Acoustic waveform singularities from supersonic rotating surface sources

This paper discusses the analytical characteristics of waveforms produced by rotating surface sources with tip Mach number >1. The analysis covers both monopole and quadrupole sources that have the greatest importance for prediction of high-speed rotor noise. By using idealized source distributions over the rectangular surfaces, it is shown that the LighthiU/Curle analogy with time derivatives taken outside the integrals poses no additional difficulty attributable to numerical error. The integrals themselves require careful analysis of critical points in the integrand so that an adaptive integration grid can be developed for each time step. A mathematical analysis of the integrands arising from the idealized sources predicts a logarithmic singularity at critical points in the monopole waveform and a single-pole singularity at such points in the quadrupole waveform. The computation bears out these predictions.