Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Abstract

Abstract Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier–Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k − ϵ RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k − ϵ turbulence model are calibrated among the five coefficients ( C μ , C ϵ 1 , C ϵ 2 , σ ϵ and σ k ). The Bayesian inference technique using the Metropolis–Hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x / h = 2 and x / h = 4 , along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k − ϵ turbulence model (baseline). The deviation of calibrated C µ is almost 50%–60% from baseline and for C ϵ 1 and C ϵ 2 it is 3%–12% and 6%–9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.