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Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

Published online by Cambridge University Press:  24 December 2009

D. CHUNG  and
D. I. PULLIN
D. CHUNG*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
D. I. PULLIN
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: dchung@caltech.edu
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Abstract

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgrid-scale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off.

JFM classification

Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 279 - 308
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Batchelor, G. K., Canuto, V. M. & Chasnov, J. R. 1992 Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349–378.CrossRefGoogle Scholar
Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.CrossRefGoogle Scholar
Cabot, W. H. & Cook, A. W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type-Ia supernovae. Nature Phys. 2, 562–568.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Chang, W., Giraldo, F. & Perot, B. 2002 Analysis of an exact fractional step method. J. Comput. Phys. 180, 183–199.CrossRefGoogle Scholar
Cook, A. W., Cabot, W. & Miller, P. L. 2004 The mixing transition in Rayleigh–Taylor instability. J. Fluid Mech. 511, 333–362.CrossRefGoogle Scholar
Cook, A. W. & Dimotakis, P. E. 2001 Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 69–99.CrossRefGoogle Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.CrossRefGoogle Scholar
Hill, D. J., Pantano, C. & Pullin, D. I. 2006 Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock. J. Fluid Mech. 557, 29–61.CrossRefGoogle Scholar
Krawczynski, J. F., Renou, B., Danaila, L. & Demoulin, F. X. 2006 Small-scale measurements in a partially stirred reactor. Exp. Fluids 40, 667–682.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2007 Buoyancy-driven variable-density turbulence. J. Fluid Mech. 591, 43–71.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2008 Variable-density mixing in buoyancy-driven turbulence. J. Fluid Mech. 605, 145–180.CrossRefGoogle Scholar
Livescu, D., Ristorcelli, J. R., Gore, R. A., Dean, S. H., Cabot, W. H. & Cook, A. W. 2009 High-Reynolds number Rayleigh–Taylor turbulence. J. Turbul. 10, N13.CrossRefGoogle Scholar
Lumley, J. L. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10, 855–858.CrossRefGoogle Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.CrossRefGoogle Scholar
Martínez, D. O., Chen, S., Doolen, G. D., Kraichnan, R. H., Wang, L.-P. & Zhou, Y. 1997 Energy spectrum in the dissipation range of fluid turbulence. J. Plasma Phys. 57, 195–201.CrossRefGoogle Scholar
Miller, P. L. 1991 Mixing in high Schmidt number turbulent jets. PhD thesis, California Institute of Technology, Pasadena.Google Scholar
Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443–2454.CrossRefGoogle Scholar
Mueschke, N. J. & Schilling, O. 2009 Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data. Phys. Fluids 21, 014106.CrossRefGoogle Scholar
Nordström, J., Nordin, N. & Henningson, D. 1999 The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. SIAM J. Sci. Comput. 20, 1365–1393.CrossRefGoogle Scholar
Overholt, M. R. & Pope, S. B. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8, 3128–3148.CrossRefGoogle Scholar
Pullin, D. I. 2000 A vortex-based model for the subgrid flux of a passive scalar. Phys. Fluids 12, 2311–2319.CrossRefGoogle Scholar
Pullin, D. I. & Lundgren, T. S. 2001 Axial motion and scalar transport in stretched spiral vortices. Phys. Fluids 13, 2553–2563.CrossRefGoogle Scholar
Pullin, D. I. & Saffman, P. G. 1993 On the Lundgren–Townsend model of turbulent fine scales. Phys. Fluids A 5, 126–145.CrossRefGoogle Scholar
Pullin, D. I. & Saffman, P. G. 1994 Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence. Phys. Fluids 6, 1787–1796.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Sandoval, D. L. 1995 The dynamics of variable-density turbulence. PhD thesis, University of Washington, Seattle.CrossRefGoogle Scholar
Schumacher, J. 2007 Sub-Kolmogorov-scale fluctuations in fluid turbulence. Europhys. Lett. 80, 54001.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297–324.CrossRefGoogle Scholar
Tong, Y., Lombeyda, S., Hirani, A. N. & Desbrun, M. 2003 Discrete multiscale vector field decomposition. ACM Trans. Graphics 22, 445–452.CrossRefGoogle Scholar
Voelkl, T., Pullin, D. I. & Chan, D. C. 2000 A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 12, 1810–1825.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Yeung, P. K., Donzis, D. A. & Sreenivasan, K. R. 2005 High-Reynolds-number simulation of turbulent mixing. Phys. Fluids 17, 081703.CrossRefGoogle Scholar