Theoretical Modeling of Vertical-Axis Wind Turbine Wakes

Abstract

In this work, two different theoretical models for predicting the wind velocity downwind of an H-rotor vertical-axis wind turbine are presented. The first model uses mass conservation together with the momentum theory and assumes a top-hat distribution for the wind velocity deficit. The second model considers a two-dimensional Gaussian shape for the velocity defect and satisfies mass continuity and the momentum balance. Both approaches are consistent with the existing and widely-used theoretical wake models for horizontal-axis wind turbines and, thus, can be implemented in the current numerical codes utilized for optimization and real-time applications. To assess and compare the two proposed models, we use large eddy simulation as well as field measurement data of vertical-axis wind turbine wakes. The results show that, although both models are generally capable of predicting the velocity defect, the prediction from the Gaussian-based wake model is more accurate compared to the top-hat counterpart. This is mainly related to the consistency of the assumptions used in the Gaussian-based wake model with the physics of the turbulent wake development downwind of the turbine.

Theoretical modelling of the three-dimensional wake of vertical axis turbines

“…In Table 1 we present the values of the super-Gaussian wake model (19) parameters, which provided the lowest error in the velocity predictions, and wake recovery rates used in the Gaussian model. The computed root-mean-square error in the velocity predictions shown later in Section 4 varied less than 2% when decreasing or increasing the super-Gaussian model input parameters , , and by 20%, similarly to the sensitivity analysis presented in Abkar (2019) for a Gaussian model.…”

“…Whilst further improvement in cases 1a and 1b would be obtained tuning the super-Gaussian parameters, we aimed at building a consistent model with a given set of parameters that yields the best predictions for the six benchmarks together. A further advantage of our Gaussian model is that the proposed initial wake width (20) enables the calculation of the velocity field in all the wake region, overcoming the limitations from previous models (Abkar, 2019) that could not provide physical estimates in the near wake for ranges of values.

Figure 10.Evolution of the maximum normalised maximum velocity deficit in the streamwise direction for all cases analysed.

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“…In the case of VATs, there is still a need for developing analytical wake models that can describe and predict the three-dimensional field (Meneveau, 2019), as the wake is three-dimensional and scales with the VAT rotor's diameter and height, unlike HAT wakes that scales with the diameter. Current theoretical VAT wake models do not account for the uneven wake expansion over the horizontal and vertical planes (Figure 1), and represent its shape with standard Gaussian functions (Abkar & Dabiri, 2017;Abkar, 2019). To overcome these limitations, a super-Gaussian shape enables a more physically realistic description of the VAT wake velocity field compared to top-hat models that assume a uniform value across the wake or Gaussian models that fail to reproduce the elliptical shape (Blondel & Cathelain, 2020).…”

Initial Design Phase and Tender Designs of a Jacket Structure Converted into a Retrofitted Offshore Wind Turbine

“…Further investigations can be performed in a future work such as tubular joint design [22] and fatigue assessment [23,24]. The influence of a different wind turbine such as vertical axis wind turbines [25] and wind turbines in other environments [26,27] is also worth investigating.…”

Development of a parameterized reduced-order vertical-axis wind turbine wake model

“…Hesaveh et al (2017) recently developed an accurate wake model based on actuator line theory, LES, and Reynolds-averaged Navier-Stokes equations, but its computational cost makes it difficult for use in large-scale wind farm layout analysis and optimization. Simpler reduced-order wake models have also been proposed in the past few years that have even shown their ability to optimize wind farm layouts (Mendoza and Goude, 2017;Lam and Peng, 2017;Abkar, 2019), however, the models only predict velocity deficits in the streamwise direction. Unlike HAWTs, closely-spaced VAWT pairs have the potential to increase the overall power production, and a VAWT wake model must account for streamwise and crosswind induced velocities to model this power increase (Dabiri, 2011;Ning, 2016;Zanforlin and Nishino, 2016).…”