Multiple steady states for various regimes of convection (natural or mixed) dominance within a lid-driven trapezoidal cavity

Present work investigates multiple steady states for mixed convection of fluids within a trapezoidal enclosure involving sliding top lid and Rayleigh–Benard thermal setup. A novel sequence of initiation and continuation schemes involving multiple perturbations has been designed to determine the spectrum of steady states as a function of the Grashof number (Gr) for various Prandtl and Reynolds numbers (Pr=0.7 and 10, Re=1 and 100). The computations are based on steady-state governing equations, and Galerkin finite element method with penalty formulation has been used to solve the equations at various steps of the computation. Current results show that a rich spectrum of steady states do exist for each of the cases. Multiple steady states are found to exist in the natural convection dominant flow regime for Re=1 (slow moving lid) and also for Re=100 in the case of Pr=0.7. On the other hand, multiple steady states are found to exist in the mixed convection zone for Re=100 in the case of Pr=10. The rigorous initiation scheme reveals the co-existence of five steady states at a given Gr for Pr=0.7 and co-existence of up to thirteen (Re=1) or eleven (Re=100) steady states for Pr=10. The regions of the existence of various steady states have been identified via the bifurcation diagrams. Different types of flow structures associated with the steady states and their effect on the thermal characteristics have been illustrated.