

The results in Tables 3-5 indicate that the hardness varies from 266 in the GBF of sample C to 457 at the center line of sample B. While this dispersion may appear significant the broad spectrum, the averages of the results suggest that the samples all meet the required hardness.

Table 3. Microhardness results for sample A (no vanadium added) H 72F (No Vanadium) +5mm

Center line

-5mm

Phase

-4

Ferrite

341

298

271

300

383 319

Pearlite

382

402

383

374

422 393

GBF

334

220

295

241

349 288

276 341 326 322 382 365 342 383 402 349

361 390 382 432 387 452 395 392 432 403

GBF

216 237 241 288 306 341 349 294 327 289

266

286

334

266

349 300

455

388

357

349

422 394

GBF

313

228

276

256

341 283

-3

-2

-1

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Avg.

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Table 4. Microhardness results for sample B (0.025 wt. % V vanadium added)

Table 5. Microhardness results for sample C (0.0120 wt. % Nb added)

3.3. Solute Elements Distribution across the Center Line (Horizontal) X-ray diffraction (XRD) analysis was performed on the samples along the center line (horizontally) to determine solute (C, P, S, and Mn) distribution pattern in those axes. A typical sample probe axis is shown in Fig. 7.

Fig. 7. Schematic of the sample used in the solute distribution probe

Plot of the solute element distribution in the sample as determined by SEM is shown in Fig. 8 for sample A. The distribution is made for relative concentration (wt. %) against spatial location in the x-direction. The sample was 1.5â&#x20AC;? long.

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Relative Element Concentration , Wt%

C_NoV S_NoV

2,5

P_NoV Mn_NoV

2 1,5 -8

-6

-4

-2

1 0,5 0 Location, #

Fig. 8. Solute element relative concentration against spatial location for sample A (no vanadium)

Fig. 8 is presented such that points above the horizontal line are from the upper half of the sample center line, while the lower portion is below the line. It is instructive to observe that P and S were mostly traced at the center line, while not much Mn was noted there, but rather at some noticeable distance above the center line. It should be noted that all efforts to find the exact center line in the finished rolled material used in the study was not successful when using a SEM. A similar distribution profile was observed for sample B, which had some intentional vanadium addition (Fig. 9).

Relative Element Concentration, Wt%

2,5

-8

C_V S_V

P_V Mn_V

2 1,5 -6

-4

-2

1 0

0,5 0 Location, #

Fig. 9. Solute element relative concentration against spatial location for sample B (vanadium added)

As for sample A, S and P are found along the center line while C and Mn are detected significantly above the center line. No effort is made to determine the exact quantities of these elements since our machine is limited in that capability; hence we report only the relative values. Fig. 10 shows the findings for sample C (niobium added). These results are comparable to those for samples A and B.

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Relative Element Concentration, wt%

C_Nb S_Nb

2,5

P_Nb Mn_Nb

2 1,5

-6

-4

-2

1 0,5 0 -0,5 Location, #

Fig. 10. Solute element relative concentration against spatial location for sample C (Nb added)

3.4. Solute Elemental Distribution (vertical direction) Similar solute distribution profiles were run in the vertical direction as indicated in Fig. 11.

Fig. 11. Schematic of the vertical direction (black dots)

Relative element distribution for sample A, which had no intentional vanadium addition, is given in Fig. 12. The distribution is along the vertical axis. Except for the small spike in carbon, the elements seem to distribute evenly along the bar. The right of the graph represent points above the center line (+Y directions) and the left represent the points below the center line (- Y direction)

Relative Element Concentration , Wt%

-6

C_NoV S_NoV

2,5

P_NoV Mn_NoV

2 1,5 -4

-2

1 0,5 0 Location, #

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Fig. 12. Solute element distribution in the vertical direction for sample A (no vanadium added) An identical profile run for sample B (vanadium added)is presented in Fig. 13. As for the sample A profile, the right of Fig. 13 (+Y direction) represents points above the center line and the left represent the points below the center line (- Y direction).

Relative Element Concentration , Wt%

2,5

-8

1,5 -6

-4

-2

C_V

P_V

S_V

Mn_V

0,5

0 Location, #

Fig. 13. Solute element distribution in the vertical direction for sample B (vanadium added, superheat 142°F)

The distribution of Mn, S and P all seem rather uniform; the carbon profile is somewhat non-linear yet not clustered. It does not show the carbon hump observed in the no vanadium alloy, sample A. A third vertical distribution curve is shown in Fig. 14 for the niobium added alloy, sample C.

Relative Elements Concentration, Wt%

-6

2,5

C_Nb

P_Nb

S_Nb

Mn_Nb

2 1,5 -4

-2

1 0

0,5 0 -0,5 Location, #

Fig. 14. Solute element distribution in the vertical direction for sample C (niobium added, superheat 82°F)

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As for sample A with no vanadium addition, this profile shows a slight carbon hump, while exhibiting some uniformity in the distribution of other solute elements traced. 3.5. Scanning Electron Microscopy Studies of the Center Line The center line of the samples was subjected to SEM examination to see if any “openings” would be detected in any of the three samples studied. Such “openings” would suggest center line decohesion and so signal physical property weakness. The purpose of the different superheats used in this study is essentially enable visibility of any such decohesion if it exists. The results are shown in Figs. 15-17.

(a)

(b)

Fig. 15. SEM micrographs of sample A (no-vanadium) with 72°F superheat; 500X magnification. The SEM micrographs show typical heterogeneities /inclusions across the center line but no “open” center line decohesion.

(a)

(b)

Fig. 16. SEM micrographs of sample B (vanadium added), 142°F superheat; 500X magnification

3.6. Discussion

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The results of this work thus far indicate that there is a relationship between the superheat of steel (in the cast billet form), the chemistry, the rolling process, the cooling rate, and the microhardness of the steel. The rolling process and the cooling rate of the rolled product enable the evolution of appropriate microstructure. This work did not study the rolling process. Hence any contribution from superheat in the hardness discussion would only be tangential or conjectural since the equiaxed zone, which is most influenced by superheat, is readily collapsed or lost in the rolling process. The influence of superheat is most evident in cast billets but not in rolled products. This work was on rolled products.

(a)

(b)

Fig. 17. SEM micrographs of sample C (niobium added), 82°F superheat; 500X magnification

Steels cast at high superheat could still make good products but must be rolled with high reduction ratios to achieve this aim. High superheat cast products without high reduction ratios could lead to more evidence of center line segregation. Another observation that was made was that there was no significant evidence of macrosegregation in the samples. This is so because the samples were from rolled products and not from the cast billets. The center line had been completely removed by the rolling process. Efforts taken to see macrosegregation included cutting the samples into two halves, and in some cases machining the samples to the center of the 0.75” diameter bar. In either case, no evidence of segregation was noted. This was evidence that the rolling process removed the segregation in spite of the starting superheats in the billet form. One major advantage of superheat control is reduction in KwH/ton. A plot of such a benefit obtained from an operating mill is shown in Fig. 18. Physical test results of the three steel samples show that they all meet ASTM Grade 60 specifications. Production cost (following quality) is always essential in alloy design. Minimization of the cost of alloying elements is a major consideration in steel making, more so in today’s market where construction bars are certainly a commodity and cheap bars flood American markets from Asia, the Middle East, and the Americas. Mills are therefore intent on making quality steels without spending too much on alloying elements but taking advantage of the metallurgy of tramp elements in the scrap mix. The similarity of the physical test results derive from a couple of points. One important reason is that each rolling was done at a high enough temperature to ensure that the RDR process was established followed by air cooling. A second possible reason is suggested to be from the amount of residual molybdenum in the scrap mix. Even though the molybdenum (Mo) residuals are identical, its presence MMSE Journal. Open Access www.mmse.xyz 24

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in the alloy is advantageous for high temperature strengthening. Andrade et al. [7] reported that Mo was next in line to niobium in retardation of static recovery and recrystallization.

Fig. 18. Plot of KWH/Ton versus superheat in actual mill setting [13]

Molybdenum also contributes to hardenability and suppresses the formation of diffusional transformation products such as ferrite or pearlite in favor of bainitic and martensitic transformations, which are known as to be nonâ&#x20AC;&#x201C;diffusional. The authors studied the high temperature strengthening produced by additions of molybdenum, niobium and vanadium using the empirical equation proposed by Akben et al. [8] as in equation (1) below,

â&#x2C6;&#x2020;đ?&#x2018;&#x2020;đ?&#x2018;&#x17D; =

đ?&#x2018;&#x192;đ??ś đ?&#x153;&#x17D;đ?&#x2018;Śđ?&#x2018; â&#x2C6;&#x2019; đ?&#x153;&#x17D;đ?&#x2018;Śđ?&#x2018; đ?&#x2018;&#x192;đ??ś đ?&#x153;&#x17D;đ?&#x2018;Śđ?&#x2018;

Ă&#x2014;

0.1 đ?&#x2018;&#x17D;đ?&#x2018;Ą.đ?&#x2018;?đ?&#x2018;?đ?&#x2018;Ą đ?&#x2018;&#x2020;

Ă&#x2014; 100

(1)

đ?&#x2018;&#x192;đ??ś where, Ď&#x192;ys represents the yield stress of the steel and â&#x20AC;&#x153;sâ&#x20AC;? the element under consideration; đ?&#x153;&#x17D;đ?&#x2018;Śđ?&#x2018; is the yield strength of the reference plain carbon steel.

Table 5 shows results from Andrade and co- workers [7] on the high temperature strengthening produced by additions of molybdenum, niobium, and vanadium. This Table 5 shows that niobium has the greatest strengthening effect followed by molybdenum and then vanadium. High residuals of molybdenum in a scrap mix are therefore an advantage to exploit. In order to generate a predominantly bainitic microstructure, accelerated cooling has to begin above the temperature at which austenite transforms to ferrite. This is at above the Ar3 temperature. Molybdenum is known to lower the Ar3 temperature more effectively than addition of the same quantities of copper, nickel or chromium [9, 10]. Usually molybdenum levels of 0.2% or above are used in high strength line pipe steels. Llopsis [11] showed that a combined addition of chromium and molybdenum is more effective in promoting bainite formation than an addition of only one of the MMSE Journal. Open Access www.mmse.xyz 25

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elements. Stallybrass and co-workers [12] showed that use of as little as 0.1% Mo and 0.2% Cr in making X80 sheet steel met the desired strength. Since the Cr and Mo levels in the current work (Table 1) are comparable and since the steel being produced is of lower strength that of the Stallybrass et al. work, it is not surprising to expect that higher strength levels.

Table 5. High temperature strengthening produced by additions of Mo, Nb and V in the steel [7]

In summary, new grade development success differs from mill to mill and truly depends on a mills specific culture and capabilities to achieve desired results. That success necessitates a thorough understanding of melting and secondary metallurgy reheat furnace characteristics, along with the mill’s cost drivers, culture, and commitment from leadership to support something new. 4. Conclusions The major conclusion from this work is therefore that making steel for requisite standards like ASTM 615/A615M Grade 60 may not be dependent on starting superheat but on the chemistry and rolling process. Study of the three chemistries indicated as A, B and C indicate that the standard was met in all three chemistries but that sample A had the lowest cost chemistry and therefore is a suggested route for this product. Acknowledgements The authors are grateful to Nucor Corporation for the generosity and provision of the Nucor NERC facilities located in Tuskegee University. The authors are also grateful to Tuskegee University for the use of its facilities and equipment. Assistance received from Jerome Jones, an undergraduate student of mechanical engineering at Tuskegee University, in laboratory works is greatly appreciated. Nucor Steel Marion, OH is truly appreciated for the supply of all the grades of steel used in this work. References [1]. Pickering, F.B., 1967, The structures and properties of bainite in steels. Paper presented at the Symposium: A transformation and hardenability of steels, February 27-28th in Ann Arbor, MI. pp. 109-132. [2]. deBoer, H., Datta, S.R., Kaiser, H.J., Lundgren, S.O., Müsgen, B., Schmedders, H., Wick, K., 1995, Naturharte bainitische Schienen mit hoher Zugfestigkeit, in: Stahl and Eisen 115, 93ff. [3]. Mesplont, C., 2002, Phase Transformations and microstructure-mechanical properties relations in Complex Phase high strength steels. Doctoral Thesis, Ingénieur Ecole Universitaire Des Ingénieurs de Lille DEA Science des Matériaux Université de Lille, Universiteit Gent. [4]. Maynier, P., Dollet, J., Bastien, P., 1978, Hardenability Concepts with Applications to Steels, D.V. Doane and J.S. Kirkaldy, eds., AIME, New York, NY, p.518. [5]. Donnay B., Herman J.C., Leroy V., Lotter U., Grossterlinden R., Pircher H., 1996, Microstructure evolution of c-mn steels in the hot deformation process: the STRIPCAM model, Proc. Modelling of Metal Rolling Processes Conf., eds. J.H. Beynon, P. Ingham, H. Teichert, K. Waterson, London, pp. 23–35 MMSE Journal. Open Access www.mmse.xyz 26

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[6]. Lagneborg, R., Siwecki, T., Zajac, S., Hutchinson, B., 1999, The Role of Vanadium in Microalloyed Steels, The Scandinavian Journal of Metallurgy, October, Vol 28, No 5, pp. 186-241. [7]. Andrade, H.L., Akben, M.G., Jonas, J.J., 1983, Effect of Molybdenum, Niobium and Vanadium on Static Recovery and Recrystallization and on Solute Strengthening in Microalloyed Steels, Metallurgical Transactions A, Vol. 14 A, pp. 1967 – 1977. [8]. Akben, M.G., Weiss, I., and Jonas, J.J., 1981, Dynamic Precipitation and Solute Hardening in AV Microalloyed Steel and two Nb Steels Containing High Levels of Mn, Acta Metallurgica, vol. 29, pp. 111-121. [9]. Klinkenberg, C. Niobium in Microalloyed Structural and Engineering Steel (Niobium Products Company GmbH, Steinstrasse 28, D-40210 Dϋsseldorf, Germany) http://www.metal.citic.com/iwcm/UserFiles/img/cd/2005-HSLA-NB/HSLA-045.pdf (accessed September 14th 2015) [10]. Ouchi, C., Sampei, T., and Kozasu, I., 1982, The effect of hot rolling condition and chemical composition on the onset temperature of γ/α transformation after hot rolling, Transactions of the Iron and Steel Institute of Japan, 22, pp. 214–222. [11]. Llopis, A.M., 1975, Effect of Alloying Elements in Steels on the Kinetics of the Austenite to Bainite transformation, (DOE Technical Report, DOI 10.2172/7283325, California University. [12]. Stallybrass, C., Konrad, J., and Meuser, H., 2015, The Effect of Low Levels of Molybdenum in High Strength Linepipe Steels, Fundamentals and Applications of Mo and Nb Alloying in High Performance Steels, Vol. 2, Hardy Mohrbacher (Ed.), NiobelCon, Belgium, pp. 125 – 140. [13]. Quality Department, Nucor Steel Marion, Private Communication.

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Thermal Conductivity of Zincblende Crystals Amelia Carolina Sparavigna1 1 – Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy

Keywords: thermal conductivity, phonons, Boltzmann equation ABSTRACT. Among materials having zincblende lattices, we find some that are characterized by a high thermal conductivity. This is a quite important feature for their application in semiconductor technologies and related devices. In this paper, we will discuss the thermal conductivity of two zincblende crystals (SiC and GaAs), stressing the role of lattice vibrations in producing high values of conductivity and of lattice defects in reducing it. In the framework of a model dealing with phonon dispersions and reliable scattering mechanisms, we will show how lattice thermal conductivity can be estimated from the Boltzmann Transport Equation in the case of any zincblende crystal.

Introduction. Measurements of thermal conductivities reveal that most of the high thermal conductors are adamantine (diamond-like) solids: among them we have Diamond, SiC, AlN, GaN and Si [1, 2]. For instance, the silicon carbide (SiC), a material which is fundamental for semiconductor technologies and for future innovations of them [3-5], has at room temperature a conductivity greater than 3 W cm−1K−1 in the CVD grade and about 1 W cm−1K−1 when sintered [6,7]. Such a high thermal conductivity could be surprising, because it is commonly believed that it is possessed just by metals, due to the presence in them of a free flowing cloud of electrons. In nonmetallic solids, electrons are not free to move and therefore phonons are the only responsible for heat transport. They are so efficient, that in the diamond at room temperature they are producing an intrinsic thermal conductivity much higher than that measured in metals. Aluminium for instance has conductivity of about 2 W cm−1K−1 [8], whereas natural diamond has a conductivity of about 20 W cm−1K−1 at room temperature. Compounds consisting of more than one element have often a crystal structure based on the cubic crystal system of the zincblende type. This crystal is like an adamantine lattice where two atom types form two interpenetrating face-centred cubic lattices. The zincblende structure has a tetrahedral coordination: each atom's nearest neighbours consist of four atoms of the opposite type, positioned like the four vertices of a regular tetrahedron. So the arrangement of atoms is the same as a diamond cubic structure, but with alternating types of atoms at the different lattice sites. Examples of compounds with this structure include gallium arsenide, boron arsenide (shown in the Figure 1), cadmium telluride and a wide assembly of other binary compounds.

Fig. 1. The lattice cell of Born Arsenide in the zincblende structure (Courtesy Wikipedia) MMSE Journal. Open Access www.mmse.xyz 28

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Some materials, such as abovementioned SiC and AlN ceramics for instance, are fundamental for the development of new devices including light emitting diode (LED) [9-11]. Since in these devices the dissipation of heat is crucial, it is important investigating their thermal conductivity and how disorder produced by point and extended defects can influence their thermal transport. For instance in diamond, the isotope disorder alone is able to strongly reduce thermal conductivity, even at room temperature [12]. And also experimental data for Silicon indicate a large rise in the thermal conductivity of isotopically pure Si when compared to natural Si [13-15]. Let us therefore discuss the thermal transport properties of zincblende crystals, in particular SiC and GaAs. We will propose for them a calculus of phononic thermal conductivity in the framework of an iterative approach used for diamond-like lattice [16-17]. In fact, this calculation can be easily applied to any other zincblende lattice, if we have phononic dispersion curves and dielectric constants for fitting parameters used in the calculation. 2. Importance of SiC and GaAs. Among adamantine compounds, Silicon Carbide and Gallium Arsenide are fundamental for electronic and optical applications: the first because it is able dissipating heat in devices, the second because components and integrated circuits obtained with this material are faster than those made of silicon, due to a large low-field electron mobility. GaAs compound is able to emit light, turning out to be useful for making lasers and light-emitting diodes in devices where the material is subjected to very high thermal gradients [11]. Silicon Carbide is an excellent abrasive and for this reason it had been produced for abrasive products under the name of Carborundum [18]. However, today, best applications of this material are in those devices where its high thermal conductivity coupled with a high strength allows enduring large thermal shocks. In this manner, SiC is very popular as wafer tray supports in semiconductor furnaces [19]. Silicon Carbide crystallizes in several polytypes; the two most common SiC polytypes are 3C-SiC and 6H-SiC. 3C polytype, also known as beta-SiC, is the only polytype with a cubic structure. In addition to 3C-SiC, several hexagonal and rhombohedral lattice SiC crystal structure arrangements are possible. They are known as alpha-SiC. 3C-SiC crystallizes is a zincblende structure, hence it can be deposited on Si [20]. Compared to Si, SiC exhibits a larger band-gap, a higher breakdown field, a higher thermal conductivity and a high saturation velocity (see Table 1, [20, 21]). These properties make SiC very attractive for the fabrication of high temperature, high-power and high frequency electronic devices. In addition, it is a material used for fabrication of microsensors that can operate at high temperatures, for instance, as pressure sensors in engines [22, 23]. In comparison to diamond, attractive features of SiC are that it can be doped both p- and n- type and it allows a natural oxide to be grown on its surface. Gallium arsenide is used in the manufacture of devices such as microwave frequency integrated circuits and light-emitting diodes [11]. Because the GaAs films are usually epitaxially grown, they are monocrystalline and have atomically flat interfaces. These films are extremely well controlled, unlike polycrystalline materials. With GaAs, lattice mismatches can be easily avoided and then GaAsbased systems, such as InP-based material systems, allow for direct incorporation of optical functions into mechanical structures [11]. Finally, its zincblende structure allows for piezoelectricity as a result of lack of center of symmetry, in contrast to silicon. This property leads to interesting sensing applications (see for instance Ref.24). Another advantage of GaAs is that it has a direct band gap, which means that it can be used to absorb and emit light efficiently [11]. 3. Phononic thermal transport in cubic SiC and GaAs. Let us apply an approach to the evaluation of thermal conductivity in zincblende crystals, which had been developed for diamond structures [16]. In this approach, solids are described by means of a microscopic model considering the discrete nature of lattice, a true Brillouin Zone for phonon dispersions (acoustic and optical) and rigorous phonon scattering mechanisms. The phononic Boltzmann equation is solved avoiding relaxation time approximations, an approximation usually made to describe a phonon collision with

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other phonons and defects. C, Si and Ge have been investigated [14, 16] and the role of isotope effects on thermal conductivity deeply discussed, finding good agreement with experimental data. Table 1. Material Properties of Common Semiconductor Materials at 300K Property

3C-SiC (6H-SiC)

GaAs

Sublimes at 1825

1238

1415 Phase Change

873 (1240)

460

300

1100

4.9

0.5

1.5

2.2 (2.9)

1.42

1.12

5.5

Dielectric Constant

9.7

13.2

11.9

5.5

Lattice constant (Å)

4.36

5.65

5.43

3.57

Melting Point (oC) Max. Operating Temp. (oC) Thermal Conductivity (W/cm oC) Energy Gap (eV)

Diamond

Let us consider a phonon system of a solid with a diamond-like lattice, with two atoms in the cell basis, but with different masses, as in the case of Figure 1. The model considers a lattice with its cell positions and atomic positions in cell basis. Crystal sites are interacting with a pair potential V(r), where r is the interatomic distance. The potential can then be described in terms of six parameters denoted by , ’, , ’,  and ’ whose definitions are given in Ref.16. The parameters , ’, , ’ are governing the equation of atomic motion and can be obtained by fitting experimental phonon dispersion curves. Parameters  and ’ are obtained from Grüneisen parameter. The crystal excitations in the harmonic approximation, that is the phonons, are described by wavevectors q of the Brillouin Zone, and polarization index p, with a frequency qp. The lattice displacement field  is then written in terms of phonon absorption and creation operators aqp, aqp [25]. After, to obtain phonon frequencies and dispersions, we expanding function V in terms of lattice site displacement operator , we obtain second and third order terms of the potential energy for two interacting atoms at different lattice positions. The pair potential has adjustable parameters used to fit phonon dispersions and Grüneisen parameter [16]. In Figure 2, the phonon dispersions for GaAs are shown in comparison with experimental data (in the same figure, the phonon dispersions for SiC are also given). The theoretical calculation is here performed by means of atomic motion equations, including in phonon Hamiltonian a perturbation term to describe the shift of longitudinal optical LO mode. The perturbation changes LO mode frequencies by a factor (o/)1/2, as discussed by Born and Huang [25]: o,  are static and high frequency dielectric constants respectively. For GaAs, LO mode shift turns out to be about 9% (o=12.9, =10.89) [26]. Let us note that the model is able to fit transverse acoustic modes in the main directions of the Brillouin Zone, with an overall good agreement with experimental data from Ref.27. The same approach for LO-mode shift is used for cubic Silicon Carbide too. For SiC, o=9.71, =6.52 give a shift of 22%, and the same value results by fitting phonon dispersion data of LO branch (see Fig.2, experimental data from Ref.28). Theoretical calculations and experimental data allow to obtain parameters of interatomic potential which are used in theoretical evaluation of scattering matrices [16]. Lattice thermal conductivity is then obtained in the framework of the iterative approach, introducing anharmonic parameters  and ’ in the three-phonon scattering probabilities. Parameters , ’, estimated through anharmonic Grüneisen constants, are the coupling factors in the three-phonon scattering processes that we have to consider when we are evaluate the thermal resistance to phononic transport [16]. In a three-phonon MMSE Journal. Open Access www.mmse.xyz 30

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scattering process, two phonons disappear to give an emerging phonon or a phonon decays in two others. Theoretical approach [16] to three-phonon processes, assumes a phonon wave-vector q belonging to a true lattice Brillouin Zone. Momentum conservation is then rigorously treated, in normal and umklapp processes.

Fig. 2. Phonon dispersions of GaAs and cubic SiC, in comparison to experimental data [27] and [28]. The frequency is given in THz. To obtain thermal conductivity, the phonon Boltzmann equation is linearized with respect to phonon distribution, which is not the equilibrium one, due to presence of thermal gradients. Introducing a deviation function Q=qp (Q indicates wave-vector and polarization q, p), proportional to the difference between perturbed nqp and unperturbed nQ0 =n0qp phonon distributions, linearized Boltzmann equation for a solid subjected to a thermal gradient T can be assumed as in Ziman’s approach, in the form [29]:







0 nQ    vQ  T   K QQ 'Q''  Q''  Q'  Q   K QQ'Q''  Q''  Q'  Q T Q 'Q ' ' Q 'Q ' '





 (1)

 D    BQ Q QQ' Q' Q Q'

The 1-st and 2-nd terms on right hand side describe three-phonon scattering processes and the 3-rd term elastic scatterings due to impurities (point defects). The last term provides a phenomenological description of boundary scattering as a relaxation time. By vQ the phonon group velocity (Q/q) = (qp/q) is denoted. Here we will consider only point defects, however other defects such as dislocations, grain boundaries, stacking faults could be introduced. An iterative procedure then solves Boltzmann equation [16]. Let us call:

(o) Q  AQ GQ

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(2)

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with

nQ0  AQ  vQ  T T

(3)

and

GQ 

   KQQ 'Q ' '   K QQ'Q ' '   DQQ'  BQ Q 'Q ' '

Q 'Q ' '

(4)

The recursive relation giving phonon deviation function is the following (n is the recursive index):

 Q( n)   Q(o) 

 1   ( n 1) ( n 1)  ( n 1) ( n1) K     K      QQ 'Q '' Q ''   QQ'Q'' Q'' Q' Q' GQ Q 'Q '' Q 'Q '' 









(5)

as in [16]. Once nQ is known, heat current density U is evaluated, and from the Ui, i-th component of heat current U with respect to a Cartesian frame, tensor kij representative of thermal conductivity in i- direction can be immediately obtained. For what concerns the so-called point defects, such as impurity atoms, substituted for the atoms of base crystal, being a point defect means a mass difference in lattice positions where defect is placed, giving an elastic scattering from a phonon qp into a phonon q'p'. Due to M mass difference between regular site and defect, the kinetic energy of lattice site is changed. If the point defect is a different isotope of the same element, only mass change has to be considered [16]. 4. Thermal conductivities. Natural isotope composition of materials acts on thermal transport reducing thermal conductivity. Gallium arsenide is a semiconductor material that, if it obtained by natural gallium, has 60.11% in 69Ga and 39.89% in 71Ga, whereas arsenide is a monoisotopic element. Since thermal conductivity in GaAs is three time smaller than in silicon, one can detect if it is possible to increase thermal transport with an enrichment of a gallium isotope. Experimental data have been obtained at the Kurchatov Institute in Moscow crystals of GaAs with an almost single 71Ga isotope composition [30]. Crystals are characterized by single grains of 2-4 mm in cross-section up to 15 mm in the direction of the crystal growth. Thermal conductivities were measured by means of the standard steady-state longitudinal method in a 2.5x2.5x22. mm3 samples. These experimental data are the first published data for isotope pure GaAs sample: some of these experimental data are reported in Table 2. Comparison between experimental data of enriched and natural samples gives a 6% increase in thermal conductivity at 250 K and a 15% increase at 100 K. Table 2. Thermal conductivity (in W cm−1 K−1) of GaAs, enriched and natural Temperature (Kelvin)

GaAs enriched Exp.

100 150

2.30 1.10

GaAs natural Exp. 1.97 1.00

GaAs enriched Theor.

GaAs natural Theor.

200

0.76

0.70

0.80

0.71

250

0.56

0.53

0.62

0.57

15 12

2.36 1.23

1.93 1.05

22 17

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Theoretical calculations done with iterative technique are shown in Table 2 for comparison: the agreement with the experimental data is good. But, it is necessary to note that the isotope effect turns out to be more relevant in theoretical calculations. It means that other scattering mechanisms could be present in the sample, interfering with isotope effect. In Ref.30, it is in fact reported the presence of impurities coming from arsenic element. Another scattering mechanism on the phonon transport can come from point defects as antisites, where a Ga atom is substituted by an As atom or vice-versa. Antisites produce a strong reduction of k, as it is obtained in the calculation of the thermal conductivity in cubic SiC. Theoretical calculations are also in agreement with estimations of Daly et al. [31], obtained with molecular dynamics. Thermal conductivity of cubic SiC must consider the presence of antisites, where a Si atom is substituted by a C atom or vice-versa, as point-defect phonon scattering mechanism. Antisites produce a strong reduction of thermal conductivity, in agreement with MD simulations and with experimental observations in irradiated specimens [32-34]. The thermal conductivity of pure cubic SiC , with a scattering mechanism produced by the presence of microcrystallites, had been discussed in [17]. Here, let us pinpoint the presence of antisites. A concentration of 0.5% point defects was considered. In Table 3, the result of calculations is shown in comparison with data obtained by means of the MD simulations [34]. In the table, thermal conductivity k for a perfect crystals is also shown. Antisites produce a strong reduction of k (in agreement with data obtained by Ju Li et al. [34] with MD simulation and with experimental observations in irradiated specimens [35, 36]). Table 3. Thermal conductivity (in W cm−1 K−1) of SiC Temperature

Thermal conductivity

(iterative approach)

Thermal conductivity with Thermal conductivity with antisite disorder antisite disorder (Molecular Dynamics) (iterative approach)

(Kelvin)

k perfect lattice in W cm−1 K−1

in W cm−1 K−1

450

2.6

0.5

0.30

600

1.7

0.45

0.30

900

1.3

0.35

0.32

2000

0.5

0.30

Let us stress that the presence of grain boundaries strongly reduces the thermal conductivity of at least 20% at room temperature (from 4.2 to 3.5 W cm−1 K−1 at 300 K) [17]. But an antisite disorder is quite strong in reducing thermal conductivity: it reduces the thermal transport of one order of magnitude when 0.5% of the lattice sites are involved as antisites. Summary. In the previously proposed approach to the evaluation of thermal conductivity, we have used a pair potential the parameters of which are estimated from fitting phononic dispersion curves and Grüneisen data. Static and high frequency dielectric constants are involved for determining the gap between acoustic and optical phonon dispersion. Since phonon dispersions, Grüneisen and dielectric constant are often available from scientific literature, this approach can be easily applied to other zincblende crystals. The proposed method for evaluating thermal conductivity is better that those using the relaxation time approximation [37], because it is based on a rigorous approach to the phonon scattering. Of course, calculations from first principles or molecular dynamics are possible too. However, the method here proposed is more intuitive, being based on parameters which can be easily evaluated from the measurements of macroscopic physical quantities. MMSE Journal. Open Access www.mmse.xyz 33

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References [1] G.A. Slack, R.A. Tanzilli, R.O. Pohl and J.W. Vandersande (1987). The Intrinsic Thermal Conductivity of AlN. J. Phys. Chem. Solids, Volume 48, Page 641. [2] K. Watari and S.L. Shinde (2001). High Thermal Conductivity Materials. MRS Bulletin, Volume 26, Issue 6, Page 440. [3] R. Maboudian, C. Carraro, D.G. Senesky and C.S. Roper (2013). Advances in Silicon Carbide Science and Technology at the Micro- and Nanoscales. Journal of Vacuum Science & Technology A, Volume 31, Issue 5, Page 050805. [4] S.E. Saddow (2012). Silicon Carbide Biotechnology: A Biocompatible Semiconductor for Advanced Biomedical Devices and Applications. Elsevier. [5] Ming Ruan, Yike Hu, Zelei Guo, Rui Dong, J. Palmer, J. Hankinson, C. Berger and W.A. De Heer (2012). Epitaxial Graphene on Silicon Carbide: Introduction to Structured Graphene. MRS Bulletin, Volume 37, Issue 12, Page 1138. [6] Insaco Inc, Quakertown Pennsylvania, 2015, http://www.insaco.com/ materials/carbides/cvdsilicon-carbide [7] Insaco Inc, http://www.insaco.com/ materials/carbides/silicon-carbide-sintered [8] A.C. Sparavigna (2012). Measuring the Thermal Diffusivity in a Student Laboratory, Engineering, Volume 4, Issue 5, Page 266. [9] K.J. Kim, Y.W. Kim, K.Y. Lim, T. Nishimura and E. Narimatsu (2015). Electrical and Thermal Properties of SiCâ&#x20AC;&#x201C;AlN Ceramics Without Sintering Additives. Journal of the European Ceramic Society, Volume 35, Issue 10, Page 2715. [10] Z. Su, J.A. Malen, J.P. Freedman, R.F. Davis, J.H. Leach and E.A. Preble (2013). Dependence of Thermal Conductivities of the AlN Film in the LED Architecture on Surface Roughness and Lattice Mismatch. ASME Paper No. HT2013-17116. [11] A.C. Sparavigna (2014). Light-Emitting Diodes in the Solid-State Lighting Systems. International Journal of Sciences, Volume 3, Issue 11, Page 9. [12] T.R. Anthony, W.F. Banholzer, J.F. Fleischer, L. Wei, P.K. Kuo, R.L. Thomas and R.W. Pryor (1990). Thermal Diffusivity of Isotopically Enriched 12C diamond. Physical Review B, Volume 42, Issue 2, Page 1104. [13] T. Ruf, R. Henn, M. Asen-Palmer, E. Gmelin, M.Cardona, H.-J. Pohl, G. Devyatych and P. Sennikov (2000). Thermal Conductivity of Isotopically Enriched Silicon, Solid State Commun., Volume 115, Page 243. [14] A. Sparavigna (2002). Influence of Isotope Scattering on the Thermal Conductivity of Diamond. Physical Review B, Volume 65, Issue 6, Page 064305. [15] M. Asen-Palmer, K. Bartkowski, E. Gmelin, M. Cardona, A.P. Zhernov, A.V. Inyushkin, A.N. Taldenkov, V.I. Ozhogin, K.M. Itoh and E.E. Haller (1997). Thermal Conductivity of Germanium Crystals with Different Isotopic Compositions. Physical Review B, Volume 56, Issue 15, Page 9431. [16] M. Omini and A. Sparavigna (1997). Heat Transport in Dielectric Solids with Diamond Structure. Nuovo Cim. D, Volume 19, Issue 10, Page 1537. [17] A. Sparavigna (2002). Lattice Thermal Conductivity in Cubic Silicon Carbide. Physical Review B, Volume 66, Issue 17, Page 174301. [18] R.S. Mulik and P.M. Pandey (2011). Ultrasonic Assisted Magnetic Abrasive Finishing of Hardened AISI 52100 Steel Using Unbonded SiC Abrasives. International Journal of Refractory Metals and Hard Materials, Volume 29, Issue 1, Page 68. MMSE Journal. Open Access www.mmse.xyz 34

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[19] H.Y. Xu, Q. Yang, X.L. Wang, X.Y. Liu, Y.L. Zhao, C.Z. Li and H. Watanabe (2015). Improving Interface Quality of 4H-SiC MOS Devices with High Temperature Oxidation Process in Mass Produce Furnace. Materials Science Forum, Volume 821, Page 484. [20] M. Gad-el-Hak (2005). MEMS: Design and Fabrication, CRC Press. [21] Data available from D.W. Palmer, www.semiconductors.co.uk, 2014. [22] R.S. Okojie, D. Lukco, V. Nguyen and E. Savrun (2015). 4H-SiC Piezoresistive Pressure Sensors at 800° C With Observed Sensitivity Recovery. Electron Device Letters, IEEE, Volume 36, Issue 2, Page 174. [23] R.S. Okojie, R.D. Meredith, C.T. Chang and E. Savrun (2014). High Temperature Dynamic Pressure Measurements Using Silicon Carbide Pressure Sensors. IMAPS High Temperature Electron. Conf., Albuquerque, NM, USA, Page 47. [24] T.T.H. Eng, S.C. Kan and G.K.L. Wong (1995). Surface-Micromachined Epitaxial Silicon Cantilevers as Movable Optical Waveguides on Silicon-on-Insulator Substrates. Sensors and Actuators A, Volume 49, Issue 1, Page 109. [25] M. Born and K. Huang (1954). Dynamical Theory of Crystal Lattices. Clarendon. [26] Data available from www.ioffe.rssi.ru/SVA/NSM/Semicond/GaAs/basic.html [27] D. Strauch and B. Dorner (1990). Phonon Dispersion in GaAs. Journal of Physics: Condensed Matter, Volume 2, Issue 6, Page 1457. [28] D.W. Feldman, J.H. Parker Jr., W.J. Choyke, and Lyle Patrick (1968). Phonon Dispersion Curves by Raman Scattering in SiC, Polytypes 3C, 4H, 6H, 15R, and 21R. Phys. Rev., Volume 173, Page 787. [29] J.M. Ziman (1960). Electrons and Phonons: the Theory of Transport Phenomena in Solids, Clarendon. [30] A.V. Inyushkin, A.N. Taldenkov, A.Yu. Yakubovsky, A.V. Markov, L. Moreno-Garsia and B.N. Sharonov (2003). Thermal Conductivity of Isotopically Enriched 71GaAs Crystal. Semiconductor science and technology, Volume 18, Issue 7, Page 685. [31] B.C. Daly, H.J. Maris, K. Imamura and S. Tamura (2002). Molecular Dynamics Calculation of the Thermal Conductivity of Superlattices. Physical Review B, Volume 66, Issue 2, Page 024301. [32] R.E. Taylor, H. Groot and J. Ferrier (1993). Thermophysical Properties of CVD SiC. TRPL 1336, Thermophysical Properties Research Laboratory Report, School of Mechanical Enginnering, Purdue University, November 1993. [33] D.J. Senor, G.E. Youngblood, C.E. Moore, D.J. Trimble, G.A. Newsome and J.J. Woods (1996). Effects of Neutron Irradiation on Thermal Conductivity of SiC-based Composites and Monolithic Ceramics. Fusion Technology, Volume 30, Issue 3, Page 943. [34] Ju Li, L. Porter and S. Yip (1998). Atomistic Modeling of Finite-Temperature Properties of Crystalline β-SiC: II. Thermal Conductivity and Effects of Point Defects. Journal of Nuclear Materials, Volume 255, Issue 2, Page 139. [35] M. Rohde (1991). Reduction of the Thermal Conductivity of SiC by Radiation Damage. Journal of Nuclear Materials, Volume 182, Page 87. [36] R.J. Price (1973). Neutron Irradiation-Induced Voids in Beta Silicon Carbide. Journal of Nuclear Materials, Volume 46, Issue 3, Page 268. [37] A.C. Sparavigna and S. Galli (2012). L'equazione di Boltzmann per la conducibilità termica fononica nell'approssimazione dei tempi di rilassamento, Lulu Enterprises, Raleigh, NC.

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Photo Degradation in Dye-Sensitized Solar Cells T. J. Abodunrin1, M. L. Akinyemi1, A. O. Boyo2, J. A. Olugbuyiro3 1– Department of Physics, Covenant University Cannan land, P.M.B 1023 Ota. 2 – Department of Physics, Lagos State University, Ojo, Lagos. 3 – Department of Chemistry, Covenant University Canaan Land, P.M.B 1023 Ota.

Keywords: degradation, dye-sensitized solar cells, absorbance index ABSTRACT. Mesoporous TiO2 of 20nm diameter is prepared in-tandem with organic dyes and based on Fluorine – doped SnO2 (FTO), conducting base is produced by hydrothermal process. The prepared mesoporous Cola Acuminata (C.acuminata), Lupinus Arboreus (L.arboreus) and Bougainvillea Spectabilis (B.spectabilis) films (0.16 cm2) are applied; individually and in combination as interfacial layer in-between nanocrystalline TiO2 (NC- TiO2) and the FTO anode in the dye-sensitized solar cell (DSSC). Absorbance index (A.I) of all three dyes was studied within wavelength range 200900 nm for a period of 11 months, equivalent to 352 sun exposure. C.acuminata had A.I value 4.00 that decreased to 2.32 under exposure to AM1.5 global conditions. B.spectabilis A.I was 1.19 but decreased to 0.520 within same period of study. Combination of C.acuminata and B.spectabilis gave A.I value 1.40, dye cocktails of C.acuminata, B.spectabilis and L.arboreus gave 2.00 A.I value for same wavelength range. A UV/Vis photo spectrometer was used to determine the prominent peaks and absorbance at such wavelengths. This exponential relationship is subject of our explorative study.

Introduction. In the last decade, harvesting energy from solar insulation and direct transformation to electricity with cheap materials is a prospect many photovoltaic fabrications [1-4] depend on. Many novel ideas for efficient solar to electric conversion of energy challenge conventional p-n junction diode photovoltaics. ‘‘Gratzel’’ cells though a low –cost substitute to traditional silicon solar cells has attained only 10% yet cannot be mass produced due to practical limitations like sealing off leaking electrolytes, toxicity of certain organic solvents, desorption of dyes over time due to electrolyte used in dye-sensitized solar cells (DSSC). DSSCs are established on photoexcitation of molecules of dye grown on sintered TiO2 mesoporous nanoparticle that traps light photons for liberating electrons from the electrolyte through the TiO2 to a load connected to the cathode [2, 4]. Recent researches concentrate on adapting the dye for improved spectral absorbance [5], increasing stability through using conducting polymers or ionic solids instead of liquid electrolytes to improve on hole transport [4, 6] and raise to excellent condition electron transport using other possible semiconductors [7] having wide-band-gap or core-shell molecular structure [8]. An important feature in DSSC is increasing its efficiency by strategic design [9] and tailoring of TiO2 porous structure on nanoscale level in order to increase adsorption of molecular dye thereby, quickening electron transport and electrolyte. In fabrication of our DSSC, NC-TiO2 is deposited on transparent conducting oxide (TCO) with a thickness of 4.5 X 10-5m and an average area of 2.8 nm. In these TiO2 nanoparticles transferring electrons through the conduction band of TiO2 would be ineffective as a result of electrons liberated from dye molecules having to pass through main grain boundaries before they reach TCO. Moreover, electrolyte transport is not efficient enough because of irregularity in pores generated; monitoring [10] TiO2 nanostructures is therefore very important to increasing efficiency and current of DSSCs. Mesoporous TiO2 (Meso-TiO2) is regarded a prospective choice [11] for nanoporous DSSC electrode due to its attributes; large surface area, limited grain boundaries, uniform pore structure and excellent connectivity of its mesopores. However, mesospores tend to breakdown under intense heat in the process to get a suitable crystal structure.

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Generally, nanoparticles clusters [12] forming big colloidal solutions to decrease surface energy. Degussa P25 used to form NC-TiO2 colloidal particle contains many hundred nanometers of particles in TiO2 paste. When the screen-printing procedure is applied, it is impossible to cover the FTO perfectly smoothly without spaces in the interface [13]. This creates a direct contact with electrolytes causing deterioration between the TCO and TiO2 layer bringing a decrease in Voc as a result of back transport of electron shown by the following expression: FTO (2e-) + I3- FTO + 3IIn our work, 3.0 nm average sized Meso-TiO2 was formed as an interfacial layer between TiO2 and TCO. The A.I was measured for three dye samples; C.acuminata, B.spectabilis and L.arboreus and plotted against wavelength. Fabrication of DSSC’s. Preparation of thin layer of meso-TiO2 in cubic mesophase was formed on FTO substrate by hydrothermal process. (Degussa P25) was stirred thoroughly into conc. HNO3 in molar ratio compositions of TiO2 / HNO3= 3: 5 until a smooth viscous paste was obtained. The TiO2 paste prepared was coated on the conducting surface of FTO using screen printing method. The coated TiO2 films were sintered to make it more compact. The produced TiO2 film was dipped into the dye solution for adsorption at room temperature. The Pt-coated FTO used as counter electrode was prepared by heating the FTO over an open Bunsen flame moving it regularly back and forth to form a uniform layer of soot. The active area of TiO2 film dye sensitized was 2.8 nm. The slide dimension (7.5cm X 2.5 cm X 0.5 cm) ALDRICH with resistivity 7Ω / m2. The initial solution was aged under room temperature of 230C for 14 days, all deposited dye sensitized films were aged for 28 days. Characterizations. Photocurrent-voltage measurements was obtained using a multimeter 4200 model. A 60 W Xenon lamp was used to simulate a source of light, the intensity was regulated to fit AM 1.5G one sun intensity approximately, measurements were taken indoors and also in the dark. The incident photon-to-current efficiency (IPCE) spectra was determined as a function of wavelength from 200 - 900 nm. Absorbance spectra parameters was determined by Genesys 10S V1.200 (Model 2L7J355002). The A.I coefficients for the three dyes and their mixture was determined by analysing and interpreting the spectrographs for all the samples for 11 months. The morphology of TiO 2 mesoporous films was examined using a scanning electron microscope ASPEX 3020. Results and Discussions. Characterizations of Interfacial Meso-TiO2. In figure d, photo-electrons network of pathway from initial nucleation on TiO2 nanoparticles and subsequent adsorption is revealed as irregular cracks. The compact TiO2 at the boundary of the TiO2 particles on conductive substrates has been studied [9, 10] and a large group concluded that recombination occurs predominantly near the conductive substrate and not across the entire TiO 2 film [11]. Commercial fluorine-doped tin oxide (FTO) glass used as the TCO layer looks hazy with a rough surface appearance considerable light scattering on its surface. The formation of a uniform TiO2 layer over the rough surface (figure 1(c- d)) of the FTO layer will therefore be difficult. In general, nanoparticles are agglomerated to form large colloids in suspensions or pastes in order to reduce the surface energy [12-14]. Although electrons move a lot in different atoms, several nanoparticle boundaries and deadends in a disorderly molecular structure restrict electron transport [14]. An electric field is created through a charge deposited on the surface of an oxidized wafer. This oxide will break at its weakest spot (Figure 1d), current is confined to the spot of breakdown due to surface corona charge not drifting along the top layer [15]. In the DSSCs with metal substrates, the oxidized layer is naturally formed at the interface of the TiO2 particles on conductive substrate during thermal annealing. However, it seems that the low quality oxidized layer induced poor blocking behaviour of the DSSCs with the untreated Ti substrates. The recombination kinetics [12] were investigated by the evaluation of the rate of photo voltage decay. The HNO3-HF treatment of the Ti substrates strongly influenced the rate of the photo voltage decay. (Fig. 1 (d)). The electron recombination may lead to a lowering of the photocurrent [13], a decrease in the recombination may lead to a lowering of the photocurrent, but also to a decrease in the photo voltage by lowering the quasi-Fermi level for the electrons under illumination due to a photo voltage (decrease in photocurrent) with increasing photo voltage [14]. If the improved optical reflection at the substrate were a dominant element of enhanced performance, MMSE Journal. Open Access www.mmse.xyz 37

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the Voc and FF would restrictively increase and decrease respectively. An obviously possible cause for the significantly improved performance is decreased recombination at the interface of the TiO2/conductive substrate after HNO3-HF treatment.

2000 nm

1000 nm (a)

(b)

4000 nm

3000 nm (c)

(d)

Fig. 1. SEM images for Meso-TiO2 deposited on FTO (a), (b) at different resolutions. (c) and (d) show images of nanoporous dyes articulating with meso-TiO2 at higher resolutions. Interactions of dyes with different electrolytes. The graphs illustrate various reactions of DSSCs with the different electrolytes; mixtute of 3:1 KBr/I, HgCl2/I and KCl /I in sunny weather and when placed indoor. Figure 2a shows C.acuminata with three electrolytes, it had 5 mA, 9 mA and 3 mA with KCl, HgCl2 and KBr respectively. KBr electrolyte did not give the desired effect; to boost the production of photocurrent. HgCl2 increased photocurrent by 125% while, KClâ&#x20AC;&#x2122;s increase was 25% under AM 1.5. Figure 2a shows three intersections, where two different electrolyte record same value with dye. At this point, the physical behaviour of C.acuminata with KBr/I is same as C.acuminata with KCl/I. First intercept occurs at (3.5 mA, 1V) for KBr/I and KCl, the second is at (4.0 mA, 4V) for KBr/I and HgCl2 in sunny weather. A third intercept is on (1.8 mA, 4V) for KBr/I and KCl/I indoors. The nanoporous C.acuminata dye combines with meso- TiO2 and their reaction is same. At this point, one could be used interchangeably for the other to produce the same result. Figure 2b MMSE Journal. Open Access www.mmse.xyz 38

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reveals π to π* transition (1 mA to 1.8 mA, 0.2V) in KCl due to the phenolic16 bond. KBr shows series of hops (1 mA to 2 mA, 0.2V to 0.5V) before attaining a measure of stability. HgCl2 experiences loss of energy due to recombination of electrons from electrolyte with holes from nanoporous dye molecules. A series of hops occur from 0.2V to 0.4V in the process of attaining stability. Figure 3a and 3b shows B.spectabilis outdoor and indoor respectively. An interesting observation is a combination of B.spectabilis with HgCl2/I. Two different intersections occur at (55 mA, 30V) and (35 mA, 40V), where it is impossible to tell the behaviour and interaction of KBr/I and HgCl 2with B.spectabilis apart, see figure 3a and 3b. Also, B.spectabilis indoor with HgCl2/I records the same value as KBr/I which proffers a solution on days where there is little or no sunlight. In Figure 4a, an intercept occurs between KBr/I and HgCl2 (2.5 mA, 10V). A π to π* transition (4 mA to 6 mA, 12V) 16 . Figure 4b shows several ‘kinks’(0.2 mA to 0.4 mA, 0.2V) for KCl/I with L.arboreus series of hops characteristic of electrons and holes combining with same, different holes or being trapped. Their subsequent release and recombination, which effectively reduces the effective Fermi level17, 18 of the DSSC. Although detected by the voltmeter, because it’s on nanoscale it assumes significant proportions. It affects the thermodynamic equilibrium at an electrode. An electronic circuit that is in thermodynamic equilibrium would have a constant Fermi level throughout its connected parts. A battery nor power source need not be connected18 but, as indicated by a voltmeter. The condition is termed ‘quasi-fermi’ because solar illumination induced the temporary condition through a temperature difference from the sun. Also, recombination occurs (0.17 mA to 0.1 mA, 0.2 V) at the same point, π to π* transition occur16. KBr /I with C.acuminata and B.spectabilis shows KBr/I short circuit current increase (14 mA to 17 mA, 5V) as photo electrons are generated from incident photons of sunlight. However, recombination happens (17 mA to 14 mA, 7 V), a steady state is revealed in figure 5a. This becomes short lived as short circuit current increases (13 mA to 15 mA, 18V) more photo electrons are liberated from KBr/I. Consequently, recombination happens as the hole ‘moves’ with the drift of electrons (15 mA to 12 mA, 20V) shown by another potential drop. Figure 5c shows an a point of intersection of HgCl2/I with KCl/I (2 mA, 15V); a juncture when C.acuminata’ s cocktail with L.arboreus act alike and it is difficult to tell apart their behaviour in the two different electrolytes. In figure 5d, cocktail of B.spectabilis and L.arboreus has an intersection (2 mA, 10V) shows HgCl2/I behaving similar to KCl/I regardless of their varying chemical composition. Cocktail of C.acuminata, L.arboreus and B.spectabilis in figure 5f has an intersection (8 mA, 10V). KBr/I acts like HgCl2/I at this point which suggests that they could be used as substitutes and generate same results but, only at this point

Fig. 2(a). I-V curve for C.acuminata dye in Sunny weather MMSE Journal. Open Access www.mmse.xyz 39

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Fig. 2(b). I-V curve for C.acuminata dye Indoor

Fig. 3(a). I-V curve for B.spectabilis dye in Sunny weather

Fig. 3(b). I-V curve for B.spectabilis dye Indoor MMSE Journal. Open Access www.mmse.xyz 40

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Fig. 4(a). I-V curve for L.arboreus dye in Sunny weather

Fig. 4(b). I-V curve for L.arboreus dye indoor

Fig. 5(a). I-V curve for C.acuminata & B.spectabilis dye Indoor MMSE Journal. Open Access www.mmse.xyz 41

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Fig. 5(b). I-V curve for C.acuminata & B.spectabilis dye in Sunny weather

Fig. 5(c). I-V curve for C.acuminata & L.arboreus dye in Sunny weather

Fig. 5(d). I-V curve for B.spectabilis & L.arboreus dye Indoor MMSE Journal. Open Access www.mmse.xyz 42

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Fig. 5(e). I-V curve for B.spectabilis & L.arboreus dye in Sunny weather

Fig. 5(f). I-V curve for C.acuminata, L.arboreus & B.spectabilis dye Indoor

Fig. 5g. I-V curve for C.acuminata, L.arboreus & B.spectabilis dye in Sunny weathe Degeneration in DSSC MMSE Journal. Open Access www.mmse.xyz 43

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Dye sensitized solar cells output efficiency decreases with age as they are exposed to ultraviolet (UV) radiation. Other obstacles are UV stabilizers that are responsible for absorbing quantized chromophores but emit only at longer wavelengths. Antioxidants used with the aim of improving cell efficiency is another hurdle that reduces the iodide ion. This iodide ion replaces the Highest Occupied Molecular Orbital (HOMO) in the dye restoring its initial form, preparing it for generation of electron again. The reaction at the anode of the photocell is represented below: I2 +I- ↔ I3-. The reaction at the counter electrode is a reduction of tri- iodide ion to iodide is as shown: .

Absorbance Index a.u

This stops the accumulation of holes which could cause recombination with electrons from the conduction band. Maximum output voltage equals to the difference between the redox potential of the mediator and the Fermi level of the semiconductor. Therefore, the DSSC can produce electricity from sunlight without going through any permanent physical and chemical change [18].The A.I of the dye cocktail of C.acuminata, L.arboreus and B.spectabilis was determined with Genesys 10S V1.200 model (2L7J355002) in 2014, this spectrograph was analysed with the spectrograph obtained in 2015. Figure 6a shows A.I of C.acuminata without electrolyte, it has a peak value of 4.0 within 200 nm to 900 nm wavelength in February, 2014. By January, 2015 (figure 6b) C.acuminata A.I had reduced to a peak value of 2.320. The series of hops were absent, indicating higher degree of stability for wavelength range of 500 nm to 800nm. Several –OH ligands have evaporated, C.acuminata is more concentrated. Figure 2a shows C.acuminata with three electrolytes, it had 5 mA, 9 mA and 3 mA with KCl, HgCl2 and KBr respectively. KBr electrolyte did not give the desired effect; to boost the production of photocurrent. HgCl2 increased photocurrent by 125% while, KCl’s increase was 25% under AM 1.5.

Wavelength (nm)

(a)

(b)

Fig. 6. A.I of C.acuminata. a) In 2014 b) by 2015 Figure 7a features pure L.arboreus with A.I of about 2.0, when a cocktail of L.arboreus with C.acuminata and B.spectabilis, the drop in value of A.I could be attributed to unfavourable inter-dye interactions, dye degeneracy or a measure of both conditions19. MMSE Journal. Open Access www.mmse.xyz 44

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UV/Vis of C.acuminata, L.arboreus and B.spectabilis

Absorbance Index

0,8 0,6 0,4 0,2 0 -0,2

(a)

200

400

600

Wavelength (nm)

800

1000

(b)

Fig. 7.a) A.I of L.arboreus b) C.acuminata, B.spectabilis and L.arboreus dye (February 2014) B.spectabilis has A.I of 1.6 (figure 8a), when mixed in cocktail with C.acuminata and B.spectabilis another A.I drop occurs to 0.520 affirming an unfavourable interaction between the three dyes19.

(a)

(b)

Fig. 8. a) A.I of B.spectabilis; b) C.acuminata, B.spectabilis and L.arboreus dye (January 2015) Figure 7b shows a cocktail of C.acuminata and B.spectabilis in February, 2014 with no electrolyte. It is characterized by several short jumps or ‘hops’ from 200 nm to 300 nm, the highest A.I is at 1.4. Dye cocktail of C.acuminata, B.spectabilis and L.arboreus dye (figure 8b) also has the period of instability or hops, electron liberation, transfer and combination or recombination with holes. The peak A.I is 2.0 for wavelength range 200 nm to 900 nm (compare with figure 5b) C.acuminata and B.spectabilis with different electrolytes under AM 1.5. The photocurrent values were 19 mA, 9 mA and 13 mA respectively with KCl, HgCl2 and KBr respectively. All three electrolytes showed very promising yield. However, by January, 2015 the yield had reduced due to degeneracy [13]. Rate of Photo Voltage Decay in DSSC. Photo voltage decay is inversely proportional to the lifetime of photo electrons in DSSCs and this lifetime in turn is inversely proportional to rate of recombination19.The photo-degradation efficiency ŋ was calculated by

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ŋc.acuminata = 80%, dye cocktail of the three dyes from the formula has a photo-degeneracy of 53.8%. This indicates rate of decomposition of ŋcocktail ˂ ŋc.acuminata although the A.I for parent dye was higher for both L.arboreus and C.acuminata. Summary. Photo-degeneracy in DSSCs is a single type contrary to Si wafers that have two lifetime. Generation and recombination lifetimes (τg and τr respectively), the dual function is combined in DSSCs. DSSCs should last at least twenty years without significant degradation when sensitized with suitable electrolytes. Standard aging test last for 1000 hours typically20, equivalent to a year of outdoor application. In practice, real outdoor tests data for years is not readily available. It implies linear degradation though a safe assumption might not affect I / V parameters in the short reaction time due to presence of large dye molecules on the electrode. Each of these molecules undergoes 91 million redox cycles in those twenty years under AM 1.5 and moderate temperature between 550C-600C 20. In an ideal condition, electron injection and regeneration occur irreversibly. In any device however, a measure of degradation occurs since a temperature of 800C is easily attained on a sunny day, the stability intrinsically is insufficient and requires improvement. Improved stability by reducing electrolyte’s vapour pressure or amending the interface of TiO2-dye are advances achieved with ionic liquids as electrode sensitizers. Initial efficiency of 8.1% has been demonstrated when this TiO2 network is immersed with quasi- solid state electrolyte. It is subject to debate if the polymer matrix can withstand intense UV irradiation without degradation. Acknowledgements The authors wish to appreciate the support of technologists in Physics and Chemistry Research Laboratory of Covenant University. References [1] B. O’Regan and M. Gratzel, Nature (London) 353, 737 (1991). [2] M. Gratzel, Nature (London) 414, 338 (2001). [3] M. Durr, A. Bamedi, A. Yasuda, and G. Nelles, Appl. Phys. Lett. 84, 3397 (2004). [4] W. U. Huynh, J. J. Dittmer and, A. P. Alivisatos, Science 295, 2425 (2002). [5] M. K. Nazeeruddin, P. Pechy, T. Renouard, S. M. Zakeeruddin, R. Humphry-Baker, P. Compte, P. Liska, L. Cevey, E. Costa, V. Shklover, L. Spiccia, G. B. Deacon, C. A. Bignozzi, and M. Gratzel, J.Am. Chem. Soc. 123, 1613 (2001). [6] D. Gebeyehu, C. J. Brabec, and N. S. Saiciftci, Thin Solid Films 403, 271 (2002). [7] K. Keis, E. Magnusson, H. Lindstrom, S. E. Lindquist, and A. Hagfeldt, Sol. Energy Mater. Sol. Cells 73, 51 (2002). [8] Z. S. Wang, C.H. Huang, Y.Y. Huang, Y.J. Hou, P.H. Xie, B.W. Zhang, and H.M. Cheng. Chem. Mater. 13, 678 (2001). [9] J. Xia, N. Masaki, K. Jiang, S. Yanagida, Chem. Commun. 138 (2007). [10] B. Peng, G. Jungmann, C. Jäger, D. Haarer, H.W. Schmidt, M. Thelakkat, Coord. Chem.Rev. 248, 1479 (2004). [11] K. Zhu, E. A. Schiff, N. -G. Park, J. V. D. Lagemaat, A. J. Frank, Appl. Phys. Lett. 80, 685, (2002). [12] A. Zaban, M. Greenshtein, J. Bisquetr, Chem. Phys. Chem 4, 859 (2003). [13] A. Hagfeldt, M. Grätzel, Chem, Rev. 95, 49 (1995). MMSE Journal. Open Access www.mmse.xyz 46

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[14] A. Kumar, P. G. Santangelo, N. S. Lewis, J. Phys. Chem. 96, 834 (1992). [15] D.K. Schroder, ‘‘Surface Voltage and Surface Photovoltage: history, theory and applications’’, Meas. Sci. technol. 12, (2001), R 16 – R 31. [16] L. Peter, ‘‘Infrared and Raman Characteristic Group Frequencies: Tables and Charts’’, 18 (2011). [17] I. Reiss, ‘‘what does a voltmeter measure?’’ Solid State Ionics, 95, 325, 1197. [18] D. Chattopadhyay, ‘‘Electronics (Fundamentals and Applications)’’. [19] B. Park, Q. Shen, Y. Ogomi, S.S. Pandey, T. Toyoda, S. Hayase, ECS Journal of Solid State Science and Technology. 2, 1 Q6 - Q11 (2013). [20] J. Vlachopoulos, Particle Coalescence (sintering) in Polymer Processing and Beyond, PPS (2014).

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II. Mechanical Engineering Analytical Description of Plastic Deformation Distribution in the Neck of a Flat Tensile Specimen Yevgeny Ye. Deryugin1a, Natalya Antipina2 1 – Institute of Strength Physics and Materials Science of the SB RAS, Tomsk, Russia 2 – National Research Tomsk Polytechnic University, Tomsk, Russia a – dee@ispms.tsc.ru

Keywords: neck of a flat specimen, plastic deformation, analytical description

ABSTRACT. This work presents an analytical description of the non-uniform field distribution of plastic deformation in a flat specimen, which determines distortion of the specimen in the necking zone. The proposed method enables to be simulated the real non-uniform distributions of plastic deformation and neck distortion according to experimental measurements data. Analytical expressions are suitable for calculation of gradients and concentration of stress in the neck of a flat specimen made of real material, using well-known analytical and numerical methods: finite element methods, boundary element methods, relaxation element methods etc.

1. Introduction. Tensile test of the material is one of the basic test types that can outline the most important mechanical properties of the materials in engineering applications. The peculiarity of many structural metals and alloys is the descending segment on the conventional stress-strain diagrams associated with plastic deformation localization in the neck emerging before the material fracture. The specimen cross-sectional area at point of necking reduces suddenly followed by load decrease required for further specimen deformation before fracture. To analyze accurately the physical mechanisms of plastic deformation and material strengthening at the pre fracture stage, we need to calculate the dependence corresponding to the material response in the neck local zone, where the plastic deformation is maximum and develops at highest rate. The true load diagram in the given local volume is not reflected if to take into account only a cross section reduction in the neck, since the plastic deformation distribution in the neck is extremely non-uniform. As experience shows [1, 2], the maximum degree of plastic deformation and the critical state of the material is reached at the center of the minimum cross section of a flat specimen. There are certain difficulties in experimental measurement of the geometric shape and plastic deformation distribution in the necking zone [3]. Experimental techniques for measuring local deformation of solid bodies under different boundary loading conditions are now being developed [18]. Therefore, description of the specimen plastic distortion related to non-uniform plastic deformation distribution in the emerging neck is one of topical problems in mechanics of the deformed solid body. In this paper, we propose a universal method for the analytical setting of a smooth field with plastic deformation gradients in the local zone of a flat tensile specimen that determines the geometric shape of the neck and plastic deformation distribution in it. The proposed form of analytical description allows one to obtain distributions, which agree with experimental measurements data qualitatively MMSE Journal. Open Access www.mmse.xyz 48

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and quantitatively, by variation of geometrical parameters in equations. An analytical setting of plastic deformation distribution in the neck zone allows calculating distribution and concentration of stresses in a solid body at the pre fraction stage using the methods of continuum theory of defects [911] and numerical methods for the deformed solid mechanics [12-14]. Calculation of stresses in the necking zone is an independent task and is not presented in this work. 2. Description of plastic deformation distribution in the neck of a flat tensile specimen. Experimental studies of plastic deformation distribution emerging in the neck of a flat tensile specimen show that generally, this distribution is extremely non-uniform and at the macro-scale level satisfy the following conditions [2 - 4, 15]: a) Maximum degree of plastic deformation is observed in the center of a symmetric neck; b) Plastic deformation degree decreases with distance from this center; c) In the minimum cross-section of a specimen, the material is subjected to the more severe plastic deformation; d) Plastic deformation zone boundary in the neck is generally expanding as it approaches to the lateral edges of a flat specimen, i.e. plastic deformation localization (LPD) zone in the neck is characterized by the X-type shape. Besides, the LPD zones in the shape of a cross band are observed in the experiments. At the macro scale level, non-uniform field of plastic deformation in the neck of a flat specimen can be presented as a smooth field with plastic deformation gradients in continuous medium, which finally should meet the above-specified conditions. The specified plastic deformation distributions hold provide equal displacement to fall the points of upper and lower ends of a flat specimen. First we define the geometrical parameters of a neck zone, which should qualitatively describe the Xshape of the LPD boundary. Let the distance d(y) in the specimen in length а and width b (Fig. 1) from the origin of coordinates in the center of symmetric neck to the boundary of LPD zone in direction, which is parallel to the tension axis x, depends on the coordinate y according to the equation

y l  y   a   (a  a  )  b

   

 

(1)

Here а1 is the maximum value of this function at the specimen’s edge, when y = ± b/2, а2 is the minimum value of this function at y = 0. In this representation, the values of а1, а2, b and γ, obviously, will affect the value and geometrical shape of the LPD zone. Figure 1 presents an example of the LPD zone, when а1, а2, b are equal to 120, 80 and 120 conventional units, respectively, γ = 1. The specimen length is described by the value of аequal to 480 conventional units. In case, when γ is 1, the LPD zone boundary is described by a parabolic shape. It is seen that dependence (1) qualitatively determines the Х-shaped LPD zones. Figure 2 illustrates the effect of γ in the equation (1) on the LPD zone distortion. It is seen that the higher γ is, the faster the X-shaped LPD zone transforms into the LPD band across the specimen. At γ→ ∞, we have a case of LPD cross band in width of 2а2. Figure 2 b shows the effect of the difference а1 - а2 on the shape of the LPD zone. At а2 → а1, the Xshaped LPD zone gradually transforms into the LPD cross band in width of 2а1. Obviously, this LPD MMSE Journal. Open Access www.mmse.xyz 49

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zone distortion will be also observed at а1 → а2. However, in the latter case, the cross band width will be equal to 2а2.

Fig. 1. LPD zone in the flat specimen neck. γ = 1

Thus, it is possible to change shape and dimensions of the LPD zone in a wide range by varying the parameters а, b, а1, а2, and γ in Eq. (1). To build a continuous (with no jumps) plastic deformation distribution in the neck, the LPD zone was divided into two areas I and II (Fig.3). The boundary of area I was positioned at a distance of α l(у) from the boundary of the LPD zone, where 0 < α < 1. In this area, the normal component distribution x of plastic deformation along the tension axis x was specified according to the equation

  x ( х, у )    ( y )    (  α ) 

 x     l( у)   

β  

,  

(2)

and in the area IIaccording to the equation

x   ( y)     x ( х, у )   β     l ( у ) 

β 

(3)

Here is the parameter determining the value and change in plastic deformation gradients in the LPD zone, L is the specimen elongation due to the plastic deformation in the neck. Equations (2)–(4) provide a smooth field of plastic deformation with no jumps at the boundaries and inside the LPD zone. The maximum gradients of plastic deformation are observed at the boundary between the areas I and II. Figure 4а illustrates the plastic deformation distribution in the specimen neck, which is obtained under the following values of parameters in equations (1) – (4): γ = = 1, α = 0.4, a/b = 4.5, a1/b = 1.5, a2/b = 1, L/b = 0.125. As seen from the presented results, the proposed description of the plastic deformation field in the neck qualitatively satisfies the distributions observed in the experiments [24, 15]. When varying the geometrical parameters of the LPD zone, one can obtain different variants of distributions. We will give a few examples varying only some of the calculated parameters, specified MMSE Journal. Open Access www.mmse.xyz 50

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above. Figure 4b presents the distribution for =4 under the same conditions. Comparison with Fig. 4а shows that increase in leads to the increase in plastic deformation gradients in front of LPD.

Fig. 2. The LPD zone distortion with increase in γ (а) and reduction in the difference of а1 – а2 (b) in Eq. (1):  = 1

Fig. 3. Half of the LPD zone in the flat specimen neck

In Eqs. (2) and (3)

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0 ( y ) 

L(  2) . 2    1    l ( у)

(4)

Fig. 4. Examples of plastic deformation distributions in the flat specimen neck. The calculated parameters are specified in the text

The condition а1=а2, as it was specified above, provides the variant of the LPD cross band. Figure 5а presents the case, when а1/b = а2/b = 1 and = 1. In this band, the plastic deformation profile x does not change along the у axis. Figure 5b illustrates the LPD cross band at = 4. Comparison of Figs. 4 and 5 shows that  determines the maximum degree value of plastic deformation  max irrespective of x а1а2. At the same time, increase in results in some decrease in max x . According to the continuum theory of defects [9-11], certain gradients and concentrations of stresses correspond to the specified non-uniform field of plastic deformation in the continuous medium. When setting the concrete plastic deformation distribution for plane stress state with Esq. (1)–(4), one can calculate numerically or analytically the non-uniform field of stresses in the volume of a solid body using the well-known methods of finite elements, boundary elements, relaxation elements etc. [1214].

Fig. 5. Examples of LPD cross bands: = 1 (а), 4 (b). The calculated parameters are specified in the text

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It should be emphasized that Eqs. (2) – (4) determine only non-uniform field of plastic deformation. Generally, a uniform field of plastic deformation should be added to these equations over the entire specimen area, characterized by the plastic deformation value outside the neck zone. It is known that uniform field of plastic deformation (without gradients) does not affect the field of internal stresses. 3. The neck distortion in a flat tensile specimen. Macro non-uniform distribution of plastic deformation with gradients determines a significant distortion of a flat specimen. As a result, configuration occurs in local zone of a specimen, which is determined in scientific literature as “neck”. Obviously, shape and dimensions of the neck depend on qualitative and quantitative distribution characteristics in the LPD zone. To describe the neck shape, it is sufficient to calculate the displacement of points at the edges of a flat specimen. This requires knowing all the plastic deformation tensor components in the specimen, namely x, у and xу. It will be assumed that for a symmetric neck, xу is 0. The values for the plastic deformation normal component x, directed along the tension axis, are set by Eqs. (2)–(6). To calculate у component, the additional assumptions are required. It is usually assumed that there is no change in the material volume under plastic deformation. For simplicity, let us assume that under tensile deformationх = the compressive deformation takes place along the х axis, that is proportional to the value of , identical for width and thickness of the specimen, i.e. у = and z = , where  is the proportionality coefficient, or the Poisson's ratio, as it is determined for elastic deformation. For the elementary volume v is xyz, so the equality can be written as xyz = x(1+)y(1)z(1), or 1 = (1)(1)2. Hence we find the value of the Poisson’s ratio   []/

(5)

As seen from the equation,  depends on the deformation degree. At small deformation degrees, when→ 0, → 0.5. One can verify it, expanding the expression 1in a series by the value of [16], being limited by the first two members 1. As increases,  decreases. In examples that we have seen in Figs. 4 and 5, the maximum degree of plastic deformation is equal to max = 0.213. When substituting this value into Eq. (5), we shall obtain  = 0.43. Further, for simplicity of calculations, we will consider as a constant and equal to 0.4. The change of the specimen width occurs due to the deformation component у. The elementary volume contribution to the displacement of point (х, b/2) on the side face of the specimen is equal to

du Iy (x) = 1(х, y)dy,

(6)

if it is found in area I (see Fig. 3). If the elementary volume is found in the area II, it provides the displacement of point (х, b/2) by an elementary value

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du IIy (x) = 2(х, y)dy.

(7)

Total displacement of points (х, b/2) is determined by the integration of elementary displacements (6) and (7) along the y variable in areas I and II, respectively. We shall write this as two integrals, summing displacements separately in areas I and II

u y ( x )  du Iy ( x )  du IIy ( x )

y I

y II

y

   I  ( x, y )dy    II   ( x, y )dy

When substituting the expressions (1)  (4) into Eq. (6) if  = const, for the first integral we shall obtain

1 L(  2)  y2I 1  1  x     1  u ( x)     dy  . 2[  1  ]  y1I l ( y )  (1  )  l ( y)        I y

(8)

Similar substitution of the expressions (1)(4) into the second integral results in the equation 1  x  L(  2)  y2II 1   . u ( x)  1  dy   2[  1  ]  y1II l ( y)  l ( y)    II y

(9)

Let us consider a concrete example, when а1(1α) < а2, presented in Fig. 6а, where four regions with different limits of integration are distinguished. In the region 1, only Eq.(8) is integrated, with I I integration limits of y = 0, y  = b/2. The boundary between the areas I and II determines the lower II I limit of integration y for Eq. (8) and upper limit of integration y  for Eq. (9) for the region 2. From

b 

x = l(y)(1α), we find yI  y II    

x  a (  ) II I . In this case, y  = b/2 and y = 0. In the (a  a )(  ) II

region 3, only Eq. (9) is integrated, with integration limits of y  = b/2 and y = 0. Finally, in the region 4, the LPD zone boundary determines the lower limit of integration for Eq.(9), equal to yII 

b   x  a  , according to the condition x = l(y). The upper limit of integration for Eq. (9)   a  a  II

thereby, is equal to y  = b/2. Figure 6b presents another variant, when а1(1α) > а2. In this case, four regions with different limits of integration are also distinguished. As seen from the comparison of Figs. 6а and 6b, in the regions 1, 2 and 4, the integration limits did not change. The difference of integration limits is observed only MMSE Journal. Open Access www.mmse.xyz 54

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in the region 3. In the last example, Eq (9) is integrated, with integration limits of yII 

x  a  (  ) b   x  a  b and y II     , and also Eq. (8) with integration limits of    ( a  a  )(  ) a  a 

yI 

b b   x  a  I and y   .    a  a 

Fig. 6. The scheme of integration regions in the neck zone: a is the first variant, b is the second variant.

Now let us define the displacements of points of the specimen’s side face along the tension axis. For this purpose, one should integrate the elementary displacement contributions of points at the edges of the specimen along the tension axis. After integration we will come to the following result 1   x   1  (1  ) x 1  0  x  a1 (1   ) ;    x ,     2  a1 (1  )      2 a   a  x  2  2  1 1 1   1 ux     , f a1 (1  )  x  а1;    (1  )a1  a1 (1   ) 2    2   a1     a1    1    , x  a1 .  2 

Here   0 (b /2) 

(10)

L(  2) . 2  a1    1   

It is easily to verify that in the interval x > а1, all the points on the side face of the specimen are displaced by the same value of ux = L/2. The displacement components ux and uy, set by Eqs. (9)–(10), completely determine the distortion of the flat specimen. Figure 7 presents the calculation data for the configuration change of the neck as MMSE Journal. Open Access www.mmse.xyz 55

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the specimen length L increases due to the non-uniform plastic deformation in the LPD zone. It is seen that plastic deformation accumulation in the LPD zone leads to the minimum cross-section reduction and increase in the specimen length.

Fig. 7. The neck distortion with increase in specimen length: L/b = 0.0125, 0.25, 0.5, 1.0, 1.5; β=γ=1

Figure 8 shows the effect of on the specimen shape. Increase in results in more rapid decrease in the specimen width. In this case, the minimum cross-section changes insignificantly.

Fig. 8. The neck distortion with increase in β in Eqs. (8) – (9): β= 1, 4, 30, 150; L/b = 1

Summary. This work presents an analytical description of the non-uniform field distribution of plastic deformation in a flat specimen, which determines distortion of the specimen in the necking zone. The proposed method enables to be simulated the real non-uniform distributions of plastic deformation and neck distortion according to experimental measurements data. Analytical expressions are suitable for calculation of gradients and concentration of stress in the neck of a flat specimen made of real material, using well-known analytical and numerical methods: finite element methods, boundary element methods, relaxation element methods etc. This work presents a theoretical description of the non-uniform field distribution of plastic deformation in a flat specimen, which determines distortion of the specimen in the necking zone. Smooth fields with plastic deformation gradients and change in the geometric shape of a flat tensile specimen can be described by the variation of geometrical parameters in the obtained equations. The proposed method enables to be simulated the real non-uniform distributions of plastic deformation MMSE Journal. Open Access www.mmse.xyz 56

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and neck distortion according to experimental measurements data. The problem is relevant due to the solid mechanics associated with transition from the "load-extension" experimental curves to the "stress-strain" loading diagrams for the material in the minimum cross section zone of the specimen, where the plastic deformation develops extremely non-uniformly and at maximum speed. It is the zone the material is subjected to all stages of deformation hardening followed by fracture. Analytical expressions are suitable for calculation of gradients and concentration of stress in the neck of a flat specimen made of real material, using well-known analytical and numerical methods: finite element methods, boundary element methods, relaxation element methods etc. Finally, the results can be used in simulation of plastic deformation and ductile fracture of different materials. Acknowledgment This work was supported by grant No. 10-08-01182-а from the Russian Foundation for Basic Research. References: [1] M.N. Gusev, I.S. Osipov, The peculiarities of deformation-plastic behavior of metals and alloys irradiated with neutrons in WWR-K and BN-350 reactors, Vestnik Udmurdtskogo Universiteta. Physics. 4 (2007) 104-112. [2] L.S. Derevyagina, V.E. Panin, A.I. Gordienko, Selforganization of plastic shears in localized deformation microbands in the neck of high-strength polycrystals and its role in material fracture under uniaxial tension, Physical mezomechanics 4 (2007) 59-71. [3] V. I. Trefilov, V. F.Moiseev et all, Deformation hardening and failure of polycrystal metals, Kiev, Naukova Dumka (1989) 256. [4] T.M. Poletika, A.P. Pshenichnikov, Nonlinear strain macrolocalization behavior in H.C.P zirconium alloys, ZTF V. 79, 3 (2009) 54-58. [5] W.H. Peters, W.F. Ranson, Digital imaging technique in experimental stress analysis, Optical Engineering 21 (1982) 427. [6] M.A. Sutton, W.J. Wolters et all, Determination of displacements using an improved digital image correlation method, Image Vision Computing V. 1, 3 (1982) 133. [7] V.E. Panin, V.S. Pleshanov, V.V. Kibitkin, S.V. Sapozhnikov, Analysis of displacement vector fields and fatigue failure diagnostics of an aluminum alloy at a mesoscale, Defektoskopiya 2 (1998) 80–87. [8] S.V. Panin, V.I.Syryamkin, P.S. Lyubutin, Rigid body deformation estimation by surface images, Avtometriya V. 41, 2 (2005) 44-58. [9] J. D. Eshelby, The continuum theory of lattice defects, Solid State Physics, V. 3, N.Y.: Acad. Press (1956) 79-144. [10] de Wit R, Linear theory of static disclinations , In: Fundamental aspects of dislocation, ed. by J.A. Simons, R. de Wit, R. Bullough, Nat. Bur. Stand. (US) Spec. Publ. 317, V. I (1970) 651-673. [11] V.A. Likhachev, A.E. Volkov, V.E. Shudegov, The continuum Theory of Defects., Leningrad: University (1986) 232. [12] R. Gallager, The finite element method. Moscow: Mir, 1984.

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[13] S.L. Crouch, A.M. Starfield, Boundary element methods in solid mechanics. London: George Allen & Unwin (1983). [14] Ye.Ye. Deryugin, G. Lasko, S. Schmauder, Relaxation Element Method in Mechanics of Deformed Solid. In: Wilhelm U. Oster. Computational Materials, NY: Nova Science Publishers, Inc. (2009) 479-545. [15] A.V. Panin, A.A. Son, Yu.F. Ivanov, V.I. Kopylov, Features of localization and stage character of plastic deformation of ultrafine-grained armco-iron with the fragmented band substructure, Fizicheskaya Mezomekhanika V. 7, No 3 (2004) 5-16. [16] M. Ya. Vygotskii, Handbook of Higher Mathematics. Moscow: AST Astrel (2005) 679.

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Computer Aided Analysis and Prototype Testing of an Improved Biogas Reactor For Biomass System Jeremy (Zheng) Li 1a 1 â&#x20AC;&#x201C; Ph.D., Associate Professor, School of Engineering, University of Bridgeport, USA a â&#x20AC;&#x201C; zhengli@bridgeport.edu

Keywords: green resource, sustainable energy, biomass system, environmental protection, fuel efficacy, cost effective, biogas enrichment.

ABSTRACT. The alternative fuel resources substituting for conventional fuels are required due to less availability of fuel resources than demand in the market. A large amount of crude oil and petroleum products are required to be imported in many countries over the world. Also the environmental pollution is another serious problem when use petroleum products. Biogas, with the composition of 54.5% CH4, 39.5% CO2, and 6% other elements (i.e., H2, N2, H2S, and O2), is a clear green fuel that can substitute the regular petroleum fuels to reduce the pollutant elements. Biogas can be produced by performing enriching, scrubbing, and bottling processes. The purification process can be further applied to take away the pollutants in biogas. The pure biogas process analyzed in this research is compressed to 2950 psi while being filled into gas cylinder. The daily produced biogas capacity is around 5480 ft 3 and the processing efficacy is affected by surrounding environment and other factors. The design and development of this biogas system is assisted through mathematical analysis, 3D modeling, computational simulation, and prototype testing. Both computer aided analysis and prototype testing show close results which validate the feasibility of this biogas system in biomass applications.

Introduction. Biomass, the biological materials, can be produced by processing some surviving or lately deceased organisms including crops or materials relevant to crops [1]. Biomass is considered as one type of energy resource that can be applied to generate heat by direct combustion or can be changed to other types of bio-fuel by some technologies [2]. The biomass can be changed to bio-fuel by alternative ways including biochemical, chemical, and thermal methodologies. The current common fuels used in commercial transportation systems are petrol or diesel and its demand is increasing sharply due to modern industrialization. Because of the shortage in natural petroleum supply, a lot of petrol-related products have to be imported from outside of country. In addition, the tightened environmental pollution control on the emission of transportation systems requires finding alternative fuel resources [3, 4]. The green and sustainable energy resources, such as bio-fuel, biogas, solar energy, wind power, and geothermal, can be used as alternative energy resources in different applications. Although the natural gas has methane, ethane, propane, butane and other elements, biogas posses 68-78% enriched methane [5, 6]. Pure methane can be potentially produced from biogas by using scrubber. Because enriched methane can be easily bottle-compressed after being produced from biogas, it can be potentially used as gas fuel for many different applications. Some organic wastes including commercial/residential wastes, sewage waste, and community solid waste can be used as source stocks to make biogas [7]. Biogas is one of the green, sustainable and clean fuels and the wastes generated during biogas production can be utilized for making fertilizer products [8, 9]. The common source materials to produce biogas are usually biodegradable wastes existed in many commercial/residential areas including wastes from human, paper, food, and many other organic materials [10]. 1. Biogas enrichment process. To produce pure methane, the contained impurities in source materials must be removed by methods of filtration, such as membrane segregation, physical absorption, chemical separation, and water absorption [11]. The physical absorption process can be used to get rid of impurities including carbon-dioxide and hydrogen-sulfide by water scrubbing technique [12]. The pressured water from pump flows into scrubber at the top section and biogas from storage vessel enters scrubber at the bottom sections. Since the weight of biogas is lighter than the MMSE Journal. Open Access www.mmse.xyz 59

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weight of water, biogas travels upward and water flows downward through scrubber baffle. As soon as biogas physically contacts water, the impurities including carbon-dioxide and hydrogen-sulfide will be absorbed by water and removed impurities can be collected in the filter at bottom of scrubber [13]. The purified biogas in biomass well system gets dry as it moves through the heat exchanger device and pressured up to 1250 psi by the first-stage compressor. The flow of biogas is controlled via a rotameter to ensure no overflow inside scrubber. When enough biogas is monitored inside scrubber, extra biogas can be temporarily stored in the first storage container for later cycle. Biogas flows through the first storage container, where its pressure being reduced, into scrubber at the bottom. After the contact between upward biogas and downward water inside scrubber, the impurities in biogas can be removed by physical absorption from water and purified biogas can continuously flow through top of scrubber into second storage container. Biogas continuously flows through gas filter, where it gets more purified, into second compressor. Biogas is pressured to 2950 psi at second compressor before being filled in biogas container.

Fig. 1. Biogas enrichment system The biogas enrichment system, shown in Fig. 1, consists of biomass well system (#1), heating device (# 2), first compressor (#3), valve (#4), first storage container (#5), rotameter (#6), scrubber (#7), second storage container (#8), second compressor (#9), and biogas container (#10). 2. Computational simulation on biogas reactor in biomass system. The computational simulation has been performed to study and modify the performance of biogas reactor in biomass system. In biogas reactor unit, the external force is used to drive the rotation of biomass mixer to produce the biogas. The heating energy needed for digester and heating energy lost in system require to be considered. The normal temperature in digester for heating biogas plant changes from 24.5Ë&#x161;C to 38.5Ë&#x161;C and heating energy required in the digester depends on environmental conditions including surrounding temperature. The heating energy needed in digester can be specified by following equation (1) [14]. MMSE Journal. Open Access www.mmse.xyz 60

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QREQ  (C P  M  TREQ  t )  QLOSS ,

(1)

where QREQ – heat energy required for starting process in digester (kWh);

C P – heat capacity of feeding material stocks (J/[kg*K°]);

M – mass of feeding material stocks (kg); TREQ – temperature change of feeding material stocks between entering and leaving digester (K°);

t – time (hours); QLOSS – heat loss through digester surface (kWh); The heat loss through digester surface QLOSS can be found from equation (2) [14].

QLOSS  S  C H  TLOSS  t ,

(2)

where, S – digester surface (m2);

C H – heat transfer coefficient (W/[m2 K°]);

TLOSS – temperature change between inside and outside digester surfaces. The raw feeding materials, driven by reactor blades, rotate rapidly to continuously produce biogas inside biogas reactor. To improve biogas reactor design, three different blade structures shown in Figs. 2 – 4 are analyzed.

Fig. 2. Bioreactor blade 1

Fig. 3. Bioreactor blade 2

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Fig. 4. Bioreactor blade 3 The Figs. 2 – 4 display that the bioreactors 1, 2, and 3 consist of vertical straight blades, inclined straight blades, and inclined curved blades respectively. The 3-D modeling of three different reactor blades and its relevant computational simulations have been performed to potentially improve functionality of biogas reactor system. The simulation results of stress profiles and deformation profiles of these three bioreactors are presented in Figs. 5 – 10.

Fig. 5. Stress profile in blade 1

Fig. 6. Deformation profile in blade 1

Fig. 7 Stress profile in blade 2

Fig. 8 Deformation profile in blade 2

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Fig. 9 Stress profile in blade 3

Fig. 10 Deformation profile in blade 3

Based on simulation results in Figs. 5 â&#x20AC;&#x201C; 10, the maximum stress of 15867.97 psi in blade 1 is less than 21754.17 psi in blade 2 and 31431.21 psi in blade 2. The results show that the vertical straight blades has less stress produced in blade root areas compared to other two blades due to its geometrical shape and less force required to rotate reactor blades. Since the yield strength of mild steel is 36300 psi, the blade 1 design in biogas reactor can function appropriately with safety factor more than 2 and the maximum deformation in blade 1 is within the material allowable limit. Since the blade 2 and 3 designs have safety factors 1.15 and 1.67 respectively, these two blades require further modification and improvement. 3. Prototype experiment. The biogas reactor has been prototyped and experiment has been performed to justify the design concept and confirm computational simulation. Tables 1, 2, and 3 display the experimental results of stress and deformation profiles in three different blades. The average maximum stress and deformation in Table 1 are 15867.79 psi and 0.00667 inches for blade 1 that are almost equal to 15867.97 psi and 0.00697 inches determined by computational simulation. The average maximum stress and deformation in Table 2 are 31431.37 psi and 0.00782 inches for blade 2 that are approximately same as 31754.17 psi and 0.00794 inches specified by computational simulation. The average maximum stress and deformation in Table 3 are 21754.29 psi and 0.00526 inches for blade 3 that are very close to 21754.17 psi and 0.00541inches found by computational simulation. Both computational simulation and prototype testing show proper function of biogas reactor and validate the feasibility of analytic methodology applied in this research. Table 1. Experimental results of stress

Table 2. Experimental results of stress

and deformation profiles in blade 1

and deformation profiles in blade 2

Number

Blade 1

Number

Blade 2

of Test

Stress

Displace

of Test

Stress

Displace

(N/mm2)

(mm)

(N/mm2)

(mm)

15867.92

0.00699

31431.54

0.00799

15867.99

0.00698

31431.29

0.00788

15867.84

0.00688

31431.18

0.00778

15867.78

0.00665

31431.24

0.00754

15867.98

0.00659

31431.38

0.00766

15867.48

0.00648

31431.48

0.00778

15867.68

0.00638

31431.15

0.00799

15867.75

0.00657

31431.48

0.00786

15867.65

0.00654

31431.54

0.00788

15867.84

0.00666

31431.39

0.00785

Average

15867.79

0.00667

Average

31431.37

0.00782

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Summary. Biogas is a green/clean fuel resource that can be potentially used in many different applications. This sustainable energy resource, an alternative to the current conventional energy market, can be used to protect environment. The byproduct from biogas production can be potentially used for agricultural fertilizer and some production processes. Both computational simulation and prototype experiment on this biogas reactor are introduced to study and analyze this biogas reactor design for turther improvement. Table 3. Experimental results of stressand deformation profiles in blade 3 Blade 3 Number

Stress

Displace

of Test

(N/mm2)

(mm)

21754.25

0.00529

21754.15

0.00548

21754.24

0.00538

21754.35

0.00524

21754.48

0.00518

21754.38

0.00522

21754.54

0.00512

21754.12

0.00518

21754.18

0.00524

21754.24

0.00525

Average

21754.29

0.00526

Both computational simulation and prototype experiment on three different reactor blades affirm that the vertical straight blade geometry in biogas reactor provides better performance than other two blade geometries. References [1] Binh, M., Phan, L., Duong, V., Nguyen, T., Tran, M., Nguyen, L., Nguyen, D. and Nguyen, L., 2014, “Evaluation of the production potential of bio-oil from Vietnamese biomass resources by fast pyrolysis”, Journal of Biomass and Bioenergy, Vol. 62, pp.74-81. [2] Dukes, C., Baker, S. and Greene, W., 2013, “In-wood grinding and screening of forest residues for biomass feedstock applications”, Journal of Biomass and Bioenergy, Vol. 54, pp.18-26. [3] Wilk, V., Schmid, J. and Hofbauer, H., 2013, “Influence of fuel feeding positions on gasification in dual fluidized bed gasifiers”, Journal of Biomass and Bioenergy, Vol. 54, pp.46-58. [4] Li, J., 2009, “Study and Development of an Energy-Saving Mechanical System”, International Journal of Recent Trends in Engineering, Vol.1, pp.51-54.

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[5] Bartley, M., Boeing, M., Corcoran, A., Holguin, F. and Schaub, T., 2013, “Effects of salinity on growth and lipid accumulation of biofuel microalga Nannochloropsis salina and invading organisms”, Journal of Biomass and Bioenergy, Vol. 54, pp.83-88. [6] Li, J., 2011, “Computer-Aided Design, Modeling and Simulation of A New Solar Still System Design”, Journal of Modeling and Simulation in Engineering, Vol. 2, pp. 1-5. [7] Starr, k., Gabarrell, X., Villalba, G., Talens, L. and Lombardi, L., 2014, “Potential CO2 savings through biomethane generation from municipal waste biogas”, Journal of Biomass and Bioenergy, Vol. 62, pp.8-16. [8] Savy, D. and Piccolo, A., 2014, “Physical–chemical characteristics of lignins separated from biomasses for second-generation ethanol”, Journal of Biomass and Bioenergy, Vol. 62, pp.58-67. [9] Li, J., 2012, “Computer-Aided Modeling and Analysis of an Energy-Saving Refrigerating System”, Journal of Mechanical Engineering and Automation, Vol. 2, pp. 9-12. [10] Melikoglu, M., 2013, “Solid-State Fermentation of Wheat Pieces by Aspergillus oryzae: Effects of Microwave Pretreatment on Enzyme Production in a Biorefinery”, International Journal of Green Energy, Vol. 10, pp.529-539. [11] Bridgwater, A., 2012, “Review of fast pyrolysis of biomass and product upgrading”, Journal of Biomass and Bioenergy, Vol. 38, pp. 68-94. [12] Baral, S., Pudasaini, S., Khanal, S. and Gurung, D., 2013, “Mathematical Modelling, Finite Element Simulation and Experimental Validation of Biogas-digester Slurry Temperature”, International Journal of Energy and Power Engineering, Vol. 2, pp.128-135. [13] Slade, R & Bauen, A., 2013, “Micro- algae cultivation for biofuels: Cost, energy balance, environmental impacts and future prospects”, Journal of Biomass and Bioenergy, Vol. 53, pp. 29-38. [14] Sukhatme, S., 2005, “A Textbook on Heat Transfer”, Universities Press, ISBN 8173715440.

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On the Evolution Theory of Identification of Mathematical Models of Corrosion Destruction at the Optimum Design of Structures George Filatov1a 1 – Dnepropetrovsk State Agrarian-Economic University, Ukraine a – filatovgv@mail.ru

Keywords: Optimal design of structures, mathematical modeling of corrosion damage, identification of mathematical models

ABSTRACT. The process of optimal design of structures, interacting with aggressive environments, can be viewed as a process of design evolution from suboptimal to optimal state. In most cases, the control variables are taken as the geometric design parameters. When designing the structure during the search of the optimal solutions of these parameters change during the transition from one structure to another intermediate state. And changing the geometrical characteristics of cross-sectional structure characterizing their stiffness, such as the area and inertia moment of the cross sections. Changing the geometrical characteristics of the cross-sections results in a change in stress and strain in the construction. Thus, it can be argued that in the process of design evolution at its optimal design of the stress-strain state (SSS) of the structure varies depending on its stiffness. Natural to assume that a change in the SSS design values of the coefficients that characterize the impact of SSS on the rate of corrosion process, and are subject to change and become functions of SSS. To test this hypothesis, we studied the theoretical aspects of the behavior of mathematical models of corrosion damage at the optimal design of structures and performed extensive numerical experiment on a computer. The experiment was conducted using four objects: membrane cylindrical shell loaded by internal pressure, smooth cylindrical shell compressed in the axial direction, statically determinate beams with rectangular cross-section, statically determinate beams welded I-section.

The basic pre-conditions and hypotheses. Over the past few decades in structural mechanics appeared a new direction of research: development of the methods of calculation of structural elements and machine parts interacting with aggressive environments. The emergence of this trend is due to a significant reduction in the carrying capacity of structures, their lifetime, reliability and durability of machines and equipment as a result of chemical or physic-chemical exposure to corrosive environments. Direct losses from corrosion are enormous. Due to the deterioration of physical-mechanical and physic-chemical properties of materials, the cost of protection against corrosion, the cost of repair affected by corrosion products in the most developed countries of the world consumes about 40% of annual production of the metal. Indirect losses associated with the deterioration of the technological and operational characteristics of the equipment and machinery subject to corrosion, their downtime, disaster recovery, leakage of valuable or hazardous products into the environment, metal inflated costs due to increased tolerance and etc. account for about 10% of national income in many countries. That is why the study of the mechanism of corrosion and to find effective ways to protect metals and other materials is becoming one of the most important and urgent problems of modern science and, in particular, structural mechanics. In an emerging economic crisis, the increase of the value of construction materials, such as steel, there is another problem  the rational use of available resources, optimal design of structures and equipment. To date, developed powerful techniques to optimize designs, working in a neutral environment: methods for linear and nonlinear mathematical programming, and stochastic gradient search high and effective methods of zero order, multi-criteria optimization, etc. These methods are well established in the design of many objects of construction and engineering industries. However, the simple transfer of the developed techniques for the design and optimization of structures especially interacting with an aggressive environment, is impossible, since the character of the MMSE Journal. Open Access www.mmse.xyz 66

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corrosion process, its kinetics are often not known in advance. To clarify the nature of the influence of aggressive environment on the behavior of the material usually put experiment under physical modeling. The results of such simulations allow us to construct a mathematical model of the corrosion process. Physical modeling of corrosion damage structures, being mandatory and very important step in the implementation of direct payments or optimal, due to its high cost and the duration of the test may not always meet the designer, as the reasons given above can not have a complete picture of the corrosion process. Using mathematical models it is possible to extrapolate the corrosion process and more fully explore its kinetics. The second possibility, represented by a mathematical model is to integrate the corrosion process in the design scheme optimized object in the form of a system of algebraic, transcendental or differential equations. However, such a model should be adequate to the real process of corrosion. The adequacy of the mathematical model is achieved by identifying the model to experimental data. The proximity of the experimental and simulated data of the corrosion process provides an introduction to the mathematical model of special factors and adjusting their values in the process of identification. And only when the in accordance with the selected criterion of similarity of the simulated and real corrosion process can be administered in such a model calculation scheme and proceed to the calculation of the design, including its optimal design. Otherwise, the designer runs the risk of a project that does not meet reality. Most of mathematical models of corrosion damage are nonlinear functions of the parameters to be optimized. Therefore, in this study to identify the mathematical models of corrosion damage are encouraged to use one of the methods of nonlinear stochastic programming - the method of random search. This method is a method of zero-order, does not require the calculation of derivatives, well take into account the functional and geometric constraints, trained in the search process and has good convergence. All mathematical models using an external parameter of damage can be divided into two types: the model does not take into account the effect of the stress-strain state (SSS) to the design speed of the corrosion process, and models that take into account the impact of SSS. Most mathematical models of corrosion damage, both the first and second groups include empirical coefficients determined by identifying models from experimental data. It is believed that the results thus the model coefficients are constant. Such a claim can be considered valid only for the first group of mathematical models whose coefficients depend on the state of the corrosive environment: temperature, concentration, pressure, etc. The coefficients of the second group of models depend on the structure of SSS and, if in the process of changing its structure calculation or geometric parameters of the physical constants (Poisson's ratio, modulus of elasticity) is changed, the SSS structure. The process of optimal design of structures can be viewed as a process of design evolution from suboptimal to optimal state. In most cases, the control variables are taken as the geometric design parameters. When designing the structure during the search of the optimal solutions of these parameters change during the transition from one structure to another intermediate state. And changing the geometrical characteristics of cross-sectional structure characterizing their stiffness, such as the area and moment of inertia of the cross sections. Changing the geometrical characteristics of the cross-sections results in a change in stress and strain in the construction. Thus, it can be argued that in the process of design evolution at its optimal design of the stress-strain state of the structure varies depending on its stiffness. Natural to assume that a change in the SSS design values of the coefficients that characterize the impact of SSS on the rate of corrosion process, and are subject to change and become functions of SSS. To test this hypothesis, we studied the theoretical aspects of the behavior of mathematical models of corrosion damage at the optimal design of structures and performed extensive numerical experiment on a computer. 2. The theorem on the influence function of the stress-strain state (SSS) on the speed of corrosion process. Consider some of the theoretical aspects of the problem of identification of mathematical models of corrosion damage. To this end, we formulate a criterion of quality received at the identification of mathematical models of corrosion damage. With regard to the mathematical MMSE Journal. Open Access www.mmse.xyz 67

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model taking into account the impact of SSS on the rate of corrosion process, this criterion has the form: n

 

J    t j  j 1

e j



j     t j    f k 1 t k  t k 1    ej  j 1  k 1  n

(1)

Take the partial derivative of the functional (1) on the parameters  and  , equate the resulting expressions to zero  we obtain: j n n   n e J 2    t j    t j  f k 1 t k  t k 1     j t j  0 ;  j 1 j 1  k 1  j 1

j n  n  j   J    t j  f k 1 t k  t k 1      f k 1 t k  t k 1   j 1  k 1 j 1  k 1  

 e j     j  f k 1 t k  t k 1   0 . j 1  k 1  n

(2)

(3)

Solving equation (3) with respect to the rate of the corrosion process unstressed material, we get: (4)



  ej j 1 n

t j

j 1

Equation (4) shows that the corrosion rate depends only on time and experimental date of depths of corrosion damage and does not depend on the level of stress and strain in the construction. In other words, the value of corrosion rate unstressed material depends on the condition of the corrosive medium, for example, the concentration of aggressive substances, temperature, etc. Equating the corrosion rate to zero and solving the equation (3) with respect to the coefficient of influence of SSS on the corrosion rate, we obtain: n



  exp j

(5)

j 1

 f k 1 t k  t k 1  j 1 k 1

From (5) it follows that the coefficient depends not only on the state of the environment, but also the function of SSS. SSS function always inversely proportional to stiffness and directly proportional to the stress. From this it follows that the dependence of the influence of SSS on the stiffness of the structure is directly proportional to stiffness: a reduction in stiffness and decreases the coefficient of influence of SSS on the speed of the corrosion process, which is confirmed by the results of numerous experiments. At the same time, the value of the coefficient of influence of SSS on the rate of corrosion MMSE Journal. Open Access www.mmse.xyz 68

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process is inversely proportional to the level of stress in the structure. Consequently, the coefficient is not the number and is the function of the stiffness and simultaneously the function of SSS of structure. The theoretical findings allow us to formulate the following theorem. Theorem. The influence function of SSS on the speed of the corrosion process is directly proportional to rigidity and inversely proportional to the stress. The proof given above. From this theorem there is a consequence. Consequence of Theorem. "Optimal" value of the coefficient of mathematical model of corrosion damage, taking into account the influence of SSS on the speed of the corrosion process, ensures the convergence of the search for the optimal solution without additional procedures of multiple identification of mathematical model. In other words, the design achieves the optimum state under "optimal" value function of influence of SSS on the rate of corrosion process. This corollary allows avoiding the procedure of multiple identification mathematical model corrosion damage at the optimal design of structures. This fact is quite important, as it gives an opportunity to significantly reduce the loss on search. The consequence asserts that if there is an "optimal" set of coefficients of a mathematical model and optimized function has an extremum, the optimal solution can be found from any point in the range of the permitted parameters. 3. Briefly on Numerical Experimentation on a computer. The experiment was conducted using four objects: membrane cylindrical shell loaded by internal pressure, smooth cylindrical shell compressed in the axial direction, statically determinate beams with rectangular cross-section, statically determinate beams welded I-section (Fig. 1).

Fig. 1. The objects The object of investigation was considered factor ď ˘ of influence of SSS on the corrosion rate for two models: MMSE Journal. Open Access www.mmse.xyz 69

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I.G. Ovchinnikov’s model [1]: V.G. Karpunin’s model [2]:

d   i  i   thr    ; dt

d   i   , dt

where   coefficient taking into account the influence of SSS on the rate of corrosion process;

  current depth of corrosion damage; t  time corrosion;

 i – intensity of deformation;

 i  stress intensity; stress threshold stress below which the influence of SSS on the rate of corrosion process is missing: if  i   thr the taking  i   thr   0 ;   the corrosion rate of the unstressed material. The order of the experiment was as follows: 1. Formulate the problem of optimal design. The target function takes a cross sectional area of the structure. 2. In the allowed parameter selects the starting point for which is realized an identification of a mathematical model based on experimental data. 3. From the starting point of the selected design optimization was performed. 4. In the search path chosen 30 starting points, each of which performs the identification. 5. The graph of dependence of coefficient  on the current stiffness of the optimized construction is built (Fig. 2).

Fig. 2. The graph of the function influence of SSS on the rate corrosion process on the stiffness of the membrane shell From the graph clearly shows that the influence of the SSS on the corrosion rate is not constant and decreases significantly when optimizing the design. If now with the optimal factor attempt to perform optimization of any arbitrarily selected point of the field parameters, it is possible to obtain an MMSE Journal. Open Access www.mmse.xyz 70

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optimum result of the project. The saving of the weight of design is significant. However, the procedure of multiple identification is rather cumbersome. Therefore, in the work have been proposed several empirical methods for determining the parameter of the SSS on the stage that precede to optimization. Summary. 1. As a result of multiple identification of mathematical models of corrosion damage, the dependence of the parameter influence of SSS on the speed of the corrosion process from the stiffness of cross-sectional design with its optimization is established. Thus, the parameter of influence of the SSS is not constant, but is a function of the stiffness of the structure at its optimal design. 2. The presence of the "optimal" value of the parameter influence of SSS on the corrosion speed is established. The main feature of the "optimal" value of the parameter influence of SSS on the corrosion rate of SSS is to comply with the optimal state structure. 3. The design, which is in optimum state, has the lowest speed of corrosion caused by the influence of SSS. 4. The theoretical aspects of the problem under investigation: formulate and prove a theorem on depending of corrosion process rate function from the rigidity of the optimized design, the technique of determining the parameters of the mathematical model of corrosion damage, providing an evolutionary transition structure in an optimal state. 5. The computer program to determine the optimal set of coefficients of a mathematical model of corrosion damage, allow you to create an effective project, is developed. The entire contents of experimental and theoretical investigations is given in the monograph [3]. References [1] Petrov, VV Calculation of structural elements, interacting with aggressive media [Text]: monograph / I.G.Ovchinnikov, Yu.M.Shihov. - Saratov: Saratov State University. 1987. – 288 P. [2] Karpunin, VG Study bending and stability of plates and shells based on a solid corrosion [Text]: Author. Dis.cand. tehn. Science / VG Karpunin. - Sverdlovsk. 1977. – 24 P. [3] Filatov, G. Theoretical Foundations of evolution matmodeley corrosion damage [Text]: monograph / GV Filatov. - Saarbrucken: LAP LAMBERT Academic Publishing.

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Proposed Design Procedure of a Helical Coil Heat Exchanger for an Orc Energy Recovery System for Vehicular Application Giacomo Bonafoni 1, Roberto Capata 1,a 1 – Department of Mechanical and Aerospace Engineering, University of Rome Sapienza, Via Eudossiana 18, 00184 Rome, Italy a – roberto.capata@uniroma1.it

Keywords: Organic Rankine Cycle; energy recovery; energy efficiency in transportation; heat exchanger; helical coiled tube; finite element analysis.

ABSTRACT. There are several systems that produce energy from low grade heat sources such as Stirling engines, thermoelectric generators, and ORC (Organic Rankine Cycle) systems. This paper shows the heat recovery from exhaust gases of a 1400 cc Diesel engine, to vaporize the working fluid of a small (<10 kW) ORC system. The main objective is to have a system as compact as possible, to make it suitable for transport applications such as cars, ships, trains, etc. Three fluids were studied for this application: water and two refrigerant fluids: R134a and R245fa, which were found to be more appropriate than water at certain pressure and temperature values. Afterwards, a design procedure was proposed, then the heat exchanger was modeled and finally a steady-state thermal and structural analysis were carried out using a commercial software to find the temperature and the effects of the thermal stress on the material of the helical coiled tube.

1. Introduction Energy recovery systems represent an interesting field of research, because they use the “waste” energy from industrial processes or from energetic processes, to produce other energy; this is a way to improve energy efficiency for a large range of activities such as agriculture, district heating, heavy industry, power plants, marine and land transportation. Different forms of waste energy can be recovered such as kinetic energy (in vehicular applications), electromagnetic energy and thermal energy. The last one is the most interesting because it provides the greatest quantity of energy compared to the others. To recover thermal energy, from low and medium temperature, the most used systems are thermodynamic systems such as the Organic Rankine cycle and Stirling engine. This paper focuses on the ORC technology for vehicular application, which can lead to a considerable increase in engine efficiency, producing extra-power from the waste heat of the exhaust gases of a Diesel engine, in this case. This increase in efficiency also means lower fuel consumption, and direct environmental and economic advantages. Another environmental advantage is the cooling, to which the exhaust gases are subject in the heat exchanger, which avoids the gas discharge at temperatures much higher than that of the environment. However, while the ORC systems are often used for stationary applications (solar, biomass, geothermal power plants and combined cycles), it is still difficult to use this technology in the transport sector, due to the complexity and the dimensions of such a system. At present, several important automotive and energetic companies such as BMW, Honda, Cummins, Opcon, Enertime are studying the suitability of the traditional and of the organic Rankine bottoming cycle to increase energy efficiency in cars, trucks, ships and trains [3]. 2. The ORC power plant 2.1. Configuration. For minimizing the dimensions and the complexity of the entire system, a direct configuration has been chosen. In this kind of system, the ORC working fluid takes the heat directly MMSE Journal. Open Access www.mmse.xyz 72

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Nomenclature II

Nomenclature I A

Area

Aex

Thermal surface

Prandtl number

exchange m2

Thermal power

Heat flux

W/m2

Radius

Reynolds number

Temperature

Th, Tc

Hot and temperature

J/(kg·K)

Isobaric specific heat

Coiled tube diameter

internal m

Helix diameter

Dean number

Equivalent diameter shell m

Δp

Pressure drop

f, fs, ftp,s Friction factor, friction factor for a straight tube, two-phase friction factor for a straight tube

K cold

fluid K

Tw,in, Internal and external wall K Tw,ex temperature u

Velocity

m/s

Thermal transmittance

W/(m2·K)

Volume

m3 W

Mass velocity

kg/(m2·s)

Thermal power transmitted

Convective coefficient

W/(m2·K)

Vapor quality

HRVG

Heat Recovery Vapor Generator

Void fraction

Viscosity

Pa·s

Density

kg/m3

χtt

Martinelli turbulentturbulent number

Thermal conductivity

W/(m·K)

Length

LMTD

Log mean temperature K difference

ṁ

Mass flow

Number of turns

Nusselt number

Pitch

kg/s

Available

Boiling

Coil

External

Gas

Internal

Inlet

Liquid

Liquid-only

Max

Maximum

Min

Minimum

Out

Outlet

Shell

Two-phase

Vapor

from the exhaust gases through a heat exchanger located inside the engine drainpipe. In an indirect configuration, instead, a thermal oil loop is integrated, to avoid a direct contact between exhaust flows and working fluid [4]. The indirect configuration is safer than the direct one, due to the MMSE Journal. Open Access www.mmse.xyz 73

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flammability of the ORC working fluids at certain temperature and pressure, but, on the other hand, it requires an oil loop, which means an increase in components and space occupied. Hence, in order to use the direct configuration, non-flammable fluids at the working conditions and hightemperature resistant materials must be used.

Fig. 1. ORC system for heat recovery from engine exhaust gases [2].

2.2. The thermodynamic cycles. The thermodynamic feasibility of the ORC power plant has already been studied in previous research papers [5, 6, 7, 8], thus the cycles were analyzed with the aim of finding out input and output data of each component of the entire system, and of choosing the most efficient cycles (and discarding the less efficient). First, the thermodynamic cycle has been studied and then developed with the software CAMEL-Pro Simulator, to simulate the energy conversion process. Many comparisons between various fluids have been carried out in several previous researches, with different results, due to the different applications, that depending on the available heat source, on plant working temperatures and pressures [9, 10]. In this paper three different fluids were preliminarily studied: water, R134a and R245fa. Main data for the exhaust gases (the hot source) from the Diesel engine and for the cooling water (the cold sink which, for both land and marine vehicular application, may be the vehicle cooling circuit) are shown in Table 1 and Table 2. The other data (enthalpy, thermal conductivity, density, viscosity, etc.) of gas, water and working fluids has been provided by FluidProp (Microsoft Excel extension), NIST [11] and Peacesoftware [12] databases. The values of cycles efficiencies in Table 3 may seem quite low compared to “conventional” theoretical efficiencies calculated for the Rankine and Organic Rankine Cycle. This is because, in this first simulation, a turbine efficiency of 85%, a pump efficiency of 90% and heat losses of 10% were assumed, with the aim of obtaining a cycle as realistic as possible. In fact, existing models present experimentally calculated efficiencies which are very similar to the values obtained in Table 3. One can immediately notice that the water cycle has the lowest thermodynamic efficiency and provides the lowest mechanical power output, so this cycle will be discarded. The best cycle in terms of power output and theoretical efficiency is the R245fa cycle. In Figure 3, an example of an ORC system is provided. The numbers represent the incoming and outgoing flows of each component. Number 1 is the mechanical power output from the turbine. Regarding the working fluid, number 2 is the outlet from the HRVG and the inlet in the turbine while number 3 represents the outlet from the turbine and the inlet in the condenser. Number 4 is the outlet from the condenser and the inlet in the pump, number 11 is the outlet from the pump and number 10 is the inlet in the HRVG (it is separated to better check the inlet and outlet flow in the HRVG and to check the process itself). Instead, number 9 represents the mechanical power used by the pump, numbers 7 and 8 represent the MMSE Journal. Open Access www.mmse.xyz 74

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inlet and outlet of the exhaust gases in the HRVG, and finally, numbers 6 and 5 are the inlet and outlet of the cooling water in the condenser.

Fig. 2. Indirect (a) vs direct (b) configuration

Table 1. Thermodynamic data for the exhaust gas Mass flow (kg/s)

Temperature Pressure (K) (kPa)

Enthalpy (kJ/kg)

Thermal Cp Density Cond. (kJ/(kg*K)) (kg/m3) (W/(m*K))

Viscosity (Pa*s)

0.15

845.15

1031.153

1.109

3.86*10-5

200

0.0596

0.824

Table 2. Main data for the cooling water for the three different cycles Mass flow (kg/s)

Temperature (K)

Pressure (kPa)

R134a

288,15

150

R245fa

0,7

288,15

150

Water

0,4

288,15

150

In Table 3, the main parameters and the results of the simulations are also shown. MMSE Journal. Open Access www.mmse.xyz 75

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Table 4 shows the ideal thermal power for the counter flow heat exchanger, sub-divided in its three parts: pre-heater, vaporizer, super-heater for each fluid. The partition of the heat exchanger was made using the same software. The state points in figure 4 represent the flows of the working fluid and exhaust gas in each heat exchanger part: point 1 represents the working fluid inlet (in liquid state) in the pre-heater, 2 is the fluid outlet from the pre-heater and, at the same time, its inlet in the evaporator. Point 3 is the outlet of the fluid (now in the state of saturated vapor) from the evaporator and the inlet in the super-heater and point 4 is the outlet of the super-heated vapor from the heat exchanger. For the exhaust gases, 5 is the inlet in the super-heater, point 6 is the outlet from the super-heater and the inlet in the evaporator (remembering that the heat exchanger is a counterflow device); 7 is the outlet from the evaporator and the inlet in the pre-heater, and 8 is the outlet from the pre-heater. In table 5, the inlet and outlet temperatures and ideal working pressures are shown, without losses in the heat exchanger for the working fluids and the exhaust gases. Table 3. Results of the thermodynamic simulations R134a

R245fa

Water

Mass flow rate (kg/s)

0.38

0.35

0.032

Turbine work (kJ/kg)

8.746

13.011

65.296

Pump work (kJ/kg)

0.702

0.378

0.152

Boiler heat (kJ/kg)

188.948

206.712

2307.912

Condenser heat (kJ/kg)

180.904

193.772

2242.768

Max. temperature (K)

333

345

433

Min. Temperature (K)

307

313

386

Max. Pressure (kPa)

1500

612

310

Min. Pressure (kPa)

950

300

210

Carnot cycle efficiency (%)

7.8

9.28

10.85

Cycle efficiency (%)

4.63

6.29

2.83

Mechanical power output Pt-Pp (kW)

3.06

4.42

2.08

3. The Heat Recovery Vapor Generator (HRVG): proposed engineering design procedure of the helical coil heat exchanger To achieve the maximum thermal exchange in the minimum volume (so a high rate A ex/V) with a simple structure, the choice of the configuration fell to a shell and coiled tube heat exchanger. Due to its shape, in fact, for an equal shellâ&#x20AC;&#x2122;s length, a coil presents a larger surface of thermal exchange than a straight tube, or even a U-tube. The space limitations for the heat exchanger design can be summarized as such: the maximum length of the entire heat exchanger must not exceed 1 meter and the maximum diameter must not exceed 30 centimeters. The package size of the turbine designed for the cycle [13], instead, is about 25x25 cm. There are different procedures for the design of this type of exchangers, often apply for certain temperatures and flow rate range, or for different working fluids. Several authors [14, 15, 16, 17, 18] have interpreted the mass flow rate, both monophasic or biphasic, introducing various dimensionless coefficients, and the various procedures for the calculation of various fractions or mixture composition. Similarly, the heat exchange has been evaluated according to their assumptions and reviews, often confirmed and validated by experimental tests. In this study the authors tried to realize, and then to propose a methodology and a procedure, which is not new, of course, but that may have general validity or a wider application range more than those described by various authors. MMSE Journal. Open Access www.mmse.xyz 76

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Table 4. Thermal power of the sub-components of the heat exchanger for R134a and R245fa cycles Thermal power (kW)

Pre-heater

Vaporizer

Super-heater

R134a

12.951

55.783

1.935

R245fa

14.758

56.393

0.536

Fig. 3. Example of an ORC system developed on Camel-PRO Simulator

Fig. 4. Partition of the counterflow heat exchanger into 3 sub-components In the design the heat exchanger, the first step is to sub-divide it in three parts: the pre-heater, the vaporizer, the super-heater. The thermal power required for all three sections and for the different working fluids to be tested are known, along with temperatures and pressures of the input and output exhaust gas and liquid/steam. It is an iterative procedure: 1) in the first iteration, the pressure is assumed constant 2) calculate the heat exchanger dimensions 3) evaluate the pressure drops.

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Table 5. Temperature, pressure and steam quality in each part of the heat exchanger for R134a (4a) and R245fa (4b) cycles R134a

Pre-heater

Vaporizer

Super-heater

T inlet (K)

307

328.202

T outlet (K)

328.202

333

Pressure (kPa)

1500

T inlet (K)

487.465

833.599

845.15

T outlet (K)

403.507

487.465

833.599

Pressure (kPa)

200

R245fa

Pre-heater

Vaporizer

Super-heater

T inlet (K)

313

343.45

T outlet (K)

343.45

345

Pressure (kPa)

612

T inlet (K)

492.54

841.95

845.15

T outlet (K)

396.864

492.542

841.95

Pressure (kPa)

200

Exhaust Gas

Figure 5. Schematic view of typical shell and coiled tube heat exchanger With the obtained pressure drops values, iterations have been carried out until convergence is reached. The first step for the design of the entire heat exchanger is the super-heater design (for the R245fa and R134a fluid, it has just the necessary length to ensure the complete evaporation of the fluid and a little superheating). 3.1 Super-heater design. Shell-side: exhaust gas Coil-side: single-phase working fluid (vapor) To design it, it is necessary to impose the values for the velocity u of the two fluids and the Reynolds number on both the shell and coil sides. 3.1.1 Shell-side. Inlet and outlet temperatures and pressure of the exhaust gases are known, so the relative values of ρ, µ, k and cp (and consequentially their average values) can be easily obtained. MMSE Journal. Open Access www.mmse.xyz 78

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áš = đ?&#x153;&#x152;đ??´đ?&#x2018;˘

(1)

Imposing u â&#x2030;¤ 40m/s the equivalent diameter is found:

đ??ˇđ?&#x2018;&#x2019; = â&#x2C6;&#x161;4 áš â &#x201E;đ?&#x153;&#x2039;đ?&#x153;&#x152;đ?&#x2018;˘

(2)

Hence, the Reynolds number:

đ?&#x2018;&#x2026;đ?&#x2018;&#x2019; =

đ?&#x153;&#x152;đ?&#x2018;˘đ??ˇđ?&#x2018;&#x2019; đ?&#x153;&#x2021;

(3)

đ?&#x2018;?đ?&#x2018;? đ?&#x153;&#x2021; đ?&#x2018;&#x2DC;

(4)

The gas Prandtl number:

đ?&#x2018;&#x192;đ?&#x2018;&#x; =

The Nusselt (turbulent) number i [16]: đ?&#x2018; đ?&#x2018;˘ = 0,023đ?&#x2018;&#x2026;đ?&#x2018;&#x2019; 0.8 đ?&#x2018;&#x192;đ?&#x2018;&#x; 0.4

(5)

And finally the coefficient of convective heat transfer shell-side:

â&#x201E;&#x17D;đ?&#x2018; =

đ?&#x2018; đ?&#x2018;˘ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC; đ??ˇđ?&#x2018;&#x2019;

(6)

3.1.2 Coil-side Inlet and outlet temperatures and working pressure of the superheated vapor are known. Consequently, the relative values of viscosity (Âľ), density (Ď ), isobaric specific heat capacity (cp) and thermal conductivity (k), can be obtained from databases and finally their average values can be calculated. The inside diameter of the tube being fixed, and knowing the mass flow (áš ) and the average density of the fluid, the (average) velocity u (this value must be less than 30 m/s) can be computed: đ?&#x2018;˘ = áš /(đ?&#x153;&#x152;đ??´).

Where MMSE Journal. Open Access www.mmse.xyz 79

(7)

Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

đ??´ = đ?&#x153;&#x2039;đ?&#x2018;&#x2018;đ?&#x2018;? 2 /4

(8)

Then, it is possible to calculate the Reynolds and Prandtl numbers for the fluid. Having also fixed the coil diameter Dc, the critical Reynolds number (transition laminar/turbulent flow) for a helical tube is (in this work the flow regime is always turbulent):

đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;đ?&#x2018;? = 2000(

đ?&#x2018;&#x2018;đ?&#x2018;? 0.32 ) đ??ˇđ?&#x2018;?

(9)

Number of Dean (Reynolds "adapted" to helical tubes considering the effects of the centrifugal forces on the flux):

đ??ˇđ?&#x2018;&#x2019; = đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;(

đ?&#x2018;&#x2018;đ?&#x2018;? 1â &#x201E; ) 2 đ??ˇđ?&#x2018;?

(10)

The turbulent Nusselt number (the flow conditions, in this work, are always turbulent): đ?&#x2018;&#x2018;đ?&#x2018;? đ?&#x2018; đ?&#x2018;˘ = 0.023đ?&#x2018;&#x2026;đ?&#x2018;&#x2019; 0.85 đ?&#x2018;&#x192;đ?&#x2018;&#x; 0.4 ( )0.1 đ??ˇđ?&#x2018;?

(11)

And finally hcoil :

â&#x201E;&#x17D;đ?&#x2018;? =

đ?&#x2018; đ?&#x2018;˘ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC; đ?&#x2018;&#x2018;đ?&#x2018;?

(12)

3.1.3. Heat Exchanger analysis The total thermal power is: đ?&#x2018;&#x201E;đ?&#x2018; = áš đ?&#x2018;&#x201D; đ?&#x2018;?đ?&#x2018;?,đ?&#x2018;&#x201D; (đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą ) = đ?&#x2018;&#x201E;đ?&#x2018;? = áš đ?&#x2018;Ł đ?&#x2018;?đ?&#x2018;?,đ?&#x2018;Ł (đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą )

(13)

And also: đ?&#x2018;&#x201E; = đ?&#x2018;&#x2C6;đ??´ â&#x2C6;&#x2122; đ??żđ?&#x2018;&#x20AC;đ?&#x2018;&#x2021;đ??ˇ

(14)

where LMTD â&#x20AC;&#x201C; is the logarithmic mean temperature difference, which, for a counter flow heat exchanger is:

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đ??żđ?&#x2018;&#x20AC;đ?&#x2018;&#x2021;đ??ˇ =

(đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; ) â&#x2C6;&#x2019; ( đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą ) (đ?&#x2018;&#x2122;đ?&#x2018;&#x203A;((đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; )/(đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;Ł,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą ))

(15)

The overall thermal transmittance is: đ?&#x2018;&#x2018; đ??´đ?&#x2018;&#x2019; ln( đ?&#x2018;&#x2019;â &#x201E;đ?&#x2018;&#x2018; ) 1 1 đ??´đ?&#x2018;&#x2019; đ?&#x2018;&#x2013; = + + đ?&#x2018;&#x2C6; â&#x201E;&#x17D;đ?&#x2018;&#x2013; đ??´đ?&#x2018;&#x2013; 2đ?&#x153;&#x2039;đ?&#x2018;&#x2DC;đ??żđ?&#x2018;? â&#x201E;&#x17D;đ?&#x2018;&#x2019;

(16)

Where Ae, de and Lc â&#x20AC;&#x201C; are the heat exchange area (external surface of the coil), the external diameter and the coil length, and Ai and di are the internal surface of the coiled tube and the internal diameter; k is the thermal conductivity of the material: đ??´ = đ?&#x153;&#x2039;đ?&#x2018;&#x2018;đ??żđ?&#x2018;?

(17)

The exchange surface can be determined: đ??´ = đ?&#x2018;&#x201E;/(đ?&#x2018;&#x2C6; â&#x2C6;&#x2122; đ??żđ?&#x2018;&#x20AC;đ?&#x2018;&#x2021;đ??ˇ)

(18)

And finally, the coilâ&#x20AC;&#x2122;s length Lc, which is also (where Rc is the helix radius and p the pitch, previously fixed): đ??żđ?&#x2018;? = đ?&#x2018; â&#x2C6;&#x161;(2đ?&#x153;&#x2039;đ?&#x2018;&#x2026;đ?&#x2018;? )2 + đ?&#x2018;?2

(19)

The number of turns of the coil N is so calculated from this expression. Finally, the shellâ&#x20AC;&#x2122;s length Ls: đ??żđ?&#x2018; = đ?&#x2018;? â&#x2C6;&#x2122; đ?&#x2018;

(20)

Coil volume: đ?&#x153;&#x2039;đ?&#x2018;&#x2018;đ?&#x2018;?2 â&#x2C6;&#x2122; đ??żđ?&#x2018;? 4

(21)

đ??ˇđ?&#x2018;&#x2019; đ?&#x153;&#x2039;đ?&#x2018;&#x2018;đ?&#x2018;&#x2019; đ??żđ?&#x2018;?â &#x201E; 4

(22)

đ?&#x2018;&#x2030;đ?&#x2018;? =

Volume available for the gas:

đ?&#x2018;&#x2030;đ?&#x2018;&#x17D; =

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Shell volume: đ?&#x2018;&#x2030;đ?&#x2018; = đ?&#x2018;&#x2030;đ?&#x2018;? + đ?&#x2018;&#x2030;đ?&#x2018;&#x17D;

(23)

In details:

đ?&#x2018;&#x2030;đ?&#x2018; =

đ?&#x153;&#x2039;đ??ˇđ?&#x2018; 2 â&#x2C6;&#x2122; đ??żđ?&#x2018; 4

(24)

From this equation, the diameter of the shell Ds is finally computed. 3.1.4. Friction factors and pressure drops Coil: Turbulent friction factor:

2 đ?&#x2018;&#x2018; đ?&#x2018;&#x201C;đ?&#x2018;? = đ?&#x2018;&#x201C;đ?&#x2018; [đ?&#x2018;&#x2026;đ?&#x2018;&#x2019; ( đ?&#x2018;?â &#x201E;đ??ˇ ) ] đ?&#x2018;?

1â &#x201E; 20

(25)

where đ?&#x2018;&#x201C;đ?&#x2018; = 0.046(đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;)â&#x2C6;&#x2019;0.2

(26)

2đ?&#x2018;&#x201C;đ?&#x2018;? đ?&#x153;&#x152;đ??żđ?&#x2018;? đ?&#x2018;˘2 â&#x2C6;&#x2020;đ?&#x2018;? = đ?&#x2018;&#x2018;đ?&#x2018;?

(27)

đ?&#x2018;&#x201C;đ?&#x2018; = 8 â&#x2C6;&#x2122; 0.023(đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;)â&#x2C6;&#x2019;0.2

(28)

đ?&#x2018;&#x201C;đ?&#x2018; đ?&#x153;&#x152;đ??żđ?&#x2018; đ?&#x2018;˘2 â&#x2C6;&#x2020;đ?&#x2018;? = 2đ??ˇđ?&#x2018;&#x2019;

(29)

Then pressure drop is calculated:

Shell: Turbulent flow

Pressure drop:

3.2. Vaporizer design 3.2.1. Shell â&#x20AC;&#x201C;side. The procedure for the shell design is the same already discussed in 3.1.1. MMSE Journal. Open Access www.mmse.xyz 82

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3.2.2. Coil â&#x20AC;&#x201C;side. During the phase change, different formulations have been used to find the dimensionless coefficients for the description of flow and heat exchange. For a more accurate calculation, the evaporator is subdivided in two parts: in the first the vapor quality is between 0 and 0,5 and the second between 0,5 and 1. For both the two parts, the procedure can be listed as below. First, calculate Martinelliâ&#x20AC;&#x2122;s number [16] for turbulent-turbulent flow:

đ?&#x153;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ą = (

1 â&#x2C6;&#x2019; đ?&#x2018;Ľ 0.9 đ?&#x153;&#x152;đ?&#x2018;Ł 0.5 Âľđ?&#x2018;&#x2122; 0.1 ) ( ) ( ) đ?&#x2018;Ľ đ?&#x153;&#x152;đ?&#x2018;&#x2122; Âľđ?&#x2018;Ł

(30)

The liquid-only Reynolds and Nusselt numbers and the convective heat transfer coefficient (calculated if all the flow was liquid, i.e. x=0) are:

đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x153; =

đ?&#x153;&#x152;đ?&#x2018;&#x2122; đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;&#x153; đ?&#x2018;&#x2018;đ?&#x2018;? đ?&#x153;&#x2021;đ?&#x2018;&#x2122;

đ?&#x2018; đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;&#x153; = 0.023đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x153; 0.85 đ?&#x2018;&#x192;đ?&#x2018;&#x;đ?&#x2018;&#x2122; 0.4 (

â&#x201E;&#x17D;đ?&#x2018;&#x2122;đ?&#x2018;&#x153; =

(31)

đ?&#x2018;&#x2018;đ?&#x2018;? 0.1 ) đ??ˇđ?&#x2018;?

đ?&#x2018; đ?&#x2018;˘đ?&#x2018;&#x2122;đ?&#x2018;&#x153; â&#x2C6;&#x2122; đ?&#x2018;&#x2DC; đ?&#x2018;&#x2018;đ?&#x2018;?

(32)

(33)

Finally, the boiling convective heat transfer coefficient is calculated: â&#x201E;&#x17D;đ?&#x2018;? = 2.5â&#x201E;&#x17D;đ?&#x2018;&#x2122;đ?&#x2018;&#x153; (1â &#x201E;đ?&#x153;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ą )0.75

(34)

3.2.3. Heat Exchanger analysis The same procedure as above with the difference that, in the heat balance, in order for the fluid to be heated, there is a difference in enthalpy (latent heat of vaporization) instead of a difference in temperature. đ?&#x2018;&#x201E;đ?&#x2018; = áš đ?&#x2018;&#x201D; đ?&#x2018;?đ?&#x2018;?,đ?&#x2018;&#x201D; (đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą ) = đ?&#x2018;&#x201E;đ?&#x2018;? = áš đ?&#x2018;&#x2122;â&#x2C6;&#x2019;đ?&#x2018;Ł (â&#x201E;&#x17D;đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą â&#x2C6;&#x2019; â&#x201E;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; )

(35)

And đ?&#x2018;&#x201E; = đ?&#x2018;&#x2C6;đ??´ â&#x2C6;&#x2122; đ??żđ?&#x2018;&#x20AC;đ?&#x2018;&#x2021;đ??ˇ

đ??żđ?&#x2018;&#x20AC;đ?&#x2018;&#x2021;đ??ˇ =

đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; (đ?&#x2018;&#x2122;đ?&#x2018;&#x203A;((đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;&#x2122;â&#x2C6;&#x2019;đ?&#x2018;Ł,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; )/ (đ?&#x2018;&#x2021;đ?&#x2018;&#x201D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;&#x2122;â&#x2C6;&#x2019;đ?&#x2018;Ł,đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą ))

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Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

3.2.4. Friction factors and pressure drops In this situation, the computation of the friction factors is different from the single-phase zone. Here the Kim correlation [16] is used. Calling x the vapor quality, viscosity, density and velocity of the fluid for x = 0 and x = 1 are known. So the void fraction Îľ, which represents the cross sectional area occupied by the vapor phase in respect to the total sectional area, can be computed:

đ?&#x153;&#x20AC;=

đ??´đ?&#x2018;Ł đ??´đ?&#x2018;Ł +đ??´đ?&#x2018;&#x2122;

(38)

Butterworth developed a generalized equation for it, and here Thomeâ&#x20AC;&#x2122;s model [16] for the exponents is used: â&#x2C6;&#x2019;1

1 â&#x2C6;&#x2019; đ?&#x2018;Ľ đ?&#x153;&#x152;đ?&#x2018;Ł 0.84 đ?&#x153;&#x2021;đ?&#x2018;&#x2122; 0.8 đ?&#x153;&#x20AC; = [1 + ( )( ) ( ) ] đ?&#x2018;Ľ đ?&#x153;&#x152;đ?&#x2018;&#x2122; đ?&#x153;&#x2021;đ?&#x2018;Ł

(39)

The density and viscosity of the two-phase mixture are calculated: đ?&#x153;&#x152;đ?&#x2018;Ąđ?&#x2018;? = đ?&#x153;&#x152;đ?&#x2018;Ł â&#x2C6;&#x2122; đ?&#x153;&#x20AC; + đ?&#x153;&#x152;đ?&#x2018;&#x2122; (1 â&#x2C6;&#x2019; đ?&#x153;&#x20AC;)

(40)

đ?&#x2018;Ľ â&#x2C6;&#x2122; đ?&#x153;&#x2021;đ?&#x2018;Ł (1 â&#x2C6;&#x2019; đ?&#x2018;Ľ)đ?&#x153;&#x2021;đ?&#x2018;&#x2122; đ?&#x153;&#x2021;đ?&#x2018;Ąđ?&#x2018;? = đ?&#x153;&#x152;đ?&#x2018;Ąđ?&#x2018;? [ + ] đ?&#x153;&#x152;đ?&#x2018;Ł đ?&#x153;&#x152;đ?&#x2018;&#x2122;

(41)

Now the friction factor for a straight pipe and for a coiled pipe (Kim) can be found [16]: â&#x2C6;&#x2019;0.25

(42)

đ??ş = đ?&#x2018;Ľđ?&#x153;&#x152;đ?&#x2018;Ł đ?&#x2018;˘đ?&#x2018;Ł + (1 â&#x2C6;&#x2019; đ?&#x2018;Ľ) đ?&#x153;&#x152;đ?&#x2018;&#x2122; đ?&#x2018;˘đ?&#x2018;&#x2122;

(43)

đ?&#x2018;&#x201C;đ?&#x2018;Ąđ?&#x2018;?,đ?&#x2018;

đ??ş â&#x2C6;&#x2122; đ?&#x2018;&#x2018;đ?&#x2018;? = 0.079 ( ) đ?&#x153;&#x2021;đ?&#x2018;Ąđ?&#x2018;?

where G â&#x20AC;&#x201C; is the two-phase mass velocity:

1â &#x201E; 20

đ?&#x2018;&#x201C;đ?&#x2018;Ąđ?&#x2018;?,đ?&#x2018;?

đ?&#x2018;&#x2018;đ?&#x2018;? 2 = đ?&#x2018;&#x201C;đ?&#x2018;Ąđ?&#x2018;?,đ?&#x2018; [1 + đ?&#x2018;&#x2026;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x153; ( ) ] đ??ˇđ?&#x2018;?

The pressure drop in the boiler is:

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Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

â&#x2C6;&#x2020;đ?&#x2018;? =

2đ?&#x2018;&#x201C;đ?&#x2018;Ąđ?&#x2018;?,đ?&#x2018;? đ??ş 2 đ??żđ?&#x2018;? đ?&#x153;&#x152;đ?&#x2018;Ąđ?&#x2018;? đ?&#x2018;&#x2018;đ?&#x2018;?

(45)

3.3. The pre-heater design The procedure is the same already discussed for the superheater, both for the shell and the coil, with the obvious difference that the fluid to be heated is in a liquid state. Same considerations for friction factor and pressure drop calculations. 3.4. Successive iterations With the values of pressure drop it is possible to continue with a second iteration, increasing the inlet pressure of each sub-part of the heat exchanger. The pump must be capable to satisfy the extra pressure request. After re-calculating the length of the heat exchanger, the computation of the pressure drop is repeated until convergence is reached. 3.5. Efficiency of the heat exchanger The efficiency is defined as the ratio between the thermal power actually transmitted and the thermal power theoretically transmittable. The second term is derived by the difference of temperature reached by the fluid with the lower thermal flow rate Cmin (product of specific heat and mass flow) if the (counter flow) heat exchanger had infinite length [19].

đ?&#x153;&#x20AC;=

đ?&#x2018;&#x160;đ?&#x2018;Ą đ?&#x2018;&#x160;đ?&#x2018;Ą = đ?&#x2018;&#x160;đ?&#x2018;Ą,đ?&#x2018;&#x161;đ?&#x2018;&#x17D;đ?&#x2018;Ľ đ??śđ?&#x2018;&#x161;đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; (đ?&#x2018;&#x2021;â&#x201E;&#x17D;,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;?,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; )

(46)

3.6. Final Results Below the design results for both R134a and R245fa HRVG are shown. Table 6. Final results of the design procedure for both R134a (5a) and R245fa (5b) HRVG Boiler

Boiler

0 â&#x2030;¤ x â&#x2030;¤ 0.5

0.5 â&#x2030;¤ x â&#x2030;¤1

3409.52

6891.9

483.848

Length of 1 coil (m)

3.96

3.65

2.21

0.12

NÂ° of turns 1 coil

15.7

14.5

8.7

0.47

Shell length (m)

0,3582

0.3298

0.1996

0.0107

R245fa

Preheater.

Boiler

0 â&#x2030;¤ x â&#x2030;¤ 0.5

0.5 â&#x2030;¤ x â&#x2030;¤ 1

Q (W)

4158.26

6818

134.156

Length of 1 coil (m)

5.3532

3.7127

2.2151

0.034

Number of turns 1coil

21.2

14.71

8.77

0.13

Shell length (m)

0.4836

0.3354

0.2001

0.003

R134a

Preheater

Q (W)

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Superheater

Mechanics, Materials Science & Engineering, October 2015 â&#x20AC;&#x201C; ISSN 2412-5954

The table below refers only to the coil-side pressure drops; shell-side losses have been neglected due to their low values (equal or less than 1 kPa). Finally, in table 8, all dimensions are listed. Table 7. Pressure drops Pressure drops (kPa)

R134a

R245fa

Pre-heater

6,5

Boiler

Super-heater

Neglected (<1kPa)

Table 8. Heat Exchangers Final Dimensions R134a

R245fa

Int. Diam. 1 Coil (m)

0.008

Ext. Diam. 1 Coil (m)

0.0104

Helix diam. (m)

0.08

Pitch (m)

0.0228

Int. Diam. 1 Shell (m)

0.106

Number of turns (1 coil)

Total length 1 coil (m)

10.094

11.608

Total length 1 shell (m)

0.9234

1.0602

Total thermal power (kW)

70.71

71.71

Efficiency Îľ (%)

82.4

84.5

The results show that, even if the R245fa cycle presents the best thermodynamic efficiency and the higher heat exchanger efficiency, the R134a heat exchanger presents a total length of 92.3 cm (14 cm less than the R245fa HRVG length). This value, in addition to economic considerations (R134a is cheaper than R245fa), make the R134a cycle more interesting for this application, so it has been definitively chosen as working fluid. In the following figure, a 3D view is provided, and a possible component assembly.

Fig. 6 and 7. 3-D view of the two coils and of the shell (R134a)

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Fig. 8 and 9. Assembly of the components and disposition of the four shells with the total occupied diameter (27.6 cm rounded up to 28 cm) 4. The thermal and the structural simulation 4.1 Average wall temperatures. First of all, the average wall temperatures from the heat balance equation were roughly found and then a steady-state thermal simulation was implemented, to check the actual temperature trend inside the thickness of the tube, and at the wall more accurately. From the heat balance:

đ?&#x2018;&#x17E;=

đ?&#x2018;&#x201E; = đ?&#x2018;&#x2C6;(đ?&#x2018;&#x2021;â&#x201E;&#x17D; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;? ) đ??´đ?&#x2018;&#x2019;đ?&#x2018;Ľ

(47)

q is the heat flux from the hot to the cold fluid and U the overall thermal transmittance, while Th and Tc are the average temperatures for the hot and cold fluids in each part of the heat exchanger. So, the average heat flux and the temperature at the internal and external diameters of the tube is:

đ?&#x2018;&#x17E;đ?&#x2018;&#x2013; =

đ?&#x2018;&#x201E; = â&#x201E;&#x17D;đ?&#x2018;? (đ?&#x2018;&#x2021;đ?&#x2018;¤,đ?&#x2018;&#x2013;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2021;đ?&#x2018;? ) đ??´đ?&#x2018;&#x2013;

(48)

đ?&#x2018;&#x17E;đ?&#x2018;&#x2019; =

đ?&#x2018;&#x201E; = â&#x201E;&#x17D;â&#x201E;&#x17D; (đ?&#x2018;&#x2021;â&#x201E;&#x17D; â&#x20AC;&#x201C; đ?&#x2018;&#x2021;đ?&#x2018;¤,đ?&#x2018;&#x2019;đ?&#x2018;Ľ ) đ??´đ?&#x2018;&#x2019;

(49)

In the previous formulas hh and hc are the convective coefficients for the hot and cold fluids. Once the thermal transmittance and Tc and Th are known, the heat flux, in each part of the heat exchanger is computed, as shown in Table 9. Table 9. Average heat flux from the heat balance R134a

Ext. Heat flux (W/m2)

Int. Heat flux (W/m2)

Pre-heater

13460.24

17498.31

Boiler (0<x<0.5)

30354.97

39461.47

Boiler (0.5<x<1)

48698.95

63308.63

Super-heater

61847.8

80402.15

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The values of hh and hc, allow to calculate the wall temperatures are: this is a first indication of the temperatures of every part of the coiled tube. Table 10. Average wall temperatures R134a

External diameter average Internal diameter temperature (°C) average temperature (°C)

Pre-heater

51.85

51.5

Boiler (0<x<0.5)

61.77

60.98

Boiler (0.5<x<1)

58.9

57.64

Super-heater

87.21

85.59

4.2 The Steady-State Thermal Simulation All simulations were conducted using the ANSYS software. However, checking the program library, a modification/insertion was necessary. The AISI 446 stainless steel, with its properties [20], has been inserted into the materials database of ANSYS, and then the geometry was imported from SolidWorks. The next step has been the mesh generation. The most important features chosen for each sub-component of the heat exchanger are (from all available in the software): - Relevance center: Medium - Smoothing: Medium - Transition: Fast - Span angle center: Medium

Fig. 10. Example of a complete mesh In the table below the number of nodes and of elements, resulting from the mesh configuration of every single part of the heat exchanger, is illustrated. Besides, the values of convective coefficients (considered constant) and temperatures (with an approximated linear trends along the axis) of refrigerant and exhaust were set. The "boundary conditions" for the simulation are as follows. Once the temperature filed is determined, starting from the HRVG outlet section, it sets the output temperature of the organic fluid of the HRVG superheated section. So, the SH inlet conditions (calculated in the above section) becomes the outlet condition for the vaporizer section, and so on. The other assumed quantity is the MMSE Journal. Open Access www.mmse.xyz 88

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fluid mass flow rate and the two convective coefficient (cold side and hot side), computed as previously described. Table 11. Number of nodes and elements of the mesh for the steady-state thermal simulation Nodes

Elements

Pre-heater

204048

30544

Boiler 0-0,5

94088

16204

Boiler 0,5-1

106848

17224

Fig. 11. Example of thermal load applied to the geometry 4.3 Results of the thermal simulation and comments In the following figures, the steady-state thermal study results for the temperature and the heat flux reached by the material for each part of the R134a helical coiled tube are shown:

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Fig. 12 (a). Temperature trend along the pre-heater (°C)

Fig. 12 (b). Heat flux trend along the pre-heater (W/m2)

Fig. 13a. Temperature trend along the first part of the boiler (0≤x≤0.5)

Fig. 13b. Heat flux trend along the first part of the boiler (0≤x≤0.5)

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Fig. 14a. Temperature trend along the second part of the boiler (0.5≤x≤1)

Fig. 14b. Heat flux trend along the second part of the boiler (0.5≤x≤1) The results indicate that the tube temperature is close to the temperature of the refrigerant. The maximum temperature reached on the external surface is 65.4 °C (Figure 12a). This depends on the difference between the flows convective coefficients on inside and outside surface of the tube (inside the order of magnitude is 103-104, outside 102). The simulation of the super-heater has not been implemented due to its very small length (less than 0.5 number of turns of the coiled tube). 4.4 The static structural simulation For the structural study, the most important mechanical properties of the AISI 446 [20] were added in the Engineering Data, as previously described. The geometry and the mash used is the same used for the thermal simulation. The tablle below shows the numbers of nodes and elements used in the calculation. Table 12. Number of nodes and elements of the mesh for the static structural simulation Nodes

Elements

Pre-heater

208040

31020

Boiler 0-0.5

96048

17104

Boiler 0.5-1

108264

18922

The external temperature field, previously determinate, has been set as "boundary condition". To act in safety conditions, the thermal load, so calculated, was applied to the entire body of the coil. Consequently, the thermal load on the internal surface was overestimated, but accepted. In fact, the program does not allow to set different temperatures on different faces, but only one temperature for the entire body. The second "boundary conditions" concern the pressure. It has been applied on the internal surface, decreased by the external pressure value. MMSE Journal. Open Access www.mmse.xyz 91

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Fig. 15. Example of an applied thermal load All the sub-components of the heat exchanger were bonded to both ends with an elastic support (as suggest by program manual) made of the same material. For the inlet pre-heater and the outlet super-heater, a fixed support has been considered.

4.5. Results of the structural simulation and comments The following figures show the total deformation of the coiled tubes and the stress safety factor, defined as the yield stress of the material divided by the equivalent stress actually computed in the simulation σs/σ. The results indicate that the material tensions stress are always below the yield stress value, thanks to the low operating temperature and pressure. The maximum level is reached at the end of the exchanger, where the fixed supports are used. But, also in this case, the value is far from the limit value. with a safety factor of 4.5 (see figure 16b). The thermal deformations, as stress one, is low, of the order of millimeter. However, the structural simulation only covers the different parts of the coil itself. So, even if the coil doesn’t present problems, a study of the thermal effects on the welded junctions between the coiled tube and the shell will be necessary, where stress concentrations are located. Finally, these values has to be checked by an experimental campaign.

Fig. 16a. Total deformation of the pre-heater (m)

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Fig. 16b. Safety factor of the pre-heater

Fig. 17a. Total deformation of the first part of the boiler(0≤x≤0.5)

Fig. 17b. Safety factor of the first part of the boiler (0≤x≤0.5)

Fig. 18a. Total deformation of the second part of the boiler (0.5≤x≤1)

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Fig. 18b. Safety factor of the second part of the boiler (0.5≤x≤1) Summary. In conclusions, the recovery of heat from the exhaust gases of an engine can lead to numerous advantages both from an economic point of view (fuel economy), once the payback time of the investment has ended, and from an environmental point of view, with consequent lower emissions of greenhouse gases and toxic atmospheric agents. The increased efficiency of the whole process, thanks to the ORC system, calculated on the efficiency of cycles with R134a and R245fa as working fluids, is about between 4% and 6% respectively. So, the cycle that provides the highest overall thermodynamic efficiency is the R245fa cycle, which also provides the highest boiler efficiency, while the R134a, cheaper than R245fa, cycle allows to have a more compact heat exchanger (14 cm shorter than the R245fa). However, it can be notice that, due the relatively high temperatures of the exhaust gases of the engine, it is necessary to carry out experimental tests. to be absolutely sure of the safety of the "direct" configuration (although the temperatures of self-ignition of working fluids are much higher than those reached by the inner wall of the heat exchanger). The final dimensions of the heat exchanger make it suitable for vehicular applications, primarily for large vehicles such as trucks, trains and large ships. It can also be suitable for smaller vehicles (cars), but more research has to be carried out, with the aim of decreasing the dimensions, thus making the ORC for small size land vehicle applications (or even for smaller stationary applications) attractive and competitive. To further decrease the size, the heat exchanger could be subdivided in 6 or 8 smaller shells, reducing the total occupied area and then checked to eventual length reduction. However, this approach could lead to an increase in head losses. The additional use of the waste heat, deriving from the engine cooling system, to pre-heat the fluid could be efficiently advantageous, but it could be complicated, and a careful investigation is required. Finally, a CFD study could undoubtedly be useful to analyze the characteristics of the outflow along the helical tube and their effect on heat transfer and pressure drop. Besides, due to computational limitations, structural and thermal studies were carried out by dividing the heat exchanger into four basic parts. However it would be appropriate to perform a complete study on the entire heat exchanger and, in particular, on the welds lines, once the heat exchanger is assembled. In addition, with the development of new industrial fluids such as HFO 1234yf and HFO1234ze, it will be possible to considerably reduce (about 400 times) the environmental impact of such a system Acknowledgments This article is part of the project “Medium/Small ORC plants for industrial application”, developed by the Mechanical and Aerospace Engineering Department of “Sapienza” University of Rome with the support of the private enterprise GEA S.p.A., which deserves acknowledgement from the authors. Author Contributions Roberto Capata dealt with the design procedure, while Giacomo Bonafoni was in charge of all aspects related to ANSYS simulations. Conflicts of Interest The authors declare no conflict of interest. MMSE Journal. Open Access www.mmse.xyz 94

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References [1] Bonafoni, G. Preliminary design of a helical coil heat exchanger for a small ORC energy recovery system. Master Degree Thesis, Department of Mechanical & Aerospace Engineering, University of Roma “Sapienza”, Rome, July 2014 [2] Wang, T.; Zhang, Y.; Peng, Z.; Shu, G. A review of researches on thermal exhaust heat recovery with Rankine cycle. Renewable and sustainable energy reviews 2011, 15, 2862-2871. [3] Saidur, R.; Rezaei, M.; Muzammil, W.K.; Hassan, M.H.; Paria, S.; Hasanuzzaman, M. Technologies to recover exhaust heat from internal combustion engines. Renewable and sustainable energy reviews 2012, 16, 5649-5659. [4] Tchanche, B.F.; Lambrinos, G.; Frangoudakis, A.; Papadakis, G. Low-grade heat conversion into power using organic Rankine cycles–A review of various applications. Renewable and Sustainable Energy Reviews 2011, 15, 3963–3979. [5] Capata, R.; Sciubba, E. A small-scale ORC energy recovery system for vehicular application: feasibility analysis and preliminary components design. In IMECE 2013-63410, Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition, San Diego, California, USA, November 15-21, 2013. [6] Capata, R.; Sciubba, E.; Toro, C. The gas turbine hybrid veichle Lethe at UdR1: the On-Board innovative Orc energy recovery system – feasibility analysis. In IMECE2012-85237, Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition, Houston, Texas, USA, November 9-15, 2012. [7] Shu, G.; Yu, G.; Tian, H.; Wei, H.; Liang, X. A Multi-Approach Evaluation System (MA-ES) of Organic Rankine Cycles (ORC) used in waste heat utilization. Applied Energy 2014, 132, 325-338. [8] Boretti, A. Recovery of exhaust and coolant heat with R245fa organic Rankine cycles in a hybrid passenger car with a naturally aspirated gasoline engine. Applied Thermal Engineering 2012, 36, 73-77. [9] Wang, E.H.; Zhang, H.G.; Fan, B.Y.; Ouyang, M.G.; Zhao, Y.; Mu, Q.H. Study of working fluid selection of Organic Rankine Cycle (ORC) for engine waste heat recovery. Energy 2011, 36, 34063418. [10] Toffolo, A.; Lazzaretto, A.; Manente, G.; Paci, M. A multi-criteria approach for the optimal selection of working fluid and design parameters in Organic Rankine Cycle systems. Applied Energy 2014, 121, 219-232. [11] National Institute of Standards and Technology. http://webbook.nist.gov/chemistry/fluid/ (accessed on 26/07/2014). [12] Peace Software. http://www.peacesoftware.de/einigewerte/einigewerte_e.html (accessed on 3/08/2014) . [13] Capata, R.; Hernandez, G. Preliminary design and simulation of a Turbo Expander for small rated power Organic Rankine Cycle (ORC). Energies 2014, 7 (11), 7067-7093; doi: 10.3390/en7117067. [14] Patil, R.K.; Shende, B.W.; Ghosh, P.K. Designing a helical-coil heat exchanger., Chemical Engineering, 13 December 1982. [15] Amori, K.E.; Sherza, J.S. An investigation of shell-helical coiled tube heat exchanger used for solar water heating system. Innovative Systems Design and Engineering, 2013, Vol. 4, No.15, ISSN 2222-1727 (Paper).

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[16] Elsayed, A.M. Heat Transfer in Helically Coiled Small Diameter Tubes for Miniature Cooling Systems. PhD Thesis, The School of Mechanical Engineering, University of Birmingham, September 2011. [17] Naphon, P.; Wongwises, S. A review of flow and heat transfer charateristics in curved tubes. Renewable and Sustainable Energy Reviews 2006, 10, 463-490. [18] Salimpour, M.R. Heat transfer coefficients of shell and coiled tube heat exchangers. Experimental Thermal and Fluid Science, 2009, 33, 203-207. [19] Kuppan, T. Heat Exchanger Design Handbook, 1st ed.; Marcel Dekker, Inc.: New York, NY, USA, 2000; pp. 29-41. [20] AZoM: Materials Science and Engineering http://www.azom.com/article.aspx?ArticleID=6817 (accessed on 28/08/2014).

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Information.

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Melting Heat Transfer in MHD Boundary Layer Stagnation-Point Flow Towards a Stretching Sheet with Thermal Radiation M. Subhas Abel1a, Jayashree Sanamani1 1 – Department of Mathematics, Gulbarga University, Gulbarga 585106, Karnataka, India a – msabel2001@yahoo.co.uk

Keywords: boundary layer, stagnation point, thermal radiation, melting parameter, runge-kutta fehlberg method.

ABSTRACT. An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching sheet. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, before being solved numerically using Runge-Kutta-Fehlberg method. Effects of Magnetic parameter, Radiation parameter, melting parameter, stretching parameter and Prandtl number on flow and heat transfer characteristics are thoroughly examined. *Note a – Parameter of the temperature distributed in stretching surface; y-direction;

B0 – Externally imposed magnetic field in the

Cb – Drag coefficient; C f – Local skin-friction coefficient; c p – Specific heat of the fluid at constant

pressure; f – Dimensionless stream function; K – Radiation number; L – Characteristic length of the flow dynamics;

Nux

– Nusselt number; Pr – Prandtl number; Nr – Radiation Parameter;

M n – Magnetic Parameter; T – Fluid temperature; T – Ambient temperature; T0 – Reference number; Tw – Wall temperature; u – fluid axial velocity; U w – Velocity

of horizontal stretching surface; Ue – Velocity of external flow; V – fluid transverse velocity; x, y – Coordinates along and normal to the vertical stretching surface plate; X – Dimensionless coordinate along the plate; Greek symbol  – Kinematic viscosity;  wx – Local shear stress;







– Thermal diffusivity;



– Coefficient of thermal expansion;

– Dimensionless heat generation /absorption parameter;





– Non-dimensional transformed variable;

– Viscosity of the fluid;  – Fluid electrical conductivity;

– Stream function;  – Fluid density;  – Dimensionless temperature; Subscripts x – local; w – Conditions on the wall; o – Reference;  – Ambient or free stream condition; ' – Differentiation with respect to 

Introduction. The study of boundary layer flow and heat transfer over a stretching surface is important and has attracted considerable interest of many researchers because of its large number of applications in industry and technology. Few of these applications are materials manufactured by polymer extrusion, drawing of copper wires, continuous stretching of plastic films, artificial fibers, hot rolling, wire drawing, glass fiber, metal extrusion and metal spinning, cooling of metallic sheets or electronic chips, and many others. In these cases, the final product of desired characteristics depends on the rate of cooling and the rate of stretching. After the pioneering work by Sakiadis [1], a large amount of literature is available on boundary layer flow of Newtonian and non-Newtonian fluids over linear and nonlinear stretching surfaces [2–10]. Stagnation point flow, describing the fluid motion near the stagnation region of a circular body, exists for both the cases of a fixed or moving body in a fluid. The two dimensional stagnation flow towards a stationary semi-infinite wall was first studied by Hiemenz[11], using a similarity transformation, to reduce the Navier-stokes equations to a nonlinear ordinary differential equation. Chiam [12] examined the stagnation point flow of viscous fluid towards a linear stretching surface. Stagnation-point flow of power-law fluid over a stretching surface was reported by Mahapatra et al. [13]. They have obtained a numerical solution of the problem by fourth-order Runge Kutta integration technique. Epstein and Cho [14] analyzed the melting heat transfer of the steady laminar flows over MMSE Journal. Open Access www.mmse.xyz 97

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a flat plate. The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream has been studied by Ishak et al. [15]. Researchers [16,17,18] have considered to investigate melting heat transfer effects on boundary layer flow and heat transfer over a stretching sheet with various flow and heat transfer conditions involved. The aim of the present paper is to study the similarity solutions of stagnation –point flow and the heat transfer from a warm, laminar liquid flow to a melting stretching sheet with the combined effect of magnetic field and thermal radiation. A thorough literature survey show that there is not any published work on melting heat transfer in boundary layer stagnation point flow towards a stretching sheet with the effect of magnetic field and thermal radiation.. We believe that the obtained results are new and original. It should be mentioned that in addition to its importance from a fundamental standpoint, the present study finds important application in magma solidification, the melting of permafrost, the thawing of frozen grounds, and the preparation of semi-conductor materials. In addition, in solidifying casting the existence of a mushy zone separating the liquid phase from the solid phase has been observed.

Fig. 1. Schematic diagram of stretching sheet Formulation of Problem. Consider a steady stagnation-point flow towards a horizontal linearly stretching sheet with the influence of magnetic field, melting at a steady rate into a constant property, warm liquid of the same material, as shown in the Figure above. It is assumed that the velocity of the external flow is ue  x   ax and the velocity of the stretching sheet is uw  x   cx , where a is a positive constant, while c is a stretching rateis also a positive constant and x is the coordinate measured along the stretching sheet. It is also assumed that the temperature of melting surface is Tm, while the temperature in the free-stream region is T , where T  Tm . Under the usual boundary layer approximations, the equations of motion with magnetic field effect, and thermal radiation, and the equation representing temperature distribution in the liquid flow must obey the following equations, u u  0 x y ,

u u u  2u  B02u v  ue e  2  x y x y  ,

(1)

(2)

T T  2T 1  qr  v  2  x y y C p  y 

(3) where x and y – the Cartesian coordinates measured, along and normal to the stretching surface; MMSE Journal. Open Access www.mmse.xyz 98

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u and v – the velocity components along the x- and y-axis;

 ,  , and qr – the kinematic viscosity, thermal diffusivity and thermal radiation of the fluid, respectively. Following Hiemenz [11] and Epstein and Cho [14], the boundary conditions of (1) – (3) are as mentioned below,

u  uw ( x)  cx,

T  Tm

y0

u  ue ( x),  ax,

T  T

y 

(4a)

and

 T  k    [  cs (Tm  T0 )]v( x,0)  y  y 0

(4b)

where  – fluid density k is the thermal conductivity;

 – latent heat of the fluid cs – heat capacity of the solid surface. Eq. (4b) states that the heat conducted to the melting surface is equal to the heat of melting plus the sensible heat required to raise the solid temperature T0 to its melting temperature Tm ( Refer, Epstein and Cho[14]).Following the classical work of Hiemenz [11], we introduce, a similarity transformation to recast the governing partial differential equations into a set of ordinary differential equations, i.e.

   a  2 xf ( ), 1

   

 

T  Tm , T  Tm

  a

 where  – the stream function , defined in the usual form as, u  y automatically satisfies the continuity equation (1).

(5)

and v  

 , which x

By using this stream function , we obtain the values of velocity components,

u  axf ( ),

v  (a )

(6)

f ( ),

, Substituting (5) and (6) into (2) and (3) gives the following nonlinear ordinary differential equations: f   ff   f 2  M n f   1  0,  Pr    f  =0,  1  Nr 

   

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(7) (8)

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where primes denote differentiation with respect to  and Pr is the Prandtl number and M n  the Magnetic parameter, and Nr 

16 T3 3K  K

 B02 is a

is the Radiation parameter.

The boundary conditions (4) takes the form, f (0)   , f ()  1,

where  

 (0)  0,  ()  1,

Prf (0)  M  (0)  0,

(9)

c – velocity ratio (   0 ) parameter a

M – dimensionless melting heat transfer parameter which is defined as

M

c p T  Tm 

(10)

  cs Tm  T0 

where c p – the heat capacity of the fluid at constant pressure. The

melting heat transfer parameter is a combination of the Stefan numbers c f T  Tm  /  and cs Tm  T0  /  for the liquid and solid phases, respectively. It is worth mentioning that for M=0 (melting is absent), Eq. (7) reduces to the classical equation first derived by Hiemenz [11]. The physical quantities of interest are the skin friction coefficient c f and the local Nusselt number

Nux or melting rate (local heat flux) at the stretching surface defined as

cf 

w ,  ue2

Nux 

xqw k T  Tm 

(11)

where  w and qw – the surface shear stress and the surface heat flux which are given by,

 u  w     ,  y  y 0

 T  qw  k    y  y 0

(12)

where  – the dynamic viscosity of the fluid. Using variables (5), we get Re1x 2 c f  f (0),

Rex1 2 Nux   (0)

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(13)

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where Re x  ue ( x) x / y – the local Reynolds number. Combining (4b) and (13), one can obtain the melting velocity at the stretching surface v(x, 0),which is represented by the following equation, i.e.

v( x,0)  

 x

(14)

MNux

This velocity is proportional to x-1and it shows that the melting process is faster near the stagnationpoint of the stretching sheet. Numerical method. Numerical solutions to the ordinary differential equation (7) and (8) with the boundary conditions (9) are obtained using the Runge-Kutta-Fehlberg method with shooting technique. The Numerical solution is obtained by setting different initial guesses for the values of skin friction coefficient f (0) and the local Nusselt number  (0) ,where the velocity and temperature profiles satisfies the far field boundary conditions (9) asymptotically. These methods have been successfully used by the following authors to solve various problems related to boundary layer flow and heat transfer (see Bachok et al. [8, 9] and Ishak et al. [15]). Results and Discussion. For the stretching sheet,  is positive,in order to validate the numerical results obtained, we compare our results with that reported by Bachok et al. [16], Hiemenz [11] Wang [17] Kimiaefar etal [18], as shown in Table 1, for f (0) which depicts an excellent agreement between our result and that of others as mentioned above which in turn gives a confidence that the numerical results obtained by us are accurate. Table1. Values of for f (0) stretching sheet ε

N.Bachok etal [16]

Hiemenz [11]

Wang [17]

M=0

Kimiaefar etal [18]

M=0 0

1.2325877

0.1

Present work M=0

M=0 1.2326

1.2325888

1.23258762

1.2325877

1.1465610

1.14656

1.14656098

1.1433610

0.2

1.0511300

1.05113

1.05112998

1.0511300

0.5

0.7132949

0.71330

0.71329495

0.71229495

-1.8873066

-1.88731

-1.88732

Effect of M on temperature and velocity profiles. influence of melting parameter M on the temperature θ(η) is captured in fig. 1. It is obviousfrom this figure that an increase in the melting effect decreases the temperature. However, thethermal boundary layer thickness is increased for large values of M. Figure 2 illustrates the influenceof melting parameter M on the velocity profile f'(η).An increase in the melting parameter M enhances the velocity and the boundary layer thickness. When a cold sheet plunges into a hot water it starts to melt. As the melting progressesthe sheet gradually transforms to a liquid causing the velocity profiles to grow rapidly. MMSE Journal. Open Access www.mmse.xyz 101

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Effect of Magnetic parameter Mn on velocity and temperature profiles. Fig 3 shows the effect of Magnetic parameter Mn on temperature profile. Clearly, increasing values of magnetic parameter Mn causes the surface temperature to blow-up monotonically. Fig 4 shows the effect of magnetic parameter Mn on dimensionless velocity profile f′(η) , and it is noticed that velocity profile of the fluid in the boundary layer significantly reduces with increase in values of Mn. This is because of the fact that, magnetic field introduces a retarding force which acts transverse to the direction of applied magnetic field. This force is Lorentz force, which decelerates the flow in the boundary layer, resulting in thickening momentum boundary layer and also it is noticed in increase of absolute value of velocity gradient at the surface of the sheet. Effect of Radiation parameter on temperature and velocity profiles. The effect of radiation parameter Nr on the velocity profile has been illustrated in Fig.5. It is noticed that radiation parameter Nr is an increasing function of velocity profile f'(η). The effects of thermal radiation parameter Nr on temperature is shown in Fig.6. It is revealed that the radiation parameter Nr causes increase in the fluid temperature θ(η). On the other hand the thermal boundary layer thickness also increases. Effect of prandtl number on temperature and velocity profiles. Fig.7-8 exhibits the effect of the Prandtl number on velocity and temperature profiles respectively. The temperature profile and thermal boundary layer thickness quickly decrease with increasing values of Pr. Prandtl number acts as a means to increase fluid viscosity resulting in lessening the flow velocity and temperature. Here thermal boundary layer thickness decreases with increasing Prandtl number, which is consistent with the findings of various reasearchers. Low prandtl number Pr indicates fluids with larger thermal conductivity and this produces thicker thermal boundary layer structures than that for high Prandtl number. Summary It is clear that the boundary layer thickness increases as both the magnetic field effect and melting heat transfer increase. The velocity field is decreasing function of magnetic parameter Mn where as it is increasing function of temperature profile.As expected, the effects of melting parameter M and Pr on the velocity and temperature are opposite.The influence of stretching ratio A is to increase the velocity and temperature fieldssignificantly.The present results are in a very good agreement with the numerical results obtained by Bachok etal. [16] for viscous fluid.Our analysis shows that the thermal radiation parameter groups with the Prandtl number, and the grouped dimensionless parameter has a complex impact on the heat transfer process.

Fig. 1. Temperature θ(η) versus η for different Fig. 2. Velocity profile f’(η) versus η for values of M different values of M

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Fig. 3. Temperature profile θ(η) versus η for Fig. 4. Velocity profile f’(η) versus η with different values of M different values of M

Fig. 5. Velocity profile f’(η) versus η for different Fig. 6. Velocity profile θ(η) versus η for values of Nr different values of Nr

Fig. 7. Velocity profile f’(η) versus η for different Fig. 8. Temperature profile θ(η) versus η for values of Prandtl number Pr different values of Pr

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References [1] B.C. Sakiadis, Boundary layer behavior on continuous solid surfaces: I Boundary layer equations for two dimensional and axisymmetric flow, AIChE J. 7 (1961) 26–28. [2] I.C. Liu, Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field, Int. J. Heat Mass Transfer 47 (2004) 4427– 4437. [3] S.K. Khan, M. Subhas Abel, M. Sonth Ravi, Viscoelastic MHD flow heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work, Int. J. Heat Mass Transfer 40 (2003) 47–57. [4] R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. Lett. A 357 (2006) 298–305. [5] B.S. Dandapat, B. Santra, K. Vajravelu, The effects of variable fluid properties And thermo capillarity on the flow of a thin film on an unsteady stretching sheet, Int. J. Heat Mass Transfer 50 (2007) 991–996. [6] S. Nadeem, A. Hussain, M. Khan, HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 475– 481. [7] N. Bachok, A. Ishak, Flow and heat transfer over a stretching cylinder with prescribed surface heat flux Malays, J. Math. Sci. 4 (2010) 159–169. [8] N. Bachok, A. Ishak, R. Nazar, Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid with prescribed surface heat flux, Int. J. Math.Mod.Meth. Appl. Sci. 4 (2010) 167– 176. [9] N. Bachok, A. Ishak, I. Pop, On the stagnation point flow towards a stretching sheet with homogeneous-heterogeneous reactions effects, Commun. Nonlinear Sci. Numer.Simulat. 16 (2011) 4296–4302. [10] N. Bachok, A. Ishak, R. Nazar, Flow and heat transfer over an unsteady stretching sheet in a micropolar fluid, Meccanica 46 (2011) 935–942. [11] Hiemenz, K., The Boundary Layer Analysis of a Uniformly Flowing Liquid Circulating in Straight Circular Cylinder (in German), Dinglers Polytech. J., 326 (1911), pp. 321-324. [12] Chiam, T. C., Stagnation-Point Flow Towards a Stretching Plate, J. Phys. Soc. Jpn., 63 (1994), 6, pp. 2443-2444 [13] Mahapatra, T. R., et al., Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid Towards a Stretching Surface, Int. J. Nonlinear. Mech., 44 (2009), 2, pp. 124-129 [14] Epstein, M., Cho, D. H., Melting Heat Transfer in Steady Laminar Flow over a Flat Plate, J. Heat transfer, 98 (1976), 3, pp. 531-533 [15] Ishak, A., et al., Melting Heat Transfer in Steady Laminar Flow over a Moving Surface, Heat Mass Transfer, 46 (2010), 4, pp. 463-468 [16]Norfifah Bachok Anuar Ishak and Ioan Pop, Melting heat transfer in boundary layer stagnationpoint flow towards a stretching/shrinking sheet,Physics letters A 374(2010)4075-4079. [17] C.Y.Wang,Int.J.Nonlinear Mech 43(2008)377 [18] A. Kimiaeifar, G.H. Bagheri, M. Rahimpour, M.A. Mehrabian, Proc. Inst. Mech. Eng. 223 (2009) 133.

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Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

Dynamic Design of Ground Transport With the Help of Computational Experiment Kravets V.V.1, Bass K.M.1, Kravets T.V.2, Tokar L.A.3 a 1 – Department of Automobiles and Transportation facilities Automobile Sector, State Higher Educational Institution “National Mining University”, Dnipropetrovsk, Ukraine 2 – Department of Theoretical Mechanics of the National University of Railway Transport, Dnipropetrovsk, Ukraine 3 – Foreign Languages Department, State Higher Educational Institution “National Mining University”, Dnipropetrovsk, Ukraine a – prof.w.kravets@gmail.com

Keywords: dynamic design, computational experiment, mathematical model, Euler-Lagrange equations, quaternion matrices, quasivelocities, Rodrigues-Hamilton parameters.

ABSTRACT. Objectives of ground transport (motor transport vehicle) have been considered. Mathematical model of nonlinear dynamics in spatial motion of asymmetric carriage in the form of Euler-Lagrange equations represented as symmetrical block structure in quaternion matrices has been developed. Kinematic equations and partition matrices of external action in which Rodrigues-Hamilton parameters have been applied describe quaternionic matrices.

Introduction. Objectives of dynamic design are to determine rational values of varied parameters of structural, layout, and construction schemes [1]. Geometrical dimensions and forms, such inertial characteristics as mass, centers of masses, inertia as well as stiffening, dissipative, power and aerodynamic characteristics are varied parameters taking into account effect of surface as screen and its contact interaction with elastic tire [2]. Process of dynamic design solves problems of controllability, stabilization, dynamic load and others [3]. The problems are formulated as nonlinear problems of car performance within spatial motion in terms of kinematic, contact, dynamic, and aerodynamic actions. In this context nonlinear problems of dynamic design can be solved with the help of computational experiment [4, 5]. 1. Dynamic scheme. Computational experiment is carried out according to mathematical models being adequate to problem formulation. Mathematical models depend on dynamic schemes being adequate to problem formulation. Carrying solid body (vehicle body and carried solid bodies) is considered as basic dynamic scheme of motor vehicle. Diversity of dynamic schemes depends on a character of carried bodies relative to carrying ones (internal relations), dynamic interference with external environment for example, wind, road surface and local varieties (kinematic relations). Mathematical model of road surface is developed in the form of ruled surface (Shukhov surface) which guide is determined with the help of spiral line corresponding to program trajectory of a vehicle movement [6]. Dynamic effect on a vehicle is determinedwith the help of gravity force distributed in terms of volume, inertial forces (centrifugal, gyroscopic, Coriolis, and tangential) aerodynamic forces as well as moments being a result of distributedsurface pressure and friction forces specified by a vehicle airflowingbased upon wind blasts,turbulent boundary layer between bottom of a vehicle and screening road surface, contact dynamic forces and moment being results of distributed surface forces of pressure and friction stipulated by interaction between elastic tire and road surface within destination, variable field for leading wheels and follower ones.

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2. Coordinate systems. Vector of force and moment, spatial vector of translation, and vector of linear velocity and angular velocity are represented by their components within following Cartesian coordinate systems: - Earth-based coordinate system (accepted as inertial one) where direction of one of axes is collinear to a direction ofplumb line characterizing gravity force and centrifugal force resulting from Earth's rotation; - Bound coordinate system (basic trihedron of a vehicle), which pole and axes orientation depend on design characteristics or other specifications (comfortable mounting, balance between geometry and weight etc.); - Aerodynamic axes are connected with geometric axes of a vehicle’s external shape symmetry; reduction centre of aerodynamic forces and moments is assumed as a pole; - Trihedron of contact forces and moments is guided by a normal to road surface and symmetry axes of elastic tire and road surface plane contact area; -Coordinate system and pole connected with axes and symmetry center of a wheel determine orientation and displacement of a wheel as regard to datum axes of a vehicle as well as other coordinate systems associated with carried bodies. Spatial rotations of principal body and carried ones are determined by quaternionic matrices which components are Rodrigues-Hamilton parameters expressed by physical angles (for example, EulerKrylov’s) [7]. 3. Mathematical model of nonlinear dynamics of a vehicle while 3D turning and displacing. 3.1. Dynamic equations by Euler-Lagrange. Mathematical model of principal body nonlinear dynamics within spatial motion is based on differential equations in the form of Euler-Lagrange ones represented with the help of quaternionic matrices [8]. Principal body angular velocity vector projection and projection of vector of linear velocity of body pole on its basic trihedron are taken as variables of integration-quasivelocities. Dynamic equations involve inertia matrix which components are axial and centrifugal inertial moments reduced to principal body weight and quaternionic matrices which components are coordinates of mass center as well as quaternionic matrices of quasivelocities. 3.2. Kinematic equations in Rodrigues-Hamilton parameters. Kinematic equations determine specified quasivelocities through Rodrigues-Hamilton parameters and their time derivatives and components of linear velocities of a pole as for inertial reference system. Principal body turning and displacing within the Earth’s coordinate system are determined by means of reverse transformation and numerical integration of kinematic dependences where quasivelocities are assumed as those identified as a result of numerical integration of dynamic equations. 3.3. Mathematical model structure. The matrix model of nonlinear dynamics of a vehicle as asymmetrical rigid solid body within spatial motion contains closed system of standard nonlinear heterogeneous differential equations of 1st order relative to six quasivelocities; three pole coordinates; four Rodrigues-Hamilton parameters; and resulting spatial vehicle turning connected by means of identical condition of standardization. Matrix dynamic equations are represented by eight differential equations of 1st order of which 1st and 5thare trivial; 2nd, 3rd, and 4th are equations of moments; and 6th, 7th, and 8th are equations of forces. Matrix kinematic equations are represented by eight differential equations of 1st order of which one to four are linear equations relative to Rodrigues-Hamilton parameters and their solutions are connected with known integral in the form of identical condition and five to eight equations are nonlinear as for basic trihedron pole velocity containing the first of the equations as trivial one. Neglecting trivial equations demonstrate expanded record in a matrix form by Euler operator describing inertial forces and moments including centrifugal, gyroscopic, and Coriolis ones: MMSE Journal. Open Access www.mmse.xyz 106

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– inertial matrix block: I11y  I12y  I13y  I 21y

I 22y  I 23y

 I 31y  I 32y

y y

1y

y3c 0  y1c

2y

 y2c y1c 0



3y

V30y

2y 1y 0

0 1

I11y  I12y  I13y

0  y3c y2c

1y

y3c 0  y1c

2y

y3c  y2c

3y V10y

y1c

1 0

V20y

y2c  y1c 0

0 1

V30y

 y3c 0

2y

3y 0  1y

y2c  y1c 0

1 0



V20y V10y

 y2c y1c 0

y1c

I 33y

2y 1y



V20y

 y3c 0

 I 31y  I 32y

V30y 0  V10y 0 

I 22y  I 23y

3y 0  1y 0

 I 21y

0  V30y V20y

c 2

0  3y 2y

y 10

c 3



I 33y

0  y3c y2c

y 3



(1)

Kinematic equations in an expanded matrix form are: – spatial turning (orientation): r0  t  r1  t  r2  t  r3  t 

 1 y  t   2 y  t   3 y  t 

0 

r0  t 

0 3 y  t   2 y  t  r1  t  1 1 y  t   2 2 y  t   3 y  t  0 1 y  t  r2  t 

(2)

r3  t 

3 y  t  2 y  t   1 y  t  0

– spatial displacement: z10  t 

r02  r12  r22  r32 2  r1r2  r0 r3  2  r0 r2  r1r3 

V10y

z20  t   2  r0 r3  r1r2 

r02  r12  r22  r32 2  r2 r3  r0 r1   V20y

z30  t 

2  r0 r1  r2 r3  r  r  r  r

2  r1r3  r0 r2 

2 0

2 1

2 2

2 3

(3)

y 30

Note that Rodrigues-Hamilton parameters are convenient to be explained, for example in EulerKrylov angles with the help of following simple dependences: – explanation of Rodrigues-Hamilton parameters in Euler-Krylov angles:

2  r1r3  r0 r2   sin  2  r2 r3  r0 r1    sin  cos  r02  r12  r22  r32  cos  cos 

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(4)

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2  r1r2  r0 r3    sin  cos  r02  r12  r32  r22  cos  cos 

3.4. External effects. Right part of dynamic equations is a sum of block matrices which structure is determined by a nature of effects on a principal body. Module of considered force and moment vectors are reduces to a principal body weight; for inertial forces (gravity force and weight) it is determined by a value of local acceleration of free fall; in terms of aerodynamic forces and moments it depends on dynamic pressure-weight ratio; for contact forces and moments it depends on the ratio between specific load within contact area and weight.A structure of block matrices of external effects is conservative containing square matrices of 4th order – zero, identity, quaternion – compiled according to the coordinates of application points of the forces under consideration: they are principal body mass centre coordinates within reference trihedron; they are coordinates of a reference point within reference trihedron; and they are coordinates of contact area symmetry center within reference trihedron. Directions of the forces and moments are described in block matrices with the help of quaternion matrices compiled on Rodrigues-Hamilton parameters determining reference trihedron orientation within inertial access for gravity force; orientation of geometrical axes of vehicle symmetry within reference trihedron for aerodynamic forces and moments; and orientation of contact force and moment trihedron within inertial axes and then within reference trihedron axes. 3.4.1. Inertial forces. Volumetric gravitational forces and inertial ones depending upon Earth rotation are reduced to resulting force applied within the center of vehicle mass. Unit director vector of the force is collinear to the lead line within reference system connected with principal body. Value of the inertial force is determined as a product of vehicle mass by a module of free fall resulting acceleration within conserved point of the Earth’s surface. Expanded record of gravity force matrix block is: 0  y3c y2c y3c 0  y1c g 

y

c 2

c 1

0 1

r02  r12  r22  r32

2  r1 r2  r0 r3  .

(5)

2  r0 r2  r1 r3 

3.4.2. Aerodynamic forces. Surface forces of pressure and friction of ram air are reduced to resulting aerodynamic forces applied within related aerodynamic axes through dynamic pressure , midsection area (or plan area), coefficient of longitudinal, standard, and cross-sectional forces or transformed to specific reference point with the help of typical linear dimension and coefficients of drifting, wandering, pitching (differenting, galloping), and rolling. Expanded record of aerodynamic force matrix block is:

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0  y3d y2d y3d qS  m

y

d 2

0  y1d d 1

0 1

r02d  r12d  r22d  r32d 2  r1d r2 d  r0 d r3d  2  r0 d r2 d  r1d r3d 

c1d

2  r0 d r3d  r1d r2 d 

r  r  r  r 2  r2 d r3d  r0 d r1d 

c2 d ,

2  r1d r3d  r0 d r2 d 

2  r0 d r1d  r2 d r3d  r02d  r12d  r22d  r32d

c3d

2 0d

2 1d

2 2d

2 3d

(7)

where c1d, c2d , c3d – coefficients of standard, longitudinal, and cross-sectional forces; r0d, r1d, r2d, r3d – Rodrigues-Hamilton parameters determining aerodynamic axes orientation in terms of related ones; y1d, y2d, y3d–are coordinates of aerodynamic forces reference point within related axes; q – dynamic pressure; S – midsection area; m – mass. Expanded record of aerodynamic moments matrix block is:

1 qSL  m

0 1

0 0 1 0 0 0 0

r02d  r12d  r22d  r32d 2  r1d r2 d  r0 d r3d  2  r0 d r2 d  r1d r3d  2  r0 d r3d  r1d r2 d 

r02d  r12d  r22d  r32d 2  r2 d r3d  r0 d r1d 

2  r1d r3d  r0 d r2 d 

2  r0 d r1d  r2 d r3d  r02d  r12d  r22d  r32d

m1d m2 d , m3d

(8)

where m1d, m2d , m3d – coefficients of moments of drifting, rolling, and pitching; L – specific linear dimension. 4.4.3. Contact forces. Surface forces of pressure and friction within contact area of wheel and road surface are reduced to resulting contact forces and moments related to characteristics point of contact area (for example, geometrical center of contact area symmetry) with coordinate axes coinciding with symmetry axes of plane area of wheel-road surface contact (tangential plane to road surface in the center of contact area symmetry) depending upon specific load (being normal to road surface of dynamic load distributed over variable zone of contact area), coefficients of wheel contact moments in terms of turning, sloping, rotating, and coefficients of longitudinal and cross-sectional contact forces. Note. It should be emphasized that coefficients of aerodynamic forces and moments depending upon external shape of a vehicle and involving stream turbulence, screening effect as well as coefficients of contact forces and moments depending upon characteristics of elastic tire and road surface are identified with the help of experimental techniques due to complexity of physical processes in terms of vehicle airflow in the neighbourhood of a screen (road surface) and in terms of wheel-road contact interaction. 4. Initial conditions. MMSE Journal. Open Access www.mmse.xyz 109

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4.1. Physical conditions. z0(0) is a position of hybrid vehicle pole within inertial coordinate system

 z10 (0), z20 (0), z30 (0) 

(9)

ż0(0) is components of linear velocity of hybrid vehicle pole within inertial coordinate system:

 z10 (0), z20 (0), z30 (0)  ,

(10)

where   0  ,   0  ,   0  – Euler-Krylov’s angles determining hybrid vehicle orientation within inertial space;

  0 ,   0  ,   0  – time derivatives (angular velocities) of Euler-Krylov’s angles determining hybrid vehicle orientation within inertial space. 4.2. Initial conditions for introduced variables. Rodrigues-Hamilton parameters determining hybrid vehicle orientation within inertial space are:

r0  0   cos

  0

cos

  0

cos

  0

 sin

  0

sin

 0

sin

 0

2 2 2 2 2 2 ,   0   0   0   0  0  0 r1  0   cos cos sin  sin sin cos 2 2 2 2 2 2 ,

r2  0   cos

r3  0   sin

  0 2

sin

cos

  0 2

cos

  0 2

 sin

 cos

  0 2

cos

sin

 0 2

  0 2

sin

(11)

 0 2

Components of hybrid vehicle angular velocity within related coordinate system are:

1 y  0    0 cos   0 cos   0    0 sin   0  , 2 y  0    0 cos   0 sin   0     0  cos   0  , 3 y  0    0  sin   0    0  . Components of hybrid vehicle pole linear velocity within related coordinate system are:

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(12)

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V1oy  0   z10  0  cos   0  cos   0   z20  0  sin   0  sin   0  cos   0   cos   0  sin   0     z30  0  sin   0  sin   0   cos   0  sin   0  cos   0   , V2oy  0   z10  0    cos   0  sin   0    z20  0  cos   0  cos   0   sin   0  sin   0  sin   0  (13)  z30  0  cos   0  sin   0  sin   0   sin   0  cos   0  ,

V3oy  0   z10  0  sin   0   z20  0   sin   0  cos   0   z30  0  cos   0  cos   0  . Summary. Properties of mathematical model. The matrix differential equations of 1st order are reduced directly to Cauchy form for which effective numerical integration techniques have been developed. Excess trivial equations – 1st, 5th, 13th, as well as identical condition of standardization are required to control (verify) accuracy of numerical integration. Following invariants also verify the objectives:

12y  22y  32y  4  r02  r12  r22  r32  , 2 V102 y  V202 y  V302 y  z102  z20  z302 ,

r0 r0  r1r1  r2 r2  r3r3  0 , r02  r12  r22  r32  1 .

Nonavailability of trigonometric functions in dynamic and kinematic equations allows excluding mathematical features typical for the functions in the process of numerical integration. That favours PC functioning reducing calculation period. The structure of proposed matrix equations of vehicle motion and symmetry properties of matrices being applied provide clearness of mathematical model, programmability, and efficient use of mathematical PC support improving mental activities on the whole. References [1] Gerasiuta, N.F., Novikov, A.V., Beletskaia, M.G. Flight dynamics. Key tasks of dynamic design of rockets. – Dnipropetrovsk.: M.K. Yangel State Design Office “Yuzhnoe”,1998. – 366 pp. [2] Hachaturov, A.A., Afanasiev, V.L., Vasiliev, V.S. Dynamics of “road-tire-vehicle-driver” system. – M.: “Mashinostroenie”, 1976. – 535 pp. [3] Igdalov, I.M., Kuchma, L.D., Poliakov, N.V., Sheptun, Yu.D. Rocket as a controlled object. – Dnipropetrovsk.: ART-press, 2004. – 544 pp. [4] Molchanov, I.N. Computer methods to solve applied problems. Differential equations. – K.: “Naukova dumka”, 1988. – 344 pp. [5] Moiseiev, N.N. Mathematics carries out an experiment. – M.: “Nauka”, 1979. – 244 pp. [6] Kravets, V., Kravets, T., Bas, K., Tokar, L. Mathematical model of a path and hodograph of surface transport // Transport problems. – 2014. – Pp. 830- 841. [7] Kravets, V. V., Kravets, T.V. On the nonlinear dynamics of elastically interacting asymmetric rigid bodies // Int. Appl. Mech. – 2006. – 42.#1. – Pp. 110-114. [8] Kravets, V. V., Kravets, T.V., Kharchenko, A.V. Using quaternion matrices to describe the kinematics and nonlinear dynamics of an asymmetricrigid body // Int. Appl. Mech. – 2009. – 44.#2. – Pp. 223-232. MMSE Journal. Open Access www.mmse.xyz 111

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Kinematics and Load Formulation of Engine Crank Mechanism Hailemariam Nigus1a 1 â&#x20AC;&#x201C; Federal TVET Institute, School of Mechanical Technology, Automotive Technology Department, Addis Ababa, Ethiopia a â&#x20AC;&#x201C; hailuqua@gmail.com

Keywords: kinematics, cranks mechanism

ABSTRACT. This paper presents the kinematics formulation of an internal combustion engine crank mechanism. The kinematics formulation of the crank mechanism is done using vector loop method and cosine rule are applied to describe the position of the piston. Following the velocity of piston and connecting rod is performed by differentiating the position in terms of the crank angle and connecting rod angle respectively. The acceleration equation with brief form is derived from the velocity in the same principle. Based on the kinematics, the equations of motion of crank mechanism components are formulated for each moving link and platform then, all motion parameters of each component about its crank angle are readily derived. Furthermore the 2D model is provided by using 2D Auto CAD software in order to visualize the system and mathematical algorithm solved by using software MATLAB. The forces acting on the crank mechanism and the torque applied are also formulated based on the angles of the crank and connecting rod.

1. Introduction. The Internal combustion engine is those that burn their fuel which is mixture of air and petrol from carburetor inside the cylinder or compress air only on the cylinder and injects diesel from injector nozzle. These IC engines convert the chemical energy stored in their fuel into heat energy during the power stroke of piston. The energy produced from burning of fuel is used for motion of piston; the working of a four stroke engine is based on simple slider crank mechanism. The kinematics of IC engine is not altering from simple slider crank mechanism. The kinematics formulation of the crank mechanism such as piston motion and connecting rod motion utilizes different software and methodologies for which it is suitable for manipulation The crank mechanism comprised of components like crank shaft, connecting rod and piston which changes the sudden displacement to a smooth rotary output which is the input to many devices such as pumps generators and compressors. A detailed procedure of getting stresses in the fillet area of a crank mechanism particularly crank shaft was introduced by Henry et al. [1], in which FEM and BEM (Boundary Element Method) were used. Obtained stresses were ratified by experimental results on turbocharged compression ignition engine with Ricardo type combustion chamber configuration. The crank mechanism durability assessment tool used in this study was developed by RENAULT Guagliano et al. [2] conducted a study on a marine diesel engine crankshaft and connecting rod. Payer et al. [3] developed a two-step technique to perform nonlinear transient analysis of crank mechanism combining a beam-mass model and a solid element model and Prakash et al. [4] performed stress and fatigue analysis on three example parts belonging to three different classes of engines, light automotive crankshaft was studied by Borges et al. [5]. The geometry of the crank mechanism was geometrically restricted due to limitations in the computer resources available to the authors. Shenoy and Fatemi [6] conducted dynamic analysis of loads in the connecting rod and piston components, which is in contact with the crankshaft. Dynamic analysis of the connecting rod is similar to dynamics of the crankshaft, since these components form a slide-crank mechanism and the connecting rod motion applies dynamic load on the crank-pin bearing. Shenoy and Fatemi [7] optimized the crank mechanism considering MMSE Journal. Open Access www.mmse.xyz 112

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dynamic service load on the component. It was shown that dynamic analysis is the proper basis for fatigue performance calculation and optimization of dynamically loaded components. A literature survey by Zoroufi and Fatemi [8] focused on durability performance evaluation and comparisons of forged steel and cast iron crankshafts. The piston-connecting rod-crankshaft assembly in the reciprocating piston-engines is used to transform the gas forces generated during combustion within the working cylinder into a piston stroke, which the crankshafts converts into useful torque available at the flywheel. The cyclic operation leads to unequal gas forces, and the acceleration and deceleration of the reciprocating power-transfer components generate inertia forces. The inertia force components are identified as inertial forces of the 1st, 2nd, 4th order, depending upon their rotational frequencies, relative to engine speed. In the case of multi-cylinder engines, free moments of inertia are present when all the complete crankshaft assemblyâ&#x20AC;&#x2122;s inertial forces combine to generate a force couple at the crankshaft. As a result of operating gas, inertia and centrifugal forces, crank mechanism is loaded with forces that can be calculated analytically by the expression. It is normal to talk about the average peak cylinder pressure and standard deviation of maximum pressure. This variability both cycle to cycle and cylinder to cylinder is one source of half order excitation. The gas force that acts on the piston also acts on the cylinder head. The force on the piston splits into two components, one acting down the rod and one acting sideways on the cylinder wall. The forces are reacted at the main bearing but a couple exists between the horizontal reaction at the bearing and the piston side force. This couple is equal to the crankshaft output torque, so the crankshaft torque is reacted by forces on the engine structure. 2. Kinematics of crank Mechanism. Crank mechanism comprises of piston, connecting rod and crank shaft. In formulation of the crank mechanism such as piston kinematics and connecting rod kinematics of an engine need parameters of already existing engine, the given parameters are stated in table 1 and 2. Table 1. Specification of the engine Capacity

345 cc

Number of Cylinders

Bore x Stroke

57.8 x 52mm

Compression Ratio

18:1

Maximum Torque

14.7 Nm @ 3600 rpm

Maximum Power

8.1hp @ 3600 rpm

Maximum gas pressure

25 bar

Table 2. Engine parameter Connecting rod length

113

Crank radius

Piston diameter

57.5

Stroke

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Fig. 1. Crank Mechanism From the crank mechanism depicted in figure 1 I calculate the crank mechanism equation as follows. The mean piston velocity of the four stroke engine is calculated as eq(1) given

vp 

2LN 60

(1)

where v p – mean piston velocity;

L –stroke (from TDC to BDC); N –engine speed, rpm.

2.1 Kinematic Modeling of Piston Motion. Piston is one of the main parts in the engine and its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a connecting rod. 2.1.1 Piston Instantaneous Position. The instantaneous piston position is formulated using the vector loop method from the figure 1 and 2 depicted

x  (l  r )  s ,

(2)

where s – position from crank center to piston pin center; l –connecting rod length; r – crank radius;

x – instantaneous piston position from piston pin to TDC.

As it is depicted in figure 1 we can draw the schematic diagram of crank mechanism components relationship. MMSE Journal. Open Access www.mmse.xyz 114

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Fig. 2. Relation b/n crank radius and connecting rod length and distance from piston pin axis to crank axis As in figure2 depicted above it is possible to formulate between the variables of crank mechanism.

s  l cos   r cos ,

(3)

l sin   r sin  .

(4)

From equation 4 we can rearrange in angle phi form

r sin  r , let   , therefore l l sin    sin  , 

sin  

(5)

cos   1  sin 2   1  2 sin 2  , 1

1  2 sin 2   (1  2 sin 2  ) 2 .

(6)

Equation 6 can be factorized and as the powers of lambda (  ) becomes higher and higher it approaches to null as a result:

cos   1 

(2 sin 2  ) , 2

And rearranging the equation 7 in suitable form gives MMSE Journal. Open Access www.mmse.xyz 115

(7)

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1  cos  

(2 sin 2  ) , 2

(8)

To formulate the piston instantaneous displacement in the crank mechanism we can calculate based on figure 1 as follows: s  l cos  r cos .

(9)

To be suitable in manipulating it is better to express the equation in easily estimated variable such that angle phi is very difficult to estimate so it is better to express the equation in terms of an angle theta which is the crank angle. Therefore, Substitute equation (9) in equation (2) provides:

x  (l  r )  (l cos   r cos ) .

(10)

Collect like terms to gather and gives

x  l (1  cos  )  r (1  cos ) .

(11)

Substitute equation (8) in to equation (11)

x  l (2 sin 2  / 2)  r (1  cos  ).

(12)

This is the instantaneous position of piston from piston pin center to TDC in crank mechanism. Where  – the ratio of crank radius to connecting rod length. 2.1.2 Piston Instantaneous Velocity. Having the instantaneous position of piston equation in equation (12) it is easy to drive the instantaneous velocity of the piston on the crank mechanism

vins 

dx dx d dx 2N   , dt d dt d 60

where dx –derivative of piston instantaneous position; d –derivative of crank angle;

dt –time derivative;

d 2N    –angular speed; dt 60 vins –instantaneous piston velocity. The first derivative of equation (12) with respect to crank angle in substitute to equation (13) MMSE Journal. Open Access www.mmse.xyz 116

(13)

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vins  r[sin  

 sin 2 2

(14)

]

2.1.3. Piston Instantaneous Acceleration. The instantaneous acceleration of the piston is done the same as in instantaneous velocity did.

ains 

dvins dvins d  . dt d dt

(15)

ains  r 2 [cos    cos 2 ]

where ains – instantaneous acceleration of piston. 2.1.4. Piston Pin Position. The displacement of the piston with respect to crank angle can be derived from simple trigonometry. This can then be differentiated to yield velocity and acceleration of the piston. The expressions obtained tend to be very complicated and can be simplified into the expression containing only first order (once per revolution), second order (twice per revolution), and a negligible fourth order. The piston pin position is the position from crank center to the piston pin center and can be formulated from cosine rule of the trigonometry in fig.2

l 2  r 2  s 2  2rs cos( )

(16)

From the above polynomial equation degree two we can drive the piston position as follows: (17)

s  r cos( )  l 2  r 2 sin 2 ( ) .

2.1.5 Piston Pin Velocity. Piston pin velocity is the upward velocity from crank center along cylinder bore center and can be calculated as the first derivative of equation 16 with respect to angle theta.

v  r sin( ) 

where v 

r 2 sin( ) cos( ) l 2  r 2 sin 2 ( )

(18) ,

ds – piston pin velocity. d

To express the velocity with respect to time

v

ds . d

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(19)

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2.1.6. Piston Pin Acceleration. Piston pin acceleration is the upward acceleration from crank center along cylinder bore center and can be calculated as the second derivative of equation 16 with respect to angle theta.

a  r cos  

r 2 (cos 2   sin 2  l 2  r 2 sin 2 



(r 2 ) 2 sin 2  cos 2  l 2  r 2 sin 2 

(20)

To express the acceleration with respect to time can be express as

a

d 2s 2  d 2

(21)

Fig. 3. Piston Kinematics

2.2. Kinematics Modeling of Connecting Rod Motion. The connecting rod is a major link inside of a combustion engine. It connects the piston to the crankshaft and is responsible for transferring power from the piston to the crankshaft and sending it to the transmission. Connecting rod as one component of the crank mechanism it is crucial to formulate the kinematics of connecting rod 2.2.1. Instantaneous Velocity Connecting Rod

vcon 

d d d  dt d dt

where vcon – instantaneous velocity of connecting rod. Differentiate equation (5) with respect to angle theta MMSE Journal. Open Access www.mmse.xyz 118

(22)

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d cos   , cos   1 , d cos 

(23)

vcon   cos 

(24)

2.2.2. Instantaneous Acceleration of Connecting Rod

acon 

dvcon dvcon d  , dt d dt

(25)

Differentiating equation 24 with respect to time

acon   2 sin 

(26)

3. Forces acting on the crank mechanism. Forces acting on the crank mechanisms are as follows

FG – Gas force act on the piston; FN – side thrust or normal force act on the piston pin direction;

Fr – vertical reaction force;

Ft – tangential force; Fcr – connecting rod force;

FI – inertial force.

Fig. 4. Forces Acting on Crank Mechanism MMSE Journal. Open Access www.mmse.xyz 119

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3.1. The Gas Force. Gas force is generated by the fuel combustion acting on the piston to be transferred to the crankshaft by connecting- rod through the expansion stroke: therefore during the complete cycle they depend on the crankshaft position. When multiplied by the crank radius, the gas forces produce a periodically variable torque value. In multiple cylinder engines, the torque curve of the individual cylinders are superimposed with a phase shift dependent on the numbers of cylinders, their configuration, crankshaft design and firing sequence. The resulting composite curve is characteristics of the engine design and covers a full working cycle. Harmonic analysis can lead to a “torsional harmonics” by a series of sinusoidal oscillations featuring whole-number multiples of the basic frequencies The cyclic torque fluctuation leads to a variations of the crankshaft’s rotation speed, called cyclic variation and defined as:



 max   min  min

(27)

where  – cyclic torque fluctuation. The gas force is the product of maximum pressure and area of the cylinder.

Fg  p max

B 2 4

(28)

3.1.1. Gas Torque. torque resulting from gas pressure alone is represented by the equation:

(29)

r Tg  Pg Ar sin( )[1  cos( ) l Where Tg – gas torque, Nm; Pg – gas pressure, Nm-2; A – area of top of piston, m-2. 3.2. Inertia Force. Inertia force is obtained by multiplying the piston acceleration by the reciprocating mass and acts only in the line of the cylinders. 3

r 1 r Fi  M REC r 2 [cos( )  cos(2 )  3 cos(4 )] l 4l where MREC – reciprocating mass (piston mass plus approximately 2/3 conrod mass).

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(30)

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Fig. 5. Torque Resulting from Gas pressure 3.2.1 Inertial Torque. The torque resulting from piston motion is often called the INERTIA torque and is represented by the equation:

TI  M REC r 2 2 [

r 1 3r sin   sin 2  sin 3 4l 2 4l

(31)

Torsional Excitation of Crankshaft and Engine Structure - The total torque acting on the crankshaft of the single cylinder engine results from the effect of the gas and inertia forces on the crank slider mechanism.

Fig. 6. Torque resulting from piston motion alone for a single cylinder engine

3.2.2. The total torque. Total torque is found by summing these two components.

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Note that the torque from gas pressure dominates (for the engine firing case).

Fig. 7. Total Torque 3.3. Other forces. The forces like tangential force, connecting rod force and side thrust force can be calculated as it depicted in figure 3 the relationship is:

FN  Fr tan  ,

Fcr 

Fr , cos 

(32) (33)

Ft  Fcr sin(   ) ,

(34)

  arcsin(  sin  ) .

(35)

Summary. The modeling methodology for kinematics of crank mechanism has been derived systematically by considering the geometric configuration of the internal combustion engine crank mechanism. The forces and torque applied to the crank mechanism also properly analyzed. The conclusions are drawn as follows: 1. Through consideration of the crank mechanism the position, velocity and acceleration is properly formulated. 2. The relationship between the forces and torques applied in the crank mechanism such as gas force, inertial force, side thrust force, and tangent force and connecting rod force are properly addressed. Acknowledgment I would like to express my heartiest thank to my beloved wife Lemlem Tadesse who has always supported my dreams and motivated me to achieve them. I dedicate this work to her unending love and unconditional support. References [1] Henry, J., Topolsky, J., and Abramczuk, M., 1992, “Crankshaft Durability Prediction – A New 3D Approach,” SAE Technical Paper No. 920087, Society of Automotive Engineers. MMSE Journal. Open Access www.mmse.xyz 122

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[2]Guagliano, M., Terranova, A., and Vergani, L., 1993, “Theoretical and Experimental Study of the Stress Concentration Factor in Diesel Engine Crankshafts,” Journal of Mechanical Design, Vol. 115, pp. 47-52. [3] Payar, E., Kainz, A., and Fiedler, G. A., 1995, “Fatigue Analysis of Crankshafts Using Nonlinear Transient Simulation Techniques,” SAE Technical Paper No. 950709, Society of Automotive Engineers. [4] Prakash, V., Aprameyan, K., and Shrinivasa, U., 1998, “An FEM Based Approach to Crankshaft Dynamics and Life Estimation,” SAE Technical Paper No. 980565, Society of Automotive Engineers. [5] Borges, A. C. C., Oliveira, L. C., and Neto, P. S., 2002, “Stress Distribution in a Crankshaft Crank Using a Geometrucally Restricted Finite Element Model”, SAE Technical Paper No. 2002-01-2183, Society of Automotive Engineers. [6] Shenoy, P. S. and Fatemi, A., 2006, “Dynamic analysis of loads and stresses in connecting rods,” IMechE, Journal of Mechanical Engineering Science, Vol. 220, No. 5, pp. 615-624. [7] Shenoy, P. S. and Fatemi, A., "Connecting Rod Optimization for Weight and Cost Reduction", SAE Paper No. 2005-01-0987, SAE 2005 Transactions: Journal of Materials and Manufacturing. [8] Zoroufi, M. and Fatemi, A., "A Literature Review on Durability Evaluation of Crankshafts Including Comparisons of Competing Manufacturing Processes and Cost Analysis", 26th Forging Industry Technical Conference, Chicago, IL, November 2005. [9] Xiaorong Zhou., Ganwei Cai., Zhuan Zhang. Zhongqing Cheng., 2009, “Analysis on Dynamic Characteristics of Internal Combustion Engine Crankshaft System,” International Conference on Measuring Technology and Mechatronics Automation. [10] Yadav Vinod and Mittal N.D , Design and Analysis of Piston Design for 4 Stroke Hero Bike Engine, International Journal of Engineering Innovation & Research, Vol. 2, page 148 – 150 , 2013. [11] Anusha B and Reddy C.Vijaya Bhaskar, Modeling and Analysis of Two Wheeler Connecting Rod by Using Ansys , Journal of Mechanical and Civil Engineering, Vol.6, Page 83-87, May. - Jun. 2013. [12] Norton R.L., Kinematics and Dynamics of Machinery, Tata McGraw Hill Education (P) Ltd., New Delhi, 2012.

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Safe Simulation Of the Manipulator In the Presence Of Static and Dynamic Obstacles by Using Fuzzy System Ali Davoodalhosseini1a, Saeed Behbahani1 1 - Ph.D., Assistant Professor, School of Mechanical Engineering, Isfahan University of Technology, IRAN a - ali_davoodalhoseini@yahoo.com

Keywords: path planning, manipulator, fuzzy controller, safe, Simulink, danger index.

ABSTRACT. Safe path planning is a necessary matter in human-robot interactions. This paper presents intelligent and safe path planning of the manipulator on a basis of the fuzzy system. This means that necessary commands for steering manipulator from departure to the destination are provided by the fuzzy controller. The fuzzy controller is a kind of controller that inspired by human decision on a basis of awareness and experience to steer the desired system. In this research, considered manipulator is located among the humans and static and dynamic obstacles. It should perform any state changing safely, in order to preserve health and tranquility of humans that work near the robot and also should avoid collision with obstacles. For this purpose, the velocity of changing of robot angle shouldn't exceed allowance. For achieving this goal, four factors are considered. These factors are known as a danger indexes including distance between human and robot, the velocity of the two links, human head orientation and changing face state. in the past researches,the researchers have not considered these danger factors in designing the manipulators. For monitoring these factors, the robot should be equipped with the different sensors. The proposed issue was simulated in Simulink environment in Matlab. Results show that the robot can avoid collision with the obstacles and arrives safely to a desirable position with the little acceptable error.

Introduction. In most existing work in autonomous navigation, a solution is attempted by separating the planning and control into two sequential stages. This may have some adverse effects. Robot motion planning with artificial potential field considers the problems of motion planning and control simultaneously. But in this research we don’t make ourselves involved in kinetic problems, i.e., the commands that our controller generates are the angle, not the momentum. Several autonomous systems have been developed using rule-based methods to control the motion of robot manipulator. Tsoukalas et al. [1] presented a neuro-fuzzy methodology for a robot to navigate in the dynamic environment. Ding and Li [2] solved the problem of obstacle avoidance for a redundant manipualator by using a fuzzy logic system. Mbede et al. [3] also designed neuro-fuzzy system in order to consider structured and unstructured uncertainity. Their robot can adapt itself by using neural network online learning. In aforementioned researches, no safety cases have been considered. Robots have been successfully employed in industrial settings to improve productivity and perform dangerous or monotonous tasks. Recently, research has focused on the potential for using robots to aid humans outside the strictly “industrial” environment, in medical, office or home settings. To this end, robots are being designed to perform homecare daily living tasks such as co-operative load carrying [4,5] and feeding [6] and to provide social interaction [7,8]. As robots move from isolated work cells to more unstructured and interactive environments, they will need to become better at acquiring and interpreting information about their environment [9]. One of the critical issues hampering the entry of robots into unstructured environments populated by humans is safety [10,11,12]. In particular, when the tasks of the interaction include manipulation tasks, such as picking up and carrying items [13] assisting with dressing, opening and closing doors, etc., large, powerful robots will be required. Such robots (e.g., articulated robots) must be able to interact with humans in a safe and friendly manner while performing their tasks. Industrial safety standards (RIA/ANSI [14]) focus on ensuring safety by isolating the robot away from humans, and are, therefore, not directly applicable to humanrobot interaction applications. However, industrial experience has shown that eliminating hazards MMSE Journal. Open Access www.mmse.xyz 124

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through the mechanical design is often the most effective safety strategy. This approach has also been applied to interactive robots, for example, by applying a whole-body robot viscoelastic covering [15]. In order to prevent collisions, safeguarding type controllers execute a safety strategy if a person is detected within the work envelope of the robot. If a human is detected in the safeguarded zone, the default robot control sequence is altered to ensure the safety of the human [15,16]. These methods consider a fixed distance around the robot as the safeguarded zone, at which point the reactive controller performs a safety action. A more sophisticated approach is to develop a dynamically sized safeguarded zone, based on an implicit or explicit evaluation of the current danger, namely, a danger index. For example, Traver et al. [17] propose two human-friendly robotic designs. The â&#x20AC;&#x153;elusive robotâ&#x20AC;? uses the distance between the robot and the human as the danger index. The â&#x20AC;&#x153;ergonomic robotâ&#x20AC;? computes a danger factor based on the robotâ&#x20AC;&#x2122;s velocity and posture, the humanâ&#x20AC;&#x2122;s direction of motion and eye gaze, and the rate of change of the distance between the robot and the human. The â&#x20AC;&#x153;ergonomic robotâ&#x20AC;? is controlled to reduce the calculated danger index. Ikuta and Nokata [18] developed a danger evaluation method using the potential impact force as an evaluation measure. In their work, the danger index is defined as a product of factors that affect the potential impact force between the robot and the human, such as relative distance, relative velocity, robot inertia and robot stiffness. Several design examples are presented, but no control-based implementation of the danger index was presented. Both safeguarding and danger evaluation approaches propose that robot behavior is modified based on the human location and motion during human-robot interaction. The safeguarding approaches define discrete behaviors while the danger evaluation methods generate a continuum of behavior. Croft et al. [19] introduced three types of danger including long term, medium term and short term danger. After that, they investigated the effect of each one, separately. They proved the effectiveness of their new danger index by experiment. 1. Robot dynamics. The equation of the dynamic of a manipulator robot is given by the equation (1): M(q) đ?&#x2018;&#x17E;Ě&#x2C6; + C(q, đ?&#x2018;&#x17E;Ě&#x2021; ) đ?&#x2018;&#x17E;Ě&#x2021; + G(q) + F(đ?&#x2018;&#x17E;Ě&#x2021; ) + Ď&#x201E;d = Ď&#x201E;

(1)

Fig. 1. Manipulator

q, and consecutively represent the angle, angular speed and angular acceleration. M is the inertia matrix, C is the Coriolis matrix, G is the gravitational acceleration vector and F represents the friction term. Ď&#x201E; is the joint torque and Ď&#x201E;d represents any disturbances or torque that is caused by a dynamic which is not modeled. 2. Robot model . There are two methods to simulate a robot in Matlabâ&#x20AC;&#x2122;s Simulink environment; one method is to use the equations of motion for a robot, and the other is to simulate the robot in the Simmechanic environment. In this study, the second method is used. MMSE Journal. Open Access www.mmse.xyz 125

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As such the input for the links can be kinematic variables as well as torques. In this study, we used the kinematic variables as inputs. To simulate the servo motor we used a transfer function to create the delay. The function is as follows;

G(s)=

(2)

đ?&#x2018;&#x2020; 2 +3S+3

This transfer function causes the input angle to slowly adjust to the desired value, and also the input angle will have a settling time and maximum overshoot. In practice, the motor in charge of providing the torque cannot supply the input torque instantaneously. The properties of the robot are given in the table below. Table 1. Properties of robot Property

Links Link 1

Link 2

Length(m)

1.3

Mass(kg)

1.09

1.12

Inertia(kg*m^2)

0.0908

0.1577

3. Danger index. Danger index specifies the current level of danger when interacting with the environment and it is used when the robot has to correct its performance. Analyzing typical collisions of robots in industry shows that most accidents occur when the operator is not aware of the movements of the robot. Therefore when the operatorâ&#x20AC;&#x2122;s line of sight is not in the direction of the robot and he is not able to see the robotâ&#x20AC;&#x2122;s movements the danger index should increase. Two indexes are used for this problem, head rotation angle, and operatorâ&#x20AC;&#x2122;s face gesture. The equation used for head rotation is a sigmoid function based on the horizontal rotation of the head. The rotation angle zero indicates that the operator is looking at the robot. The sigmoid function was used to ensure the gradual adjustment of this function. Also the changes in the function when the head rotation angle is between the angles of -15 and +15 degrees, doesnâ&#x20AC;&#x2122;t have a big effect on the function. Furthermore; when the rotation angle of the head is between 60 and 90 degrees the value of the function must be at its maximum because the robot is hardly visible at this degree. The change in the values of the function between the angles of 60 and 90 degrees must be very fast.

KOR = 1 +

MoR 1+eâ&#x2C6;&#x2019;SoR(Î¸hâ&#x2C6;&#x2019;Î¸c)

(3)

Kor is the head orientation scaling factor Mor is the maximum increase in scaling due to the orientation Ř&#x152;Sor controls the slope of the sigmoid function, Î¸h is the horizontal head orientation and Î¸c is the rotation of the head at the midpoint of the sigmoid. Mor =2 , Sor=0.2 , Î¸c =30 Similarly, a sigmoid function was used for the affective state.

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The excitation of the face has a direct relationship with an individual’s anxiety and excitement. A sigmoid function is used so that it can filter the low excitation gestures, since estimating the excitation of the face is approximate.

KAS = 1 +

Mas 1+e−Sas(a−ac)

(4)

Kas is the affective state scaling factor ، Mas is the maximum increase in scaling due to the affective state، Sas controls the slope of the affective state sigmoid function, ac is the midpoint of the arousal scale. Mas =2 , Sas=0.2 , ac=0.5 For each link, the closest point to the operator is called the critical point. Danger index is calculated for each critical point, this function also includes the distance between the robot and operator at a critical point. The distance coefficient is calculated by the following equation. 1

FD(s) = KD ( s −

1 Dmax

for S ≤ Dmax

(5)

It is clear that if S ≥ Dmax , FD(s) equals to zero. S is the critical distance with the closest person. The constant KD is used to increase this coefficient. When the distance between the critical point and the closest person is greater than the specified value Dmax , the value of the function is zero. When this distance is at its minimum the value of the function is one. The value of more than one indicates unsafe conditions [19]. The other index is the speed index. If the speed exceeds a certain value (15 degrees per second), as the output of index, the value of speed will be multiplied by 0.1. By multiplying the 4 factors and multiplying the resulted value by 0.01, the total danger index is calculated. This value will be reduced from the input torque. Depending on the level of safety which is needed the coefficient 0.01 is variable. 4. Different types of obstacles and their simulation. In this study two types of obstacles are used, dynamic and static. In practice, robot is equipped with several sensors which automatically send the distance to nearest obstacle to the control system in order to avoid hitting them. Sensors can also detect whether the obstacle is approaching or the robot has passed the obstacle and is getting further away. However in the present study no tests were done and there was no actual robot involved. Therefore the distance between the two points of robot’s links and different obstacles are calculated at each instance using mathematical equations, and the nearest distance is used as the input for control system. The both ends of robot’s links are the point that we tried to prevent from hitting any obstacles in the simulation. However because this assumption may cause other parts of the link to hit obstacles, the minimum allowed distance specified is about 0.5 meter. Also in this study, we differentiated between moving close short distance and moving away a short distance, considering the situation in which the distance is close, but the obstacle is moving away from the robot. In such situation, the distance between the obstacle and robot should not affect the control system’s decision. To nullify the effect of this situation we specified a large value for the distance (4.9 meters).To simulate obstacles ramp function was used. To accomplish this, a point which is moving away from the departure zero point is placed on the robot’s links movement path. 5. Control structure. Two fuzzy controllers with a slight difference were used for two links. Designed fuzzy controller includes two inputs and one output. First input is an error of angle (needed MMSE Journal. Open Access www.mmse.xyz 127

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angle to reach to the desired angle) and the second input is the distance to obstacles. Also, Output of the controller is the angle. The desired angle for the first link is 120 degrees and the desired angle for the second link is -60 degrees. Properties of inputs and output and table of rules are shown consecutively in table 2 and 3. 5.1. Fuzzification. The angle error e is partitioned into nine fuzzy sets: right very very big (R2VB), right very big (RVB), right big (RB), right (R), zero (Z), left (L), left big (LB), left very big (LVB), and left very very big (L2VB). Its fuzzy membership functions are symmetric and shown in Figure 3(a). The distance to obstacle d is partitioned into six fuzzy sets: VVnear, Vnear, near, good, far, Vfar. Its fuzzy membership functions are shown in Figure 3(b). The output angle θ is partitioned into eleven fuzzy sets: right very very big (R2VB), right very big (RVB), right big (RB), right (R), right small (RS), zero (Z), left (L), left small (LS), left big (LB), left very big (LVB), and left very very big (L2VB). Its fuzzy membership functions are symmetric and shown in Figure 3(c). 5.2. Rule Base. The rule base is generalized as follows: Ri: if e(k) is µ1i (e(k)) and … and e(k-n+1) is µni (e(k-n+1)) and d(k) is µ1i (d(k)) and … …and d(k-m+1) is µmi (e(k-m+1)) Then Fi(k+1) is ri. where Ri ( i =1, 2, … , i) denotes the ith implication, l is the number of fuzzy rules, ri is the output from the ith implication, n is the number of input variable e, and m is the number of input variable d. Our fifty four rule bases are arranged into a look-up table and shown in Table 3. The two inputs µ(d) and µ(e) represent the fuzzy sets, which indicate the distance between robot and obstacle, and the position error, respectively. The outputs of the base are Fj which describe the angle output. For example, the rule 1 is: R1: If d is VVnear and e is R2VB Then Fi is LB

Fig. 2. Control structure

Figure 2 shows the structure of the control in the Simulink environment. MMSE Journal. Open Access www.mmse.xyz 128

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Table 2. Properties of inputs and the output of the Fuzzy controller Parameter

Range

Number of membership functions

Membership functions

Input-angle error (e)

-180-180

R2VB-RVB-RB-R-Z-L-LB-LVBL2VB

Input-distance to obstacle (d)

0-5

Collision-Vnear-near-good-far-Vfar

Outputangle(θ)

-180-180

RVVB-RVB-RB-RS-RVS-Z-LVSLS-LB-LVB-LVVB

Table 3. Rules of the Fuzzy controller e /d

VVnear

Vnear

near

good

far

Vfar

R2VB

RSV

RVB

RSV

RVS

LSV

LVS

LSV

LVB

LSV

L2VB

LSV

LVB

First row and first column consecutively determine membership function of d (distance to obstacle) and e (error of angle). Other cells determine output of fuzzy system.

(a)

(b)

(c)

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Fig. 3. Membership function plot for inputs and output,(a) – input-e, (b) – input-d, (c) – output-θ 6. Results and graphs. Time Series Plot:

Time Series Plot: 200

150

-20 100

-40

data

50 0

-60

-50

-80 -100

-100 -150 -200

-120

Time (seconds)

(a)

(b)

Fig. 4. Angle of the links (Degree Vs. Second) (a)-First link, (b)-Second link

Time Series Plot:

Time Series Plot: 160

140

-10

-20

data

100

data

120

-30

-40

-50

-60

-20

-70

-40

-80

Time (seconds)

(a)

(b)

Fig. 5. Velocity of the links (Degree/S Vs. Second) (a)-First link, (b)-Second link

Time Series Plot:

Time Series Plot: 5

4.5

3.5

3.5 3

data

2.5

2.5 2

1.5

0.5

Time (seconds)

(a)

(b)

Fig. 6. Distance between links and obstacles (Meter Vs. Second), (a)-First link, (b)-Second link As it can be seen in the diagrams, both of the links’ distances with obstacles are greater than the specified value (0.5 meters) and no accident occurred. Parts of the diagram which are fixed on 4.9 meters are points in which the distance between links and obstacles are more than 4.9 meters, but the fuzzy controller input send the value of 4.9; which is a relatively large distance; to the fuzzy controller MMSE Journal. Open Access www.mmse.xyz 130

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input. Because the values greater than 4.9 are outside of the range specified for this study. The number 1 and 2 links reach their specific angles in approximately 5 seconds that suggests robotâ&#x20AC;&#x2122;s high speed. Although the link number 1 has a 5 degrees error margin. Time Series Plot: 10

Time Series Plot: 4

9 3.8

8 3.6

7 3.4

data

3.2 3

5 4

2.8

2.6 2.4

2.2

0 0

Time (seconds)

(a)

(b)

Time Series Plot:

8 7 6

data

5 4 3

2 1

Time (seconds)

(c)

(d)

Fig. 7. Danger indexs, (a)-Head orientation and Affective state, (b)-Human closing, (c)-Velocity of link1, (d)- Velocity of link2 Because at each instance one of the danger indexes is zero the total danger index is always zero which means that the individuals in the vicinity of the robot are not in danger. Summary. In this study, a manipulator robot is simulated using a fuzzy system. Also, dynamic and static obstacles were modeled. Furthermore to consider safety measures four different factors were considered as danger indexes which multiplying these four factors together and by 0.01 gives the total danger index. The results show that the robot while avoiding static and dynamic obstacles reaches its desired angle with proper speed and low error margin. After about 5 seconds the link number one reaches the 125 degrees angle. Despite the fact that the desired angle for link number one was 120 degrees. Link number 2 reaches the desired angle although it has a slight oscillation at -60 degrees. Results show that the amplitude of the oscillation is reduced over time.Therefor, fuzzy system can be recommended in order to control the path of a robot. For future works, it is recommended to use a neural network in order to overcome uncertainity and also consider some conditions like using damping term to neutralize oscillation near desirable position. References [1] Tsoukalas, L. H., Houstis, E. N., & Jones, G. V. (1997). Neurofuzzy motion planners for intelligent robots. Journal of Intelligent and Robotic Systems,19(3), 339-356. MMSE Journal. Open Access www.mmse.xyz 131

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[2] Ding, H., & Li, H. X. (1999). Fuzzy avoidance control strategy for redundant manipulators. Engineering Applications of Artificial Intelligence, 12(4), 513-521. [3] Mbede, J. B., Ele, P., & Xinhan, H. (2002). Neuro-Fuzzy Dynamic Obstacle Avoidance for Autonomous Robot Manipulators. JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, 45(1), 286-297. [4] Arai, H., Takubo, T., Hayashibara, Y., & Tanie, K. (2000). Human-robot cooperative manipulation using a virtual nonholonomic constraint. In Robotics and Automation, 2000. Proceedings. ICRA'00. IEEE International Conference on (Vol. 4, pp. 4063-4069). IEEE. [5] Fernandez, V., Balaguer, C., Blanco, D., & Salichs, M. A. (2001). Active human-mobile manipulator cooperation through intention recognition. InRobotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on (Vol. 3, pp. 2668-2673). IEEE. [6] Guglielmelli, E., Dario, P., Laschi, C., Fontanelli, R., Susani, M., Verbeeck, P., & Gabus, J. C. (1996, November). Humans and technologies at home: from friendly appliances to robotic interfaces. In Robot and Human Communication, 1996., 5th IEEE International Workshop on (pp. 71-79). IEEE. [7] Breazeal, C. (2001). Socially intelligent robots: research, development, and applications. In Systems, Man, and Cybernetics, 2001 IEEE International Conference on (Vol. 4, pp. 2121-2126). IEEE. [8] Wada, Kazuyoshi, et al. "Effects of robot-assisted activity for elderly people and nurses at a day service center." Proceedings of the IEEE 92.11 (2004): 1780-1788. [9] Pentland, A. (2000). Perceptual user interfaces: perceptual intelligence.Communications of the ACM, 43(3), 35-44. [10] Corke, P. I. (1999). Safety of advanced robots in human environments.Discussion paper for IARP. [11] Heinzmann, J., & Zelinsky, A. (2003). Quantitative safety guarantees for physical human-robot interaction. The International Journal of Robotics Research, 22(7-8), 479-504. [12] Ikuta, K., Ishii, H., & Nokata, M. (2003). Safety evaluation method of design and control for human-care robots. The International Journal of Robotics Research, 22(5), 281-297. [13] Kosuge, K., & Hirata, Y. (2004, August). Human-robot interaction. In Robotics and Biomimetics, 2004. ROBIO 2004. IEEE International Conference on (pp. 8-11). IEEE. [14] RIA/ANSI 1999. RIA/ANSI R15.06—1999 American National Standard for Industrial Robots and Robot Systems—Safety Requirements. American National Standards Institute. New York. [15] Yamada, Y., Hirasawa, Y., Huang, S., Umetani, Y., & Suita, K. (1997). Human-robot contact in the safeguarding space. Mechatronics, IEEE/ASME Transactions on, 2(4), 230-236. [16] Zurada, J., Wright, A. L., & Graham, J. H. (2001). A neuro-fuzzy approach for robot system safety. Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, 31(1), 49-64. [17] Traver, V. J., & Perez-Francisco, M. (2000). Making service robots human-safe. In Intelligent Robots and Systems, 2000.(IROS 2000). Proceedings. 2000 IEEE/RSJ International Conference on (Vol. 1, pp. 696-701). IEEE. [18] Ikuta, K., Ishii, H., & Nokata, M. (2003). Safety evaluation method of design and control for human-care robots. The International Journal of Robotics Research, 22(5), 281-297. [19] Kulić, D., & Croft, E. (2007). Pre-collision safety strategies for human-robot interaction. Autonomous Robots, 22(2), 149-164.

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III. Machine Building Feasible Ways To Improve The Durability Of The Pumps’ Parts Operating With Hydroabrasive Mixtures S. Patsera1a ,V. Protsiv2b V. Kosmin3 1 – candidate of technical sciences, associate Professor at the Technology of Mining Machinery Department, National mining University, Dnipropetrovsk, Ukraine 2 – doctor of technical sciences, Professor of the Machinery Design Fundamentals Department, National mining University, Dnipropetrovsk, Ukraine 3 – lecturer, National Mining University, Dnepropetrovsk, Ukraine a – bwitiw@rambler.ru b – protsiv@ukr.net

Keywords: pump, water jet mixture, wear resistance, abrasive, pumping equipment, lifetime. ABSTRACT. The analysis of insufficient wear resistance of the pumps’ parts, which operate with hydroabrasive mixtures, is provided. The ways to improve the wear resistance of the pumps’ wet ends by the usage of the stamped units instead of the molded and carbon fiber composite materials are observed.

Introduction. The problem of pumping equipment lifetime, primarily pulp pumps, for the mining industry remains complex issue. Pulp pumps operate with medium and high abrasive materials and mounted in technological lines of crushing after the mills first and second grinding steps, exposed by high-pressure transportation of concentrates and tailings of concentrating mill, etc [1]. Analysis of the reasons for the insufficient wear resistance of the pumps parts for hydroabrasive mixes and the methods used to improve it to develop new design and technological solutions in this area. Present engineering companies offer a wide range of pumping equipment, including [1]: • pumps GrA, GrU, GrT, produced by Bobruisk Machine-Building Plant (Russia), which used for pumping abrasive slurries with density up to 1600 kg/m3, temperature up to 70 ° C, solids inclusion’s size of up to 25 mm and a volume concentration of 30 %; • pumps WARMAN, produced by Weir Group. The range of operating conditions of these pumps is quiet wide. For example, model AH is used to dedicate for severe conditions of operation and has the dimensions of the suction and discharge ports 20 and 18 inches, respectively; • pumps produced by Metso Minerals: from a large variety of slurry pumps Metso Minerals pumps X used in severe conditions of operation and pumps H and M for medium and light severe conditions of operation; • pumps produced by American company Krebs; which distinctive feature is a new patented design suction part of the pump, significantly declines the internal recycling within the flow of the pump; • pumps produced by company GIW has a wide range of applications and marked LCC, LCV, LSA, LSR, MEGA, WBC. MMSE Journal. Open Access www.mmse.xyz 133

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In addition, there are some pumps produced by other campaigns, such as Habermann, Zulser, Ahlstrom, Flygt, Ritz, Damen Dredging, Flowserve [1]. Despite the fact that the developers and manufacturers of pumps constantly working on improving the durability of the pumps, the problem does not become less relevant. On the fig. 1 the worn wheel is depicted. The productivity of the wheel is 5000 m 3/h (outer wheel diameter 1260 mm).

(a)

(b)

Fig. 1. The worn pump wheel. a) dimensional view; b) the view from flow channel The wheel has been working for 3 months at one of the Ukrainian mining and processing plant. The extreme worn appeared in the area of outer diameter. The chemical composition of the wheelâ&#x20AC;&#x2122;s material is the following: carbon (> 3%), chromium (> 33%) and nickel (> 3%). On the fig. 2 the picture of the worn pump wheel WARMAN with productivity 4000 m3/h with significant abrasive wear is provided. As noted in [2, 3], the main factors determining the loss of performance are: 1. Hydroabrasive wear of the flowing pumps parts, which makes the volume losses and increase vibration, which leads to rotor imbalance and performance reduction. 2. Corrosion wears on pump components due to water influence. 3. Cavitation wear leads to steep increase of vibration and the destruction of the flowing pumps parts. 4. The main measures to increase the wear resistance of the flowing pumps parts, which using known developers, are shown in Table 1.

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Fig. 2. The worn wheel disk of the WARMAN pump The WARMAN research in the field of ensuring wear resistance are most indicative [2]. Noted, that various materials applied by production of pumps behave at abrasive wear differently. Wear resistance of white cast iron depends on two main components of their structure: carbide and matrix. Usually the matrix (as a rule, martensite with austenite inclusions) collapses with greater speed, than carbides. Process of wear begins with emergence of microsinks between carbide and a matrix. Formation of sinks is a result of separation of a matrix from carbide, which occurs at the time of blow of a particle. As particles continue to influence a surface, microsinks extend and unite. Less strong matrix collapses the first. Later the combination of the unprotected and not fastened with a matrix carbides and existence of microcracks leads to gradual removal (washout) of carbides. Process of wear of rubber is usually followed by lengthening of material in a point of contact with a particle with the subsequent stretching and deformation of other material in a ledge. Consecutive collisions of particles with a surface of ceramics lead to emergence of cracks and their distribution in the course of work. Parts of ceramics are broken, fatigue deformation collects in process of deepening of cracks. The gradual destruction happens. At the moments of powerful collisions there can be deep cracks and occur a material break. The mechanism of removal the particles of material from ceramics depends on its composition and an internal microstructure and is specific to different types of ceramics. Wear of surfaces can be uniform (with smooth or rough polishing), quasiuniform (a wavy surface) or local (local flutes or dot erosion) [2]. WARMAN makes experiments at the special stand for detection of influence of geometry of parts on wear in various details of the pump. The main direction of this experimental work is development of mathematical methods of forecasting of specific types of wear.

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Table 1. The main measures to increase the wear resistance of the flowing pumps parts, which using their developers Trade-mark or pump brand GrA, GraU, GrT by Bobruisk MachineBuilding Plant

Design and technological solutions The running pumps parts can be made of super-hard alloys, the abrasive material on the organic binder, rubber and polyurethane [1]. The types of XR, XM, HR, HM, MR and MM have a rubber lining and a metal inner surface of the case.

Metso Minerals

Standard wear parts are made of natural rubber (Elastaslayd et al.) or carbide (Metahrom, Metahard, Metalsayz et al.), as well as synthetic rubbers [1]. New patented design of the suction area of the pump greatly decreases the internal recycling within the flow of the pump.

Krebs

LCC-M by GIW

Habermann

The pump mill Max by Krebs has a cast metal case and a metal impeller, the pump Max has a rubber lined case and a metal impeller [1]. A metal details are made of high-chromium alloys, which received the name Krebs alloy, a rubber details are made of natural rubber. The pumps LCC-M have monohull design and high strength material Gasite used for wear parts. The pumps LCC-R have a rubber lining and force-pipe sizes up to 12 inches, flow rates up to 2260 m3 / h and heads up to 45 m of water column. Impellers can be manufacturing of polyurethane [1]. The pumps NP and NPK are intended for pumping abrasive slurries and sand particles, KB и КВР are intended for pumping large, including gravel particles over 100 millimeters. Material HBN450VG is used for production metal components of these pumps and has 650 units Brielle hardness [1]. The worn-out parts made from solid high-chromium alloys (for example, Hyperchrome® A61 and Ultrachrome® AS1) так and from various cast elastomers.

WARMAN

Along with improvements of a hydraulic design work on improvement of properties of materials of the worn-out details is continued. The pumps with a metal internal surface and natural rubber lining was gained the greatest distribution, but examples of use of polyurethane, synthetic rubber and ceramics are known. Material of the metal worn-out details usually consists of an alloy of iron and carbon with the high content of chrome (ranging from 23 to 30%) and various alloying additives. Vacuum casting is used for production of similar materials. As a result the declared hardness sizes reach 750 Brinell and more. Natural rubber lining is less strong, but is more elastic [1, 2].

Summary. The companies making the pump equipment offer the modern enterprises rather wide choice of pumps with various technical characteristics and wear resistance of details. MMSE Journal. Open Access www.mmse.xyz 136

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But it is impossible to claim that all reserves of increase of wear resistance of flowing part of slurry pumps are used. It is possible to refer replacement of cast designs of bladed wheels of pumps by combined designs consisting, for example, of stamped elements, of details of the alloyed rolled metal with a high superficial hardness. The use of composite materials on a basis carbon - carbon components which are widely applied in designs of flowing part snuffled the solid propellant rocket engines which are exposed to intensive erosive influence is perspective [5]. The offered directions of increase of wear resistance of flowing part of pumps will demand certainly carrying out research and developmental works. References [1] Kondrashov V.I. Review of pulp pumps. URL: http://library.stroit.ru/articles/pulpnas/index.html. [2] Fedoseev A.Ju. WARMAN research of the pumps. Mining industry: scientific-technical journal. – 1999. – № 2. URL: http://www.mining-media.ru/ru/article/newtech/2021-issledovaniya-warman-voblasti-shlamovykh-nasosov.htm [3] Aliev N.A. Development of the scientific basis for mining pump with extended life-time. PhD thesis mining machines  Donetsk. Scientific-research of mining mechanics named after MM. Fedorov, 2006  375 P. [4] C. Walker, K. Burgess, K. Dolman, A. Roudnev (2009) Wear in slurry pumps. / Minerals Technical Bulletin Bulletin #9 Version 2. URL: http://www.weirminerals.com/PDF/Technical%20Bulletin%209%20v.2.%20-%20082109.pdf [5] Fahrutdinov I.Kh. Design of solid fuel jet engines – Moscow: Mashinistroenije, 1987. – 328 P.

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IX. Economics & Management On Relations Between Dump Truck Efficiency and Service Facilities Structure Savchenko A.A.1, Zubariev M.S.1,a 1 – National Mining University, Department of Automobile Economy, Dnepropetrovsk, Ukraine a – mykola.zubariev@gmail.com

Keywords: production facility, dump truck, open-pit, mine, zero mileage, dump truck productivity

ABSTRACT. The analysis of dump truck fleet of the open-pit mine, which possesses industrial real estates for technical maintenance and other operations, is provided. Several exploitation indexes are defined and analyzed subject to the corresponding mine. Basing on the provided analysis, factors and conditions, which define the production facility structure, are described. A list of production facility structures is provided. The influence of production facility structure on dump truck productivity is observed. Also some relations between zero mileage and mine areas for different hauling distances are provided.

Introduction. Increasing the quarry depth the haulage distance from the mining area to fleet department growths either. This affects the early wear of all aggregates, parts, tires and fuel consumption while unproductive range. Analysis of the structure of industrial dump trucks’ fleet will help to reduce non-productive range. The production base is one of the objects of transport subsystem. Organizational changes in this object affect the subsystem (career transport) and system of mining and processing plants (MPP). The main study. The production facility has an extensive career vehicle structure. The main elements of the production base are industrial buildings and structures for the technical service. The enterprise facilities include parking, roads, driveways and etc. In the parking regime executed operation, storage of cars waiting for service maintenance (TO), repair (TR) and departure. Service facilities for TO, TR located in a building with an adjacent production areas for the production and restoration parts, dump sites and warehouses. As a rule, buildings are designed for one model of dump trucks. A multy make fleet leads to remodeling or building new service station. Mines of Krivoy Rog (Ukraine) designed for the production base with 12 dump trucks with carrying capacity 25 t. The classical scheme involves placing the entire complex of buildings on the same production site. On receipt of dump trucks with careening capacity 27 ... 40 tons the facilities can be redesigned. Thus, all buildings, structures can not be used in the process of technical operation, and then develop a position in which the area is occupied unnecessarily production base of dump trucks and the cost of its maintenance are significantly increases. Placed in abandoned industrial site, industrial base of dump trucks usually created for the entire open pit. In this regard, specific indicators of utilization of production databases are quite high. Production MMSE Journal. Open Access www.mmse.xyz 138

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area per one ton of the average car, is an average of 16 m2. Cost of buildings per one ton of the average auto-ranges from 469 to 888 y.u, costs Garage-machining equipment have reached 150 y.u. However, the relationship indicators of dump trucks utilization and indicators characterizing the level of development of the production base, is not visible. For example, in Poltava Mining production area per one average auto-ton (16 m2), the cost of buildings and facilities (888 units.) â&#x20AC;&#x201C; the highest of these figures consider a career. However, the coefficient of technical readiness of the CTG are lower in comparison with the coefficient on Ternovskaya quarry Northern Mining, specific production area of 13 m2, and the present value of buildings and structures - 603 y. u on Ingulets GOK specific production area of 16 m2, and the present value of buildings and structures - 465 y. u. One of the reasons for this discrepancy is the structure and parameters of production bases operating conditions career vehicles. As already mentioned, vehicle production base of career, as a rule, is not transferred to the zone of operation of vehicles. This increases the distance from the work area to dump the respective production unit (workshop, storage sites, filling stations and so on. D.). Each year, this distance is increased by 10%. Wherein the move is 30 ... 40 minutes. Delivery time faulty dump out of the zone for the production base is increased in 5 ... 6 times. The time spent on travel serviceable dump trucks and dump trucks from delivering faulty work zone at the industrial site quarry vehicles are 10 ... 15% of the time they work. It is characteristic that the higher utilization of the park, the more time spent on the zero runs. High costs reduce the travel time ratio of run and thus have an impact on the entire economy of operation of technological transport. The structure of the production base of vehicles defined by the following factors and conditions: - Fleet structure and dump characteristic of technical influences regimes. - The number of quarries, which provides transportation of mine rock, dump motor unit mining enterprise, the distance between them, the distribution of traffic volumes of the rock mass in the zones. - Shape and size of the quarries, the direction of development of mining operations, characteristic of areas of work vehicles, the number of road driveways. - Distance from the existing production base to car driveways in operation deposits of minerals or the distance from the construction site established manufacturing base vehicle, based on the situational plan of the industrial site, to car driveways during the development of the deposit [5]. Road transport is represented by three models of class-duty dump trucks and used as the assembly of transport on the depth of the quarry, and the main - for the transport of loose overburden external dumps. Taking intoaccount the design features of the dump trucks, the technical effects of various models technologically aligned, thus there is a possibility of specialization of production units for technical influences. The production base is located at a distance l from the beginning of the automotive driveways. This may be the case following options for the structure of production base: 1. On the pit formed units to perform certain types of technical effects (TE) and mode of operations. 2. In addition, formed as production unit in the depth of the pit. 3. Production units are formed in each work area and dump pit. Each production unit consists of buildings and specialized equipment for performing certain types of TE and regime operations. Universal characteristics of the production units is a parametric measure of the volume of work performed on TE at a time. For example, the daily amount of the daily service (DS), then minor running repairs and so on. MMSE Journal. Open Access www.mmse.xyz 139

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Consider the effect of parameters and structure of production bases for the use of trucks. In general, the influence of the parameters and the structure of production bases will be expressed in terms of distance from the production base of up-front work. In general, the mileage per shift dump written by [2].

Ltot 



j 1

A  l j



(1)

 lнj ,

where j = 1, m – the routes number; le – productive range of a dump truck on j-th route, km; lн – zero mileage of a dump truck per shift on the j-th route, km; Aj – dump truck amount on the j-th route per shift.

le  l гр  l x ,

(2)

where lгр – dump truck haulage range per shift, km; lx – inefficient dump truck range per shift, km. For dump truck le can be defined as:

le  lег  nег  nег  1 ,

(3)

where leг – average loaded range, km; neг – the number of haulages.

lн  l01  l02 ,

(4)

where l01 – zero mileage of a dump truck between fleet facilities and mine, km; l02 – zero mileage between loading area and fleet facilities, km. Zero mileage determined by the distance between the production units of motor transport, slaughter and transfer points in the area of career fields. The total range of the dump truck will be equal to Ltot per year:

Ltot  Dw  nсм 



j 1

A  l j



 lнj ,

where Dw – amount of working days; ncм – shift coefficient. For that options the total zero mileage range will be calculated by the following relations:

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(5)

Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

– For the current conditions, when the production base is located at the distance l01 from the beginning of the route

Lн  Dw  nсм 



j 1

A  l j



 dl j  l2 j  2l01 ,

(6)

where l1j – zero mileage between road and mine face, km; (7)

dl   l  l  t эк  1 , t

l – average mine road growth while mining operations, km; tэк – mine exploitation life-time; l2j – zero mileage between dump area and open-pit route, km. Industrial facility is situated in the open-pit, where all kind of service can be provided:

Lн  Dw  nсм 



j 1

A  l j

01 j



 dl j  l02 j 

 NTO  NTP   2l02

(8) ,

where l01j – zero mileage from service facility to mine, km; l02j – zero mileage from dump area to service point, km; l02 – zero mileage from service facility to fleet parking, km; NTO – quantity of technical service per period; NTP – quantity of repairs per period. – In case when the service facility is located within open-pit and while low labour intensity, then

Lн  Dw  nсм 



j 1

A  l j

01 j



 dl j  l02 j 

 NTO  nTO   NTP  nTP   2l02

(9) ,

where nTO – quantity of service operation; nTP – quantity of repairs. – If industrial facilities are forming in the open-pit, where service and repair can be filled, then Lн must be calculated by the following relation:

Lн  D раб  nсм 

Aj  l01 j  dl j  l02 j  j 1

(10)



 2l2  nTO  nTP    2l3  NTO  nTO   NTP  nTP 

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Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

The increasing amount of technical service within the mining area can reduce the inefficient ranges, that, in its turn, will increase the coefficient , which is one of the indexes influencing on the dump truck efficiency. Daily productivity of the average truck amount, Wа (km), is represented by the relation:

Wa 

Tн  VT     q  ler  q ler  t n. p    VT

(11)

where Тн – shift duration, h; VT – road speed, km/h;

q – load factor; ler – average haul distance, km; q – nominal load capacity, t; tn.p – waiting time, h. Annual productivity of the dump truck calculates by the following equation:

Qг  Wa  Au  K u  D раб ,

(12)

where Aи – amount of trucks; Ки – fleet utilization. Summary. The structure of the production bases reflected in the technical and economic performance of career motor transport. By changing the structure of production databases can be reduced zero runs of the dump trucks, optimizing the maintenance system. This can increase the life time of the dump trucks. With the reduction of zero runs, the percentage of miles laden will increase, which in turn, increases the productivity of the fleet. References [1] Vasiliev M.V. Transport of deep open-pits. – Moscow.: Nedra, 1983. – 295 p. [2] Vorkut A.I. Trucking. – Kiev.: Vishaya skola, 1986. – 447 p. [3] Voronov Ju.E. Complex evaluation and forecasting of mining dump traucl exploitation // Herald of KuzGTU. – 2003. – № 6. – P. 52-55. [4] Mariev P.L. Specific features, actual tasks of mining trucks design development // Mining industry – Ekaterinburg, 2002. – Iss. 6 – P. 4-10. [5] Tarashkevich V.V. Development of mining operations // Mining journal – Ekaterinburg, 2002. – Iss. 11-12. – P. 6-10.

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Mechanics, Materials Science & Engineering, October 2015 – ISSN 2412-5954

ISSN 2412-5954 Published by Magnolithe GmbH Printed by Magnolithe GmbH

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