Chivaee, Hamid Sarlak1; Sørensen, Jens Nørkær1; Mikkelsen, Robert Flemming1
1 Department of Wind Energy, Technical University of Denmark2 Fluid Mechanics, Department of Wind Energy, Technical University of Denmark
Large eddy simulation of an arbitrary wind farm is studied in the neutral and thermally stratified atmospheric boundary Layer. Large eddy simulations of industrial flows usually requires full resolution of the flow near the wall and this is believed to be one of the main deficiencies of LES because the computational costs scale rapidly with Reynolds number and domain size. An approach to overcome these deficiencies is to use a wall modeling near the walls and then use a coarser grid at the first grid level above the ground. This could be performed by using simplified Navier-Stokes equations in the boundary layer. In the current study, another approach has been implemented to simulate the flow in a fully developed wind farm boundary layer. The approach is based on Immersed Boundary Method and involves implementation of an arbitrary prescribed initial boundary layer. An initial boundary layer is enforced through the whole domain, without wind turbines included, while the body forces that are required to maintain that flow field is calculated. The body forces are then stored and applied on the domain through the simulation of wind turbine and the boundary layer shape will be modified based on the turbine wakes and buoyancy contributions. The implemented method is capable of capturing the most important features of wakes of wind farms  while having the advantage of resolving the wall layer with a coarser grid than a typical required grid size for such problems. LES simulations are performed in laminar as well as turbulent inflow condition. For generating turbulent inflow, a model is used in which a turbulent plane is introduced in the domain and convected in each time step, using Taylor's frozen hypothesis. The results of different simulations are analysed and compared in terms of mean values and higher moments. As an example, figure (1) shows a 2D snapshot of stream-wise velocity contours (in SI units) in an infinite row of wind turbines simulated in stably stratified flow. Simulations are performed usind the in-house CFD code Ellipsys3D, which is a multi-block general purpose, parallelized Navier-Stokes solver and has been developed in DTU/Risoe for the past two decades. In the simulations, the domain size is 1.5 km by 1.5 km by 6 km in spanwise, vertical and streamwise dimensions, respectively and a uniform grid consisting of 144 grids is used in each dimension. No slip wall boundary condition is used in the bottom, a symmetry boundary on the top and periodic boundaries on the sides as well as inlet and outlet boundaries. For the temperature, a fixed value of 285 K is applied from the ground up to a height of 1 km and the temperature increases linearly with the rate of 3.5 degrees per kilometer. For the simulation of wind turbine, the actuator disc (AD) model of Mikkelsen  is used. The idea behind the AD is to represent the turbine with an equivalent virtual disc that exerts body forces through the simulation domain. This requires table look up for the drag and lift coefficients of the specific turbine, however the method reduces the computational costs significantly while giving accurate prediction of wakes and statistical quantities behind the turbine. The simulations start with a neutral prescribed boundary layer that follows a logarithmic profile with the velocity of 8 m/s at the hub height and the flow development is seen based on the temperature variations and wind turbine wake generations and interactions of wakes occurs as soon as the wakes of the upwind turbine reach the downwind turbines. References:  U. Piomelli, Wall-layer models for large-eddy simulations, Progress in Aerospace Sciences 44. 2008 p 437–446.  N. Troldborg, Actuator line modeling of wind turbine wakes, PhD thesis, DTU Denmark, 2008, pp 142.  R. Mikkelsen, Actuator disc methods applied to wind turbines, PhD thesis, DTU Denmark, 2003, pp 121.
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20th Symposium on Boundary Layers and Turbulence, 2012