Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-19T22:37:37.148Z Has data issue: false hasContentIssue false
  • English
  • Français

The k-L turbulence model for describing buoyancy-driven fluid instabilities

Published online by Cambridge University Press:  21 September 2006

VINCENT P. CHIRAVALLE
VINCENT P. CHIRAVALLE
Affiliation:
Los Alamos National Laboratory, Los Alamos, New Mexico
Get access Rights & Permissions [Opens in a new window]

Abstract

The k-L turbulence model, where k is the turbulent kinetic energy and L represents the turbulent eddy scale length, is a two-equation turbulence model that has been proposed to simulate turbulence induced by Rayleigh-Taylor (RT) and Richtmyer Meshkov (RM) instabilities, which play an important role in the implosions of inertial confinement fusion (ICF) capsule targets. There are three free parameters in the k-L model, and in this paper, I calibrate them independently by comparing with RT and RM data from the linear electric motor (LEM) experiments together with classical Kelvin-Helmoholtz (KH) data. To perform this calibration, I numerically solved the equations of one-dimensional (1D) Lagrangian hydrodynamics, in a manner similar to that of contemporary ICF codes, together with the k-L turbulence model. With the three free parameters determined, I show that the k-L model is successful in describing both shear-driven and buoyancy-driven instabilities, capturing the experimentally observed separation between bubbles and spikes at high Atwood number for the RT case, as well as the temporal mix width recorded in RM shock tube experiments.

Keywords

1D Lagrangian hydrodynamicsInertial confinement fusionNumerical methodsRayleigh Taylor instabilitiesTurbulence modeling
Type
Research Article
Information
Laser and Particle Beams , Volume 24 , Issue 3 , September 2006 , pp. 381 - 394
Copyright
© 2006 Cambridge University Press

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

Amendt, P., Colvin, J.D., Tipton, R.E., Hinkel, D.E., Edwards, M.J., Landen, O.L., Ramshaw, J.D., Suter, L.J., Varnum, W.S. & Watt, R.G. (2002). Indirect-drive noncryogenic double-shell ignition targets for the national ignition facility: Design and analysis. Phys. Plasmas 9, 2221–2233.CrossRefGoogle Scholar
Bowers, R. & Wilson, J. (1991). Numerical Modeling in Applied Physics and Astrophysics. Boston: Jones & Bartlett Publishers.
Brouillette, M. (2002). The Richtmyer-Meshkov instability. Annu. Rev. Fluid Mech. 34, 445–468.CrossRefGoogle Scholar
Brown, G.L. & Roshko, A. (1974). On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.CrossRefGoogle Scholar
Chiravalle, V.P. (2004). The implementation of the k-l turbulence model for buoyancy-driven instabilities in a 1Dlagrangian hydrocode. LA-UR-04-7626. Los Alamos, NM: Los Alamos National Laboratory.
Dimonte, G. (2000). Span wise homogeneous buoyancy-drag model for Rayleigh-Taylor mixing and experimental evaluation. Phys. Plasmas 7, 2255–2269.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
Dittrich, T.R., Haan, S.W., Marinak, M.M., Hinkel, D.E., Pollaine, S.M., Mceachern, R., Cook, R.C., Roberts, C.C., Wilson, D.C., Bradley, P.A. & Varnum, W.S. (1999). Capsule design for the national ignition facility. Laser Part. Beams 17, 217–224.CrossRefGoogle Scholar
Holmes, R.L., Dimonte, G., Fryxell, B., Gittings, M.L., Grove, J.W., Schneider, M., Sharp, D.H., Velikovich, A.L., Weaver, R.P. & Zhang, Q. (1999). Richtmyer-Meshkov instability growth: Experiment, simulation and theory. J. Fluid Mech. 389, 55–79.CrossRefGoogle Scholar
Haan, S.W., Pollaine, S.M., Lindl, J.D., Suter, L.J., Berger, R.L., Powers, L.V., Alley, W.E., Amendt, P.A., Futterman, J.A., Levedahl, W.K., Rosen, M.D., Rowley, D.P., Sacks, R.A., Shestakov, A.I., Strobel, G.L., Tabak, M., Weber, S.V., Zimmerman, G.B., Krauser, W.J., Wilson, D.C., Coggeshall, S.V., Harris, D.B., Hoffman, N.M. & Wilde, B.H. (1995). Design and modeling of ignition targets for the national ignition facility. Phys. Plasmas 2, 2480–2487.CrossRefGoogle Scholar
Marinak, M.M., Tipton, R.E., Landen, O.L., Murphy, T.J., Amendt, P., Haan, S.W., Hatchet, S.P., Keane, C.J., Mceahern, R. & Wallace, R. (1996). Three-dimensional simulations of nova high growth factor capsule implosion experiments. Phys. Plasmas 3, 2070–2076.CrossRefGoogle Scholar
Peterson, R.R., Haynes, D.A., Golovkin, I.E. & Moses, G.A. (2002). Inertial fusion energy target output and chamber pressure response: Calculations and experiments. Phys. Plasmas 9, 2287–2292.CrossRefGoogle Scholar
Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (1992). Numerical Recipes in C: The Art of Scientific Computing. New York: Cambridge University Press.
Poggi, F., Thorembey M.H., &Rodriguez, G. (1998). Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability. Phys. Fluids 10, 2698–2700.CrossRefGoogle Scholar
Read, K.I. (1984). Experimental investigation of turbulent mixing by the Rayleigh-Taylor instability. Physica D 12, 45–48.Google Scholar
Scannapieco, A.J. & Cheng, B. (2002). A multifluid interpenetration mix model. Physics Lett. A. 299, 49–64.CrossRefGoogle Scholar
Slessor, M.D., Zhuang, M. & Dimotakis, P.E. (2000). Turbulent shear-layer mixing: growth-rate compressibility scaling. J. Fluid Mech. 414, 35–45.CrossRefGoogle Scholar
Speziale, C.G. (1991). Analytical methods for the development of Reynolds-stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107–157.CrossRefGoogle Scholar
Tannehill, J.C., Anderson, D.A. & Pletcher, R.H. (1997). Computational Fluid Mechanics and Heat Transfer. Washington, DC: Taylor & Francis Publishers.
Tipton, R.E. (1999). A phenomenological k-l mix model for NIF targets in 1, 2 and 3 dimensions. Proc. 7th International Workshop on the Physics of Compressible Turbulent Mixing, Sarov, Russia: RFNC-VNIIEF.
Van Leer, B. (1977). Towards the ultimate conservative difference scheme III: Upstream-centered finite-difference schemes for ideal compressible flow. J. Comp. Phys. 23, 263–275.CrossRefGoogle Scholar
Vetter, M. & Sturtevant, B. (1995). Experiments on the Richtmyer-Meshkov instability of an air/sf6 interface. Shock Waves 4, 247–252.CrossRefGoogle Scholar
Weber, S.V., Dimonte, G. & Marinak, M.M. (2003). Arbitrary lagrange-eulerian code simulations of turbulent Rayleigh-Taylor instability in two and three dimensions. Laser Part. Beams 21, 455–461.Google Scholar
Youngs, D.L. (1994). Numerical simulation of turbulent mixing by Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Laser Part. Beams 12, 725–750.CrossRefGoogle Scholar
Youngs, D.L. (1989). Modeling turbulent mixing by Rayleigh-Taylor instability. Physica D 37, 270–287.Google Scholar