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.

In this paper, we develop an axisymmetric boundary integral equation that derives from a reformulation of the 3D Helmholtz integral formula for the acoustic radiation problems in a subsonic uniform flow. Through the use of a new non-standard derivative operator, the axisymmetric convected Helmholtz integral equation substantially reduces the effects of flow incorporated in the classical convected boundary integral formulations, and involved in the normal derivative and the derivative in the flow direction of the axisymmetric convected Green's function. As for the free term derived from the singular integrals, it is given by a new expression independent of complete elliptic integrals and evaluated analytically as a convected angle in the meridian plane. The numerical treatment of singular integrals requires only the use of standard Gauss quadrature rules. Different test cases are presented.

This work is the result of a collaboration between the Re@ Renault and the University of Compilgne. Optimization techniques are applied here to minimize the mass of sand casting pieces by varying the thickness distribution of non-Cunctional parts. A car suspension arm is taken as example. Finite element modelling is realized with triangular 3-node elements by using MEF/MOSAIC software. The middle surface of the shell is assumed to be fixed; the design variables are the thicknesses of elements or poups of elements (444 elements, 45 variables). The result is then smoothed to provide a feasible solution. Constraints are imposed to limit the stresses values on the critical parts of the structure. The minimization algorithm rquires their gradients which are expressed by using the adjoint state method. The numerical results show that the optimization of thickness leads to a 25% decrease of the mass.

Using the free-field convected Green’s function, the integral formulation for the acoustic velocity potential and its normal derivatives associated with Helmholtz’s equation in a uniform flow is established. An original development for the calculation of the Cauchy principal value in the singular integrals is presented. As far as the finite part in the hypersingular integral is concerned, a new transformation of the convected double-layer potential normal derivative is proposed. The result of this transformation avoids the explicit calculation of the finite part. Moreover, it generalizes the famous works [M. P. Stallybrass, J. Math. Mech. 16, 247–1286 (1967)] [A. W. Maue, Zeit. für Phys. 126, 601 (1949)] on the resolution of the Helmholtz’s equation, by integral equations, in a fluid with null veloc- ity. This new variational method by integral equations can easily be coupled with the variational formulation for studying the convection and refraction effects of the acoustic waves in a nonuniform flow [M. Beldi, Third International Conference on Theoretical and Computational Acoustics, Newark (14–18 Aug. 1997)]. The numerical results shows the importance of these effects.

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