Effect of Rotor Thrust on the Average Tower Drag of Downwind Turbines

A new analysis method to calculate the rotor-induced average tower drag of downwind turbines in the blade element momentum (BEM) method was developed in this study. The method involves two parts: calculation of the wind speed distribution using computational fluid dynamics, with the rotor modeled as a uniform loaded actuator disc, and calculation of the tower drag via the strip theory. The latter calculation considers two parameters, that is, the decrease in wind speed and the pressure gradient caused by the rotor thrust. The present method was validated by a wind tunnel test. Unlike the former BEM, which assumes the tower drag to be constant, the results obtained by the proposed method demonstrate much better agreement with the results of the wind tunnel test, with an accuracy of 30%.


Introduction
Horizontal axis wind turbines are categorized as upwind and downwind turbines according to the position of the rotor relative to the tower.Among these, upwind turbines have been predominant throughout the 30 year history of commercial wind turbines.The most essential reason for the unpopularity of the downwind turbines is the presence of a strong aerodynamic interaction between the rotor and the tower, which is commonly known as the "tower shadow effect".This phenomenon generates impulsive loads and infrasound when one of the blades passes through the wake of the tower [1].The modeling of the tower shadow effect is a critical technical problem of downwind turbines.
Design loads are calculated on the basis of the international design standard IEC61400-1 [2] or the guidelines for certification bodies DNV GL [3].In a large number of cases in which the design load is combined with the wind model, the wind turbines can experience failure conditions, as well as various types of wind and marine conditions.The flexibilities of the structure and the controls, in addition to the aerodynamics, hydrodynamics, aero-elastics, and control of the wind turbines, considerably influence the load.The blade element momentum (BEM) method is the most popular tool for determining these characteristics [4,5].Therefore, the modeling of the tower shadow effect in the BEM is one of the most important technical challenges in the design and development of downwind wind turbines.However, most of the tower shadow models are too simple to express such phenomena, as they consider only the wind speed profile behind an isolated tower [5,6] and not the aerodynamic interaction between the rotor and the tower.
Several studies have been conducted until now that have focused on the variable loads of the downwind turbines caused by the tower shadow effect.Zhao et al. [7] studied the loads on a tower by performing a comparison between two-and three-bladed upwind and downwind rotors in two different rotor speed conditions using computational fluid dynamics (CFD).The peak to average values of the hub bending moment and the tower base bending moment of the downwind turbine were shown to be 5-6 times and 2.5 times larger, respectively, than those of the upwind turbine.Zahle et al. [8] conducted 2-dimensional CFD analysis for three typical tower concepts of downwind turbines as well as for an upwind turbine; a steep load variation was noted for the downwind turbine, and the implementation of streamlined and four-leg towers was shown to be an effective technique to reduce the load variation caused by the tower shadow effects.Matiz-Chicacausa and Lopez [9] investigated the possibilities of the application of the actuator line model (ALM) to the CFD analysis of the tower shadow effects.The ALM was shown to be useful for load estimation of a downwind turbine under specific conditions.
Although the abovementioned research contributed to the expansion of the understanding of the phenomenon, the authors did not aim to develop models for extensive load calculations based on the design standards and guidelines.Wang and Coton [10] developed a high-resolution tower shadow model for downwind turbines based on the prescribed wake vortex model and an efficient near wake dynamics model of the vorticity trailing the blades.The model demonstrated reasonable agreement with the experimental results, with the exception of the blades passing through the tower wake.However, the load of the tower was not discussed in this research.Yoshida and Kiyoki [11,12] developed the load equivalent tower shadow modeling method.The method considered a bell-shaped wind speed profile behind the tower, which helped obtain the equivalent rotor load variation with the wind turbine CFD analysis.This model was applied to the development of the first multimegawatt-scale commercial downwind turbines, including the SUBARU 80/20 [13] and, later, the Hitachi 2 MW, to realize high performance and safety in complex terrains [14,15].The technology was extended to the later produced Hitachi 5 MW [16] offshore wind turbines.The model has been successfully applied in engineering applications so far; however, two major problems remained unsolved.The first concern was that the CFD modeling of the rotor-tower configuration required for each operating condition was time-consuming, which made the technique inconvenient for use in the design optimization process.The second issue was that no model was established for the tower shadow effects on the tower drag.Considering the situation, the tower load variation caused by the tower shadow effect was modeled by Yoshida by combining the BEM and the Lifting Line Theory [17].However, the average tower drag was still not discussed in that research.
Considering these situations, this paper proposes a BEM model for the tower average drag.The formulation is presented in Section 2, and the validation of the method by a wind tunnel test is discussed in Sections 3-5.

Methodology
The formulation of the average loads of the towers of the downwind turbine by using the BEM is discussed in this chapter.The following two calculations are considered: (1) Wind speed distribution by CFD (2) Rotor thrust-induced tower average drag

Wind Speed Distribution by CFD
The wind speed distribution in front of the rotor is calculated using CFD. Figure 1 shows the top view of the rotor and the tower of a downwind turbine.The tower, which has the diameter D T , is located in front of the rotor.The free stream wind speed U 0 decreases to U 0 (1 − a) at the rotor plane as a result of the rotor thrust.Here, a is the axial induction factor.Figure 2 is the schematic of the CFD involved in the present study.The tower is not included in the model, but the position is termed "virtual tower position" in this research.Further, u T is the wind speed at the virtual tower position, which is between U 0 and U 0 (1 − a), depending on the condition.The rotor is modeled by an actuator disc model (ADM).The load distribution is assumed to be uniform to realize a convenient application to the BEM.The thrust per unit volume σ of the ADM is as shown in Equation (1): where w is the thickness of the ADM.
Energies 2019, 12, x FOR PEER REVIEW 3 of 15 where w is the thickness of the ADM.

Rotor Thrust-Induced Tower Average Drag
The wind speed at the tower and the tower drag decrease as the rotor thrust increases due to the aerodynamic interaction.Two factors, that is, the wind speed and the ambient pressure gradient caused by the rotor thrust, are considered in this research.The formulation is based on the where w is the thickness of the ADM.

Rotor Thrust-Induced Tower Average Drag
The wind speed at the tower and the tower drag decrease as the rotor thrust increases due to the aerodynamic interaction.Two factors, that is, the wind speed and the ambient pressure gradient caused by the rotor thrust, are considered in this research.The formulation is based on the

Rotor Thrust-Induced Tower Average Drag
The wind speed at the tower and the tower drag decrease as the rotor thrust increases due to the aerodynamic interaction.Two factors, that is, the wind speed and the ambient pressure gradient caused by the rotor thrust, are considered in this research.The formulation is based on the assumption of the strip theory, according to which the flow between the sections normal to the tower axis is not taken into account.
(1) Wind Speed Effect The tower drag decreases proportionally to the square of the wind speed when the tower section drag coefficient remains constant.This influence is modeled herein.
The section drag f XT0 of the isolated tower with no rotor interaction is as shown in Equation ( 2): where C dT0 is the drag coefficient at the tower section.
In case the effect of the rotor thrust comes into play, the wind speed at the tower position decreases.Furthermore, the tower section drag also decreases from f XT0 to f XT .This is expressed in the following two ways, based on the wind speeds at the free stream and at the virtual tower position, as shown in Equation ( 3): where C dT is the tower section drag based on the free stream wind speed, and u T is the wind speed at the virtual tower position, which is calculated by CFD without incorporating a tower model, as explained in the previous section.Here, the drag coefficient C dT0 is assumed to be constant as in Equation ( 2).Therefore, the tower section drag deviation induced by the rotor thrust ∆f XT is calculated as in Equation ( 4): where the normalized wind speed at the virtual tower is Therefore, the change in the relevant drag coefficient caused by the wind speed change ∆C dTV is calculated by Equation ( 4), as given in Equation ( 5): This indicates that the term of the tower section drag decreases as the normalized wind speed at the virtual tower, induced by the rotor thrust, decreases.
(2) Effect of the Ambient Pressure Gradient The tower drag is also dependent on the ambient pressure gradient around the tower.This influence is modeled herein.
The pressure at the virtual tower position p T is calculated by Bernoulli's law, as in Equation ( 4): where p 0 and p T are the pressures at the free stream and the virtual tower center, respectively.Therefore, the windward pressure gradient ∂p T / ∂x T at the virtual tower center is calculated as shown in Equation ( 5) by the differential of Equation ( 4): The section drag by the pressure gradient at the tower section ∆f XTP is calculated as in Equation ( 6) by employing the pressure deviation from the front and back sides of the tower and the tower diameter.The pressure deviation is calculated by the pressure gradient and the windward reference distance ∆x T : Assuming a uniform pressure gradient, the tower section drag is expressed as in Equation ( 7): The reference distance is calculated as in Equation ( 8) using Equations ( 6) and ( 7): Therefore, the change in the tower section drag owing to the pressure gradient is calculated as in Equation ( 9): where ξ T is the normalized distance and can be written as Therefore, the change in the relevant drag coefficient caused by the pressure gradient ∆C dTP can be written as in Equation (10): This indicates that the term of the tower section drag decreases as the negative pressure gradient caused by the rotor thrust increases.
(3) Total Average Tower Drag From ( 1) and ( 2), the deviation of the drag ∆f XT and the drag coefficient ∆C dT induced by the rotor thrust are derived as Equations ( 11) and ( 12), respectively:

Outline
A wind tunnel test for a wind turbine was conducted to validate the theory described in the previous chapter.The rotor-tower interaction was simulated by a dummy tower placed in front of the rotor of the upwind turbine.

Facility
The Boundary Layer Wind Tunnel at the Research Institute for Applied Mechanics, Kyushu University [18], was used for the test.The wind tunnel has a test section with a width of 3.6 m, a height of 2.0 m, and a length of 15 m.The maximum wind speed is 30 m/s.

Test Model
The general specifications and the outline of the model and the tower installed in the wind tunnel are presented in Table 1.The blockage ratio, which is the ratio of the rotor area to the cross section of the wind tunnel, is as small as 5.3%.The rotor speed is controlled by the variable dump load.Figure 3 shows the schematic of the test model and the dummy tower.Although the model is an upwind turbine supported by a tower with a diameter of 50.8 mm, a dummy tower is installed in front of the model to mimic the downwind turbine tower.The diameter of the dummy tower is 64 mm, which is 200% the value of the blade chord length.The dummy tower was placed at two positions; −6D T and −4D T .Figure 4 shows an image of the test model.The dummy tower is shown as located in front of the turbine.

Test Model
The general specifications and the outline of the model and the tower installed in the wind tunnel are presented in Table 1.The blockage ratio, which is the ratio of the rotor area to the cross section of the wind tunnel, is as small as 5.3%.The rotor speed is controlled by the variable dump load.Figure 3 shows the schematic of the test model and the dummy tower.Although the model is an upwind turbine supported by a tower with a diameter of 50.8 mm, a dummy tower is installed in front of the model to mimic the downwind turbine tower.The diameter of the dummy tower is 64 mm, which is 200% the value of the blade chord length.The dummy tower was placed at two positions; −6DT and −4DT.Figure 4 shows an image of the test model.The dummy tower is shown as located in front of the turbine.

Test Results
The measurements for the power coefficient CP and the thrust coefficient CT for the isolated rotor model are shown in Figure 5.The rotor torque was calculated from the rolling moment at the top of the tower.The value of thrust force at the top of the tower was used as the rotor thrust.The maximum value of CP was noted at approximately λ = 8 and θ = 6 deg.However, CT tended to increase with an increase in the tip speed ratio or a decrease in the pitch angle.

Test Results
The measurements for the power coefficient C P and the thrust coefficient C T for the isolated rotor model are shown in Figure 5.The rotor torque was calculated from the rolling moment at the top of the tower.The value of thrust force at the top of the tower was used as the rotor thrust.The maximum value of C P was noted at approximately λ = 8 and θ = 6 deg.However, C T tended to increase with an increase in the tip speed ratio or a decrease in the pitch angle.

Test Results
The measurements for the power coefficient CP and the thrust coefficient CT for the isolated rotor model are shown in Figure 5.The rotor torque was calculated from the rolling moment at the top of the tower.The value of thrust force at the top of the tower was used as the rotor thrust.The maximum value of CP was noted at approximately λ = 8 and θ = 6 deg.However, CT tended to increase with an increase in the tip speed ratio or a decrease in the pitch angle.The pressure distributions on the dummy tower in typical cases are shown in Figure 6.Here, 0 deg indicates the upwind side of the tower.The pressure on the 50%R was relatively higher than that at 80%R.In general, the pressures around the downwind side of the tower (180 deg) tended to be higher as the rotor thrust was larger.
The details of other characteristics are discussed in Section 5.
The pressure distributions on the dummy tower in typical cases are shown in Figure 6.Here, 0 deg indicates the upwind side of the tower.The pressure on the 50%R was relatively higher than that at 80%R.In general, the pressures around the downwind side of the tower (180 deg) tended to be higher as the rotor thrust was larger.
The details of other characteristics are discussed in Section 5.

Outline
The relationship between the rotor thrust and the tower drag coefficient was determined by the proposed method described in Section 2. The model is generally the same as the one described in Section 3.3; however, the influence of the support was neglected as the support was located far downwind of the rotor, and this distance was fairly large compared to the support's diameter.In addition, the influence of the nacelle was neglected, as it does not affect the outboard sections, as discussed in this study.

CFD Outline
A CFD analysis was conducted for the rotor using ANSYS CFX [19] considering the k-ω SST turbulence model.The rotor was modeled by an ADM with uniform load distribution.
The simulation domain and the boundary conditions are summarized in Table 2.The model consisted of structured cells around the ADM with y+ is about 1 and unstructured ones otherwise.The total number of cells was approximately 50 million.The typical cells are shown in Figures 7 and 8.

Outline
The relationship between the rotor thrust and the tower drag coefficient was determined by the proposed method described in Section 2. The model is generally the same as the one described in Section 3.3; however, the influence of the support was neglected as the support was located far downwind of the rotor, and this distance was fairly large compared to the support's diameter.In addition, the influence of the nacelle was neglected, as it does not affect the outboard sections, as discussed in this study.

CFD Outline
A CFD analysis was conducted for the rotor using ANSYS CFX [19] considering the k-ω SST turbulence model.The rotor was modeled by an ADM with uniform load distribution.
The simulation domain and the boundary conditions are summarized in Table 2.The model consisted of structured cells around the ADM with y+ is about 1 and unstructured ones otherwise.The total number of cells was approximately 50 million.The typical cells are shown in Figures 7 and 8.

Wind Distributions in Front of the Rotor
The wind speed distributions in typical conditions, C T = 0.4 and 0.9, are shown in Figures 9 and 10.The circles in these figures denote the positions of the dummy towers at −6D T and −4D T .The wind speed tended to decrease in front of the tower in general, and the wind speed was lower in the vicinity of the rotor.A comparison between the two conditions shows that the wind speed around the dummy tower decreased as C T increased.A comparison between the two sections shows that the wind speed in front of the rotor was lower at 50%R compared to that at 80%R.The load was uniform on the rotor, and the inboard sections were considerably affected by the rotor.

Wind Speed Distributions in Front of the Rotor
The wind speed distributions in typical conditions, CT = 0.4 and 0.9, are shown in Figures 9 and 10.The circles in these figures denote the positions of the dummy towers at −6DT and −4DT.The wind speed tended to in front of the tower in general, and the wind speed was lower in the vicinity of the rotor.A comparison between the two conditions shows that the wind speed around dummy tower decreased as CT increased.A comparison between the two sections shows that the wind speed in front of the rotor was lower at 50%R compared to that at 80%R.The load was uniform on the rotor, and the inboard sections were considerably affected by the rotor.Energies 2019, 12, x FOR PEER REVIEW 10 of 15

Wind Speed Distributions in Front of the Rotor
The wind speed distributions in typical conditions, CT = 0.4 and 0.9, are shown in Figures 9 and 10.The circles in these figures denote the positions of the dummy towers at −6DT and −4DT.The wind speed tended to decrease in front of the tower in general, and the wind speed was lower in the vicinity of the rotor.A comparison between the two conditions shows that the wind speed around the dummy tower decreased as CT increased.A comparison between the two sections shows that the wind speed in front of the rotor was lower at 50%R compared to that at 80%R.The load was uniform on the rotor, and the inboard sections were considerably affected by the rotor.The distributions of the normalized wind speed µ T and its differential ∂µ T / ∂ξ T with respect to the normalized distance T front of the rotor are shown in Figures 11 and 12

Drag Coefficients of the Virtual Tower
The deviation of the drag coefficient of the virtual tower calculated by the present theory is shown in Figure 13.The x-axis denotes the virtual tower position, and the y-axis denotes the thrust coefficient.The diameter of the tower DT was assumed to be 64 mm, as in the experiment.As indicated by Figures 11 and 12, the drag coefficient tended to be smaller as the rotor-tower clearance decreased and the thrust coefficient increased.The drag tended to be smaller at 50%R than at 80%R.
As shown in Equation ( 14), the rotor thrust-induced tower drag deviation consisted of the wind speed term and the pressure gradient term.Figure 14 shows the share of the wind speed term to the total deviation.It indicates that approximately 80% of the change in the drag wss caused by the first term of Equation ( 12), i.e., the decrease in the wind speed, rather than the pressure gradient.

Drag Coefficients of the Virtual Tower
The deviation of the drag coefficient of the virtual tower calculated by the present theory is shown in Figure 13.The x-axis denotes the virtual tower position, and the y-axis denotes the thrust coefficient.The diameter of the tower DT was assumed to be 64 mm, as in the experiment.As indicated by Figures 11 and 12, the drag coefficient tended to be smaller as the rotor-tower clearance decreased and the thrust coefficient increased.The drag tended to be smaller at 50%R than at 80%R.
As shown in Equation ( 14), the rotor thrust-induced tower drag deviation consisted of the wind speed term and the pressure gradient term.Figure 14 shows the share of the wind speed term to the total deviation.It indicates that approximately 80% of the change in the drag wss caused by the first term of Equation ( 12), i.e., the decrease in the wind speed, rather than the pressure gradient.

Drag Coefficients of the Virtual Tower
The deviation of the drag coefficient of the virtual tower calculated by the present theory is shown in Figure 13.The x-axis denotes the virtual tower position, and the y-axis denotes the thrust coefficient.The diameter of the tower D T was assumed to be 64 mm, as in the experiment.As indicated by Figures 11 and 12, the drag coefficient tended to be smaller as the rotor-tower clearance decreased and the thrust coefficient increased.The drag tended to be smaller at 50%R than at 80%R.
As shown in Equation ( 14), the rotor thrust-induced tower drag deviation consisted of the wind speed term and the pressure gradient term.Figure 14 shows the share of the wind speed term to the total deviation.It indicates that approximately 80% of the change in the drag wss caused by the first term of Equation ( 12), i.e., the decrease in the wind speed, rather than the pressure gradient.

Validation
The thrust-induced drag deviations ΔCdT to the thrust coefficient at −6DT and −4DT are shown in Figure 15.The lines are approximations for which the intercepts are at ΔCdT = 0 and CT = 0 by definition.The ΔCdT values for all the cases are shown to be almost proportional to CT.The proportion factors are summarized in Table 3.The factors of the former BEM are zero, as the method does not consider the influence of the rotor thrust on the tower drag.On the other hand, the proposed method shows good agreement with the test.The drag coefficients tended to decrease as the rotor thrust increased.The drag coefficient at the 50%R section was smaller than at the 80%R section.Further, the drag coefficient decreased as the tower was placed closer to the rotor.

Validation
The thrust-induced drag deviations ΔCdT to the thrust coefficient at −6DT and −4DT are shown in Figure 15.The lines are approximations for which the intercepts are at ΔCdT = 0 and CT = 0 by definition.The ΔCdT values for all the cases are shown to be almost proportional to CT.The proportion factors are summarized in Table 3.The factors of the former BEM are zero, as the method does not consider the influence of the rotor thrust on the tower drag.On the other hand, the proposed method shows good agreement with the test.The drag coefficients tended to decrease as the rotor thrust increased.The drag coefficient at the 50%R section was smaller than at the 80%R section.Further, the drag coefficient decreased as the tower was placed closer to the rotor.

Validation
The thrust-induced drag deviations ∆C dT to the thrust coefficient at −6D T and −4D T are shown in Figure 15.The lines are approximations for which the intercepts are at ∆C dT = 0 and C T = 0 by definition.The ∆C dT values for all the cases are shown to be almost proportional to C T .The proportion factors are summarized in Table 3.The factors of the former BEM are zero, as the method does not consider the influence of the rotor thrust on the tower drag.On the other hand, the proposed method shows good agreement with the test.The drag coefficients tended to decrease as the rotor thrust increased.The drag coefficient at the 50%R section was smaller than at the 80%R section.Further, the drag coefficient decreased as the tower was placed closer to the rotor.

Figure 1 .
Figure 1.Top view of a downwind turbine.U0, free stream wind speed, DT, tower diameter.

Figure 2 .
Figure 2. Computational fluid dynamics (CFD) with actuator disc model (ADM).uT, wind speed at the virtual tower position.

Figure 1 .
Figure 1.Top view of a downwind turbine.U 0 , free stream wind speed, D T , tower diameter.

Figure 1 .
Figure 1.Top view of a downwind turbine.U0, free stream wind speed, DT, tower diameter.

Figure 2 .
Figure 2. Computational fluid dynamics (CFD) with actuator disc model (ADM).uT, wind speed at the virtual tower position.

Figure 2 .
Figure 2. Computational fluid dynamics (CFD) with actuator disc model (ADM).u T , wind speed at the virtual tower position.

Figure 3 .
Figure 3. Schematic of the test model (dummy tower at −4D T ).

Figure 4 .
Figure 4. Test model and dummy tower installed in the wind tunnel.

Figure 5 .
Figure 5. Relationship between the power (CP) and thrust (CT) coefficients and the tip speed ratio.θ, blade pitch angle.

Figure 4 .
Figure 4. Test model and dummy tower installed in the wind tunnel.

Figure 4 .
Figure 4. Test model and dummy tower installed in the wind tunnel.

Figure 5 .
Figure 5. Relationship between the power (CP) and thrust (CT) coefficients and the tip speed ratio.θ, blade pitch angle.

Figure 5 .
Figure 5. Relationship between the power (C P ) and thrust (C T ) coefficients and the tip speed ratio.θ, blade pitch angle.

Figure 6 .
Figure 6.Distribution of the pressure coefficient on the dummy tower in typical cases.

Figure 6 .
Figure 6.Distribution of the pressure coefficient on the dummy tower in typical cases.
. The distributions at CT = 0.4 and 0.9were identical to those in Figures 9 and 10 in the symmetrical plane.The top subplots correspond to the distributions at 50%R, and the bottom ones correspond to those at 80%R.The wind speed was lower in the vicinity of the rotor and decreased as the thrust coefficient increased, as mentioned above.

Figure 9 .
Figure 9. Wind speed distribution in front of the rotor at C T = 0.4, U 0 = 6 m/s.(The circles indicate the dummy tower positions at −6D T and −4D T ).
. The distributions at CT = 0.4 and 0.9were identical to those in Figures 9 and 10 in the symmetrical plane.The top subplots correspond to the distributions at 50%R, and the bottom ones correspond to those at 80%R.The wind speed was lower in the vicinity of the rotor and decreased as the thrust coefficient increased, as mentioned above.

Figure 10 .
Figure 10.Wind speed distribution in front of the rotor at C T = 0.9, U 0 = 6 m/s.(The circles indicate the dummy tower positions at −6D T and −4D T ).
. The distributions at C T = 0.4 and 0.9were identical to those in Figures 9 and 10 in the symmetrical plane.The top subplots correspond to the distributions at 50%R, and the bottom ones correspond to those at 80%R.The wind speed was lower in the vicinity of the rotor and decreased the thrust coefficient increased, as mentioned above.

11 .
Wind speed in front of the rotor as obtained by CFD.μT, normalized wind speed, ξT, normalized distance.

Figure 12 .
Figure 12.Spatial differential of wind speed in front of the rotor (∂μT/∂ξT) as obtained by CFD.

Figure 11 .
Figure 11.Wind speed in front of the rotor as obtained by CFD.µ T , normalized wind speed, ξ T , normalized distance.

Figure 11 .
Figure 11.Wind speed in front of the rotor as obtained by CFD.μT, normalized wind speed, ξT, normalized distance.

Figure 12 .
Figure 12.Spatial differential of speed in front of the rotor (∂μT/∂ξT) as obtained by CFD.

Figure 12 .
Figure 12.Spatial differential of wind speed in front of the rotor (∂µ T / ∂ξ T ) as obtained by CFD.

Figure 13 .
Figure 13.Relationship between tower section drag and rotor thrust and the virtual tower position.ΔCdT, drag coefficient.

Figure 14 .
Figure 14.Share of the wind speed term CdTV in the total CdT tower section drag coefficient.

Figure 13 .
Figure 13.Relationship between the tower section drag and rotor thrust and the virtual tower position.∆C dT , drag coefficient.

Figure 13 .
Figure 13.Relationship between the tower section drag and rotor thrust and the virtual tower position.ΔCdT, drag coefficient.

Figure 14 .
Figure 14.Share of the wind speed term CdTV in the total CdT tower section drag coefficient.

Figure 14 .
Figure 14.Share of the wind speed term C dTV in the total C dT tower section drag coefficient.

Table 1 .
Specifications of the test model and the dummy tower.

Table 1 .
Specifications of the test model and the dummy tower.

Table 2 .
Simulation domain and boundary conditions.

Table 2 .
Simulation domain and boundary conditions.

Table 2 .
Simulation domain and boundary conditions.