1-D Rans Model Optimization for Turbulent Richtmyer-Meshkov Instability Experiments in the University of Arizona Vertical Shock Tube

Abstract

In this study, a comparison of experimental and computational results for the Richtmyer-Meshkov instability in a shock tube at the University of Arizona with a diffuse interface is carried out. Two turbulence models, the K-L-a and K-L-a-V models, are used to obtain the computational data using 1D simulations. The models are optimized for a new set of membraneless experiments performed in the University of Arizona vertical shock tube. The varied parameters are L_0, the initial turbulent length scale, and α_b, the Rayleigh-Taylor bubble growth parameter. One parameter, the Richtmyer-Meshkov growth exponent θ, was adjusted from a value of 0.25 to 0.5 to match the experimental setup. The experiments used to calibrate these models used membranes to initially separate the two gases in the shock tube. The presence of a membrane affects the development of the fluid instability and turbulence. However, the model has an option to model a diffuse interface. It was therefore desired to determine if this model can accurately model the membraneless experiments by utilizing this diffuse interface modeling. Many different optimization parameter pairs were tested and the goodness of fit to the experimental data was calculated. The diagnostic metrics used to evaluate the goodness of fit were the width of the turbulent mixing region and the turbulent kinetic energy (TKE) over time. Experimental data with both high and low amplitude initial perturbations were used. The best fits for each of these metrics are presented. It was found that the parameters that provided the best fits for these experiments did not match the model defaults. When α_b is not changed from its default value of 0.06, it was found that the model fits the data well before reshock, but overpredicts the post-reshock growth of both mixed width and TKE. Better fits were found when α_b was able to vary over a range of [0.02,0.06] and L_0 was varied as well. For the best fits, the values of α_b were not the same for the high and low amplitude cases. The best fit values of α_b did agree when comparing mixed width and TKE in the high amplitude case, but not for the low amplitude case. A value of α_b=0.025 was found to work for all metrics fairly well. Although this did not provide the best fit overall, it did provide a reasonable fit for both the low and high amplitude cases. It should be, however, expected that there is a relationship between α_b and the amplitude of the initial perturbation.