Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.