Mechanism-Separated Closed-Form Transition Modeling via Field Inversion and Symbolic Regression

Abstract

Next-generation aircraft, rotorcraft, and wind turbines demand improved aerodynamic efficiency, making drag reduction a central design objective; in transition-sensitive configurations, the extent of laminar flow strongly affects viscous drag and performance. Accurate prediction of laminar-turbulent transition is therefore essential. Transport-equation-based transition models, however, increase computational cost and implementation complexity. Neural-network-based closures can be difficult to interpret and integrate into independent flow solvers, while a single compact correction trained on heterogeneous transition data may fail to preserve mechanism-specific behavior. This study develops a mechanism-separated transition model using field inversion and symbolic regression. The framework treats natural, crossflow, and separation-induced transition with separate correction branches and yields explicit, closed-form corrections to the Spalart-Allmaras production term, without additional transport equations or runtime neural-network inference. The closed-form model is implemented in an independent flow solver to assess implementation portability and is evaluated on canonical cases and complex three-dimensional configurations, including a natural-laminar-flow transport wing and a hovering rotor. Across the tested cases, the model captures the principal transition-front trends and associated aerodynamic-performance changes. For the hovering-rotor case, it requires about 55% of the wall-clock time of the comparable transport-equation transition model.