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 Numerically determined empirical relationships for a transitional turbulence model Author(s): Gareth Erfort, Theodor von Backström, Gerhard Venter Keywords: Transitional turbulence model, optimization, NACA foil Turbulence models in computational fluid dynamics (CFD) aim to capture a complex phenomenon through simplified mathematical models. The models themselves range in terms of application, complexity and methodology. This work looked at a transitional model for Reynolds averaged Navier Stokes equations. In particular the focus was on the correlation based intermittency and momentum thickness Reynolds number ($\gamma$ - $\tilde{Re}_{\theta_t}$) model. The original model has high order correlations, that were determined and calibrated from flat plate tests of various pressure gradients. In this work the correlations were simplified to reduce the number of calibration coefficients and help in understanding the effect of each parameter. Flat plate test data, from the ERCOFTAC T3A series, were used to verify the lower order approximations through OpenFOAM simulations. The reduced order model was then applied to a NACA 0012 foil at a transitional Reynolds number of 340 000 as a means of validation. The reduced order, the original $\gamma$ - $\tilde{Re}_{\theta_t}$ and the fully turbulent k - omega shear stress transport ($k -\omega$~SST) turbulence models are compared over a range of angles of attack to highlight the difference between models.