Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T21:27:32.716Z Has data issue: false hasContentIssue false
  • English
  • Français

Trailing-edge noise reduction using derivative-free optimization and large-eddy simulation

Published online by Cambridge University Press:  23 January 2007

ALISON L. MARSDEN ,
MENG WANG ,
J. E. DENNIS jr  and
PARVIZ MOIN
ALISON L. MARSDEN
Affiliation:
Mechanical Engineering Department, Stanford University, CA 94305, USA
MENG WANG
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, IN 46556, USA
J. E. DENNIS jr
Affiliation:
Department of Computational and Applied Mathematics, Rice University, TX 77005, USA
PARVIZ MOIN
Affiliation:
Mechanical Engineering Department, Stanford University, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Derivative-free optimization techniques are applied in conjunction with large-eddy simulation (LES) to reduce the noise generated by turbulent flow over a hydrofoil trailing edge. A cost function proportional to the radiated acoustic power is derived based on the Ffowcs Williams and Hall solution to Lighthill's equation. Optimization is performed using the surrogate-management framework with filter-based constraints for lift and drag. To make the optimization more efficient, a novel method has been developed to incorporate Reynolds-averaged Navier–Stokes (RANS) calculations for constraint evaluation. Separation of the constraint and cost-function computations using this method results in fewer expensive LES computations. This work demonstrates the ability to fully couple optimization to large-eddy simulation for time-accurate turbulent flow. The results demonstrate an 89% reduction in noise power, which comes about primarily by the elimination of low-frequency vortex shedding. The higher-frequency broadband noise is reduced as well, by a subtle change in the lower surface near the trailing edge.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 13 - 36
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Audet, C., Booker, A. J., Dennis, J. E. Jr, Frank, P. D. & Moore, D. W. 2000 A surrogate-model-based method for constrained optimization. AIAA Paper 2000–4891.CrossRefGoogle Scholar
Audet, C. & Dennis, J. E. Jr 2004a Mesh adaptive direct search algorithms for constrained optimization. Tech. Rep. G–2004–04. Les Cahiers du GERAD, École Polytechnique de Montréal, Département de Mathématiques et de Génie Industriel, C.P. 6079, Centre-ville, Montréal (Québec), H3C 3A7 Canada.Google Scholar
Audet, C. & Dennis, J. E. Jr 2004b A pattern search filter method for nonlinear programming without derivatives. SIAM J. Optimization 14 (4), 980–1010.Google Scholar
Blake, W. K. 1975 A statistical description of pressure and velocity fields at the trailing edge of a flat strut. DTNSRDC Rep. 4241. David Taylor Naval Ship R & D Center, Bethesda, Maryland.Google Scholar
Blake, W. K. 1986 Mechanics of Flow-induced Sound and Vibration, Vols. I and II. Academic.Google Scholar
Blake, W. K. & Gershfeld, J. L. 1988 The aeroacoustics of trailing edges. In Frontiers in Experimental Fluid Mechanics (ed. Gad-el-Hak, M.), chap. 10. Springer.Google Scholar
Booker, A. J., Dennis Jr, J. E., Frank, P. D., Serafini, D. B., Torczon, V. & Trosset, M. W. 1999 A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization 17 (1), 1–13.Google Scholar
Brooks, T. F. & Hodgson, T. H. 1981 Trailing edge noise prediction from measured surface pressures. J. Sound Vib. 78, 69–117.Google Scholar
Crighton, D. G. & Leppington, F. G. 1971 On the scattering of aerodynamic noise. J. Fluid Mech. 46, 557–597.Google Scholar
Ffowcs Williams, J. E. & Hall, L. H. 1970 Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane. J. Fluid Mech. 40, 657–670.Google Scholar
Fletcher, R. & Leyffer, S. 2002 Nonlinear programming without a penalty function. Math. Programming 91, 239–269.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. 1991 A dynamic subgrid-scale eddy-viscosity model. Phys. Fluids A 3, 1760–1765.Google Scholar
Goldstein, M. E. 1976 Aeroacoustics. McGraw-Hill.Google Scholar
Howe, M. S. 1978 A review of the theory of trailing edge noise. J. Sound Vib. 61 (3), 437–465.Google Scholar
Howe, M. S. 2001 Edge-source acoustic Green's function for an airfoil of arbitrary chord, with application to trailing edge noise. Q. J. Mech. Appl. Maths 50 (1), 139–155.Google Scholar
Jameson, A., Martinelli, L. & Pierce, N. A. 1998 Optimum aerodynamic design using the Navier-Stokes equations. Theoret. Comp. Fluid Dyn. 10, 213–237.Google Scholar
Lilly, D. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635.Google Scholar
Lund, T. S., Wu, X. & Squires, K. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.Google Scholar
Marsden, A. L., Wang, M., Dennis Jr, J. E. & Moin, P. 2004a Optimal aeroacoustic shape design using the surrogate management framework. Optimization Engng 5 (2), 235–262, Special Issue: Surrogate Optimization.Google Scholar
Marsden, A. L., Wang, M., Dennis Jr, J. E. & Moin, P. 2004b Suppression of airfoil vortex-shedding noise via derivative-free optimization. Phys. Fluids 16 (10), L83–L86.Google Scholar
McKay, M. D., Conover, W. J. & Beckman, R. J. 1979 A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245.Google Scholar
Oberai, A. A., Roknaldin, F. & Hughes, T. J. R. 2002 Computation of trailing-edge noise due to turbulent flow over an airfoil. AIAA J. 40 (11), 2206–2216.Google Scholar
Olson, S. & Mueller, T. J. 2004 An experimental study of trailing edge noise. UNDAS-IR 0105. Dept. of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN.Google Scholar
Serafini, D. B. 1998 A framework for managing models in nonlinear optimization of computationally expensive functions. PhD thesis, Rice University, Houston, TX.Google Scholar
Wang, M. 2005 Computation of trailing-edge aeroacoustics with vortex shedding. Annual Research Briefs, pp. 379–388, Center for Turbulence Research, Stanford University.Google Scholar
Wang, M. & Moin, P. 2000 Computation of trailing-edge flow and noise using large-eddy simulation. AIAA J. 38 (12), 2201–2209.Google Scholar