Uncertainty Quantification: A Stochastic Method for Heat Transfer Prediction Using LES

Abstract

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.