The steady and unsteady regimes in a cubic lid-driven cavity with viscoplastic fluid solved with the lattice Boltzmann method

Abstract

This work builds upon the previously published analysis of a lid-driven cavity filled with viscoplastic fluid. We extend the study from a two-dimensional case to a three-dimensional one, employing the moment representation of the lattice Boltzmann method to obtain numerical results. The findings expand the existing dataset, which can potentially serve as benchmark results for inertial regimes of viscoplastic flows. In this study, we investigate the Reynolds and Bingham numbers until the flow transition from stationary to a transient regime. The results reveal that, similarly to the Newtonian case, there is an effective Reynolds number for the bifurcation, approximately Re^⁎ = Re₀ (1 + Bn), where Re₀ represents the bifurcation point for a Newtonian fluid. Like the Newtonian cases, there were instances where the Taylor-Görtler-like vortices moved toward the cavity's side periodically. In other cases, more than two vortices simultaneously formed, with their number changing over time. Finally, similar to the two-dimensional case, the bifurcation initiated after the Moffat eddies in the downstream corner broke down into plugs.