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

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 » 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.« less
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  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 2332-9017; 651471
Grant/Contract Number:
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
American Society of Mechanical Engineers
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) (NA-10)
Country of Publication:
United States
42 ENGINEERING; eddies (fluid dynamics); viscosity; simulation; shrinkage (materials); vorticity; calibration; Reynolds-averaged Navier-Stokes equations; flow (dynamics); errors; turbulence
OSTI Identifier: