Spanwise flow correction model for blade element theory considering geometric effects by symbolic regression

The finite span and twist of wind turbine blades induce spanwise flow, along with a tip vortex. Conventional blade element theory, rooted in a two-dimensional assumption, cannot capture these spanwise effects. However, most existing three-dimensional (3-D) corrections neglect intrinsic geometric effects leading to inaccuracies near the tip and in non-rotating cases. To address this, we propose the 3-D geometric effects model incorporating axial and radial velocity factors (3-DGAR model), a physically consistent correction to blade element momentum theory. The model captures two fundamental phenomena: downwash that modifies the local effective angle of attack and tip pressure loss driven by radial velocity transport. A coherent physical pathway from the tip vortex to load reduction is established: the spanwise flow transports energy from the tip element into the tip vortex, reducing suction-side velocity and thereby weakening suction at the equivalent angle of attack. Furthermore, symbolic regression is then used to determine two unknown velocity factors from limited experimental data, serving as closure terms. The model identifies the local aspect ratio as a key parameter governing downwash and reveals an exponential decay of tip-loss effects along the span. Validation across blades of varying geometries and operating conditions confirms accurate spanwise flow correction. The results establish a clear link between the correction factors and the underlying flow physics, thereby connecting aerodynamic predictions to flow mechanisms. Overall, the 3-DGAR model provides a functional mapping from geometric inputs to aerodynamic loads, ensuring broad applicability across diverse blade designs.