Some New Results for the Study of Acoustic Radiation within a Uniform Subsonic Flow Using Boundary Integral Method

Abstract:

In this paper, a reformulation of the Helmholtz integral equation for tridimesional acoustic radiation in a uniform subsonic flow is presented. An extension of the Sommerfeld radiation condition, for a free space in a uniform movement, makes possible the determination of the convected Green function, the elementary solution of the convected Helmholtz equation. The gradients of this convected Green function are, so, analyzed. Using these results, an integral representation for the acoustic pressure is established. This representation has the advantage of expressing itself in terms of new surface operators, which simplify the numerical study. For the case of a regular surface, the evaluation of the free term associated with the singular integrals shows that it is independent of the Mach number of the uniform flow. A physical interpretation of this result is offered. A numerical approximation method of the integral representation is developed. Furthermore, for a given mesh, an acoustic discretization criterion in a uniform flow is proposed. Finally, numerical examples are provided in order to validate the integral formula.

• Periodical: Advanced Materials Research (Volumes 488-489)
• Pages: 383-395
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.488-489.383
• Online since: March 2012
• Authors: M. Beldi, A. Maghrebi
• Keywords: Acoustic Discretization Criterion, Convected Green Function, Convected Helmholtz Integral Formula, Singular Integral, Sommerfeld Radiation Condition, Uniform Flow-Wave Interaction

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