Direct Numerical Simulations of Three-Dimensional Cavity Flows

Abstract

Three-dimensional direct numerical simulations of the full compressible Navier–Stokes equations are performed for cavities that are homogeneous in the spanwise direction. The formation of oscillating spanwise structures is observed inside the cavity. We show that this 3D instability arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. In general, the three-dimensional mode has a spanwise wavelength of approximately 1 cavity depth and oscillates with a frequency about an order-of-magnitude lower than 2D Rossiter (flow/acoustics) instabilities. The 3D mode properties are in excellent agreement with predictions from our previous linear stability analysis. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. We connect these results with the observation of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows. Preliminary results on the connections between the 3D centrifugal instabilities and the presence/suppression of the wake mode are also presented.