INFLUENCE OF LOW MACH NUMBER SHEAR FLOW ON ACOUSTIC PROPAGATION IN DUCTS

An experimental and theoretical investigation of the influence of a parallel shear flow on the sound propagation in a circular duct is described. The theoretical model is based on a perturbation expansion at low Mach number of the modal equation for parallel shear flows (Pridmore-Brown equation). In this model one assumes a rigid wall and no viscous or thermal effects. The experimental study was performed at low Mach number (M<0·05) with two propagating acoustic modes, and the Reynolds number range (0<Re<8500) allowed various profiles for the mean flow. Measurement of the pressure gave the behaviour of the axial wavenumber of modes 0 and 1 that were propagating in our experiment. A good agreement between experimental and theoretical results was obtained.

[1]  M. K. Bull,et al.  Acoustic wave propagation in a pipe with fully developed turbulent flow , 1989 .

[2]  R. S. Brand,et al.  Boundary layer effects on sound in a circular duct , 1982 .

[3]  D. Pridmore‐Brown,et al.  Sound Propagation in a Fluid Flowing through an Attenuating Duct , 1958 .

[4]  S. D. Savkar,et al.  Propagation of sound in ducts with shear flow , 1971 .

[5]  P. N. Shankar.  Acoustic refraction and attenuation in cylindrical and annular ducts , 1972 .

[6]  Vincent Pagneux,et al.  A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I. Theory and validation , 1996 .

[7]  Sung‐Hwan Ko.  New approach to the solution of eigenvalue problems in circular flow ducts (a Taylor series method) , 1981 .

[8]  Ml Munjal,et al.  Analytical Solution Of Sound Propagation In Lined Or Unlined Circular Ducts With Laminar Mean Flow , 1993 .

[9]  Vincent Pagneux,et al.  A study of wave propagation in varying cross-section waveguides by modal decomposition. Part II. Results , 1997 .

[10]  R. F. Lambert,et al.  Influence of Shear Flow on Sound Attenuation in a Lined Duct , 1965 .

[11]  The Propagation of Sound in Cylindrical Ducts with Mean Flow and Bulk-reacting Lining I. Modes in an Infinite Duct , 1980 .

[12]  Sung‐Hwan Ko.  Theoretical Prediction of Sound Attenuation in Acoustically Lined Annular Ducts in the Presence of Uniform Flow and Shear Flow , 1973 .

[13]  M. A. Swinbanks.  The sound field generated by a source distribution in a long duct carrying sheared flow , 1975 .

[14]  D. Pridmore‐Brown,et al.  Sound propagation in a fluid flowing through an attenuating duct , 1958, Journal of Fluid Mechanics.

[15]  P. N. Shankar,et al.  On acoustic refraction by duct shear layers , 1971, Journal of Fluid Mechanics.

[16]  Y. Hayashi,et al.  Over-reflection and shear instability in a shallow-water model , 1992, Journal of Fluid Mechanics.

[17]  P. N. Shankar.  Sound propagation in duct shear layers , 1972 .

[18]  Börje Einar Nilsson.  The propagation of sound in cylindrical ducts with mean flow and bulk-reacting lining , 1980 .

[19]  R. Mani,et al.  Sound propagation in parallel sheared flows in ducts: the mode estimation problem , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[20]  A. H. Nayfeh,et al.  Effect of mean-velocity profile shapes on sound transmission through two-dimensional ducts , 1974 .