Bayesian calibration of a k-ε turbulence model for predictive jet-in-crossflow simulations

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; Dechant, Lawrence

doi:10.2514/6.2014-2085

Cited by 18 publications

(21 citation statements)

References 37 publications

(47 reference statements)

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“…This result is, of course, consistent with the 2-d wake/jet flow field 5 but is also valid for transverse jet near field behavior. The existence of two length and velocity scales describing near and far-field behavior of jet-in-crossflow has been described by several researchers 15 though clearly the farfield behavior dominates the jet trajectory behavior and is almost always described by the decay rates associated with equation 11 16,17 .…”

Section: A Self-similaritysupporting

confidence: 86%

“…al. 2,3,4,5 likely succeeds because it honors the underlying physics associated with the jet-in-crossflow problem. It also suggests that compressibility effects at these downstream locations are weak, since our incompressible formulation provides relatively good agreement with experimental data.…”

Section: A Rans Computational Study Utilizing Analytical Parametersmentioning

confidence: 96%

“…al. 2,3,4,5 has demonstrated significant improvement in predictive ability for a class of jet-incrossflow problems. This process requires significant input from high quality simulation and/or experimental measurement.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

Dechant

Ray

Lefantzi

et al. 2017

8th AIAA Theoretical Fluid Mechanics Conference

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Section: A Self-similaritysupporting

confidence: 86%

Section: A Rans Computational Study Utilizing Analytical Parametersmentioning

confidence: 96%

See 1 more Smart Citation

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

Dechant

Ray

Lefantzi

et al. 2017

8th AIAA Theoretical Fluid Mechanics Conference

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“…As a first step towards improving the predictive accuracy of RANS in JinC, we hypothesized that more relevant parameter values could obtained by calibrating to a strongly vortical flow. In our previous work [1], we tested this hypothesis by designing a Bayesian calibration technique to estimate 3 RANS parameters, C = (C µ ,C ε2 ,C ε1 ), from data from an incompressible, flow over a square cylinder (FOSC) experiment. The parameters were estimated as a 3D joint PDF (JPDF), capturing the uncertainty in the estimates due to limited data and the inherent shortcomings of RANS.…”

Section: Introductionmentioning

confidence: 99%

“…While our previous work showed the inadequacy of C nom and a way to overcome it, it nevertheless did not address whether k − ε models for JinC could be improved further. The prediction errors in [1] contained contributions from the structural error as well as parametric sub-optimality -recall that the joint PDF was obtained by calibrating to FOSC, not JinC, experimental data. In this work, we seek to isolate the impact of the structural error by calibrating to JinC experimental data.…”

Section: Introductionmentioning

confidence: 99%

Estimation of k-ε parameters using surrogate models and jet-in-crossflow data

Lefantzi

Ray

Arunajatesan

et al. 2014

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We demonstrate a Bayesian method that can be used to calibrate computationally expensive 3D RANS (Reynolds Averaged Navier Stokes) models with complex response surfaces. Such calibrations, conditioned on experimental data, can yield turbulence model parameters as probability density functions (PDF), concisely capturing the uncertainty in the parameter estimates. Methods such as Markov chain Monte Carlo (MCMC) estimate the PDF by sampling, with each sample requiring a run of the RANS model. Consequently a quick-running surrogate is used instead to the RANS simulator. The surrogate can be very difficult to design if the model's response i.e., the dependence of the calibration variable (the observable) on the parameter being estimated is complex. We show how the training data used to construct the surrogate can be employed to isolate a promising and physically realistic part of the parameter space, within which the response is well-behaved and easily modeled. We design a classifier, based on treed linear models, to model the "well-behaved region". This classifier serves as a prior in a Bayesian calibration study aimed at estimating 3 k − ε parameters (C µ ,C ε2 ,C ε1) from experimental data of a transonic jet-in-crossflow interaction. The robustness of the calibration is investigated by checking its predictions of variables not included in the calibration data. We also check the limit of applicability of the calibration by testing at off-calibration flow regimes. We find that calibration yield turbulence model parameters which predict the flowfield far better than when the nominal values of the parameters are used. Substantial improvements are still obtained when we use the calibrated RANS model to predict jet-in-crossflow at Mach numbers and jet strengths quite different from those used to generate the experimental (calibration) data. Thus the primary reason for poor predictive skill of RANS, when using nominal values of the turbulence model parameters, was parametric uncertainty, which was rectified by calibration. Post-calibration, the dominant contribution to model inaccuraries are due to the structural errors in RANS.

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Data-driven Bayesian inference of turbulence model closure coefficients incorporating epistemic uncertainty

et al. 2021

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We introduce a framework for statistical inference of the closure coefficients using machine learning methods. The objective of this framework is to quantify the epistemic uncertainty associated with the closure model by using experimental data via Bayesian statistics. The framework is tailored towards cases for which a limited amount of experimental data is available. It consists of two components. First, by treating all latent variables (non-observed variables) in the model as stochastic variables, all sources of uncertainty of the probabilistic closure model are quantified by a fully Bayesian approach. The probabilistic model is defined to consist of the closure coefficients as parameters and other parameters incorporating noise. Then, the uncertainty associated with the closure coefficients is extracted from the overall uncertainty by considering the noise being zero. The overall uncertainty is rigorously evaluated by using Markov-Chain Monte Carlo sampling assisted by surrogate models. We apply the framework to the Spalart–Allmars one-equation turbulence model. Two test cases are considered, including an industrially relevant full aircraft model at transonic flow conditions, the Airbus XRF1. Eventually, we demonstrate that epistemic uncertainties in the closure coefficients result into uncertainties in flow quantities of interest which are prominent around, and downstream, of the shock occurring over the XRF1 wing. This data-driven approach could help to enhance the predictive capabilities of computational fluid dynamics (CFD) in terms of reliable turbulence modeling at extremes of the flight envelope if measured data is available, which is important in the context of robust design and towards virtual aircraft certification. The plentiful amount of information about the uncertainties could also assist when it comes to estimating the influence of the measured data on the inferred model coefficients. Finally, the developed framework is flexible and can be applied to different test cases and to various turbulence models.

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Bayesian calibration of a k-ε turbulence model for predictive jet-in-crossflow simulations

Cited by 18 publications

References 37 publications

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution

Estimation of k-ε parameters using surrogate models and jet-in-crossflow data

Data-driven Bayesian inference of turbulence model closure coefficients incorporating epistemic uncertainty

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