Boundary Element Method Formulation for axisymmetric acoustic problems in a subsonic uniform flow

This paper presents a new analysis method and numerical development of the direct boundary element method formulation for axisymmetric acoustic radiation and propagation problems in a subsonic uniform flow. It governed by the homogeneous axisymmetric convected Helmholtz equation independent of the flow direction based on the Fourier coefficient , the three-dimensional convected Green's function in free space according to the azimuth angle represented by the modal kernel arising in the acoustic sources. This ax-isymmetric integral formula is expressed only in two new operators; the first, concerned the particular normal derivative similar to the temporal derivative and the other, concerned the convected normal derivative reduce the convective terms of normal derivative and the flow direction derivative used in the classical formulations developed in the literature. When, the main source is taken on the generator, the integration modal Green kernel and its convected derivative are performed partly analytically in terms of Laplace coefficients evaluate by a simple recursive formula and partly numerically using a Gauss-Legendre quadrature standard formula to facilitate the analytical resolution and the conventional numerical problems. The boundary element method formulation used to illustrated and tested by applying the infinite axisymmetric cylindrical duct in a subsonic uniform flow

An improved axisymmetric convected boundary element method formulation with uniform flow

This paper presents an improved form of the convected Boundary Element Method (BEM) for axisymmetric problems in a subsonic uniform flow. The proposed formulation based on the axisymmetric Convected Helmholtz Equation (CHE) and its fundamental solution that describes the sound radiation from a monopole source. The variables in the new axisymmetric boundary integral formulation can be expressed explicitly in terms of the acoustic pressure and its particular normal derivative. Also, the constant coefficients are expressed only in terms of the axisymmetric convected Green’s function and its convected normal derivative. The particular and convected derivatives reduce the flow effects of the normal and the flow direction derivatives incorporated in the conventional convected boundary integral formulas. The advanced form of the axisymmetric boundary integral representation with flow is a similar form of the axisymmetric boundary element method without flow. Precisely, the two new operators significantly reduce the computational burden of the classical BEM and then becomes the CPU time of BEM without flow. The formula is verified comparing to both analytical and Finite Element Methods (FEM) of an axisymmetric infinite rigid duct in a subsonic uniform flow

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method (BEM) is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation (BIE) representation solves the two-dimensional convected Helmholtz equation (CHE) and its fundamental solution, which must satisfy a new Sommerfeld radiation condition (SRC) in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Greenâs kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole, dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation. Keywords: Two-dimensional convected Helmholtz equation, Two-dimensional convected Greenâs function, Two-dimensional convected boundary element method, Arbitrary uniform mean flow, Two-dimensional acoustic source