Experimental and numerical study of molecular mixing dynamics in Rayleigh-Taylor unstable flows

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 fluctuating density statistics and the molecular mixing parameter theta 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 field via an equation of state. For the Sc ∼ 103 case, the degree of molecular mixing was measured by monitoring a diffusion-limited chemical reaction between the two fluid streams. The degree of molecular mixing was quantified by developing a new mathematical relationship between the amount of chemical product formed and the density variance r'2 . Comparisons between the Sc = 7 and SC ∼ 10 3 cases are used to elicidate the dependence of theta on the Schmidt number.;To further examine the turbulent mixing processes, a direct numerical simulation (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 influence the growth of turbulent Rayleigh-Taylor mixing layers, the budgets of the exact mean mass fraction m˜1, turbulent kinetic energy E''&d15; , turbulent kinetic energy dissipation rate e''&d15; , mass fraction variance m''21&d15; , and mass fraction variance dissipation rate c''&d15; equations were examined. The budgets of the unclosed turbulent transport equations were used to quantitatively assess the relative magnitudes of different production, dissipation, transport, and mixing processes.;Finally, three-equation ( E''&d15;- e''&d15;- m''21&d15; ) and four-equation ( E''&d15;- e''&d15;- m''21&d15; -c''&d15; ) turbulent mixing models were developed and calibrated to predict the degree of molecular mixing within a Rayleigh-Taylor mixing layer. The DNS data sets were used to assess the validity of and calibrate the turbulent viscosity, gradient-diffusion, 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 appropriate model constants for the mass fraction variance m''21&d15; transport equation for the Sc ∼ 103 case.