Numerical Simulation of Fluid Flow in the Vicinity of an Oscillating Cavity: Verification and Validation

Abstract

The focus of this paper is on the verification and validation of the numerical solutions of flow due to an infinitely long oscillating wall with periodic cavities. The wall was allowed to oscillate sinusoidally with the fluid initially at rest. This wall motion set up an interesting pattern of vortex entrainment and ejection from the cavity. The problem was numerically modeled with a commercial CFD code, FLUENT v 6.2.16. To circumvent the need for a moving mesh, a reference frame attached to the wall was used. For numerical uncertainty estimation, the Grid Convergence Index (GCI) method was used for both temporal and spatial resolutions at a Reynolds Number (based on the cavity height) of 200. The spatial grid resolution study was done at different time-steps (in the oscillation cycle) on the cross-streamwise velocity on a plane connecting the two open edges of the cavity (lip of the cavity). For this parameter, a local mesh size was used to calculate the GCI with 20, 40 and 80 node points. With the cavity at rest, low GCI percentages (less than 1%) were observed on this parameter for the fine grid solution. As the cavity began to accelerate, some discrete points on the cavity lip plane showed higher GCI percentages (some even as high as 100%); the higher uncertainties were associated with very small velocities (close to zero). The numerical uncertainty on the shear stress on the lower wall as well as on the mass efflux from the cavity over an oscillation cycle were also estimated using the GCI and were observed to be very low numbers (global variables). Validation was done by comparing the results to (1) The Stokes’ second problem and (2) a few similar experimental and numerical results published in the literature.