Effect of Cavity Width on the Unsteady Pressure in a Low-Mach-Number Cavity

Abstract

T HE flow over a cavity (Fig. 1) has drawn the attention of many researchers (e.g., see the review articles by Rockwell and Naudascher [1] and Colonius [2]) because of its relevance to a range of engineering applications. These include the flow past windows and sunroofs in automobiles, airplane wheel wells, and dump combustors. The flow in these circumstances is characterized by selfsustained, high-pressure fluctuations, which can produce vibration and fatigue of the underlying structure, a high level of noise, and drastic increase in the drag force on the body containing the cavity. Hence, understanding and controlling the unsteadiness associated with cavity flows are important. Rossiter [3] identified the basic mechanism leading to strong, selfsustained oscillations in cavities. More specifically, he proposed that small disturbances in the shear layer separating at the upstream edge of the cavity are amplified, forming periodic vortex structures that travel downstream and interact with the aft edge of the cavity, generating strong pressurefluctuations. Thesefluctuations propagate (“feedback”) acoustically to the separation edge and reexcite the shear layer, hence, sustaining the cavity oscillations. A notable deviation from the Rossiter mechanism is the case where the vortex structures do not form upstream of the cavity’s aft edge. In this situation, self-sustained oscillations could still exist, but they are driven by convective waves, which cause large lateral motion (or “flapping”) of the shear layer near the downstream lip of the cavity (e.g., Sarohia [4] and Chatellier et al. [5]). Another important aspect of self-sustained oscillations of a cavity is the nature of the feedback. As M ! 0, the disturbance-edge interaction is inefficient in producing acoustic disturbances and the feedback is driven by the conservation of the fluid mass within the cavity (e.g., see Martin et al. [6] and Rockwell [7]). Although there is a large body of literature on cavity flows, very few studies have focused on three-dimensional aspects of the flow. Cell structures along the span of the cavity were found in the experiments of Maull and East [8]. Rockwell and Knisely [9] found that secondary, spanwise-periodic, streamwise vortices formed and distorted the primary spanwise vortex structures. More recently, three-dimensional instability analysis of a two-dimensional cavity flowwas carried out by Bres and Colonius [10]. It was found that the most amplified three-dimensional mode had a typical frequency that was an order of magnitude smaller than the frequency of the selfsustained cavity oscillations. This modewas linked to the centrifugal instability of the primary recirculation flow inside the cavity. The objective of this study is to examine the influence of the cavity width on the behavior of the unsteady pressure acting on the cavity floor and how this behavior depends on Reynolds number. A unique aspect of the present investigation is that an axisymmetric cavity geometry is employed to establish a “reference” condition that is free of any end-wall influences. The behavior of this cavity flow can then be compared against that of finite-width cavities byfilling portions of the axisymmetric cavity (see the next section for further details). It is significant to contrast the present work to the study ofMaull and East [8], who employed a rectangular cavity geometry that had to be terminated with end walls (even for the widest cavity). In addition, Maull and East did not report any quantitative measurements of the cavity unsteadiness. As will be seen, the present findings show that, asM ! 0, the accepted criteria, based on cavity depth and length as well as boundary layer thickness, for the occurrence of self-sustained oscillation are not sufficient to guarantee the establishment of the oscillation. The cavity width must also be accounted for; this offers a possible explanation for the discrepancy between recent (Grace et al. [11] and Ashcroft and Zhang [12]) and earlier studies at a low Mach number.