Self-excited oscillations of flow past deep cavities: Effect of variable damping.

摘要

The overall objective of this investigation is to determine the effect of variable damping on the pressure response characteristics of a deep cavity. The pressure fluctuations arise from coupling between the unsteady shear layer along the cavity opening and a resonant acoustic mode of the cavity. Damping of the cavity is represented by the quality (Q) factor, which is determined from external acoustic excitation in the absence of mean flow. The value of the Q factor can be varied continuously with a damping device, which is located at the dead end of the cavity; it allows variation of the magnitude of damping without changes of the geometry or parameters of the deep cavity.;The amplitude of the pressure fluctuation as a function of flow velocity is characterized for the first, second and third depth-wise acoustic modes, which are generated in cavities with different depths. For each mode, the value of the Q factor is varied over a relatively wide range. Substantial attenuation of the pressure amplitude is attained. For higher acoustic modes, and at sufficiently high values of cavity damping, corresponding to low values of Q factor, abrupt decreases or drop-offs of the pressure amplitude occur at threshold values of flow velocity. Moreover, the peak response amplitude occurs at values of dimensionless frequency (Strouhal number) that increase with decreasing values of the Q factor.;The amplitude of the unsteady pressure oscillations (normalized by the freestream dynamic head) generally exhibits a linear variation with Q factor, for four depth-wise acoustic modes of the cavity. Furthermore, the strength of lock-on (SoL) of the pressure oscillation, as a function of Q factor, is evaluated in terms of the coherent and broadband (background) pressure amplitudes. Not only the coherent pressure amplitude, but also the broadband amplitude, is attenuated for decreasing values of Q factor. As a consequence, variation of the strength of lock-on with Q factor must account for both of these effects.;Quantitative imaging, in the form of high-image-density particle image velocimetry (PIV), is employed to characterize the flow structure of coupled oscillations arising from the shear layer along the opening of the deep cavity. Time- and phase-averaged patterns provide insight into the effect of resonator damping on the flow structure. In essence, when the Q factor of the cavity decreases, attenuation of the pressure amplitude at the dead end of the cavity is accompanied by corresponding attenuation of the shear layer undulation along the cavity opening. Cross-comparison of patterns of velocity vectors, streamwise and transverse velocity components, as well as vorticity, illustrate the detailed features of the damped oscillations of the shear layer.;Quantitative imaging also provides a basis for determination of the hydrodynamic contributions to the acoustic power, as well as calculation of the total acoustic power, which is generated by the oscillating shear layer in presence of the resonant acoustic field of the cavity. The manner in which this power is altered in relation to the damping of the cavity is assessed, and patterns of the spatial distribution of acoustic power are related to corresponding patterns of vorticity, as well as to patterns of streamwise and transverse components of the hydrodynamic contribution to the acoustic power integral.;Prediction of the pressure oscillation amplitudes within the resonator, and the frequencies at which these oscillations occur, were undertaken using a published theoretical model, which was adapted for the deep cavity system of interest herein. Comparison of predictions with experiments shows generally good agreement, and verifies the Q factor as a representation of cavity damping, even in presence of flow.