As shown in this gives a good combination of accuracy and efficiency for this problem class. Having a well-designed boundary-layer mesh in wind-turbine simulations is critical for achieving engineering accuracy with a reasonable number of degrees of freedom. During operation, wind turbine blades undergo large global rotational motions, as well as local flap wise and edgewise bending, and axial torsion deformations. As a result, in order to account for the blade motion and to simultaneously maintain good-quality boundary-layer discretization, a moving-mesh technique should be employed where the boundary-layer mesh follows the blades as they moves through space. In the case of standalone wind-turbine-rotor FSI computations this may be accomplished by applying a global rotation to the entire aerodynamics mesh, and handling the remaining blade deflection using elastic mesh moving as in [18]. A jacobian-based stiffening technique in elastic mesh moving is essential for maintaining the integrity of the elements in the blade boundary layers. In the case a full machine is considered, the spinning rotor interacts with the tower. This interaction is strong and needs to be modeled explicitly. In the recent wind-turbine FSI computations presented in the wind-turbine hub was assumed to spin with a fixed, prescribed angular velocity, and the tower was assumed to be stationary. The aerodynamics of rotor-tower interaction was handled using a sliding-interface technique. In this technique, 2×4 flood tray rather than rotating the entire computational domain, only the inner cylindrical subdomain that encloses the rotor undergoes a spinning motion inside the cylindrical cut-out of the outer stationary domain. The two domains do not overlap, and, as a result, create a sliding cylindrical interface with a priori non-matching discretizations on each side.
The continuity of the kinematic and traction variables across the non-matching sliding interface is enforced weakly.In order to simulate more complicated FSI scenarios, such as rotor yawing for HAWTs, or even basic operation for VAWTs, additional computational technology is required. In the case of HAWT rotor yawing motion, the entire gearbox undergoes rotation parallel to the tower axis, and this rotation must be transferred to the rotor and hub without interfering with the rotor spinning motion. In the case of basic VAWT operation, the air flow spins the rotor, which is connected to a flexible tower with struts. Furthermore, the moving-mesh aerodynamics formulation for this expanded problem class can no longer have a fixed sliding interface. For example, in the case of the rotor yawing motion, in order to keep the good quality of the aerodynamics mesh and prevent the rotor blades from crossing the boundary of the rotor cylindrical domain, it is preferred that the sliding interface follows the motion of the gearbox, while accommodating the spinning rotor. This results in two cylindrical surfaces moving together while one spins inside the other. Another challenge in FSI simulations is to model the geometrically complex structures with its nonlinear material distribution, which undergoes large deformation. A combination of a rotation-free multilayer composite Kirchhoff–Love shell and beam allows for the rotor to spin freely and for the tower and blades to undergo elastic deformations. An isogeometric analysis with NURBS based elements representation is used to construct analysis-suitable geometry. The NURBS-based IGA may be seen as a combination of CAD basis functions and the isoparametric concept and may be extended to T-splines and subdivision surfaces. Because of the rational nature of the basis functions the circular shapes can be represented exactly which reduce the geometrical-approximation error when modeling complex-shaped wind turbine blades.
Furthermore, the higher order continuity is achieved with NURBS basis functions and the geometry is preserved unchanged under the mesh refinement process, which is not the case in FEM. The dissertation is outlined as follows. In Chapter 2 we state the ALE-VMS formulation of aerodynamics in combination with our sliding interface approach for the simulation of mechanical components in relative motion. To validate our aerodynamic formulation we show the computations of a small-scale Darrieus-type wind turbines. One is a 3.5 kW wind turbine tested in NRC wind tunnel. For this turbine two cases were simulated: A single turbine, and two counter-rotating turbines placed side-by-side in close proximity to one another. For a single turbine a mesh refinement study was performed, and results were compared to experimental data. Another turbine is designed by Windspire with rated power of 1.2 kW. For this case the computational results were compared to a field test experiments conducted by the National Renewable Energy Lab and Caltech Field Laboratory for Optimized Wind Energy. In Chapter 3 we present the coupled Kirchhoff–Love shell for an arbitrary composite layup of wind turbine blades. To verify the model we perform the eigen frequency analysis of recently designed offshore wind turbine blade and CX-100 blade, which compare favorably to the experimental data. In Chapter 4 we introduce the coupled FSI formulation employed in this work with non matching discretization of the aerodynamic and structural domains. Later in the chapter we present FSI computations of the Micon 65/13M wind turbine. Both the aerodynamics and FSI torque results fall within the range predicted by the field tests for this wind turbine. The FSI case shows high-frequency fluctuations in the aerodynamic torque, which are due to the high-frequency vibration of the blades. Next, the FSI computations of offshore HAWT under yawing motion is presented and the discretization techniques employed and the aforementioned enhancement of the sliding-interface formulation are described.
We conclude with the FSI computations of the Windspire VAWT and discuss start-up issues. In Chapter 5 we draw conclusions and discuss possible future research directions.The aerodynamics simulations are performed for a three-blade, high-solidity VAWT with the rated power of 3.5 kW. The prototype is a Darrieus H-type turbine designed by Cleanfield Energy Corporation. Full-scale tests for this turbine were conducted in the National Research Council low-speed wind tunnel at McMaster University . Experimental studies for this turbine focused on the application of VAWTs in urban areas. The turbine has a tower height of 7 m. The blades, 3 m in height, are connected to the tower by the struts of length 1.25 m. This value is taken as the rotor radius. A symmetric NACA0015 airfoil profile with chord length of 0.4 m is employed along the entire length of the blades. See Figure 2.1 for an illustration. The computations were carried out for constant inflow wind speed of 10 m/s, and constant, fixed rotor speed of 115 rpm. This set up corresponds to the tip speed ration of 1.5, which gave maximum rotor power as reported in [32,58]. However, it was also reported for the wind tunnel tests that the control mechanism employed was able to maintain an average rotor speed of 115 rpm with the deviation of ±2.5 rpm. This means the actual rotor speed was never constant. The air density and viscosity are set to 1.23 kg/m3 and 1.78 × 10−5 kg/, respectively. On the inflow, flood and drain table the wind speed of 10 m/s is prescribed. On the top, bottom and side surfaces of the stationary domain no-penetration boundary conditions are prescribed, while zero traction boundary condition is set on the outflow. No-slip boundary conditions are imposed weakly on the rotor blades and tower. The struts are not modeled in this work to reduce computational cost. The struts are not expected to significantly influence the results for this VAWT design. The computations were carried out in a parallel computing environment. The meshes, which consist of linear triangular prisms in the boundary layers and linear tetrahedra elsewhere, are partitioned into subdomains using METIS, and each subdomain is assigned to a compute core. The parallel implementation of the methodology may be found in [80]. The time step is set to 1.0 × 10−5 s for all cases.We first compute a single VAWT and assess the resolution demands for this class of problems. The stationary domain has the outer dimensions of 50 m, 20 m, and 30 m in the stream-wise, vertical, and span-wise directions, respectively. The VAWT centerline is located 15 m from the inflow and side boundaries. The radius and height of the spinning cylinder are both 4 m. Three meshes are used with increasing levels of refinement. The overall mesh statistics are summarized in Table 2.1. The finest mesh has over 17M elements. The details of the boundary-layer discretization are as follows. For Mesh 1, the size of the first element in the wall-normal direction is 0.000667 m, and 15 layers of prismatic elements were generated with a growth ratio of 1.15.
For Mesh 2, the size of the first element in the wall-normal direction is 0.000470 m, and 21 layers of prismatic elements were generated with a growth ratio of 1.1. For Mesh 3, the size of the first element in the wall-normal direction is 0.000333 m, and 30 layers of prismatic elements were generated with a growth ratio of 1.05. Figure 2.14 shows a 2D slice of Mesh 2, focusing on the boundary-layer discretization of the blade.Time history of the computed aerodynamic torque is plotted in Figure 2.5 together with the experimental value reported for these operating conditions. Only the mean value of the torque was reported in [32, 58]. Note that after a couple of cycles a nearly periodic solution is attained. Mesh 1 predicts the average torque of about 52 Nm, Mesh 2 gives the average torque of about 70 Nm, and Mesh 3 predicts the average torque of about 80 Nm, while the targeted experimental value is about 90 Nm. Looking further at the curves we observe that the largest differences between the predicted values of the torque between the meshes occur at the maxima and minima of the curves. Also note that the torque fluctuation during the cycle is nearly 200 Nm, which is over twice the average. One way to mitigate such high torque variations is to allow variable rotor speed.Figure 2.6 shows a snapshot of vorticity colored by flow speed. The upstream blade generates tip vortices near its top and bottom sections. Note that no large vortices are present in the middle section of the blade. There, as the flow separates on the airfoil surface, larger vortices immediately break up into fine-grained trailing-edge turbulence. The tip vortex and trailing-edge turbulence are then convected with the ambient windvelocity, and impact the tower, as well as the blade that happens to be in the downwind position in the spin cycle. However, as it is evident from the torque time histories shown in Figure 2.5, these do not produce a major impact on the rotor loads, at least for a chosen set of wind and rotor speeds. The situation may, of course, change for a different set of operating conditions.Here we investigate two counter-rotating turbines placed side-by-side in close proximity to one another. The wind and rotor speeds are the same as before, however, the turbines rotate out of phase, with the difference of 60◦ . The distance between the towers of the two turbines is 2.64R, where R =1.25 m is the rotor radius. This distance between the turbines falls in the range investigated in the experimental work of [1].The stationary domain has the outer dimensions of 50 m, 20 m, and 33.3 m in the stream-wise, vertical, and span-wise directions, respectively. The centerline of each VAWT is located 15 m from the inflow and 15 m from its closest side boundary. The radius and height of the spinning cylinders are 1.45 m and 4 m, respectively. A 2D slice of the computational-domain mesh focusing on the two rotors is shown in Figure 2.7. The boundary layer discretization employed for this computation is the same as that of Mesh 2 in the previous section.Figure 2.8 shows the time history of the aerodynamic torque for the two-turbine case. The time history of the torque for a single VAWT simulation is shown for comparison. Note that while the maxima of all curves are virtually coincident, the minima are lower for the case of multiple turbines. Also note that the multiple-turbine torque curves exhibit some fluctuation near their minima, while the single-turbine torque curve is smooth near its minima.