Systematic identification of missing physics in turbulence models

Different physical mechanisms, such as laminar effects, turbulence, mean-flow development and pressure gradients, contribute to drag in wall-bounded turbulent boundary layers (TBLs). Discrepancies in these contributions vary across different Reynolds averaged Navier-Stokes (RANS) models and identifying where these models deviate is information that can be used to diagnose and improve them. In this study, we present a method to systematically identify these errors associated with the flow physics that are not being captured by turbulence modeling. We extend the skin-friction (C_f) decomposition based on the angular momentum integral (AMI) equation, proposed by Elnahhas & Johnson (2022), to include three-dimensional effects and apply them to RANS models, namely the Menter’s k-ω SST, Spalart-Allmaras (SA), Chien’s k-ε and ω-based SSG-LRR Reynolds stress model (RSM). We first examine the zero-pressure gradient flat-plate TBL case for C_f contributions produced by these models against Direct Numerical Simulation (DNS) data available in literature. While all models predict C_f with reasonable accuracy, this is achieved by varying degrees of error cancellation. Errors in turbulent torque and total mean flux contributions are observed to be dominant across all models, exceeding 20% of C_f in some cases. Furthermore, we investigate these errors for a more complex case of TBL flow over a three-dimensional hill. Wall-resolved large eddy simulation (WRLES), with grid-resolution close to DNS, are performed for the BeVERLI hill geometry oriented at an angle of 30° with respect to the streamwise flow, for a hill-height based Reynolds number of Re_H = 14940. In this configuration, the dominant error term varies by model and can exceed beyond 10 times the local C_f , depending on where it is measured with respect to the hill.