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Research Papers: Techniques and Procedures

A Lattice Boltzmann Method Based Numerical Scheme for Microchannel Flows

[+] Author and Article Information
S. C. Fu, R. M. C. So

Department of Mechanical Engineering, The Hong Kong Polytechnic University, P.R.C.

W. W. F. Leung1

Department of Mechanical Engineering, The Hong Kong Polytechnic University, P.R.C.; Research Institute of Innovative Products and Technologies, The Hong Kong Polytechnic University, P.R.C.riwl@polyu.edu.hk

1

Corresponding author.

J. Fluids Eng 131(8), 081401 (Jul 07, 2009) (11 pages) doi:10.1115/1.3155993 History: Received September 23, 2008; Revised May 12, 2009; Published July 07, 2009

Conventional lattice Boltzmann method (LBM) is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The LBM has been applied to different types of complex flows with varying degrees of success, and with increased attention focusing on microscale flows now. Due to its small scale, microchannel flows exhibit many interesting phenomena that are not observed in their macroscale counterpart. It is known that the Navier–Stokes equations can still be used to treat microchannel flows if a slip-wall boundary condition is assumed. The setting of boundary conditions in the conventional LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of a finite difference LBM (FDLBM) based numerical scheme suitable for microchannel flows to solve the modeled Boltzmann equation using a splitting technique that allows convenient application of a slip-wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the FDLBM is carried out against microchannel and microtube flows, a driven cavity flow, and a two-dimensional sudden expansion flow. Excellent agreement is obtained between numerical calculations and analytical solutions of these flows.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Schematic of the circular Poiseuille flow

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Figure 5

Non-Newtonian Poiseuille flow with a biviscous model: (–) analytical solution and (x) FDLBM solution

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Figure 12

Schematic of the flow in a channel with sudden symmetric expansion

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Figure 13

Streamline plots for flow in a 2D sudden expansion

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Figure 1

D2Q9 Lattice velocity model

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Figure 2

Schematic of the Couette flow

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Figure 3

Newtonian Couette flows with a slip velocity boundary condition: (–) analytical solution and (x) FDLBM solution

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Figure 6

Non-Newtonian Poiseuille flow with a shear-thinning model (n=1/3 in the power-law model): (–) analytical solution and (x) FDLBM solution

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Figure 7

Non-Newtonian Poiseuille flow with a shear-thickening model (n=3 in power-law model): (–) analytical solution and (x) FDLBM solution

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Figure 8

Schematic of the driven cavity flow

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Figure 9

Horizontal velocity u of a driven cavity flow along y at x=0.5, Re=100: (–) FDLBM solution (no slip), (x) result from Ref. 32, and (- - -) FDLBM solution with slip wall

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Figure 10

Vertical velocity v of driven cavity flow along x at y=0.5, Re=100: (–) FDLBM solution (no slip), (x) result from Ref. 32, and (- - -) FDLBM solution with slip wall

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Figure 11

Vorticity contours for flow in a driven cavity; same contour level setting as that given in Ref. 32

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Figure 14

Centerline (y=0) velocity distribution in a sudden expansion flow: (–) FDLBM solution, (x) result from Ref. 34, (○) and (●)⋅results from Ref. 35 for N=3 and N=5, respectively

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Figure 15

Vorticity distribution at the upper wall (y=h) for flow in a channel with sudden symmetric expansion: (–) FDLBM solution, (x) result from Ref. 34, (○) and (●)⋅results from Ref. 35 for N=3 and N=5, respectively

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