Database Approach for Laminar-Turbulent Transition Prediction: Navier-Stokes Compatible Reformulation

摘要

This paper presents a transition prediction model that adds additional equations to the Reynolds-averaged Navier-Stokes set. It is based on the so-called N-factor method, which is valid for natural transition on wings due to the hypothesis that it relies on (modal instabilities disturbing the boundary layer). It consists of an integration of the disturbance growth rates along the edge streamline. Herein, the disturbance growth rates are obtained via a database approach: ONERA-The French Aerospace Lab's so-called parabolas method. Numerically, integration of the growth rates along the edge streamline is performed through additional transport equations, thus removing the need for any topology specification from the end user. Implementation caveats are illustrated on the ONERA-D airfoil in incompressible conditions. This method is then successfully applied for transition prediction on a two-dimensional industrial laminar airfoil at transonic conditions, with varying upstream conditions and angles of attack. Satisfactory agreements with both the experimental data and the conventional transition predictions (local, linear stability results) are obtained, which illustrate the accuracy of the predicted transition location.