Numerical Simulation of 2-D Incompressible Flow in Micro Semi-circular Cavity by LBM

Since the field of micro electromechanical systems (MEMS) continues to grow, the flow in micro devices have become an area that receives a significant attention. Microscopic flows are usually characterized by the Knudsen number (Kn). When the characteristic size of the particle decreases down to a value comparable to the mean free path of the molecules, the continuum assumption fails and the Navier-stokes equations with No-slip boundary conditions cannot be applied, so the numerical method which is not based on continuity of the flow is needed. Recently the Lattice Boltzmann Method (LBM) has received considerable attention by fluid dynamic researchers. The LBM is based on the lattice Boltzmann equation with Bhatnagar-Groos-Krook (BGK) collision approximation. In this paper the incompressible laminar flow in a 2D micro semi-circular cavity with the lid, driven is simulated by LBM. It should be mentioned that the flow in semi-circular cavity in macro scale has also been simulated and the obtained results were found to be in good agreement with those given from the finite volume method. In the present work, the computational results showed that the slip could have influence on the centre of vortex and actually moved it in horizontal and vertical directions in semi-circular cavity. Computing the friction coefficient on the lid driven circular cavity presented that the friction coefficient was increased as Kn was increased. The slip also had a decreasing effect on the maximum velocity in the cavity.