Research on Numerical Simulation of Micro-Scale Couette Flow System

Abstract:

In this paper, Couette flow which is a sort of flow system simplified in MEMS is explored mainly. The corresponding mathematical model has been built based on N- S Equation, Fourier’s Law and idea gas state equation. Applying the generalized differential quadrature method (GDQ) , the numerical simulation is made. The new model is verified using the direct simulation of Monte Carlo approach finally. The solutions of two different approaches are analyzed and compared. This model can been used to simulate the gas flow in the slip and transition region. The program of GDQ is simpler than DSMC’s and it’s running cost is much lower. The theoretical model is only able to predict the low speed flowing characteristic when Kn < 1. 2.

• Periodical: Advanced Materials Research (Volumes 347-353)
• Pages: 2645-2650
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.347-353.2645
• Online since: October 2011
• Authors: Xue Tao Duan, Hao Luo, Bin Xu, Jian Bin Luo
• Keywords: Couette Flow, Direct Simulation of Monte Carlo Approach, Generalized Differential Quadrature Method, Knudsen Number, Micro-Electromechanical System (MEMS)

References

[1] X. Minglun, L. Zhanhua: Some limitations of the digital micro propulsion miniature[J]. Micro-Nanometer Science &Technology, Vol.5(2000), p.125

[2] C. Shu, B. C. Khoo, K.S. Yeo, in: Numerical Solutions of Incompressible Navier-Stokes Equations by Generalized Differential Quadrature[J], Finite Elements in Analysis and Design, ,18(1994), p.83

DOI: 10.1016/0168-874x(94)90093-0

[3] J.N. Pfahler, J. Harley, H. Bau, in: Liquid and Gas Transport in Small Channels[J]. Micromechnical Sensors,Actuators and systems. ASME.1991.DSC32.49-60.

[4] H. Xue, L.Xie. Ji, S. K. Chou: Modeling of flow characteristic and heat transfer for micro Couette Flow[J]. International Journal of Heat and Mass Transfer, 34(2000), p.3139

DOI: 10.1115/imece2001/htd-24146

[5] C. Shu, B. C. Khoo, K.S. Yeo: Numerical Solutions of Incompressible Navier-Stokes quations by Generalized Differential Quadrature, Finite Elements in Analysis and Design,,18(1994), p.83.

DOI: 10.1016/0168-874x(94)90093-0

[6] S. A. Schaaf, P. L. Chambré: Flow of Rarefied Gases, Vol. 8, Princeton Aeronautical Paperbacks, Princeton University Press, Princeton, New Jersey, 1961.

[7] R. E. Bellman, J. Casti: Differential Quadrature and Long-Term Integration, J. Math. Anal. Appl., 34(1971),p.235

[8] A.Beskok, G.E, Karniadarkis: A Model for Flow in Channels, Pipes, and Ducts at Micro and Nano Scales[J]. Microscale Thermophysical Engineering, 5(1999), p.43.

DOI: 10.1080/108939599199864

[9] C. Shu, B. E. Richards: Parallel Simulation of Incompressible Viscous Flows by Generalized Differential Quadrature, Comput. System Engr., 3(1992), p .271.

DOI: 10.1016/0956-0521(92)90112-v