A methodology for the uncertainty quantification and sensitivity analysis of turbulence model coefficients

This thesis is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters. These empirical coefficients and parameters are determined from experiments or direct numerical simulation results performed on turbulent flows and are subject to uncertainty. In this work, the widely used k -- epsilon turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and the rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed in the form of probability density functions. The study, presented here, is carried out for a flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte-Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties in the form of box plots. The results of the uncertainty quantification show that model coefficient variability has significant effects on the streamwise mean velocity in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly influenced by the uncertainties of the coefficients. A sensitivity analysis has been performed to compliment the uncertainty quantification and is used to determine correlations between the coefficients and the outputs of interest. Partial Rank Correlation Coefficients are implemented as the sensitivity analysis method. The results of the sensitivity analysis show the smoothness parameter B to be the most critical.