The K-Algorithm and the modeling of the emission surface from supersonically rotating bodies

Since the early 80 s the prediction of the high speed noise from rotating blades has represented one of the most challenging aeroacoustic problems. Approaching the high transonic regime, the shock wave occurring on the blade surface delocalizes out of the tip region and forces to account for the contribution of supersonic sources. At those conditions, the Doppler singularity prevents the use of the standard solving approaches to predict the noise and can be no way managed or bypassed by some numerical artifice, as it is strictly related to a well-defined physical phenomenon: the appearance of multiple sources. In an emission surface formulation the effects of the singularity are moved from the integral kernels to the integration domain; in this case, however, the multi-emissive status of supersonic sources makes the reconstruction of this domain a very complex task. The paper provides a detailed description of the K-Algorithm, a procedure conceived and developed to model an emission surface from a body rotating at supersonic speed. (C) 2020 Elsevier Inc. All rights reserved.