Numerical solution of acoustic response due to hydro/aerodynamic turbulence

In this work, a new methodology has been proposed which determines the acoustic response due to interaction of unsteady hydro/aero-dynamic sources with rigid/flexible structures. This methodology is based on Lighthill's acoustic analogy in which acoustic sources are pre-determined from unsteady flow calculations. The key feature of this methodology is the numerical solution of the acoustic problem. For this purpose, a new variational formulation of Lighthill's acoustic analogy has been developed which can be solved using the finite element method. This enables the true geometry of the structure and acoustically non-compact sources to be considered with relative ease. The feasibility of the approach has been investigated by studying the trailing-edge noise of the Eppler 387 airfoil due to a single quadrupole source, and the noise due to vortices shed from the NACA 0018 airfoil. In both cases the results are compared with analytical solutions that are available for certain limits. As an application to a practical problem, this methodology is used to compute the acoustic signature due to the boundary layer/wake turbulence over and behind the Eppler 387 wing at a cruise condition. Turbulent sources were obtained via Large Eddy Simulation, over an infinite span wing, using an unstructured grid finite element method in conjunction with the Dynamic Smagorinsky subgrid model. For this problem, sufficient numbers of grid points were used to resolve the wall layer. Flow separation, transition and turbulent reattachment were all captured and compared with the experimental data available from other sources. Finally, the acoustic problem is solved to obtain directivity patterns of acoustic pressures. The analysis indicates the importance of both wing geometry and the extent of acoustic sources on directivity.