Uncertainty Quantification, Rare Events, and Mission Optimization: Stochastic Variations of Metal Temperature During a Transient

Gas turbines are designed to follow specific missions and the metal temperature is usually predicted with deterministic methods. However, in the real life, the mission is subjected to strong variations which can affect the thermal response of the components. This paper presents a stochastic analysis of the metal temperature variations during a gas turbine transient. A Monte Carlo method (MCM) with meta-model is used to evaluate the probability distribution of the stator disk temperature. The MCM is applied to a series of computational fluid dynamics (CFD) simulations of a stator well, whose geometry is modified according to the deformations predicted during the engine cycle by a coupled thermomechanical analysis of the metal components. It is shown that even considering a narrow band for the stochastic output, ±σ, the transient thermal gradients can be up to two orders of magnitude greater than those obtained with a standard deterministic analysis. Moreover, a small variation in the tail of the input probability density function (PDF), a rare event, can have serious consequences on the uncertainty level of the temperature. Rare events although inevitable they are not usually considered during the design phase. In this paper, it is shown for the first time that is possible to mitigate their effect, minimizing the maximum standard deviation induced by the tail of the input PDF. The mission optimization reduces the maximum standard deviation by 15% and the mean standard deviation of about 12%. The maximum thermal gradients are also reduced by 10%, although this was not the parameter used as the goal in the optimization study.