Bakhshan, Y., Omidvar, A. (2015). Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method. Transp Phenom Nano Micro Scales, 3(1), 14-28. doi: 10.7508/tpnms.2015.01.002

Y. Bakhshan; A. R. Omidvar. "Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method". Transp Phenom Nano Micro Scales, 3, 1, 2015, 14-28. doi: 10.7508/tpnms.2015.01.002

Bakhshan, Y., Omidvar, A. (2015). 'Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method', Transp Phenom Nano Micro Scales, 3(1), pp. 14-28. doi: 10.7508/tpnms.2015.01.002

Bakhshan, Y., Omidvar, A. Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method. Transp Phenom Nano Micro Scales, 2015; 3(1): 14-28. doi: 10.7508/tpnms.2015.01.002

Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method

^{}Mechanical Engineering Department, University of Hormozgan, Bandar Abbas, I.R. Iran

Abstract

Micro scale gas flows has attracted significant research interest in the last two decades. In this research, the fluid flow of gases in the stepped micro-channel at a wide range of Knudsen number has been analyzed with using the Lattice Boltzmann (MRT) method. In the model, a modified second-order slip boundary condition and a Bosanquet-type effective viscosity are used to consider the velocity slip at the boundaries and to cover the slip and transition regimes of flow and to gain an accurate simulation of rarefied gases. It includes the slip and transition regimes of flow. The flow specifications such as pressure loss, velocity profile, streamline and friction coefficient at different conditions have been presented. The results show good agreement with available experimental data. The calculation shows that the friction coefficient decreases with increasing the Knudsen number and stepping the micro-channel has an inverse effect on the friction coefficient. Furthermore, a new correlation is suggested for calculation of the friction coefficient in the stepped micro-channel as below:

[1] H. Xue, S. Chen, DSMC Simulation of Microscale Backward-Facing Step Flow, Microscale Thermophysical Engineering 7 (2003) 69-86

[2] S. Ansumali, I. V. Karlin, Kinetic boundary conditions in the lattice Boltzmann method, Physical Review E 66 (2002) 026311.

[3] G. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows Fundamentals and Simulation, Springer, USA, 2005.

[4] R.W. Barber, D.R. Emerson, Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition, Heat Transfer Engineering 27 (2006) 3-12.

[5] H. Lai, C. Ma, Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation, Physica A, Statistical Mechanics and its Applications 388 (2009) 1405-1412.

[6] M. Sbragaglia, S. Succi, Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions, Physics of Fluids (1994-present) 17 (2005).

[7] E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long microchannels, Microelectromechanical Systems 6 (1997) 167-178.

[8] K. Pong, C. Ho, J. Liu, Y. Tai, Non-linear pressure distribution in uniform microchannels., in: Application of Microfabrication to Fluid Mechanics, ASME Winter Annual Meeting (1994) 51-56.

[9] G.E.K. Ali Beskok, A Model For Flows In Channels, Pipes, And Ducts At Micro And Nano Scales, Microscale Thermophysical Engineering 3 (1999) 43-77.

[10] J. Suehiro, G. Zhou, H. Imakiire, W. Ding, M. Hara, Controlled fabrication of carbon nanotube NO2 gas sensor using dielectrophoretic impedance measurement, Sensors and Actuators B 108 (2005) 398-403.

[11] A. Agrawal, L. Djenidi, R.A. Antonia, Simulation of gas flow in microchannels with a sudden expansion or contraction, Journal of Fluid Mechanics (2005) 135-144.

[12] Z. Guo, T.S. Zhao, Y. Shi, Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows, Journal of Applied Physics 99 (2006).

[13] Z. Guo, B. Shi, T.S. Zhao, C. Zheng, Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows, Physical Review E 76 (2007) 056704.

[14] Z. Guo, C. Zheng, Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer, International Journal of Computational Fluid Dynamics 22 (2008) 465-473.

[15] Z. Guo, C. Zheng, B. Shi, Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow, Physical Review E 77 (2008) 036707.

[16] T. Lee, C.-L. Lin, Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel, Physical Review E 71 (2005) 046706.

[17] F. Verhaeghe, L.-S. Luo, B. Blanpain, Lattice Boltzmann modeling of microchannel flow in slip flow regime, Journal of Computational Physics 228 (2009) 147-157.

[18] X. Shan, X.-F. Yuan, H. Chen, Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation, Journal of Fluid Mechanics (2006) 413-441.

[19] S. Ansumali, I.V. Karlin, S. Arcidiacono, A. Abbas, N.I. Prasianakis, Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy, Physical Review Letters 98 (2007) 124502.

[20] Y.-H. Zhang, X.-J. Gu, R.W. Barber, D.R. Emerson, Capturing Knudsen layer phenomena using a lattice Boltzmann model, Physical Review E 74 (2006) 046704.

[22] A. Homayoon, A.H.M. Isfahani, E. Shirani, M. Ashrafizadeh, A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number, International Communications in Heat and Mass Transfer 38 (2011) 827-832.

[23] H. Shokouhmand, A.H. Meghdadi Isfahani, An improved thermal lattice Boltzmann model for rarefied gas flows in wide range of Knudsen number, International Communications in Heat and Mass Transfer 38 (2011) 1463-1469.

[24] S.S. Chikatamarla, I.V. Karlin, Entropy and Galilean Invariance of Lattice Boltzmann Theories, Physical Review Letters 97 (2006) 190601.

[25] T. Ohwada, Y. Sone, K. Aoki, Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard‐sphere molecules, Physics of Fluids A: Fluid Dynamics 1 (1989) 1588-1599.

[26] P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E 61 (2000) 6546-6562.

[27] C.Y. Lim, C. Shu, X.D. Niu, Y.T. Chew, Application of lattice Boltzmann method to simulate microchannel flows, Physics of Fluids (1994-present) 14 (2002) 2299-2308.

[28] V. Michalis, A. Kalarakis, E. Skouras, V. Burganos, Rarefaction effects on gas viscosity in the Knudsen transition regime, Microfluid Nanofluid 9 (2010) 847-853.

[29] S.H. Kim, H. Pitsch, I.D. Boyd, Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows, Physical Review E 77 (2008) 026704.

[30] S.H. Kim, H. Pitsch, I.D. Boyd, Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers, Journal of Computational Physics 227 (2008) 8655-8671.

[31] Y. Zhang, R. Qin, D.R. Emerson, Lattice Boltzmann simulation of rarefied gas flows in microchannels, Physical Review E 71 (2005) 047702.

[32] Y.-H. Zhang, X.J. Gu, R.W. Barber, D.R. Emerson, Modelling thermal flow in the transition regime using a lattice Boltzmann approach, EPL (Europhysics Letters) 77 (2007) 30003.

[33] S. Succi, Mesoscopic Modeling of Slip Motion at Fluid-Solid Interfaces with Heterogeneous Catalysis, Physical Review Letters 89 (2002) 064502.

[34] M.N. Oliveira, L. Rodd, G. McKinley, M. Alves, Simulations of extensional flow in microrheometric devices, Microfluid Nanofluid 5 (2008) 809-826.

[35] T.-M. Liou, C.-T. Lin, Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method, Microfluid Nanofluid, 16 (2014) 315-327.

[36] L. Talon, D. Bauer, N. Gland, S. Youssef, H. Auradou, I. Ginzburg, Assessment of the two relaxation time Lattice-Boltzmann scheme to simulate Stokes flow in porous media, Water Resources Research 48 (2012) W04526.

[37] S. Kandlikar, S. Garimella, D. Li, S. Colin, M. King, Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier Amsterdam, Netherlands, San Diego, CA, Oxford, UK, 2005.

[38] H.P. Kavehpour, M. Faghri, Y. Asako, Effects of compressibility and rarefaction on gaseous flows in microchannels, numerical heat transfer, part a: applications 32 (1997) 677-696.