Comparative study of two-relaxation time lattice Boltzmann and finite element methods for a planar 4:1 contraction flow: a Newtonian fluid at finite Reynolds numbers

Abstract

We study the flow behavior of a Newtonian fluid in a planar 4:1 contraction channel using two numerical methodologies: the two-relaxation time lattice Boltzmann method (TRT-LBM) and the finite element method (FEM). To confirm the validity of the TRT-LBM, hydrodynamic quantities such that velocity, pressure, and vortex are carefully investigated at the wide ranges of Reynolds numbers (Re = 0.1–100). At first, we analyze the velocity along the channel. The results of TRT-LBM look reasonable and also coincide with the analytical solution and FEM results. Richer features are observed in the pressure profile along the flow direction. At low Reynolds numbers, the one-step change of the slope in the pressure profile is observed near the contraction region. The slope gradually grows up with the increase of Reynolds numbers, and eventually, this evolves the two-step change. Non-monotonic behavior is observed in the characteristics of the vortex. The size of the vortex non-linearly decreases as the Reynolds number increases. Also, the center of the vortex gradually moved toward the corner of the channel as an increase of Reynolds numbers with non-linearity. Not only the velocity and the pressure profiles but also the characteristics of the vortex quantitatively coincide in TRT-LBM and FEM results. Through this study, we confirm the robustness of the TRT-LBM as a simulation tool to investigate inertial flow in a planar contraction geometry.