Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness
A two dimensional numerical simulation has been
performed for incompressible and compressible fluid flow through
microchannels in slip flow regime. The Navier-Stokes equations have
been solved in conjunction with Maxwell slip conditions for
modeling flow field associated with slip flow regime. The wall
roughness is simulated with triangular microelements distributed on
wall surfaces to study the effects of roughness on fluid flow. Various
Mach and Knudsen numbers are used to investigate the effects of
rarefaction as well as compressibility. It is found that rarefaction has
more significant effect on flow field in microchannels with higher
relative roughness. It is also found that compressibility has more
significant effects on Poiseuille number when relative roughness
increases. In addition, similar to incompressible models the increase
in average fRe is more significant at low Knudsen number flows but
the increase of Poiseuille number duo to relative roughness is sharper
for compressible models. The numerical results have also validated
with some available theoretical and experimental relations and good
agreements have been seen.
[1] Yan Ji, Kun Yuan, J.N. Chung, Numerical simulation of wall roughness
on gaseous flow and heat transfer in a microchannel, Int. J. Heat Mass
Transfer 49, 2006 1329-1339.
[2] S.G. Kandlikar, S. Joshi, S. Tian, Effect of channel roughness on heat
transfer and fluid flow characteristics at low Reynolds numbers in small
diameter tubes, in: Proceedings of NHTC_01 35th National Heat
Transfer Conference, Anaheim, CA, June 2001, pp. 1-10.
[3] G.M. Mala, D. Li, Flow characteristics of water in microtubes, Int. J.
Heat Mass Transfer 20 (1999) 142-148.
[4] P.Y. Wu, W.A. Little, Measurement of friction factor for the flow of
gases in very fine channels used for microminiature Joule-Thomson
refrigerator, Cryogenics 23 (1983) 273-277.
[5] P.Y. Wu, W.A. Little, Measurement of the heat transfer characteristics of
gas flow in fine channel heat exchangers used for microminiature
refrigerators, Cryogenics 24 (1984) 415-420.
[6] S. B. Choi, R. F. Barron, and R. O. Warrington, Fluid Flow and Heat
Transfer in Microtubes,
[7] M. Usami, T. Fujimoto, S. Kato, Mass-flow reduction of rarefied flow
roughness of a slit surface, Trans. Jpn. Soc. Mech. Eng., B 54 (1988)
1042-1050.
[8] H. Sun, M. Faghri, Effect of surface roughness on nitrogen flow in a
icrochannel using the direct simulation Monte Carlo method, umer. Heat
Transfer Part A 43 (2003) 1-8.
[9] G.E. Karniadakis, A. Beskok, Micro Flows, Fundamental and imulation,
Springer, Berlin, 2002.
[10] E. Turner, H. Sun, M. Faghri, O.J. Gregory, Effect of surface roughness
on gaseous flow through micro channels, 2000 IMECE, TD 366 (2)
(2000) 291-298.
[11] W. Sugiyama, T. Sawada, K. Nakamori, Rarefied gas flow between two
flat plates with two dimensional surface roughness, Vacuum 47 1996)
791-794.
[12] Sugiyama, T. Sawada, M. Yabuki, Y. Chiba, Effects of surface
roughness on gas flow conductance in channels estimated by conical
roughness model, Appl. Surf. Sci. 169-170 (2001) 787-791.
[13] R. Valses, J. Miana, Luis Pelegay, Luis Nunez, Thomas Putz. Numerical
investigation of the influence of roughness on the laminar
incompressible fluid flow through annular microchannels, Int. J. Heat
Mass Transfer 50 (2007) 1865-1878.
[14] Yan Ji, Kun Yuan, J.N. Chung, Numerical simulation of wall roughness
on gaseous flow and heat transfer in a microchannel, Int. J. Heat Mass
Transfer 49 (2006) 1329-1339.
[15] Choi, Hyung-il, Lee, Dong-ho and Lee, Dohyung , (2005) 'Complex
Microscale Flow Simulations Using Langmuir Slip Condition',
Numerical Heat Transfer, Part A: Applications, 48:5, 407 - 425
[16] A. Beskok, G.E. Karniadakis, A model for flows in channels, pipes and
ducts at micro and nanoscales, Microscale Thermophys. Eng. 3 (1999)
43-77.
[17] Porodnov BT, Suetin PE, Borisov SF, Akinshin VD (1974) J Fluid Mech
64:417-437
[18] Arkilic EB, Schmidt MA, Breuer KS (1997) J Microelectromech Syst
6(2):167-178
[19] Maurer J, Tabeling P, Joseph P, Willaime H (2003) Phys Fluid 15:2613-
2621
[20] Colin S, Lalonde P, Caen R (2004) Heat Transfer Eng 25(3):23-30
[21] T. Ewart, P.Perrier, I.Graur, J.Gilbert, "Tangential momemtum
accommodation in microtube", Microfluid nanofluid, (2007) 3:689-695
[22] A. Beskok, G.E. Karniadakis, A model for flows in channels, pipes and
ducts at micro and nanoscales, Microscale Thermophys. Eng. 3 (1999)
43-77.
[23] J.C. Shih, C.M. Ho, J.Q. Liu, Y.C. Tai, Monatomic and polyatomic gas
flow through uniform microchannels, Microelectromechanical Syst. 59
(1996) 197-203.
[24] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat
transfer, Int. J. Heat Mass Transfer 46 (2003) 149-159.
[25] S.E. Turner, Experimental investigation of gas flow in microchannels,
ASME J. Heat Transfer 126 (2004) 753-762.
[1] Yan Ji, Kun Yuan, J.N. Chung, Numerical simulation of wall roughness
on gaseous flow and heat transfer in a microchannel, Int. J. Heat Mass
Transfer 49, 2006 1329-1339.
[2] S.G. Kandlikar, S. Joshi, S. Tian, Effect of channel roughness on heat
transfer and fluid flow characteristics at low Reynolds numbers in small
diameter tubes, in: Proceedings of NHTC_01 35th National Heat
Transfer Conference, Anaheim, CA, June 2001, pp. 1-10.
[3] G.M. Mala, D. Li, Flow characteristics of water in microtubes, Int. J.
Heat Mass Transfer 20 (1999) 142-148.
[4] P.Y. Wu, W.A. Little, Measurement of friction factor for the flow of
gases in very fine channels used for microminiature Joule-Thomson
refrigerator, Cryogenics 23 (1983) 273-277.
[5] P.Y. Wu, W.A. Little, Measurement of the heat transfer characteristics of
gas flow in fine channel heat exchangers used for microminiature
refrigerators, Cryogenics 24 (1984) 415-420.
[6] S. B. Choi, R. F. Barron, and R. O. Warrington, Fluid Flow and Heat
Transfer in Microtubes,
[7] M. Usami, T. Fujimoto, S. Kato, Mass-flow reduction of rarefied flow
roughness of a slit surface, Trans. Jpn. Soc. Mech. Eng., B 54 (1988)
1042-1050.
[8] H. Sun, M. Faghri, Effect of surface roughness on nitrogen flow in a
icrochannel using the direct simulation Monte Carlo method, umer. Heat
Transfer Part A 43 (2003) 1-8.
[9] G.E. Karniadakis, A. Beskok, Micro Flows, Fundamental and imulation,
Springer, Berlin, 2002.
[10] E. Turner, H. Sun, M. Faghri, O.J. Gregory, Effect of surface roughness
on gaseous flow through micro channels, 2000 IMECE, TD 366 (2)
(2000) 291-298.
[11] W. Sugiyama, T. Sawada, K. Nakamori, Rarefied gas flow between two
flat plates with two dimensional surface roughness, Vacuum 47 1996)
791-794.
[12] Sugiyama, T. Sawada, M. Yabuki, Y. Chiba, Effects of surface
roughness on gas flow conductance in channels estimated by conical
roughness model, Appl. Surf. Sci. 169-170 (2001) 787-791.
[13] R. Valses, J. Miana, Luis Pelegay, Luis Nunez, Thomas Putz. Numerical
investigation of the influence of roughness on the laminar
incompressible fluid flow through annular microchannels, Int. J. Heat
Mass Transfer 50 (2007) 1865-1878.
[14] Yan Ji, Kun Yuan, J.N. Chung, Numerical simulation of wall roughness
on gaseous flow and heat transfer in a microchannel, Int. J. Heat Mass
Transfer 49 (2006) 1329-1339.
[15] Choi, Hyung-il, Lee, Dong-ho and Lee, Dohyung , (2005) 'Complex
Microscale Flow Simulations Using Langmuir Slip Condition',
Numerical Heat Transfer, Part A: Applications, 48:5, 407 - 425
[16] A. Beskok, G.E. Karniadakis, A model for flows in channels, pipes and
ducts at micro and nanoscales, Microscale Thermophys. Eng. 3 (1999)
43-77.
[17] Porodnov BT, Suetin PE, Borisov SF, Akinshin VD (1974) J Fluid Mech
64:417-437
[18] Arkilic EB, Schmidt MA, Breuer KS (1997) J Microelectromech Syst
6(2):167-178
[19] Maurer J, Tabeling P, Joseph P, Willaime H (2003) Phys Fluid 15:2613-
2621
[20] Colin S, Lalonde P, Caen R (2004) Heat Transfer Eng 25(3):23-30
[21] T. Ewart, P.Perrier, I.Graur, J.Gilbert, "Tangential momemtum
accommodation in microtube", Microfluid nanofluid, (2007) 3:689-695
[22] A. Beskok, G.E. Karniadakis, A model for flows in channels, pipes and
ducts at micro and nanoscales, Microscale Thermophys. Eng. 3 (1999)
43-77.
[23] J.C. Shih, C.M. Ho, J.Q. Liu, Y.C. Tai, Monatomic and polyatomic gas
flow through uniform microchannels, Microelectromechanical Syst. 59
(1996) 197-203.
[24] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat
transfer, Int. J. Heat Mass Transfer 46 (2003) 149-159.
[25] S.E. Turner, Experimental investigation of gas flow in microchannels,
ASME J. Heat Transfer 126 (2004) 753-762.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:59307", author = "M. Hakak Khadem and M. Shams and S. Hossainpour", title = "Effects of Rarefaction and Compressibility on Fluid Flow at Slip Flow Regime by Direct Simulation of Roughness", abstract = "A two dimensional numerical simulation has been
performed for incompressible and compressible fluid flow through
microchannels in slip flow regime. The Navier-Stokes equations have
been solved in conjunction with Maxwell slip conditions for
modeling flow field associated with slip flow regime. The wall
roughness is simulated with triangular microelements distributed on
wall surfaces to study the effects of roughness on fluid flow. Various
Mach and Knudsen numbers are used to investigate the effects of
rarefaction as well as compressibility. It is found that rarefaction has
more significant effect on flow field in microchannels with higher
relative roughness. It is also found that compressibility has more
significant effects on Poiseuille number when relative roughness
increases. In addition, similar to incompressible models the increase
in average fRe is more significant at low Knudsen number flows but
the increase of Poiseuille number duo to relative roughness is sharper
for compressible models. The numerical results have also validated
with some available theoretical and experimental relations and good
agreements have been seen.", keywords = "Relative roughness, slip flow, Poiseuille number.", volume = "2", number = "5", pages = "708-7", }