Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al.(2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.Comment: 40 page

Numerical and experimental investigation of a new film cooling geometry with high P/D ratio

In order to improve the coolant surface coverage, in the past years new geometries have been proposed with higher lateral fan-shaped angle and/or greater inter-hole pitch distance (P/D). Unfortunately it is not possible to increase the fan angle or the pitch distance even further without inducing a coolant separation and a drop in the overall effectiveness. This study proposes an innovative design which improves the lateral coverage and reduces the jet lift off. The results have been validated by a combination of numerical and experimental analyses: the experimental work has been assessed on a flat plate using thermo chromic liquid crystals and the results have been confirmed numerically by the CFD with the same conditions. The CFD simulations have been carried out considering a stochastic distribution for the free stream Mach number and the coolant blowing ratio. The experimental and computational results show that the inducing lateral pressure gradients there is a minimum increase in lateral averaged adiabatic effectiveness of +30% than the baseline case until a distance downstream of 20 times the coolant diameter. © 2013 Elsevier Ltd. All rights reserved

Quantification of airfoil geometry-induced aerodynamic uncertainties - comparison of approaches

Uncertainty quantification in aerodynamic simulations calls for efficient numerical methods since it is computationally expensive, especially for the uncertainties caused by random geometry variations which involve a large number of variables. This paper compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry which is parameterized by 9 independent Gaussian variables. The results show that gradient-enhanced surrogate methods achieve better accuracy than direct integration methods with the same computational cost

Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport. An approach based on non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected by any number of high-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability of the multifidelity polynomial chaos approach, two model problems were explored. The first was supersonic airfoil with three levels of modeling fidelity, each capturing an additional level of physics. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Both problems illustrate the applicability and significant computational savings of the multifidelity polynomial chaos method

Quantification of uncertainty in aerodynamic heating of a reentry vehicle due to uncertain wall and freestream conditions

The primary focus of this study is to demonstrate an efficient approach for uncertainty quantification of surface heat flux to the spherical non-ablating heatshield of a generic reentry vehicle due to epistemic and aleatory uncertainties that may exist in various parameters used in the numerical solution of hypersonic, viscous, laminar blunt-body flows with thermo-chemical non-equilibrium. Two main uncertainty sources were treated in the computational fluid dynamics (CFD) simulations: (1) aleatory uncertainty in the freestream velocity and (2) epistemic uncertainty in the recombination efficiency for a partially catalytic wall boundary condition. The Second-Order Probability utilizing a stochastic response surface obtained with Point-Collocation Non-Intrusive Polynomial Chaos was used for the propagation of mixed (aleatory and epistemic) uncertainties. The uncertainty quantication approach was validated on a stochastic model problem with mixed uncertainties for the prediction of stagnation point heat transfer with Fay-Riddell relation, which included the comparison with direct Monte Carlo sampling results. In the stochastic CFD problem, the uncertainty in surface heat transfer was obtained in terms of intervals at different probability levels at various locations including the stagnation point and the shoulder region. The mixed uncertainty results were compared to the results obtained with a purely aleatory uncertainty analysis to show the difference between two uncertainty quantication approaches. A global sensitivity analysis indicated that the velocity has a stronger contribution to the overall uncertainty in the stagnation point heat transfer for the range of input uncertainties considered in this study --Abstract, page iii

Development of Methods for Uncertainty Quantification in CFD Applied to Wind Turbine Wake Prediction

The CFD 2030 vision aims to improve computer simulations of fluid dynamics in fields like aerospace and energy. They focus on managing uncertainties in these simulations. This study presents two methods:1. Intrusive Polynomial Chaos (IPC) Stochastic Solver: This method employs Polynomial Chaos expansion to tackle uncertainties linked to fluid flow simulations. It characterizes parametric uncertainties, studying their nonlinear effects. The solver is tested on various scenarios, showing its promise for reliable Uncertainty Quantification (UQ) analysis in CFD without being overly intrusive or costly.2. Surrogate Based Uncertainty Quantification (SBUQ) using Deep Learning: A novel approach involves constructing a surrogate model using a neural network, capable of predicting wind flow within a wind farm based on single wind turbine data. This model is used to assess uncertainty in wind farm predictions, accounting for parameter and model form uncertainties.These techniques were tested on different scenarios and demonstrated their capability to analyze complex CFD simulations under various uncertainties. They contribute to the potential of enhancing accuracy and efficiency in UQ analysis. The IPC-based stochastic solver integrates efficiently with existing code, while the SBUQ approach utilizes data from individual wind turbine simulations to predict flow patterns in wind farms.Both methods enhance the accuracy of fluid simulations under different uncertainties. This research contributes to more dependable simulations for aerospace, energy, and environmental engineering applications