MATHEMATICAL MODELING OF FLOW PARAMETERS FOR SINGLE WIND TURBINE

It is known that on the territory of the Russian Federation the construction of several large wind farms is planned. The tasks connected with design and efficiency evaluation of wind farm work are in demand today. One of the possible directions in design is connected with mathematical modeling. The method of large eddy simulation developed within the direction of computational hydrodynamics allows to reproduce unsteady structure of the flow in details and to determine various integrated values. The calculation of work for single wind turbine installation by means of large eddy simulation and Actuator Line Method along the turbine blade is given in this work. For problem definition the numerical method in the form of a box was considered and the adapted unstructured grid was used.The mathematical model included the main equations of continuity and momentum equations for incompressible fluid. The large-scale vortex structures were calculated by means of integration of the filtered equations. The calculation was carried out with Smagorinsky model for determination of subgrid scale turbulent viscosity. The geometrical parametersof wind turbine were set proceeding from open sources in the Internet.All physical values were defined at center of computational cell. The approximation of items in equations was executed with the second order of accuracy for time and space. The equations for coupling velocity and pressure were solved by means of iterative algorithm PIMPLE. The total quantity of the calculated physical values on each time step was equal to 18. So, the resources of a high performance cluster were required.As a result of flow calculation in wake for the three-bladed turbine average and instantaneous values of velocity, pressure, subgrid kinetic energy and turbulent viscosity, components of subgrid stress tensor were worked out. The received results matched the known results of experiments and numerical simulation, testify the opportunity to adequatelycalculate the flow parameters for a single wind turbine.

wind farms, wind turbine, solver, large eddy simulation, Smagorinsky model, numerical domain, vortex wake, airfoil profile, angle of attack, velocity profile

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