Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

Schaefer, John A.; Hosder, Serhat; West, Thomas K.; Rumsey, Christopher L.; Carlson, Jan-Reneé; Kleb, William L.

doi:10.2514/1.j054902

Cited by 89 publications

(48 citation statements)

References 37 publications

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“…A summary of Spalart-Allmaras closure coefficients to be varied and their associated epistemic intervals are reported in Table 1. The choice of the epistemic intervals, some of which differ slightly from [14], lies on empirical suggestions, physical constraints, and experimental evidence [1,14,21].…”

Section: Flow Solvermentioning

confidence: 99%

“…Similar to the approach in [13], we employ the generated response surface models to assess how the uncertainty characterizing the turbulence model coefficients impacts the values of the SSE metric. The latter provides a global quantification of the deviation occurring between experimental and numerical pressure coefficients along the section of the airfoil.…”

Section: Generation Of the Response Surface Modelmentioning

confidence: 99%

“…Reference [14] quantified the uncertainty and sensitivity of three turbulence models (Spalart-Allmaras, Wilcox k − , and Menter shear-stress transport models) due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows. The analysis was carried out using point-collocation nonintrusive polynomial chaos technique.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties

et al. 2019

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The solution of Reynolds-averaged Navier-Stokes equations employs an appropriate set of equations for the turbulence modelling. The closure coefficients of the turbulence model were calibrated using empiricism and arguments of dimensional analysis. These coefficients are considered universal, but there is no guarantee this property applies to test cases other than those used in the calibration process. This work aims at revisiting the calibration of the closure coefficients of the original Spalart-Allmaras turbulence model using machine learning, adaptive design of experiments and accessing a highperformance computing facility. The automated calibration procedure is carried out once for a transonic, wall-bounded flow around the RAE 2822 aerofoil. It was found that: (a) an optimal set of closure coefficients exists that minimises numerical deviations from experimental data; (b) the improved prediction accuracy of the calibrated turbulence model is consistent across different flow solvers; and (c) the calibrated turbulence model outperforms slightly the standard model in analysing complex flow features around additional test cases (ONERA M6 wing, axisymmetric transonic bump, forced sinusoidal motion of NACA 0012 aerofoil). A by-product of this study is a fully calibrated turbulence model that leverages on current state-of-the-art computational techniques, overcoming inherent limitations of the manual fine-tuning process.

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Section: Flow Solvermentioning

confidence: 99%

Section: Generation Of the Response Surface Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties

et al. 2019

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“…From the turbulence side, uncertainty associated to this modelling has been also matter of study in CFD. In [78], epistemic uncertanty from turbulence modelling for transonic wallbounded flows is under study in several problems with different eddy-viscosity models. Similarly, in [72] Probabilistic Collocation is employed to quantify uncertainty in CFD RANS simulations of a turbulent flat plate and an airfoil.…”

Section: Introductionmentioning

confidence: 99%

On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust

et al. 2019

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A classic approach to computational fluid dynamics is to perform simulations with a fixed set of variables in order to account for parameters and boundary conditions. However, experiments and real-life performance are subject to variability in their conditions. In recent years, the interest of performing simulations under uncertainty is increasing, but this is not yet a common rule, and simulations with lack of information are still taking place. This procedure could be missing details such as whether sources of uncertainty affect dramatic parts in the simulation of the flow. One of the reasons of avoiding to quantify uncertainties is that they usually require to run an unaffordable number of CFD simulations to develop the study. To face this problem, Non-Intrusive Uncertainty Quantification (UQ) has been applied to 3D Reynolds-Averaged Navier-Stokes simulations of an under-expanded jet from an aircraft exhaust with the Spalart-Allmaras turbulent model, in order to assess the impact of inaccuracies and quality in the simulation. To save a large number of computations, sparse grids are used to compute the integrals and built surrogates for UQ. Results show that some regions of the jet plume can be more sensitive than others to variance in both physical and turbulence model parameters. The Spalart-Allmaras turbulent model is demonstrated to have an accurate performance with respect to other turbulent models in RANS, LES and experimental data, and the contribution of a large variance in its parameter is analysed. This investigation explicitly outlines, exhibits and proves the details of the relationship between diverse sources of input uncertainty, the sensitivity of different quantities of interest to said uncertainties and the spatial distribution arising due to their propagation in the simulation of the high-speed jet flow. This analysis represents first numerical study that provides evidence for this heuristic observation.

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“…In their study, the measured velocity profiles of the synthetic jet actuator case could be enveloped by the 95% confidence interval. Another example is from Schaefer et al [15,16] and Stephanopoulos et al [17], where the non-intrusive polynomial chaos method was applied to investigate the parametric uncertainty of the SA model. The idea was to train a metamodel of RANS equations based on the response surface and then propagate the SA model coefficients with uniform PDFs through the metamodel.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Uncertainty Quantification of Spalart-Allmaras Turbulence Model for Compressors

He¹,

Zhao²,

Vahdati³

2019

Proceedings of Global Power &Amp; Propulsion Society

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Turbulence models in Reynolds-Averaged Navier-Stokes simulations have a crucial effect on the compressor stability boundary. In this paper, the parametric uncertainty of the Spalart-Allmaras turbulence model on compressor flows is quantified by a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the Reynolds stress distribution, the shock front location and pressure coefficient and the separation size. An artificial neural network from machine learning is applied as the metamodel, which is tuned, trained, and tested by databases from the flow solver to achieve an error below 1% of the database range. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the measured data of Reynolds stress profiles in separated regions, shock front location and pressure coefficient and shock-induced separation size cannot be well captured. Crucial model coefficients on the quantities of interest are identified by a sensitivity analysis. However, re-calibration of these coefficients is contradictory in different quantities of interest and flow regimes. It indicates the need for a modified Spalart-Allmaras turbulence model form to improve the accuracy in predicting compressor flows.

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Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

Cited by 89 publications

References 37 publications

Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties

Sensitivity and calibration of turbulence model in the presence of epistemic uncertainties

On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust

Machine Learning Uncertainty Quantification of Spalart-Allmaras Turbulence Model for Compressors

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