Analysis on Physical Mechanism of Sound Generation inside Cavities Based on Acoustic Analogy Method

Affiliation(s)

State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, China.

High Speed Aerodynamics Research Institute, China Aerodynamics Research and Development Center, Mianyang, China.

State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, China.

High Speed Aerodynamics Research Institute, China Aerodynamics Research and Development Center, Mianyang, China.

ABSTRACT

Analysis of coupling aerodynamics and acoustics are performed to investigate the self-sustained oscillation and aerodynamic noise in two-dimensional flow past a cavity with length to depth ratio of 2 at subsonic speeds. The large eddy simulation (LES) equations and integral formulation of Ffowcs-Williams and Hawings (FW-H) are solved for the cavity with same conditions as experiments. The obtained density-field agrees well with Krishnamurty’s experimental schlieren photograph, which simulates flow-field distributions and the direction of sound wave radiation. The simulated self-sustained oscillation modes inside the cavity agree with Rossiter’s and Heller’s predicated results, which indicate frequency characteristics are obtained. Moreover, the results indicate that the feedback mechanism that new shedding-vortexes induced by propagation of sound wave created by the impingement of the shedding-vortexes in the shear-layer and rear cavity face leads to self-sustained oscillation and high noise inside the cavity. The peak acoustic pressure occurs in the first oscillation mode and the most of sound energy focuses on the low-frequency region.

Analysis of coupling aerodynamics and acoustics are performed to investigate the self-sustained oscillation and aerodynamic noise in two-dimensional flow past a cavity with length to depth ratio of 2 at subsonic speeds. The large eddy simulation (LES) equations and integral formulation of Ffowcs-Williams and Hawings (FW-H) are solved for the cavity with same conditions as experiments. The obtained density-field agrees well with Krishnamurty’s experimental schlieren photograph, which simulates flow-field distributions and the direction of sound wave radiation. The simulated self-sustained oscillation modes inside the cavity agree with Rossiter’s and Heller’s predicated results, which indicate frequency characteristics are obtained. Moreover, the results indicate that the feedback mechanism that new shedding-vortexes induced by propagation of sound wave created by the impingement of the shedding-vortexes in the shear-layer and rear cavity face leads to self-sustained oscillation and high noise inside the cavity. The peak acoustic pressure occurs in the first oscillation mode and the most of sound energy focuses on the low-frequency region.

Cite this paper

D. Yang, J. Li, J. Liu, Y. Zhang and Y. Li, "Analysis on Physical Mechanism of Sound Generation inside Cavities Based on Acoustic Analogy Method,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 1, 2013, pp. 23-31. doi: 10.4236/ojfd.2013.31003.

D. Yang, J. Li, J. Liu, Y. Zhang and Y. Li, "Analysis on Physical Mechanism of Sound Generation inside Cavities Based on Acoustic Analogy Method,"

References

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[2] D. Rockwell and E. Naudascher, “Review: Self-Sustaining Oscillations of Flow Past Cavities,” Journal of Fluids Engineering, Vol. 100, No. 2, 1978, pp. 152-165. doi:10.1115/1.3448624

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[6] A. J. Bilanin and E. E. Covert, “Estimation of Possible Excitation Frequencies for Shallow Rectangular Cavities,” The American Institute of Aeronautics and Astronautics, Vol. 11, No. 3, 1973, pp. 347-351. doi:10.2514/3.6747

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[10] W. J. E. Ffowcs and D. L. Hawkings, “Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Proceedings of the Royal Society of London, Vol. 264, No. 1151, 1969, pp. 321-342.

[11] F. Felten, Y. Fautrelle, Y. Du Terrail and O. Metais, “Numerical Modeling of Electrognetically-Riven Turbulent Flows Using LES Methods,” Applied Mathematical Modelling, Vol. 28, No. 1, 2004, pp. 15-27. doi:10.1016/S0307-904X(03)00116-1

[12] L. Doris, C. Tenaud and L. T. Phuoc, “LES of Spatially Developing 3D Compressible Mixing Layer[J],” Computational Fluid Mechanics, Vol. 328, No. 7, 2000, pp. 567-573.

[13] H.-W. Wu and S.-W. Perng, “LES Analysis of Turbulent Flow and Heat Transfer in Motored Engines with Various SGS Models[J],” International Journal of Heat and Mass Transfer, Vol. 45, No. 11, 2002, pp. 2315-2328. doi:10.1016/S0017-9310(01)00325-8

[14] P. R. Spalart, R. D. Moser and M. M. Rogers, “Spectral Methods for the Navier-Stokes one Infinite and Two Periodic Directions,” Journal of Computational Physics, Vol. 96, No. 2, 1991, pp. 297-324. doi:10.1016/0021-9991(91)90238-G

[15] S. Aradag and D. D. Knight, “Simulation of Supersonic Cavity Flow Using 3D RANS Equations,” AIAA Paper 2004-4966, 2004.

[16] M. Inagaki, T. Kondoh and Y. Nagano, “A MixedTime-Scale SGS Model with Fixed Model Parameters for Practical LES,” Eng. Turb. Modelling and Expt. 5, W. Rodi and N. Fueyo, Eds., Elsevier, Amsterdam, 2002, pp. 257-266.

[17] S-E. Kim, S. R. Mathur, J. Y. Murthy and D. Choudhury, “A Reynolds-Averaged Navier-Stokes solver Using Unstructured Mesh Based Finite-Volume Scheme,” AIAA Paper 1998-0231, 1998.

[18] M. Giles, “Non-Reflecting Boundary Conditions for Euler Equation Calculation,” The American Institute of Aeronautics and Astronautics Journal, Vol. 42, No. 12, 1990, pp. 2050-2058. doi:10.2514/3.10521

[19] W. J. E. Ffowcs and D. L. Hawkings, “Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Proceedings of the Royal Society of London, Vol. 264, No. 1151, 1969, pp. 321-342.

[20] D. Casalino, “An Advanced Time Approach for Acoustic Analogy Predictions,” Journal of Sound and Vibration, Vol. 261, No. 4, 2003, pp. 583-612. doi:10.1016/S0022-460X(02)00986-0

[21] F. Farassat and G. P. Succi, “The Prediction of Helicopter Discrete Frequency Noise,” Vertica, Vol. 7, No. 4, 1983, pp. 309-320.

[22] F. Farassat and K. S. Brentner, “The Acoustic Analogy and the Prediction of Rotating Blades,” Theoretical and Computational Fluid Dynamics, Vol. 10, No. 1-4, 1998, pp. 155-170. doi:10.1007/s001620050056

[23] S.-E. Kim, Y. Dai and E. K. Koutsavdis, “A Versatile Implementation of Acoustic Analogy Based Noise Prediction Method in a General-Purpose CFD,” AIAA Paper, 2003-3202, 2003.

[24] J. D. Revell, R. A. Prydz and A. P. Hays, “Experimental Study of Airframe Noise vs. Drag Relationship for Circular Cylinders,” Lockheed Report 28074, 1997.

[25] K. Krishnamurty, “Acoustic Radiation from Two Dimensional Rectangular Cutouts in Aerodynamic Surfaces,” NACA TN-3478, 1955.

[1] N. Delprat, “Rossiter’s Formula: A Simple Spectral Model for a Complex Amplitude Modulation Process?” Physics of Fluids, Vol. 18, No. 7, 2006, Article ID: 071703. doi:10.1063/1.2219767

[2] D. Rockwell and E. Naudascher, “Review: Self-Sustaining Oscillations of Flow Past Cavities,” Journal of Fluids Engineering, Vol. 100, No. 2, 1978, pp. 152-165. doi:10.1115/1.3448624

[3] J. E. Rossiter, “Wind Tunnel Experiments of the Flow over Rectangular Cavities at Subsonic and Transonic Speeds,” ARCR & M, 1964, p. 3458.

[4] C. W. Rowley, T. Colonius and A. J. Basu, “On SelfSustained Oscillations in Two-Dimensional Compressible Flow over Rectangular Cavities,” Journal of Fluid Mechanics, Vol. 455, 2002, pp. 315-346. doi:10.1017/S0022112001007534

[5] H. H. Heller and D. B. Bliss, “Aerodynamically Induced Pressure Oscillations in Cavities. Physical Mechanisms and Suppression Concepts,” Defense Technical Information Center, Fort Belvoir, 1975.

[6] A. J. Bilanin and E. E. Covert, “Estimation of Possible Excitation Frequencies for Shallow Rectangular Cavities,” The American Institute of Aeronautics and Astronautics, Vol. 11, No. 3, 1973, pp. 347-351. doi:10.2514/3.6747

[7] C. K. W. Tam and P. J. W. Block, “On the Tones and Pressure Oscillations Induced by Flow over Rectangular Cavities,” Journal of Fluid Mechanics, Vol. 89, No. 2, 1978, pp. 373-399. doi:10.1017/S0022112078002657

[8] A. Galperin and S. A. Orszag, “Large Eddy Simulation of Complex Engineering and Geophysical Flows,” Cambridge University Press, Cambridge, 1993.

[9] E. Lillberg and C. Fureby, “Large Eddy Simulations of Supersonic Cavity Flow,” AIAA-00-2411, 2000.

[10] W. J. E. Ffowcs and D. L. Hawkings, “Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Proceedings of the Royal Society of London, Vol. 264, No. 1151, 1969, pp. 321-342.

[11] F. Felten, Y. Fautrelle, Y. Du Terrail and O. Metais, “Numerical Modeling of Electrognetically-Riven Turbulent Flows Using LES Methods,” Applied Mathematical Modelling, Vol. 28, No. 1, 2004, pp. 15-27. doi:10.1016/S0307-904X(03)00116-1

[12] L. Doris, C. Tenaud and L. T. Phuoc, “LES of Spatially Developing 3D Compressible Mixing Layer[J],” Computational Fluid Mechanics, Vol. 328, No. 7, 2000, pp. 567-573.

[13] H.-W. Wu and S.-W. Perng, “LES Analysis of Turbulent Flow and Heat Transfer in Motored Engines with Various SGS Models[J],” International Journal of Heat and Mass Transfer, Vol. 45, No. 11, 2002, pp. 2315-2328. doi:10.1016/S0017-9310(01)00325-8

[14] P. R. Spalart, R. D. Moser and M. M. Rogers, “Spectral Methods for the Navier-Stokes one Infinite and Two Periodic Directions,” Journal of Computational Physics, Vol. 96, No. 2, 1991, pp. 297-324. doi:10.1016/0021-9991(91)90238-G

[15] S. Aradag and D. D. Knight, “Simulation of Supersonic Cavity Flow Using 3D RANS Equations,” AIAA Paper 2004-4966, 2004.

[16] M. Inagaki, T. Kondoh and Y. Nagano, “A MixedTime-Scale SGS Model with Fixed Model Parameters for Practical LES,” Eng. Turb. Modelling and Expt. 5, W. Rodi and N. Fueyo, Eds., Elsevier, Amsterdam, 2002, pp. 257-266.

[17] S-E. Kim, S. R. Mathur, J. Y. Murthy and D. Choudhury, “A Reynolds-Averaged Navier-Stokes solver Using Unstructured Mesh Based Finite-Volume Scheme,” AIAA Paper 1998-0231, 1998.

[18] M. Giles, “Non-Reflecting Boundary Conditions for Euler Equation Calculation,” The American Institute of Aeronautics and Astronautics Journal, Vol. 42, No. 12, 1990, pp. 2050-2058. doi:10.2514/3.10521

[19] W. J. E. Ffowcs and D. L. Hawkings, “Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Proceedings of the Royal Society of London, Vol. 264, No. 1151, 1969, pp. 321-342.

[20] D. Casalino, “An Advanced Time Approach for Acoustic Analogy Predictions,” Journal of Sound and Vibration, Vol. 261, No. 4, 2003, pp. 583-612. doi:10.1016/S0022-460X(02)00986-0

[21] F. Farassat and G. P. Succi, “The Prediction of Helicopter Discrete Frequency Noise,” Vertica, Vol. 7, No. 4, 1983, pp. 309-320.

[22] F. Farassat and K. S. Brentner, “The Acoustic Analogy and the Prediction of Rotating Blades,” Theoretical and Computational Fluid Dynamics, Vol. 10, No. 1-4, 1998, pp. 155-170. doi:10.1007/s001620050056

[23] S.-E. Kim, Y. Dai and E. K. Koutsavdis, “A Versatile Implementation of Acoustic Analogy Based Noise Prediction Method in a General-Purpose CFD,” AIAA Paper, 2003-3202, 2003.

[24] J. D. Revell, R. A. Prydz and A. P. Hays, “Experimental Study of Airframe Noise vs. Drag Relationship for Circular Cylinders,” Lockheed Report 28074, 1997.

[25] K. Krishnamurty, “Acoustic Radiation from Two Dimensional Rectangular Cutouts in Aerodynamic Surfaces,” NACA TN-3478, 1955.