Correlation for Transitional Reynolds Number and Assessment of RANS for Bypass Transition

Abstract

Abstract. Direct numerical simulations (DNSs) of bypass transition are performed for zero-pressure-gradient flat-plate boundary layers with inlet freestream turbulence intensity (FSTI) ranging from 0.75% to 6%. The DNS database exhibits excellent agreement with the Blasius solution in the laminar region, with deviation occurring only near transition onset, providing improved fidelity compared to previous computational studies. A novel skin-friction-based intermittency definition is proposed and validated against conventional temporal intermittency measurements, demonstrating equivalent transition prediction capability without requiring time-resolved data. Using this definition, a new transition Reynolds number correlation is developed that incorporates the effects of FSTI, turbulent length scales, and intermittency threshold. The correlation reduces to the classical Abu-Ghannam and Shaw formulation at zero intermittency and achieves 16.2% average error when validated against independent experimental data from Fransson and Shahinfar (2020). Reynolds-averaged Navier–Stokes (RANS) simulations using the k−ω shear-stress transport (SST) and γ−Reθ transition models reveal significant sensitivity to inlet length scale specification, with integral length scale predictions deviating from DNS in both pretransitional and transitional regions. The transported intermittency in RANS shows wall-normal-dependent transition onset that differs from the skin-friction-based definition. This comprehensive DNS database and associated correlations provide improved benchmarks for transition model development and validation.