Aeroacoustic computations of tones generated from low mach number cavity flows, using a preconditioned method

The hydrodynamically generated noise produced from flow over cavities is both broadband and tonal. The frequency content and amplitude of the resulting noise is a function of the cavity geometry (often characterized by the cavity length to depth ratio (L/D)) and the characteristics of the approaching boundary layer. While both of the noise components are important this work focuses on the production of cavity tones. Cavity tones typically have higher sound pressure levels and can propagate over longer distances than the broadband noise. The enhancements to the numerical code shown in this work result in the first non-hybrid tool for the prediction of low speed cavity noise [1 ]. The numerical solver CHOPA (Compressible, High-Order Parallel Acoustics) is extended in this work for the accurate and fast calculation of low Mach number cavity flows. A time-derivative preconditioner equalizes the acoustic wave and turbulence convective speeds to allow for a more efficient time step selection and shorter calculation times. Because the preconditioner destroys the time accuracy of the solution a dual-time step approach is used for the time integration. An extension by Buelow of Choi-Merkle’s viscous preconditioner is selected for this work. Other modifications to the code are required to facilitate the proper implementation of the preconditioner. These include matrix-based artificial dissipation, buffer zones, and extrapolation boundary conditions. Different numerical validations are performed on the preconditioned Navier-Stokes solver to ensure high quality solutions. Following the validation of the preconditioner, cavity tones from a deep (L/D = 0.78) and shallow (L/D = 2.35) cavity are simulated and are compared with experimental measurements. The Mach number of these simulations varies from 0.05 to 0.4. At the lower Mach numbers the predicted cavity tone frequencies match the measurements well for the deep cavity. However, the shallow cavity tones are almost independent of the flow speed, an indication that standing waves in the cavity are likely responsible for the tones from this geometry. Other cavity simulations are compared with experiments for L/D = 5.42 and L/D = 6.25 at a Mach number of 0.2. The time-averaged wall pressure fluctuations are compared to measurements. The predicted wall pressures do not match the experiment. This is explained due to the existence of a “wake mode” behavior in the numerical results. This is a two-dimensional phenomenon where a large vortex is generated in the cavity and then violently ejected from the cavity, significantly increasing drag.