AIAA 2002-2476 Aerodynamic noise induced by laminar and turbulent boundary layers over rectangular cavities * Xavier Gloerfelt † , Christophe Bogey ‡ , Christophe Bailly § and Daniel Juv´ e ¶ Laboratoire de M´ ecanique des Fluides et d’Acoustique Ecole Centrale de Lyon & UMR CNRS 5509 BP 163, 69131 Ecully cedex, France. Abstract The structure of an unsteady flow past a rectangular, open cavity is investigated using numerical simulations. Particular attention is drawn to the three-dimensional geometry effects, and to the turbulent state of the in- coming boundary layer. The consequences on noise gen- eration are studied. Two-dimensional DNS allows a re- construction of the feedback loop giving rise to the self- sustained oscillations, but DNS is restricted to thick lam- inar upstream boundary layers. Cavity flows with higher Reynolds numbers are computed by 3-D Large Eddy Simulations, based on high order algorithms, by consid- ering that the interactions of coherent structures with the downstream edge are predominant in such flows. The three-dimensional structure of the recirculating zone is illustrated and its influence on the shear layer dynamics is shown . In the same way as the incoming turbulence level, these modulations induce jittering of vortex-corner interactions, a decrease in feedback coherence, and thus a reduction of the radiated noise. 1. Introduction Flow past an open cavity is known to give rise to self- sustained coherent oscillations of the impinging shear layer, as well as intense associated noise radiation. It has been studied by numerous investigators in the past be- cause of its practical interest and because of the diversity of the theoretical questions involved. The self-sustained oscillations arise from a feedback loop consisting of the following chain of events : impingement of vortical per- turbations on the downstream corner, generation of pres- sure disturbances (both acoustic and aerodynamic), in- fluence from the impingement region on the receptive region of the shear layer located at the upstream corner, * Copyright @ 2002 by the Authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. † Post-doc student ‡ Research scientist, Member AIAA § Assistant Professor, Member AIAA ¶ Professor, Member AIAA conversion of this influence into new fluctuations, ampli- fication of the vortical perturbations with convection by the shear layer resulting in a new impingement, closing the loop. This complex phenomenon is often greatly simplified to build lumped models such as the Rossiter formula 1 : the free shear layer is viewed as two-dimensional, and the recirculating flow is neglected. These approxima- tions have provided insight into the principal oscillation frequencies. In this kind of semi-empirical model, a good deal of significance is attached to the highly localized vortices. However, experimental observations for fully turbulent cases have not always indicated their presence. Although, for the purpose of predicting the frequencies of discrete tones, the details of these physical processes may not be extremely crucial, their knowledge is of im- portance to noise suppression efforts. The three-dimensional features of cavity flows have received relatively less attention. The streamwise vor- tices in the shear layer, side walls effects on the shear layer and in the cavity, or Taylor-G¨ ortler type instabil- ities arising from the strong curvature of the recirculat- ing flow can provide different sources of three-dimensio- nalities. The spanwise structure of the free shear layer along the mouth of a cavity has been visualized by Rock- well and Knisely 2 using the hydrogen bubble technique and reveals the interaction of secondary (longitudinal) and primary (Kelvin-Helmholtz) vorticity. The large- scale recirculation vortex between the shear layer and the walls of the cavity is felt to influence this three dimen- sionality. The existence of this zone can alter the average trajectory of the incident vortices, and may modulate the corresponding vortex-corner interaction. In the 2-D numerical study of Pereira and Sousa, 3 the modulations seem to occur at the upstream region of the separated layer due to recirculation unsteadiness. In the early ex- periments of Maull and East 4 and Kistler and Tan, 5 the flow inside the cavity is organized in cellular streamwise structures. The studies of driven-cavity flow 6 also in- dicate that the spanwise aspect ratio has a significant effect upon the mean eddy structure inside the cavity. Kuo and Huang 7 have investigated the effects of either 1 American Institute of Aeronautics and Astronautics