Digital aeroacoustics: sound sources and their radiation

Computational Fluid Dynamics (CFD), which integrates the Euler and Navier-Stokes equations, has come into its own over the last few decades thanks to the increasing power of computers. Acoustics is a small perturbation of the mean aerodynamic field and is therefore included in CFD, but Computational AeroAcoustics (CAA) has quickly emerged as a discipline in its own right due to its specific features: in most cases, the calculation includes a chain of CFD and CAA software, with CFD providing the sound source data for CAA. Such methods are often referred to as "hybrid". The aim of this document is to highlight the many different approaches available and to guide the engineer in his or her choice, while indicating certain precautions to be taken.

CAA is based on the Lighthill equation, leading to the Ffowcs Williams and Hawkings integral form. The presentation begins with these theoretical foundations, and the application to jet noise, for which they were established. AAC makes use of many other approaches, which are discussed in the following paragraphs.

• For propagation in a fluid with non-uniform flow, it is necessary to integrate the Euler equations, either linearized or written on the perturbations (the latter derived from CFD) in the domain where acoustic propagation is non-linear.

• More simply, efficient off-the-shelf software solves the Helmholtz equation using the boundary element method; the mean fluid must then be at rest (or in uniform motion), which limits its relevance if there is heterogeneous fast flow. On the other hand, the algorithm is generally written in the frequency domain, which makes it easy to introduce boundary conditions (acoustic impedance) on the walls.

• Finally, if CFD conserves acoustic fluctuations up to a closed surface containing all sound sources and where the fluid is in uniform flow, the Kirchhoff integral on this surface directly provides the acoustic field at any point outside this surface. This provides an appreciable gain over integration in the source volume. The Williams and Hawkings Ffowcs equation with a porous surface improves on this technique in certain cases.

The choice of hybrid method depends on a number of factors, such as the configuration being studied, or the type of CFD being used. Computation time also plays a key role, depending on the objective: requirements are different for research, industrial operation or aeroacoustic optimization.