MODELLING OF TURBULENT WAKE FOR TWO WIND TURBINES

The construction of several large wind farms (The Ulyanovsk region, the Republic of Adygea, the Kaliningrad region, the North of the Russian Federation) is planned on the territory of the Russian Federation in 2018–2020. The tasks, connected with the design of new wind farms, are currently important. One of the possible direction in the design is connected with mathematical modeling. Large eddy method (eddy-resolving simulation), developed within the Computational Fluid Dynamics, allows to reproduce unsteady structure of the flow in details and define various integrated characteristics for wind turbines. The mathematical model included the main equations of continuity and momentum equations for incompressible viscous flow. The large-scale vortex structures were calculated by means of integration the filtered equations. The calculation was carried out using lagrangian dynamic Smagorinsky’s model to define turbulent subgrid viscosity. The parallelepiped-shaped numerical domain and 3 different unstructured meshes (with 2,4,8 million cells) were used for numerical simulation.

The geometrical parameters of wind turbine were set proceeding to open sources for BlindTest 2–4 project from Internet. All physical values were defined at the center of computational cell. The approximation of items in the equations was performed with the second order of accuracy for time and space. The equations for coupling of velocity, pressure were solved by means of iterative algorithm PIMPLE. The total quantity of the calculated physical values at each time step was equal 18. So, the resources of a high performance computer were required. As a result of flow simulation in the wake for two three-bladed wind turbines the average and instantaneous values of velocity, pressure, subgrid kinetic energy, turbulent viscosity, components of stress tensor were calculated. The received results qualitatively matching the known results of experiment and numerical simulation testify to an opportunity to adequately calculate flow parameters for several wind turbines.

1. Stevens R.J.A.M., Meneveau C. Flow Structure and Turbulence in Wind Farms. Annu. Rev. Fluid Mech., 2017, Vol. 49, pp. 311–339.

2. Medici D., Alfredsson P.H. Measurements on a Wind Turbine Wake: 3-D Effects and Bluff Body Vortex Shedding, Wind Energy, 2006, Vol. 9, pp. 219–236.

3. Cal R.B., Lebron J., Castillo L., Kang H.-S., Meneveau C. Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer. Journal of Renewable and Sustainable Energy, 2010, Vol. 2, pp. 103–106.

4. Chamorro L.P., Port´e-Agel F. Turbulent flow inside and above a wind farm: a wind-tunnel study. Energies, 2011, Vol. 11, pp. 1916–1936.

5. Weller H.G., Tabor G., Jasak H., Fureby C. A tensorial approach to computational continuum mechanics using object oriented techniques. Computers in Physics, 1998, Vol. 12, No. 6, pp. 620–631.

6. Churchfield M.J., Lee S., Michalakes J., Moriarty P.J. A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics. Journal of Turbulence, 2012, Vol. 13, No. 14, pp. 1–32.

7. Sørensen J.N., Shen W.Z. Numerical Modeling of Wind Turbine Wakes. Journal of Fluids Engineering, 2002, Vol. 124, pp. 393–399.

8. Krogstad P. Å., Eriksen P.E. "Blind test" calculations of the performance and wake development for a model wind turbine. Renewable Energy, 2013, Vol. 50, pp. 325–333.

9. Pierella F., Krogstad P.Å., Sætran L. Blind Test 2 calculations for two in-line model wind turbines where the downstream turbine operates at various rotational speeds. Renew. Energ., 2014, Vol. 70, pp. 62–77.

10. Somers DM. The S825 and S826 Airfoils. National Renewable Energy Laboratory 2005. NREL/SR-500-36344. 67 p.

11. Bartl J., Sætran L. Blind test comparison of the performance and wake flow between two in-line wind turbines exposed to different turbulent inflow conditions. Wind Energ. Sci., 2017, Vol. 2, pp. 55–76.

12. Strijhak S.V. Matematicheskoe modelirovanie parametrov techeniya odinochnoi vetroelektricheskoyi ustanovki [Mathematical modelling of flow parameters for single wind turbine]. Nauchniy Vestnik MGTU GA [Сivil Aviation High Technologies], 2016, Vol. 19, № 6, pp. 176–184.