Machine-Learning-Enhanced Four-Equation Model for Predicting Roughness-Induced Transition

Surface roughness significantly influences flow behavior across natural phenomena and engineering applications. Accurate prediction of these effects is essential for engineering design, yet modeling roughness-induced transition remains challenging due to the intricate interactions among surface roughness, boundary-layer development, and laminar separation. This study develops a novel machine-learning-enhanced [Formula: see text] transition model by introducing a transport equation for the roughness amplification factor [Formula: see text]. The key correction function associated with [Formula: see text] is explicitly derived using a multicase, computational-fluid-dynamics-driven machine-learning framework. The proposed model is assessed on canonical flat-plate boundary layers, airfoils, and turbine cascades under diverse flow conditions. Results demonstrate that the model effectively captures boundary-layer transition influenced by surface roughness and flow separation, achieving good agreement with both experimental and direct numerical simulation data. Further analysis reveals that [Formula: see text] plays a critical role in amplifying disturbances and promoting earlier transition onset. Overall, the present machine-learning framework provides a promising pathway for extending traditional RANS transition models to incorporate complex physical effects.