Abstract
In the development of the newer supersonic and hypersonic flight vehicles, an increased need for the analysis of acoustic fields and the response of structures to acoustic loads in the presence of high temperature and large mean flow velocities have become necessary. A major concern has been in the area of pressure fields associated with ducts. Such acoustic ducts are frequently used to test the response of various structural elements of flight vehicles. Many new methods have been created and used to approximate the sound fields in ducts. Since the region or boundary of an acoustic problem can extend to infinity, some approximating methods require much time and effort to solve the problem. Many ways have been examined to simplify the acoustic problem and still obtain reasonable results. In the past thirty years, the boundary element method (BEM) has been researched and proven to be an extremely simplified and accurate method for solving acoustic problems. Since BEM only discretizes the boundary, the dimensionality of the problem is reduced by one.
This paper presents a boundary element formulation to predict the pressure field in a two-dimensional acoustic duct. The boundary conditions basically consist of two types: known pressure or known normal derivative of pressure. In order to examine the boundary element method, a 2-D rectangular duct problem will be investigated. The example problem will consist of a duct with rigid walls and a specified pressure distribution at the entrance. Pressure values will be calculated for boundary nodes using the boundary element method. These values will be compared with the available classical solutions.
A novel dual reciprocity boundary element formulation for two-dimensional transient convection–diffusion–reaction problems with variable velocity