An efficient and robust method for predicting helicopter high-speed impulsive noise

A new formulation for the Ffowcs Williams–Hawkings quadrupole source is presented for helicopter-rotor noise prediction. The formulation is a far-field approximation which is exact for a far-field in-plane observer. The approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with 1/r2and 1/r3dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer is in motion (e.g., the wind tunnel case). The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Because it is a retarded-time formulation, the current implementation is intentionally limited to subsonic source motion to avoid singular integrals. 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. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.