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Measurements of molecular mixing in a high-Schmidt-number Rayleigh–Taylor mixing layer

Published online by Cambridge University Press:  27 July 2009

NICHOLAS J. MUESCHKE ,
OLEG SCHILLING ,
DAVID L. YOUNGS  and
MALCOLM J. ANDREWS
NICHOLAS J. MUESCHKE
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
OLEG SCHILLING
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
DAVID L. YOUNGS
Affiliation:
Atomic Weapons Establishment, Aldermaston, Reading, Berkshire RG7 4PR, UK
MALCOLM J. ANDREWS*
Affiliation:
Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
†Email address for correspondence: [email protected]
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Abstract

Molecular mixing measurements are reported for a high-Schmidt-number (Sc ~ 103), small-Atwood-number (A ≈ 7.5 × 10−4) buoyancy-driven turbulent Rayleigh–Taylor (RT) mixing layer in a water channel facility. Salt was added to the top water stream to create the desired density difference. The degree of molecular mixing was measured as a function of time by monitoring a diffusion-limited chemical reaction between the two fluid streams. The pH of each stream was modified by the addition of acid or alkali such that a local neutralization reaction occurred as the two fluids molecularly mixed. The progress of this neutralization reaction was tracked by the addition of phenolphthalein – a pH-sensitive chemical indicator – to the acidic stream. Accurately calibrated backlit optical techniques were used to measure the average concentration of the coloured chemical indicator. Comparisons of chemical product formation for pre-transitional buoyancy- and shear-driven mixing layers are given. It is also shown that experiments performed at different equivalence ratios (acid/alkali concentrations) can be combined to obtain a mathematical relationship between the coloured product formed and the density variance. This relationship was used to obtain high-fidelity quantitative measures of the degree of molecular mixing which are independent of probe resolution constraints. The dependence of molecular mixing on the Schmidt and Reynolds numbers is examined by comparing the current Sc ~ 103 measurements with previous Sc = 0.7 gas-phase and Pr = 7 (where Pr is the Prandtl number) liquid-phase measurements. This comparison indicates that the Schmidt number has a large effect on the quantity of mixed fluid at small Reynolds numbers Reh < 103. At larger Reynolds numbers, corresponding to later times in this experiment, all mixing parameters indicated a greater degree of molecular mixing and a decreased Schmidt number dependence. Implications for the development and quantitative assessment of turbulent transport and mixing models appropriate for RT instability-induced mixing are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 632 , 10 August 2009 , pp. 17 - 48
Copyright
Copyright © Cambridge University Press 2009

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