Modeling and Control of Helmholtz Resonance in Cavities

Abstract

A cavity when exposed to grazing flow, gives rise to an unstable shear layer at the opening, which can cause the occurrence of Helmholtz resonance in the cavity under appropriate conditions. In this paper, we present numerical modeling and the control of the onset of Helmholtz Resonance in cavities through the control of the shear layer at the cavity opening. The effects of geometric parameters on the instability amplitude are analyzed along with the control of these instabilities. A wide variety of control concepts are analyzed and their effectiveness characterized in terms of the flow conditions and the geometry of the control devices. The results indicate that the interruption of any one of the main processes sustaining these instabilities can be an effective means of controlling the flow field. ULLS on Naval vessels contain cavities exposed to the ambient flow. The shear flow over these cavities can under certain conditions, generate resonant oscillations in pressure that can lead to large dynamic loads and loud tonal noise. The dynamic loads can result in structural fatigue, while the radiated resonant tones can propagate very long distances and represents a detection problem. These oscillations occur when resonance occurs between the natural tones of the shear layer over the opening match the natural modes of the cavity itself. Prediction of the flow conditions when this could happen and the control of this phenomenon is the subject of this paper. The onset of coupling between the inherent instability of the shear flow along the opening of a cavity and the Helmholtz resonance mode of the cavity typically occurs in the following manner. As the freestream velocity is increased to successively higher values, the self-sustaining oscillation of the shear layer passes through a sequence of hydrodynamic modes (stages), each having a well-defined frequency. When the frequency of this oscillation reaches a value that is compatible with the frequency of the Helmholtz resonator, the onset of shear layer-resonator coupling can occur if the resonator damping is sufficiently low. The sequence of events described in the foregoing involves two basic classes of oscillations: (i) A type I oscillation that is due solely to the instability of the shear flow along the cavity opening. This oscillation occurs prior to the onset of significant coupling with the resonator, (ii) A type II oscillation that involves coupling between the instability of the shear flow and the natural modes of the Helmholtz resonator. Even when shear layer oscillation is fully coupled with the resonator mode, however, many identifiable features of the purely unstable type I oscillation defined in (i) may still be prevalent. The type I oscillation necessarily precedes and extends into, the type II oscillation. The opportunity therefore exists to avoid a type II oscillation by effectively attenuating the type I oscillation. This approach is central to the objectives of this research program. The aim of the control techniques addressed herein is to attenuate the shear layer instability along the cavity opening prior to the onset of resonance; the attenuation technique, if sufficiently robust, will then preclude the onset of shear layer-resonator coupling, and thereby vibration of the walls of the resonator. In order to be able to effectively control the type I oscillations, detailed understanding of the mechanisms involved and the response of the flow field when subjected to any type of flow modification is required. Hence, there is a need to understand the behavior of control techniques commonly used. In addition, several platforms exist where openings of the cavities are covered by perforated or slotted plates. The instabilities in these configurations are very different from standard shear layer instabilities over open cavities. These are typically characterized by much higher amplitude tonal noise and a more robust instability that is relatively more difficult to control. In an earlier paper 1 , we presented an effective numerical technique to model these flow fields accurately. In this paper, we apply this technique to the modeling of geometric variations of the slotted plate covering the cavity and to examine control of the instabilities in the shear layer.