New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

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This paper presents a new dynamic inflow model for vertical-axis wind turbines (VAWTs). The model uses the principle of Duhamel's integral. The indicial function of the inflow-and crossflow-induction required to apply Duhamel's integral is represented by an exponential function depending on the thrust coefficient and the azimuthal position. The parameters of this approximation are calibrated using a free wake vortex model. The model is compared with the results of a vortex model and higher fidelity computational fluid dynamic (CFD) simulations for the response of an actuator cylinder to a step input of the thrust and to a cyclic thrust. It is found that the discrepancies of the dynamic inflow model increase with increasing reduced frequency and baseline thrust. However, the deviations remain small. Analysing the application of a finite-bladed floating VAWT with non-uniform loading and validating it against actuator line CFD results that intrinsically include dynamic inflow shows that the new dynamic inflow model significantly outperforms the Larsen and Madsen model (which is the current standard in fully coupled VAWT models) and enhances the modelling of VAWTs.

normalΦ

, are described by Equation .…”

Section: The Derivation Of a New Dynamic Inflow Modelsupporting

confidence: 82%

“…The development of the model is based on the methodology presented by Yu et al and is using the principle of Duhamel's integral. The indicial response functions of the

x

‐ and

y

‐induction, required to be able to apply Duhamel's equation, are determined using a three‐step process.…”

Section: Resultsmentioning

confidence: 99%

Section: The Derivation Of a New Dynamic Inflow Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new dynamic inflow model for vertical‐axis wind turbines

Tavernier

Ferreira

2020

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“…The model was later extended to yawed conditions 7 . The formulae of the vortex cylinder model were, for instance, applied by Medici et al to assess the velocity deficit on the axis upstream of a turbine 8 and applied to study different aspects of aerodynamics, such as dynamics inflow models, 9,10 far‐wake models, 11‐13 kite aerodynamics, 14 actuator surface methods, 15 or regularized actuator disks 16 …”

Section: Introductionmentioning

confidence: 99%

Assessing the blockage effect of wind turbines and wind farms using an analytical vortex model

Branlard

Forsting

2020

Wind farm blockage effects are currently neglected in the prediction of wind farm energy yield, typically leading to an overestimation of the production. This work presents a novel method to assess wind farm production, while accounting for blockage effects. We apply a vortex model, based on a cylindrical wake, to assess induction effects. We present variations of the model to account for finite wake length, finite tip-speed ratios, and the proximity to the ground. The results are applied to single rotors in aligned and yawed conditions and to different wind farm layouts. We provide far-field approximations for faster estimates of the velocity field. Further, this article includes a new methodology to couple the induction model to engineering wake models, such as the ones present in the FLOw Redirection and Induction in Steady State (FLORIS). We compare the results to actuator disk simulations for various operating conditions of a single turbine and different wind farm layouts. We found that the mean relative error of the model in the induction zone is typically around 0.2% compared with actuator disk simulations. The computational time of the velocity field using the analytical vortex model is three orders of magnitude less than the one obtained with the actuator disk simulation.

Rotor‐integrated modeling of wind turbine aerodynamics

Chabaud

2021

A novel approach for the modeling of rotor‐integrated aerodynamic loads is suggested to answer the need for a comprehensive, insightful, and analytical actuator disc model. All the six degrees of freedom (including tangential components) are considered. It is shown that loads may be written as a quadratic form of a reduced six‐component velocity vector at the hub. The individual contributions of lift and drag, azimuthal variations, as well as blade pitching and tip losses are isolated. Errors introduced by the necessary approximations are discussed, and parametric corrections are considered. Parameter identification methods are then suggested, and the performance of the resulting calibrated analytical models is assessed. Results show that the new modeling approach is able to accurately model both the mean values of the thrust and power coefficients and their derivatives with respect to tip‐speed ratio and pitch angle across the full range of operating wind speeds. Furthermore, it is able to reconstruct the general rotor behavior with a minimal amount of information available. Tangential components are also well modeled, although they require the knowledge of airfoil properties. The model's architecture leaves room for extensions to dynamic flow, skewed flow, and azimuthal load variations.