Computer simulation of wind turbine dynamics.

Fig. 3. Blades of a turbine

Fig. 4. Main characteristics

A 3D Reynolds averaged Navier-Stokes equations (3D RANS) were integrated in the numerical model. A standard к-? model was used as a closure relation for turbulence; an incompressible viscous gas (air) was used as a working media. All simulations were performed in ANSYS CFX 12.0 enjeneering package.

The developed approach includes all stages of high performance computations (HPC): reading of geometrical data from dwg files, development of a solid-state turbine model, mesh generation, creation of physical and mathematical model (choice of computational domain and subdomains, initial and boundary conditions), and finally methodological and parametric studies.

A complete solid-state CAD model that includes a rotor with three blades, a nacelle and a conical tower is shown on Fig. 5. An individual blade with a curvilinear downwind adge is shown on Fig. 6.

Fig. 5. A complete solid-state CAD model

Fig 6. Blade CAD model

Several types of flow setup were considered in this study. Simulations were performed with and without taking the earth surface into account, with or without nacelle and tower. Simulations revealed minor influence of the presence of the tower, of the nacelle and the earth’s surface (for tower height of 20 m) on the integral parameters of the turbine. The critical contribution in power generation is related to the rotation of the blades with a prescribed angular velocity.

In order to make a proper choice of topology and dimensions of the computational domain a series of runs was done. As a main scenario a steady-state flow with uniformed wind profile in the far field with a presence of stationary nacelle was used for hydrodynamic simulations. Computational domain in this case contains two cylindrical sub-domains: the outer non-rotating cylinder has a radius of 50 m and length of 100 m. It is used for far-field steady uni-axial flow. The inner domain is a cylinder rotating with constant angular velocity that envelops turbine blades. It has the radius of 9.5 m and the length of 2.5 m (Fig. 7,8).

Fig. 7. Computational domain

Fig. 8. Rotating sub-domain

For flux exchange between two domains standard interfaces like “Stage” and/or “Frozen Rotor” were used.

Mesh was generated in semi-automatically in CFX-Mesh grid generator. A 3D hybrid tetrahedral mesh with prismatic layers in boundary layers on solid surfaces wit total amount of 8.85 million cells was generated. 7.6 million cells were located in the inner rotating sub-domain and 1.25 million cells – in the outer stationary sub-donain. A fragment of the mesh on the surface of the nacelle, main shaft, rotor and blades is represented on Fig. 9 (the wind direction is shown by an arrow).

Fig.9. A fragment of triangular mesh on the surface of the nacelle and blades

The simulation of one set of parameters with a fixed wind speed and angular velocity in steady state took approximately 30 hours on high performance graphics station.

Below is the series of computer flow visualization that allows to reveal main features and local flow characteristics is shown.

Fig. 10. Streamlines in rotating frame

Fig. 11. Streamlines in the absolute frame of reference, showing appearance of inductive sidewash after rotating blades due to flow deviation

Fig.12. Streamlines at the exit from rotating sub-domain after blades

Fig. 13. Visualization of a vortex, escaping from the blade edge

Fig. 14. Visualization of a vortex sheet leaving the flank of the blade in the attachment area of the blade to the rotor

Fig. 15. Visualization of the central axis vortex leaving the main spindle

The comparison of the main aerodynamical characteristics and mechanical power with experimental measurements that was done after intense parametric studies is shown on Fig. 16. There is a very good agreement between experimental and calculated values taking into account that many parameters for which experimental measurements were done (e.g. wind district, wind profile, type of the terrain, degree of turbulent pulsations, etc.) was not known during numerical simulations.

Fig. 16. Power and angular torque: experimental and calculated data

Power of a wind generator within a classical theory framework can be determined approximately in the following way:

where wind utilization coefficient, usually 0.4-0.45, R – rotor radius, r –density of the air (1,25 кг/м3), V – wind velocity, hred – reduction unit efficiency (usually 0,9-0,95), hgen – generator efficiency – (usually 0,7-0,9).
Electrical power of a wind generator Nel is related to mechanical power Nmec, calculated as a product of torque on a rotor spindle Mr and angular blade velocity w, by the following approximate relationship:

Typically an electrical power of a wind generator reaches up to 65-85% of mechanical power on the rotor. Our simulations show that for an optimal wind speed the efficiency of the wind generator is equal to 87% that is close to the upper bound of the efficiency range.