Numerical simulations of the Navier-Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator line and disc methodologies. In the actuator line and disc methods the blades are represented by a line or a disc on which body forces representing the loading are introduced. The body forces are determined by computing local angles of attack and using tabulated aerofoil coefficients. The advantage of using the actuator disc technique is that it is not necessary to resolve blade boundary layers. Instead the computational resources are devoted to simulating the dynamics of the flow structures. In the present study both the actuator line and disc methods are used. Between approximately six to fourteen million mesh points are used to resolve the wake structure in a range from a single turbine wake to wake interaction in a farm containing 80 turbines. These 80 turbines are however represented by 20 actuator discs due to periodicity because of numerical limitations. In step one of this project the objective was to find a numerical method suitable to study both the flow structures in the wake behind a single wind turbine and to simulate complicated interaction between a number of turbines. The study resulted in an increased comprehension of basic flow features in the wake, but more importantly in the use of a numerical method very suitable for the upcoming purpose. The second objective of the project was to study the basic mechanisms controlling the length of the wake to obtain better understanding of the stability properties of wakes generated by wind turbine rotors. The numerical model was based on large eddy simulations of the Navier-Stokes equations using the actuator line method to generate the wake and the tip vortices. To determine critical frequencies the flow is disturbed by inserting a harmonic perturbation. The results showed that instability is dispersive and that growth occurs only for specific frequencies and mode types. The study also provides evidence of a relationship between the turbulence intensity and the length of the wake. The relationship however needs to be calibrated with measurements. In the last project objective, full wake interaction in large wind turbine farms was studied and verified to measurements. Large eddy simulations of the Navier-Stokes equations are performed to simulate the Horns Rev off-shore wind farm 15 km outside the Danish west coast. The aim is to achieve a better understanding of the wake interaction inside the farm. The simulations are performed by using the actuator disc methodology. Approximately 13.6 million mesh points are used to resolve the wake structure in the park containing 80 turbines. Since it is not possible to simulate all turbines, the 2 central columns of turbines have been simulated with periodic boundary conditions. This corresponds to an infinitely wide farm with 10 turbines in downstream direction. Simulations were performed within plus/minus 15 degrees of the turbine alignment. The infinitely wide farm approximation is thus reasonable. The results from the CFD simulations are evaluated and the downstream evolution of the velocity field is depicted. Special interest is given to what extent production is dependent on the inflow angle and turbulence level. The study shows that the applied method captures the main production variation within the wind farm. The result further demonstrates that levels of production correlate well with measurements. However, in some cases the variation of the measurement data is caused by the different measurement conditions during different inflow angles. / QC 20100720

<p>Numerical simulations using CFD methods are performed for wind turbine applications. The aim of the project is to get a better understanding of the wake behaviour, which is needed since today’s industrial design codes for wind power applications are based on the BEM (Blade Element Momentum) method. This method has been extended with a number of empirical corrections not based on physical flow features. The importance of accurate design models does also increase as the turbines become larger. Therefore, the research is today shifting toward a more fundamental approach, aiming at understanding basic aerodynamic mechanisms. The result from the CFD simulation is evaluated and special interest is given to the circulation and the position of vortices. From these evaluations, it will hopefully be possible to improve the engineering methods and base them, to a greater extent, on physical features instead of empirical corrections.</p><p>The simulations are performed using the program ”EllipSys3D” developed at DTU (The Technical University of Denmark). The Actuator Line Method is used, where the blade is represented by a line instead of a large number of panels. The forces on that line are introduced by using tabulated aerodynamic coefficients. In this way, the computer resource is used more efficiently since the number of node points locally around the blade is decreased, and they can instead be concentrated in the wake behind the blades.</p><p>An evaluation method to extract values of the circulation from the wake flow field is developed.</p><p>The result shows agreement with classical theorems from Helmholtz, from which it follows that the wake tip vortex has the same circulation as the maximum value of the bound circulation on the blade.</p>

Numerical simulations using CFD methods are performed for wind turbine applications. The aim of the project is to get a better understanding of the wake behaviour, which is needed since today’s industrial design codes for wind power applications are based on the BEM (Blade Element Momentum) method. This method has been extended with a number of empirical corrections not based on physical flow features. The importance of accurate design models does also increase as the turbines become larger. Therefore, the research is today shifting toward a more fundamental approach, aiming at understanding basic aerodynamic mechanisms. The result from the CFD simulation is evaluated and special interest is given to the circulation and the position of vortices. From these evaluations, it will hopefully be possible to improve the engineering methods and base them, to a greater extent, on physical features instead of empirical corrections. The simulations are performed using the program ”EllipSys3D” developed at DTU (The Technical University of Denmark). The Actuator Line Method is used, where the blade is represented by a line instead of a large number of panels. The forces on that line are introduced by using tabulated aerodynamic coefficients. In this way, the computer resource is used more efficiently since the number of node points locally around the blade is decreased, and they can instead be concentrated in the wake behind the blades. An evaluation method to extract values of the circulation from the wake flow field is developed. The result shows agreement with classical theorems from Helmholtz, from which it follows that the wake tip vortex has the same circulation as the maximum value of the bound circulation on the blade. / QC 20101203

In the present thesis the wake flow behind wind turbines is analyzed numerically using large-eddy simulations. The wind turbine rotors are modeled by using either the actuator disc method or the actuator line method in which the blades are represented by body forces computed with airfoil data. Using these models, the boundary layers of the turbine blades are not resolved and most of the computational power is preserved to simulate the wake flow. The actuator disc method is used for the wake interaction studies of the Lillgrund wind farm. In this study the power production is simulated for two different wind directions and compared to measurements. A grid sensitivity study and a turbulence intensity study are also performed. As a last step the front row turbines are derated in an attempt to increase the total production of the farm. The results show that it is important to impose atmospheric conditions at the inlet in the simulations, otherwise production will be unrealistically low for some turbines in the farm. The agreement between the simulated and measured power is very good. The study based on derating the front row turbines does not show any positive increase on the farm production. The actuator line method is used for near wake analysis of the MEXICO rotor. In this study the near wake is simulated for five different flow cases and compared with particle image velocimetry (PIV) measurements. The analysis is performed by comparing size and circulation of the tip vortices, the radial and streamwise velocity distributions, the spatial expansion of the wake and the axial induction factor. The simulations and measurements generally are in agreement. In some cases, however, the measurements are affected by tunnel effects which are not captured in the simulations. In connection to the actuator disc method a power control strategy for operating conditions below rated power is implemented and tested. The strategy is first validated using an in-house developed blade element momentum code and then is implemented in the actuator disc method used in the EllipSys3D code. The initial tests show that the strategy responds as expected when changing the moment of inertia of the rotor and when varying the inlet conditions. Results from the implementation of the strategy in the actuator disc method in EllipSys3D show that the turbine adapts to the conditions it is operating in by changing its rotational velocity and power output when the inlet conditions are varied. / <p>QC 20130111</p>

The optimization of new generation of the wind farms is dependent on our understanding of wind turbine wake development, wake dynamics and the interaction of the wakes. The overall goal of the optimization is decreasing the fatigue loading and increasing the power production of the wind farms. To this end, numerical simulations of the wake of wind turbine are performed by means of applying fourth order finite volume code, EllipSys3D along with the actuator line method. The basic idea behind such actuator line method is representing the blades  by employing the body forces in the Navier--Stokes equations. The forces are then determined through a combination of Blade Element Momentum (BEM) method and tabulated airfoil data. In the first part of thesis, the dynamics of the tip vortices behind a single wind turbine is investigated. The generated wind turbine wake is perturbed using small amplitude disturbances. The amplification of the wave along the spiral triggers some modes leading to wake instability. The perturbed wake is then analyzed using modal decomposition in which  the dominant modes leading to the onset of instability can be identified. Two different cases are studied; symmetric configuration, in that the wake is excited by identical perturbation near each blade tip; and non-symmetric configuration, in which general perturbations are used. The corresponding result confirms that the instability is dispersive and the growth occurs only for specific frequencies in symmetric case. However in general non-symmetric case, all the modes have positive spatial growth rate. This can be explained through the fact that breaking the symmetry results in superposition of the unstable modes related to three-bladed, two-bladed and one-blade wind turbine wake. A rotor experiment has been recently carried out at NTNU wind tunnel using horizontal axis model scale rotors, for detailed investigation of the wake development. A single rotor configuration was first tested and then a setup of two rotors inline was investigated.  Previous numerical investigation of single wind turbine wake using actuator line method shows that the quality of the result depend on the input tabulated airfoil data. Due to absence of the reliable data, a series of experiments using 2-D airfoil were carried out at DTU wind tunnel to obtain the tabulated airfoil data for the Reynolds number corresponding to NTNU rotor operating conditions. The numerical simulations using actuator line method together with the new experimental airfoil data were then carried out for studying the  phenomenon of wake interaction between the two wind turbines. Different cases are simulated with various tip speed ratio of the downstream turbine specifically adjusted to match the NTNU experiments. The characteristics of the interacting wakes were extracted including the rotor performance and the averaged velocity and turbulence fields as well as the development of wake generated vortex structures. The obtained  results were in agreement of NTNU experimental data showing that  numerical computations are reliable tools for prediction of wind turbine aerodynamics. The third aim of the project is to perform a comparison between an analytical vortex model and the actuator line of an isolated horizontal axis wind turbine (simulated with the ACL approach) to assess whether the predictions by the vortex model can substitute more expensive CFD approaches. The model is based on the constant circulation along three blade (Joukowsky rotor) and it is able to determine the geometry of the tip vortex filament in the rotor wake, allowing the free wake expansion and changing the local tip-vortex pitch. Two different wind turbines have been simulated: one with constant circulation along the blade, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind turbine conditions (Tj\ae reborg wind turbine). The vortex model matched the numerical simulation of the turbine withconstant blade circulation in terms of the near wake structure and the local forces along the blade. The simple vortex codeis therefore able to provide an estimation of the flow around the wind turbine similar to the actuator line code but with anegligible computational effort. The results from the Tj\ae reborg turbine case showed some discrepancies between the twoapproaches although the overall agreement is qualitatively good. This could be considered as a validation for the analytical method for more general conditions. / <p>QC 20130412</p> / Nordic Consortium: Optimization and Control of large wind farms

More and larger wind farms are planned offshore. As the most suitable build sites are limited wind farms will be constructed near to each other in so called wind farm clusters. Behind the wind turbines in these farms there is a disrupted flow of air called a wake that is characterized by reduced wind speed and increased turbulence. These individual turbine wakes combine to form a farm wake that can travel a long distance. In wind farm clusters farm to farm interaction will occur, i.e. the long distance wake from one wind farm will impact the wind conditions for other farms in the surrounding area. The thesis contains numerical studies of these long distance wakes. In this study Large Eddy Simulations (LES) using an Actuator Disc method (ACD) are used. A prescribed boundary layer is used where the wind shear is introduced using body forces. The turbulence, based on the Mann model, is introduced as fluctuating body forces upstream of the farm. A neutral atmosphere is assumed. The applied method has earlier been used for studies of wake effects inside farms but not for the longer distances needed for farm to farm interaction. Numerical studies are performed to get better knowledge about the use of this model for long distance wakes. The first study compares the simulation results with measurements behind an existing farm. Three parameter studies are thereafter setup to analyze how to best use the model. The first parameter study examines numerical and physical parameters in the model. The second one looks at the extension of the domain and turbulence as well as the characteristics of the flow far downstream. The third one gathers information on the downstream development of turbulence with different combinations of wind shear and turbulence level. The impact of placing the turbines at different distances from the turbulence plane is also studied. Finally a second study of an existing wind farm is performed and compared with a mesoscale model. The model is shown to be relevant also for studies of long distance wakes. Combining LES with a mesoscale model can be of interest.