A new tip correction for actuator line computations

Abstract

The actuator line method (ALM) is today widely used to represent wind turbine loadings in computational fluid dynamics (CFD). As opposed to resolving the whole blade geometry, the methodology does not require geometry-fitted meshes, which makes it fast to apply. In ALM, tabulated airfoil data are used to determine the local blade loadings, which subsequently are projected to the CFD grid using a Gaussian smearing function. To achieve accurate blade loadings at the tip regions of the blades, the width of the projection function needs to be narrower than the local chord lengths, requiring CFD grids that are much finer than what is actually needed in order to resolve the energy containing turbulent structures of the atmospheric boundary layer (ABL). On the other hand, employing large widths of the projection function may result in too large tip loadings. Therefore, the number of grid points required to resolve the blade and the width of the projection function have to be restricted to certain minimum values if unphysical corrections are to be avoided. In this paper, we investigate the cause of the overestimated tip loadings when using coarse CFD grids and, based on this, introduce a simple and physical consistent correction technique to rectify the problem. To validate the new correction, it is first applied on a planar wing where results are compared with the lifting-line technique. Next, the NREL 5-MW and Phase VI turbines are employed to test the correction on rotors. Here, the resulting blade loadings are compared with results from the blade-element momentum (BEM) method. In both cases, it is found that the new correction greatly improves the results for both normal and tangential loads and that it is possible to obtain accurate results even when using a very coarse blade resolution. KEYWORDSactuator line, LES of wind turbines, tip correction, wind turbine blade loadings INTRODUCTIONThe actuator line method (ALM) was developed as a numerical technique to facilitate the representation of the rotor blades in computational fluid dynamics (CFD) simulations of wind turbines. 1 The ALM is based on a blade-element approach in which body forces are introduced in the Navier-Stokes equations along lines representing the blades of the wind turbine. It was originally developed for simulating the wake behind a single horizontal axis wind turbine, 1-4 and has later been extended to simulate flows in wind farms, 5-12 and applied to vertical axis wind turbines, 13,14 tidal turbines, 15-17 and helicopters. 18 For a review of the ALM and related methods, the reader is referred to Breton et al. 19 In the ALM, the body forces are obtained from tabulated airfoil data employing the local angle of attack along the blades as input. The local angle of attack is defined from the local relative velocity, which is determined at each time step while running a simulation. After having determined the local forces, they are projected from the lines representing the rotor blades to the CFD grid points. A main issue of the technique is that it ...

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

“…In this work in particular, for stability reasons, the relationship between the lift coefficient CL,i and the angle of attack is assumed to be linear, , = ⋅ 4. under-relaxation is applied, Γ , = Γ + ⋅ (Γ , − Γ ), with D = 0.05 [20] Steps 2-4 are repeated until the circulation error Γ , − Γ is reduced below a certain tolerance, here taken as 10 -3 . It must be noted that the procedure described so far, in contrast with the original work of Dağ and Sørensen [9], does not account for the contribution of the vorticity shed in the wake. For Darrieus machines in fact, the vortex lines shed by the blades tend to self-intersect as the wake develops downstream, making the evaluation of the corresponding induced velocity extremely challenging.…”

“…Dağ-Sørensen (DS) correction. The Dağ-Sørensen correction is based on the observation that, when using an isotropic Gaussian smearing function, the insertion of ALM forces has the same effect on the local flow field of a Lamb-Oseen vortex with a viscous radius equal to the force projection width β [9]. The same vorticity pattern is propagated to the vortex sheet developing in the airfoil wake, which is responsible for the downwash effect commonly associated to tip vortexes.…”

“…Although effective, both methodologies require case-specific tuning and finer grids than the baseline ALM. In order to overcome the stricter mesh requirements associated to the direct ALM simulation of tip vortexes and minimize the dependence on the kernel width value, researchers at the National Renewable Energy Laboratory (NREL) [8] and Danmarks Tekniske Universitet (DTU) [9,10] recently introduced a novel hybrid tip loss model. The latter makes use of LLT to compute the contribution to the downwash induced by tip vortexes, which is lost in the ALM due to the characteristic smearing of the blade forces in the computational domain, yielding accurate results without increasing the approach set-up and computational effort.…”

“…ALM simulations were first performed without any correction (baseline) 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 for tip losses [13] and a new methodology recently proposed by Dağ and Sørensen (DS) for HAWTs [9] and here adapted to VAWTs. Eventually, the blade spanwise load profiles coming from the three methods were compared.…”

Development and Validation of an Advanced Actuator Line Model for Wind Turbines

“…It must be noted how, since the ALM already resolves the full three dimensional flow field around the actuator line, the use of a tip loss correction might seem redundant. In many studies [17][18][19] however, it has been observed how the base ALM formulation alone is unable to account for this effect, probably because of the use of the regularization kernel to insert the volume forces into the domain. Therefore, its adoption is justified in this work.…”