On three-dimensionality and control of incompressible cavity flow

Abstract

The incompressible large eddy simulation technique, coupled with the Lighthill-Curle acoustic analogy, is used to investigate the oscillation mechanism and sound source of a two-dimensional cavity with a length-to-depth ratio of L∕D=4 and Reynolds number of ReD=5000. It is demonstrated that the development of the three-dimensional flow field, initiated by the introduction of a random inflow disturbance, is eventually accompanied by transition from the wake to the shear layer oscillation mode, regardless of the amplitude and shape of the inflow disturbance. Once the transition to the shear layer mode is accomplished, the amplitude and frequency of oscillations are not very sensitive to the particular shape of the inflow disturbance. The effectiveness of controlling the flow oscillations by applying simultaneous steady injection and suction through the front and rear cavity walls, respectively, is demonstrated. The results show that, for injection levels exceeding a certain threshold value, the oscillations are quenched, and for levels below that value, the oscillation process is virtually unaffected. The major difference between the averaged uncontrolled and controlled velocity fields is the amount of reverse flow in the rear part of the cavity. With the aid of linear stability analysis, it is demonstrated that for injection levels leading to the quenching of the oscillations the mean velocity profiles in the cavity region are only convectively unstable, whereas for the uncontrolled case there is an absolutely unstable region. This suggests that, at least for incompressible flow, the reduction of the reverse flow inside the cavity can reduce or eliminate the oscillation process.