Steady flow simulations inside a driven cavity up to Reynolds number 35,000
Steady flow simulations inside a driven cavity have been reported extensively in CFD literature. Simulations for Reynolds number (Re) values up to 5000 are abundant and consistent; however at larger Re values there is no agreement whether steady flow simulations are computable or not. Some studies state that driven cavity flow at higher Re values undergo a supercritical Hopf bifurcation leading to an unsteady flow state. Other studies tend to disagree, providing steady flow computations up to a maximum Re value of 21,000. In the present study, we adopt a stream function-vorticity formulation and a compact fourth-order-accurate central difference scheme to show that steady flow simulations are, in fact, computable up to Re = 35,000. It is shown that for Re = 35,000, the steady flow inside the cavity is comprised of thin boundary layers along the cavity walls and a core flow which resembles an inviscid rotational vortex with uniform vorticity. Present numerical results agree well with previous analytical solutions in the limit of infinite Reynolds number. Tabulated results for the properties of the primary vortex and the velocity components are also provided spanning the entire range from the creeping flow limit, Re = 0 up to Re = 35,000 for benchmarking purposes. (C) 2012 Elsevier Ltd. All rights reserved.
driven cavity flow high reynolds number stream function-vorticity form