A Laplace Transform Potential Theoretic Method For Transient Acoustic Propagation In Three Dimensional Subsonic Flows PDF Download

This dissertation presents the development of a semi-analytic technique developed for the determination of far field acoustic radiation in the time domain. This method solves linear, time dependent wave propagation in an unbounded medium using a numerical Laplace transform and potential theory. The end result is a robust procedure that is accurate and computationally efficient. The Transform Potential Theoretic (TPT) method is meshless and can handle arbitrary geometries. The procedure assumes the linearity of the sound field away from a bounded region surrounding the object. The TPT method depends on the sound pressure on the boundary of this region (referred to as the Kirchhoff surface). The Euler equations are linearized about a uniform mean flow. First, the problem is transformed via the Laplace transform (with appropriate initial conditions) into a reduced wave equation. By application of a dependent variable transformation, the anisotropic terms are removed and a Helmholtz-like equation with complex wave number is obtained where both single and double layer potential theory applies. This allows the calculation of the far-field acoustic pressure in the Laplace domain. Then, an inversion of the dependent variable transform is applied. Upon application of numerical inverse Laplace transform techniques, far-field acoustic pressure is then successfully obtained as a function of space and time. Using transient monopole radiation in a uniform freestream, accuracy is analyzed with excellent results. This method shows many advantages over direct simulation, including vast savings in computational time. The freestream Mach number is only a parameter in the TPT method and has no bearing on the run time, unlike direct methods.