Wake Flow Simulation of a Vertical Axis Wind Turbine Under the Influence of Wind Shear

The current trend of the wind energy industry aims for large scale turbines installed in wind farms. This brings a renewed interest in vertical axis wind turbines (VAWTs) since they have several advantages over the traditional Horizontal Axis Wind Tubines (HAWTs) for mitigating the new challenges. However, operating VAWTs are characterized by complex aerodynamics phenomena, presenting considerable challenges for modeling tools. An accurate and reliable simulation tool for predicting the interaction between the obtained wake of an operating VAWT and the flow in atmospheric open sites is fundamental for optimizing the design and location of wind energy facility projects. The present work studies the wake produced by a VAWT and how it is affected by the surface roughness of the terrain, without considering the effects of the ambient turbulence intensity. This study was carried out using an actuator line model (ALM), and it was implemented using the open-source CFD library OpenFOAM to solve the governing equations and to compute the resulting flow fields. An operational H-shaped VAWT model was tested, for which experimental activity has been performed at an open site north of Uppsala-Sweden. Different terrains with similar inflow velocities have been evaluated. Simulated velocity and vorticity of representative sections have been analyzed. Numerical results were validated using normal forces measurements, showing reasonable agreement.


Introduction
The amount of wind farms that are being built is increasing considerably, and it produces a relevant interest in the scientific community for the understanding of the interaction between the produced wake from the turbines and the atmospheric turbulent flow [1][2][3][4][5]. Even more, today there is a renewed interest for vertical axis wind turbines (VAWTs) for offshore floating arrays and wind farms with closer spacing due to their faster wake recovery [6,7]. Aditionally, the omni-directionality of VAWTs makes them insensitive to the wind direction, resulting in a simpler mechanical design with a few moving parts, which excludes the yawing equipment and (often) the pitching mechanism. This characteristic is considerably appreciated in offshore farm facilities, because the yawing mechanism is one of the biggest sources of failures in the horizontal wind turbines (HAWT) [8][9][10]: the operation and maintenance take big part of the total energy cost. Another relevant advantage in VAWTs, is the fact that the generator can be placed at sea level, which stabilizes the structure due to its low center of gravity and therefore could reduce the size and cost of the floating base. Consequently, generators with larger dimensions and weight can be used, which allows for heavy direct drive generators with permanent magnets [11]. Compared to HAWTs, VAWTs have higher potential for scalability [12,13] VAWTs are characterized by complex and unsteady three-dimensional aerodynamics which present considerable challenges for both simulations and measurements to describe it. The nearwake structure of a VAWT has been revealed to be mainly dominated by the effects of the blade tip vortex, which produces levels of recovery (due to the vertical advection) considerably higher than those from turbulent variations [14]. This effect is not present in HAWT wakes. The energy conversion process in VAWTs is based on the variation of the blade's circulation along the rotation axis of the turbine, producing a different creation of the wake compared to HAWTs, in which the wake is only generated by the tip vortices. In order to understand the performance of VAWTs better, it is necessary to have a fundamental knowledge about the flow phenomena involved. Moreover, to maximize the efficiency of a singular VAWT within a wind farm facility, an accurate prediction of the resulting flow from an operating VAWT is essentially required. For this goal, numerical simulations can contribute useful qualitative and quantitative understanding of VAWTs wakes in a relatively fast and economical way.
The numerical works that have been carried out to investigate wakes behind VAWTs can be separated into two principal approaches. The first one consists in the full resolution of the boundary layers around the blades [15][16][17][18]. Through this method it is possible to obtain detailed information about the load distribution and the flow fields within the rotor and near wake regions. However, there is a considerable computational cost inherently involved, which restricts its utilization for wake studies in realistic large scale environments. Additionally, the accuracy of the results is directly related to the numerical method and the applied turbulence model [19,20]. In the second approach, the blades are simulated by using the actuator type technique, which excludes the need of the full resolution of the boundary layer flow around the blade. Therefore, these simplifications makes it feasible to run studies of the far wake of VAWTs and VAWT wind farms [4,5,21,22].
The present work aims to simulate the produced wake from a VAWT applying an actuator line model (ALM), and also to identify the effects of the interaction between the wake structure and the incident flow. Different terrains with their own aerodynamic roughness length have been considered. A turbulent inflow generator was not used, in order to isolate the effect of wind shear from that of turbulence intensity. The model has been implemented using the opensource CFD toolbox library OpenFOAM to solve the governing equations and to compute the resulting wake [23]. An operational H-shaped VAWT model was tested, for which experimental activity has been performed at an open site north of Uppsala-Sweden [24]. Numerical results were compared to normal forces from experimental data.

Methodology
An actuator line model (ALM) coupled to a dynamic stall model (DSM) has been implemented to solve the governing equation of the involved phenomena. The ALM samples the velocity from the Navier-Stokes solver, and then it calculates the angle of attack and relative velocity in each blade element. The DSM computes blade force coefficients, which the ALM uses to impart back the body force into the flow field solver. The main characteristics of the model were described in this section, it is suggested to read [25,26] for more detailed information.

Actuator Line Model
The applied ALM is a three-dimensional and unsteady aerodynamics model developed by Sørensen and Shen [27], and created to study the surrounded flow of wind turbines. It is a coupling between a Navier-Stokes solver for the flow field with the actuator line technique, which distributes body force along lines representing the blades of the turbine. The used forces are determined through the DSM, based on empirical data.

Dynamic Stall Modeling
The DSM is represented by the Leishman and Beddoes model [28], with the variation of Sheng et al. [29] and Dyachuk [26]. It is able to compute the unsteady lift, pithing moment and drag, giving a physical description of the aerodynamics. It has been validated with experimental results in [30]. A division of three subsystems is considered in the model: an attached flow model for unsteady linear airloads, a separated flow model for non-linear airloads, and a dynamic stall model for the airloads induced by the leading edge vortex. In [25], the results have shown small improvements in the accuracy and agreement with experimental data compared to the results where the attached flow correction of the DSM is not included.

Simulation Parameters: Validation case
Experimental data from a 12 kW VAWT with diameter of 6.48 m were used to validate the model ( Figure 1). This device is operating in a open site in the north of Uppsala. The measurement campaign and the obtained forces are published in [31] and [24], respectively; four load cells were used to measure forces on one blade and its support arms. Due to the lack of experimental results for the far wake of VAWTs in open sites, normal forces for a TSR of λ = 3.44 are used as the validation parameter. The chosen TSR value is close to the optimal one. Specifications of the turbine are shown in Table 1. In order to represent the results in an easier way, a rectangular coordinate system has been used with the origin placed at the base of the turbine, such that the x-axis is pointing positively in the downwind direction. Central shaft and supporting struts were included in the computation.
where z 0 is the roughness length and K = 0.40 is the von Kármán constant. A uniform flow with a non-slip boundary condition for the ground (common configuration used for simulations), and logarithmic inlet velocity profiles in snow, long grass and bushes have been tested. These parameters are summarized in Table 2. Simulations were carried out with a domain considering open site boundary conditions.  Figure 2 displays the main characteristics of the calculated mean wind shears over the different surface types. These fields were used as incoming flows for the simulations of the resulting wake.

Results and discussion
In this section, streamwise velocity for representative planes are analyzed in order to study the wake behind the operating VAWT over the flat surfaces with different roughness lengths. The obtained normal forces were compared to experimental data. A LES Smagorinsky model has been used to predict the turbulence effects.

Mesh sensitivity
A reference mesh topology with local refinement around the region close to the turbine and in the downwind direction (in order to capture details of the obtained wake) has been used to study the mesh sensitivity of the model, see Figure 3. This topology was kept constant and proportionally scaled in every direction for the refinements.    Figure 6 shows for all the cases,that the resulting wake has similar shape and position; hence the model is able to represent the global structure of the wake independently of the mesh size. However, the refinement is necessary to capture the details of the generated vortex which has an essential contribution to the wake recovery. The wake transition to the turbulent regime is closer to the upwind direction when the mesh is finer: at x/D 12 and 8 for the meshes of 17.3 and 46.7×10 6 cells, respectively.  Regarding to the temporal discretization, previous studies have shown that the model is less sensitive to temporal than spacial discretization [25,32]. Nonetheless, the Courant-Friedrichs-Lewy (CFL) condition must be taken in account for the time discretization, to ensure convergence.  Figures 7 and 8 reveal the resulting wake produced by the turbine. These results were obtained using a mesh resolution of 17.3×10 6 cells. In all the cases the wake shape (geometry) and position are similar. Furthermore, expansion and recovery of the wake in the downwind direction is clearly identified, as well as the uniform and logarithmic profiles at the inlet of the domain.

Terrain roughness variation
In the vertical plane of velocity (Figure 7), it is shown that the flow is accelerated in the upper part of the wake after facing the turbine. For the uniform flow, an acceleration is also observed in the lower part of the wake. The general characteristics are mainly dominated by the vortical structures from the blade tips and the blade pitching. It could be noticed in Figure 8 that there is strong creation of vortical structures in the interface between the resulting wake and the ground and, as expected, the rougher the surface the larger turbulence. Inside the wake there is a region with no vorticity, and this becomes smaller when the surface roughness increases, which means that the wake breaks earlier to the turbulent regime. In general, larger turbulence levels lead to faster wake recovery because of the improvement of the mixing process and momentum transfer. In order to distinguish quantitatively the resulting wake structure from the different results, both horizontal and vertical profiles of normalized velocity deficit ( U x /U ∞ ) inside the wake region are revealed in Figure 9 for the same representative sections, where U x = U x − U inflow is the time-averaged velocity deficit, and U inflow is the mean streamwise inflow velocity shown in Figure 2. As can be observed, the wake has a slight asymmetry in the horizontal direction, and a strong influence from the ground in the vertical structure. No significant changes are noticed until the section x/D = 10. After this, the velocity deficit decreases approximately from 50% to 30% in the equatorial area at x/D = 15. Effects leaded from the wind shears are mainly in the perpendicular direction to the main flow. Figure 10 displays the vertical contour of the streamwise turbulence intensity for the different terrains. An evident production of turbulence intensity is noticed after the section x/D = 10,

Conclusions
The presented ALM is able to reproduce the main pattern of a wake produced by an operating VAWT in an open site, revealing its shape and position. The numerical results showed reasonable agreement with experimental results of normal forces. The model allows to evaluate qualitatively and quantitatively the most relevant parameters and phenomenas involved in the flow pattern: velocity field with its zones of acceleration and deceleration, regions with high and low concentration of vorticity and turbulence production. Interaction between the wake and the ground is captured. Effects on the contribution from the wind shears in the mixing process and the transition to turbulent regime are clearly identified for the terrain roughness variation. The model shows stability for the tested cases, which makes it suitable for application in VAWTs simulations.