Analysis of Different Sound Source Formulations to Simulate Combustion Generated Noise Using a Hybrid LES/APE-RF Method

Abstract

Combustion noise and sound source mechanisms of the DLR-A flame are investigated. A hybrid large-eddy simulation/computational aeracoustics (LES/CAA) approach is employed. In the first step of the hybrid analysis the flamelet/progress variable (FPV) model is employed as combustion model followed by the acoustic simulation in the second step using the acoustic perturbation equations for reacting flows (APE-RF). The flamelet/progress variable database has been extended in terms of acoustic source terms. The analysis of the acoustic field of low MACH number reacting flows induced by the thermoacoustic sources such as the unsteady heat release leads to a very stiff problem formulation, since the related sources require highly resolved regions in the source area, which restricts the possible time step. To simulate combustion generated noise using such a hybrid approach, a suitable source description has to be used, which preferably satisfies two requirements, i.e, to efficiently and accurately predict the generated sound field, while the source term can be easily evaluated from the LES. Using the source term, which is expressed via the scaled partial time derivative of the density, the acoustic field can be reproduced best up to a maximum Strouhal number of St_D = 2. However, this source formulation requires a rigorous constraint at the interface of the hybrid approach to avoid spurious noise due to artificial acceleration caused by interpolation. To be more precise, the convection speed of density inhomogeneities has to be preserved during interpolation. A compromise between efficiency and accuracy can be achieved using the source formulation expressed via the scaled material derivative of the density, since by definition this formulation does not describe the convection of density inhomogeneities.

References

Strahle

W. C.

, “Some results in combustion generated noise,” J. Sound Vibration, Vol. 23, No. 1, 1972, pp. 113–125.

Klein

S. A.

and Kok

J. B. W.

, “Sound Generation of Turbulent Non-premixed Flames,” Combust. Sci. and Tech., Vol. 149, 1999, pp. 267–295.

Hassan

H. A.

, “Scaling of combustion-generated noise,” J. Fluid Mech., Vol. 66, No. 3, 1974, pp. 445–453.

Chiu

H. H.

and Summerfield

, “Theory of combustion noise,” Acta Astronautica, Vol. 1, No. 7-8, 1974, pp. 967–984.

Truffaut

J. M.

Searby

, and Boyer

, “Sound emission by non-isomolar combustion at low Mach numbers,” Combust. Theory Modelling, Vol. 2, 1998, pp. 423–428.

Lighthill

M. J.

, “On Sound Generated Aerodynamically: I. General Theory,” Proc. R. Soc. London Ser. A, Vol. 211, 1952, pp. 564–587.

Phillips

O. M.

, “On the Generation of Sound by Supersonic Turbulent Shear Layers,” J. Fluid Mech., Vol. 9, 1960, pp. 1–28.

Ihme

and Pitsch

, “Radiation of Noise in Turbulent Flames,” Proc. Combust. Inst., Vol. 32, 2008, pp. accepted for publication.

Ihme

Bodony

D. J.

, and Pitsch

, “Prediction of combustion-generated noise in non-premixed turbulent jet flames using large-eddy simulation,” AIAA Paper 2006-2614, 2006.

10.

Ihme

Kaltenbacher

, and Pitsch

, “Numerical simulation of flow- and combustion-induced sound using a hybrid LES/CAA approach,” Proceedings of the Summer Program, 2006, pp. 497–510.

11.

Flemming

Sadiki

, and Janicka

, “Investigation of combustion noise using a LES/CAA hybrid approach,” Proc. Combust. Inst., Vol. 31, 2007, pp. 3189–3196.

12.

Ewert

and Schröder

, “Acoustic perturbation equations based on flow decomposition via source filtering,” J. Comput. Physics, Vol. 188, 2003, pp. 365–398.

13.

Bui

T. P.

Meinke

Schröder

Flemming

Sadiki

, and Janicka

, “A Hybrid Method for Combustion Noise Based on LES and APE,” AIAA Paper 2005-3014, 2005.

14.

Bui

T. P.

Meinke

, and Schröder

, “Source Term Evaluation of the APE-RF System,” AIAA Paper 2006-2678, 2006.

15.

Peters

, “Local quenching due to flame stretch and non-premixed turbulent combustion,” Combust. Sci. Tech., Vol. 30, 1983, pp. 1–17.

16.

Peters

, “Laminar diffusion flamelet models in non-premixed turbulent combustion,” Prog. Energy Combust. Sci., Vol. 10, No. 3, 1984, pp. 319–339.

17.

Pierce

and Moin

, “Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion,” J. Fluid Mech., Vol. 504, 2004, pp. 73–97.

18.

Ihme

Cha

C. M.

, and Pitsch

, “Prediction of local extinction and reignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach,” Proc. Combust. Inst., Vol. 30, 2005, pp. 793–800.

19.

Germano

Piomelli

Moin

, and Cabot

, “A dynamic subgrid-scale eddy viscosity model,” Phys. Fluids A, Vol. 3, No. 7, 1991, pp. 1760–1765.

20.

Lilly

, “A proposed modification of the Germano subgrid-scale closure method,” Phys. Fluids A, Vol. 4, No. 3, 1992, pp. 633–635.

21.

Pierce

and Moin

, “A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar,” Phys. Fluids, Vol. 10, No. 12, 1998, pp. 3041–3044.

22.

Crighton

D. G.

Dowling

A. P.

Ffowcs Williams

J. E.

Heckl

, and Leppington

F. G.

, Modern Methods in Analytical Acoustics, Springer, 1992.

23.

Bui

T. P.

Schröder

, and Meinke

, “Acoustic perturbation equations for reacting flows to compute combustion noise,” Int. J. Aeroacoustics, Vol. 6, No. 4, 2007, pp. 335–355.

24.

Gröschel

Schröder

Meinke

, and Comte

, “Noise Prediction for a Turbulent Jet Using Different Hybrid Methods,” Computers & Fluids, Vol. 37, Issue 4, May 2008, pp. 414–426.

25.

Bowman

Hanson

Davidson

Gardiner

Lissianski

Smith

Golden

Frenklach

, and Goldenberg

, “GRI-Mech 2.11,” 1997, available from http://www.me.berkeley.edu/gri-mech/.

26.

Turns

, An Introduction to Combustion: Concepts and Applications, McGraw Hill, 2000.

27.

Bergmann

Meier

Wolff

, and Stricker

, “Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH₄/H₂/N₂ jet diffusion flame,” Appl. Phys. B, Vol. 66, No. 4, 1998, pp. 489–502.

28.

Meier

Barlow

Chen

, and Chen

, “Raman/Rayleigh/LIF measurements in a turbulent CH₄/H₂/N₂ jet diffusion flame: Experimental techniques and turbulence-chemistry interaction,” Combust. Flame, Vol. 123, No. 3, 2000, pp. 326–343.

29.

Schneider

Dreizler

Janicka

, and Hassel

, “Flow field measurements of stable and locally extinguishing hydrocarbon-fuelled jet flames,” Combust. Flame, Vol. 135, No. 1-2, 2003, pp. 185–190.

30.

Moin

Squires

Cabot

, and Lee

, “A dynamic subgrid-scale model for compressible turbulence and scalar transport,” Phys. Fluids A, Vol. 3, No. 11, 1991, pp. 2746–2757.

31.

Ihme

Cha

C. M.

, and Pitsch

, “Prediction of local extinction and reignition effects in non-premixed turbulent combustion using a flamelet/progress variable approach,” Proc. Combust. Inst., Vol. 30, 2005, pp. 793–800.

32.

Pitsch

and Ihme

, “An unsteady/flamelet progress variable method for LES of non-premixed turbulent combustion,” 43rd AIAA Aerospace Sciences Meeting and Exhibit, paper AIAA-2005-557, Jan. 2005, Reno, NV, USA.

33.

Tam

C. K. W.

and Webb

J. C.

, “Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics,” J. Comput. Physics, Vol. 107, No. 2, 1993, pp. 262–181.

34.

F. Q.

Hussaini

M. Y.

, and Manthey

J. L.

, “Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics,” J. Comput. Physics, Vol. 124, No. 1, 1996, pp. 177–191.

35.

Shang

J. S.

, “High-order compact-difference schemes for time dependent maxwell equations,” J. Comput. Physics, Vol. 153, 1999, pp. 312–333.

36.

Vasilyev

O. V.

Lund

T. S.

, and Moin

, “A general class of commutative filters for LES in complex geometries,” J. Comput. Physics, Vol. 146, 1998, pp. 82–104.

37.

Schröder

and Ewert

, “LES-CAA Coupling, LES for Acoustics”, Cambridge University Press, 2005.

38.

Bui

T. P.

Meinke

, and Schröder

, “Numerical analysis of the acoustic field of reacting flows via acoustic perturbation equations,” Computers & Fluids, Volume 37, Issue 9, October 2008, pp. 1157–1169.

39.

Smith

T. J. B.

and Kilham

J. K.

, “Noise Generation by Open Turbulent Flames,” J. Acoust. Soc. America, Vol. 35, No. 5, 1963, pp. 715–724.