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Acoustic mode scattering from a heat source

Published online by Cambridge University Press:  30 April 2010

O. V. ATASSI*
Affiliation:
Department of Aerodynamics, Pratt and Whitney, 400 Main Street, East Hartford, CT 06108, USA
J. J. GILSON
Affiliation:
Department of Aerodynamics, Pratt and Whitney, 400 Main Street, East Hartford, CT 06108, USA
*
Email address for correspondence: oliver34@comcast.net

Abstract

The scattering of an incident acoustic wave by a non-uniform mean flow resulting from a heat source is investigated. The heat source produces gradients in the mean flow and the speed of sound that scatter the incident duct acoustic mode into vortical, entropic, and higher-order acoustic modes. Linear solutions utilizing the compact source limit and nonlinear solutions to the Euler equations are computed to understand how variations in the amplitude and axial extent of the heat source as well as the incident acoustic wave propagation angle and amplitude modify the scattered solution. For plane wave excitation, significant entropy waves are produced as the net heat addition increases at the expense of the transmitted acoustic energy. When the net heat addition is held constant, increasing the axial extent of the heat source results in a reduction of the entropy waves produced downstream and a corresponding increase in the downstream scattered acoustic energy. For circumferential acoustic mode excitations the incident acoustic wave angle, characterized by the cutoff ratio, significantly modifies the scattered acoustic energy. As the propagating mode cutoff ratio approaches unity, a rise in the scattered vortical disturbance and a decrease in the entropic disturbance amplitude is observed. As the cutoff ratio increases, the scattered solution approaches the plane wave results. Moreover, incident acoustic waves with different frequencies and circumferential mode orders but similar cutoff ratios yield similar scattered wave coefficients. Finally, for large amplitude incident acoustic waves the scattered solution is modified by nonlinear effects. The pressure field exhibits nonlinear steepening of the wavefront and the nonlinear interactions produce higher harmonic frequency content which distorts the sinusoidal variation of the outgoing scattered acoustic waves.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Atassi, H. M., Ali, A. A., Atassi, O. V. & Vinogradov, I. V. 2004 Scattering of incident disturbances by an annular cascade in a swirling flow. J. Fluid Mech. 499, 111138.CrossRefGoogle Scholar
Atassi, O. V. 2003 Computing the sound power in non-uniform flow. J. Sound Vib. 266, 7592.CrossRefGoogle Scholar
Atassi, O. V. 2007 Propagation and stability of the vorticity-entropy waves in a non-uniform flow. J. Fluid Mech. 545, 149176.CrossRefGoogle Scholar
Atassi, O. V. & Ali, A. 2002 Inflow/outflow conditions for internal time-harmonic Euler equations. J. Comput. Acoust. 10, 155182.CrossRefGoogle Scholar
Atassi, O. V. & Galan, J. M. 2008 The implementation of nonreflecting boundary conditions for the nonlinear Euler equations. J. Comput. Phys. 227, 16431662.CrossRefGoogle Scholar
Bohn, M. S. 1977 Response of a subsonic nozzle to acoustic and entropy disturbances. J. Sound Vib. 52, 283.CrossRefGoogle Scholar
Chagelishvili, G. D., Tevzadze, A. G., Bodo, G. & Moiseev, S. S. 1997 Linear mechanism of wave emergence from vortices in smooth shear flows. Phys. Rev. Lett. 79, 31783181.CrossRefGoogle Scholar
Courant, R. & Hilbert, D. 1937 Methods in Mathematical Physics. Wiley & Sons.Google Scholar
Dowling, A. P. 1995 The calculation of thermoacoustic oscillations. J. Sound Vib. 180, 557581.CrossRefGoogle Scholar
Dowling, A. P. 1997 Nonlinear self-excited oscillations of a ducted flame. J. Fluid Mech. 346, 271290.CrossRefGoogle Scholar
Evesque, S. & Polifke, C. 2002 Low-order acoustic modelling for annular combustors: validation and inclusion of modal coupling. ASME paper gt-2002-30064.CrossRefGoogle Scholar
Evesque, S., Polifke, C. & Pankiewitz, C. 2003 Spinning and azimuthally standing acoustic modes in annular combustors. AIAA paper 2003-3182.CrossRefGoogle Scholar
George, J. & Sujith, R. I. 2009 Linear mechanism of wave emergence from vortices in smooth shear flows. Phys. Rev. E 79, 046321-1–046321-6.Google Scholar
Golubev, V. V. & Atassi, H. M. 1998 Acoustic-vorticity waves in swirling flows. J. Sound Vib. 209, 203222.CrossRefGoogle Scholar
Karimi, N., Brear, M. J. & Moase, W. H. 2008 Acoustic and disturbance energy analysis of a flow with heat communication. J. Fluid Mech. 597, 6789.CrossRefGoogle Scholar
Kim, J. S. & Williams, F. A. 1998 Eigenmodes of acoustic pressure in combustion chambers. J. Sound Vib. 209, 821843.CrossRefGoogle Scholar
Lamarque, N. & Poinsot, T. J. 2008 Boundary conditions for acoustic eigenmodes in gas turbine combustion chambers. AIAA J. 46, 22822292.CrossRefGoogle Scholar
Mani, R. 1981 Low-frequency sound propagation in a quasi-one-dimensional flow. J. Fluid Mech. 104, 8192.CrossRefGoogle Scholar
Marble, F. E. & Candel, S. M. 1977 Gas non-uniformities convected through a nozzle. J. Sound Vib. 55, 225243.CrossRefGoogle Scholar
Moase, W. H., Brear, M. J. & Manzie, C. 2007 The forced response of choked nozzles and supersonic diffusers. J. Fluid Mech. 585, 281304.CrossRefGoogle Scholar
Rayleigh, J. W. S. 1896 The Theory of Sound. Macmillan.Google Scholar
Roux, S., Lartigue, G., Poinsot, T., Meier, U. & Berat, C. 2005 Studies of mean and unsteady flow in a swirled combustor using experiments, acoustic analysis and large eddy simulations. Combust. Flame 41, 4054.CrossRefGoogle Scholar
Saad, Y. & Martin, H. S. 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. Sci. Comput. Stat. 7 (3), 856869.CrossRefGoogle Scholar
Stow, S. R., Dowling, A. P. & Hynes, T. P. 2002 Reflection of circumferential modes in a choked nozzle. J. Sound Vib. 467, 215239.Google Scholar
Subrahmanyam, P. B., Sujith, R. I. & Lieuwen, T. C. 2001 A family of exact transient solutions for acoustic wave propagation in inhomogeneous, non-uniform area ducts. J. Sound Vib. 240 (4), 705715.CrossRefGoogle Scholar
Sujith, R. I., Waldherr, G. A. & Zinn, B. T. 1995 An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient. J. Sound Vib. 184 (3), 389402.CrossRefGoogle Scholar
Tsien, H. S. 1952 The transfer functions of rocket nozzles. Am. Rocket Soc. J. 22, 139143.CrossRefGoogle Scholar
Tyagi, M. & Sujith, R. 2003 Nonlinear distortion of travelling waves in variable-area ducts with entropy gradients. J. Fluid Mech. 492, 122.CrossRefGoogle Scholar