The Frequency-Domain Formulations of the Quadrupole Correction for the Ffowcs Williams-Hawkings Integration

摘要

In the present article, frequency-domain formulations of the quadrupole correction are sought for the Ffowcs Williams-Hawkings equation with permeable control surface. The effectiveness of the quadrupole correction has been demonstrated by the present authors in previous studies, originally derived in time domain. The difficulty of the derivation in frequency domain, however, is its mathematical methodology that has been employed conventionally in the literature, different from time-domain Ffowcs Williams-Hawkings formulations. First, the mathematical framework in frequency domain is shown to be equivalent to that in time domain. Then, the frequency-domain formulation is directly derived via a Fourier transform applied to the time-domain form of the quadrupole correction. The results of the derived formulation agree precisely with the time-domain solutions, in the application to a jet noise prediction, as well as two-dimensional fundamental verification studies, which ensures the validity of the present derivation.