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

Nowadays wind turbines are clustered in wind farms and the wake development plays an important role in energy production and blade fatigue load of tubines. The actuator line method is an effective modeling approach that gives improtant wake flow characterstics of a wind turbine. In the last few years, numerous studies have been conducted based on this method using Ellipsys3D, a computational fluid dynamics (CDF) flow solver based on finitie volume approach. However, due to the limited order of accuracy of this solver, it is not capable of a linear stability analysis with small amplitude of perturbation. Therefore, the present work investigates implementing the actuator line ethos into a  high order method, Nek5000, a flow solver based on the spectral element approach. The main goal of the present work is to validate the code implementation by comparing the simulations results with the previous Ellipsys3D data. Both 2-D and 3-D Gaussian distribution functions are discussed for the actuator line force distribution. Parametric study is carried out regarding the smoothing parameter ε and the partitioning of the actuator line.

Self propulsion modelling is important in order to accurately simulate ships and submarinesusing Computational Fluid Dynamics (CFD). However, fully resolved simulations of hull andpropeller geometries are computationally heavy and time consuming. As such there is a greatinterest in lower order CFD models of propellers. This work investigates three lower ordermodels of a non-cavitating generic submarine propeller (INSEAN E1619) in OpenFOAM. Themodels investigated are Actuator Disk (AD). Rotor Disk (RD) and Actuator Line Model (ALM).The AD model applies a momentum change based on propeller performance coefficients overa disc cell set. The RD uses Blade Element Method (BEM) to calculate a more realistic thrustdistribution over the disk. Finally the ALM applies BEM over seven rotating lines within the cellset disc. The source code to the RD model was modified according to suggestions provided fromearlier studies on the model. The ALM used was originally designed for turbines which wasrectified by changing the force projection vectors in the source code to model propellers instead.There was not enough published data to directly utilize BEM on the E1619 propeller, thus thedata was generated by conducting 2D simulations on every element. The simulations were setup to replicate results provided in earlier works with higher order models in order to compareboth quantitative and qualitative results. It was found the ALM matched the reference databest out of the models tested in this work. The RD was qualitatively similar to the time averageof the ALM fields but numerically inaccurate. The AD results were poor, both quantitativelyand qualitatively.

<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

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Understanding the flow around wind turbines is a highly relevant research question due to the increased interest in harvesting energy from renewable sources. This thesis approaches the topic by means of numerical simulations using the actuator line method and the incompressible Navier–Stokes equations in the spectral element code Nek5000. The aim is to gain enhanced understanding of the wind turbine wake structure and wind turbine wake interaction. A verification study of the method and implementation is performed against the finite volume solver EllipSys3D using two types of turbines, an idealized constant circulation turbine and the Tjæreborg turbine. It is shown that Nek5000 requires significantly lower resolution to accurately compute the wake development, however, at the cost of a smaller time step.The constant circulation turbine is investigated further with the goal of establishing guidelines for the use of the actuator line method in spectral element codes, where the mesh is inherently non-equidistant and currently used guidelines of force distribution based on Gaussian kernels are difficult to apply. It is shown that Nek5000 requires a larger kernel width in the fixed frame of reference to remove numerical instabilities. Further, the impact of different Gaussian widths on the wake development is investigated in the rotating frame of reference, showing that the convection velocity and the breakdown of the spiral tip and root vortices are dependent on the Gaussian width. In the second part, the flow around single and multiple wind-turbine setups at different operating conditions is investigated and compared with experimental results. The focus is placed on comparing the power and thrust coefficients and the wake development based on the time-averaged streamwise velocity and turbulent stresses. Further the influence of the tower model is investigated both upstream and downstream of the turbine. The results show that the wake is captured accurately in most cases. The loading exhibits a significant dependence on the Reynolds number at which the airfoil data is extracted. When the helical tip vortices are stable the turbulent stresses at the tip vortices are underestimated in the numerical simulations. This is due to the finite resolution and the projection of the actuator line forces in the numerical domain using a prescribed Gaussian width, which leads to lower induced velocities in the helical vortices. / <p>QC 20170523</p>

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

Anthropogenic climate change is approaching predicted tipping points and there is an urgent need to de-carbonize energy systems on a global scale. Generation technologies that do not emit greenhouse gas need to be rapidly deployed, and energy grids need to be updated to accommodate an intermittent fluctuating supply. Rapidly advancing battery technology, cost reduction of solar and wind power and other emerging generation technologies are making the needed changes technically and economically feasible. Extracting energy from fast-flowing tidal currents using turbines akin to those used in wind farms, offers a reliable and predictable source of GHG free energy. The tidal power industry has established the technical feasibility of tidal turbines, and is presently up-scaling deployments from single isolated units to large tidal farms containing many turbines. However there remains significant economic uncertainty in financing such projects, partially due to uncertainty in predicting the long-term energy yield. Since energy yield is used in calculating the project revenue, it is of critical importance. Predicting yield for a prospective farm has not received sufficient attention in the tidal power literature. this task has been the primary motivation for this thesis work, which focuses on establishing and validating simulation-based procedures to predict flows through large tidal farms with many turbines, including the back effects of the turbines. This is a challenging problem because large tidal farms may alter tidal flows on large scales, and the slow-moving wake downstream of each rotor influences the inflow to other rotors, influencing their performance and loading. Additionally, tidal flow variation on diurnal and monthly timescales requires long-duration analysis to obtain meaningful statistics that can be used for forecasting. This thesis presents a hybrid simulation method that uses 2D coastal flow simulations to predict tidal flows over long durations, including the influence of turbines, combined with higher-resolution 3D simulations to predict how wakes and local bathymetry influence the power of each turbine in a tidal farm. The two simulation types are coupled using a method of bins to reduce the computational cost within reasonable limits. The method can be used to compute detailed 3D flow fields, power and loading on each turbine in the farm, energy yield and the impact of the farm on tidal amplitude and phase. The method is demonstrated to be computationally tractable with modest high-performance computing resources and therefore are of immediate value for informing turbine placement, comparing turbine farm-layout cases and forecasting yield, and may be implemented in future automated layout optimization algorithms. / Graduate