An analysis of flow induced acoustic resonance in cavities
Authors:   , Watson George H.(Houston) 
Published: June 2024

"Interest in cavity flows originated within the aircraft industry when buffeting in open bomb bays and cockpits of military aircraft became a matter of concern with regard to the structural loading on the aircraft. There were fears that the occurrence of periodic pressure disturbances associated with the buffeting could oscillate at frequencies close to one of the natural frequencies of the aircraft and possibly lead to structural failure of some component. Investigations were subsequently carried out to determine the amplitude and frequencies of the pressure disturbances encountered in such configurations (1,2). Cavity configurations may also occur in aerodynamic surfaces. An example of such cavities would be the discontinuity in the surface between an airfoil and its flap. The effect of such cavities on the drag of an aircraft is, quite naturally, of major interest. Also, the presence of a cavity in an aerodynamic surface can affect the location of boundary layer separation downstream from the cavity. Cavities in the surfaces of re-entry vehicles have generated interest in the heat transfer mechanisms between the cavity and the freestream. The determination of the influence of a cavity on drag or heat transfer necessitates a study of the flow field within the cavity. It is then possible to predict momentum transfer to the cavity, which provides a means for calculating drag, and to predict flow velocities induced within the cavity, which allows for determining heat transfer coefficients along the cavity walls. Mathematical models of cavity flow fields have been formulated which rather accurately predict velocities induced in circular cavities (3,4). To a lesser extent, models of flow fields within rectangular cavities have been suggested (5,6,7,8,9), but these models are necessarily more descriptive than analytical due to the complex nature of the flow fields induced in rectangular cavities. The validity of these models is determined in part by how accurately the mixing process between the freestream and the fluid within the cavity is simulated by the model. The mixing process may be treated with single stream mixing theory (10) or some other form of fluid entrainment modeling. Past investigations have shown that such models produce accurate results provided the flow fields are not subjected to periodic pressure disturbances which may be either selfinduced or the result of some external source. However, experiment (3,11) has also shown that the heat transfer rates and drags predicted by such models become inaccurate when the cavity is subjected to periodic pressure fluctuations. These self-induced periodic pressure oscillations appear to be produced by the interaction between the freestream and the cavity. Under proper flow conditions, a sound field of distinct frequency can be heard and a periodic pressure oscillation can be detected within the cavity. Under such conditions the cavity may be said to be acoustically resonating, the acoustic resonance being sustained by energy from the freestream. The conditions necessary to sustain acoustic resonance in cavities have not yet been rigorously identified. Investigations (1,2,3,12) in the past have shown that resonance is a function of freestream velocity and cavity geometry. These two basic parameters have been used to express resonant frequencies in non-dimensional form as the Strouhal number (St = L/Uf), which provides a convenient method for correlating data. Two other parameters may be of significance in defining conditions conducive to resonance; these are the nature of the approaching boundary layer and the length of the region throughout which the mixing processes take place between the freestream and the fluid within the cavity (the mixing region). An understanding of how these parameters, as well as freestream velocity and cavity geometry, affect the capacity of a cavity to resonate could lead to a method of predicting the flow conditions which must exist in order to achieve a given resonant state. The research described herein attempts to quantitatively define the effect of the approaching boundary layer on the intensity and frequency of the resonant accoustic field induced in circular cavities. The thickness of the approaching boundary layer is controlled by means of a boundary layer removal unit. The boundary layer thickness and momentum thickness are determined and presented as functions of freestream velocity. The influence of the approaching boundary layer on resonance can then be described in terms of the boundary layer thickness and the momentum thickness. Provisions for observing the influence of mixing length on resonance are provided through the use of a sliding plate extending over the downstream edge of the cavity. The length of the mixing region can then be independently controlled and its influence on resonance identified. The influence of flow disturbances in the freestream and in the internal cavity flow field on acoustic resonance are investigated. Spectral analyses of the frequencies at which velocity fluctuations occur in the shear layer are made in order to observe the influence of acoustic resonance on velocity distributions in the shear layer. The influence of the approaching boundary layer and mixing length on acoustic resonance is then discussed with regard to techniques for predicting resonance."--Introduction.