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Numerical simulation study of the heat transfer characteristic in Ω-shape grooved heat pipes
Available online at www.sciencedirect.com
ScienceDirect
Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia
Procedia Engineering 205 (2017) 3916–3922
10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China
Numerical simulation study of the heat transfer characteristic in Ωshape grooved heat pipes Kaimin Yanga,b,c*, Zhuang Congd, Yudong Maoa,b,c, Xiuli Zhanga School of Thermal Engineering, Shandong Jianzhu University, Jinan 250101, China Key Laboratory of Renewable Energy Technologies for Buildings, Ministry of Education, Jinan 250101, China cc Shandong Key Laboratory of Renewable Energy Technologies for Buildings, Jinan 250101, China d d Zhongshi Yitong Group, Jinan 250101, China a a
bb
Abstract Heat pipes are devices capable of very high heat transfer and have been widely used in many thermal management applications. An experimental investigation and CFD simulation of thermal characteristics of heat pipe was presented in the present work. It can be found that using FLUENT can simulate the evaporation and condensation in heat pipe. With the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. With the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the equivalent thermal conductivity reduces gradually. Results in the present work can provide guidance to further research of grooved heat pipe. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Conditioning. Air Conditioning. Keywords: Grooved heat pipe; Numerical simulation; Steam chamber diameter; Channel number
1. Introduction Grooved heat pipe is a reliable and efficient heat transport device. The heat pipe has been used in several technologically important processes requiring augmented heat transfer e.g., in the electronic packaging industry, in micro-gravity environments, and spacecraft thermal control because of its high efficiency, reliability and cost effectiveness[1-6]. Cotter[7] firstly proposed the concept of micro-heat pipe. That is essentially a wickless heat pipe * Corresponding author. Tel.: +086-0531-86361236; fax: +086-0531-86361236. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.10.033
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for the uniform temperature distribution in electronic chips. After Cotter’s research, 1D model[8], 2D model[9-10] and 3D model[11] for theory analysis of fluid flow and heat transfer in heat pipe were built. Tiselj et al.[12] simulated the single phase flow in a 3D model using the CFD code CFX. Sandra C. K. [13] and Huang Mei et al. [14] modeled the phase change and two phase flow in a pipe using FLUENT. There are a few papers aiming to solve the multi-phase flow in different cases[15-17]. In the present study, 3D model of two phase flow and heat transfer in a Ω-shaped heat pipe was built. The evaporation and condensation in heat pipe were simulated using FLUENT, and the experimental data are compared with the simulating results in order to verifying the simulating model. 2. Experimental facilities Ω-shape grooved heat pipe changes periodically in structure, and exactly the same for each channel. In figure 1, one of the pipes with different geometry has been shown. The package of heat pipe is aluminium alloy, and working fluid is ammonia.
Fig. 1. Geometry of heat pipe for experiments
Fig. 2. Schematic of experimental set up 1-heat pipe, 2-thermocouples, 3-electrical heaters, 4-DC electrical source, 5-watercooling jacket, 6thermostatic waterbath, 7-data acquisition system, 8-computer, 9-insulating layer
As shown in Figure 2, the evaporator section was heated by the heater band, and the test error of the input power is within the range of 1W. The condenser section was cooled by cooling water with constant temperatures. And the glass rotameters having 5% error range are used to measure the water flow rate, which is controlled by the valve. The experiments are carried out at the room temperature, about 20℃, the axial temperature distribution of the heat pipe is measured by thermocouples with an uncertainty of ±0.25℃, and the working temperature is regarded as the mean value of these measured temperatures. The numbers of thermocouples, which are symmetrically distributed at evaporator sector, adiabatic sector and condenser sector, are 3, 3 and 3 respectively. An intermediate plate having thickness of 0.2mm is placed between the thermocouples and the resistor. This intermediate plate can protect the thermocouples against a direct contact with resistor and can help to evenly heat the evaporator sector.
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The electrical power to the band heaters was supplied using a 220V variable DC power source with uncertainty ±2.5W. 3. Physical models From figure 1, it can be seen that Ω-shape grooved heat pipe changes periodically in structure, and exactly the same for each channel. Therefore, in order to reduce the time and resources required by calculation, a single channel was selected as the study object to handle, as shown in Figure 3(a). Table 1. Parameters of heat pipe models Parameters
(a) Groove
(b) Mesh
Value
Out diameter Do (mm)
16
Core diameter Dv (mm)
8
Channel diameter d (mm)
1.2
Slit width W (mm)
0.4
Slit depth δ (mm)
0.6
Length of evaporation section Le (mm)
200
Length of adiabatic section La (mm)
500
Length of condensation section Lc (mm)
300
Filling ratio FR
0.346
Saturation temperature(K)
283, 293, 303
Fig. 3. Schematic diagram of calculation models
To compare with experimental data, heat pipe model of 1000mm long was first established. The length of the evaporator, adiabatic section and condensation section respectively are 200mm, 500mm and 300mm, that the same with experimental sets. Completely filling quantity of heat pipe in the present work refers that the grooves are occupied by liquid totally, then the liquid portion is 0.346 for the pipe’s total volume that means the filling ratio is 0.346. Structure parameters and other relevant variable parameters of heat Pipes are shown in Table 1, where the saturation temperature equals to heat pipe operating temperature corresponding to the experimental data. 4. Numerical methods Initial conditions: temperature of the entire simulation zone has been set to the operating temperature of heat pipe, speed of the fluid field is 0, and pressure is the saturation pressure corresponding to the operating temperature. Boundary conditions: for the surfaces of outer wall in evaporation section, adiabatic section, and condensation section, heat fluxes through boundaries are all constant. Heat flux density in the adiabatic section is 0, which on the surfaces of evaporation and condenser section equal to the ratio of power and surface areas respectively. Eulerian model has been chosen, and the processing method of source terms is the same with that in the literature[10]. SIMPLE algorithm has been chosen to solve pressure-speed coupling. The first-order upward difference was chosen to solve momentum equations and energy equations. The entire calculation process is a transient calculation, the time step-length is 0.001s.
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5. Numerical verification In the present work, the grid independence verification has been made initially. Then graphics software Pro-E was chosen to build geometrical model, and structured grid was chosen which generated by ANSYS ICEM 14.0, as shown in Figure 3(b). There are four sorts of different grid density meshes to verify grid independence, and the specific parameters are shown in Table 2. As it has been shown in figure 4, there has a relationship between calculation results and mesh density. The error between results calculated separately with mesh M1 and M2 is 16.74%, which is 10.80% for M2and M3, and 2.29% for M3and M4 respectively. So it is acceptable to calculate using mesh M3. It is also can be seen that the number of elements of M3 is much less than that of M4, which means more less computing resources. All of calculation in the present work adopted the density of mesh M3. Table 2. Mesh parameters Parameters
Value
No.
M1
M2
M3
Mesh Nodes
1727276
2880896
3578112
4739696
Mesh elements
1578536
2655336
3331328
4444160
0.150 0.145 0.140 0.135
R t(K/W)
Rt(K/W)
0.130 0.125 0.120 0.115 0.110 0.105 0.100
M4
1
2
3
Mesh number
Fig. 4. Thermal resistance versus mesh grid
4
0.160 0.155 0.150 0.145 0.140 0.135 0.130 0.125 0.120 0.115 0.110 0.105 0.100 0.095
Experimental data Simulation results
20
40
60
80
100 120 140 160 180 200 220
Input power(W)
Fig. 5. Comparison of thermal resistance between experimental data and numerical results
In order to verify the reliability of numerical method, some cases were simulated corresponding experimental conditions, and a group comparison of thermal resistance between the experimental data and numerical results is shown in figure 5. As shown in the figure, the error between the simulation and experimental results is in the range of 9.68%-15.77%, which is permissible, indicating it is good at accuracy and reliability for the calculation model. 6. Discussion 6.1. Chamber diameter From figure 6, it can be seen that, with the constantly increase of steam chamber diameter from 7.6mm to 8.4mm, thermal resistance is on a decline trend. The reason for this is, with the increase of chamber diameter, metal between channels and chamber becomes less, which leads to both decrease in rib thermal resistance and flow resistance, and the total thermal resistance of heat pipe reduces finally. Under different operating temperatures, the thermal resistance of heat pipe do not show a significant difference between each other, and the trend of which is also obvious. As the working temperatures rising, thermal resistance gradually increases. That is because the
Kaimin Yang et al. / Procedia Engineering 205 (2017) 3916–3922 Kaimin Yang, et al./ Procedia Engineering 00 (2017) 000–000
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transmission factor and other physical properties will change when temperature of working fluid rises, that leads to decrease of heat transfer capacity. 0.109
twork=283K
0.108
twork=293K twork=303K
Rt(K/W)
0.107 0.106 0.105 0.104 0.103 0.102 7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig. 6. Thermal resistance versus chamber diameter
From figure 7, it can be seen that, with the constantly increase of steam chamber diameter from 7.6mm to 8.4mm, maximum heat transfer capacity of heat pipe is on an increasing trend which varies almost linearly. The increase of chamber diameter can leads to decrease in flow resistance of steam in steam chamber, but that also makes slit depth smaller which leads to contact area between the steam in steam chamber and reflux liquid in channels becomes bigger and bigger, and interaction force between them has been enhanced. So the total heat transfer has been enhanced, but not so great. Under different operating temperatures, the maximum heat transfer capacity of do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the maximum heat transfer capacity reduces gradually, that mainly determined by the changes in thermal physical properties of working fluid. 250 245
36600
twork=283K
240
36200
Keff(W/(m ∗Κ)
220
2
Qmax(W)
twork=303K
35800
225 215 210 205 200
35600 35400 35200 35000 34800 34600
195
34400
190 185
twork=293K
36000
twork=303K
230
twork=283K
36400
twork=293K
235
34200
7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig. 7. Maximum heat transfer capacity versus chamber diameter
7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig.8. Equivalent thermal conductivity versus chamber diameter
From figure 8, it can be seen that, with the constantly increase of chamber diameter from 7.6mm to 8.4mm, the equivalent thermal conductivity of heat pipe is on an increasing trend. Under different operating temperatures, the equivalent thermal conductivity of heat pipe do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the equivalent thermal conductivity of heat pipe gradually increases. From the discussion above, in the scope of chamber diameter considered in the present work, with the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. The bigger chamber size can lead to reduce in flow resistance and increase in interaction force between vapor and liquid, so the improvement of heat transfer capability of heat pipe is not so great finally.
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6.2. Channel number From figure 9, it can be seen that, with the constantly increase of channel number from 15 to 19, thermal resistance is on an increasing trend. The reason for this is, with the increase of channel number, metal between channels become less, that leads to increase of rib thermal resistance, and the total thermal resistance of the heat pipe increases finally. Under different operating temperatures, the thermal resistance of the heat pipe do not show a significant difference between each other, and the trend of which is also obvious. As the working temperature rising, thermal resistance gradually increases. The reason for this is the same with that for chamber diameter. 0.120 0.118
twork=283K
0.116
twork=293K
0.114
twork=303K
Rt(K/W)
0.112 0.110 0.108 0.106 0.104 0.102 0.100 0.098
15
16
17
18
19
N
Fig. 9. Thermal resistance versus channel number
From figure 10, it can be seen that, with the constantly increase of channel number from 15 to 19, maximum heat transfer capacity of heat pipe is on an increasing trend which varies almost linearly. The increase of channel number can leads to increase in the flow section of liquid in grooves, then the liquid pressure drop becomes smaller. So the total heat transfer has been enhanced. Under different operating temperatures, the maximum heat transfer capacity of do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the maximum heat transfer capacity reduces gradually, that mainly determined by the changes in thermal physical properties of working fluid. From figure 11, it can be seen that, with the constantly increase of channel number from 15 to 19, the equivalent thermal conductivity of heat pipe is on a decline trend. Under different operating temperatures, the equivalent thermal conductivity of do not show a significant difference between each other, and the trend of which is obvious. As working temperature rising, the equivalent thermal conductivity of heat pipe gradually decreases. 38000 280
twork=293K
twork=303K
35000
2
Keff(W/(m ∗Κ)
Qmax(W)
220 200 180
34000 33000 32000
160 140
twork=293K
36000
twork=303K
240
twork=283K
37000
twork=283K
260
31000 15
16
17
18
19
N
Fig.10. Maximum heat transfer capacity versus channel number
15
16
17
18
19
N
Fig.11. Equivalent thermal conductivity versus channel number
From the discussion above, in the scope of channel number considered in the present work, with the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing
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trend, however, the equivalent thermal conductivity reduces gradually. The bigger channel number can lead to reduce in flow resistance and even more increase in thermal resistance, so heat transfer capability of heat pipe declines finally. 7. Conclusions 1) The model established in the present work can simulate the operation of heat pipe well. 2) The physical property changes of working fluid have been considered. 3) With the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. 4) With the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the equivalent thermal conductivity reduces gradually. Acknowledgement This paper is supported by Research Fund for the Doctoral Program of Shandong Jianzhu University (0000601337), and Natural Science Foundation of Shandong Province of China (ZR2016EEB15). References [1] Zhuang Jun, Zhang Hong. Heat Pipe Technology and Engineering Application. Beijing: Chemical Industry Press, 2000. [2] XIN Gongming, DU Wenjing, WANG Naihua. Development of thermal control system for AMS electronic units on ISS. Chinese Science Bulletin, 2012, 57 (5): 382–389. [3] Y. Tang, P. Chen, X. W. Wang. Experimental investigation into the performance of heat pipe with micro grooves fabricated by Extrusionploughing process. Energy Conversion and Management, 2010, 51: 1849–1854. [4] Chen Yongping, Zhu Wangfa et al. Thermal Characteristics of Heat Pipe with Axially Swallow-tailed Microgrooves. Chinese Journal of Chemical Engineering, 2010, 18(2): 185–193. [5] A. Faghri. Heat Pipe science and technology. Washington DC: Taylor & Francis, 1995. [6] T. P. Cotter. Principles and prospects for micro heat pipes. In: Fifth international heat pipe conference, Tsukuba, Japan, 1984. [7] T. P. Cotter. Theory of heat pipes. Los Alamos Scientific Lab: Report No. LA–3246–MS, 1965. [8] J. P. Longtin et al. A one-dimensional model of a micro heat pipe during steady-state operation. Journal of Heat Transfer, 1994, 116(3):709. [9] P. C. Stephan, C. A. Busse. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int J Heat Mass Transfer, 1992, 35(2): 383. [10] H. B. Ma, G. P. Peterson. Temperature variation and heat transfer in triangular grooves with an evaporating film. J Thermophys Heat Transfer, 1997, 11(1): 90. [11] Sartre V. et al. Effect of interfacial phenomena on evaporative heat transfer in micro heat pipes. Int J Therm Sci, 2000: 39: 498–504. [12] Tiselj I et al. Effect of axial conduction on the heat transfer in micro-channels. Int J Heat Mass Transfer, 2004, 47(12–13): 2551. [13] Sandra C. K. De Schepper et al. Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker. Computers and Chemical Engineering, 2009, 33: 122–132. [14] Huang Mei, Yang Zhen, Wang Buxuan. Simulation of bubbly flow heat transfer in a serpentine tube. CIESC Journal, 2011, 62(12): 3345– 3351. [15] J. D. Li. CFD simulation of water vapour condensation in the presence of non-condensable gas in vertical cylindrical condensers. International journal of heat and mass transfer, 2013, 57: 708–721. [16] L. M. Pan, Z. W. Tan, D. Q. Chen, L. C. Xue. Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel. Nuclear Engineering and Design, 2012, 248: 126–136. [17] Z. R. Lin, S. F. Wang, Ryo. Shirakashi, L. W. Zhang. Simulation of a miniature oscillating heat pipe in bottom heating mode using CFD with unsteady modeling. International journal of heat and mass transfer, 2013, 57: 642–656.
ScienceDirect
Available online at www.sciencedirect.com Procedia Engineering 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia
Procedia Engineering 205 (2017) 3916–3922
10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China
Numerical simulation study of the heat transfer characteristic in Ωshape grooved heat pipes Kaimin Yanga,b,c*, Zhuang Congd, Yudong Maoa,b,c, Xiuli Zhanga School of Thermal Engineering, Shandong Jianzhu University, Jinan 250101, China Key Laboratory of Renewable Energy Technologies for Buildings, Ministry of Education, Jinan 250101, China cc Shandong Key Laboratory of Renewable Energy Technologies for Buildings, Jinan 250101, China d d Zhongshi Yitong Group, Jinan 250101, China a a
bb
Abstract Heat pipes are devices capable of very high heat transfer and have been widely used in many thermal management applications. An experimental investigation and CFD simulation of thermal characteristics of heat pipe was presented in the present work. It can be found that using FLUENT can simulate the evaporation and condensation in heat pipe. With the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. With the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the equivalent thermal conductivity reduces gradually. Results in the present work can provide guidance to further research of grooved heat pipe. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Conditioning. Air Conditioning. Keywords: Grooved heat pipe; Numerical simulation; Steam chamber diameter; Channel number
1. Introduction Grooved heat pipe is a reliable and efficient heat transport device. The heat pipe has been used in several technologically important processes requiring augmented heat transfer e.g., in the electronic packaging industry, in micro-gravity environments, and spacecraft thermal control because of its high efficiency, reliability and cost effectiveness[1-6]. Cotter[7] firstly proposed the concept of micro-heat pipe. That is essentially a wickless heat pipe * Corresponding author. Tel.: +086-0531-86361236; fax: +086-0531-86361236. E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.10.033
2
Kaimin Yang et al. / Procedia Engineering 205 (2017) 3916–3922 Kaimin Yang, et al. / Procedia Engineering 00 (2017) 000–000
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for the uniform temperature distribution in electronic chips. After Cotter’s research, 1D model[8], 2D model[9-10] and 3D model[11] for theory analysis of fluid flow and heat transfer in heat pipe were built. Tiselj et al.[12] simulated the single phase flow in a 3D model using the CFD code CFX. Sandra C. K. [13] and Huang Mei et al. [14] modeled the phase change and two phase flow in a pipe using FLUENT. There are a few papers aiming to solve the multi-phase flow in different cases[15-17]. In the present study, 3D model of two phase flow and heat transfer in a Ω-shaped heat pipe was built. The evaporation and condensation in heat pipe were simulated using FLUENT, and the experimental data are compared with the simulating results in order to verifying the simulating model. 2. Experimental facilities Ω-shape grooved heat pipe changes periodically in structure, and exactly the same for each channel. In figure 1, one of the pipes with different geometry has been shown. The package of heat pipe is aluminium alloy, and working fluid is ammonia.
Fig. 1. Geometry of heat pipe for experiments
Fig. 2. Schematic of experimental set up 1-heat pipe, 2-thermocouples, 3-electrical heaters, 4-DC electrical source, 5-watercooling jacket, 6thermostatic waterbath, 7-data acquisition system, 8-computer, 9-insulating layer
As shown in Figure 2, the evaporator section was heated by the heater band, and the test error of the input power is within the range of 1W. The condenser section was cooled by cooling water with constant temperatures. And the glass rotameters having 5% error range are used to measure the water flow rate, which is controlled by the valve. The experiments are carried out at the room temperature, about 20℃, the axial temperature distribution of the heat pipe is measured by thermocouples with an uncertainty of ±0.25℃, and the working temperature is regarded as the mean value of these measured temperatures. The numbers of thermocouples, which are symmetrically distributed at evaporator sector, adiabatic sector and condenser sector, are 3, 3 and 3 respectively. An intermediate plate having thickness of 0.2mm is placed between the thermocouples and the resistor. This intermediate plate can protect the thermocouples against a direct contact with resistor and can help to evenly heat the evaporator sector.
Kaimin Yang et al. / Procedia Engineering 205 (2017) 3916–3922 Kaimin Yang, et al./ Procedia Engineering 00 (2017) 000–000
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The electrical power to the band heaters was supplied using a 220V variable DC power source with uncertainty ±2.5W. 3. Physical models From figure 1, it can be seen that Ω-shape grooved heat pipe changes periodically in structure, and exactly the same for each channel. Therefore, in order to reduce the time and resources required by calculation, a single channel was selected as the study object to handle, as shown in Figure 3(a). Table 1. Parameters of heat pipe models Parameters
(a) Groove
(b) Mesh
Value
Out diameter Do (mm)
16
Core diameter Dv (mm)
8
Channel diameter d (mm)
1.2
Slit width W (mm)
0.4
Slit depth δ (mm)
0.6
Length of evaporation section Le (mm)
200
Length of adiabatic section La (mm)
500
Length of condensation section Lc (mm)
300
Filling ratio FR
0.346
Saturation temperature(K)
283, 293, 303
Fig. 3. Schematic diagram of calculation models
To compare with experimental data, heat pipe model of 1000mm long was first established. The length of the evaporator, adiabatic section and condensation section respectively are 200mm, 500mm and 300mm, that the same with experimental sets. Completely filling quantity of heat pipe in the present work refers that the grooves are occupied by liquid totally, then the liquid portion is 0.346 for the pipe’s total volume that means the filling ratio is 0.346. Structure parameters and other relevant variable parameters of heat Pipes are shown in Table 1, where the saturation temperature equals to heat pipe operating temperature corresponding to the experimental data. 4. Numerical methods Initial conditions: temperature of the entire simulation zone has been set to the operating temperature of heat pipe, speed of the fluid field is 0, and pressure is the saturation pressure corresponding to the operating temperature. Boundary conditions: for the surfaces of outer wall in evaporation section, adiabatic section, and condensation section, heat fluxes through boundaries are all constant. Heat flux density in the adiabatic section is 0, which on the surfaces of evaporation and condenser section equal to the ratio of power and surface areas respectively. Eulerian model has been chosen, and the processing method of source terms is the same with that in the literature[10]. SIMPLE algorithm has been chosen to solve pressure-speed coupling. The first-order upward difference was chosen to solve momentum equations and energy equations. The entire calculation process is a transient calculation, the time step-length is 0.001s.
4
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5. Numerical verification In the present work, the grid independence verification has been made initially. Then graphics software Pro-E was chosen to build geometrical model, and structured grid was chosen which generated by ANSYS ICEM 14.0, as shown in Figure 3(b). There are four sorts of different grid density meshes to verify grid independence, and the specific parameters are shown in Table 2. As it has been shown in figure 4, there has a relationship between calculation results and mesh density. The error between results calculated separately with mesh M1 and M2 is 16.74%, which is 10.80% for M2and M3, and 2.29% for M3and M4 respectively. So it is acceptable to calculate using mesh M3. It is also can be seen that the number of elements of M3 is much less than that of M4, which means more less computing resources. All of calculation in the present work adopted the density of mesh M3. Table 2. Mesh parameters Parameters
Value
No.
M1
M2
M3
Mesh Nodes
1727276
2880896
3578112
4739696
Mesh elements
1578536
2655336
3331328
4444160
0.150 0.145 0.140 0.135
R t(K/W)
Rt(K/W)
0.130 0.125 0.120 0.115 0.110 0.105 0.100
M4
1
2
3
Mesh number
Fig. 4. Thermal resistance versus mesh grid
4
0.160 0.155 0.150 0.145 0.140 0.135 0.130 0.125 0.120 0.115 0.110 0.105 0.100 0.095
Experimental data Simulation results
20
40
60
80
100 120 140 160 180 200 220
Input power(W)
Fig. 5. Comparison of thermal resistance between experimental data and numerical results
In order to verify the reliability of numerical method, some cases were simulated corresponding experimental conditions, and a group comparison of thermal resistance between the experimental data and numerical results is shown in figure 5. As shown in the figure, the error between the simulation and experimental results is in the range of 9.68%-15.77%, which is permissible, indicating it is good at accuracy and reliability for the calculation model. 6. Discussion 6.1. Chamber diameter From figure 6, it can be seen that, with the constantly increase of steam chamber diameter from 7.6mm to 8.4mm, thermal resistance is on a decline trend. The reason for this is, with the increase of chamber diameter, metal between channels and chamber becomes less, which leads to both decrease in rib thermal resistance and flow resistance, and the total thermal resistance of heat pipe reduces finally. Under different operating temperatures, the thermal resistance of heat pipe do not show a significant difference between each other, and the trend of which is also obvious. As the working temperatures rising, thermal resistance gradually increases. That is because the
Kaimin Yang et al. / Procedia Engineering 205 (2017) 3916–3922 Kaimin Yang, et al./ Procedia Engineering 00 (2017) 000–000
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transmission factor and other physical properties will change when temperature of working fluid rises, that leads to decrease of heat transfer capacity. 0.109
twork=283K
0.108
twork=293K twork=303K
Rt(K/W)
0.107 0.106 0.105 0.104 0.103 0.102 7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig. 6. Thermal resistance versus chamber diameter
From figure 7, it can be seen that, with the constantly increase of steam chamber diameter from 7.6mm to 8.4mm, maximum heat transfer capacity of heat pipe is on an increasing trend which varies almost linearly. The increase of chamber diameter can leads to decrease in flow resistance of steam in steam chamber, but that also makes slit depth smaller which leads to contact area between the steam in steam chamber and reflux liquid in channels becomes bigger and bigger, and interaction force between them has been enhanced. So the total heat transfer has been enhanced, but not so great. Under different operating temperatures, the maximum heat transfer capacity of do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the maximum heat transfer capacity reduces gradually, that mainly determined by the changes in thermal physical properties of working fluid. 250 245
36600
twork=283K
240
36200
Keff(W/(m ∗Κ)
220
2
Qmax(W)
twork=303K
35800
225 215 210 205 200
35600 35400 35200 35000 34800 34600
195
34400
190 185
twork=293K
36000
twork=303K
230
twork=283K
36400
twork=293K
235
34200
7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig. 7. Maximum heat transfer capacity versus chamber diameter
7.6
7.8
8.0
8.2
8.4
Dv(mm)
Fig.8. Equivalent thermal conductivity versus chamber diameter
From figure 8, it can be seen that, with the constantly increase of chamber diameter from 7.6mm to 8.4mm, the equivalent thermal conductivity of heat pipe is on an increasing trend. Under different operating temperatures, the equivalent thermal conductivity of heat pipe do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the equivalent thermal conductivity of heat pipe gradually increases. From the discussion above, in the scope of chamber diameter considered in the present work, with the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. The bigger chamber size can lead to reduce in flow resistance and increase in interaction force between vapor and liquid, so the improvement of heat transfer capability of heat pipe is not so great finally.
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6.2. Channel number From figure 9, it can be seen that, with the constantly increase of channel number from 15 to 19, thermal resistance is on an increasing trend. The reason for this is, with the increase of channel number, metal between channels become less, that leads to increase of rib thermal resistance, and the total thermal resistance of the heat pipe increases finally. Under different operating temperatures, the thermal resistance of the heat pipe do not show a significant difference between each other, and the trend of which is also obvious. As the working temperature rising, thermal resistance gradually increases. The reason for this is the same with that for chamber diameter. 0.120 0.118
twork=283K
0.116
twork=293K
0.114
twork=303K
Rt(K/W)
0.112 0.110 0.108 0.106 0.104 0.102 0.100 0.098
15
16
17
18
19
N
Fig. 9. Thermal resistance versus channel number
From figure 10, it can be seen that, with the constantly increase of channel number from 15 to 19, maximum heat transfer capacity of heat pipe is on an increasing trend which varies almost linearly. The increase of channel number can leads to increase in the flow section of liquid in grooves, then the liquid pressure drop becomes smaller. So the total heat transfer has been enhanced. Under different operating temperatures, the maximum heat transfer capacity of do not show a significant difference between each other, and the trend of which is obvious. As working temperatures rising, the maximum heat transfer capacity reduces gradually, that mainly determined by the changes in thermal physical properties of working fluid. From figure 11, it can be seen that, with the constantly increase of channel number from 15 to 19, the equivalent thermal conductivity of heat pipe is on a decline trend. Under different operating temperatures, the equivalent thermal conductivity of do not show a significant difference between each other, and the trend of which is obvious. As working temperature rising, the equivalent thermal conductivity of heat pipe gradually decreases. 38000 280
twork=293K
twork=303K
35000
2
Keff(W/(m ∗Κ)
Qmax(W)
220 200 180
34000 33000 32000
160 140
twork=293K
36000
twork=303K
240
twork=283K
37000
twork=283K
260
31000 15
16
17
18
19
N
Fig.10. Maximum heat transfer capacity versus channel number
15
16
17
18
19
N
Fig.11. Equivalent thermal conductivity versus channel number
From the discussion above, in the scope of channel number considered in the present work, with the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing
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trend, however, the equivalent thermal conductivity reduces gradually. The bigger channel number can lead to reduce in flow resistance and even more increase in thermal resistance, so heat transfer capability of heat pipe declines finally. 7. Conclusions 1) The model established in the present work can simulate the operation of heat pipe well. 2) The physical property changes of working fluid have been considered. 3) With the increase of chamber diameter, the equivalent thermal conductivity and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the thermal resistance reduces gradually. 4) With the increase of channel number, the thermal resistance and maximum heat transfer capacity of heat pipe are both on an increasing trend, however, the equivalent thermal conductivity reduces gradually. Acknowledgement This paper is supported by Research Fund for the Doctoral Program of Shandong Jianzhu University (0000601337), and Natural Science Foundation of Shandong Province of China (ZR2016EEB15). References [1] Zhuang Jun, Zhang Hong. Heat Pipe Technology and Engineering Application. Beijing: Chemical Industry Press, 2000. [2] XIN Gongming, DU Wenjing, WANG Naihua. Development of thermal control system for AMS electronic units on ISS. Chinese Science Bulletin, 2012, 57 (5): 382–389. [3] Y. Tang, P. Chen, X. W. Wang. Experimental investigation into the performance of heat pipe with micro grooves fabricated by Extrusionploughing process. Energy Conversion and Management, 2010, 51: 1849–1854. [4] Chen Yongping, Zhu Wangfa et al. Thermal Characteristics of Heat Pipe with Axially Swallow-tailed Microgrooves. Chinese Journal of Chemical Engineering, 2010, 18(2): 185–193. [5] A. Faghri. Heat Pipe science and technology. Washington DC: Taylor & Francis, 1995. [6] T. P. Cotter. Principles and prospects for micro heat pipes. In: Fifth international heat pipe conference, Tsukuba, Japan, 1984. [7] T. P. Cotter. Theory of heat pipes. Los Alamos Scientific Lab: Report No. LA–3246–MS, 1965. [8] J. P. Longtin et al. A one-dimensional model of a micro heat pipe during steady-state operation. Journal of Heat Transfer, 1994, 116(3):709. [9] P. C. Stephan, C. A. Busse. Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Int J Heat Mass Transfer, 1992, 35(2): 383. [10] H. B. Ma, G. P. Peterson. Temperature variation and heat transfer in triangular grooves with an evaporating film. J Thermophys Heat Transfer, 1997, 11(1): 90. [11] Sartre V. et al. Effect of interfacial phenomena on evaporative heat transfer in micro heat pipes. Int J Therm Sci, 2000: 39: 498–504. [12] Tiselj I et al. Effect of axial conduction on the heat transfer in micro-channels. Int J Heat Mass Transfer, 2004, 47(12–13): 2551. [13] Sandra C. K. De Schepper et al. Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker. Computers and Chemical Engineering, 2009, 33: 122–132. [14] Huang Mei, Yang Zhen, Wang Buxuan. Simulation of bubbly flow heat transfer in a serpentine tube. CIESC Journal, 2011, 62(12): 3345– 3351. [15] J. D. Li. CFD simulation of water vapour condensation in the presence of non-condensable gas in vertical cylindrical condensers. International journal of heat and mass transfer, 2013, 57: 708–721. [16] L. M. Pan, Z. W. Tan, D. Q. Chen, L. C. Xue. Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel. Nuclear Engineering and Design, 2012, 248: 126–136. [17] Z. R. Lin, S. F. Wang, Ryo. Shirakashi, L. W. Zhang. Simulation of a miniature oscillating heat pipe in bottom heating mode using CFD with unsteady modeling. International journal of heat and mass transfer, 2013, 57: 642–656.