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.

Analysis of the fluctuations of a laser beam due to thermal turbulence

“…The good agreement of how experimental values with relevant literature substantiate our use of this technique and paves the ways for future research into the effects of perturbations (thermal or directional) on a propagating laser beam. The difficulty in fully classifying thermal turbulence effects is not limited to experimental work, recent works have shown this to be numerically challenging as well [24,25]. The results correspond to previous works in the field [20,21], even though the experimental technique is new.…”

Uncertainty quantification and race car aerodynamics

“…The model used in this paper has been fully validated in [7,5,14]. The code has been validated against Monte Carlo Simulations in several applications, from multi-physics problems [5] to turbulence closures uncertainty [14] and geometrical uncertainty [4].…”

“…The code has been validated against Monte Carlo Simulations in several applications, from multi-physics problems [5] to turbulence closures uncertainty [14] and geometrical uncertainty [4]. Table 1 shows the variations which were considered in this work and the number of simulations required to build the stochastic space: The Uncertainty Quantification comparison gives to the designer the probability to achieve higher downforce under random variations of the car position.…”

Stochastic Variation of the Aero-Thermal Flow Field in a Cooled High-Pressure Transonic Vane Configuration

“…An extensive review for such methods is available in Montomoli et al (2015). Carnevale et al (2013) applied a subclass of these methods (Probabilistic Collocation Methods, PCM) based on Hermite's polynomials, for heat transfer predictions for internal cooling devices. However, PCM techniques, such as all purely continuous polynomial expansions, are not suitable when a discontinuity is present in the system response.…”