Lattice Boltzmann very large eddy simulations of a turbulent flow over covered and uncovered cavities

Abstract

Microphone measurements in a closed test section wind tunnel are affected by turbulent boundary layer (TBL) pressure fluctuations. These fluctuations are mitigated by placing the microphones at the bottom of cavities, usually covered with a thin, acoustically transparent material. Prior experiments showed that the cavity geometry affects the propagation of TBL pressure fluctuations toward the bottom. However, the relationship between the cavity geometry and the flowfield within the cavity is not well understood. Therefore, a very large-eddy simulation was performed using the lattice Boltzmann method. A cylindrical, a countersunk and a conical cavity are simulated with and without a fine wire-cloth cover, which is modeled as a porous medium governed by Darcy's law. Adding a countersink to an uncovered cylindrical cavity is found to mitigate the transport of turbulent structures across the bottom by shifting the recirculation pattern away from the cavity bottom. Covering the cavities nearly eliminates this source of hydrodynamic pressure fluctuations. The eddies within the boundary layer, which convect over the cover, generate a primarily acoustic pressure field inside the cavities and thus suggesting that the pressure fluctuations within covered cavities can be modeled acoustically. As the cavity diameter increases compared to the eddies' integral length scale, the amount of energy in the cut-off modes increases with respect to the cut-on modes. Since cut-off modes decay as they propagate into the cavity, more attenuation is seen. The results are in agreement with experimental evidence.