Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-23T23:03:47.666Z Has data issue: false hasContentIssue false
  • English
  • Français

Theoretical methods for the determination of mixing

Published online by Cambridge University Press:  03 March 2004

BAOLIAN CHENG ,
JAMES GLIMM ,
HYEONSEONG JIN  and
DAVID SHARP
BAOLIAN CHENG
Affiliation:
Applied Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico
JAMES GLIMM
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York Center for Data Intensive Computing, Brookhaven National Laboratory, Upton, New York
HYEONSEONG JIN
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York
DAVID SHARP
Affiliation:
Applied Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
Get access Rights & Permissions [Opens in a new window]

Abstract

Acceleration-driven fluid mixing is studied here from a theoretical point of view. Considerable progress has been achieved in the understanding of mix. Theories of the authors are reviewed that allow prediction of the edge of the mixing zone, in agreement with experimental data. Theories that describe the distribution of masses within the mixing region are also reviewed. The theory we present describes a chunk mix regime, in which two phases are mixed at a chunk level, but for which there is no atomic mixing. Thus the two phases are segregated into disjoint regions of space.

Keywords

MixingMultiphase flowRayleigh–Taylor instability
Type
Research Article
Information
Laser and Particle Beams , Volume 21 , Issue 3 , July 2003 , pp. 429 - 436
Copyright
© 2003 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

Alon, U. & Shvarts, D. (1996). Two phase flow model for Rayleigh–Taylor and Richtmyer–Meshkov mixing. In Proc. Fifth Int. Workshop for Compressible Turbulent Mixing, pp. 14–22. Singapore: World Scientific.
Chen, Y., Deng, Y., Glimm, J., Li, G., Sharp, D.H. & Zhang, Q. (1993). A renormalization group scaling analysis for compressible two phase flow. Phys. Fluids A. 5, 2929–2937.Google Scholar
Cheng, B., Glimm, J., Saltz, D. & Sharp, D.H. (1999). Boundary conditions for a two pressure two phase flow model. Physica D. 133, 84–105.Google Scholar
Cheng, B., Glimm, J. & Sharp, D.H. (2000). Density dependence or Rayleigh–Taylor and Richtmyer–Meshkov mixing rates. Phys. Lett. A 268, 366–374.Google Scholar
Cheng, B., Glimm, J. & Sharp, D.H. (2002a). A three-dimensional renormalization group bubble merger model for Rayleigh–Taylor mixing. Chaos 12, 267–274.Google Scholar
Cheng, B., Glimm, J. & Sharp, D.H. (2002b). Multi-temperature multi-phase flow model. Zeitschrift fur Angewandte Mathematik und Physik. 53, 211–238.Google Scholar
Dimonte, G. & Schneider, M. (1996). Turbulent Rayleigh–Taylor instability experiments with variable accelerations. Phys. Rev. E 54, 3740–3743.Google Scholar
Dimonte, G. & Schneider, M. (2000). Density ratio dependence of sustained acceleration histories. Phys. Fluids 12, 304–321.Google Scholar
George, E. Glimm, J., Li, X.L., Marchese, A., &Xu, Z.L. (2002). A comparison of experimental, theoretical, and numerical simulation of Rayleigh–Taylor mixing rates. Proc. Natl. Acad. Sci. USA 99, 2587–2592.Google Scholar
Glimm, J., Grove, J., Li, X., Oh, W. & Sharp, D.H. (2001). A critical analysis of Rayleigh–Taylor growth rates. J. Comp. Phys. 169, 652–677.Google Scholar
Glimm, J. & Jin, H. (2001). An asymptotic analysis of two-phase fluid mixing. Bol. Soc. Bras. Mat. 32, 213–236.Google Scholar
Glimm, J., Saltz, D. & Sharp, D.H. (1998). Two-pressure two phase flow. In Nonlinear Partial Differential Equations. pp. 124–128. Singapore: World Scientific. pp. 124–148.
Glimm, J., Saltz, D. & Sharp, D.H. (1999). Two phase modeling of a fluid mixing layer. J. Fluid Mech. 378, 119–143.Google Scholar
Glimm, J. & Sharp, D.H. (1990). Heater mixing as a renormalization group fixed point. Phys. Rev. Lett. 64, 2137–2139.Google Scholar
Glimm, J. & Sharp, D.H. (1997). Stochastic partial differential equations: Selected applications in continuum physics. In Stochastic Partial Differential Equations: Six Perspectives. Providence: American Mathematical Society.
Jin, H. (2001). The incompressible limit of compressible multiphase flow equations. Ph.D. Thesis. Stony Brook, NY: University at Stony Brook.
Oron, D., Arazi, L., Kartoon, D., Rikanati, A. Alon, A., &Shvarts, D. (2001). Dimensionality dependence of Rayleigh–Taylor and Richtmyer–Meshkov instability late time scaling laws. Phys. Plasmas 8, 2883–2889.Google Scholar
Read, K.I. (1984). Experimental investigation turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 45–58.Google Scholar
Sharp, D.H. & Wheeler, J.A. (1961). Late stage of Rayleigh–Taylor instability. Institute for Defense Analysis.
Smeeton, V.S. & Youngs, D.L. (1987). Experimental investigation of turbulent mixing by Rayleigh–Taylor instability (Part 3). Report number 0 35/87. Atomic Weapons Establishment, Aldermaston, UK.