Uncertainty Quantification of Hot Gas Ingestion for a Gas Turbine Nozzle Using Polynomial Chaos

One of the most critical parameters in the design process of cooled hot gas components, is the Back Flow Margin (BFM). This dimensionless parameter quantifies the margin to hot gas ingestion through a cooled component wall. A correct evaluation of this parameter is crucial in order to avoid component failure. In presence of combustion chambers that exhibit low pressure losses, BFM becomes one of the most restrictive requirements in the thermal design of cooled components. In this work, a conceptual BFM assessment of the first nozzle of an HP gas turbine is described. The component is subject to the highest thermal load; complex cooling systems are required to ensure an acceptable metal temperature and to match life time requirement. Due to manufacturing tolerances and fluid dynamic uncertainties, hot gas ingestion events are possible also for a nozzle that exhibits BFM higher than zero in nominal conditions, even if with a low probability. Here, the cooling scheme of the nozzle is modeled using an in-house fluid network tool that allows a quick and accurate computation of the equivalent cooling scheme and thus the occurrence of hot gas ingestion, corresponding to a negative flow rate in one of the cooling sub-models. However, as the probability of hot gas ingestion is rather small, an accurate estimation of this event based on the standard Monte Carlo method requires a huge number of runs. A more efficient estimation of this probability can be obtained using stochastic expansion methods, such as the Polynomial Chaos Expansion. Pseudospectral approximations based on either a tensor-product expansion or the Sparse Pseudospectral Approximation Method (SPAM) are used, in order to estimate the probability of hot gas ingestion and the sensitivity to random parameters. The results are compared with those coming from Monte Carlo method, showing the superior accuracy of the stochastic expansion methods.