A numerical study of strut and tower influence on the performance of vertical axis wind turbines using computational fluid dynamics simulation

This paper presents the influence of the strut and the tower on the aerodynamic force of the blade for the vertical axis wind turbine (VAWT). It has been known that struts degrade the performance of VAWTs due to the inherent drag losses. In this study, three-dimensional Reynolds-averaged Navier – Stokes simulations have been conducted to investigate the effect of the strut and the tower on the flow pattern around the rotor region, the blade force distribution, and the rotor performance. A comparison has been made for three different cases where only the blade; both the blade and the strut; and all of the blade, the strut, and the tower are considered. A 12-kW three-bladed H-rotor VAWT has been studied for tip speed ratio of 4.16. This ratio is relatively high for this turbine, so the influence of the strut is expected to be crucial. The numerical model has been validated first for a single pitching blade and full VAWTs. The simulations show distinguished differences in the force distribution along the blade between two cases with and without struts. Since the wake from the struts interacts with the blades, the tangential force is reduced especially in the downwind side when the struts are considered. The calculated power coefficient is decreased by 43 %, which shows the importance of modeling the strut effect properly for accurate prediction of the turbine performance. The simulations also indicate that including the tower does not yield significant difference in the force distribution and the rotor power.


| INTRODUCTION
Nowadays, the demand of renewable energy is increasing, and wind power is one of the natural sources of energy which is capable of supplying the required electricity in society.According to statistics published by World Wind Energy Association (WWEA), 1 93-GW capacity of the global wind power has been newly installed in 2020, and the overall capacity has reached 744 GW.WindEurope 2 states that Europe installed 15 GW of new wind capacity in 2020, and 80% of the new wind installations were onshore.Now the wind energy industry is exploring better solutions for cost reduction, while maintaining or even improving its efficiency of the power generation.
A vertical axis wind turbine (VAWT) is one type of wind turbines which has a rotor shaft perpendicular to the wind direction.The advantage of this type of wind turbines is that it can absorb wind from any directions, so no yaw control is needed.It leads to fewer mechanical components required, which results in simpler design.Also, the main components consisting of the generator and the gearbox can usually be placed close to the ground, which gives easy access for maintenance and repair.As for floating offshore VAWTs, the generator lowers the center of gravity to the platform level, and therefore, the cost of the floating structure can be mitigated.However, the complex and unsteady phenomena that is characteristic to the VAWTs make both measurements and simulations extremely challenging.The aerodynamics of VAWTs is quite complicated due to variation of the relative wind speed that the blade experiences during their rotation.The circular path of the blade also makes their aerodynamics, such as the dynamic stall and flow curvature effects, differ from those seen in static blades.Moreover, the blade in the downwind region inherently operates within the wake created by blades upwind and other components, that is, a tower and struts.As a result, the torque downwind is decreased compared to that in the upwind region, and this fact is directly related to the overall performance.This is not the case seen in horizontal axis wind turbines.Therefore, understanding flow features in VAWTs is a key for further improvement to increase the efficiency of the total system.Many researchers have attempted to clarify how the operational condition of VAWTs affects the performance and how the configuration can be optimized to maximize the efficiency.7][8] The streamtube model considers the balance of the momentum for each single streamtube encompassing the turbine.The vortex method formulates the Navier-Stokes equations in terms of vorticity instead of velocity and pressure to track vorticity.The algorithm for the ALM combines the Navier-Stokes solver and represents the blade force distribution along lines.For instance, Shamsoddin and Porté-Agel 9 or Mendoza et al 10 employed the ALM for studying the blade loads and wakes of VAWTs.Dynamic stall is a significant problem for the streamtube model, the vortex model, and the ALM, and these models only work for airfoils with known characteristics over a large range of angles of attack.Although they don't require high computational cost and are suitable for quickly checking the turbine performance, they are all limited to blade force models and cannot handle arbitrary profiles or shapes.Therefore, it is difficult for these models to reproduce the detailed flow characteristics of VAWTs.
Computational fluid dynamics (CFD) simulations which solve the wall-bounded flow around the structure surface are computationally expensive but one of the most reliable tools for investigating the complex flow fields of VAWTs.The effect of the airfoil profile on the power coefficient of a Darrieus H-rotor turbine has been investigated using 2D Reynolds-averaged Navier-Stokes (RANS) simulations, for example, by Mohamed 11 who found that the turbines consisted of the symmetric airfoils have a higher performance than the nonsymmetric airfoil turbines.
Danao et al, 12 Sabaeifard et al, 13 and Beri and Yao 14 highlighted the influence of the airfoil thickness and camber on the rotor performance.There are some literature by researchers, such as Howell et al, 15 Cheng et al., 16 Lam and Peng, 17 Li et al, 18 and Zhang et al, 19 which show large differences between the power coefficient predicted by 2D and 3D simulations.These differences occur due to the presence of the blade tip vortices, the flow divergence, and the addition of struts which are mounted horizontally to the rotational axis.
Previous studies 15,20,21 state that the performance of VAWTs is reduced due to the drag loss caused by struts.At the same time, struts must be strong and stiff enough to prevent excessive deflections and carry weight of blades and themselves.Therefore, the design of struts involves a trade-off between aerodynamic and structural requirements. 22However, most of the numerical studies neglect the contribution of the strut forces to the net rotor power.This impact has not been assessed quantitatively so far, even though it needs to be taken into account for precise estimation.
CFD methods resolving the boundary layer are suitable to properly model the aerodynamic performance for VAWTs including the influence of struts.The numerical models commonly employed, that is, the streamtube model, the vortex model, or the ALM, are based on the simplified approaches which cannot accurately describe the effect of struts and blade-struts joint.The ALM, for example, replaces the blade and the strut with a set of point forces, so it is not able to reflect the three-dimensional geometry of the surface highly accurately.The streamtube model is also not able to take into account the three-dimensional effect that can alter the aerodynamic performance.Wall-resolved CFD simulations are able to handle the complex geometry of the structure by solving the boundary layer around the wall and thus represent the detailed influence on the flow fields around the rotor region more accurately than other methods.Several studies have presented the decrease of the rotor power caused by struts using CFD models.De Marco et al 23 conducted three-dimensional CFD simulations for the VAWT model with the inclined arms of airfoilshaped cross-sections and found that a shorter chord length of the arms gives higher performance at high tip speed ratios (TSRs).Elkhoury et al 20 performed CFD analysis for VAWT blades linked to the rotational shaft through straight cylindrical rods.They concluded that the effect of the strut drag has a great influence on the power especially at high TSRs.Marsh et al 24 evaluated the power output for three different designs of vertical axis tidal turbines using CFD models.They found the significant effect of the difference of designs, such as the strut cross-section, the attachment locations, and the blade joints.This work presents the aerodynamics of VAWTs using three-dimensional CFD simulations in order to reveal how the presence of the struts and the tower contributes to the flow field around the turbine, the blade force distribution, and the rotor power.The turbine model studied in this paper is a three-bladed H-rotor VAWT, which has 6 m hub height and 6.5 m diameter.The turbine operating at the high TSR of 4.16 is investigated.While the dominant force of horizontal struts is drag, the struts of this VAWT are jointed with an angle and can therefore produce lift.The aerodynamic force is calculated using the incompressible RANS model based on the finite volume method.After the numerical model is validated by comparing forces for a single pitching blade and full VAWTs, the influence of the struts and the tower is analyzed by differentiating results among three cases which consider only the blade; both the blade and the struts; and all of the blade, the strut, and the tower.

| TURBINE GEOMETRY
The reference model is the VAWT located at Marsta in Sweden, which has been designed and built by the Division of Electricity at Uppsala University.The main parameters of the geometry are listed in Table 1.The radius of the rotor is 3.24 m, and the hub is located at 6 m from the ground.It consists of three blades which have the cross-sectional profile of an NACA 0021 airfoil.Each blade has a length of H ¼ 5 m.The chord length is c ¼ 25 cm.It is tapered on both sides, starting from 1 m from the blade tip, with the chord linearly decreasing to 15 cm at the tip.Two inclined struts are attached to each blade at the heights of 0.27H and 0.73H with the mounting angles of ±17.6 relative to the horizontal plane, as shown in Figure 1.The cross-section of the struts is designed based on an NACA 0025 profile but with modification at the trailing edge to have a blunt edge.The chord length varies linearly from 32 cm at the root up to 20 cm at the attachment point.A detailed description of the strut geometry can be referred to Goude and Rossander. 25The tower is modeled in the simulation as a circular cylinder with the radius of 0.10 m.
The top view of the rotor is shown in Figure 2. It rotates with an angular velocity ω, and the azimuth angle is denoted by θ.The TSR is defined as Rω/U ∞ , where R is the radius of the rotor and U ∞ is the freestream velocity at hub height.The normal and tangential forces are shown by F n and F t .These forces are positive when they are in the outward and the rotational directions, respectively, as illustrated.the realizable k À ε turbulence model. 27This turbulence model performs well for flows which include rotation, separation, recirculation, and flow under high level of adverse pressure gradients, 28 and there are many studies [28][29][30] which use this model for VAWT simulations.
The PIMPLE algorithm developed for transient problems is applied to solve the coupled pressure-velocity equations.The PIMPLE algorithm is a combination of the pressure-implicit split-operator (PISO) algorithm and the semi-implicit method for pressure-linked equations (SIMPLE) algorithm.Contrary to the PISO algorithm, the PIMPLE algorithm recalculates the pressure-velocity coupling in one time step.
Time steps are adjusted so that the maximum Courant number is satisfied to be below 0.9.The average time step increment is around 2 Â 10 À6 s, which corresponds approximately to time of rotating by azimuth angle of 0.006 .
Figure 3 shows the computational domain and the boundary conditions.The domain consists of a rotational inner part and a stationary outer part.The rotational region is represented as the circular area of 1.5D diameter in the figure.When the tower is included in the center, the circular area of 0.068D diameter is set to be nonrotating.The rotor is located in the center, and the dimensions of the entire domain in both the stream and cross-stream directions are 20.1D.Rezaeiha et al 31 stated that the distance from the center to lateral boundaries of 10D minimizes the effect of the domain, so the domain size used here should be sufficient.Additionally, the blockage effect needs to be considered properly to ensure that the lateral boundaries in y direction are placed far enough away from the rotor to avoid interference.The blockage ratio, that is, the frontal swept area of the turbine to the computational domain area at inlet, is around 0.4 %.Ross and Altman 32 concluded from their wind tunnel test for a VAWT model that the blockage less than 3.5 % does not have a profound influence on the freestream pressure, so the value of our case can be considered to be small enough.The dimension of the domain in the vertical directions is 9.3D.The hub of the wind turbine is set to be positioned at the same height as in the real turbine.
The inlet velocity is expressed by the log law.The log wind profile varies with the height z and is defined as Figure 4 shows the view of the discretized mesh at the hub height for the rotational inner domain and the area near the blade, and the surface mesh around the blade tip.The sliding interface between the rotating and the stationary zones can be seen as a circular line.A major local refinement has been implemented in the region around the blades, as shown with the rectangular area in the left picture.The mesh is refined with the same resolution over the entire surface of the blades, the struts, and the tower including the region near the blade tips.The blunt edge of the blades is not modeled to save the computational cost.The thickness of the first layer of these surfaces is 2 mm, and wall functions are applied to the boundaries at the surface.The mesh resolution meets the requirement for the wall functions that y + should be less than 300.
Three simulation cases are studied in this paper: One case contains the three blades, another one additionally contains the six struts, and the last one contains the tower as well.The numbers of total mesh cells for each case are 19, 33, and 38 millions, respectively.
First, the steady-state flow is solved to obtain the initial fields.Next, more than 21 revolutions are simulated using a coarse mesh for the wake to develop by a few rotor-diameter distances.Simulations can reach a statistically steady-state condition after 20 turbine revolutions according to Rezaeiha et al, 33 thus the number of simulated revolutions should be sufficient.Then, another five revolutions are computed with the finer mesh explained earlier.Figure 5 shows the history of all revolutions for the torque coefficient C T of one blade run using the fine mesh without struts.C T is defined as T=0:5ρARU 2 ∞ where T is the torque produced by one blade.The differences of the maximum and minimum values are less than 0.2% between the last two revolutions, and it is considered that more revolutions will not yield large differences in the results.The same procedure is carried out for the other two cases.F I G U R E 5 Torque coefficient of one blade for all calculated revolutions from the case without struts using fine mesh F I G U R E 3 Computational domain (not to scale) and boundary conditions For the discretization of the convective terms, the first-order upwind scheme is applied in the revolutions calculated using the coarse mesh and the second-order upwind total variation diminishing (TVD) scheme is applied in the last revolution.In all time steps, the diffusive terms are discretized by the central difference scheme.The bounded first-order implicit scheme is used for the time differencing.
The parallel computation is run using 256 processors on the Tetralith cluster provided by the National Supercomputer Center at Linköping University.The computational domain is split into 256 subdomains, and each subdomain is assigned to one of the processors.It takes 149 h to compute one revolution for the case including the blade and the struts.

| Sensitivity analysis
It is necessary to analyze the mesh independence, as very fine meshes are required to obtain reliable results for Darrieus rotor flows. 34The flow fields are susceptible especially to the resolution of the mesh in the region around the airfoil, and thus, the independence for the difference of the grid points along the airfoil is investigated.Three different meshes are tested as shown in Table 2 which lists the numbers of nodes along the cross-section of the airfoil, the total faces on one blade surface, and the total mesh cells of the computational domain.The resolution of refinement for the mesh A2 corresponds to that of the reference mesh used for the main analysis, which is presented in Section 5.The meshes A1 and A3 have approximately the half and double numbers of nodes along the airfoil of the mesh A2, respectively.The cell height around the airfoil surface is equivalent among three mesh cases.The cells of the stationary part have double the larger size compared to the cells of the reference mesh for all three mesh cases in order to reduce the CPU time.
Figure 6 shows the tangential forces F t for each mesh case.The curves obtained from the cases of A1 and A2 differ largely, but those of A2 and A3 become closer.The resulting power coefficient C power is presented in Table 2. C power is defined as ωT avg =0:5ρAU 3 ∞ where T avg is the average torque of three blades during one revolution.The difference between the C power values of A1 and A3 is 53 %, while the difference between A2 and A3 is 9 %.There is still a small discrepancy between A2 and A3, but the reference mesh of the resolution equivalent to A2 is a good compromise considering the reasonable computational cost.

| Single blade pitching motion
The motion of a sinusoidally pitching airfoil is analyzed to test the applicability of the numerical model.This validation is made because the blade of VAWTs experiences the sinusoidal variation of angle of attack during rotation where the blade oscillation is dependent on the TSR.Although Wi sniewski et al 35 state that the variation of the angle of attack in the Darrieus-type cycloidal motion cannot be modeled as a pure pitching T A B L E 2 Test cases for sensitivity analysis of the mesh resolution

Mesh
Nodes along airfoil F I G U R E 6 Tangential force simulated using meshes with different number of nodes along airfoil motion, we assume that this validation case can sufficiently be a good approximation for the motion of the blade of VAWTs to check the force amplitude.Another reason for conducting this validation is that, although the VAWT case is examined later, there are some uncertainties with the measurements for the VAWT and this makes the validation less reliable.The focus here is an accurate representation of the dynamic stall, which is an essential phenomenon of VAWTs.
The measurement was conducted by Angell et al 36  VAWT in this study are within the above pitching angles as will be shown in Figure 12.
The measurement condition is reproduced with three-dimensional simulations.The mesh around the airfoil has the same resolution as that of the reference mesh used for the turbine.The domain sizes in the directions parallel and perpendicular to the freestream velocity are 123 and 41 chord lengths.The span length simulated is 3.4 chord length, but only the center part accounting for 20% of the total simulated span is used for force calculation to avoid including the boundary effect.
The normal and the tangential force coefficients C n and C t are compared against measurements in Figure 7. C n and C t are defined as the normal and tangential forces normalized with 0:5ρU 2 ∞ cL where ρ is the density of air, U ∞ ¼ 29:7 m/s is the freestream velocity, and L is the span length.The comparison shows that the peak values of C n and C t are close to the measurements.The cyclic variation of the force is reproduced well at the TSRs of 3.44 and 4.19, although there is a small discrepancy in C t at the TSR of 3.44 at positive angles that correspond to the upstroke phase.A feature of dynamic stall is identified by the wide shape of the curves caused due to the delay on the flow reattachment, and this is more pronounced at lower TSR.There is a large difference in the curve of C t at the TSR of 2.60, and the simulation predicts deeper stall than the measurement.It can be concluded from these results that the present model would be appropriate to simulate the flow condition when the flow is mostly attached with no deep stall, but the model may fail to predict the reattachment point highly accurately when the large dynamic stall takes place

| VAWT at Marsta
Measurement data are used to validate the full VAWT model in addition to the validation for a single pitching blade.The measurement was conducted by Dyachuk et al 37,38 using force sensors.These sensors are load cells which can measure tension and compression, and they are installed F I G U R E 7 Normal and tangential force coefficients C n and C t measured by Angell et al 36 and predicted by the present model for the pitching blade with the amplitude of angles of 22.6 , 17.4 , and 13.8 corresponding to the TSRs of 2.60 (left), 3.34 (middle), and 4. 19 (right)  to one of the blades between the hub and the struts as shown in Figure 8. Spacers of equal radial distance are installed to the other two blades.
Four load cells are used, and the sum of the measured forces F 0 , F 1 , F 2 , and F 3 represents the radial force.It is assumed that the centrifugal force is constant when the rotational speed is nearly constant.The normal force F n is the difference between the radial force and the centrifugal force, that is, Since both wind speed and wind direction had large variations at the measurement site, conditions of steady flow were defined in order to extract data bins.The flow was considered steady when the deviation of the asymptotic wind speed is low enough.More detailed description of the experimental method can be found in Dyachuk et al. 37,38 F I G U R E 8 Load cells and spacers installed between the hub and the struts on the 12-kW VAWT (figure from Dyachuk et al 39 ) F I G U R E 9 Normal forces from the case considering only the blade (red), the case with the blade and the strut (light blue), and the case with the blade, the strut and the tower (black), compared with measurement represented with the range between the maximum and minimum values (blue) A comparison is made between the simulation model and the measurement for the normal force of the VAWT blade.Figure 9 shows the normal force of one blade (and two struts) during one revolution for the three simulation cases, comparing with the measurement.The measurement data averaged from eight revolutions are represented with a solid line, and the maximum and minimum values at each azimuth before averaging are represented with dotted lines.The amplitude of the predicted forces is close to the measurement in the upwind side of rotation, but the simulation does not reproduce the noticeable drop seen in the measurement at 270 .The measurement shows a sharp increase when the blade moves from 90 to 220 , while the simulated curves represent a moderate increase.When the two predicted cases without the tower are compared, it can be seen that there is almost no significant difference between them in the upwind side.The force considering struts slightly decreases in the downwind, with the maximum reduction of 33 N found at 282 .It is also observed that adding the tower does not produce any noticeable difference during one revolution.
Additionally, it is validated against another RANS model by Nguyen et al, 40 who also simulated the aerodynamics for the same turbine.They performed two-dimensional CFD simulation using the SST k À ω turbulence model.The forces for the TSR of 3.44 are compared between their model and the present model without struts, as shown in Figure 10.The amplitude of the normal forces agrees well, but the peak of the tangential force in the upwind is predicted slightly higher by the SST model.The power coefficient C power for the SST model and the present model are 0.35 and 0.33, and the value from the SST model is higher than that of the present model.Three-dimensional simulations take into consideration phenomena such as blade tip losses that two-dimensional analysis cannot represent, and this dimensional effect can be one of the reasons arising this discrepancy.A small drop can be seen at around 270 in the SST model.A tower located in the rotational center is included in the SST model but not in the present model, and this reduction is considered to arise due to the wake created by the tower.

| VAWT at Mie University
Another validation is made for the case studied by Li et al, 21 who experimentally examined the effect of solidity on aerodynamic forces of the VAWT.They studied a H-rotor turbine with NACA 0021 profile blades, and blade forces were measured for various configurations of different numbers of the blades.The data measured for the turbine with three blades are referred here.The freestream velocity is 8.0 m/s, and the rotor diameter is 2 m.The blades have the chord length of 0.265 m and the span length of 1.2 m with the pitch angle of 8 .The ratio of the domain size to the rotor diameter and the resolution of the boundary layer mesh are kept equivalent to those used in the reference mesh.
Figure 11 shows a comparison between the measurement and the simulation for the normalized tangential force C t of a single blade during one revolution.The measured and simulated maximum values of C t are 2.02 and 1.91, respectively, and the two curves in the upwind side agree well.However, the numerical model overpredicts the force in the downwind.This is probably because the simulation only considers the blades but not the support structure such as the strut and the tower, which can create the wake and affect the blade force in the downwind.

| Flow characteristics
First, the angle of relative wind is estimated in the following manner.The angle of relative wind ϕ can be expressed as Comparison between the measurement by Li et al 21 and the present model for the normalized tangential force C t of a single blade of the VAWT during one revolution where U rel,n and U rel,t are the normal and the tangential components of the relative wind speed, and U wind,x and U wind,y are the x and y components of the induced velocity at the blade position.ϕ is defined to be positive when the inner surface of the airfoil is on the suction side.With the pitch angle ϕ pitch , the angle of relative wind will be ϕ À ϕ pitch .The angle of relative wind when the wind is undisturbed, denoted as ϕ 0 , is expressed using λ ¼ Rω=U wind as tan ϕ 0 ¼ sin θ=ðλ þ cos θÞ.
The value of ϕ is estimated from the relative wind speed by monitoring the wind speed along the blade trajectory.The wind speed U wind is determined as follows: the velocity along the blade path at a certain height is sampled each time step at every 1 of azimuth angle, and then the mean velocity is calculated at each azimuth angle.There are some moments when the blades pass through the sampling points, but it is assumed that this moment is short enough that the velocity sampled during that time steps is averaged out.The Reynolds number is calculated from the obtained wind speed, and the average value during one revolution is 3.7 Â 10 5 .
The estimated values of ϕ obtained for the case with only the blade and the case with the blade and the strut, and the value of ϕ 0 are shown in Figure 12.It shows that ϕ varies within the range of ±10 for two cases at the height 0.5H.The value of ϕ at 0.5H becomes maximum at θ = 102 and minimum at 223 .There is no significant difference between these two cases with the maximum difference of 1.0 .The drastic reduction of ϕ for these two cases from ϕ 0 can be recognized especially in the downwind side, which indicates that the freestream flow is altered significantly by the wake from the preceding blades.The value of ϕ is closer to ϕ 0 at the height near the blade tip, 0.9H.At this height, the blade suffers from the wake less, and thus, the induced velocity is low.
Figure 13 shows the instantaneous velocity field normalized by U ∞ in the vertical plane intersecting the turbine center with the illustration of blades positioned most upwind and downwind for all the three simulated cases.Three blades are located at 15 , 135 , and 255 .These pictures indicate that the velocity decreases especially at the height swept by the struts, and the presence of struts makes the wake behind the rotor more complicated.It is also observed that the tower creates the wake downwind.
Figure 14 shows the vortex structure around the rotor.The left and the right plots in both figures correspond to the case with only the blade and the case with the blade and the strut.The Q-criterion is used to vizualize the vortex formation.It calculates the second invariant of the velocity gradient tensor, which is expressed as is the rate-of-strain tensor.Figure 14 represents the iso contour for Q ¼ 5 1/s 2 .It can be observed from the right picture in Figure 14 that Instantaneous velocity field in the vertical plane for the case with only the blade (left), the case with the the strut (middle), and the case with the strut and the tower (right) Angle of relative wind ignoring the induced velocity ϕ 0 and the angle of relative wind ϕ at the heights 0.5H and 0.9H for the case with only the blade and the case with the blade and the strut additional vortices are generated from the height of the attachment points.In both cases, tip vortices are released from the top and bottom sides and convected downstream.Small trailing edge vortices are also created and shed from the trailing edge of the blade and the struts.
Figure 15 shows the pressure coefficient C p when the blade is located at θ = 240 , 260 , 280 , and 300 for the case with only the blade and the case with the blade and the strut.These plots show C p at the height 0.64H which corresponds to the middle between the hub height and the upper strut attachment points.C p is calculated by C p ¼ p=0:5ρU 2 ∞ where p is the surface pressure, ρ ¼ 1:20 kg/m 3 is the density of air, and U ∞ is the freestream velocity at hub height.It is observed that the negative peak of C p is reduced in all four plots, and this decrease is prominent especially at 280 .There are also differences on the pressure side, with lower values of C p when the strut is considered.The blade surface is split into 25 segments along the span, and the force of each segment is monitored during simulations.F * n is the force per unit length that are calculated by F * n ¼ f n =l where f n is the normal forces of each segment and l is the length of the segment that is approximately H/25.Thus, the unit of F * n is N/m.The same applies to F * t .The struts strongly affect the forces in both the upwind and downwind sides of rotation, as there is a clear difference between cases with and without the strut in the contour plots at the height of the strut attachment, 0.27H and 0.73H.Moreover, they show an irregular distribution in the downwind side, which can be considered to be produced by the complex wake created in the upwind side.The normal and tangential forces are relatively high along the blade at around θ = 210 and start to decrease toward 270 then increase again.This blade surface area where the force is reduced is coincident to the projection area of the rotating struts.It can be seen from Figures 18 and 19 that the influence of struts is more remarkable for the tangential force.If two cases without the tower are compared, the largest reduction of F * n along the height by considering the struts is 18.1 and that of F * t is 6.5 at θ = 90 .At θ = 270 , the largest reduction of F * n is 23.1 and that of F * t is 2.1.For the case including the tower, no noticeable difference is observed in the contour plots of the normal and tangential forces.The force seems to be slightly reduced in the middle and the lower part of the blade height at θ = 270 as can be seen in Figures 18 and 19, but overall the profiles of the force are almost identical between the two cases including the strut.

| Blade forces
F I G U R E 1 4 Vortex structure represented using iso contour of Q ¼ 5 for the case with only the blade (left) and the case with the blade and the strut (right) F I G U R E 1 5 Pressure coefficient at the the height 0.64H when the blade is located at θ = 240 , 260 , 280 , and 300 for the case with only the blade (dotted) and the case with the blade and the strut (solid) To further investigate the strut force, the contour plot of the normal and tangential force distribution of the struts, F * n and F * t , during one revolution is plotted in Figures 20 and 21.They are the data for the case without the tower.The top and the bottom plots correspond to the force of the and the lower struts.Each upper and lower strut is split into 23 segments along the span.F * n is the force per unit length, that is, F * n ¼ f n =l, where f n is the forces of each segment and l is the segment length, and so is F * t .The radial distance of each segment normalized with R is used as y axis, and the distances of 0 and 1 correspond to the positions at the root and the tip of struts respectively.Figures 22 and 23 show F * n and F * t calculated from three representative segments located at distances of 0.20, 0.50, and 0.98 during one revolution for both upper and lower struts.
Figure 20 illustrates that the large negative force in the upwind side is concentrated at around the tip. Figure 21 shows that the tangential force becomes positive in the upwind side, which can contribute to the rotor torque.When the forces of the upper and the lower struts are compared at a certain radial distance, the largest differences are found at the distance closest to the strut tips for both the normal and tangential forces.These maximum differences for F * n and F * t are 3.5 and 1.1, as can be read in the upwind side in the top plot of Figures 20 and 21.Nonetheless, as observed in Figure 22, it can be considered that these differences are small, and thus, the behavior of the forces are almost symmetric between the upper and the lower struts.Therefore, there is not a considerable influence in produced strut forces due to either ground or wind shear effects.the force when all the components are modeled.These curves indicate that the amplitude of the tangential force is decreased significantly by considering struts especially in the downwind side.Regarding the two blue curves for the second simulated case, the force considering both the blade and the struts is slightly higher at around 90 than the force only from the blade, which is caused by the contribution from the lift force of the struts.The curve for the case with the tower is reduced slightly at around 270 compared to the values for the second case, but simulating the tower does not significantly change the amplitude of the tangential force.
The power coefficient C power is reduced when the struts are included.The values of C power are 0.277, 0.158, and 0.152 for the cases without the strut, with the strut, and with the strut and the tower, respectively.A drop of C power by considering the strut is 43.0%, which is not negligible at all.On the other hand, the difference is insignificant even if the tower is additionally included.It is important to consider the contribution from the strut for accurate prediction of the power, but the tower is not the component which mainly determines the total rotor output.

| CONCLUSIONS
This numerical study presents the strut and tower effect of the VAWT on the blade force distribution and the rotor performance.A threedimensional RANS model is employed, as it is a reliable tool which can investigate the flow field around the VAWT more in detail among other numerical models.Incompressible flows are solved to study the aerodynamic characteristics for a H-rotor VAWT operating at the high TSR of 4.16.First, the validation for the numerical model has been made by reproducing the blade force for both a single pitching blade and full VAWTs.
The simulation results for the VAWT show that there is almost no significant difference in the total normal force between two cases where the struts are and are not considered.However, the contour plots of the blade force distribution indicate the influence of the struts clearly.The struts reduce the blade force at the height of attachment point and also over a large area of the blade section where the wake from the preceding rotating struts can interact.The strut influence is more significant for the tangential force, and it is reduced especially in the downwind side when the struts are considered.The power coefficient is decreased from 0.28 to 0.16 if the struts are included.On the other hand, the results simulated with the tower do not produce any remarkable differences in the force distribution and the power.These facts suggest the importance of taking the strut effect into account properly in order to predict the rotor performance with high accuracy, but not necessarily the tower effect.The forces exerted on the blades, and the struts will be expected to differ depending on the turbine configuration.There might be an optimal strut design which produces less influence of struts on the rotor performance, and this should be investigated furthermore in future study.

PEER REVIEW
The peer review history for this article is available at https://publons.com/publon/10.1002/we.2704.
F I G U R E 2 3 Tangential force distribution of the upper and the lower struts at three radial distances during one revolution

1
Geometry of the VAWT Incompressible flow simulations are performed using the open source code OpenFOAM, 26 which solves the continuity and momentum equations based on the finite volume method.The flow field around the VAWT is obtained by solving unsteady three-dimensional RANS simulations with 025 m is the roughness length, and K ¼ 0:41 is the Kármán constant.U ref is the velocity at reference height z ref .The velocity 5.3 m/s at the hub height z ref is used here as U ref .The turbulence kinetic energy k at the inlet is set so that the turbulence intensity I ¼ ffiffiffiffiffiffiffiffiffiffi ffi 2k=3 p =U ∞ is equivalent to around 0.15%.The pressure is assumed to be zero at the outlet boundary.The slip condition is applied at boundaries in the cross-stream and the vertical directions, except for the boundary on the bottom side at z ¼ 0 where the wall boundary conditions are used to represent the ground.

F
I G U R E 4 View of the mesh at the hub height for the rotational domain (left), for the area near the blade (middle), and the discretized surface around the blade tip (right) for pitching motion of an NACA 0021 airfoil blade oscillating around the quarter chord position.The blade model has the chord length of 0.55 m and the span length of 1.61 m.The reduced frequency of the pitching oscillation is expressed as k red = cΩ/2U ∞ where Ω represents the angular pitching frequency, and it is validated for the case when k red ¼ 0:049.The amplitude of the pitching angle tested here are 22.6 , 17.4 , and 13.8 .The angle of the oscillation of the turbine blade is a function of the TSR, and these pitching angles correspond to the blade motion with the TSRs of 2.60, 3.34, and 4.19, respectively.The Reynolds number is 1 Â 10 6 , and the Mach number is 0.086.This condition is in a reasonable range of the operational VAWT, and the expected angles experienced by the airfoil of the where F C = mω 2 L C is the centrifugal force, m ¼ 35:79 kg is the mass of the blade and the struts, and L C ¼ 1:83 m is the center of mass of the blade and the struts.

1 0
Comparison of the normal (left) and tangential (right) forces between the results from the SST À ω model by Nguyen et al and the realizable k À ε model by the present model for the TSR of 3.44

Figures 16 and 17
Figures 16 and 17 show the contour plots of the normal and tangential force distribution over the blade, F * n and F * t , during one revolution for the three cases.Figures18 and 19show the force distribution along the blade height at selected azimuth angles, 90 , 180 , 225 , 270 , and 315 .

F I G U R E 1 6
Contour plot of the normal force distribution of the blade for the case with only the blade (left), the case with the strut (middle), and the case with the strut and the tower (right) F I G U R E 1 7 Contour plot of the tangential force distribution of the blade for the case with only the blade (left), the case with the strut (middle), and the case with the strut and the tower (right) F I G U R E 1 8 Comparison of the normal force distribution along the blade at selected azimuth angles F I G U R E 1 9 Comparison of the tangential force distribution along the blade at selected azimuth angles F I G U R E 2 0 Contour plot of the normal force distribution of the upper and the lower struts

Figure 23
Figure23shows the tangential force of a single blade (and two struts) during one revolution for the three simulated cases.The red curve represents the force for the case with only the blade.The dotted and solid blue lines represent the result from the case with the strut, and each This work was conducted within the STandUP for Energy strategic research framework and is part of STandUP for Wind.The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC at Linköping University partially funded by the Swedish Research Council through Grants 2019/3-383 and 2020/5-360.