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Subgrid-scale effects in compressible variable-density decaying turbulence

Published online by Cambridge University Press:  08 May 2018

Sidharth GS Open the ORCID record for Sidharth GS [Opens in a new window]  and
Graham V. Candler
Sidharth GS*
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Graham V. Candler
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: [email protected]
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Abstract

Many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative to the SGS specific stress, which is the only SGS term active in incompressible constant-density turbulence. It is found that while the variable-density SGS terms in the homentropic case are negligible, they are dynamically significant in the thermally inhomogeneous flows. Investigation of the variable-density SGS terms is therefore important, not only to develop variable-density closures but also to improve the understanding of scale interactions in variable-density flows.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Isotropic turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 428 - 459
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Copyright
© 2018 Cambridge University Press 

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References

Adumitroaie, V., Ristorcelli, J. R. & Taulbee, D. B. 1999 Progress in Favre–Reynolds stress closures for compressible flows. Phys. Fluids 11 (9), 2696–2719.Google Scholar
Bakosi, J. & Ristorcelli, J. 2011 Extending the Langevin model to variable-density pressure-gradient-driven turbulence. J. Turbul. 12, N19.Google Scholar
Banerjee, A., Gore, R. A. & Andrews, M. J. 2010 Development and validation of a turbulent-mix model for variable-density and compressible flows. Phys. Rev. E 82 (4), 046309.Google ScholarPubMed
Bilger, R. 1976 Turbulent jet diffusion flames. Prog. Energy Combust. Sci. 1 (2–3), 87–109.CrossRefGoogle Scholar
Boersma, B. J. & Lele, S. K. 1999 Large eddy simulation of compressible turbulent jets. In Center for Turbulence Research Annual Research Briefs, pp. 365–377. Stanford University.Google Scholar
Bray, K., Libby, P. A., Masuya, G. & Moss, J. 1981 Turbulence production in premixed turbulent flames. Combust. Sci. Technol. 25 (3–4), 127–140.CrossRefGoogle Scholar
Brenner, H. 2009 Bi-velocity hydrodynamics. Physica A: Statist. Mech. Appl. 388 (17), 3391–3398.Google Scholar
Brouillette, M. 2002 The Richtmyer–Meshkov instability. Annu. Rev. Fluid Mech. 34 (1), 445–468.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775–816.Google Scholar
Candler, G. V., Subbareddy, P. K. & Brock, J. M. 2015 Advances in computational fluid dynamics methods for hypersonic flows. J. Spacecr. Rockets 52 (1), 17–28.Google Scholar
Chakraborty, N., Wang, L., Konstantinou, I. & Klein, M. 2017 Vorticity statistics based on velocity and density-weighted velocity in premixed reactive turbulence. J. Turbul. 18 (9), 825–853.Google Scholar
Chassaing, P. 1997 Some problems on single point modeling of turbulent, low-speed, variable density fluid motions. In IUTAM Symposium on Variable Density Low-Speed Turbulent Flows, pp. 65–84. Springer.CrossRefGoogle Scholar
Chassaing, P. 2001 The modeling of variable density turbulent flows. A review of first-order closure schemes. Flow Turbul. Combust. 66 (4), 293–332.CrossRefGoogle Scholar
Chassaing, P., Antonia, R., Anselmet, F., Joly, L. & Sarkar, S. 2013 Variable Density Fluid Turbulence. Springer Science & Business Media.Google Scholar
Chassaing, P., Harran, G. & Joly, L. 1994 Density fluctuation correlations in free turbulent binary mixing. J. Fluid Mech. 279, 239–278.Google Scholar
Chesnel, J., Reveillon, J., Menard, T. & Demoulin, F.-X. 2011 Large eddy simulation of liquid jet atomization. Atomiz. Sprays 21 (9), 711–736.CrossRefGoogle Scholar
Chomiak, J. & Nisbet, J. 1995 Modeling variable density effects in turbulent flames: some basic considerations. Combust. Flame 102 (3), 371–386.Google Scholar
Donzis, D. A., Sreenivasan, K. & Yeung, P. 2010 The Batchelor spectrum for mixing of passive scalars in isotropic turbulence. Flow Turbul. Combust. 85 (3), 549–566.Google Scholar
Favre, A. 1969 Statistical equations of turbulent gases. In Problems of Hydrodynamics and Continuum Mechanics, pp. 231–266. SIAM.Google Scholar
Favre, A. J. 1992 Formulation of the statistical equations of turbulent flows with variable density. In Studies in Turbulence, pp. 324–341. Springer.Google Scholar
Ferrer, P. J. M., Lehnasch, G. & Mura, A. 2017 Compressibility and heat release effects in high-speed reactive mixing layers. I. Growth rates and turbulence characteristics. Combust. Flame 180, 284–303.Google Scholar
Fontane, J. & Joly, L. 2008 The stability of the variable-density Kelvin–Helmholtz billow. J. Fluid Mech. 612, 237–260.Google Scholar
Freund, J. B., Lele, S. K. & Moin, P. 2000 Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate. J. Fluid Mech. 421, 229–267.Google Scholar
Frieler, C. & Dimotakis, P. 1988 Mixing and reaction at low heat release in the non-homogeneous shear layer. In First National Fluid Dynamics Congress, AIAA.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.Google Scholar
Germano, M. 1996 Averaging procedures for the large eddy simulation of variable density flows. In IUTAM Symposium on Variable Density Low-Speed Turbulent Flows, pp. 101–108. Springer.Google Scholar
Germano, M., Abb, A., Arina, R. & Bonaventura, L. 2014 On the extension of the eddy viscosity model to compressible flows. Phys. Fluids 26 (4), 041702.Google Scholar
Getsinger, D. R., Hendrickson, C. & Karagozian, A. R. 2012 Shear layer instabilities in low-density transverse jets. Exp. Fluids 53 (3), 783–801.Google Scholar
Gill, A., Green, J. & Simmons, A. 1974 Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. In Deep Sea Research and Oceanographic Abstracts, vol. 21, pp. 499IN1509–508528. Elsevier.Google Scholar
Gottlieb, S., Shu, C.-W. & Tadmor, E. 2001 Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (1), 89–112.Google Scholar
Grigoriev, I. A., Wallin, S., Brethouwer, G. & Johansson, A. V. 2015 Capturing turbulent density flux effects in variable density flow by an explicit algebraic model. Phys. Fluids 27 (4), 045108.Google Scholar
Hamba, F. 1999 Effects of pressure fluctuations on turbulence growth in compressible homogeneous shear flow. Phys. Fluids 11 (6), 1623–1635.CrossRefGoogle Scholar
Joly, L., Fontane, J. & Chassaing, P. 2005 The Rayleigh–Taylor instability of two-dimensional high-density vortices. J. Fluid Mech. 537, 415–431.Google Scholar
Klein, M., Kasten, C., Gao, Y. & Chakraborty, N. 2015 A priori direct numerical simulation assessment of sub-grid scale stress tensor closures for turbulent premixed combustion. Comput. Fluids 122, 1–11.Google Scholar
Kovasznay, L. S. 1953 Turbulence in supersonic flow. J. Aerosp. Sci. 20 (10), 657–674.Google Scholar
Kreuzinger, J., Friedrich, R. & Gatski, T. B. 2006 Compressibility effects in the solenoidal dissipation rate equation: a priori assessment and modeling. Intl J. Heat Fluid Flow 27 (4), 696–706.Google Scholar
Lagha, M., Kim, J., Eldredge, J. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23 (1), 015106.Google Scholar
LaRue, J. C. & Libby, P. A. 1977 Measurements in the turbulent boundary layer with slot injection of helium. Phys. Fluids 20 (2), 192–202.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1991 Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3 (4), 657–664.Google Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26 (1), 211–254.Google Scholar
Libby, P. A. & Bray, K. 1977 Variable density effects in premixed turbulent flames. AIAA J. 15 (8), 1186–1193.Google Scholar
Libby, P. A. & Bray, K. 1981 Countergradient diffusion in premixed turbulent flames. AIAA J. 19 (10), 657–674.Google Scholar
Lindstedt, R. & Vaos, E. 1999 Modeling of premixed turbulent flames with second moment methods. Combust. Flame 116 (4), 461–485.Google Scholar
Lipatnikov, A. & Chomiak, J. 2010 Effects of premixed flames on turbulence and turbulent scalar transport. Prog. Energy Combust. Sci. 36 (1), 1–102.Google Scholar
Livescu, D. & Ristorcelli, J. 2007 Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591, 43–71.CrossRefGoogle Scholar
MacCormack, R. W. 2014 Numerical Computation of Compressible and Viscous Flow. American Institute of Aeronautics and Astronautics.Google Scholar
Miller, M., Bowman, C. & Mungal, M. 1998 An experimental investigation of the effects of compressibility on a turbulent reacting mixing layer. J. Fluid Mech. 356, 25–64.Google Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
O’Brien, J., Urzay, J., Ihme, M., Moin, P. & Saghafian, A. 2014 Subgrid-scale backscatter in reacting and inert supersonic hydrogen–air turbulent mixing layers. J. Fluid Mech. 743, 554–584.CrossRefGoogle Scholar
Pantano, C. & Sarkar, S. 2002 A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371.Google Scholar
Patel, A., Boersma, B. J. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.Google Scholar
Pierrehumbert, R. & Swanson, K. 1995 Baroclinic instability. Annu. Rev. Fluid Mech. 27 (1), 419–467.Google Scholar
Ranjan, D., Oakley, J. & Bonazza, R. 2011 Shock–bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140.Google Scholar
Reinaud, J., Joly, L. & Chassaing, P. 2000 The baroclinic secondary instability of the two-dimensional shear layer. Phys. Fluids 12 (10), 2489–2505.Google Scholar
Ristorcelli, J.1993 A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence. ICASE Rep. (93-88).Google Scholar
Ristorcelli, J. R. & Blaisdell, G. A. 1997 Consistent initial conditions for the DNS of compressible turbulence. Phys. Fluids 9 (1), 4–6.Google Scholar
Robin, V., Mura, A. & Champion, M. 2011 Direct and indirect thermal expansion effects in turbulent premixed flames. J. Fluid Mech. 689, 149–182.CrossRefGoogle Scholar
Rubinstein, R. & Erlebacher, G. 1997 Transport coefficients in weakly compressible turbulence. Phys. Fluids 9 (10), 3037–3057.Google Scholar
Sabelnikov, V. A. & Lipatnikov, A. N. 2017 Recent advances in understanding of thermal expansion effects in premixed turbulent flames. Annu. Rev. Fluid Mech. 49, 91–117.Google Scholar
Samtaney, R., Pullin, D. I. & Kosović, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.Google Scholar
Sandoval, D. L.1995 The dynamics of variable-density turbulence. PhD thesis.CrossRefGoogle Scholar
Sarkar, S. 1992 The pressure-dilatation correlation in compressible flows. Phys. Fluids A 4 (12), 2674–2682.Google Scholar
Schumacher, J., Scheel, J. D., Krasnov, D., Donzis, D. A., Yakhot, V. & Sreenivasan, K. R. 2014 Small-scale universality in fluid turbulence. Proc. Natl Acad. Sci. USA 111 (30), 10961–10965.Google Scholar
Schwarzkopf, J. D., Livescu, D., Gore, R. A., Rauenzahn, R. M. & Ristorcelli, J. R. 2011 Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids. J. Turbul. 12, N49.Google Scholar
Serra, S., Robin, V., Mura, A. & Champion, M. 2014 Density variations effects in turbulent diffusion flames: modeling of unresolved fluxes. Combust. Sci. Technol. 186 (10–11), 1370–1391.Google Scholar
Shih, T.-H., Lumley, J. L. & Janicka, J. 1987 Second-order modelling of a variable-density mixing layer. J. Fluid Mech. 180, 93–116.CrossRefGoogle Scholar
Sidharth, G., Candler, G. V. & Dimotakis, P. E. 2014 Baroclinic torque and implications for subgrid-scale modeling. In 7th AIAA Theoretical Fluid Mechanics Conference.Google Scholar
Sinha, K. & Candler, G. V. 2003 Turbulent dissipation-rate equation for compressible flows. AIAA J. 41 (6), 1017–1021.Google Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26 (1), 287–319.Google Scholar
Sreenivasan, K., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7 (5), 309–317.Google Scholar
Subbareddy, P. K., Bartkowicz, M. D. & Candler, G. V. 2014 Direct numerical simulation of high-speed transition due to an isolated roughness element. J. Fluid Mech. 748, 848–878.Google Scholar
Subbareddy, P. K. & Candler, G. V. 2009 A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows. J. Comput. Phys. 228 (5), 1347–1364.Google Scholar
Sun, X.-B. & Lu, X.-Y. 2006 A large eddy simulation approach of compressible turbulent flow without density weighting. Phys. Fluids 18 (11), 118101.Google Scholar
Taulbee, D. & Vanosdol, J.1991 Modeling turbulent compressible flows: the mass fluctuating velocity and squared density. AIAA Paper 91-524.Google Scholar
Thomas, G., Bambrey, R. & Brown, C. 2001 Experimental observations of flame acceleration and transition to detonation following shock–flame interaction. Combust. Theor. Model. 5 (4), 573–594.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.Google Scholar
Van Driest, E. R. 1951 Turbulent boundary layer in compressible fluids. J. Aero. Sci. 18 (3), 145–160.Google Scholar
Veynante, D. & Poinsot, T. 1997 Effects of pressure gradients on turbulent premixed flames. J. Fluid Mech. 353, 83–114.Google Scholar
Veynante, D., Trouvé, A., Bray, K. & Mantel, T. 1997 Gradient and counter-gradient scalar transport in turbulent premixed flames. J. Fluid Mech. 332, 263–293.CrossRefGoogle Scholar
Vreman, A. W. 1995 Direct and Large-Eddy Simulation of the Compressible Turbulent Mixing Layer. University of Twente.Google Scholar
Vreman, A. W., Sandham, N. & Luo, K. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258.Google Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29 (7), 2152–2164.Google Scholar
Yoshizawa, A., Fujiwara, H., Abe, H. & Matsuo, Y. 2009 Mechanisms of countergradient diffusion in turbulent combustion. Phys. Fluids 21 (1), 015107.Google Scholar
Yoshizawa, A., Matsuo, Y. & Mizobuchi, Y. 2013 A construction of the Reynolds-averaged turbulence transport equations in a variable-density flow, based on the concept of mass-weighted fluctuations. Phys. Fluids 25 (7), 075105.Google Scholar
Zeman, O. 1990 Dilatation dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A 2 (2), 178–188.CrossRefGoogle Scholar
Zeman, O. 1991 On the decay of compressible isotropic turbulence. Phys. Fluids A 3 (5), 951–955.Google Scholar