Lid Driven Triangular and Trapezoidal Cavity Flow: Vortical Structures for Steady Solutions and Hopf Bifurcations

Abstract

A numerical study of two dimensional lid-driven triangular and trapezoidal cavity flow is performed via using the lattice Boltzmann method (LBM) for steady solutions. The equilateral and right-angled isosceles triangular cavity flow at Reynolds numbers, respectively, 500 and 100 is employed as the benchmark case for code validation. The isosceles right-angled triangular cavity flow is studied for Reynolds numbers sweeping from 100 to 8100. Flow topologies are captured and analyzed. The critical Reynolds number of Hopf bifurcation is predicted by calculating the perturbation decay rate. Two different geometries of right-angled isosceles trapezoidal cavities, bowl-shaped and pyramid-shaped trapezoids, are studied at Reynolds numbers 1000 and 7000. For each type of the trapezoidal cavity, a geometric parameter λ (top-line/base-line ratio) is presented to distinguish different geometries of trapezoidal cavities. The flow patterns regarding the streamlines, vortical structures, and velocity profiles are discussed. The impact of parameter λ on the fluid characteristics are investigated.