## Mechanical Engineering Faculty Research

#### Title

A Laplace Transform/Potential-Theoretic Method for Acoustic Propagation in Subsonic Flows

#### Document Type

Article

#### Publication Date

Winter 2-10-2003

#### Abstract

This paper introduces a competitive computational approach for determining time-dependent far-field sound generated by subsonic flows around lifting airfoils. The procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil. It is assumed that the sound pressure on the boundary of this enclosed region (referred to as the Kirchhoff surface) is specified, possibly by another procedure such as solving the full Euler equations. Away from the Kirchhoff surface, the Euler equations are linearized about a uniform mean flow. It is well known that linearized Euler equations can be uncoupled into a scalar convective wave equation. However, due to the anisotropy present in the convective wave equation, it is difficult to compute solutions. In this context, direct numerical simulation of the convective wave equation requires proper numerical descriptions of far-field boundary conditions which is a non-trivial task. Moreover, if accurate far-field conditions can be formulated, the computational cost of direct simulation can be prohibitive even in a modest computational domain. In this paper, we present an alternate solution procedure. First, the problem is transformed via the Laplace transform (with appropriate initial conditions) into a reduced wave equation. The convective term in the reduced wave equation is removed using a dependent variable transformation. Then we use Gothert’s rule, to obtain a Helmholtz like equation with complex wave number, which is subsequently solved using double layer potential theory. Finally upon application of numerical inverse Laplace transform techniques, far-field acoustic pressure is obtained as a function of space and time.

#### Publication Title

Journal of Computational Physics

#### Volume

185

#### Issue

1

#### First Page

252

#### Last Page

270

#### Recommended Citation

Hariharan, S. I.; Sawyer, Scott; and Quinn, D, Dane, "A Laplace Transform/Potential-Theoretic Method for Acoustic Propagation in Subsonic Flows" (2003). *Mechanical Engineering Faculty Research*. 839.

http://ideaexchange.uakron.edu/mechanical_ideas/839