A Laplace transform/potential-theoretic method for acoustic propagation in subsonic flows

Hariharan, S. I.; Sawyer, Stanley; Quinn, D. Dane

doi:10.1016/s0021-9991(02)00056-6

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…It can be treated subtracting off the singularity from the integrand function and using Hermite interpolation techniques for the successive integration. Using the convected nonreflecting boundary conditions equations (39) and (40) and the classical procedure to isolate the singularity parts of the modal Green’s function and its convected normal derivative equations (57) and (58) 41,49,85 , we get a new original form of the generalized modal boundary integral formulation with arbitrary uniform mean flow wearing on the modal acoustic field at any point m as follows in which c±(m) is a novel free term solving the singular integrals arising from the limit integral formulation. It is derived from the exterior and anterior acoustic media, rewritten by the following simplified integral form where θ∓(m) is the convected axisymmetric angle of center m and moving between two convected angles (θ1*,θ2*) such as θ∓=±(θ2*−θ1*).…”

Section: Generalized and Improved Modal Boundary Element Methodsmentioning

confidence: 99%

“…7 Its based on a combination of Linearised Euler Equations in space variables. 85 To overcome the Helmoltz problem, the interior and exterior acoustic domains are necessary to impose boundary conditions at its closed boundaries. In order to relate the flow variables on the upper side Ω e of the boundary Γ to the variables on the lower side Ω i , the continuity of the acoustic field for the exterior and interior media can be given by Taylor and Myers conditions on the generator Γ.…”

Section: Modal Formulationsmentioning

confidence: 99%

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A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

Barhoumi

Bessrour

2020

International Journal of Aeroacoustics

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This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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