In computational fluid dynamics (CFD), it is possible to identify namely two uncertainties: epistemic, related to the turbulence model, and aleatoric, representing the random-unknown conditions such as the boundary values and or geometrical variations. In the field of epistemic uncertainty, large eddy simulation (LES and DES) is the state of the art in terms of turbulence closures to predict the heat transfer in internal channels. The problem is still unresolved for the stochastic variations and how to include these effects in the LES studies. In this paper, for the first time in literature, a stochastic approach is proposed to include these variations in LES. By using a classical uncertainty quantification approach, the probabilistic collocation method is coupled to numerical large eddy simulation (NLES) in a duct with pin fins. The Reynolds number has been chosen as a stochastic variable with a normal distribution. The Reynolds number is representative of the uncertainties associated with the operating conditions, i.e., velocity and density, and geometrical variations such as the pin fin diameter. This work shows that assuming a Gaussian distribution for the Reynolds number of ±25%, it is possible to define the probability to achieve a specified heat loading under stochastic conditions, which can affect the component life by more than 100%. The same method, applied to a steady RANS, generates a different level of uncertainty. New methods have been proposed based on the different level of aleatoric uncertainties which provides information on the epistemic uncertainty. This proves, for the first time, that the uncertainties related to the unknown conditions, aleatoric, and those related to the physical model, epistemic, are strongly interconnected. This result, which is idealized for this specific issue, can be extrapolated, and has direct consequences in uncertainty quantification science and not only in the gas turbine world.

This work shows an Uncertainty Quantification (UQ) study of film cooling with shock impingement. A numerical method is proposed to use high order polynomials for the reconstruction of the stochastic output, without the instabilities characteristic of UQ with shock dominated flows. At the same time it is shown that the region with highest uncertainty is driven by a complex flow physics involving shock–boundary layer interaction and the generation of tornado vortices that merge with kidney ones. High-pressure turbine stages are characterized by transonic conditions with the suction side of the nozzle affected by the shock shed by the trailing edge of the adjacent aerofoil. Due to manufacturing deviations and in service degradation the geometrical parameters, such as trailing edge thickness and hole diameter, are subjected to random variations, changing the shock location and the heat transfer loading on the stator nozzle. For these reasons an UQ methodology has been used in this study to model the interaction between the impinging shock and film cooling. The variability of the geometrical parameters has been represented with uniform probability distributions and the stochastic output is obtained using Probabilistic Collocation Method with Padè’s polynomials. Transonic flows are challenging in Uncertainty Quantification because a better reconstruction of the stochastic output can be achieved increasing the order of polynomials but higher order polynomials become unstable for the Runge’s phenomenon. This work proposes a method that allows the application of high order Padè’s polynomial without having instabilities in the stochastic output. The proposed methodology can be applied to other transonic configurations in gas turbines, requiring only a limited number of simulations to reconstruct the stochastic output. The results show that the maximum level of uncertainty is located downstream the region of interaction between shock and boundary layer. In particular the shock generates complex flow structures that develop into tornado vortices, highly dependent on the uncertainty input.

Conjugate heat transfer is gaining acceptance for predicting the thermal loading in high pressure nozzles. Despite the accuracy nowadays of numerical solvers, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution, or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high-pressure nozzle. The domain simulated is the high pressure nozzle of an F-type Mitsubishi Heavy Industries gas turbine. The complete coolant system is included: impingement, film, and trailing edge cooling. The stochastic variations are included by coupling uncertainty quantification methods and conjugate heat transfer. Two uncertainty quantification methods have been compared: a probabilistic collocation method (PCM) and a stochastic collocation method (SCM). The stochastic distribution of thermal barrier coating thickness, used in the simulations, has been measured at the midspan. A Gaussian distribution for the turbulence intensity and hot core location has been assumed. By using PCM and SCM, the probability to obtain a specific metal temperature at midspan is evaluated. The two methods predict the same distribution of temperature with a maximum difference of 0.6%, and the results are compared with the experimental data measured in the real engine. The experimental data are inside the uncertainty band associated to the CFD predictions. This work shows that one of the most important parameters affecting the metal temperature uncertainty is the pitch-wise location of the hot core. Assuming a probability distribution for this location, with a standard deviation of 1.7 deg, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is 1 order of magnitude less important.

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