Epistemic uncertainties in RANS model free coefficients
Résumé
The epistemic uncertainty in the free coefficients of two popular Reynolds-averaged Navier–Stokes (RANS) eddy-viscosity turbulence models is quantified. In particular, the Launder–Sharma low-Reynolds K-εK-ε and the Menter K-ωK-ω SST models are considered. The free coefficients present in turbulence models are retrieved from some properties of benchmark turbulent flows, viz. the energy power law exponent for decaying homogeneous isotropic turbulence, the value of the Von Karman constant, the turbulence production over dissipation rate estimated in the asymptotic regime of a homogeneous shear flow and the dimensionless turbulent kinetic energy in the logarithmic layer. The values presented in literature for these quantities, obtained from experiments or direct numerical simulations (DNS), show a significant dispersion, indicating the presence of an epistemic uncertainty. Starting from the data collected in literature, realistic continuous probability density functions of the basic flow properties, and hence of the RANS model coefficients, are obtained through generalized Polynomial Chaos (gPC). The impact of this uncertainty on the results of RANS simulations of the turbulent channel flow is then investigated for different Reynolds numbers through comparison with DNS data. The solution over the continuous multi-dimensional uncertainty space of the considered random variables is reconstructed through the application of a surrogate model (response surface) obtained by means of gPC. In general, the predictions of the K-ωK-ω SST model are less sensitive to the uncertainty in the model parameters than those of the low-Reynolds K-εK-ε model. For both models and for any combination of the coefficients, the predictions of the turbulent kinetic energy profile are not satisfactory, while low errors can be obtained for friction and mean velocity. Evaluation of optimal values of free parameters is a Data Assimilation (DA) problem. An example of the use of the gPC response surface for an efficient calibration of the model coefficients in order to minimize the error in the prediction of these two last variables is provided. The result accuracy estimated through the gPC surrogate model well agrees with that obtained in deterministic simulations carried out with the calibrated values of the model constants.