A potential-theoretic method for far-field sound radiation calculations

The far-field acoustic radiation due to the interaction of upstream, unstea dy vortical disturbances with an airfoil in subsonic, compressible flow is calculated using potential theory. A Kirchhoff surface is placed in the nea r field surrounding the airfoil and the pressure on this surface is calcula ted from the unsteady flow field, obtained using a second-order finite-diff erence code. The governing equation is reduced to the Helmholtz equation in the frequency domain and the solution is written in terms of an integral o ver the Kirchhoff surface involving the free-space Green's function and an unknown single-layer density function. The single-layer density is then det ermined from the boundary condition on the Kirchhoff surface. This method i s presented as an alternative to classical Kirchhoff methods. It has the ad vantage of bring able to accommodate arbitrarily shaped Kirchhoff surfaces and is also readily extendable to three-dimensional problems. Numerical res ults are presented for thin, symmetric, and loaded airfoils. Thin-airfoil r esults are compared to the analytical solution, and thick-airfoil results a re checked for numerical convergence and compared to results obtained from a time-domain Euler solver. (C) 2000 Academic Press.