Data-driven turbulence modeling for fluid flow and heat transfer in peripheral subchannels of a rod bundle

Abstract

This study presents a comparison of the performance of machine learning (ML) techniques, specifically multi-dimensional gene expression programming (MGEP), tensor basis neural network (TBNN), and also proposes a novel universally interpretable machine learning architecture to model the turbulent scalar flux (UIML-s) to enhance turbulence models for fluid flows at different Prandtl numbers in channels with complex shapes of walls in the channel cross section. In particular, peripheral subchannels of rod bundles are of primary interest. However, the accuracy of mean velocity and scalar distributions predicted by commonly used turbulence models still poses a challenge compared to data extracted from high-fidelity eddy-resolving numerical simulations, particularly for engineering applications involving complex geometry flows. In the present study, by utilizing an explicit algebraic expression for the nonlinear Reynolds-stress term obtained through both the evolutionary MGEP optimization and TBNN, the secondary flow structure has been adequately predicted in the cross-wise mean velocity distributions in the square duct and the rectangular channel with three longitudinal rods. This structure is also observed in the data from the concurrent runs performed by direct numerical simulation (DNS) but is completely absent in the results produced by a baseline Reynolds-averaged Navier–Stokes (RANS) closure, which employs the linear eddy viscosity model for the Reynolds stress tensor. Comparison of MGEP and TBNN has shown their nearly equal performance in a square duct flow; however, MGEP works better for the more complex geometry channel with three rods. Furthermore, based on the velocity field produced by the RANS-MGEP model, the ML modification of the gradient diffusion hypothesis, integrated into the aforementioned novel RANS-ML model called as UIML-s, significantly improves the mean scalar distributions in a flow with three bumps serving as a prototype for the peripheral subchannel of rod bundle. The normalized root mean squared error decreases from 13.5% to 7.6%, bringing the predicted distributions closer to the DNS data, particularly in the near-wall region. Another approach, MGEP-s, also yields the acceptable results, which are nearly identical to those from UIML-s. These findings highlight the potential of using data-driven calibration of turbulence models with nonlinear closures to enhance the predictability for RANS simulations of fluid flows, heat, and mass transfer in channels with complex geometry.