Aeroacoustic integral methods,formulation and efficient numerical implementation

The paper makes a contribution to the clearer understanding of the physical meaning and domain of applicability of the Ffowcs Williams–Hawkings (FW-H) and Kirchhoff aeroacoustic integral methods. The analytical relationship between the two approaches, and the physical implications involved in the use of the Kirchhoff approach are discussed. In particular, where the Kirchhoff surface cuts into a domain where non-negligible volume sources of Lighthill's Acoustic Analogy are present (domain crossed by a shock, non-uniform flow or vortices for instance), the Kirchhoff integral must be complemented by additional surface integrals to recover the FW-H surface integral. The paper goes on to describe a fast, robust integration technique for computing FW-H or Kirchhoff surface integrals. This integration technique starts from emission time, and treats each integration surface element as non-compact. It obviates the need to build retarded acoustic surfaces and avoids some of the drawbacks of current methods, such as the Doppler singularity when using supersonically rotating grids. The paper then recalls formulas for calculations in the aircraft reference frame, and the computational efficiency of the proposed integration method is demonstrated by its application to the prediction of helicopter rotor noise directivity contours.