An efficient and robust method for computing quadrupole noise

A new far-field approximation to the Ffowcs Williams - Hawkings quadrupole source, which is valid for an in-plane observer and utilizes preintegration in the direction normal to the rotor disk, is presented. This approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r^-2 and r^-2 dependence are retained. The far-field approximation leads to quadrupole integrals of the same form as thickness and loading noise. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. The predicted noise agrees well with both experimental data and Euler predictions for a hovering rotor up to a hover Mach number M_H=0.9, even though only subsonic quadrupole sources are utilized in the present implementation. The method is robust and requires computer resources comparable to thickness and loading noise prediction.