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Sound generation by turbulent boundary-layer flow over small steps

Published online by Cambridge University Press:  11 May 2010

MINSUK JI  and
MENG WANG
MINSUK JI
Affiliation:
Center for Flow Physics and Control, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
MENG WANG*
Affiliation:
Center for Flow Physics and Control, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
*
†Email address for correspondence: [email protected]
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Abstract

The aeroacoustics of low-Mach-number boundary-layer flow over backward and forward facing steps is studied using large-eddy simulation and Lighthill's theory. The Reynolds number based on the step height and free-stream velocity ranges from 21000 to 328 as the step height is varied from 53% to 0.83% of the unperturbed boundary layer thickness at the step. For the largest step size, statistics of wall pressure fluctuations such as the root mean square values and frequency spectral density yield favourable comparisons with available experimental measurements. A low-frequency Green's function for the step geometry, valid for an acoustically compact step height, is employed to evaluate the volume integral in the solution to Lighthill's equation. Consistent with the result of previous theoretical studies, the steps act primarily as a dipole source aligned in the streamwise direction. The sound from the forward step is shown to be significantly louder than that from the backward step and the underlying reason is analysed in terms of source strength and distribution relative to the Green's function. The forward step generates stronger sources in regions closer to the step corner, which is heavily weighted by the Green's function. A detailed analysis of flow field and Green's function weighted sources reveals that the backward step generates sound mainly through a diffraction mechanism, while the forward step generates sound through a combination of diffraction and turbulence modification by the step. As the step height decreases, the difference in noise level between forward and backward steps is much reduced as turbulence modification becomes less significant.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 654 , 10 July 2010 , pp. 161 - 193
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Addad, Y., Laurence, D., Talotte, C. & Jacob, M. C. 2003 Large eddy simulation of a forward-backward facing step for acoustic source identification. Intl J. Heat Fluid Flow 24, 562–571.CrossRefGoogle Scholar
Akselvoll, K. & Moin, P. 1995 Large eddy simulation of turbulent confined coannular jets and turbulent flow over a backward facing step. Tech. Rep. TF-63. Department of Mechanical Engineering, Stanford University, Stanford, CA.CrossRefGoogle Scholar
Ali, I., Krey, F., Becker, S., Munz, C.-D. & Utzmann, J. 2007 Coupling of LES with LEE for forward facing step noise prediction. Paper 2007–3507. AIAA.Google Scholar
Badri Narayanan, M. A., Khadgi, Y. N. & Viswanath, P. R. 1974 Similarities in pressure distribution in separated flow behind backward-facing steps. Aeronaut. Q. 25, 305–312.CrossRefGoogle Scholar
Becker, S., Escobar, M., Hahn, C., Ali, I., Kaltenbacher, M., Basel, B. & Grünewald, M. 2005 Experimental and numerical investigation of the flow induced noise from a forward facing step. Paper 2005–3006. AIAA.CrossRefGoogle Scholar
Bradshaw, P. & Wong, F. Y. F. 1972 The reattachment and relaxation of a turbulent shear layer. J. Fluid Mech. 52, 113–135.Google Scholar
Camussi, R., Guj, G. & Ragni, A. 2006 Wall pressure fluctuations induced by turbulent boundary layers over surface discontinuities. J. Sound Vib. 294, 177–204.CrossRefGoogle Scholar
Chandrsuda, C. & Bradshaw, P. 1981 Turbulent structure of a reattaching mixing layer. J. Fluid Mech. 110, 171–179.CrossRefGoogle Scholar
Cherry, N. J., Hillier, R. & Latour, M. E. M. P. 1984 Unsteady measurements in a separated and reattaching flow. J. Fluid Mech. 144, 13–46.CrossRefGoogle Scholar
Conlisk, A. T. & Veley, D. 1985 The generation of noise in impinging vortex motion past a step. Phys. Fluids 28, 3004–3012.CrossRefGoogle Scholar
Crighton, D. G. 1975 Basic principles of aerodynamic noise generation. Prog. Aerosp. Sci. 16, 31–96.Google Scholar
Dhanak, M. R. & Gundlapalli, R. 1992 Flow noise due to interaction between an eddy and a forward facing step. In International Symposium of Flow Induced Vibration and Noise (ed. Farabee, T. M. & Païdoussis, M. P.), Flow-Structure and Flow-Sound Interactions, vol. 3, pp. 11–22. ASME.Google Scholar
Eaton, J. K. & Johnston, J. P. 1981 A review of research on subsonic turbulent flow reattachment. AIAA J. 19, 1093–1100.CrossRefGoogle Scholar
Efimtsov, B. M., Kozlov, N. M., Kravchenko, S. V. & Andersson, A. O. 1999 Wall pressure fluctuation spectra at small forward facing steps. Paper 99–1964. AIAA.CrossRefGoogle Scholar
Efimtsov, B. M., Kozlov, N. M., Kravchenko, S. V. & Andersson, A. O. 2000 Wall pressure fluctuation spectra at small backward facing steps. Paper 2000–2053. AIAA.CrossRefGoogle Scholar
Fadlun, E. A., Verzicco, R., Orlandi, P. & Mohd-Yusof, J. 2000 Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60.CrossRefGoogle Scholar
Farabee, T. M. & Casarella, M. J. 1984 Effects of surface irregularity on turbulent boundary layer wall pressure fluctuations. ASME J. Vib., Acoust., Stress Reliab. Des. 106, 343–350.CrossRefGoogle Scholar
Farabee, T. M. & Casarella, M. J. 1986 Measurements of fluctuating wall pressure for separated/reattached boundary layer flows. ASME J. Vib., Acoust., Stress Reliab. Des. 108, 301–307.Google Scholar
Farabee, T. M. & Zoccola, P. J. 1998 Experimental evaluation of noise due to flow over surface steps. In Proceedings of the ASME International Mechanical Engineering Congress Exposition 1998, vol. 25, pp. 95–102.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy-viscosity model. Phys. Fluids A 3, 1760–1765.CrossRefGoogle Scholar
Goldstein, M. E. 1976 Aeroacoustics, 2nd edn. McGraw-Hill.Google Scholar
Howe, M. S. 1989 Sound produced by turbulent boundary layer flow over a finite region of wall roughness, and over a forward facing step. J. Fluids Struct. 3, 83–96.CrossRefGoogle Scholar
Howe, M. S. 1997 Influence of separation on sound generated by vortex-step interaction. J. Fluids Struct. 11, 857–872.CrossRefGoogle Scholar
Howe, M. S. 1998 On the contribution from skin steps to boundary-layer generated interior noise. J. Sound Vib. 209, 519–530.CrossRefGoogle Scholar
Howe, M. S. 2003 Theory of Vortex Sound. Cambridge University Press.Google Scholar
Jacob, M. C., Louisot, A., Juve, D. & Guerrand, S. 2001 Experimental study of sound generated by backward-facing steps under wall jet. AIAA J. 39, 1254–1260.CrossRefGoogle Scholar
Kargus, W. A. IV, & Lauchle, G. C. 1997 Flow-induced sound from turbulent boundary layer separation over a rearward facing step. Tech. Rep. Report TR 97-007. Applied Research Laboratory. Penn State University.Google Scholar
Kim, J. & Sung, H. J. 2006 Wall pressure fluctuations and flow-induced noise in a turbulent boundary layer over a bump. J. Fluid Mech. 558, 79–102.CrossRefGoogle Scholar
Kiya, M. & Sasaki, K. 1983 Structure of a turbulent separation bubble. J. Fluid Mech. 137, 83–113.CrossRefGoogle Scholar
Largeau, J. F. & Moriniere, V. 2007 Wall pressure fluctuations and topology in separated flows over a forward-facing step. Exp. Fluids 42, 21–40.Google Scholar
Lauchle, G. C. & Kargus, W. A. IV, 2000 Scaling of turbulent wall pressure fluctuations downstream of a rearward facing step. J. Acoust. Soc. Am. 107, L1–L6.Google Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.CrossRefGoogle Scholar
Leclercq, D. J. J., Jacob, M. C., Louisot, A. & Talotte, C. 2001 Forward-backward facing step pair: aerodynamic flow, wall pressure and acoustic characterization. Paper 2001–2249. AIAA.CrossRefGoogle Scholar
Lee, I. & Sung, H. J. 2001 Characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step. Part I. Time-mean statistics and cross-spectral analyses. Exp. Fluids 30, 262–272.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. General theory. Proc. R. Soc. Lond. Ser. A 211, 564–587.Google Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure model. Phys. Fluids A 4, 633–635.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.Google Scholar
Mohsen, A. M. 1968 Experimental investigation of the wall pressure fluctuations in subsonic separated flows. Tech. Rep. No. D6-17094. Boeing Company Report.CrossRefGoogle Scholar
Morris, S. C. & Foss, J. F. 2003 Turbulent boundary layer to single-stream shear layer: the transition region. J. Fluid Mech. 494, 187–221.Google Scholar
Moss, W. D. & Baker, S. 1980 Re-circulating flows associated with two-dimensional steps. Aeronaut. Q. 151–172.CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation. J. Fluid Mech. 377, 347–373.CrossRefGoogle Scholar
Wang, M., Freund, J. B. & Lele, S. K. 2006 Computational prediction of flow-generated sound. Annu. Rev. Fluid Mech. 38, 483–512.CrossRefGoogle Scholar
Wang, M., Lele, S. K. & Moin, P. 1996 Computation of quadrupole noise using acoustic analogy. AIAA J. 34, 2247–2254.CrossRefGoogle Scholar
Wang, M. & Moin, P. 2000 Computation of trailing-edge flow and noise using large-eddy simulation. AIAA J. 38, 2201–2209.CrossRefGoogle Scholar
Wang, M., Moreau, S., Iaccarino, G. & Roger, M. 2009 LES prediction of wall-pressure fluctuations and noise of a low-speed airfoil. Intl J. Aeroacoust. 8, 177–198.CrossRefGoogle Scholar
Yang, Q. & Wang, M. 2009 Computational study of roughness-induced boundary layer noise. AIAA J. 47, 2417–2429.CrossRefGoogle Scholar
You, D., Moin, P., Wang, M. & Mittal, R. 2004 Study of tip clearance flow in a turbomachinery cascade using large eddy simulation. Tech. Rep. TF-86. Department of Mechanical Engineering, Stanford University, Stanford, CA.Google Scholar
You, D., Wang, M., Moin, P. & Mittal, R. 2007 Large-eddy simulation analysis of mechanisms for viscous losses in a turbomachinery tip-clearance flow. J. Fluid Mech. 586, 177–204.Google Scholar