3.4.2. Tower

The tower is now considered for study. The same conditions of simulation were set for both the proposed tool and FAST. The loads were transmitted from the rotor to the tower, considering the dynamic behavior of the rotor loads. The elasticity of the tower together with the aerodynamic and gravitational loads of the tower itself were also considered. As observed from the dynamic responses of the blade, the out-of-plane quantities are more significant than the in-plane ones, and hence, the out-of-plane properties for the tower are shown for comparison.

It is observed in Figures 14 and 15 that there is a very good agreemen<sup>t</sup> between the results of the present tool compared to FAST. Discrepancies appear in the tower dynamics in the initial runs as well. This is due to difference in the rotor loads, which appeared in the blade's results, as well as differences in the natural frequencies of the tower itself.

**Figure 14.** Tower-base, fore-aft bending moment.

**Figure 15.** Tower-top, fore-aft deflection.

For both the blade and tower dynamic responses, the results of the proposed tool have shown credibility in modeling the aeroelastic behavior of a wind turbine. So far, the tool is able to generate loads and deflections' time series for the turbine parts in case of a steady wind. In the next section, another rotor is added on the same tower, and the tower dynamics are studied.

#### **4. Simulation of the Twin-Rotor Model**

#### *4.1. Twin-Rotor Wind Turbine Model*

In this section, the tower of a twin-rotor turbine with two NREL 5MW rotors is modeled. The support structure is assumed to be a T-shaped structure, with the main tower and two side booms connecting the rotors. The side booms are assumed to be a scaled-down structure of the NREL 5MW main tower, each of 63.5 m in length from the main tower center point, such that the two rotors are distanced at 127 meters from hub to hub. These booms' lengths were chosen such that the tips of each of the 126 m diameter rotors are 1 m apart.

It is also assumed that there is no aerodynamic interaction between the two rotors. This assumption can be only accepted as preliminary study, as in reality, rotors affect each other. However, to account for that assumption, a pitch misalignment of 0.2◦ and −0.2◦ is added to each rotor's second and third blades, respectively, which is common to generate aerodynamic imbalance. Figure 16 shows a sketch of the proposed twin-rotor configuration.

For comparison of the tower's structural behavior between single and twin rotor configurations, the main tower's geometry and structural properties are changed such that the natural frequency of the first fore-aft mode is the same for both towers. The outer diameter of the tower is changed while the thickness is kept constant. It was found that an outer diameter 1.25 times the diameter of the

single-rotor configuration turbine will cause the first fore-aft natural frequency of both configurations' towers to be equal. Table 3 shows the differences in the geometry between both configurations.

**Figure 16.** Sketch of the twin-rotor configuration.


 87.600  87.600

Tower height

**Table 3.** Tower geometry.

Figure 17 shows the difference in the mass and stiffness distributions between the single rotor and twin rotor configurations' towers.

**Figure 17.** Tower structural properties: single rotor vs. twin rotor: (**a**) tower mass density distribution; (**b**) tower stiffness distribution.

The natural frequencies in case of the twin rotor configuration are shown in Table 4.

The natural frequencies other than the first fore-aft mode are changed compared to the single rotor configuration. This means that the tower stiffness and structural damping matrices in the mathematical model in the case of the twin rotor are different. Moreover, the loads are increased significantly due to the addition of another rotor, and hence the deformations are expected to change in a non-straightforward way.


**Table 4.** Natural frequencies for the tower – Single Vs. Twin rotor configuration.

## *4.2. Simulation Conditions*

Two load cases were investigated for the twin rotor configuration; one is in a steady wind condition, and the other is in turbulent wind conditions.

In the steady wind case, the rotors are subject to the same conditions as in the case of single rotor: a steady wind velocity of 11.4 m/s, rotating the rotors at 12.1 rpm. This case studies the aeroelastic properties when the two rotors are rotating simultaneously, such that the rotor loads are superimposed in all the loads' value ranges, and then investigates when the rotors have a 60◦ phase change in the blades' azimuth positions.

In the turbulent wind condition case, the rotors are subject to a turbulent wind field created by NREL's tool TurbSim [21]. The rotors are subject to different turbulence classes according to IEC 61400-1 standards [22] at an average wind speed at the hub height of 8 m/s and turbulence intensities of class A (high turbulence), B (moderate turbulence), and C (low turbulence). A variable speed control algorithm is used in the turbulent case.

In all cases, the out-of-plane dynamic responses—deflection and bending moment—of the tower are shown.

#### 4.2.1. Case 1: Steady Flow Condition

In this case, the two rotors' loads superimpose in the whole range of values, in the peak values at the beginning of rotation and until it settles for the nominal value of the load, while the blades of both rotors are in the same azimuth position.

First, the tower was modeled as a stiff tower, and the bending moment at the tower base is calculated. Then this model is compared to an elastic tower model to see the differences in results. The results of this simulation are shown in Figure 18.

**Figure 18.** Tower-base fore-aft bending moment: stiff vs. elastic tower.

The stiff tower model doesn't show the dynamic behavior of the load; moreover, the values are less than those in the elastic tower model. The gravity effects due to the vibration of the tower are eliminated in the case of the stiff tower, and hence the loads are far from the real values. This proves that it is not proper to consider the tower to be a stiff for load calculations and it is important to model it as an elastic tower.

Dynamic responses for the elastic tower model were then calculated, Figures 19 and 20 show the tower-base bending moment and tower-top deflection in the fore-aft direction.

**Figure 19.** Tower-base, fore-aft bending moment.

**Figure 20.** Tower-top, fore-aft deflection.

As was expected, the change in the values of deflection of the tower top and bending moment of the tower base is not linear with the addition of an extra rotor. The change is affected by both the added load and the change in the natural frequencies of the new tower's geometrical properties and hence the stiffness and damping matrices in the mathematical model. The difference is elaborated clearly in Figure 21, where the results of the single-rotor and twin-rotor are shown together.

**Figure 21.** Dynamic responses of the tower: single-rotor vs. twin-rotor load case 1: (**a**) tower-base, fore-aft bending moment, and (**b**) tower-top, fore-aft deflection.

For a tower with the same first fore-aft natural frequency as the single-rotor configuration, the effect of adding one more rotor on the dynamic responses is not straightforward. Two simultaneously rotating rotors on the same tower increase the tower loads and deflections are more than doubled. This is due to the change in the structure of the mathematical model and the added weight and rotor inertias on the top of the tower, which change the natural frequencies in the second fore-aft and first side-side directions.

Then, a phase difference in the initial azimuth position of the first blade of each rotor of 60◦ is investigated for comparison. The dynamic responses of the tower are shown in Figures 22 and 23.

**Figure 22.** Tower-base, fore-aft bending moment.

**Figure 23.** Tower-top, fore-aft deflection.

Here, the dynamic responses of the tower are almost identical with the no phase difference case, but there is a very slight difference which can only be seen only by zooming into the graph. However, with the phase change between the azimuth position of the rotors' blades, there is a slight phase change in the rotor loads, and hence a twisting moment is generated on the tower causing a yawing deflection, which should be studied to anticipate its effect. The yawing deflection of the tower-top is shown in Figure 24.

When the two rotors were rotating simultaneously and under the same aerodynamic conditions, there was no twisting moment for the tower and hence no deflection. When only a phase change between the rotors occurred, a twisting moment was generated causing angular deflection. For different wind conditions the effect of twist can be severe and cause torsional fatigue and hence failure. So, for a twin-rotor configuration, torsional stiffness should be carefully considered in the tower design.

**Figure 24.** Tower top yawing deflection - Load case 2.

#### 4.2.2. Case 2: Turbulent Flow Condition

In this case, the rotors are subject to a turbulent flow field, using the IEC Kaimal spectral model. Fields having turbulence intensities of IEC 61400 classes A, B, and C, with an average wind speed of 8 m/s, were created with TurbSim. The turbulent grid width was doubled to be able to cover both rotors. Variable speed control was applied to control the rotating speed of the rotors. The generator specifications are available in the NREL 5MW definition report [14]. For a gear ratio of 97:1 and a generator efficiency of 94.4%, the optimal constant of proportionality will be 0.0255764 N.m/rpm2. The simulation was run for 10 minutes, and the tower dynamic responses were calculated. Figure 25 shows the wind speed at the hub height for all the turbulent cases. Figure 26 shows the tower-base for-aft bending moment and the tower-top fore-aft deflection time series.

**Figure 25.** Wind Speed at Hub Height.

Since the turbulent domain covers both rotors, it is expected that each rotor experiences different wind conditions, which indicates the presence of torsional moment over the tower. The yawing deflection over the tower is shown for each turbulence case in Figures 27–29.

It is clear that the turbulent nature of the flow has affected the behavior of the yawing deflection. The deflection is quite random and does not have a general trend, unlike the case of steady wind where the deflection had a periodic nature. This randomness indicates unfavored instability in the dynamics, which affect the lifetime of the turbine, and a thorough fatigue study must be made to avoid sudden failures.

**Figure 26.** Tower Dynamic Responses; (**a**) Tower-Base Fore-aft Bending Moment, Turb. Class A; (**b**) Tower-Top Fore-aft Deflection, Turb. Class A; (**c**) Tower-Base Fore-aft Bending Moment, Turb. Class B; (**d**) Tower-Top Fore-aft Deflection, Turb. Class B; (**e**) Tower-Base Fore-aft Bending Moment, Turb. Class C; and (**f**) Tower-Top Fore-aft Deflection, Turb. Class C.

**Figure 27.** Tower top yawing deflection: turb. class A.

**Figure 28.** Tower top yawing deflection: turb. class B.

**Figure 29.** Tower top yawing deflection: turb. class C.

Frequency analysis has been made for the bending moment dynamic response of the tower. Figures 30–32 show the results.

**Figure 30.** Frequency analysis, tower-base bending moment, turb. class A.

Frequency analyses in all turbulent cases shows that the dominant frequencies are at 0.32 Hz and 3 Hz, which are the same as the free vibration natural frequencies of the tower.

Comparison between dynamic response of the tower-base bending moment for the turbulent flow load cases is shown in Table 5.

**Figure 31.** Frequency analysis, tower-base bending moment, turb. class B.

**Figure 32.** Frequency analysis, tower-base bending moment, turb. class C.



Statistical analysis in Table 5 has shown that the tower's natural frequencies are dominant over the flow condition. For the high turbulence intensity, the mean value of the load is less than the other intensities; however a higher standard deviation occurs, which indicates severe oscillation of the loads.
