Numerical Simulations of Transonic Flow Acoustic Resonance in Cavity

Direct numerical simulations are used to investigate transonic flow acoustic resonance in an open cavity. The numerical scheme minimizes the errors due to dispersion and dissipation of acoustic waves, and resolves both the unsteady flow and radiated acoustic field. Implicit solution of the compressible Navier-Stokes equations is obtained using a compact high-order spacial differencing scheme, coupled with high-order implicit filters. Second order temporal accuracy is achieved using a time-implicit approximately-factorization, and Newton-like subiterations. Computational results are presented at sequential times to show the vortical structure and shock waves at two transonic free stream Mach numbers. The corresponding acoustic response is presented for the pressure fluctuations and sound pressure level spectra near the rear bulkhead. Comparison of the computed discrete frequencies with Rossiter’s correlation indicates that the feedback mechanism, which induces self-sustained flow oscillations in the cavity is well captured. Introduction High-speed flow over deep open cavities is characterized by shear layer instability and acoustically dominated flow oscillations. Strong pressure fluctuations inside the cavity, intensive noise radiation, and large shock motion negatively impact the operation and structural integrity. Recent interest in cavity acoustic resonance is motivated by the need to develop flow control strategies to reduce acoustic emissions from aircrafts and insure the structural integrity of weapons bays. Current bay spoilers fail to provide adequate acoustic suppression above Mach one. Some degree of acoustic suppression control has been achieved experimentally by stimulating the shear layer spanning the bay with various actuators [1,2]. Optimizing the performance of these devices requires detailed knowledge of the unsteady flow field. Many numerical investigations of high-speed flow over open cavities [3] are based on the solution of the time dependent Reynolds-Averaged Navier-Stokes equations [4,5]. Colonius et al. [6], used Direct Numerical Simulations (DNS) to study unsteady subsonic flow over two-dimensional cavities, and predicted transition from the shear layer mode to the wake for higher Mach numbers and cavity length to depth ratios. Shieh and Morris [7] used Detached Eddy Simulations (DES) to study subsonic cavity flow, and predicted the wake mode in the two-dimensional but not in the three-dimensional results. They reported better agreement with Rossiter’s correlation [8] for the threedimensional results. Henderson et al. [9] presented computational and experimental results for the Sound Pressure Level (SPL) at the cavity floor. Direct numerical simulations are used in the current investigation to study transonic flow over twodimensional cavities. The results obtained using high order compact differencing in conjunction with high order non-dispersive filters, are presented for the vorticity and Mach number contours to illustrate the roll up vortex structure in the shear layer and the shock waves motion at two transonic free stream Mach numbers. Sample pressure fluctuations, and sound