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


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.

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Allred, J. C. & Blount, G. H. 1954 Experimental studies of Taylor instability. Report LA-I-600, University of California.
Andreopoulos, J. 1983 Statistical errors associated with probe geometry and turbulence intensity in triple hot-wire anemometry. J. Phys. E Sci. Instrum. 16, 12641271.
Andrews, M. J. 1986 Turbulent mixing by Rayleigh–Taylor instability. PhD thesis, Imperial College of Science and Technology, London.
Andrews, M. J. & Spalding, D. B. 1990 A simple experiment to investigate two-dimensional mixing by Rayleigh–Taylor instability. Phys. Fluids A 2, 922927.
Antonia, R. A. 1981 Conditional sampling in turbulence measurement. Annu. Rev. Fluid Mech. 13, 131156.
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, 157160.
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. 129194. Oxford University Press.
Banerjee, A. 2006 Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. PhD dissertation, Texas A&M University, College Station, TX.
Banerjee, A. & Andrews, M. J. 2006 Statistically steady measurements of Rayleigh–Taylor mixing in a gas channel. Phys. Fluids 18, 035107.
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, 14941505.
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.
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, 52575267.
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.
Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127144.
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775816.
Bruun, H. H. 1972 Hot-wire corrections in low and high turbulence intensity flows. J. Phys. E Sci. Instrum. 5, 812818.
Bruun, H. H. 1995 Hot-Wire Anemometry. Oxford University Press.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
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. 79117. Kluwer Academic.
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, 8992.
Cole, R. L. & Tankin, R. S. 1973 Experimental study of Taylor instability. Phys. Fluids 16, 18101820.
Cook, A. W. & Cabot, W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type-Ia supernovae. Nat. Phys. 2, 562568.
Cook, A. W., Cabot, W. & Miller, P. L. 2004 The mixing transition in Rayleigh–Taylor instability. J. Fluid Mech. 511, 333362.
Cook, A. W. & Dimotakis, P. E. 2001 Transition stages of Rayleigh–Taylor instability between miscible fluids. J. Fluid Mech. 443, 6999. Corrigendum. 2002 J. Fluid Mech. 457, 410–411.
Corrsin, S. 1949 Extended applications of the hot-wire anemometer. Tech. Rep. TA 1864. NACA.
Cui, A. Q. & Street, R. L. 2004 Large-eddy simulation of coastal upwelling flow. Environ. Fluid Mech. 4, 197223.
Daly, B. J. 1967 Numerical study of two-fluid Rayleigh–Taylor instability. Phys. Fluids 10, 297307.
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, 148.
Danckwerts, P. V. 1952 The definition and measurement of some characteristics of mixtures. Appl. Sci. Res. 3, 279296.
Dimonte, G. & Schneider, M. 1996 Turbulent Rayleigh–Taylor instability experiments with variable acceleration. Phys. Rev. E 54, 37403743.
Dimonte, G. & Schneider, M. 2000 Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories. Phys. Fluids 12, 304321.
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, 16681693.
Dimotakis, P. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.
Dimotakis, P. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329356.
Eckart, C. 1948 An analysis of stirring and mixing processes in incompressible fluids. J. Mar. Res. 7, 265275.
Emmons, H. W., Chang, C. T. & Watson, B. C. 1960 Taylor instability of finite surface waves. J. Fluid Mech. 7, 177193.
Fabris, G. 1983 a Third-order conditional transport correlations in the two-dimensional turbulent wake. Phys. Fluids 26, 423427.
Fabris, G. 1983 b Higher-order statistics of turbulent fluctuations in the plane wake. Phys. Fluids 26, 14371445.
Fox, R. O. 2003 Computational Models for Turbulent Reacting Flows. Cambridge University Press.
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, 1523.
Goncharov, V. N. 2002 Analytical model of nonlinear, single mode, classical Rayleigh–Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett. 88, 134502.
Gull, S. F. 1975 The X-ray, optical and radio properties of young supernova remnants. R. Astron. Soc. Mon. Not. 171, 263278.
Hishida, M. & Nagano, Y. 1978 Simultaneous measurements of velocity and temperature in nonisothermal flows. Trans. ASME J. Heat Transfer 100, 340345.
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, 169177.
Jitschin, W., Weber, U. & Hartmann, H. K. 1995 Convenient primary gas flow meter. Vacuum 46, 821824.
John, J. E. A. 1984 Gas Dynamics. Prentice-Hall.
Jorgenson, F. E. 1971 Directional sensitivity of wire and fibre-film probes. DISA Info 11, 3137.
Koop, G. K. 1976 Instability and turbulence in a stratified shear layer. PhD dissertation, University of Southern California, Los Angeles, CA.
Kovasznay, L. S. G. 1950 The hot-wire anemometer in supersonic flow. J. Aerosp. Sci., 17, 565572.
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.
Kraft, W. N., Banerjee, A. & Andrews, M. J. 2009 On hot-wire diagnostics in Rayleigh–Taylor mixing layers. Experiments in Fluids 47, 4968.
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, 2531.
LaRue, J. C. & Libby, P. A. 1980 Further results related to the turbulent boundary layer with slot injection of helium. Phys. Fluids 23, 11111118.
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Engng 3, 269289.
Leicht, K. A. 1997 Effects of initial conditions on Rayleigh–Taylor mixing development. MS thesis, Texas A&M University, College Station, TX.
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, 8196.
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. 95104. Princeton University.
Linden, P. F., Redondo, J. M. & Youngs, D. L. 1994 Molecular mixing in Rayleigh–Taylor instability. J. Fluid Mech. 265, 97124.
Loehrke, R. I. & Nagib, H. M. 1972 Experiments on management of free-stream turbulence. Tech. Rep. AGARD Report 598. Illinois Institute of Technology.
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73111.
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, 9231042.
Molchanov, O. A. 2004 On the origin of low- and middle-latitude ionospheric turbulence. Phys. Chem. Earth 29, 559567.
Mueschke, N. J. & Andrews, M. J. 2006 Investigation of scalar measurement error in diffusion and mixing processes. Exp. Fluids 40, 165175. Erratum. Exp. Fluids 40, 176 (2006).
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, 2763.
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, 1748.
Mydlarski, L. 2003 Mixed velocity-passive scalar statistics in high-Reynolds-number turbulence. J. Fluid Mech. 475, 173203.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Ramaprabhu, P. & Andrews, M. J. 2003 Simultaneous measurements of velocity and density in buoyancy-driven mixing. Exp. Fluids 34, 98106.
Ramaprabhu, P. & Andrews, M. J. 2004 Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers. J. Fluid Mech. 502, 233271.
Ratafia, M. 1973 Experimental investigation of Rayleigh–Taylor instability. Phys. Fluids 16, 12071210.
Rayleigh, Lord 1884 Investigation of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170177.
Read, K. I. 1984 Experimental investigation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 4558.
Ristorcelli, J. R. & Clark, T. T. 2004 Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations. J. Fluid Mech. 507, 213253.
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.
Sharp, D. H. 1984 An overview of Rayleigh–Taylor Instability. Physica D 12, 310.
Snider, D. M. 1994 A study of buoyancy and shear mixing. PhD dissertation, Texas A&M University, College Station, TX.
Snider, D. M. & Andrews, M. J. 1994 Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification. Phys. Fluids 6, 33243334.
Snider, D. M. & Andrews, M. J. 1996 The simulation of mixing layers driven by compound buoyancy and shear. J. Fluids Engng 118, 370376.
Speziale, C. G. 1991 Analytical methods for the development of Reynolds-stress closures in turbulence. Annu. Rev. Fluid. Mech. 23, 107157.
Steinkamp, M. J. 1995 Spectral analysis of the turbulent mixing of two fluids. PhD dissertation, University of Illinois, Urbana, IL.
Steinkamp, M. J., Clark, T. & Harlow, F. H. 1995 Stochastic interpenetration of fluids. Tech Rep. LA-131016. Los Alamos National Laboratory.
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, 7389.
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, 501528.
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. Ser. A 164, 476490.
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. Lond. 201, 192196.
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, 703711.
White, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517519.
Wilson, P. N. & Andrews, M. J. 2002 Spectral measurements of Rayleigh–Taylor mixing at low Atwood number. Phys. Fluids A 14, 938945.
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327361.
Youngs, D. L. 1984 Numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Physica D 12, 3244.
Youngs, D. L. 1989 Modelling turbulent mixing by {Rayleigh–Taylor} instability. Physica D 37, 270287.
Youngs, D. L. 1991 Three-dimensional numerical simulation of turbulent mixing by Rayleigh–Taylor instability. Phys. Fluids A 3, 13121320.
Youngs, D. L. 1994 Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Laser Part. Beams 12, 725750.
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.
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