EFFECTS OF THE REYNOLDS AND KNUDSEN NUMBERS ON THE FLOW OF A MICRO-VISCOUS PUMP

Reynolds 수와 Knudsen 수가 초소형 점성펌프에 미치는 영향

  • Published : 2008.06.30

Abstract

Effects of the Reynolds and Knudsen numbers on a micro-viscous pump are studied by using a Navier-Stokes code based on a finite volume method. The micro viscous pump consists of a circular rotor and a two-dimensional channel. The channel walls are treated by using a slip velocity model. The Reynolds number is studied in the range of $0.1{\sim}50$. The Knudsen number varies from 0.01 to 0.1. Numerical solutions show that the pump works efficiently when two counter rotating vortices formed on both sides of the rotor have the same size and intensity. As the Reynolds number increases, the size and intensity of the vortex on the inlet side of the pump decrease. It disappears when the Reynolds number is larger than about Re=20. The characteristics of the performance of the pump is shown to deteriorate, in terms of mean velocity and pressure rise, as the Reynolds number increases. The Knudsen number shows a different effect on the characteristics of the pump. As it increases, the mean velocity and pressure rise decrease but the characteristics of the vortex flow remains unchanged, unlike the effect of Reynolds number.

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References

  1. 1999, Gad-el-Hak, M., "The Fluid Mechanics of Microdevices - The Freeman scholar Lecture," Journal of Fluid Engineering, ASME, Vol.121, pp.5-33 https://doi.org/10.1115/1.2822013
  2. 1990, Bart, S.F., Tavrow, L.S., Mehregany, M. and Lang, J.H., "Microfabricated Electrohydrodynamic Pumps," Sensors and Actuators A, Vol.21, pp.193-197 https://doi.org/10.1016/0924-4247(90)85037-5
  3. 1991, Moroney, R.M., White, R.M. and Howe, R.T., "Ultrasonically Induced Microtransport," Proceedings IEEE MEMS 91 (Nara, Japan), IEEE New York, pp.278-282
  4. 1996, Sen, M., Wajerski, D. and Gad-el-hak, M., "A Novel Pump for MEMS Applications," Journal of Fluid Engineering, ASME, Vol.118, pp.624-627 https://doi.org/10.1115/1.2817807
  5. 1988, Van Lintel, H.T.G., Van de Pol, F.C.M. and Bouwstra, S., "A Piezoelectric Micropump Based on Micromachining of Silicon," Sensors and Actuators, Vol.15, pp.153-167 https://doi.org/10.1016/0250-6874(88)87005-7
  6. 1972, Taylor, Sir G., "Low Reynolds Number Flows," Illustrated Experiments in Fluid Mechanics, National Committee for Fluid Mechanics Films, M.I.T. Press, Cambridge, MA., pp.47-53
  7. 2006, 강동진, "초소형 점성펌프의 Navier-Stokes 해석," 한국전산유체공학회, 제11권 제4호, pp.75-80
  8. 1998, Kang, D.J., Bae, S.S. and Joo, S.W., "비압축성 점성 유동장 해석을 위한 비정렬유한체적법에 관한 연구," 대한기계학회논문집, Vol.22, No.10, pp.1410-1421
  9. 1879, Maxwell, J.C., "On Stresses in Rarefied Gases Arising from Inequalities of Temperature," Philosophical Transactions of the Royal Society, Part I, Vol.170, pp.231-256 https://doi.org/10.1098/rstl.1879.0067
  10. 1961, Schaaf, S.A. and Chambre, P.L., "Flow of Rarefied Gases," Princeton University Press, Princeton, NJ
  11. 1994, Beskok, A. and Karniadakis, G.E., "Simulation of Heat and Momentum Transfer in Complex Micro-Geometries," AIAA J. of Thermophysics and Heat Transfer, Vol.8, No.4, pp.355-370
  12. 1997, Scharatchandra, M.C., Sen, M. and Gad-el-hak, "Navier-Stokes Simulations of a Novel Viscous Pump," Journal of Fluid Engineering, ASME, Vol.119, pp.372-383 https://doi.org/10.1115/1.2819144
  13. 1976, Lord, R.G., "Tangential Momentum Coefficient of Rare Gases on Polycrystalline Surfaces," Proceedings of the 10th Int. Symposium on Rarefied Gas Dynamics, L. Potter, ed., AIAA, New York, pp.531-538