Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid

This paper explores the flow behavior of a bi-dimensional lid-driven cavity filled with a viscoplastic fluid. The results were obtained numerically using the moment representation of the lattice Boltzmann method for a Bingham fluid. The lid-driven cavity is a classic problem in computational fluid dynamics, often used to compare numerical methods due to the presence of singularities in its corners and complex flow structures. It is wellknown that the flow bifurcates from a stationary to a periodic regime in Newtonian fluids as the Reynolds number exceeds a certain threshold. This information can be used as a benchmark for numerical methods at high Reynolds numbers. However, results for viscoplastic fluids at high Reynolds numbers fall short. The data obtained in this work, with Reynolds numbers up to 20,000 and Bingham numbers up to 10, show how the bifurcation point increases with the fluid's yield stress. Below the bifurcation point, the primary vortex center converges towards a single point, independently of the Bingham number. Above the bifurcation point, most cases present a single dominant frequency, while double or quasi-periodic regimes were obtained under certain conditions. We observed that the time required to reach a permanent state increases with the Bingham number. Finally, the flow exhibits stationary and moving yield surfaces, with some of the latter traveling inside the primary vortex.