A robust intermittency equation formulation for transition modeling in Spalart-Allmaras simulations of airfoil flows across a wide range of Reynolds numbers

TL;DR

This paper develops a robust intermittency equation formulation for transition modeling in Spalart-Allmaras simulations, improving numerical stability and applicability across various Reynolds numbers in airfoil flows.

Contribution

It introduces a stabilized logarithmic form of the intermittency equation and additional modifications to enhance robustness in RANS simulations with the SA model.

Findings

Effective stabilization of the $oldsymbol{eta}$ transport equation.

Consistent robustness across a wide Reynolds number range.

Improved simulation accuracy around airfoil transition regions.

Abstract

This paper introduces a new robust formulation for local correlation-based laminar-to-turbulent transition models. This mechanism is incorporated into Reynolds-Averaged Navier-Stokes (RANS) equations, coupled with the Spalart-Allmaras (SA) turbulence model, considering both $\gamma$ and $\gamma$-${\widetilde{\mathrm{Re}}_{\theta,t}}$ transition frameworks. In this context, special attention is placed on numerical stabilization of the $\gamma$ transport equation, which is identified as the root cause of instabilities observed in both $\gamma$ and $\gamma$-${\widetilde{\mathrm{Re}}_{\theta,t}}$ based models. To this end, the intermittency equation is reformulated in logarithmic form and further stabilized through an energy--based limiting to bound excessively high positive values. In order to suppress unphysical pressure oscillations in the transition region, a gradient-driven artificial viscosity is also introduced. Additionally, the SA equation is augmented with strain-rate modulated production and rotation correction terms. The presented approach has demonstrated consistent effectiveness and robustness in the simulation of flow fields around airfoils over a wide range of Reynolds numbers, making it suitable for practical aerodynamic design applications.