Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

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

doi:10.1115/1.4037557

Title: Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study

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Abstract

In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscosity model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of itsmore »« less

Authors:

Ray, Jaideep ^[1]; Lefantzi, Sophia ^[1]; Arunajatesan, Srinivasan ^[2]; Dechant, Lawrence ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Thu Sep 07 00:00:00 EDT 2017

Research Org.:: Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

OSTI Identifier:: 1399494

Report Number(s):: SAND2017-2412J
Journal ID: ISSN 2332-9017; 651471

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering

Additional Journal Information:: Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2332-9017

Publisher:: American Society of Mechanical Engineers

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; eddies (fluid dynamics); viscosity; simulation; shrinkage (materials); vorticity; calibration; Reynolds-averaged Navier-Stokes equations; flow (dynamics); errors; turbulence

Citation Formats


                    Ray, Jaideep, Lefantzi, Sophia, Arunajatesan, Srinivasan, and Dechant, Lawrence. Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study.  United States: N. p., 2017. 
Web.  doi:10.1115/1.4037557.

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                    Ray, Jaideep, Lefantzi, Sophia, Arunajatesan, Srinivasan, & Dechant, Lawrence. Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study.  United States.  https://doi.org/10.1115/1.4037557

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                    Ray, Jaideep, Lefantzi, Sophia, Arunajatesan, Srinivasan, and Dechant, Lawrence. Thu .  
"Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study".  United States.  https://doi.org/10.1115/1.4037557.  https://www.osti.gov/servlets/purl/1399494.

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@article{osti_1399494,

  title        = {Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A Jet-in-Crossflow Case Study},

  author       = {Ray, Jaideep and Lefantzi, Sophia and Arunajatesan, Srinivasan and Dechant, Lawrence},

  abstractNote = {In this paper, we demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynolds-averaged Navier–Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscosity model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models (“curve-fits”). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. Finally, we find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.},

  doi          = {10.1115/1.4037557},

  journal      = {ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering},

  number       = 1,

  volume       = 4,

  place        = {United States},

  year         = {Thu Sep 07 00:00:00 EDT 2017},

  month        = {Thu Sep 07 00:00:00 EDT 2017}

}

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