Uncertainty quantification of the turbulent flow field and heat transfer of film cooling

In the present paper, Uncertainty Quantification (UQ) of the turbulent flow field and heat transfer of film cooling is investigated. For this end, two stochastic flow and heat transfer parameters, namely, the Reynolds number (Re) and the turbulent Prandtl number (Pr_t) with the uniform Probability Distribution Functions (PDFs), along with six stochastic film cooling parameters, namely, the blowing ratio (M), the density ratio (DR), the turbulent intensity and the length scales of mainstream and coolant flow (I_h,I_c,L_h,L_c) all with the Beta PDF are considered. To quantify uncertainty in different flow conditions, UQ analysis is firstly investigated in the low blowing ratio (i.e., M=0.5) and then in the high blowing ratio (i.e., M=2). The uncertainties are propagated in the turbulent flow field and heat transfer using the Non-Intrusive Polynomial Chaos Expansion (NIPCE) method with polynomial order p=3. The non-deterministic CFD results show that considering stochastic conditions yield to a significant effect on the film cooling effectiveness. In addition, among the considered random parameters, the uncertain variables of Re, DR and M mostly influence the cooling effectiveness. While the remaining of random parameters (i.e. I_h,I_c,L_h and L_c) show a negligible effect.