Sound radiated from a single airfoil and a cascade of airfoils in three-dimensional gusts is directly calculated. Euler’s equations are linearized about the mean flow of the airfoil or cascade. The velocity field is split into a vortical part and a potential part. The latter is governed by a single nonconstant-coefficient convective wave equation. For a single airfoil, the radiated sound is calculated using Kirchhoff’s method from the mid field of the unsteady pressure obtained through the unsteady aerodynamic solver. The results indicate the importance of the contribution of the quadrupole effects to the sound field. For a cascade of airfoils, the acoustic pressure is directly obtained by solving the partial differential equation. The results show that, as the maximum Mach number on the blade surface nears unity, there is a significant rise in the local unsteady pressure, and also a significant increase in the upstream acoustic pressure.
Recent research has shown the feasibility of performing inverse aeroacoustic problems for streamlined bodies. The unsteady pressure on a flat-plate airfoil, due to a convected vortical disturbance in the mean flow, can be recovered from the far-field radiated sound. The present paper extends this analysis to oscillating airfoils in a uniform mean flow. In this case, the oscillating airfoil creates an unsteady pressure field on the airfoil surface. The inverse problem, then, is to determine the surface pressure from the radiated sound. For the oscillating airfoil problem, the normal pressure gradient does not vanish along the airfoil surface, rendering the inversion process more complex than for the gust problem, however it is still feasible. This paper also compares the oscillating airfoil application to acoustic holography. While the two problems are similar mathematically, far-field input data are, in general, not sufficient for acoustic holography applications while they are sufficient for the inverse aeroacoustic problem.
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