Non-iterative vortex-based smearing correction for the actuator line method

Abstract

The actuator line method (ALM) is used extensively in wind turbine and rotor simulations. However, its original uncorrected formulation overestimates the forces near the tip of the blades and does not reproduce well forces on translating wings. The recently proposed vortex-based smearing correction for the ALM is a correction based on physical and mathematical properties of the simulation that allows for a more accurate and general ALM. So far, to correct the forces on the blades, the smearing correction depended on an iterative process at every time step, which is usually slower, less stable and less deterministic than direct methods. In this work, a non-iterative process is proposed and validated. First, we propose a formulation of the nonlinear lifting line that is equivalent to the ALM with smearing correction, showing that the results are practically identical for a translating wing. Then, by linearizing the lifting line method, the iterative process of the correction is substituted by the direct solution of a small linear system. No significant difference is observed in the results of the iterative and non-iterative corrections, in both wing and rotor simulations. Additional contributions of the present work include the use of a more accurate approximation for the velocity induced by a smeared vortex segment and the implementation of a free-vortex wake model to define the vortex sheet, which contribute to the accuracy and generality of the method. The results presented here may motivate the adoption of the ALM by other communities, for example, in fixed-wing applications.

Investigation of blade flexibility effects over the loads and wake of a 15 MW wind turbine using a flexible actuator line method

“…However, this accuracy is often questioned, especially at the blade tip, mostly due to the regularization of the forces that reduces the induced velocity. To mitigate this issue, it is either possible to use tip corrections (see (Dag and Sørensen, 2020;Meyer Forsting et al, 2019;Martínez-Tossas and Meneveau, 2019;Kleine et al, 2023)) or to use regularization kernels that lead to a more accurate prediction of the forces (Caprace et al, 2019;Jha and Schmitz, 2018). The second approach is used here, by using the 2D Gaussian regularization for both the evaluation of the effective velocity and the forces distribution.…”

The effective velocity model: An improved approach to velocity sampling in actuator line models

“…The subfilter-scale velocity correction presented in Martínez-Tossas and Meneveau 10 and shortly introduced in Section 1.3 can also be seen as a variant of a vortexbased correction. Kleine et al 17 observed that these methodologies introduce an error dependent on the difference of circulation between time steps and on the weighting/relaxation factors used.…”

Combination of Advanced Actuator Line/Disk Model and High-Order Unstructured Finite Volume Solver for Helicopter Rotors

“…However, it may exhibit numerical instability near the blade tip and present difficulties when extending to the ADM. Although vortex-based correction has recently been devised [17], its demanding assumptions and intricate computing techniques make it unsuitable for extension to rotor computations. Additionally, a filtered ALM [18] was first used in fixed-wing applications and has been expanded to wind turbine simulations, using a finite difference methodology.…”