Compressibility corrections to extend a smooth local correlation-based transition model to transonic flows

This paper presents progress towards a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are developed and investigated to extend commonly used empirical correlations to transonic flight conditions while retaining their accuracy at low speeds. A compressibility correction for Tollmien-Schlichting instabilities is developed and applied to a smooth local correlation-based transition model and a stationary crossflow instability compressibility correction is included by adding a new crossflow source term function. Two- and three-dimensional transonic transition test cases demonstrate that the Tollmien-Schlichting compressibility correction produces substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications where the effects of flow compressibility are expected to be more significant, such as the NASA CRM-NLF wing-body configuration, while the crossflow compressibility correction prevents an inaccurate, upstream transition front. The compressibility corrections and modifications do not significantly affect the numerical behaviour of the model, which provides an efficient alternative to non-local and higher-fidelity approaches, and can be applied to other transport-equation-based transition models with low-speed empirical correlations without affecting their predictive capability in the incompressible regime.