Invention Journal of Research Technology in Engineering & Management (IJRTEM) ISSN: 2455-3689 www.ijrtem.com Volume 1 Issue 12-Version-4 ǁ December. 2017 ǁ PP 01-16
Cooling of plastic on metallic mandrel 1, 1,2,3
Karel Adámek , 2,Jan Kolář, 3,Pavel Peukert
,(Department of flow numerical simulations, VUTS Liberec a.s., Czech Republic)
ABSTRACT : The feasibility study summarizes results of preliminary numerical simulations of both flow and heat exchange in plastic tube on calibrating mandrel. Results used for increasing of some operational parameters of the equipment, as production output, quality and reliability.
KEYWORDS : cooling, efficiency, flow numerical simulation, heat exchange, plastic production I. INTRODUCTION The thin-wall plastic tube is extruded from melted polymer, from outside it is cooled in water bath and from inside is cooled and calibrated by shifting on metallic mandrel, cooled by inner water, inflates by internal pressure and in the next phase [1, 2 and 3] is gradually cooled at the surroundings temperature. The priority problem is the solidification and next cooling of extruded material, because it is the limit of production increasing – at production velocity increasing the material is not well cooled. Therefore, they are performed numerical simulations of both flows and heat transfers in several design cases of observed system. The result of simulation is the description of flows and heat transfer in system and determination of transferred heat.
II. INITIAL MODEL From given dimensions, temperatures, production velocity and used material is determined heat quantity, which must be transferred from just extruded plastic into cooling water – for next simulations 250 W approx. Calculated heat flow enters from cooled plastic into mandrel and is taken away by defined flow of cooling water, its theoretical warming is calculated, too. The first initial model serves for obtaining of initial information and for seeking and tuning a suitable solving procedure. We observe first the heat transfer from plastic in the metallic calibrating mandrel, internally cooled by water; at the beginning, here is not thinking about heat transfer on the outer side in large water bath. The main parameters of designed model are as follows: Geometry : Calibrating mandrel diameter/ length of 10/300 mm, inside are situated two water channels for inlet and outlet of cooling water (total cross section of 27.71 mm2). Their max. possible diameter of 4.2 mm is given by min. thicknesses of mandrel and tubes of 0.5 mm (after manufacturing possibilities, strength of material etc., but the smallest as possible). At the end an elbow of 180° connects both channels. Along sides of water channels it remains the place for two air channels of diameter 2.4 mm. Thickness of cooled plastic is of 0.1 mm, the length of 300 mm, identical with mandrel. At the initial position, the plastic is outside the mandrel length, during the simulation it feeds on the mandrel surface by defined velocity. Mesh : Without substantial simplification of the entire geometry is practically unreal to model and simulate dimensions, which differ in the range of four orders approx. (tube wall thicknesses in tenths of mm, lengths of hundreds mm). The size of mesh elements of 0.25 mm crosswise, 3 mm lengthwise. Boundary layers on the inner surfaces of channels are not defined, due to substantially longer time of solution. Initial and boundary conditions : Large tables of parameters of used materials are not presented here, but used during simulations, only. Initial plastic temperature of 400 K (127°C), needed cooling of 100 K. Flow of cooling water of 0.01 kg/s (flow velocity of about 0.5 m/s), its inlet temperature of 300 K (27°C). The air in tubes is immobile – it inflates only the just created inner volume in plastic by pressure of 200-300 kPa. Feed velocity of plastic of 1.2 m/s (72 m/min). The time step of the solution of 2.5 ms, therefore the shift of plastic 3 mm/step, the total shift of plastic of 300 mm needs just 100 time steps. The condition „interface“ is defined on both surfaces of mandrel and plastic, here both bodies are shifted mutually. The density of heat flow calculated from parameters and dimensions above is of 26 400 W/m2. Solver: Unsteady solution, model with moving mesh, turbulence model k-ω.
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Cooling of plastic on metallic mandrel‌ III. RESULTS The Fig. 1 and Fig. 2 present the pressure and velocity fields in lengthwise section for given water flow of 0.01 kg/s, the Fig. 3 presents the surface temperature of plastic just shifted on the entire length of mandrel, after 100 time steps of calculation. It is clear that in the last third (right) length of calibrating mandrel the plastic is cold yet. Decreasing the feed velocity the point of cooled plastic shifts over one-half of mandrel length, see the Fig. 4. It means that for cooling output increasing must be used longer calibrating (cooling) mandrel.
Fig. 1: Pressure field in cooling water For given water flow (here 0.01 kg/s) it is necessary to create pressure gradient, sufficient for covering of flow resistances.
Fig. 2: Velocity field of cooling water Velocity field is constant in general, minimum at walls (friction), and local disturbance at the end with returning of 180°.
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Cooling of plastic on metallic mandrel‌
Fig. 3: Surface temperature of cooled plastic For operating parameters as above, plastic feeding from left, the 38% of the entire length is cooled, therefore the plastic leaving the mandrel is sufficiently cold.
Fig. 4: Surface temperature of plastic at one-half feeding velocity At lower feed velocity of plastic the longer part is cold yet, here of 62%, it is less than theoretic double value for one-half feeding velocity.
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Cooling of plastic on metallic mandrel‌ Fig. 5 to Fig. 7 present serial of cross section in the temperature field in the system for positions of 50-100-200300 mm from the water inlet. Individual figures have different scales for better contrast. Due to used rough mesh, the temperature isolines are rough, too.
Fig. 5: Temperature in cross section of 50 mm
Fig. 7: Temperature in cross section of 200 mm
Fig. 6: Temperature in cross section of 100 mm
Fig. 8: Temperature in cross section of 300 mm
In general, it is visible the difference between inlet water (up) and outlet water (below), higher at the inlet/outlet side and zero at the side of reversal elbow. In the lengthwise section, the water temperature is higher at the inlet, where the hot plastic is coming in, contrary to the reversal elbow, where the plastic is cold yet. Temperature distribution in the cross section is uniform, the influence of air channels (thermal insulant), situated in horizontal plane is not significant in steady mode. At the mandrel axis, the temperature is lower, because here is relative higher influence of channels with cooling water or it is lower influence of distant warmer outside surface. On the mandrel periphery there is local temperature increasing, not only near the air channels, but also near water channels, where is the minimum gap to the mandrel surface. The Fig. 9 shows the detail of plastic temperature in two positions of 50 and 200 mm – on previous cross sections the small thickness of 0.1 mm is not well visible. The temperature inside to the cooling mandrel is lower than the temperature at outer (not cooled) side.
Fig. 9: Detail of plastic temperature in cross section of 50 mm (left) and 200 mm (right)
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Cooling of plastic on metallic mandrel… Note: The outer side is in reality cooled by large water bath, too; in this preliminary case, it is neglected. For information, the detail in the Fig. 10 presents the velocity field in such outer surroundings, generated first by friction forces (by plastic movement in viscous fluid). In vertical arrangement the spontaneous water movement will be present, in addition, due to change of water density with its temperature – here is neglected. At the outer surface, (here up) the mass of outer cooling water moves, on the inner surface (here down) is analogous movement of thin layer of lubricating oil.
Fig. 10: Detail of velocity field (up to 1 m/s) along the moving plastic The same task, but with unsteady start shows the Fig. 11: Water flow of 0.01 kg/s needs pressure gradient of 2260 Pa, flow velocity inlet-outlet of 0.53-0.58 m/s, temperatures inlet-outlet of 301.9-303.3 K. Average plastic temperature of 320.8 K from initial value of 400 K at the inlet water temperature of 300 K, plastic feed velocity of 1.2 m/s, water flow velocity of 0.053 m/s. Heat flow taken away in water of 44.1 W from the simulation, from the mass and energy balances of 58.6 W, i.e. of 32% more. The difference is given probably by the rough mesh and by unsuitable procedure – from the start takes place simultaneously the unsteady calculation of water warming and plastic cooling, but really, the water is in motion before start. Deformation of isolines in the central part of profile is given by the near position of air channel in the lengthwise section, used for displaying – locally here is a little worse cooling.
Fig. 11: Unsteady temperature field of the plastic surface Model modifications :This part presents several possibilities, how to remove or remedy errors of simulation and to increase the heating output of observed device. Fine mesh : The aim of this model is to verify possible influence of fine mesh on the temperature field in narrow gaps between channels and mandrel, solved as half-model. For simplification here are not air channels – after the previous case their influence can be neglected. In the narrow gaps between surfaces of mandrel and water channels is generated min. 5 layers of mesh elements, see the Fig. 12 (step by step from the outer surface: plastic – interface – mandrel wall – water gap – water channel).
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Cooling of plastic on metallic mandrel‌
Fig. 12: Detail of fine mesh between water channel and calibrating mandrel The Fig. 13 presents temperature field in cross section at 50 mm from the inlet. In the fine mesh, the details of the field are better, comparing with Fig. 5 of rough mesh, but the local temperature increasing in the narrow gap between surfaces of water channel and calibrating mandrel remains. The mesh density has not any influence on the character of temperature field, but on its details, only. Next Fig 14 shows the detail of the temperature field in such narrowed area.
Fig. 13: Temperature field in cross section at 50 mm from the inlet
Fig. 14: Local temperature increasing in the narrow area between surfaces of channel and mandrel
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Fig. 15: Temperature field on the plastic surface Here of 49% of total length is cooled, therefore the plastic at the end is fully cooled. Further, the procedure of solution was modified a little. After the reality the starting of water flow is modelled as the first and after reaching of steady state the plastic is moved in unsteady mode (100 time steps of 2.5 ms at the feed velocity of 1.2 m/s = 72 m/min., as above).
Fig. 16: Velocity field at the inlet/outlet Velocity field – at the inlet (here below) the velocity is constant in the entire cross section, due to definition of the mass flow in the inlet. Along the long channel (300 mm) the classical velocity profile is creating, see the outlet channel (here up) – maximum in the axis, zero at walls. The same is visible in the cross section at the distance of 50 mm from inlet/outlet in the following Fig. 17. Really, some velocity profile is creating in the inlet to the mandrel, yet, here not solved.
Fig. 17: Velocity field in cross section 50 mm from inlet/outlet
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Cooling of plastic on metallic mandrel‌ Long cooling mandrel : The main result of the Par. 2 is that to get higher production output it must be used longer cooling mandrel. This case was tested for double mandrel length (600 mm) and double feed velocity of cooled plastic (2.4m/s=144 m/min.). The resulting temperature field after the same cooling time of 0.025 s see the Fig. 18. The ratio of cooling outputs is of 1.7:1. Theoretic ratio of thermal outputs should be 2:1, some influence have here plastic and water temperatures and movements in time. The cooled length is here of 44%, similar to the Par. 2. Real values of thermal outputs are not available, due to very long-time measuring and evaluation both temperatures and movements in time. The similar dependence is in the Par. 2 for various feed velocities of plastic. Values there are not fully comparable with here, because another procedure was used there (it is not realized the initial start of water on steady mode).
Fig. 18: Temperature field on the plastic surface Influence of mandrel material : In the same model as above are defined two different materials with high and low thermal conductivity – aluminum 200 W/(m.K) and stainless steel 17 W/(m.K). The heat flow is defined as above, too, constant of 26 400 W/m2 on the mandrel surface, after mass and heat flow balances and for given mandrel dimensions. In such a case, the temperature distribution on the surface or its unevenness will be different. From realized numerical simulation is clear that higher thermal conductivity means lower average temperature and its lower variance, too, on the surface, the total heat flow is identical (small difference of 0.1% means numerical error of simulation). It is possible to suppose that for given configuration the thermal conductivity of used material has not any influence on transferred heat, but on the local temperature distribution on the surface, only, see the Tab. 1. Tab. 1: Surface temperature distribution for two different materials material thermal conductivity thermal flow Tavg Tstd Tmin Tma
W/(m.K) W K K K K
aluminum 200.0 256.6 310.0 1.6 303.4 313.8
stainless steel 17.0 256.9 315.1 7.8 302.1 340.4
water
300.4 306.7
Influence of the surface for heat transfer on the waterside : In the mandrel of the same diameter of 10 mm as above it is possible to insert as an alternative 4 water channels of diameter 3.6 mm and 2 air channels of diameter 1.4 mm, the total cross section is 40.72 mm2, so the surface for heat transfer is 1.47 times higher than in the initial mode above. Detail of return elbows see the Fig. 19, next Fig. 20 to Fig. 22 present temperature fields in cross section in distances of 100-200-300 mm from water inlet/outlet, and so for 8 times higher heat flow compared with the value defined for simulation of initial model in the Par. II, to get more distinctive temperature differences. Due to the rough mesh, the isolines are rough, too. This model shows that higher or lower heat flow through the mandrel surface takes out by cooling water without problem. Possible increasing of surface for heat transfer on the waterside has not any influence, compared with the previous model.
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Cooling of plastic on metallic mandrel‌
Another shape of channel : Instead two pairs of cylindrical channels here are designed two half-cylindrical channels. The cooling surface of such water channel is situated along the mandrel axis; the consequence of it is better cooling of outer surface. Spiral channels could solve the locally lower cooling in the horizontal plane, where the partition between channels is situated. Manufacturing of it is possible by method of precise casting or by 3D print. Parameters of the solved case: thermal flow of 23.8 W, water flow of 3.25 g/s, water warming of 3.1 K, pressure gradient of 952 Pa, flow velocity of 0.28-0.30 m/s. Three views on the temperature field present Fig. 23 to Fig. 25.
Fig. 23: Temperature field in the cross section
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Cooling of plastic on metallic mandrel…
Fig. 24: Temperature field of the cooling water along the mandrel
Fig. 25: Temperature field of the cooled plastic along the mandrel Next possible solutions : Heat exchanger pipe in pipe – see below. Micro channels – high surface for heat transfer, but high flow resistance, too, complicated manufacturing of long and narrow channels. Thermal pipes – to manufacture pipes of specific dimensions, given by product dimensions. Turbulisating insert in the form of a spiral, inserted in water channel [4].
IV. REALISATION From the manufacturing reasons did not realize long and narrow holes in solid material, but in outer thin-walled tube (mandrel body) are inserted next thin-walled tubes (needles) for cooling water and air. The cooling of the mandrel surface it then realized by backflow water (warmer) and the assembly is immersed in large water bath. To reduce the friction, between mandrel and plastic is used lubricating oil. The procedure of model creating and its solution is similar as above, therefore without next details. When the water velocity and temperatures reach their steady values, the movement of cooled plastic is started (100 time steps of 2.5 ms). Without detailed analyze, this case gives more suitable results, compared with previous one: water flow of 0.001 kg/s (0.064 m/s approx.), water warming from 300 k at 313 K, flow resistance of 517 Pa, cooling output of 47.2 W. Interesting details of the flow field see Fig. 26 to Fig. 28 below.
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Cooling of plastic on metallic mandrel‌
Fig. 26: Detail of the longitudinal velocity component wx in the inlet part of mandrel
Fig. 27: Detail of temperature field in the inlet part of the mandrel
Fig. 28: Temperature field on the plastic surface The plastic body was here just shifted from the left side to the right end; the right part is cold yet (see the arrow). This arrangement has its problems. As mentioned above, in the area of minimum distance between water inlet tubes and mandrel tube there is worse local cooling of the mandrel. In the narrow gap, there is relatively higher flow resistance, so lower velocity and so lower heat transfer, too. Practically it is necessary to take into account that long and flexible tubes come in random contacts during both assembly and operation. Manufacturing documentation states that shape and dimension tolerances of used tubes are not right and individual needles must be deformed during the assembly. This failure must be repaired. Such contacts of individual tubes (singular points) must be avoided not only by assembly, but during model creation, too, due to problems of meshing and of numerical solution stability (convergence). For illustration next Fig. 29 and Fig. 30 present main results of one solved problem. The inlet water is coming in axial channel and at its end returns back in the free end volume in mandrel. It is visible, that the free end of mandrel (here right) is not flowed by water at all, so is not cooled, too.
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Cooling of plastic on metallic mandrel‌ The free length for water return could be shorter, or in other words by prolongation of the central inlet tube the area of intensive cooling will be longer, here for given dimensions of 10% approx. This fact confirms the real operation, the cooling of the mandrel end is not intensive enough, the temperature is a little increasing back again, see also graphs on the Fig. 35 and Fig. 36 below.
Fig. 29: Velocity field in the area of water return
Fig. 30: Directional field in the area of water return
Fig. 31: Detail of velocity field (up to 1 m/s) around moving plastic (→) The Fig. 31 shows the detail of velocity field in any middle part of mandrel, caused by the moving plastic layer in viscous fluids. On the outer surface (here up) is the movement of adjoining volume of the cooling water bath, on the inner surface (here down) is moving thin layer of lubricating oil. At the mandrel wall, the velocity is equal to zero.
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Cooling of plastic on metallic mandrel…
Fig. 32: Temperature field in the entry area From the temperature field in the Fig. 32 is clear that some length of incoming plastic is cooled before the entry in the observed cooling zone, simply by heat conduction in the direction of plastic movement, from mass of plastic into mass of mandrel and of cooling water.
Fig. 33: Detail of temperature field in the middle part of mandrel In the detail of temperature field in the Fig. 33 is visible the temperature stratification into the surrounding water (up) and into the inner water (down) through oil layer and mandrel wall. In the plastic thickness, the highest temperature is in the middle, decreasing to both surfaces in radial direction (here up and down). In the movement direction (here from left to right), the warm area becomes more narrow, the temperature of the plastic volume is decreasing. Up is situated cool water bath, in some boundary layer is warmed from cooled plastic. Plastic is more cold on the side of outer water (up) than on the side of mandrel (down), where the heat transfer through both mandrel wall and oil layer must be expected. Inside the mandrel (here down) the cooling water is flowing, which is warmer at the wall than in the mandrel axis. For next information, some longitudinal temperature profiles of temperature (K) as function of mandrel length (m) are evaluated below. Concentric cylindrical surfaces for displaying of such profiles in the Fig. 34 are marked as follows: 342 – Outer surface of plastic – maximum at the inlet, gradually decreasing, the minimum temperature at the beginning. 336 – The middle of plastic thickness – minimum cooling, medium temperature at the beginning. 330 – Inner surface of plastic (= outer oil temperature) – the cooling in the inlet part is lower than the outer surface, consequence of composed thermal resistance of oil, mandrel and inner water. The highest temperature at the beginning. 325 – Inner oil surface (= outer mandrel surface) is more cold than „330“ in general, difference of both temperature is given by low thermal conductivity of oil. This profile is used in next Figures below.
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Cooling of plastic on metallic mandrel‌
K
330 336 342
m
Fig. 34: Longitudinal temperature profiles after plastic passing through the calibrating zone (time step of 4 ms) Longer time step shorts the time of solution, but in the area of high temperature gradients, the temperature decreasing is not smooth. Therefore, the solution was repeated with time step of 1 ms, see the Fig. 35. The result is the same; the temperature profile is smooth enough. To three profiles as above here is added the next 325 on the mandrel surface – the lowest value, with small increasing at the end, where the mandrel cooling is bad, see also the Fig. 29. At the end, next calculations were realized for higher plastic velocities of 2 m/s and 4 m/s, with the time step of 1 ms (for mandrel length of 360 mm it means 180 or 90 time steps). Temperature profiles see the Fig. 35 and Fig. 36. The temperature stratification is logical; the cooling along the mandrel length is decreasing. The jump in the first step of the solution is probably the consequence of a transitional condition in the starting part of the model. K
330 336 342 325
m
Fig. 35: The same temperature profiles, time step of 1 ms K
330 336 342 325 m
Fig. 36: Longitudinal temperature profiles for plastic velocity of 2 m/s
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Cooling of plastic on metallic mandrel‌
K
330 336 342 325
m
Fig. 37: Longitudinal temperature profiles for plastic velocity of 4 m/s For information the Fig. 38 presents the cross profile of temperature in random cross section. Gradually from the mandrel axis (x = 0 m) are visible next intervals: 0.00045-0.00145: temperature of inner inlet water 0.00145-0.00160: heat conduction through the wall of water tube 0.00160-0.00205: heat transfer between back flow of inner water and inner wall of mandrel 0.00205-0.00325: heat conduction in mandrel wall 0.00325-0.00330: heat conduction in oil layer 0.00330-0.00342: heat conduction in cooled plastic 0.00342-0.00500: heat transfer between plastic and outer water. On the outer side, it is well visible the typical temperature profile in the boundary layer between the fluid and the surface. On the inner side where the structure is more complicated, the gradient is lower.
K
m
Fig. 38: Cross temperature profile in the middle part of mandrel (0 m = mandrel axis, 0.005 m = area boundary)
V. CONCLUSION The aim of presented results is to show the possibilities of numerical solution of flow together with heat transfer, to tune proposed procedure and to document possible results of temperature and velocity fields in designed cases of various shapes and operational conditions of observed system. It is clear that using method of numerical simulation it is possible simply and without extreme costs to verify many designed variants and the best to manufacture and verify by experiment. Additionally, method of numerical solution gives good overview about solved flow fields in small areas, where is not possible to insert any measuring device or sensor. The main results, useful as base for next designing of system with intensive cooling are as follows:
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Cooling of plastic on metallic mandrel… 1.
Cooling of plastic on needed final temperature in the actual geometry at given fee velocity seems to be sufficient; at higher operational velocity the temperature is higher, too, but sufficiently low for the next treatment.
2.
Increasing of inner water velocity or use of material of high heat conductivity has not any influence on the final plastic temperature. It means that for necessary cooling at higher operation velocity is necessary to use longer calibrating mandrel – it is more demanding from the point of view of manufacturing. The temperature decreasing has asymptotic character; therefore, it is not possible to expect any linear proportionality between mandrel length and final plastic temperature.
3.
Shortening of the free volume at the end of mandrel cavity, the part of minimum heat transfer will be removed and the length of intensive heat transfer will be prolonged. Such long volume is not useful, information from operation confirms the result of simulation – at the end the plastic temperature does not decrease, sometimes a little increases!
4.
The actual configuration with contacts of tubes means areas without water flowing and it is supposed locally lower cooling. After manufacturing documentation is not possible to insert internal needles in mandrel tube without assembly contacts and deformations. The reconstructions lead to better heat transfer in the device.
5.
In the actual configuration there is high velocity of inlet water (inside needles) and low velocity of outlet water (in mandrel cavity), but just it is important for heat transfer from mandrel into inner water. It should be to change the velocity direction, i.e. the inlet of cold water in the mandrel cavity and at higher velocity and the back flow of lower velocity through internal needles. The heat transfer depends first on the velocity.
6.
Reproducible and practically any arrangement of tubes without contacts and deformations of individual tube sis possible to realize using the method of 3D print.
7.
At the entry of cooling water to insert simple blades to swirl the water flow, the time of water contact with walls will be longer and the total transferred heat increases. Used as intensification of oil cooling in truck engines [4].
8.
To consider more intensive heat transfer into the surrounding water bath, using a counter flow, eventually turbulized. Now the water moves spontaneously, only, due to the product movement and a little by density change with temperature change.
9.
The solution supposes that the main part of transferred heat between the plastic and surrounding water realizes along the above-simulated calibrating length of the mandrel. Here is not solved the supply of hot plastic before and following cooling after this device, partially solved in [1, 2 and 3].
ACKNOWLEDGMENT Our acknowledgment is given to VUTS Liberec – Center for Development in Machinery Research for the support in the framework of the grant NPU-LO1213 “National program of sustainability, granted by the Ministry of education, youth and sports.
REFERENCES Here are mentioned reports of VUTS, only, with presented our own results of numerical simulations and experiments. During the solution standard knowledge of fluid mechanics and thermo mechanics were used, which are well known in technical community. It is a pity that they are not practically used to reach a solution, optimal from the technical and economic point of view. [1] [2] [3] [4]
J. Kolář, K. Adámek, Study of intensive cooling (Studie modernizace chlazení), report VÚTS Liberec, 2010, unpublished J. Kolář, K. Adámek, Numerical simulation of new solution (Numerická simulace nového řešení), report VÚTS Liberec, 2010, unpublished J. Kolář, K. Adámek, Heating of annular surface (Ohřev povrchu anuloidu), report VÚTS Liberec, 2010, unpublished Engine M630, handbook LIAZ Jablonec n. N., 1970
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