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NATIONAL CONFERENCE ON RECENT RESEARCH IN ENGINEERING AND TECHNOLOGY (NCRRET-2015) 1 INTERNATIONAL JOURNAL OF ADVANCE ENGINEERING AND RESEARCH DEVELOPMENT (IJAERD) E-ISSN: 2348 - 4470 , PRINT-ISSN:2348-6406

Basic Design Consideration of coil Finned Tube Type Heat Exchanger for Cryogenic Apllication Jay M Patel1, S.M. Mehta2, (P.G. Student, Cryogenic Engineering,L.D. collage of Engineering,Ahmedabad,India,jaypatel2588@gmail.com) 2 (Associate Proffesor, Mechanical Engineering, L.D. collage of Engineering, Ahmedabad, India, shreya74@gmail.com) 1

Abstract— Coiled finned-tube heat exchangers have been used in small and medium helium refrigerators/liquefiers, miniature J–T refrigeration systems for many years. The efficiency of these cryogenic systems strongly depends on the thermal and pressure drop performance of these heat exchangers. A considerable improvement in the performance of heat exchanger is poss ible by choosing an appropriate geometrical configuration f or a given process requirement. In the present study, geometry of heat exchanger has been deriv ed taking into consideration the clearance provided for manufacturing of the heat exchangers.

Index Terms— Helium (B); Heat Transfer (C); Heat Exchanger (E)

——————————  —————————— finned-tube heat exchangers. To the best of the knowledge of present A series of coiled finned-tube heat exchanger is used in a authors, a little information cryogenic refrigerator/liquefier. These heat exchangers were first has been published in open literature regarding the designing of used by Collins in his helium liquefier [1]. The main requirements of coiled finned-tube heat exchangers. Geist and Lashmet [4] presented these heat exchangers are high effectiveness and low pressure drops the heat transfer factor and friction factor for different fin geomein both of fluid streams to stipulated limits. These parameters govern tries. Croft and Tebby [5] presented the expressions for thermal dethe performance of the whole system. In fact, a cryogenic liquefier sign and they have suggested the correlations for calculation of heat will produce no liquid if the heat exchanger effectiveness is less than transfer coefficients for shell side and tube side flow. They used their approximately 85% in contrast to a conventional heat exchanger, designing method for the Clarendon laboratory helium liquefier heat used in other process plants, with lesser effectiveness [2]. Atrey [3] exchangers [6]. Croft and Cosier [7] also designed a new form of has shown in his analysis that decrease in heat exchanger effective- finned-tube heat exchanger by applying the design method described ness from 97% to 95% reduces the liquefaction yield in helium li- by Croft and Tebby [5]. However, design proposed by Croft et al. quefier by 12%. This necessitates thorough understanding of differ- does not consider the effect of diametrical clearance on thermal and ent loss contributing mechanisms that affect the performance of heat pressure drop performance.

In the present work, the expressions have been derived exchanger to arrive at an optimum geometrical configuration.

One of the major issues of developing these heat exchang- taking in to account of clearance. These presented expressions can be ers are to ensure uniform flow distribution over the finned tubes of used as design charts for thermal and pressure drop design of finnedheat exchanger by controlling the manufacturing clearance to tube heat exchanger. The methodology prescribed in the present achieve the higher order of magnitude of effectiveness. However, work has been used to compare four end temperatures of one heat some diametrical clearance is provided in order to ease the assembly exchanger tested in our lab. of the finned-tube bundle and there is always some leakage of flow The correction factor in respect of ideal finned-tube bundle through the diametric clearance. Hence, in addition to other losses, for heat transfer coefficients and pressure drop performance has been there is always detrimental effect on the thermal performance of heat presented in graphical form which can be useful for practicenor enexchanger due to leakage of flow through clearance. This is due to gineers for quick estimation. The maximu m allowable diametrical the fact that there is no heat exchange with the finned tube as the clearance (when 50% flow passes through clearance) for different fin flow passes through this clearance. On the other hand, the pressure height and number of fins has been presented in graphical form for drop performance is improved due to increase in available cross - quick reference. section area.

2. Geometry for thermal and pressure drop deThe design of cryogenic heat exchangers is always subject sign to limited pressure drop conditions. If the clearance effect is not conIn this section, we have presented the derived formulae by sidered for predictions of pressure drops then it may be overesti- considering the diametrical clearance. Fig. 1 shows the typical geomated and it will require the larger shell diameter to keep the pres- metrical parameters of coiled finned-tube heat exchangers. sure drop with in stipulated limits. This will result in lower flow velocity within heat exchangers and herefore lower heat transfer The total shell side free flow area Asc, is given by coefficient in the shell side. Hence, it will require larger unit and as a consequence of this there is a need to optimize the geometry of heat Asc= π Dc(df + c) – πDe[(df – do)nt + do] (1) exchanger to • minimize the cool down time of the system, Free flow area offered by the fins cross-section, Afc • minimize the refrigeration loss to cool the unit, • minimize the radiation loss, and to • reduce the cost of the system.

So, fact is that the clearance provided for ease of manufacturing can be used for adjusting the thermal and pressure drop performance of

1 Introduction

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Nomenclature AS Afc Acc C C Df do Dc Dh F G H hf Jsh Jsp K L L ṁ ṁf N NTU P ΔP

Surface area (m2) Q Free flow area (m2) Re Clearance cross section area (m2) S Heat capacity flow rates of fluids defined by the product t of mass flow rate ṁ and specific heat cc or ch(W/K) T Tm Diametrical clearance (m) ΔTLMT D Fin diameter (m) U fin root diameter (m) mean diameter of shell (m) μ hydraulic diameter (m) ρ friction factor ἠ mass velocity (kg/m2s) ἐ heat transfer coefficient (W/ m2K) fin height (m) c correction factor for shell side heat transfer coefficient h I correction factor for shell side pressure drop O bypass area factor = Acc/Afc In axial length of shell (m) out length of finned tube (m) T mass flow rate (g/s) S actual mass flow rate passes through fins (g/s) Max number of fins per meter length overall number of transfer units * absolute pressure (bar) pressure drop (bar)

Afc= π De[(df – do)(1 – nt)]

heat transfer from either fluid (W) Reynolds number perimeter of tube (m) mean thickness of fin (m) temperature (K) fluid mean temperature (K) log mean temperature difference (K) overall heat transfer coefficient(W/m K) Greeks viscosity of fluid(kg/m s) density of fluid (kg/m3) fin efficiency effectiveness of heat exchanger Subscripts cold fluid hot fluid Inner Outer Inlet Outlet Tube shell maximum Superscript non-dimensional quantity

(2)

Free flow area offered by the clearance cross -section, Acc Acc= π Dec

(3)

If free flow area offered by the fins is greater than free flow area offered by the clearance then maximum flow will pass through the fins. If the free flow area offered by the fins is equal to the area offered by the clearance, then half of the flow of total flow rate will be diverted through the clearance. In the present analysis, it is assumed that the maximum area offered by the clearance should be equal or less than the actual area offered by the finned-tube crosssection. On the basis of above assumptions, the maximum allowable clearance for the thermal and pressure drop performance, the case when 50% flow passes through clearance, can be given by Cmax=[(df – do)(1 – nt)]

(4)

It should be noted that if there is no clearance (c = 0) then Eq. (1) is reduced to Eq. (2). It means that the total projected free flow area Asc will be equal to the free flow area offered by the fins, Afc. The surface area offered by the outer finned surface in one coil; As

n As  π2 [ (d 2f  d o2 )  d o (1  nt )  d f nt ]De 2

(5)

The perimeter of outer finned surface (surface area per unit axial length), so Fig. 1 Sectional view of heat exchanger

n so  π2 [ (d 2f  d o2 )  d o (1  nt )  d f nt ]De / d f 2

(6)

The perimeter of inner tube surface (surface area per unit axial length), si 2

Si = π De d f/d i

G= (7)

The equations derived above considering the effect of clearance can be used for the heat exchanger optimization. The heat transfer coefficients and pressure drop coefficients will be calculated on the basis of these areas prescribed above.

3 Design fundamentals In a coiled finned-tube heat exchanger, the high pressure gas passes through finned tube in spiral form from top to bottom and the low pressure cold gas passes over the finned tube in cross flow pattern as shown in Fig. 1. Therefore, the advantage of this design is the high cross flow heat transfer coefficient on the shell side and high overall effectiveness of counter-flow globally.

The assembly of these heat exchangers consists of the inner shell, outer shell and finned tube. The finned tube is wound on the inner shell and then it is jacketed by the outer shell. The dead space between two consecutive coils has to be filled by some cord as shown in Fig. 1. A diametrical clearance between the shell and tube periphery has to be provided in order to make the assembly easy. The thermal and pressure drop performance of heat exchanger is influenced by this clearance. A part of the cold stream passes through this clearance without taking part in heat exchange process, making the heat exchanger ineffective. On the other hand, the pressure drop performance will be improved by increasing the available cross -section area. The effect of clearance on the thermal and pressure drop performance of heat exchangers is considered in the present study.

If we assume the mass flow rate of the cold stream flowing in the shell side is given by _mc then the actual mass flow rate passing through the fins is

mf=

mc k 1

(8)

mc Asc

(13)

where G is the mass flow rate per unit free-flow area and will be used for calculating the heat transfer coefficients. In Eqs. (12) and (13) Asc will be equal to Afc, if there is not any clearance.

4 Assumptions Following assumptions are made for carrying out the analysis.

1. The pressure drops due to other effects are negligible in comparison to the core frictional pressure drop.

2. All thermo physical properties have been calculated at the mean temperature Tm of the individual fluid stream.

5 Design 5.1 Thermal Design For the usual heat exchanger design problem, where all end temperatures are given, the heat transfer area can be calculated by using the overall heat transfer coefficient based on either hot fluid heat transfer area or cold fluid heat transfer area. In the present study, we will follow the design procedure described by Croft and Tebby [5]. And therefore, the overall heat transfer coefficient,U (W/m K), will be based on axial length of the heat exchanger I stead of the heat transfer area of either fluid by applying the concept of wetted perimeter of heat exchanger per unit axial length.

Fluid properties are evaluated at mean temperature given by

Tm =

Th ,in  Th ,out 2

Or

Tc ,in  Tc ,out 2

(14)

where Th, Tc are the respective inlets and outlets temperatures of hot and cold streams of heat exchanger.

The total heat duty ðQ_ Þ of the hot fluid which has to be removed by exchanging the energy with the cold fluid is expressed as follows Q = Ch(Th,in – Th,out) = UL ΔTLMTD

(15)

where k is bypass area factor and it is given by

Acc A fc

k=

(9)

where L is the axial length of heat exchanger and ΔTLMTD is the log mean temperature difference, given by ΔTLMTD =

The Reynolds number will be calculated based on the actual flow passes through the fins and can be given by

Re

f

=

Re woc k 1

(10)

where ReWOC is the Reynolds number based on the total crosssection area available for shell side flow when there is no clearance and can be calculated as follows

Re

woc

=

m c Dh A fc 

4 Asc Dh= As L

ΔThot end = Th,in – Tc,out and ΔTcold end = Th,out –Tc,in (17)

The overall heat transfer coefficient U (W/m K) based on per unit axial length of heat exchanger can be given by U= [

(12)

(16)

where DThot end and DTcold end are the hot and cold end temperature differences

(11)

The characteristic dimension for the Reynolds number in Eq. (11) is the equivalent diameter, or the hydraulic diameter Dh

Thotend  Tcoldend T ln hotend Tcoldend

1 1 -1  ] hi si ho so

(18)

where hi and ho are the heat transfer coefficients defined as the rate of heat transfer across unit area of separating wall for unit temperature difference between gas stream and separating wall (W/m2 K). si and so are the perimeters (surface area per unit axial length) as de-

fined in Eqs. (6) and (7) across which heat is transferred. The thermal resistance of separating wall is omitted in Eq. (18) as it is small enough as compared to fluid resistances. The fin efficiency  can be assumed 100% for cupper finned tube in Eq. (18) [5,9].

The value of heat transfer coefficients for the inner and outer stream is calculated using the same correlations as described by Croft and Tebby [5] and are reproduced here h i = 0.033 c h m

0 .8 h



0.2 1.8 h di

c c m 0f.8  c0.2 A sc1.0 s0.2

c c m f m f 0.2  c0.2 A sc1.0 s 0.2

4m f

 c so

) 0.2

(20)

(21)

(22)

Eq. (22) can be expressed in terms of Reynolds number as follows: h o = 0.027 c c G f Re

0 . 2 f

(23)

5.2. Pressure drop design

0 .2

(26)

P * =

P Pc

(27)

6 Conclusions The design and optimization of coiled finned-tube heat exchangers with the consideration of clearance provided for the ease of manufacturing have been presented. The thermal and pressure drop performance of a coiled finned-tube heat exchanger depend on the clearance between the shell and finned tube in addition to other geometric and operating parameters. The comparison of predictions of four end temperatures, obtained from present study, with experimental results confirms the importance of clearance effect on the final design calculations. The results of the present study show that the effect of clearance can be used for adjusting the thermal and pressure drop performance of heat exchangers in many situations such as to find out an optimum configuration for given fin geometries. The results of the present study also indicate that the heat exchanger can be optimized either by choosing the suitable mean diameter of shell with an appropriate clearance for given fin geometries or by selecting the optimized fin geometries.

REFERENCES

The pressure drop design is equally important as the thermal design of heat exchanger for any cryogenic systems. The tube side pressure drop across the heat exchanger will reduce the amplitude of high pressure stream thereby reducing the area of the expansion space in PV diagram and the gross refrigeration produced by the refrigerator/ liquefier.

On the other hand, pressure drop in the shell side is extremely important for any cryogenic systems such as helium liquefier/refrigerator.

In a helium liquefier/refrigerator (helium normal boiling point 4.2 K and critical pressure 2.2 bar), the total pressure drop of the shell side should not be more than 0.2 bar because of the constraint of critical pressure of the helium.

The amplitude of the pressure drop (DP), either shell side or tube side, per unit working length through the heat exchanger is given by

fG 2 P = 2 Dh

f = 1.904 Re

In the present analysis, the pressure drop for the tube side and shell side is presented as dimensionless quantity and it is defined as follows.

The above Eq. (21) can be rearranged as follows

h o = 0.027 c c G f (

(25)

(19)

Eq. (20) can directly be used for calculating the heat transfer coefficient in the shell side as used by Croft and Tebby [5] for calculating the overall heat transfer coefficient, U (W/m K). However, it can also be deduced in terms of Reynolds number based on the actual flow passes through the fins.

Eq. (20) can be written as h o = 0.021

di ) De

For shell side flow: The shell side flow is generally laminar in the coiled finned tube heat exchanger and the friction factor for the shell side is given by [11] for 400 < Re < 104

and h o = 0.021

f = 0.184 Re 0.2 (1+3.5

(24)

In Eq. (24) the value of friction factor, f, has to be calculated as follows.

For the tube side: For turbulent flow inside a smooth tube of any crosssection, the friction factor was calculated by the empirical equation as suggested by Timmerhaus and Flynn [10].

[1] [2]

Collins SC. A helium cryostat. Rev Sci Instr 1947;18:157–67 Barron RF. Cryogenics systems. 2nd ed. Oxford: Oxford University Press; 1985 [3] Atrey MD. Thermodynamic analysis of Collins helium liquefaction cycle. Cryogenic s 1998;38:1199–206.

[4] Geist JM, Lashmet PK. Miniature Joule–Thomson refrigeration systems. Adv Cryo Eng 1960;5:324–31.

[5] Croft AJ, Tebby PB. The design of finned-tube cryogenic heat exchangers. Cryogenics 1970(June):236–8.

[6] Croft AJ, Bligh BR. The Clarendon laboratory helium liquefier.

Cryogenics 1961(June):231–4.

[7] Croft AJ, Cosier J. A new form of finned-tube heat exchanger.

Cryogenics 1970(June):239–40 [8] Gupta Prabhat, Sharma RC, Kush PK. Development of crosscounter flow heat exchanger for cryogenic temperature range. In: Proceedings of national seminar and conference on cryogenic s and its rontier application. Bengal Engineering College; How rah, India, 2004. p.

125–7.

[9] Hew itt GF. Heat exchanger design hand book. New York: Begel House Inc; 1998.

[10] Timmerhaus KD, Flynn TM. Cryogenic process engineering. New York, USA: Plenum Press; 1989.

[11] Trumpler PR, Dodge BF. Heat transfer and fric tion factors for edgewound coil fins. AIChE 1947;43:75–84.