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The document summarizes a numerical simulation of flow through microchannels in bipolar plates. It studies the effect of various obstruction geometries (rectangular, triangular) and heights on the pressure drop across single obstructions at different Reynolds numbers. The pressure drop increases nonlinearly with obstruction height and Reynolds number. It also decreases linearly as the obstruction geometry changes from rectangular to triangular, as the change in velocity is more gradual. The study provides insight into flow behavior and pressure variations in serpentine microchannels with wall obstructions.

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Proceedings of ICMM2005 2005 3rd International Conference on Microchannels and Minichannels June 13-15, 2005, Toronto Canada ICMM2005-75251 NUMERICAL SIMULATION OF FLOW THROUGH MICROCHANNELS IN BIPOLAR PLATE A. S. Rawool Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India S. K. Mitra Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India Email: skmitra@me.iitb.ac.in A. Agrawal Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India S. Kandlikar Department of Mechanical Engineering Rochester Institute of Technology Rochester, NY 14623-5603 KEYWORDS serpentine; bipolar plate; numerical; obstructions; two dimen- sional; modeling ABSTRACT In this paper, the 鍖ow through a serpentine microchannel with obstructions on wall is studied. Various obstruction geome- tries ranging from rectangular to triangular are considered. For each geometry pressure drop across single obstruction is stud- ied at various Reynolds numbers. Also the effect of obstruc- tion height on the pressure drop is investigated. A parametric study is conducted for different obstruction heights, geometries and Reynolds numbers. NOMENCLATURE 袖 Viscosity of liquid Density of liquid u Velocity component in x-direction Corresponding Author v Velocity component in y-direction P Pressure Hobs Height of obstruction l1 Streamwise length of obstruction at top l2 Streamwise length of obstruction at bottom L1 Length of longer section of channel L2 Length of shorter section of channel Re Reynolds number 1 Introduction Serpentine channels are widely used in fuel cell bipolar plates as 鍖ow passages for fuel (hydrogen) and oxidizer (air). Serpentine channels have the advantage of compact size for channel with a long length. The 鍖ow through these channels is different from straight channels due to their serpentine geom- etry. Various types of obstructions are placed on the walls of these channels in order to improve momentum transfer and dif- fusion through the corresponding anode/cathode diffusion layer. The 鍖ow through channels and the effect of obstructions at the entrance is studied in macro domain by Kabir et al. [1]. Pressure 1 Copyright c 2005 by ASME
losses in 鍖ow through fuel cell stack has been studied by Ma- harudrayya et al. [2]. The pressure drop over wall obstructions in microchannels is of interest, as it departs signi鍖cantly from the pressure drop calculated using classical sudden contraction and expansion correlations [3]. This paper aims at numerically sim- ulating the 鍖ow through a serpentine microchannel with obstruc- tions placed on channel walls and studying the effect of various parameters such as Reynolds number, obstruction geometry and height. 2 Problem Statement A schematic of the channel considered is shown in Fig. 1. A two dimensional case is consider to reduce the computational L2 L1 Figure 1. Geometry of serpentine channel efforts required. The width of the channel considered is 100袖m with L1 = 1000袖m and L2 = 700袖m. The radius of curvature of channel axis is 150袖m. The enlarged view of the obstruction is shown in Fig. 2. An aspect ratio for the obstruction is de鍖ned as Figure 2. Geometry of obstruction. A = l1 l2 (1) which is varied from 1(for rectangular obstruction) to 0 (for tri- angular obstruction). Typical values of l1 and l2 for A = 0.5 are 50 袖m and 100 袖m, respectively. The height of the obstruction is varied from 10袖m to 50袖m. A normalized height of obstruction is de鍖ned as h = height of obstruction width of the channel (2) h is varied from 0.1 to 0.5. Following assumptions are made in the problem: 1. Steady 鍖ow of air through the channel. 2. Constant properties. 3. Two dimensional 鍖ow. 3 Results and Discussion Commercial CFD code CFD-ACE+ [4] is used to numer- ically simulate the 鍖ow through the channel. Constant veloc- ity boundary condition is used at inlet and constant pressure is speci鍖ed at outlet. Velocities corresponding to Reynolds number range of 10 to 50 are used for solving the problem. The velocity solutions around the obstruction given by the model are shown in Fig. 3 for the case of Re = 40, h = 0.1 and A = 1. The ve- locity vectors show the recirculation of air around the corners of the obstruction. Figures 4-6 show velocity and pressure pro- Figure 3. Velocity vector map around obstruction. 鍖les along channel cross section at upstream of obstruction, at obstruction and at the downstream of obstruction respectively. It can be seen that the velocity pro鍖les correspond to parabolic pro- 鍖le of laminar 鍖ow. Pressure across any section in the channel is not uniform but it is 鍖uctuating along the cross section. 2 Copyright c 2005 by ASME
Figure 4. Velocity and pressure pro鍖le before obstruction. Figure 5. Velocity and pressure pro鍖le at obstruction. Figure 6. Velocity and pressure pro鍖le after obstruction. The pressure drop predicted by the simulation across single obstruction is considered to study the effect of various parame- ters on the 鍖ow. 3.1 Effect of obstruction height: Figure 7. Variation of pressure drop with height at Re = 10 Figures 7 to 11 show the effect of the height of obstruction on the pressure drop across the channel, for various channel ge- ometries. It can be seen that the pressure drop increases nonlin- early with height of obstruction. Initially pressure drop increases slowly, but as the height of obstruction increases there is a rapid increase in the pressure drop. This is due to the decrease in 鍖ow area with corresponding increase in velocity. The pressure drop across a sudden contraction-expansion is directly proportional to square of maximum velocity (i.e. the velocity at the obstruction), hence there is a second order increase in the pressure drop with increasing height of obstruction. The rate of increase is high- Figure 8. Variation of pressure drop with height at Re = 20 3 Copyright c 2005 by ASME
Figure 9. Variation of pressure drop with height at Re = 30 Figure 10. Variation of pressure drop with height at Re = 40 est for rectangular obstruction and it goes on decreasing as the geometry is changed towards triangular obstruction. As the ge- ometry is changed from rectangular to triangular, the change in velocity is more gradual. It is also observed that the nature of variation of pressure drop with height is similar for the given Reynolds number range. The rate of increase of pressure drop is the same for all Reynolds numbers, if all the other parameters remain the same. 3.2 Effect of Reynolds number: The effect of Reynolds number on pressure drop variation is depicted in Fig. 12-16. It can be seen that the pressure drop in this case also changes nonlinearly with Reynolds number, but this non-linearity is not as severe as the case with chang- Figure 11. Variation of pressure drop with height at Re = 50 Figure 12. Variation of pressure drop with Re at Hobs = 10袖m ing obstruction height. This may be due to very small values of Reynolds number used, which are typical of microchannel 鍖ows. The effect of obstruction geometry is the same as previous case, i.e., for rectangular obstructions the pressure drop is highest and as the geometry is changed to triangle, the pressure drop goes on decreasing. 3.3 Effect of obstruction geometry: Figures 17 to 21 show the effect of the obstruction geom- etry on the pressure drop. It can be seen from the 鍖gures that with increasing the aspect ratio, the pressure drop across the ob- struction increases almost linearly. This is expected since, as the aspect ratio is changed from 0 (for triangular obstruction), to 1 (for rectangular obstruction), the transition from lower to higher velocity takes place more suddenly. Hence, there is more pres- sure drop for rectangular obstruction. Also, as the geometry de- parts from rectangular shape the relations for sudden expansion and contraction become inapplicable as the change in velocity is 4 Copyright c 2005 by ASME
Figure 13. Variation of pressure drop with Re at Hobs = 20袖m Figure 14. Hobs = 30袖m Figure 15. Variation of pressure drop with Re at Hobs = 40袖m more gradual and not sudden. 4 Conclusion: The effect of three parameters, obstruction height, geome- try and Reynolds number on pressure drop is studied for 鍖ow Figure 16. Hobs = 50袖m Figure 17. Variation of pressure drop with aspect ratio at Re = 10 Figure 18. Variation of pressure drop with aspect ratio at Re = 20 through a serpentine microchannel with obstructions on wall. It is found that the pressure drop across the obstruction increases in a non-linear fashion with increase in obstruction height. The pressure drop also increases with increasing Reynolds number but the non-linearity is less pronounced in this case. The pressure drop is found to decrease as the obstruction geometry is changed from rectangular to triangular. 5 Copyright c 2005 by ASME
Figure 19. Variation of pressure drop with aspect ratio at Re = 30 Figure 20. Variation of pressure drop with aspect ratio at Re = 40 Figure 21. Variation of pressure drop with aspect ratio at Re = 10 5 Acknowledgment The support of Suman Mashruwala MEMS Laboratory, IITB is highly appreciated. REFERENCES [1] Kabir, M. A., Khan, M. M. K., and Bhuiyan, M. A., 2004. Flow phenomena in a channel with different shaped ob- structions at the entrance. Fluid Dynamic Research, 35 , pp. 391408. [2] Maharudrayya, S., Jayanti, S., and Deshpande, A. P., 2004. Pressure losses in laminar 鍖ow through serpentine channels in fuel cell stacks. Journal of Power Sources, 138 , pp. 1 13. [3] Fox, R. W., McDonald, A. T., and Pritchard, P. J., 2001. In- troduction to Fluid Mechanics. John Wiley and Sons. [4] CFD-ACE+ software manuals. CFD Research Corpora- tion. 6 Copyright c 2005 by ASME

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  • 1. Proceedings of ICMM2005 2005 3rd International Conference on Microchannels and Minichannels June 13-15, 2005, Toronto Canada ICMM2005-75251 NUMERICAL SIMULATION OF FLOW THROUGH MICROCHANNELS IN BIPOLAR PLATE A. S. Rawool Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India S. K. Mitra Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India Email: skmitra@me.iitb.ac.in A. Agrawal Department of Mechanical Engineering Indian Institute of Technology, Bombay Mumbai, 400076 India S. Kandlikar Department of Mechanical Engineering Rochester Institute of Technology Rochester, NY 14623-5603 KEYWORDS serpentine; bipolar plate; numerical; obstructions; two dimen- sional; modeling ABSTRACT In this paper, the 鍖ow through a serpentine microchannel with obstructions on wall is studied. Various obstruction geome- tries ranging from rectangular to triangular are considered. For each geometry pressure drop across single obstruction is stud- ied at various Reynolds numbers. Also the effect of obstruc- tion height on the pressure drop is investigated. A parametric study is conducted for different obstruction heights, geometries and Reynolds numbers. NOMENCLATURE 袖 Viscosity of liquid Density of liquid u Velocity component in x-direction Corresponding Author v Velocity component in y-direction P Pressure Hobs Height of obstruction l1 Streamwise length of obstruction at top l2 Streamwise length of obstruction at bottom L1 Length of longer section of channel L2 Length of shorter section of channel Re Reynolds number 1 Introduction Serpentine channels are widely used in fuel cell bipolar plates as 鍖ow passages for fuel (hydrogen) and oxidizer (air). Serpentine channels have the advantage of compact size for channel with a long length. The 鍖ow through these channels is different from straight channels due to their serpentine geom- etry. Various types of obstructions are placed on the walls of these channels in order to improve momentum transfer and dif- fusion through the corresponding anode/cathode diffusion layer. The 鍖ow through channels and the effect of obstructions at the entrance is studied in macro domain by Kabir et al. [1]. Pressure 1 Copyright c 2005 by ASME
  • 2. losses in 鍖ow through fuel cell stack has been studied by Ma- harudrayya et al. [2]. The pressure drop over wall obstructions in microchannels is of interest, as it departs signi鍖cantly from the pressure drop calculated using classical sudden contraction and expansion correlations [3]. This paper aims at numerically sim- ulating the 鍖ow through a serpentine microchannel with obstruc- tions placed on channel walls and studying the effect of various parameters such as Reynolds number, obstruction geometry and height. 2 Problem Statement A schematic of the channel considered is shown in Fig. 1. A two dimensional case is consider to reduce the computational L2 L1 Figure 1. Geometry of serpentine channel efforts required. The width of the channel considered is 100袖m with L1 = 1000袖m and L2 = 700袖m. The radius of curvature of channel axis is 150袖m. The enlarged view of the obstruction is shown in Fig. 2. An aspect ratio for the obstruction is de鍖ned as Figure 2. Geometry of obstruction. A = l1 l2 (1) which is varied from 1(for rectangular obstruction) to 0 (for tri- angular obstruction). Typical values of l1 and l2 for A = 0.5 are 50 袖m and 100 袖m, respectively. The height of the obstruction is varied from 10袖m to 50袖m. A normalized height of obstruction is de鍖ned as h = height of obstruction width of the channel (2) h is varied from 0.1 to 0.5. Following assumptions are made in the problem: 1. Steady 鍖ow of air through the channel. 2. Constant properties. 3. Two dimensional 鍖ow. 3 Results and Discussion Commercial CFD code CFD-ACE+ [4] is used to numer- ically simulate the 鍖ow through the channel. Constant veloc- ity boundary condition is used at inlet and constant pressure is speci鍖ed at outlet. Velocities corresponding to Reynolds number range of 10 to 50 are used for solving the problem. The velocity solutions around the obstruction given by the model are shown in Fig. 3 for the case of Re = 40, h = 0.1 and A = 1. The ve- locity vectors show the recirculation of air around the corners of the obstruction. Figures 4-6 show velocity and pressure pro- Figure 3. Velocity vector map around obstruction. 鍖les along channel cross section at upstream of obstruction, at obstruction and at the downstream of obstruction respectively. It can be seen that the velocity pro鍖les correspond to parabolic pro- 鍖le of laminar 鍖ow. Pressure across any section in the channel is not uniform but it is 鍖uctuating along the cross section. 2 Copyright c 2005 by ASME
  • 3. Figure 4. Velocity and pressure pro鍖le before obstruction. Figure 5. Velocity and pressure pro鍖le at obstruction. Figure 6. Velocity and pressure pro鍖le after obstruction. The pressure drop predicted by the simulation across single obstruction is considered to study the effect of various parame- ters on the 鍖ow. 3.1 Effect of obstruction height: Figure 7. Variation of pressure drop with height at Re = 10 Figures 7 to 11 show the effect of the height of obstruction on the pressure drop across the channel, for various channel ge- ometries. It can be seen that the pressure drop increases nonlin- early with height of obstruction. Initially pressure drop increases slowly, but as the height of obstruction increases there is a rapid increase in the pressure drop. This is due to the decrease in 鍖ow area with corresponding increase in velocity. The pressure drop across a sudden contraction-expansion is directly proportional to square of maximum velocity (i.e. the velocity at the obstruction), hence there is a second order increase in the pressure drop with increasing height of obstruction. The rate of increase is high- Figure 8. Variation of pressure drop with height at Re = 20 3 Copyright c 2005 by ASME
  • 4. Figure 9. Variation of pressure drop with height at Re = 30 Figure 10. Variation of pressure drop with height at Re = 40 est for rectangular obstruction and it goes on decreasing as the geometry is changed towards triangular obstruction. As the ge- ometry is changed from rectangular to triangular, the change in velocity is more gradual. It is also observed that the nature of variation of pressure drop with height is similar for the given Reynolds number range. The rate of increase of pressure drop is the same for all Reynolds numbers, if all the other parameters remain the same. 3.2 Effect of Reynolds number: The effect of Reynolds number on pressure drop variation is depicted in Fig. 12-16. It can be seen that the pressure drop in this case also changes nonlinearly with Reynolds number, but this non-linearity is not as severe as the case with chang- Figure 11. Variation of pressure drop with height at Re = 50 Figure 12. Variation of pressure drop with Re at Hobs = 10袖m ing obstruction height. This may be due to very small values of Reynolds number used, which are typical of microchannel 鍖ows. The effect of obstruction geometry is the same as previous case, i.e., for rectangular obstructions the pressure drop is highest and as the geometry is changed to triangle, the pressure drop goes on decreasing. 3.3 Effect of obstruction geometry: Figures 17 to 21 show the effect of the obstruction geom- etry on the pressure drop. It can be seen from the 鍖gures that with increasing the aspect ratio, the pressure drop across the ob- struction increases almost linearly. This is expected since, as the aspect ratio is changed from 0 (for triangular obstruction), to 1 (for rectangular obstruction), the transition from lower to higher velocity takes place more suddenly. Hence, there is more pres- sure drop for rectangular obstruction. Also, as the geometry de- parts from rectangular shape the relations for sudden expansion and contraction become inapplicable as the change in velocity is 4 Copyright c 2005 by ASME
  • 5. Figure 13. Variation of pressure drop with Re at Hobs = 20袖m Figure 14. Hobs = 30袖m Figure 15. Variation of pressure drop with Re at Hobs = 40袖m more gradual and not sudden. 4 Conclusion: The effect of three parameters, obstruction height, geome- try and Reynolds number on pressure drop is studied for 鍖ow Figure 16. Hobs = 50袖m Figure 17. Variation of pressure drop with aspect ratio at Re = 10 Figure 18. Variation of pressure drop with aspect ratio at Re = 20 through a serpentine microchannel with obstructions on wall. It is found that the pressure drop across the obstruction increases in a non-linear fashion with increase in obstruction height. The pressure drop also increases with increasing Reynolds number but the non-linearity is less pronounced in this case. The pressure drop is found to decrease as the obstruction geometry is changed from rectangular to triangular. 5 Copyright c 2005 by ASME
  • 6. Figure 19. Variation of pressure drop with aspect ratio at Re = 30 Figure 20. Variation of pressure drop with aspect ratio at Re = 40 Figure 21. Variation of pressure drop with aspect ratio at Re = 10 5 Acknowledgment The support of Suman Mashruwala MEMS Laboratory, IITB is highly appreciated. REFERENCES [1] Kabir, M. A., Khan, M. M. K., and Bhuiyan, M. A., 2004. Flow phenomena in a channel with different shaped ob- structions at the entrance. Fluid Dynamic Research, 35 , pp. 391408. [2] Maharudrayya, S., Jayanti, S., and Deshpande, A. P., 2004. Pressure losses in laminar 鍖ow through serpentine channels in fuel cell stacks. Journal of Power Sources, 138 , pp. 1 13. [3] Fox, R. W., McDonald, A. T., and Pritchard, P. J., 2001. In- troduction to Fluid Mechanics. John Wiley and Sons. [4] CFD-ACE+ software manuals. CFD Research Corpora- tion. 6 Copyright c 2005 by ASME