A Bi-Fidelity Approach for Uncertainty Quantification of Heat Transfer in a Rectangular Ribbed Channel

Abstract

This paper presents a bi-fidelity simulation approach to quantify the effect of uncertainty in the thermal boundary condition on the heat transfer in a ribbed channel. A numerical test case is designed where a random heat flux at the wall of a rectangular channel is applied to mimic the unknown temperature distribution in a realistic application. To predict the temperature distribution and the associated uncertainty over the channel wall, the fluid flow is simulated using 2D periodic steady Reynolds-Averaged Navier-Stokes (RANS) equations. The goal of this study is then to illustrate that the cost of propagating the heat flux uncertainty may be significantly reduced when two RANS models with different levels of fidelity, one low (cheap to simulate) and one high (expensive to evaluate), are used. The low-fidelity model is employed to learn a reduced basis and an interpolation rule that can be used, along with a small number of high-fidelity model evaluations, to approximate the high-fidelity solution at arbitrary samples of heat flux. Here, the low- and high-fidelity models are, respectively, the one-equation Spalart-Allmaras and the two-equation shear stress transport k–ω models. To further reduce the computational cost, the Spalart-Allmaras model is simulated on a coarser spatial grid and the non-linear solver is terminated prior to the solution convergence. It is illustrated that the proposed bi-fidelity strategy accurately approximates the target high-fidelity solution at randomly selected samples of the uncertain heat flux.