Hostname: page-component-7bb8b95d7b-qxsvm Total loading time: 0 Render date: 2024-09-26T03:26:14.273Z Has data issue: false hasContentIssue false
  • English
  • Français

Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers

Published online by Cambridge University Press:  27 August 2010

ARINDAM BANERJEE ,
WAYNE N. KRAFT  and
MALCOLM J. ANDREWS
ARINDAM BANERJEE*
Affiliation:
Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA
WAYNE N. KRAFT
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77840, USA
MALCOLM J. ANDREWS
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77840, USA Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
†Email address for correspondence: banerjeea@mst.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The self-similar evolution to turbulence of a multi-mode miscible Rayleigh–Taylor (RT) mixing layer has been investigated for Atwood numbers 0.03–0.6, using an air–helium gas channel experiment. Two co-flowing gas streams, one containing air (on top) and the other a helium–air mixture (at the bottom), initially flowed parallel to each other at the same velocity separated by a thin splitter plate. The streams met at the end of the splitter plate, with the downstream formation of a buoyancy unstable interface, and thereafter buoyancy-driven mixing. This buoyancy-driven mixing layer experiment permitted long data collection times, short transients and was statistically steady. Several significant designs and operating characteristics of the gas channel experiment are described that enabled the facility to be successfully run for At ~ 0.6. We report, and discuss, statistically converged measurements using digital image analysis and hot-wire anemometry. In particular, two hot-wire techniques were developed for measuring the various turbulence and mixing statistics in this air–helium RT experiment. Data collected and discussed include: mean density profiles, growth rate parameters, various turbulence and mixing statistics, and spectra of velocity, density and mass flux over a wide range of Atwood numbers (0.03 ≤ At ≤ 0.6). In particular, the measured data at the small Atwood number (0.03–0.04) were used to evaluate several turbulence-model constants. Measurements of the root mean square (r.m.s.) velocity and density fluctuations at the mixing layer centreline for the large At case showed a strong similarity to lower At behaviours when properly normalized. A novel conditional averaging technique provided new statistics for RT mixing layers by separating the bubble (light fluid) and spike (heavy fluid) dynamics. The conditional sampling highlighted differences in the vertical turbulent mass flux, and vertical velocity fluctuations, for the bubbles and spikes, which were not otherwise observable. Larger values of the vertical turbulent mass flux and vertical velocity fluctuations were found in the downward-falling spikes, consistent with larger growth rates and momentum of spikes compared with the bubbles.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 127 - 190
Copyright
Copyright © Cambridge University Press 2010

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

Allred, J. C. & Blount, G. H. 1954 Experimental studies of Taylor instability. Report LA-I-600, University of California.CrossRefGoogle Scholar
Andreopoulos, J. 1983 Statistical errors associated with probe geometry and turbulence intensity in triple hot-wire anemometry. J. Phys. E Sci. Instrum. 16, 1264–1271.CrossRefGoogle Scholar
Andrews, M. J. 1986 Turbulent mixing by Rayleigh–Taylor instability. PhD thesis, Imperial College of Science and Technology, London.Google Scholar
Andrews, M. J. & Spalding, D. B. 1990 A simple experiment to investigate two-dimensional mixing by Rayleigh–Taylor instability. Phys. Fluids A 2, 922–927.CrossRefGoogle Scholar
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13, 131–156.CrossRefGoogle Scholar
Anuchina, N. N., Kucherenko, Y. A., Neuvazhaev, V. E., Ogibina, V. N. & Shibarshov, L. I. 1978 Turbulent mixing at an accelerating interface between liquids of different densities. Translated from Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 6, 157–160.Google Scholar
Atzeni, S. & Meyer-ter-Vehn, J. 2004 The physics of inertial fusion: beam plasma interaction, hydrodynamics, hot dense matter. In International Monographs on Physics (ed. Birman, J., Edwards, S. F., Friend, R., Rees, M., Sherrington, D. & Veneziano, G.), vol. 125, pp. 129–194. Oxford University Press.Google Scholar
Banerjee, A. 2006 Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. PhD dissertation, Texas A&M University, College Station, TX.CrossRefGoogle Scholar
Banerjee, A. & Andrews, M. J. 2006 Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. Phys. Fluids 18, 035107.CrossRefGoogle Scholar
Banerjee, A. & Andrews, M. J. 2007 A convection heat transfer correlation for a binary air–helium mixture at low Reynolds number. J. Heat Transfer 129, 1494–1505.CrossRefGoogle Scholar
Besnard, D. C., Harlow, F. H., Rauenzahn, R. M. & Zemach, C. 1992 Turbulence transport equations for variable-density turbulence and their relationship to two-field models. Tech. Rep. LAUR-12303. Los Alamos National Laboratory.CrossRefGoogle Scholar
Betti, R., Umansky, M., Lobatchev, V., Goncharov, V. N. & McCrory, R. L. 2001 Hot-spot dynamics and deceleration-phase Rayleigh–Taylor instability of imploding inertial confinement fusion capsules. Phys. Plasmas 8, 5257–5267.CrossRefGoogle Scholar
Blackwell, B. F. 1973 The turbulent boundary layer on a porous plate: an experimental study of the heat transfer behaviour with adverse pressure gradients. PhD dissertation, Stanford University, Stanford, CA.Google Scholar
Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127–144.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816.CrossRefGoogle Scholar
Bruun, H. H. 1972 Hot-wire corrections in low and high turbulence intensity flows. J. Phys. E Sci. Instrum. 5, 812–818.CrossRefGoogle Scholar
Bruun, H. H. 1995 Hot-Wire Anemometry. Oxford University Press.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarkar, S. 2002 Variable density fluid turbulence. In Fluid Mechanics and its Applications (ed. Moreau, R.), vol. 69, pp. 79–117. Kluwer Academic.Google Scholar
Clarke, J. S., Fisher, H. N. & Mason, R. J. 1973 Laser-driven implosion of spherical DT targets to thermonuclear burn conditions. Phys. Rev. Lett. 30, 89–92.CrossRefGoogle Scholar
Cole, R. L. & Tankin, R. S. 1973 Experimental study of Taylor instability. Phys. Fluids 16, 1810–1820.CrossRefGoogle Scholar
Cook, A. W. & Cabot, W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type-Ia supernovae. Nat. Phys. 2, 562–568.Google 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. Corrigendum. 2002 J. Fluid Mech. 457, 410–411.CrossRefGoogle Scholar
Corrsin, S. 1949 Extended applications of the hot-wire anemometer. Tech. Rep. TA 1864. NACA.Google Scholar
Cui, A. Q. & Street, R. L. 2004 Large-eddy simulation of coastal upwelling flow. Environ. Fluid Mech. 4, 197–223.CrossRefGoogle Scholar
Daly, B. J. 1967 Numerical study of two-fluid Rayleigh–Taylor instability. Phys. Fluids 10, 297–307.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
Danckwerts, P. V. 1952 The definition and measurement of some characteristics of mixtures. Appl. Sci. Res. 3, 279–296.CrossRefGoogle Scholar
Dimonte, G. & Schneider, M. 1996 Turbulent Rayleigh–Taylor instability experiments with variable acceleration. Phys. Rev. E 54, 3740–3743.CrossRefGoogle ScholarPubMed
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
Dimonte, G., Youngs, D. L., Dimits, A., Weber, S., Marinak, M., Wunsch, S., Garasi, C., Robinson, A., Andrews, M. J., Ramaprabhu, P., Calder, A. C., Fryxell, B., Biello, J., Dursi, L., Macneice, P., Olson, K., Ricker, P., Rosner, R., Timmes, H., Tufo, H., Young, Y.-N. & Zingale, M. 2004 A comparative study of the turbulent Rayleigh–Taylor (RT) instability using high-resolution 3D numerical simulations: the Alpha-Group collaboration. Phys. Fluids 16, 1668–1693.CrossRefGoogle Scholar
Dimotakis, P. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–98.CrossRefGoogle Scholar
Dimotakis, P. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.CrossRefGoogle Scholar
Eckart, C. 1948 An analysis of stirring and mixing processes in incompressible fluids. J. Mar. Res. 7, 265–275.Google Scholar
Emmons, H. W., Chang, C. T. & Watson, B. C. 1960 Taylor instability of finite surface waves. J. Fluid Mech. 7, 177–193.CrossRefGoogle Scholar
Fabris, G. 1983 a Third-order conditional transport correlations in the two-dimensional turbulent wake. Phys. Fluids 26, 423–427.CrossRefGoogle Scholar
Fabris, G. 1983 b Higher-order statistics of turbulent fluctuations in the plane wake. Phys. Fluids 26, 1437–1445.CrossRefGoogle Scholar
Fox, R. O. 2003 Computational Models for Turbulent Reacting Flows. Cambridge University Press.CrossRefGoogle Scholar
Frota, M. N. & Moffat, R. J. 1983 Effect of combined roll and pitch angles on triple hot-wire measurements of mean and turbulence structure. DISA Inf. 28, 15–23.Google Scholar
Goncharov, V. N. 2002 Analytical model of nonlinear, single mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett. 88, 134502.CrossRefGoogle ScholarPubMed
Gull, S. F. 1975 The X-ray, optical and radio properties of young supernova remnants. R. Astron. Soc. Mon. Not. 171, 263–278.CrossRefGoogle Scholar
Hishida, M. & Nagano, Y. 1978 Simultaneous measurements of velocity and temperature in nonisothermal flows. Trans. ASME J. Heat Transfer 100, 340–345.CrossRefGoogle Scholar
Jacobsen, R. T., Clarke, W. P., Penoncello, S. G. & McCarty, R. D. 1990 A thermodynamic property formulation for air. Part I. Single-phase equation of state from 60 to 873 K at pressures to 70 MPa. Intl J. Thermophys. 11, 169–177.CrossRefGoogle Scholar
Jitschin, W., Weber, U. & Hartmann, H. K. 1995 Convenient primary gas flow meter. Vacuum 46, 821–824.CrossRefGoogle Scholar
John, J. E. A. 1984 Gas Dynamics. Prentice-Hall.Google Scholar
Jorgenson, F. E. 1971 Directional sensitivity of wire and fibre-film probes. DISA Info 11, 31–37.Google Scholar
Koop, G. K. 1976 Instability and turbulence in a stratified shear layer. PhD dissertation, University of Southern California, Los Angeles, CA.Google Scholar
Kovasznay, L. S. G. 1950 The hot-wire anemometer in supersonic flow. J. Aerosp. Sci., 17, 565–572.Google Scholar
Kraft, W. N. 2008 Simultaneous and instantaneous measurements of velocity and density in Rayleigh–Taylor mixing layers. PhD dissertation, Texas A&M University, College Station, TX.Google Scholar
Kraft, W. N., Banerjee, A. & Andrews, M. J. 2009 On hot-wire diagnostics in Rayleigh–Taylor mixing layers. Experiments in Fluids 47, 49–68.CrossRefGoogle Scholar
Kucherenko, Y. A., Balabin, S. I., Cherret, R. & Haas, J. F. 1997 Experimental investigation into inertial properties of Rayleigh–Taylor turbulence. Laser and Particle Beams 15, 25–31.CrossRefGoogle Scholar
LaRue, J. C. & Libby, P. A. 1980 Further results related to the turbulent boundary layer with slot injection of helium. Phys. Fluids 23, 1111–1118.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Engng 3, 269–289.CrossRefGoogle Scholar
Leicht, K. A. 1997 Effects of initial conditions on Rayleigh–Taylor mixing development. MS thesis, Texas A&M University, College Station, TX.Google Scholar
Lewis, D. J. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Part 2. Proc. R. Soc. Lond. 202, 81–96.Google Scholar
Linden, P. F., Redondo, J. M. & Caulfield, C. P. 1992 Molecular mixing in Rayleigh–Taylor instability. In Advances in Compressible Turbulent Mixing (ed. Dannevik, W. P., Buckingham, A. C. & Leith, C. E.), pp. 95–104. Princeton University.Google Scholar
Linden, P. F., Redondo, J. M. & Youngs, D. L. 1994 Molecular mixing in Rayleigh–Taylor instability. J. Fluid Mech. 265, 97–124.CrossRefGoogle Scholar
Loehrke, R. I. & Nagib, H. M. 1972 Experiments on management of free-stream turbulence. Tech. Rep. AGARD Report 598. Illinois Institute of Technology.Google Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
McCarty, R. 1973 Thermodynamic properties of helium 4 from 2 to 1500 K at pressures up to 108 Pa. J. Phys. Chem. Ref. Data 2, 923–1042.CrossRefGoogle Scholar
Molchanov, O. A. 2004 On the origin of low- and middle-latitude ionospheric turbulence. Phys. Chem. Earth 29, 559–567.CrossRefGoogle Scholar
Mueschke, N. J. & Andrews, M. J. 2006 Investigation of scalar measurement error in diffusion and mixing processes. Exp. Fluids 40, 165–175. Erratum. Exp. Fluids 40, 176 (2006).CrossRefGoogle Scholar
Mueschke, N., Andrews, M. J. & Schilling, O. 2006 Experimental characterization of initial conditions and spatio-temporal evolution of a small Atwood number Rayleigh–Taylor mixing layer. J. Fluid Mech. 567, 27–63.CrossRefGoogle Scholar
Mueschke, N., Schilling, O., Youngs, D. L. & Andrews, M. J. 2009 Measurements of molecular mixing in a high-Schmidt-number Rayleigh–Taylor mixing layer. J. Fluid Mech. 632, 17–48.CrossRefGoogle Scholar
Mydlarski, L. 2003 Mixed velocity-passive scalar statistics in high-Reynolds-number turbulence. J. Fluid Mech. 475, 173–203.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ramaprabhu, P. & Andrews, M. J. 2003 Simultaneous measurements of velocity and density in buoyancy-driven mixing. Exp. Fluids 34, 98–106.CrossRefGoogle Scholar
Ramaprabhu, P. & Andrews, M. J. 2004 Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers. J. Fluid Mech. 502, 233–271.CrossRefGoogle Scholar
Ratafia, M. 1973 Experimental investigation of Rayleigh–Taylor instability. Phys. Fluids 16, 1207–1210.CrossRefGoogle Scholar
Rayleigh, Lord 1884 Investigation of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Read, K. I. 1984 Experimental investigation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 45–58.CrossRefGoogle Scholar
Ristorcelli, J. R. & Clark, T. T. 2004 Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations. J. Fluid Mech. 507, 213–253.CrossRefGoogle Scholar
Rose, W. C. 1973 The behaviour of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient. PhD dissertation, University of Washington, Seattle, Washington.CrossRefGoogle Scholar
Sharp, D. H. 1984 An overview of Rayleigh–Taylor Instability. Physica D 12, 3–10.CrossRefGoogle Scholar
Snider, D. M. 1994 A study of buoyancy and shear mixing. PhD dissertation, Texas A&M University, College Station, TX.Google Scholar
Snider, D. M. & Andrews, M. J. 1994 Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification. Phys. Fluids 6, 3324–3334.CrossRefGoogle Scholar
Snider, D. M. & Andrews, M. J. 1996 The simulation of mixing layers driven by compound buoyancy and shear. J. Fluids Engng 118, 370–376.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
Steinkamp, M. J. 1995 Spectral analysis of the turbulent mixing of two fluids. PhD dissertation, University of Illinois, Urbana, IL.CrossRefGoogle Scholar
Steinkamp, M. J., Clark, T. & Harlow, F. H. 1995 Stochastic interpenetration of fluids. Tech Rep. LA-131016. Los Alamos National Laboratory.Google Scholar
Stillinger, D. C., Head, M. J., Helland, K. N. & Van Atta, C. W. 1983 A closed-loop gravity- driven water channel for density-stratified flow. J. Fluid Mech. 131, 73–89.CrossRefGoogle Scholar
Tan-Atichat, J., Nagib, H. M. & Loehrke, R. I. 1982 Interaction of free-stream turbulence with screens and grids: a balance between turbulence scales. J. Fluid Mech. 114, 501–528.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. Ser. A 164, 476–490.CrossRefGoogle Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. Lond. 201, 192–196.Google Scholar
Vukoslavcevic, P. V., Radulovic, I. M. & Wallace, J. M. 2005 Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow. Exp. Fluids 3, 703–711.CrossRefGoogle Scholar
White, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517–519.CrossRefGoogle Scholar
Wilson, P. N. & Andrews, M. J. 2002 Spectral measurements of Rayleigh–Taylor mixing at low Atwood number. Phys. Fluids A 14, 938–945.CrossRefGoogle Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327–361.CrossRefGoogle Scholar
Youngs, D. L. 1984 Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 32–44.CrossRefGoogle Scholar
Youngs, D. L. 1989 Modelling turbulent mixing by {Rayleigh–Taylor} instability. Physica D 37, 270–287.CrossRefGoogle Scholar
Youngs, D. L. 1991 Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3, 1312–1320.CrossRefGoogle Scholar
Youngs, D. L. 1994 Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Part. Beams 12, 725–750.CrossRefGoogle Scholar
Youngs, D. L. 2003 Application of MILES to Rayleigh–Taylor and Richtmeyer–Meshkov mixing. In Sixteenth AIAA Computational Fluid Dynamics Conference. Tech. Rep. no. 4102.CrossRefGoogle Scholar