Hostname: page-component-6bf8c574d5-9nwgx Total loading time: 0 Render date: 2025-02-14T10:37:07.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Buoyancy-driven variable-density turbulence

Published online by Cambridge University Press:  30 October 2007

D. LIVESCU  and
J. R. RISTORCELLI
D. LIVESCU
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87544, [email protected]; [email protected]
J. R. RISTORCELLI
Affiliation:
Los Alamos National Laboratory, Los Alamos, NM 87544, [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007 , pp. 43 - 71
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

Batchelor, G. K., Canuto, V. M. & Chasnov, J. R. 1992 Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349–378.CrossRefGoogle Scholar
Besnard, D., Harlow, F. H., Rauenzahn, R. M. & Zemach, C. 1992 Turbulence transport equations for variable-density turbulence and their relationships to two field models. Tech. Rep. Los Alamos National Laboratory, lA-12303-MS.CrossRefGoogle Scholar
Blaisdell, G. A., Mansour, N. N. & Reynolds, W. C. 1993 Compressibility effects on the growth and structure of homogeneous turbulent shear flows. J. Fluid Mech. 256, 443–485.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
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.Google 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
Cook, A. W., Cabot, W. H. & Miller, P. L. 2004 The mixing transition in Rayleigh–Taylor instability. J. Fluid Mech. 511, 333–362.CrossRefGoogle Scholar
Dalziel, S. B., Linden, P. F. & Youngs, D. L. 1999 Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability. J. Fluid Mech. 399, 1–48.CrossRefGoogle Scholar
Dimonte, G. & Schneider, M. 2000 Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321.CrossRefGoogle Scholar
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Eswaran, V. & Pope, S. B. 1988 Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids 31, 506–520.CrossRefGoogle Scholar
Givi, P. 1989 Model-free simulations of turbulent reacting flows. Prog. Energy Combust. Sci. 15, 1–107.CrossRefGoogle Scholar
Jang, Y. & de Bruyn Kops, S. M. 2007 Pseudo-spectral numerical simulation of miscible fluids with a high density ratio. Comput. Fluids 36, 238–247.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–2719.CrossRefGoogle Scholar
Livescu, D. & Ristorcelli, J. R. 2007 Variable density mixing in buoyancy-driven turbulence. J. Fluid Mech. (submitted).CrossRefGoogle Scholar
Livescu, D., Jaberi, F. A. & Madnia, C. K. 2002 The effects of heat release on the energy exchange in reacting turbulent shear flow. J. Fluid Mech. 450, 35–66.CrossRefGoogle Scholar
McMurtry, P. A. 1987 Direct numerical simulation of a reacting mixing layer with chemical heat release. PhD thesis, University of Washington.Google Scholar
Ristorcelli, J. R. 1997 A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: an analytical theory. J. Fluid Mech. 347, 37–70.CrossRefGoogle Scholar
Ristorcelli, J. R. & Clark, T. T. 2004 Rayleigh-Taylor turbulence: self-similar analysis and direct numerical simulations. LANL Rep. 03-4273 and J. Fluid Mech. 507, 213–253.Google Scholar
Ristorcelli, J. R. & Livescu, D. 2004 Decay of isotropic turbulence: fixed points and solutions for nonconstant G ~ R λ palinstrophy. Phys. Fluids 16, 3487–3490.CrossRefGoogle Scholar
Ristorcelli, J. R. & Livescu, D. 2007 Second-order moment modelling of buoyantly driven variable density turbulence. In preparation.Google Scholar
Sandoval, D. L. 1995 The dynamics of variable density turbulence. PhD thesis, University of Washington LANL Rep. LA-13037-T.CrossRefGoogle Scholar
Sandoval, D. L., Clark, T. T. & Riley, J. J. 1996 Buoyancy-generated variable density turbulence. In Proc. IUTAM Symp. on Variable Density Low Speed Turbulent Flows, pp. 847–864. Kluwer.CrossRefGoogle Scholar
Young, Y. N., Tufo, H., Dubey, A. & Rosner, R. 1999 On the miscible Rayleigh–Taylor instability: two and three dimensions. J. Fluid Mech. 447, 377–408.CrossRefGoogle Scholar