CFD analysis of a Darrieus Vertical-Axis Wind turbine installation on the rooftop of a buildings under turbulent inflow conditions

The behavior of a rooftop mounted generic H-rotor Darrieus vertical axis wind turbine (H-VAWT) is investigated numerically in realistic urban terrain. The interaction of the atmospheric boundary layer with the different buildings, topography, and vegetation present in the urban environment leads to the highly turbulent inflow conditions with continuously changing inclination, and direction. Consequently, all these factors can influence the performance of a VAWT significantly. In order to 5 simulate a small H-VAWT at rooftop locations in the urban terrain under turbulent inflow conditions, a computational approach is developed. First, the flow field in the terrain is initialized and computed with inflow turbulence. Later, the wind turbine grids are superimposed for further computation in the turbulent flow field. The behavior of the H-VAWT is complex due to the 3D unsteady aerodynamics resulting from continuously changing the angle of attack, blade wake interaction, and dynamic stall. To get more insights into the behavior of a rooftop mounted H-VAWT in turbulent flow, high fidelity DDES simulations are 10 performed at different rooftop positions and compared the results against the behavior at uniform inflow conditions in the absence of inflow turbulence, built environment. It is found that the performance of wind turbine is significantly increased near the rooftop positions. The skewed flow at the rooftop location increases the complexity. However, this effect contributes positively to increasing the performance of wind turbines.

The FLOWer is a compressible, block-structured Reynolds Averaged Navier Stokes (RANS) solver developed by the German Aerospace Center (DLR) (Rossow et al., 2014) and is continuously furthered to incorporate new features and improve the 95 performance at the Institute of Aerodynamics and Gas Dynamics (IAG, University of Stuttgart). The overlapping grid technique CHIMERA enables the assembly of independent grids of each component by embedding them into a background mesh (Benek 4 https://doi.org/10.5194/wes-2021-112 Preprint. Discussion started: 11 October 2021 c Author(s) 2021. CC BY 4.0 License. et al., 2014). Furthermore, the solver is extended with the functionality of higher-order finite difference weighted essentially non-oscillatory (WENO) scheme (Schäferlein et al., 2014), and different Detached Eddy Simulation (DES) models (Weihing et al., 2018). Also, it has been extended with vegetation modeling capabilities . The FLOWer has proven 100 capabilities for wind turbine and helicopter simulations in several projects.

Generation of inflow turbulence
The inflow turbulence is generated using the in-house code PROFGEN, which is adopted from the work of Mann (1992). This model is based on the von Karman iso-tropic spectrum φ(κ) and uses the rapid distortion theory to estimate the effect of shear.
Three input parameters are required: length scale l 0 , stretching factor Γ, and energy dissipation α 2/3 . Moreover, l 0 and α 2/3 105 determine the magnitude and the distribution of energy in the spectral domain. Γ controls the level of shear and anisotropy.
The fluctuating components of atmospheric turbulence u are transformed into a volume force term f s and is applied to a transverse plane downstream from the inlet. It is defined as force per unit volume applied to accelerate the mean velocity field fromū toū + u , and as per Troldborg et al. (2014), is given by 110 Hereū n and u n , are the magnitude of the mean and the fluctuating velocity with index n and ∆x is the grid spacing normal to the transverse plane.

Vegetation modeling
The forest blocks are modeled as a porous medium. The drag caused by the vegetation is added to the momentum and energy equations of the Navier-Stokes equations via the volume force source term. It is based on the approach of Shaw et al. (1992). 115 The drag depends on the local foliage density a(z). It is possible to model the forest heterogeneously, considering local foliage density and height values for different parts of the vegetated area. The drag source term is given by where, ρ, c d , |u| and u are density, the drag coefficient, local magnitude of velocity, and velocity vector. The Leaf Area Index (LAI) over the height is defined as A lower value of LAI represents sparse vegetation, while higher values of LAI represents dense vegetation. The examined wind turbine is based on a generic two-bladed H-rotor VAWT designed by Li et al. (2016) with the airfoil section 125 NACA0021. Also, it has been investigated experimentally in the wind tunnel as well as in the field. It has a diameter of 2 m, a blade height of 1.2 m, and a blade chord length of 0.265 m. The blade cross-section area is constant over the complete length.
The central shaft has a diameter of 0.216 m. For rooftop application in present work, it is scaled up by a factor of 3.5, keeping the geometrical parameter solidity constant. The solidity σ is calculated as follows where n is the number of blades, c is the blade chord length, and D is the diameter of a VAWT. For the investigation, the "Morgenstelle" campus of the University of Tübingen from south Germany is selected as depicted in Fig. 1. Also, the synthetic wind atlas data presented in Fig. 1 shows the southwest as the main wind direction with densely forested hill lying in the upstream region of the built environment. There are 4-5 high-rise buildings with a height of 40 m and more.

CFD model 140
The wind turbine at the original scale is numerically investigated and validated using the FLOWer flow solver at IAG by Dessoky et al. (2019). As described in section 2.4.1, the grids are also scaled with same the scaling factor as a wind turbine.
The blades and shaft grids have a fully resolved boundary layer (y + 1) with 32 cell layers. The shaft is considered only in the region of the rotor. The blades are meshed using Pointwise and Gridgen commercial mesh generation applications. Based on the convergence study for different grids with the original wind turbine with FLOWer, the blade mesh is composed of 336 145 cells in the chord-wise direction and 48 cells in the span-wise direction. The CHIMERA intersection area is defined near the outer periphery of the rotating zone to assemble the wind turbine in the background grid. There are no changes made in the wind turbine grid throughout the study.
The computational approach is discussed in the next section 2.5. For the investigations in uniform inflow, the background grid is created by using the in-house automated tool. The background grid is a Cartesian type of dimension 215 m x 84.5 m x 150 76.8 m in x,y, and z-direction, respectively. The grid has hanging nodes enabling different levels of refinements. However, the background grid used for the uniform flow condition is not shown in this article. The near wake region has a grid refinement size of 8.625% of the chord shown in fig. 3. No inflow turbulence is applied. The background grid specific to the uniform inflow investigations is not relevant to the urban terrain investigations.
In the case of urban terrain simulations, the computation grids for the buildings are created using Pointwise and Gridgen.   For the present work, DDES simulations were performed employing a dual time-stepping scheme for temporal discretization.
Menter-SST model is used for turbulence modeling (Menter, 1994). A second-order scheme with the Jameson-Schmidt-Turkel (JST) artificial dissipation term (Jameson, 1981) is used for spatial discretization in the boundary layer. The fifth-order WENO

Computational approach
In the absence of the experimental or field measurements for the scaled-up VAWT, the performance at uniform flow conditions without inflow turbulence is considered a basis for comparison with realistic conditions. Ferreira et al. (2007)

studied 2D
VAWT numerically and experimentally. They showed that the delayed eddy simulations (DES) results reasonably predict the generation and shedding of vorticity and exhibit acceptable sensitivity to spatial and temporal grid refinement. It implies that 185 scale resolving DES simulations can be used where validation data is limited or nonexistent. Therefore in the present work, the scaled-up VAWT is investigated first by applying a high-fidelity approach at the reference condition of uniform inflow 8 ms −1 for different operating points. The power coefficient vs. tip speed ratio (Cp − λ ) curve serves as one of the basis for selecting the operating point and comparing the behavior of the wind turbine in realistic urban terrain.
In order to have a well-developed flow field before the investigation of the wind turbines in urban terrain, the simulations are 190 divided into two distinct phases, as depicted in fig. 5. In the first phase, the urban landscape is simulated without wind turbines with turbulent inflow. Once the flow field is well developed in the domain, averaging of the flow variables is started. This point also serves as the start for the wind turbine simulations. The mean wind profile, turbulence intensity, and skew angles are derived from the averaged solution. In the second phase, the wind turbine and wake refinement region are introduced to the urban terrain's existing computational set-up and flow field and computed further. The flow field in the refinement region is interpolated from the background grid's 205 existing solution, and the wind turbine structures are initialized with reference flow velocity and calculated further. This approach helps to save some computational costs. If the wind turbines are simulated in urban terrain from the start, it will increase the computation cost drastically as the pace of the simulation is limited by the small-time steps required for the wind turbines. In this approach, as the wind turbines are not present in the first phase, the domain can be simulated with a relatively larger time step than the wind turbine simulations. It is assumed that the wind turbine is rotating at constant rotational speed 210 under turbulent inflow. The rotational speeds are determined from the averaged local wind velocity over a longer period and the selected tip-speed ratio as an operating point. The active pitch control or dynamic changes in rotation speed as per variations in the incoming wind are not considered.
To sum up, there are three different cases with individual objectives are included in the present work. In the first case, investigations are carried out at uniform flow conditions. In the second case, the turbulent flow field in the urban terrain is 215

Evaluation
The scaled-up variant of the H-Darrieus rotor is evaluated at reference conditions. After some revolutions, the forces and moment converge, and the trend shows periodic nature. Revolutions after this point are considered for evaluation. The moment is averaged to calculate the power coefficient for the Cp − λ curve at reference conditions. 90°-100°, and then decreases reaching to zero or negative at 180°. Due to the rotational frame of reference, the notations for the tangential force are opposite to the moment. Tangential force, which is responsible for the production of the moment, shows correlation with the moment in second plot. Except λ =1.2, with increasing tip speed ratio, the normalized tangential 250 force also increases between 75°≤ θ°≤ 180°. The negligible difference is observed in peak moment and tangential force for λ =1.8 and 2.0. In the case of λ =1.2, the rapid decrease in the moment and tangential force can be attributed to the dynamic stall phenomena, which is persistent at low tip speed ratio. This is in line with the behavior of the un-scaled H-VAWT, which has been studied by Bangga et al. (2017) for the dynamic stall phenomenon. Also, Rezaeiha et al. (2018) performed 2.5D simulations for the a two-bladed H-VAWT with airfoil NACA0012 for the influence of the operational parameters. They found 255 similar behavior at lower λ while studying the influence of the tip speed ratio on the performance.
In the second half revolutions (180°≤ θ°≤ 360°), the moments and tangential forces show a not-linear trend. The wind speed experienced by a blade for these azimuth positions is slowed down due to the moment extraction in the first half revolutions, which leads to the stalled conditions. Also, the blade wake interactions dominate in the second half revolutions. Therefore, fluctuations can be seen in the moment and tangential forces. The influence of the wake arising from the shaft can 260 be distinguished by the sudden drops and jumps around 270°. Compared to other operating points, λ =1.8 and 2.0 generate a relatively higher moment in the second half revolution. However, the magnitude is far lower than the first half of the revolution.
With increasing λ , the nature of the curve flattens in the second half of the revolutions.
The third plot of fig. 7 shows variations in the normalized normal forces experienced by a single blade over revolution for different tip-speed ratios. At 0°, the blade is almost aligned with the flow direction and experiencing a small angle of attack.

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As the blade moves further over azimuth, the normal force decreases, gradually reaching a minimum around azimuth 100-105°a s the blade position is normal to the flow direction and then increases. In the considered notation, when directed towards the axis of rotation, the force has a "negative sign". When force is directed away from the axis of rotation, it has a "positive sign".  fig. 7. On the contrary, the normalized moment for λ = 2 and 2.75 varies considerably, but C p differs by a small margin. These differences are be attributed mainly to the changes in rotational 275 speed and subsequently to the operating point.

Urban terrain simulations under turbulent inflow
This section analyzes the flow field in the urban terrain under application of a log law wind profile and inflow turbulence, and without wind turbines. However, the results from these studies are the basis for the wind turbine investigations in turbulent urban conditions in the following subsection.

Wind turbines simulations in urban terrain
This section presents the analysis of the wind turbine at different heights above the rooftops of A and B under turbulent inflow.
As discussed in section 2.5, the wind turbines are initialized in the developed turbulent flow field and simulated further. The  objective of these simulations is to investigate the behavior of the H-Darrieus wind turbine under the turbulent inflow influence by the vegetation and the topography of the urban terrain.

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At the considered heights, the long averaged wind speeds vary slightly from each other in the range ±0.5 ms −1 , as shown in the table 2. Also, for the considered time series for the wind turbine investigations, the velocity fluctuates roughly around the respective mean values except for some large deviations. Therefore, it was assumed that the wind turbines positioned at 10 m, 12 m heights above rooftops of A and B operate at a mean wind speed of 7 ms −1 and other positioned at 20 m heights operate at a mean wind speed of 7.2 ms −1 . Later, the same values are used for the normalization of the forces and the moments.  standard deviations are seen in the first half revolutions, including at peak position around 90-95°implying the influence by the complex inflow conditions. Also, in the second half revolutions, the tangential forces show higher magnitudes and standard deviations than the uniform inflow case of λ = 2.75. The higher magnitude of the standard deviation indicates that blade wake interaction is not periodic in nature like the uniform inflow case. Despite experiencing complex operating conditions near rooftop heights, the averaged moments and tangential forces of a single blade do not show significant difference. The third 335 plots from fig. 14 and fig. 15 show the normalized normal forces experienced by a single blade at different heights above the rooftop of A and B. The lower magnitudes of standard deviations and overlapping curves for the different heights for the first half revolutions indicate that normal forces are less sensitive to turbulence and skewed inflow. However, in the second half revolutions, the increase in the normal forces around azimuth 240-270°for heights above B building can be seen. Due to the skew angles, the blade experiences relatively higher velocities in downwind passage than in uniform inflow case, and at these  as (a + b) 3 − a 3 > a 3 − (a − b) 3 . It translates that even if the mean wind speed is the same, the higher turbulence case will contain more power (Möllerström et al., 2016). Figure 16 and 17 show that wind turbines perform better at near rooftop heights above buildings A and B. For a fixed λ for an H-VAWT, over a reasonable range of free-stream velocities, the coefficient of power increase with the increase in free-stream velocity. In the present work, even though the averaged wind speeds at all 355 considered heights are lower than the uniform inflow case, the coefficients of power are still higher than that of the uniform case of λ = 2.75 shown in fig. 8. It is attributed to the combined impact of the turbulence and the skewed flow. At near rooftop heights above building A and B, the H-VAWT shows a significant increase in performance. Figure 18 shows the resolved wake of H-VAWT in turbulent inflow at a height of 10m above building B.

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In the present paper, a numerical investigation of the influence of the complex and urban terrain on the behavior of the rooftop mounted VAWT under turbulent inflow conditions are performed. With the help of high-fidelity scale resolving DDES simulation and higher order numerical scheme, the in-stationary characteristics of the forces and moment are studied. The The second study investigates the flow field in the realistic terrain consisting of different buildings, vegetation, and topographical features under turbulent inflow. Based on the mean wind profiles and turbulence levels, possible locations above the rooftops of two distinct buildings are considered for H-VAWT investigations. In the latter study, the wind turbines are 370 placed in the turbulent flow field at different heights above the rooftop of buildings by applying overlapping grid technique and simulated further. By this simulation strategy, the wind turbines can be investigated in a turbulent flow field with convenience and a significant reduction in the computation cost. In a subsequent study, the characteristics of the H-VAWT is studied for the tip speed ratio λ = 2.75 in urban terrain.
Based on the averaged forces and moments over multiples revolutions, the H-VAWT shows significant improvement in 375 the performance at heights of 10 m and 12 m from the rooftop of buildings. At these heights, it operates in the flow with a relatively higher level of turbulence and skewed angle than the 20 m height. Due to the skewed flow, the reduced blade wake interaction in the second half revolutions (downwind) increases tangential forces and moment extraction compared to the uniform non-skewed flow case. Large deviations are observed in the tangential forces and moments due to temporal changes.
The improvement in the performance at near rooftop heights is attributed to the combined influence of the turbulence and 380 skewed angle of the flow. Also, the H-VAWT placed at the height of 20 m from rooftops shows a better power coefficient than