Numerical Study of Gas Microflow within a Triangular Lid-driven Cavity - Youssef Elguennouni; Mohamed Hssikou; Jamal Baliti; Mohammed Alaoui (Advances in Science, Technology and Engineering Systems Journal, 2020)
A rarefied gas flow is modeled inside two cases of triangular lid-driven microcavity using single (SRT) and multi-relaxation time (MRT) lattice Boltzmann approaches. In the first one, the right angle is in the top-left corner and the upper wall moves with positive horizontal velocity. However, in the second case, the right angle is in the bottom-left corner and the bottom wall moves with negative horizontal velocity. Unlike the classical form of square cavities, widely treated in the literature, the triangular form has a diagonal wall that affects the flow motion. At the moving wall, diffuse scattering boundary condition (DSBC) is employed while at the stationary sides, a combination of bounce-back and specular reflection boundary conditions (BSBC) is used. The computations are primarily performed in the slip and early transition regimes. The rarefaction effect, given by the Knudsen number (Kn) value, on the profiles of velocity components, is examined for both approaches. This study proves that for the higher values of Kn, the SRT-LBM approach cannot provide accurate results, particularly, near the inclined wall. However, the MRT-LBM approach confirms its validity even in the transition regime. A comparison with Direct Simulation Monte Carlo (DSMC) results for horizontal velocity contours shows the efficiency of the MRT-LBM approach than the SRT-LBM one which breaks down for rarefied flows.
Keywords: SRT-LBM; MRT-LBM; DSBC; BSBC; lid-driven; micro-cavity; Knudsen number; vortex