A computational approach for flow-acoustic coupling in closed side branches.

The quarter-wave resonator, which produces a narrow band of high acoustic attenuation at regularly spaced frequency intervals, is a common type of silencer used in ducts. The presence of mean flow in the main duct, however, is likely to promote an interaction between these acoustic resonances and the flow. The coupling for some discrete flow conditions leads to the production of both large wave amplitudes in the side branch and high noise levels in the main duct, thereby transforming the quarter-wave silencer into a noise generator. The present approach employs computational fluid dynamics (CFD) to model this complex interaction between the flow and acoustic resonances at low Mach number by solving the unsteady, turbulent, and compressible Navier-Stokes equations. Comparisons between the present computations and the experiments of Ziada [PVP-Vol. 258, ASME, 35-59 (1993)] for a system with two coaxial side branches show that the method is capable of reproducing the physics of the flow-acoustic coupling and predicting the flow conditions when the coupling occurs. The theory of Howe [IMA J. Appl. Math. 32, 187-209 (1984)] is then employed to determine the location and timing of the acoustic power production during a cycle.

[1]  Michael S. Howe,et al.  On the Absorption of Sound by Turbulence and Other Hydrodynamic Flows , 1984 .

[2]  Edward Naudascher.  From Flow Instability to Flow-Induced Excitation , 1967 .

[3]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[4]  Mark C. Thompson,et al.  Aerodynamic sources of acoustic resonance in a duct with baffles , 1990 .

[5]  D. Rockwell,et al.  Review—Self-Sustaining Oscillations of Flow Past Cavities , 1978 .

[6]  Leonard L. Shaw,et al.  Suppression of Aerodynamically Induced Cavity Pressure Oscillations , 1977 .

[7]  E. E. Covert,et al.  An approximate calculation of the onset velocity of cavity oscillations , 1970 .

[8]  K. Botros,et al.  Cylindrical side-branch as tone generator , 1989 .

[9]  F. Demetz,et al.  Laminar and turbulent shear flow induced cavity resonances , 1977 .

[10]  P. Jenvey.  The sound power from turbulence: A theory of the exchange of energy between the acoustic and non-acoustic fields , 1989 .

[11]  R. L. Sarno,et al.  Suppression of flow-induced pressure oscillations in cavities , 1990 .

[12]  Ronald L. Panton.  Effect of orifice geometry on Helmholtz resonator excitation by grazing flow , 1990 .

[13]  O. Baysal,et al.  Navier-Stokes Computations of Cavity Aeroacoustics with Suppression Devices , 1994 .

[14]  M. Franke,et al.  Effect of geometry on open cavity flow-induced pressure oscillations , 1975 .

[15]  Mark C. Thompson,et al.  Coupling of vortex shedding with the fundamental resonant mode of a resonator tube , 1993 .

[16]  William W. Durgin,et al.  Tone Generation by Flow Past Deep Wall Cavities , 1987 .

[17]  Samir Ziada,et al.  Self-excited resonances of two side-branches in close proximity , 1992 .

[18]  A. D. Gosman,et al.  The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme , 1986 .

[19]  K. K. Botros,et al.  Tone generation by flow past confined, deep cylindrical cavities , 1987 .

[20]  Implicit and explicit computations of flows past cavities with and without yaw , 1990 .

[21]  M. S. Howe.  The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations , 1981, Journal of Fluid Mechanics.

[22]  K. Krishnamurty,et al.  Acoustic radiation from two-dimensional rectangular cutouts in aerodynamic surfaces , 1955 .

[23]  J. S. Anderson,et al.  The effect of an air flow on a single side branch helmholtz resonator in a circular duct , 1977 .

[24]  A Avraham Hirschberg,et al.  High amplitude vortex-induced pulsations in a gas transport system , 1995 .

[25]  A Avraham Hirschberg,et al.  Self-sustained aero-acoustic pulsations in gas transport systems: Experimental study of the influence of closed side branches , 1991 .

[26]  J. W. Ball.  Hydraulic Characteristics of Gate Slots , 1959 .

[27]  Xin Zhang,et al.  Progress in Computational Aeroacoustics in Predicting the Noise Radiated from Turbulent Flows , 1997 .

[28]  C. Tam,et al.  On the tones and pressure oscillations induced by flow over rectangular cavities , 1978, Journal of Fluid Mechanics.

[29]  J. Hardin,et al.  Sound Generation by Flow over a Two-Dimensional Cavity , 1995 .

[30]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[31]  Oktay Baysal,et al.  Unsteady viscous calculations of supersonic flows past deep and shallow three-dimensional cavities , 1988 .

[32]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[33]  W. L. Hankey,et al.  Analyses of Pressure Oscillations in an Open Cavity , 1980 .

[34]  Michael S. Howe,et al.  Edge, cavity and aperture tones at very low Mach numbers , 1997, Journal of Fluid Mechanics.

[35]  Alan S. Hersh,et al.  Effect of grazing flow on the acoustic impedance of Helmholtz resonators consisting of single and clustered orifices , 1978 .

[36]  L. F. East,et al.  Aerodynamically induced resonance in rectangular cavities , 1966 .

[37]  P. Nelson,et al.  Fluid dynamics of a flow excited resonance, Part II: Flow acoustic interaction , 1983 .

[38]  K. K. Ahuja,et al.  Prediction and measurement of flows over cavities - A survey , 1987 .

[39]  William W. Durgin,et al.  Shear Layer Coupling with Side-Branch Resonators , 1986 .

[40]  Peter J. Disimile,et al.  Algebraic turbulence model simulations of supersonic open-cavity flow physics , 1996 .

[41]  Donald P. Rizzetta,et al.  Numerical Simulation of Supersonic Flow Over a Three-Dimensional Cavity , 1987 .

[42]  J. Gorter.  GAS FLOW THROUGH PIPE-LINES WITH SIDE-BRANCH CAVITIES: A SEMI-EMPIRICAL MODEL , 1986 .

[43]  N. Chokani,et al.  Suppression of pressure oscillations in an open cavity by passive pneumatic control , 1991 .