Ffowcs Williams-Hawkings (FW-H) Models

The Ffowcs Williams-Hawkings (FW-H) acoustics integral formulation is the preferred strategy for far-field noise prediction such as overhead aircraft noise. The FW-H models allow you to calculate the far-field sound signal that is radiated from near-field flow data from a CFD solution. The goal is to predict small amplitude acoustic pressure fluctuations at the locations of point receivers.

The FW-H acoustic model for stationary motion can simulate wind tunnel aeroacoustic measurements with stationary sources such as aircraft landing gear or an airfoil trailing edge. The FW-H acoustic model is used only to predict the propagation of sound in free space. It does not include effects such as sound reflections, refraction, or material property change.

The Ffowcs Williams-Hawkings formulations are based on Farassat’s Formulation 1A ([46], [55]) and Dunn Farassat Padula 1A ([65]), both for the non-convective form of FW-H. Therefore, numerical accuracy is not an issue of great concern compared to the full Computational Aeroacoustics approach, which explicitly resolves propagation of sound waves all the way to the far field. With the FW-H approach, a second order discretization scheme, both spatial and temporal, together with judicious choices for mesh resolution and time-step size, can give accurate far-field noise prediction.

For input, the FW-H model needs time-accurate data on the near field flow, corresponding to a fine mesh on the near field. The fine meshes used for accurate prediction of the boundary layer or other requirements for turbulence models (such as y+ for LES) are sufficient. The computational domain for this model does not need to include the location of the receivers. However, to use non-reflecting boundary conditions requires a larger domain so a buffer layer can be added to reduce and dissipate the acoustic waves.

The depth of the computational domain must be greater than, or equal to, the acoustic correlation length. This depth is sometimes different from the depth that is required for a good LES simulation. Currently, the FW-H model uses the same solution domain for acoustic sources estimation. When three-dimensional CFD solutions with the FW-H model are periodic in the spanwise direction (for example an infinite cylinder), replicate the solution domain in the spanwise direction. For two-dimensional simulations, a correlation length can be used to overcome this issue.

The FW-H models are available to simulations with porous media. These models describe the propagation of sound in free space and are suited to simulations where porous regions do not affect sound propagation from FW-H surfaces to the receivers. It is a misuse of the FW-H models to use a simulation with porous regions between FW-H surface and receiver points. For simulations with both fluid and porous regions, the FW-H Surface filters allow you to select impermeable and permeable FW-H surfaces from fluid regions, but not from porous regions.

The following Ffowcs Williams-Hawkings models are available in Simcenter STAR-CCM+: