Study of Free Vortex Wake Method With Curved Filament Correction

Lin, Yi. (State Key Laboratory of Ocean Engineering) | Duan, Lei (State Key Laboratory of Ocean Engineering) | Li, Ye (State Key Laboratory of Ocean Engineering)



In most of free vortex wake models (FVWMs), the induced velocity is computed by Biot-Savart law. But the details of velocity calculation are still incomplete in their self-integrated loss of adjacent segment's influence. Curved filament correction has already been studied to recover the FVWM in helicopter problems. In this work, an extended FVWM with the correction is developed intended to improve aerodynamic predictions of wind turbines. Numerical simulations are performed on ring vortices and practical modeling of flow state of both fixed and floating wind turbines. It has been shown that the newly-designed technique may generate higher fidelity.


Among multiple modeling methods in aerodynamics of wind turbines, vortex lattice method (VLM) with straight line segmentation have been commonly used. The trailing filaments generated by the blades are assumed to convect freely with material lines of concentrated vorticity in potential flow. Such force free motion is governed by the vortex transportation equation. The governing equation is a partial differential equation which can be solved by various numerical approximation with high-order accuracy in both time and space domain.

It has been studied that for the straight-line segmentation, the approximation of induced velocity is relatively accurate with respect to corresponding theoretical result with the exclusion of self-induced velocity. It means that the collocation points lie in nowhere in vicinity to the discrete vortex segments (Gupta and Leishman, 2005). When it comes to the case that collocation points are extremely close to the discrete segments, the self-induced velocities tend to be infinite. The solutions for this singularity can be eliminated by “cutoff’ process (Bhagwat and Leishman, 2001) and vortex core models (Leishman,2006). These solutions are initially introduced by core regularization to eliminate singularity of the collocation points or simply fulfill the physical mechanism. However, techniques with these processes are incomplete because they fail to add up the total induced velocity.