Compact Assumption Applied to Monopole Term of Farassat’s Formulations

This paper presents compact forms for the monopole term of several of Farassat’s formulations. When the physical surface is elongated, such as in the case of a high aspect ratio rotorcraft blade, one can derive compact forms that are shown to be a function of the blade cross-sectional area by reducing the computation from a surface integral to a line integral. The compact forms of all formulations are applied to two example cases: a short span wing with constant airfoil cross-section moving at three forward flight Mach numbers and a rotor at two advance ratios. Acoustic pressure time histories and power spectral densities predicted from the compact forms are shown to resemble very closely the predictions from their noncompact counterparts. A study on the influence of the rotorcraft blade shape on the high-frequency content shows that there is a direct correlation between the aspect ratio of the airfoil and the error incurred. Finally, a prediction of the pressure gradient from the noncompact and compact forms of the thickness term of formulation G1A shows that using the compact forms results in a 99.6% improvement in computation time, which will be critical when noise is incorporated in a design environment.