Simulating tip effects in vertical-axis wind turbines with the actuator line method

Abstract

Simulation of the complex, unsteady aerodynamics characterizing Darrieus rotors requires computational tools with a fidelity higher than the ubiquitous Blade Element Momentum (BEM) theory. Among them, the Actuator Line Method (ALM) stands out in terms of accuracy and computational cost. This approach, however, still fails to resolve the vortex-like structures shed at the blade ends, overestimating turbine performance at the higher rotational speeds. Moving from this background, in this study a comprehensive investigation on the ALM’s capability to simulate tip effects and their impact on rotor performance is carried out. To this end, the ALM tool developed by the authors in the ANSYS® FLUENT® environment (v. 20.2) and specifically tailored to the simulation of vertical-axis machines was employed. Both a steady finite wing and a fictitious one-blade Darrieus H-rotor, for which high-fidelity blade-resolved CFD data are available as benchmark, were considered as test cases. ALM simulations were first performed without any correction for different cell sizes and force projection radii, so that the limits of the original approach could be assessed. Then, two different sub-models were applied: the classical semi-empirical Glauert correction and a new methodology based on the Lifting Line Theory (LLT), which was recently proposed by Dağ and Sørensen (DS). The latter was here adapted to vertical-axis machines. Eventually, the blade spanwise load profiles coming from the three approaches were assessed and compared, proving the superior performance of the DS model.

Tuning the Actuator Line Method to Properly Modelling Tip Effects in Finite-Length Blades

“…The standard isotropic Gaussian kernel is used as projection function, using a β constant along the span and equal to 0.1c. This value ensures a correct description of the tip vortex core [12]. As observed in a previous study of the authors [11], this approach leads to two contrasting trends.…”

“…The k- Shear Stress Transport (SST) model is used for turbulence closure. Discretization schemes, computational domain, and grid derive from the optimal setup found in a previous work on the same test case [12]. Figure 1a illustrates the adopted computational domain, whose dimensions are selected to minimize blockage effects and allow the blade wake to properly develop.…”

“…This study builds on these findings to further investigate how the ALM base formulation -in terms of angle of attack (α) sampling and force insertion -can be tuned to effectively describe tip effects. To this end, an in-house ALM tool was employed to simulate a finite wing, for which high-fidelity bladeresolved CFD (BR-CFD) data are available as benchmark [12]. In the first part of the work, different sampling and force insertion strategies are compared for a fixed blade pitch angle of 6°.…”

Near-tip correction functions for the actuator line method to improve the predicted lift and drag distributions

“…This approach does not allow one to compare the effect of the mollification with that of the virtual camber effect. Melani, Balduzzi & Bianchini (2022) performed a comparison of both a fixed and rotating wing between ALM and wall-resolved Reynolds-averaged Navier–Stokes (RANS) simulations, and found that, although the correction was beneficial for the accuracy, the lift obtained using wall-resolved RANS simulations still differed from the ALM on the last 20 % of the blade, likely due to the virtual camber. Moreover, the corrections that require the use of a free-vortex wake model are not straightforward to apply, and increase the computational cost of the force evaluation.…”