Uncertainty quantification and film cooling

In gas turbine cooling, hundreds of ducts are fed by common plenums connected to small channels. The inlet stagnation pressure, temperature and turbulence levels are unknown in the ducts and subjected to a strong variability, due to the uncertainty associated with operating conditions and/or manufacturing defects. Despite the uncertainty level in boundary values, it is a common practice to use deterministic values.In this work, a Monte Carlo Method Lattice Sampling (MCMLS) and a Probabilistic Collocation Method (PCM) are used to assess the uncertainty quantification problem in film cooling. By assuming truncated Gaussian distributions for the inlet total pressures, 242 CFD simulations have been performed for MCMLS and the probabilistic distribution of the adiabatic effectiveness is obtained. It provides the average value for the stochastic output and the level of confidence related to that value. The results show that about 20% variation in the stochastic inputs provides a variation of the adiabatic effectiveness of about 100%, and reduces the blade life by more than five times.The MCMLS is robust and accurate, less computational expensive than a standard MCM but still computationally expensive for everyday design. Therefore, using the MCMLS as baseline, an innovative technique has been proposed: the Probabilistic Collocation Method (PCM), in order to both reduce the number of simulations and obtain accurate results. The developed PCM methodology is 10 times faster than the MCMLS with negligible differences in the results. This work shows that in nowadays design, computational fluid dynamics must use stochastic methods and it is possible to integrate probabilistic analysis in the design phase to investigate the robustness by using PCM and MCMLS.

► We model a standard fan shaped hole for film cooling using CFD and RANS.
► We model the total inlet pressure for the coolant and the main stream as Gaussian inputs.
► We examine the impact of the stochastic inputs to the performance of the cooling hole.
► Probabilistic Collocation Method gives comparable results with Monte Carlo simulations.
► Uncertainty in the inputs gives up to five times reduction in life performance.