Assessing turbulence model budgets in supersonic rectangular jets using large Eddy simulations

Abstract

This work aims to identify the sources of inaccuracies in Reynolds Averaged Navier-Stokes (RANS) and discuss the areas of improvements to enhance the predictions rectangular supersonic jets using LES, particularly for potential core lengths, jet mixing, and turbulence anisotropy. Budgets are analyzed for Turbulent kinetic energy (TKE) and Reynolds stress in various RANS models for a non-axisymmetric supersonic jet using well-validated Large Eddy Simulations (LES) as reference database. Examined RANS closures include Boussinesq (BSQ) $k-\omega$ Shear Stress Transport (SST), quadratic $k-\omega$ SST (QCR), and Reynolds stress model (RSM). A term-to-term comparison of Turbulent Kinetic Energy (TKE) and Reynolds stress budgets between RANS and LES is presented. In two-equation RANS, production in the shear layer is balanced by dissipation, with minimal diffusion. Thus, the diffusion along the jet centerline in RANS is delayed, resulting in slower mixing and longer potential cores. Although QCR accounts for the Reynolds stress anisotropy, it does not bring significant improvement to the TKE budget, suggesting that TKE transport remains minimally affected by the constitutive relation. RSM reproduces Reynolds stress budget trends, for production and pressure strain acting as source and sink respectively. However, the reduction in pressure strain correlation with increasing convective Mach number, is not predicted well. Primary areas for RANS improvement are identified, emphasizing the need to move beyond linear RANS, towards directly capturing the stress-strain relationship.