Experimental and Numerical Study of Molecular Mixing Dynamics in Rayleigh- Taylor Unstable Flows
Date
2010-01-16
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Abstract
Experiments and simulations were performed to examine the complex processes that
occur in Rayleigh�Taylor driven mixing. A water channel facility was used to examine
a buoyancy-driven Rayleigh�Taylor mixing layer. Measurements of �uctuating den-
sity statistics and the molecular mixing parameter were made for Pr = 7 (hot/cold
water) and Sc 103 (salt/fresh water) cases. For the hot/cold water case, a high-
resolution thermocouple was used to measure instantaneous temperature values that
were related to the density �eld via an equation of state. For the Sc 103 case, the
degree of molecular mixing was measured by monitoring a di�usion-limited chemical
reaction between the two �uid streams. The degree of molecular mixing was quanti-
�ed by developing a new mathematical relationship between the amount of chemical
product formed and the density variance 02. Comparisons between the Sc = 7 and
Sc 103 cases are used to elucidate the dependence of on the Schmidt number.
To further examine the turbulent mixing processes, a direct numerical simu-
lation (DNS) model of the Sc = 7 water channel experiment was constructed to
provide statistics that could not be experimentally measured. To determine the key
physical mechanisms that in�uence the growth of turbulent Rayleigh�Taylor mixing
layers, the budgets of the exact mean mass fraction em1, turbulent kinetic energy fE00,
turbulent kinetic energy dissipation rate e 00, mass fraction variance gm002
1 , and mass
fraction variance dissipation rate f 00 equations were examined. The budgets of the unclosed turbulent transport equations were used to quantitatively assess the relative
magnitudes of di�erent production, dissipation, transport, and mixing processes.
Finally, three-equation (fE00-e 00-gm002
1 ) and four-equation (fE00-e 00-gm002
1 -f 00) turbulent
mixing models were developed and calibrated to predict the degree of molecular mix-
ing within a Rayleigh�Taylor mixing layer. The DNS data sets were used to assess
the validity of and calibrate the turbulent viscosity, gradient-di�usion, and scale-
similarity closures a priori. The modeled transport equations were implemented in a
one-dimensional numerical simulation code and were shown to accurately reproduce
the experimental and DNS results a posteriori. The calibrated model parameters
from the Sc = 7 case were used as the starting point for determining the appropri-
ate model constants for the mass fraction variance gm002
1 transport equation for the
Sc 103 case.
Description
Keywords
Turbulent Mixing, Rayleigh-Taylor Instability, Molecular Mixing, Reacting Flows, Turbulence Model