Computational aeroacoustics as applied to the diffraction of sound by cylindrical bodies

Abstract

The problem of the diffraction of sound by two-dimensional rigid cylindrical objects has been formulated in generalized curvilinear coordinates. The governing equations for the aeroacoustic field are derived by perturbing the unsteady Euler equations and then extracting the steady mean flow equations from them. The governing equations are then solved by an explicit, four-stage Runge-Kutta, time-marching, finite-volume numerical scheme. The scheme has been implemented with far-field radiation and time-accurate wall boundary conditions. The cases of diffraction by a knife edge and a cylinder have been computed and compared against their corresponding analytical solutions in order to demonstrate the prediction capability of the numerical scheme. The acoustic field resulting from the interaction of the incident, reflected, and diffracted fields has been predicted very well in both the shadow and the illuminated zones. The scheme has also been applied to compute the diffraction of plane waves as well as that of a monopole acoustic field by a GA(W)-1 airfoil. I. Introduction W HEN sound waves impinge upon large rigid obstacles in their path, the resultant aeroacoustic field comprises of the incident waves, the reflected waves, and the diffracted waves. The diffraction of sound waves in the shadow zone plays a key role in assessing the acoustic shielding capability of aerodynamic bodies and forms a problem of fundamental importance in the field of aeroacoustics . The various fluctuating quantities that describe the aeroacoustic field are governed by the Euler equations which are, of course, nonlinear. Even if the governing equations are linearized, it is extremely difficult to obtain analytical solutions in the cases of the realistic twodimensional obstacles such as airfoils without some unacceptable drastic simplifications. The difficulty can be essentially attributed to the complexities associated with the treatment of the boundary conditions. These difficulties pertaining to the analytical solutions have been appreciated by many investigators14 and have led to the emergence of a new field of computational aeroacoustics (CAA). Progress in the methods of CAA has now advanced because of the considerable advances in the fields of computational fluid dynamics (CFD) and computer technology. The aim of both CFD and CAA is to find solutions to the practical problems numerically, but the main differences between the two lie in the nature of the problems one deals with and in the type of the information one wishes to obtain. CFD treats steady as well as unsteady problems, whereas all the CAA problems are, by definition, unsteady. In current CFD problems, interests are focused primarily on the flowfield in the immediate vicinity of an aerodynamic body, and the objectives are to determine aerodynamic quantities such as pressure distributions, skin friction, lift and drag, etc. On the other hand, in CAA problems, attention is directed to both the near-field acoustic vibrations and the far-field noise radiation away from the body, and the objectives are to find the directivity and the spectral characteristics of the acoustic field. Therefore, while the well-established techniques of CFD can be utilized in order to develop the