Simulating fluid flow over sinusoidal surfaces using the lattice Boltzmann method
Computers & Mathematics with Applications
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The objective of this paper is to analyze the laminar flow of a Newtonian fluid, pressurized and sheared, through a twodimensional channel with one sinusoidal wall. The motivation of this work is the investigation of shear flows in lubrication. The effects of Reynolds number and the geometrical dimensions on the velocity distributions and on the flow factors are studied numerically using the lattice Boltzmann method (LBM). The results are verified with analytical and other numerical solutions. c © 2007 Elsevier Ltd. All rights reserved.
17 Figures and Tables
Fig. 1. Schematic diagram of a real rough surface.
Fig. 2. The geometry and boundary conditions of a smooth journal bearing.
Fig. 3. Velocity distributions across the channel at three different non-dimensional pressure gradients (B).
Fig. 4. Velocity distributions across the smooth channel using four different grid resolutions.
Fig. 5. The LBM discretization error as a function of the grid resolution (δy ).
Fig. 6. Schematic diagram of the sinusoidal channel.
Fig. 7. Velocity distributions at Re = 1 for different values of and α = 0.01 (top) and α = 0.2 (bottom). Left: at x̂ = 1/4, right: at x̂ = 3/4.
Fig. 8. The pressure flow factors at Re = 1 and different values of and α. The solid line represents the analytical solution for large wave length channels (low α).
Fig. 9. Comparison of the velocity distributions obtained by the finite volume (STAR-CD) and LBM methods. Left: at x̂ = 1/4, right: at x̂ = 3/4.
Fig. 10. Streamlines in a sinusoidal channel of dimensions = 0.25 and α = 0.1 at different Reynolds numbers. (a) Re = 1, (b) Re = 10, (c) Re = 100 and (d) Re = 500.
Fig. 11. Velocity distributions across a sinusoidal channel of dimensions = 0.25 and α = 0.1 at different Reynolds numbers. Left: at x̂ = 1/4, right: at x̂ = 3/4.
Fig. 12. Effect of Reynolds numbers on the pressure flow factor in a sinusoidal channel of dimensions = 0.25 and α = 0.1 and 0.3.
Fig. 13. Velocity distributions in a sinusoidal channel of dimensions α = 0.01 (top) and α = 0.01 (bottom) in a shear flow test. Left: at x̂ = 1/4, right: at x̂ = 3/4.
Fig. 14. The shear flow factor as a function of and α. The solid line represents the analytical solution for large wave length channels (low α).
Fig. 15. Effect of Reynolds number on the velocity distributions in a sinusoidal channel of dimensions = 0.2 and α = 0.1. Left: at x̂ = 1/4, right: at x̂ = 3/4.
Fig. 16. Effect of Reynolds number on the shear flow factor in a sinusoidal channel of dimensions = 0.2 and α = 0.1.
Fig. 17. Effect of the grid resolution on the velocity across a sinusoidal channel of dimensions = 0.25 and α = 0.1 at Re = 1. Left: at x̂ = 1/4, right: at x̂ = 3/4.
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