Bayesian estimates of parameter variability in the k-ε turbulence model

Authors:
W. N. Edeling;P. Cinnella;R. P. Dwight;H. Bijl
Affiliations:
ENSAM ParisTech, DynFluid laboratory, 151 Boulevard de lHospital, 75013 Paris, France and Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft, The Netherlands;ENSAM ParisTech, DynFluid laboratory, 151 Boulevard de lHospital, 75013 Paris, France;Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft, The Netherlands;Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, Delft, The Netherlands
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

In this paper we are concerned with obtaining estimates for the error in Reynolds-averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k-@e turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coefficients, for wall-bounded flows at a variety of favorable and adverse pressure gradients. In order to estimate the spread of closure coefficients which reproduces these flows accurately, we perform 13 separate Bayesian calibrations - each at a different pressure gradient - using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model-inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the total solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncertainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.