Abstract

This thesis presents a method for computational aeroacoustics, primarily aimed at computing sound propagation in, and radiation from, turbofan inlets. The physics of sound propagation is modeled by the system of partial differential equations that describe conservation of mass, momentum and energy in inviscid flows. The equations are solved numerically in the time domain as an initial and boundary value problem to obtain the time-dependent acoustic pressure in the flow field, from which sound pressure levels are obtained by integration. A multidomain spectral method is used to discretize the space terms. Complex geometries are handled by the use of unstructured grids of non-overlapping hexahedra that may have curved boundaries. An isoparametric mapping is used to transform each hexahedron on the master element, on which an efficient collocation spectral approximation can be defined by the use of tensor products. Continuity of the solution in space is enforced as part of the solution process by the use of a set of staggered grids that do not involve the element corners. A set of Runge-Kutta methods optimized for wave propagation and with minimal storage requirements are developed for integration in time. Several radiation boundary conditions are implemented and tested, and a way to construct the spectral grids within the elements starting from given edge descriptions is proposed. A transformation that alleviates the time step restriction while keeping the exponential accuracy is also discussed. Numerical results that validate the methodology are presented for several test cases representative of the fan noise problem. The thesis ends with a brief description of a modification that allows computation of noise superposed on a mean flow known from other sources, such as experiments, and its application to turbulent mixing noise from a supersonic jet.