Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A JetinCrossflow Case Study
Abstract
In this paper, we demonstrate a statistical procedure for learning a highorder eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynoldsaveraged Navier–Stokes (RANS) simulator. The method is tested in a threedimensional (3D), transonic jetincrossflow (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 (“curvefits”). 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 »
 Authors:

 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLCA), Livermore, CA (United States); Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA10)
 OSTI Identifier:
 1399494
 Report Number(s):
 SAND20172412J
Journal ID: ISSN 23329017; 651471
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 ASCEASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering
 Additional Journal Information:
 Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 23329017
 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; Reynoldsaveraged NavierStokes 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 JetinCrossflow Case Study. United States: N. p., 2017.
Web. doi:10.1115/1.4037557.
Ray, Jaideep, Lefantzi, Sophia, Arunajatesan, Srinivasan, & Dechant, Lawrence. Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A JetinCrossflow Case Study. United States. doi:10.1115/1.4037557.
Ray, Jaideep, Lefantzi, Sophia, Arunajatesan, Srinivasan, and Dechant, Lawrence. Thu .
"Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A JetinCrossflow Case Study". United States. doi:10.1115/1.4037557. https://www.osti.gov/servlets/purl/1399494.
@article{osti_1399494,
title = {Learning an Eddy Viscosity Model Using Shrinkage and Bayesian Calibration: A JetinCrossflow 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 highorder eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynoldsaveraged Navier–Stokes (RANS) simulator. The method is tested in a threedimensional (3D), transonic jetincrossflow (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 (“curvefits”). 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 = {ASCEASME Journal of Risk and Uncertainty in Engineering Systems. Part B. Mechanical Engineering},
number = 1,
volume = 4,
place = {United States},
year = {2017},
month = {9}
}