A three-dimensional boundary element scheme for acoustic radiation in low mach number flows

A boundary element scheme is proposed for acoustical radiation in moving flows. The scheme relies upon a transformation, valid at low Mach numbers, which permits the case with flow to be restated as an equivalent problem, in the absence of flow but with modified boundary conditions. This restatement of the original problem is then amenable to boundary integral representation and boundary element solution. Results obtained by using this approach are presented for the test case of a pulsating or juddering sphere of finite dimensions in a uniform low Mach number flow. A fully three-dimensional boundary element model is used. The validity of the results is established by comparison with an analytic perturbation solution (where applicable) and by comparison with results from an alternative, axisymmetric numerical scheme.

[1]  A. H. Nayfeh,et al.  Transmission of sound through nonuniform circular ducts with compressible mean flows , 1976 .

[2]  M. K. Myers,et al.  On the acoustic boundary condition in the presence of flow , 1980 .

[3]  S. J. Horowitz,et al.  An iterative finite element-integral technique for predicting sound radiation from turbofan inlets , 1981 .

[4]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Ben T. Zinn,et al.  Prediction of the sound field radiated from axisymmetric surfaces , 1979 .

[6]  R. J. Astley,et al.  Wave envelope and infinite elements for acoustical radiation , 1983 .

[7]  Ben T. Zinn,et al.  Boundary integral solutions of three dimensional acoustic radiation problems , 1978 .

[8]  R. J. Astley,et al.  A Note on the Utility of a Wave Envelope Approach in Finite Element Duct Transmission Studies , 1981 .

[9]  O. C. Zienkiewicz,et al.  Diffraction and refraction of surface waves using finite and infinite elements , 1977 .

[10]  R. K. Sigman,et al.  Determination of Turbofan Inlet Acoustics Using Finite Elements , 1978 .

[11]  R. J. Astley,et al.  Acoustic Transmission in Non-Uniform Ducts with Mean Flow, Part II: The Finite Element Method , 1981 .

[12]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[13]  C.H.E. Warren.  A note on moving multipole sources of sound , 1976 .

[14]  R. J. Astley,et al.  Finite element formulations for acoustical radiation , 1983 .

[15]  G. R. Cowper,et al.  Gaussian quadrature formulas for triangles , 1973 .

[16]  C. Piaszczyk,et al.  Acoustic radiation from vibrating surfaces at characteristic frequencies , 1984 .

[17]  K. J. Baumeister,et al.  Time-dependent difference theory for noise propagation in a two-dimensional duct. [of a turbofan engine] , 1979 .

[18]  S. J. Horowitz,et al.  Optimization of acoustic liners by the hybrid finite element-integral approach , 1983 .

[19]  R. J. Astley.  A finite element, wave envelope formulation for acoustical radiation in moving flows , 1985 .

[20]  S. J. Horowitz,et al.  An iterative finite element-integral technique for predicting sound radiation from turbofan inlets in steady flight , 1982 .

[21]  A. Cabelli,et al.  Duct acoustics—A time dependent difference approach for steady state solutions , 1982 .

[22]  K. Taylor,et al.  Acoustic generation by vibrating bodies in homentropic potential flow at low Mach number , 1979 .

[23]  Ann P. Dowling,et al.  CONVECTIVE AMPLIFICATION OF REAL SIMPLE SOURCES , 1976 .

[24]  K. Taylor.  A transformation of the acoustic equation with implications for wind-tunnel and low-speed flight tests , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.