Uncertainty quantification and sensitivity analysis of the k-epsilon turbulence model closure coefficients for the prediction of cavitating and non-cavitating flows around the NACA66(MOD) hydrofoil and the PPTC propeller

The following Thesis presents the Uncertainty quantification and Sensitivity Analysis of the $k \varepsilon$ turbulence model applied to the numerical prediction of the cavitating and non-cavitating flows around the NACA66(MOD) hydrofoil and the PPTC (Potsdam Propeller Test Case) marine propeller. The turbulence model parameters are treated as epistemic uncertain variables, and the forward propagation of uncertainty is evaluated by using the Non-Intrusive Polynomial Chaos and the Polynomial Chaos-based Kriging approaches. The required simulations are performed by using a commercial CFD solver, namely the Simcenter Star CCM+. The Sobol indices are used to rank the relative contribution of closure coefficients to the total uncertainty in the output quantities. For the NACA66(MOD) hydrofoil, the ranking of the model parameters seems to be unaffected by the presence of the sheet cavity flow, while it varies with respect to the considered output quantity. Comparing the results of Polynomial Chaos and Polynomial Chaos Kriging, the Polynomial Chaos Kriging seems to be better performance than the Polynomial Chaos Expansion in terms of predictability when the DOE (Design OF Experiment) is composed by a set of few points. Instead, the both models have shown a similar predictability for a DOE of many points. For the PPTC propeller, the ranking of the model parameters seems to be affected by the presence of the sheet cavity flow. The ranking varies by varying the output of interest and comparing the results of Polynomial Chaos Expansion and Polynomial Chaos-based Kriging, as for the NACA66(MOD) hydrofoil, the Polynomial Chaos Kriging shows a lower prediction error than the Polynomial Chaos. In conclusion, a direct correlation between the ranking of coefficients of NACA66(MOD) and PPTC seems to not be present.

The following Thesis presents the Uncertainty quantification and Sensitivity Analysis of the $k \varepsilon$ turbulence model applied to the numerical prediction of the cavitating and non-cavitating flows around the NACA66(MOD) hydrofoil and the PPTC (Potsdam Propeller Test Case) marine propeller. The turbulence model parameters are treated as epistemic uncertain variables, and the forward propagation of uncertainty is evaluated by using the Non-Intrusive Polynomial Chaos and the Polynomial Chaos-based Kriging approaches. The required simulations are performed by using a commercial CFD solver, namely the Simcenter Star CCM+. The Sobol indices are used to rank the relative contribution of closure coefficients to the total uncertainty in the output quantities. For the NACA66(MOD) hydrofoil, the ranking of the model parameters seems to be unaffected by the presence of the sheet cavity flow, while it varies with respect to the considered output quantity. Comparing the results of Polynomial Chaos and Polynomial Chaos Kriging, the Polynomial Chaos Kriging seems to be better performance than the Polynomial Chaos Expansion in terms of predictability when the DOE (Design OF Experiment) is composed by a set of few points. Instead, the both models have shown a similar predictability for a DOE of many points. For the PPTC propeller, the ranking of the model parameters seems to be affected by the presence of the sheet cavity flow. The ranking varies by varying the output of interest and comparing the results of Polynomial Chaos Expansion and Polynomial Chaos-based Kriging, as for the NACA66(MOD) hydrofoil, the Polynomial Chaos Kriging shows a lower prediction error than the Polynomial Chaos. In conclusion, a direct correlation between the ranking of coefficients of NACA66(MOD) and PPTC seems to not be present.