This is likely due to the fact that the blade from one turbine, as it approaches the plane defined by the centerlines of the two towers, encounters the wake of the blade from another turbine. This, in turn, produces higher drag on that blade and results in reduction of the aerodynamic torque. A snapshot of vorticity colored by flow speed depicted in Figure 2.9 shows that the short distance between the turbines has a noticeable effect on the resulting aerodynamics. This effect may be seen more clearly in Figure 2.10, which shows that one of the blades from the VAWT on the right is about to enter the turbulent region between the turbines.The computations presented in this section are performed for a 1.2 kW Windspire design, a three-bladed Darrieus VAWT . The total height of the VAWT tower is 9.0 m, and the rotor height is 6.0 m. The rotor uses the DU06W200 airfoil profile with the chord length of 0.127 m, and is of the Giromill type with straight vertical blade sections attached to the main shaft with horizontal struts. The aerodynamics simulations are carried out at realistic operating conditions, hydroponic flood table reported in the field test experiments conducted by the National Renewable Energy Lab and Caltech Field Laboratory for Optimized Wind Energy. For all cases, the air density and viscosity are set to 1.23 kg/m3 and 1.78×10−5 kg/, respectively.
The outer aerodynamics computational domain has the dimensions of 50 m, 20 m, and 30 m in the stream-wise, vertical, and span-wise directions, respectively,and is shown in Figure 2.12. The VAWT centerline is located 15 m from the inflow and side boundaries. The radius and height of the inner cylindrical domain that encloses the rotor are 1.6 m and 7 m, respectively. At the inflow, a uniform wind velocity profile is prescribed. On the top, bottom and side surfaces of the outer domain no-penetration boundary conditions are prescribed, while zero traction boundary conditions are set at the outflow. The aerodynamics mesh has about 8 M elements, which are linear triangular prisms in the blade boundary layers, and linear tetrahedra elsewhere. The boundary layer mesh is constructed using 18 layers of elements, with the size of the first element in the wall-normal direction of 0.0003 m, and growth ratio of 1.1. The 2D slice of the mesh near the rotor is shown in Figure 2.13. Blade 1 is placed parallel to the flow with the airfoil leading edge facing the wind. Blades 2 and 3 are placed at an angle to the flow with the trailing edge facing the wind. Figure 2.14 shows the zoom on the boundary-layer mesh near one of the blades. The mesh design employed in this simulation is based on a refinement study performed for a Darrieus-type experimental turbine in Section 2.3.1. All computations are carried out in a parallel computing environment. The mesh is partitioned into subdomains using METIS, and each subdomain is assigned to a compute core.
The parallel implementation of the methodology may be found in. The time step is set to 1.0 × 10−5 s. Two aerodynamic simulations are performed for the Windspire VAWT, one using the wind speed of 8.0 m/s and rotor speed of 32.7 rad/s, and another using the wind speed of 6.0 m/s and rotor speed of 20.6 rad/s. The time history of the aerodynamic torque for both cases is plotted in Figure 2.15 together with the experimental values reported from field-test experiments. After the rotor undergoes a full revolution, a nearly periodic solution is attained in both cases. For 8.0 m/s wind the predicted average torque is 18.9 Nm, while its the experimentally reported value is about 12.7 Nm. For 6.0 m/s wind the predicted average torque is 9.5 Nm, while its the experimentally reported value is about 4.8 Nm. In both cases the experimental value of the aerodynamic torque is derived from the average power produced by the turbine at the target rotor speed. The difference in the predicted and experimentally reported aerodynamic torque is likely due to the mechanical and electrical losses in the system, which are not reported.The main structural components of wind turbines are modeled using a combination of the recently proposed displacement-based Kirchhoff–Love shell and beam/cable formulations. The shell formulation is used to represent wind turbine rotor, nacelle and a tower while the beam/cable formulation is used to describe the main shaft, struts in VAWT design and mooring cables in an application to offshore turbine designs, which however would not be covered in this work .
Both are discretized using IGA techniques based on Non-Uniform Rational B-Splines. This approach gives a good combination of structural mechanics accuracy due to the higher-order and higher-continuity representation of the geometry and solution, and efficiency due to the lack of rotational degrees of freedom in the formulation.The blade surface is comprised of five primary zones: leading edge, trailing edge, root, spar cap, and shear web. The zones are shown in Figure 3.4. Each zone is made up of a multilayer composite layup. The different materials used for the layups are summarized in Table 3.2. The root area has many layers of fiberglass plies to strengthen the region where the blade is mounted on the hub flange. The leading and trailing edge zones have a similar layup. Both include the outer gel coat and fiberglass layers, with the total thickness of 0.51 mm, as well as additional layers of fiberglass material DBM-1708, 0.89 mm each, and one 6.35 mm layer of balsa wood. Balsa wood is only present in the core section of the blade and not on the edges. The leading edge zone has additional layers of fiberglass material DBM-1208, with a total thickness of 0.56 mm, between the DBM-1708 and balsa core. The layups of the core regions of the trailing and leading edge zones are shown in Figure 3.3. The spar-cap zone has a nonuniform thickness distribution, ranging from 5.79 mm to 9.65 mm, due to the decreasing number of carbon fiber laminate layers along the blade length. The sparcap layup is also shown in Figure 3.3, and has the thickest carbon fiber layer. The shear web, which is designed to carry most of the surface loads, has a C-shape structure containing four layers of DBM-1708 fiberglass, 0.74 mm each, and 9.53 mm of balsa wood core. The balsa wood layer is terminated in the tip zone. As a result, the tip region is only comprised of one layer of gel coat and several layers of fiberglass material. This layout leads to 32 zones with constant total thickness and unique laminate stacking in each zone. The effective material properties for each of the zones are computed using the procedures described in the previous section. All 32 zones are identified on the blade surface and are shown in Figure 3.4.We perform eigenfrequency calculations using the CX-100 blade using three quadratic NURBS meshes. The coarsest mesh has 1,846 elements, while the finest mesh has 18,611 elements. The mesh statistics are summarized in Table 3.3. Table 3.4 gives the blade mass and position of the center of gravity . Note that, although the blade geometry is “exact” and stays unchanged with mesh refinement, ebb and flood table because the mesh linesdo not conform to the 32 different material zones, there is a very small variation in the blade mass and center-of-gravity position from one mesh to the other.
The eigenfrequency results are compared with the experimental data from. We compute the case with free boundary conditions and the case when the blade is clamped at the root. For the free case the eigenfrequencies for the first and second flapwise bending modes and for the first edgewise bending mode are summarized in Table 3.5. The experimental eigenfrequencies are obtained for this blade at Sandia National Laboratories , Los Alamos National Laboratory , and the University of Massachusetts Lowell Structural Dynamics and Acoustics Laboratory , and reported in [87]. Table 3.5 provides a range of experimental eigenfrequency values. For the clamped case, the eigenfrequencies for the first three bending modes are compared with the results of the tests performed at the National Renewable Energy Laboratory. In both cases, the computed natural frequencies are in good agreement with the experimental data . The medium mesh shows a good balance between the computational cost and accuracy of the results. For this reason, this mesh is chosen for the FSI computations presented in Chapter 4. The mode shapes computed using the medium mesh are shown in Figures 3.5 and 3.6.A 100 m baseline wind turbine blade design analyzed in this section is developed by Sandia National Laboratory. It was initially developed based on the geometry and composite layup of the 61 m baseline offshore designs employed in the NREL, DOWEC and UpWind projects. The details of blade geometry are provided in Table 3.7. The SNL 100-00 blade was obtained by a simple scaling of the 61 m design and its additional minor modifications to increase the load carrying capacity. Three shear webs were placed to minimize the length of the unsupported panel . The blade laminate has six principal regions: root, spar cap, trailing edge reinforcement,leading edge panels, aft panels and shear webs. Tables 3.8 and 3.9 list the materials used in the blade design. The root buildup is composed of triaxial material , and the whole internal and external blade surfaces have a 5 mm layer of this material. As the root buildup tapers down in thickness, the spar cap increases in thickness. The maximum thickness of the spar cap is 136 mm at maximum chord , while the minimum thickness of the spar cap is 5 mm, starting at 94.4% of the blade span and continuing almost all the way to the tip. The trailing edge is reinforced with uniaxial laminate E-LT-5500/EP-3 and foam materials. The trailing edge reinforcement has a constant width of 1.0 m that continues until 94.4% span, and then tapers to the tip. To improve buckling resistance and minimize the weight, foam is also chosen as the core material for the leading panel and aft panels. Longitudinal fibers of E-LT-5500/EP-3 are placed on the spar cap to improve the flap wise bending stiffness. The spar cap has a constant width of 1.5 m. As a result, the two principal shear webs, which begin at 2.4 m and terminate at 94.4 m, are positioned 0.75 m before and after the pitch axis. The third shear web starts at 14.6 m and terminates at 60.2 m, and is positioned at 78% chord at its starting location and 68% chord at its terminal location. A combination of foam and Saertex/EP-3 is used in shear webs to enhance the shear stiffness. An extra 5 mm of epoxy resin is included in the internal blade surface, and the external surface includes 0.6 mm of gelcoat. The same layup is employed for both lowand high-pressure blade surfaces. We perform the natural frequency analysis of the blade model assumed to be clamped at the root. Three quadratic NURBS meshes of increasing resolution are employed in the computations. The medium and fine meshes and shown in Figure 3.8. The mesh statistics are summarized in Table 3.10. The blade total mass for each meshis reported in Table 3.11, and the mass distribution along the blade axis is plotted in Figure 3.9. The eigenfrequencies for the three meshes are summarized in Table 3.12 and, where applicable, compared to the results reported in [6]. Very good agreement is observed in all the quantities reported. Convergence of the natural frequencies occurs from the high side, as expected. This is the first time that natural frequencies beyond the first flapwise and edgewise modes are reported for this blade design. For the FSI computation presented in Chapter 4 the medium NURBS mesh is employed. Furthermore, for the FSI computation, the 100 m blade is scaled back to 61 m.We start with the FSI simulations of the Micon 65/13M wind turbine. This is a three-blade, fixed-pitch, upwind turbine with the total rotor diameter of 19.3 m and rated power of 100 kW. The hub is located at the height of 23 m,with a mounting flange positioned 0.6 m from the centerline of the low-speed shaft.