The flow around an isolated horizontal-axis wind turbine is estimated by means of a new vortex code based on the Biot-Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, 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 (Tjaereborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near-wake structure and local forces along the blade. The results from the Tjaereborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator-line approach but with a negligible computational effort.

The actuator line technique was introduced as a numerical tool to be employed in combination with large eddy simulations to enable the study of wakes and wake interaction in wind farms. The technique is today largely used for studying basic features of wakes as well as for making performance predictions of wind farms. In this paper, we give a short introduction to the wake problem and the actuator line methodology and present a study in which the technique is employed to determine the near-wake properties of wind turbines. The presented results include a comparison of experimental results of the wake characteristics of the flow around a three-bladed model wind turbine, the development of a simple analytical formula for determining the near-wake length behind a wind turbine and a detailed investigation of wake structures based on proper orthogonal decomposition analysis of numerically generated snapshots of the wake.

This paper presents wind tunnel measurements of the NREL S826 airfoil at Reynolds number Re 100,000 for angles of attack in a range of -10° to 25° the corresponding Large Eddy Simulation (LES) for selected angles of attack. The measurements have been performed at the low speed wind tunnel located at Fluid Mechanics laboratory of the Technical University of Denmark (DTU). Lift coefficient is obtained from the forge gauge measurements while the drag is measured according to the integration of the wake profiles downstream of the airfoil. The pressure distribution is measured by a set of pressure taps on the airfoil surface. The lift and drag polars are obtained from the LES computations using DTU's inhouse CFD solver, EllipSys3D, and good agreement is found between the measurement and the simulations. At high angles of attack, the numerical computations tend to over-predict the lift coefficients, however, there is a better agreement between the drag measurements and computations. It is concluded that LES computations are able to capture the lift and drag polars as well as the pressure distribution around the airfoil with an acceptable accuracy.

A numerical study on the wake behind a wind turbine is carried out focusing on determining the length of the near-wake based on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method. The wake is perturbed by applying stochastic or harmonic excitations in the neighborhood of the tips of the blades. The flow field is then analyzed to obtain the stability properties of the tip vortices in the wake of the wind turbine. As a main outcome of the study it is found that the amplification of specific waves (traveling structures) along the tip vortex spirals is responsible for triggering the instability leading to wake breakdown. The presence of unstable modes in the wake is related to the mutual inductance (vortex pairing) instability where there is an out-of-phase displacement of successive helix turns. Furthermore, using the non-dimensional growth rate, it is found that the pairing instability has a universal growth rate equal to π/2. Using this relationship, and the assumption that breakdown to turbulence occurs once a vortex has experienced sufficient growth, we provide an analytical relationship between the turbulence intensity and the stable wake length. The analysis leads to a simple expression for determining the length of the near wake. This expression shows that the near wake length is inversely proportional to thrust, tip speed ratio and the logarithmic of the turbulence intensity.

A numerical study on a single wind turbine wake has been carried out focusing on the instability properties of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations together with the actuator line method to simulate the wake behind the Tjaereborg wind turbine. The wake is perturbed by low amplitude stochastic excitations located in the neighborhood of the tip spiral, giving rise to spatially developing instabilities. Dynamic mode decomposition (DMD) is then utilized for identification of the coherent flow structures. The DMD results indicate that the amplification of specific waves along the spiral is responsible for triggering the instability leading to wake breakdown. Two types of dynamic structures dominates the flow; low and high frequency groups. Examination of these structures reveals that the dominant modes have the largest spatial growth.

Two modal decomposition techniques are employed to analyse the stability of wind turbine wakes. A numerical study on a single wind turbine wake is carried out focusing on the instability onset of the trailing tip vortices shed from the turbine blades. The numerical model is based on large-eddy simulations (LES) of the Navier-Stokes equations using the actuator line (ACL) method to simulate the wake behind the Tj ae reborg wind turbine. The wake is perturbed by low-amplitude excitation sources located in the neighbourhood of the tip spirals. The amplification of the waves travelling along the spiral triggers instabilities, leading to breakdown of the wake. Based on the grid configurations and the type of excitations, two basic flow cases, symmetric and asymmetric, are identified. In the symmetric setup, we impose a 120 degrees symmetry condition in the dynamics of the flow and in the asymmetric setup we calculate the full 360 degrees wake. Different cases are subsequently analysed using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). The results reveal that the main instability mechanism is dispersive and that the modal growth in the symmetric setup arises only for some specific frequencies and spatial structures, e.g. two dominant groups of modes with positive growth (spatial structures) are identified, while breaking the symmetry reveals that almost all the modes have positive growth rate. In both setups, the most unstable modes have a non-dimensional spatial growth rate close to pi/2 and they are characterized by an out-of-phase displacement of successive helix turns leading to local vortex pairing. The present results indicate that the asymmetric case is crucial to study, as the stability characteristics of the flow change significantly compared to the symmetric configurations. Based on the constant non-dimensional growth rate of disturbances, we derive a new analytical relationship between the length of the wake up to the turbulent breakdown and the operating conditions of a wind turbine.

Wake interaction between two model scale wind turbines with span-wise offset is investigated numerically using Large Eddy Simulation (LES) and the results are validated against the experimental data. An actuator line technique is used for modeling the rotor. The investigated setup refers to a series of experimental measurements of two model scale turbines conducted by NTNU in low speed wind tunnel in which the two wind turbines are aligned with a span-wise offset resulting in half wake interaction. Two levels of free-stream turbulence are tested, the minimum undisturbed level of about Ti 0.23% and a high level of about Ti = 10% using a passive upstream grid. The results show that the rotor characteristics for both rotors are well captured numerically even if the downstream rotor operates into stall regimes. There are however some difficulties in correct prediction of the thrust level. The interacting wake development is captured in great details in terms of wake deficit and streamwise turbulence kinetic energy. The present work is done in connection with Blind test 3 workshops organized jointly by NOWITECH and NORCOWE.

When investigating limits of rotor aerodynamic models, the Betz limit serves as a solid marker of an upper limit which no model should be able to exceed. A century ago Joukowsky (1912) proposed a rotor aerodynamic model utilizing a rotating actuator disc with a constant circulation. This model has since then been the subject of much controversy as it predicts a power performance that for all tip speed ratios exceeds the Betz limit and which goes to infinity when the tip speed ratio goes to zero. Recently, it was demonstrated that the Joukowsky model is fully consistent with the inviscid Euler equations and that the apparent inconsistency partly can be explained by the lack of viscous effects (Sprensen and van Kuik [4]). However, even including a term to account for the effect of viscosity at small tip speed ratios, the model still predicts a power yield that exceeds the Betz limit. In the present work we study in detail, using a CFD actuator line model, the flow behavior for rotors at small tip speed ratios. It is shown that the excessive swirl appearing towards the rotor center at small tip speed ratios generates vortex breakdown, causing a recirculating zone in the wake that limits the power yield of the rotor. The appearance of vortex breakdown has a similar effect on the flow behavior as the vortex ring state that usually appears at higher tip speed ratios. Limits to where vortex breakdown might occur with tip speed ratio and rotor loading as parameter are investigated and presented in the paper. The limits found correspond to well-known criterion for vortex breakdown onset for swirling flows in general. By applying a criterion for vortex breakdown in combination with the general momentum theory, the power performance always stays below the Betz limit.