Actuator Disk Research Articles

An Investigation of Tidal Stream Turbine Wake Development Using Modified BEM–AD Model

Tidal stream turbines (TST) are a promising option for electricity generation to meet the ever-increasing demand for energy. The actuator disk (AD) method is often employed to represent a TST, to evaluate the TST operating in a tidal flow. While this method can effectively reduce the computational cost and provide accurate prediction of far-wake flow conditions, it falls short of fully characterising critical hydrodynamics elements. To address this limitation, a hybrid method is implemented by coupling AD with the blade element momentum (BEM) theory, using detailed performance data, such as thrust, to enhance the prediction of the wake effects. This work focuses on the development of a hybrid BEM–AD method using Reynolds-Averaged Navier–Stokes (RANS) turbulence models within computational fluid dynamics (CFD). Two variations and a hybrid modification of an AD model are presented in this paper. The first modified variation is a velocity variation that takes into account velocity profile inflow into the disk’s configuration. The second modified variation is a radial variation that integrates the blade element theory into the disk’s configuration. The hybrid modified model combines both the velocity profiles influenced and blade element theory in the design and analysis of the actuator disk. Several key investigations on some of the pre-solver parameters are also investigated in this research such as the effect of changing velocity and radial distance on the porosity and loss coefficient of the actuator disk performance. Importantly, this work provides an improved method to evaluate the key wake effects from a TST array which is crucial to determine the power performance of the TST array.

Propeller-Wing Interaction: A Simplified Method for Coupling BEM and CFD

This paper presents a numerical procedure for studying the interaction between the wake generated by a propeller and the wing, considering a tiltrotor model framed within the T-TECH Italian project, which has the scope to develop innovative technologies for a flight demonstrator. A tiltrotor is an aircraft that generates lift and propulsion by way of powered rotors mounted on rotating shafts or nacelles at the ends of a fixed wing; in which, in contrast with conventional aircraft, the dimension of the propeller is comparable with the vehicle one. The procedure proposes to couple a 3D low-order unsteady Boundary Element Method (BEM) approach, to evaluate the performance of the isolated propeller, and a Reynolds-Averaged Navier-Stokes (RANS) solution for the analysis of the flow field interaction between the propeller (simulated as actuator disk) and the wing.

Development and assessment of an actuator volume method in rotating frame for predicting the flow-field of horizontal-axis wind turbines

The prediction of the unsteady flow-field in horizontal-axis wind turbines using blade-resolved CFD simulations is challenging and computationally demanding. The simulations become more affordable when using a representation of the blades based on the generalized actuator disc concept; however, the projection of the computed forces in the computational domain introduces additional mesh parameters and requires codes that impact the computation time in unstructured solvers and parallel computing. In this work, a new approach to model the effects of the rotating blades using source terms and a sliding mesh technique is proposed. The developed framework also includes the tower and nacelle. The force distributions are obtained using an in-house code, which incorporates Buhl’s correction, three-dimensional effects, and tip and hub loss corrections. The validation was performed against blade-resolved simulations and experimental data at three tip-speed ratios. At design conditions, both models are in good agreement in terms of velocity deficit and angle of attack, being underestimated at off-design conditions. The local effects of the actuator volumes, the induction region, and the near-wake have been analysed in detail. This new approach is flexible, robust, and provides good accuracy, whereas the computational cost is considerably lower than high-fidelity simulations.

Resolvent-based motion-to-wake modelling of wind turbine wakes under dynamic rotor motion

We propose a linearized deterministic model for predicting coherent structures in the wake of a floating offshore wind turbine subject to platform motions. The model's motion-to-wake predictive capability is achieved through two building blocks: a motion-to-forcing (M2F) part and a forcing-to-wake (F2W) part. The M2F model provides a unified framework to parameterize the effects of arbitrary floating wind turbine motions as unsteady loads of a fixed actuator disk, requiring only the radial distribution of the aerodynamics force coefficient on the blade as input. The F2W model is derived based on a bi-global resolvent model obtained from the linearized Navier–Stokes equations, using the time-averaged wake of a fixed wind turbine as input. In addition to its capability of predicting sensitive frequency ranges, the model excels linear stability analysis by providing spatial modes of the wake response in a motion-specific and phase-resolved manner. The model successfully predicts the wake pulsing mode induced by surge, as well as the similarity and difference of the wake meandering modes caused by sway and yaw. Large-eddy simulations under different inflow turbulence intensities (TIs) and length scales are further conducted to analyse the wake meandering triggered by the simultaneous excitation of free-stream turbulence and sway motion. The results show distinct frequency signatures for the wake dynamics induced by ambient turbulence and sway motion. The inflow TI is found to have a stabilizing effect on the wake, reducing the motion-induced wake responses. Such a stabilizing effect is captured satisfactorily with the proposed model, provided that the effective viscosity is calibrated properly using the data from the fixed turbine wake under the corresponding turbulent inflow.

TOSCA – an open-source, finite-volume, large-eddy simulation (LES) environment for wind farm flows

Abstract. The growing number and growing size of wind energy projects coupled with the rapid growth in high-performance computing technology are driving researchers toward conducting large-scale simulations of the flow field surrounding entire wind farms. This requires highly parallel-efficient tools, given the large number of degrees of freedom involved in such simulations, and yields valuable insights into farm-scale physical phenomena, such as gravity wave interaction with the wind farm and farm–farm wake interactions. In the current study, we introduce the open-source, finite-volume, large-eddy simulation (LES) code TOSCA (Toolbox fOr Stratified Convective Atmospheres) and demonstrate its capabilities by simulating the flow around a finite-size wind farm immersed in a shallow, conventionally neutral boundary layer (CNBL), ultimately assessing gravity-wave-induced blockage effects. Turbulent inflow conditions are generated using a new hybrid off-line–concurrent-precursor method. Velocity is forced with a novel pressure controller that allows us to prescribe a desired average hub-height wind speed while avoiding inertial oscillations above the atmospheric boundary layer (ABL) caused by the Coriolis force, a known problem in wind farm LES studies. Moreover, to eliminate the dependency of the potential-temperature profile evolution on the code architecture observed in previous studies, we introduce a method that allows us to maintain the mean potential-temperature profile constant throughout the precursor simulation. Furthermore, we highlight that different codes do not predict the same velocity inside the boundary layer under geostrophic forcing owing to their intrinsically different numerical dissipation. The proposed methodology allows us to reduce such spread by ensuring that inflow conditions produced from different codes feature the same hub wind and thermal stratification, regardless of the adopted precursor run time. Finally, validation of actuator line and disk models, CNBL evolution, and velocity profiles inside a periodic wind farm is also presented to assess TOSCA’s ability to model large-scale wind farm flows accurately and with high parallel efficiency.

Aerodynamic interactions between distributed propellers and the wing of an electric commuter aircraft at cruise conditions

Beneficial interactions that occur between propellers and the wing can be used to increase the overall efficiency of an aircraft in cruise flight. Different concepts with such interacting propellers are distributed propulsion (DP) and wingtip mounted propellers (WTP). For DP, a full distribution over the entire span can be distinguished from a partial distribution, concentrating the propellers at the wing tip area. The paper focuses on the energy efficiency in cruise flight as a result of the interactions and provides a general comparison of the concepts (WTP, full and partial DP) with a Beechcraft 1900D commuter aircraft as a reference. Parametric CFD studies varying the number and the position of the propellers are performed with a half-wing model. The simulations are performed with the second-order finite-volume flow solver TAU, developed by the German Aerospace Center (DLR), employing Reynolds-averaged Navier–Stokes (RANS) equations. The propellers are modeled using an Actuator Disk (ACD). An algorithm is used to reach cruise condition by iteratively adjusting the propeller rotational speed and the wing angle of attack. The CFD results are analyzed and evaluated with respect to the overall efficiency including the aerodynamic efficiency of the wing as well as the propulsive efficiency of the propellers. The parameter study shows that in cruise flight partial DP is more efficient than a full DP. The pure WTP configuration was found as the optimum of the propeller distribution along the wing, resulting in a saving of required power of 5.6%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5.6\\%$$\\end{document}, relative to the reference configuration.

Moving actuator surfaces: a new concept for wind turbine aerodynamic analysis

The actuator disk is a concept often used in wind turbine aerodynamics, where the action of the turbine on the flow is averaged over time and space. This simplification stills retain sufficient physical information for wind turbine aerodynamic design. Its limitations are essentially related to the impossibility to model the blade shed vorticity. This paper presents a more general approach that uses rotating actuator surfaces carrying velocity and pressure discontinuities which are set from knowledge of the circulation around the model blade sections and using blade element analysis. The mathematics of rotating actuator surfaces, as well as an application to the TUDelft rotor are presented in this paper. The results are encouraging.

An optimization framework for wind farm layout design using CFD-based Kriging model

Wind farm layout optimization (WFLO) seeks to alleviate the wake loss and maximize wind farm power output efficiency, and is a crucial process in the design and planning of wind energy projects. Since the optimization algorithms typically require thousands of numerical evaluations of the wake effects, conventional WFLO studies are usually carried out with the low-fidelity analytical wake models, while the higher-fidelity computational-fluid-dynamics-based (CFD-based) methods are seldom used due to the excessive computational cost. In this paper, we develop a self-adaptive optimization framework for wind farm layout design using CFD-based Kriging model to maximize the annual energy production (AEP) of wind farms. This surrogate-based optimization (SBO) framework uses latin hypercube sampling to generate a group of wind farm layout samples, based on which CFD simulations with the turbines modeled as actuator disks are carried out to obtain the corresponding AEPs. This initial wind farm layout dataset is used to train the Kriging model, which is then integrated with an optimizer based on genetic algorithm (GA). As the optimization progresses, the intermediate optimal layout designs are again fed into the dataset to re-train the Kriging model. Such adaptive update of wind farm layout dataset continues until the algorithm converges to the optimal layout design. To evaluate the performance of the proposed SBO framework, we apply it to four representative wind farm cases. Compared to the conventional staggered layout along the dominant wind direction, the optimized wind farm produces significantly higher total AEP, which is more evenly distributed among the turbines. In particular, the SBO framework requires significantly smaller number of CFD calls to yield the optimal layouts that generates almost the same AEP with the direct CFD-GA method. Further analysis on the velocity fields show that the optimization framework always attempts to locate the downstream turbines away from the wakes of upstream ones along the dominant wind directions. The proposed CFD-based surrogate model provides a more accurate and flexible alternative to the conventional analytical-wake-model-based methods in WFLO tasks, and has the potential to be used for designing efficient wind farm projects.

Potential for Energy Recovery from Boundary-Layer Ingesting Actuator Disk Propulsion

The theoretical benefits of highly integrated propulsion systems are highlighted herein by assessing the potential for energy recovery utilization using actuator disk propulsion. Decomposing aerodynamic forces into thrust and drag for closely integrated bodies, particularly those employing boundary-layer ingestion, becomes challenging. In this work, a mechanical energy-based approach was taken using the power balance method. This allowed the performance to be analyzed through the mechanical flow power in the fluid domain, disregarding the need for any explicit definition of thrust and drag. Through this, the benefit of boundary-layer ingestion was observed from a wake energy perspective as a decrease in the downstream mechanical energy deposition and associated viscous dissipation. From a propulsion perspective, the reduction in power demand necessary to produce propulsive force indicated the possibility of power savings by utilizing the energy contained within the ingested boundary-layer flow.

A dynamic wall modeling approach for large eddy simulation of offshore wind farms in realistic oceanic conditions

Due to the multitude of scales present in realistic oceanic conditions, resolving the surface stress is computationally intensive, motivating modeling approaches. In this work, a dynamic wave drag model is developed for large eddy simulation (LES) to quantify the effects of multiscale dynamically rough surfaces on the atmospheric boundary layer. The waves are vertically unresolved, and the total drag due to the horizontally resolved portion of the wave spectrum is computed through a superposition of the force from each mode. As LES can only resolve the horizontal wind–wave interactions to the filter scale Δ, the effects of the horizontally unresolved, subfilter waves are modeled by specifying a roughness length scale characterizing the unresolved wave energy spectrum. This subfilter roughness is set proportional to the subfilter root mean square of the wave height distribution, and the constant of proportionality is evaluated dynamically during the simulation based on the assumption that the total drag force at the wave surface is independent of the filter scale. The dynamic approach is used to simulate the airflow over a spectrum of moving waves, and the results are validated against high-fidelity phase-resolved simulations. The dynamic approach combined with the wave spectrum drag model is then used to study flow through a fixed-bottom offshore wind farm array, equivalent to an infinite farm, with each turbine represented using an actuator disk model. The dynamic model accurately adapts to the changing velocity field and accurately predicts the mean velocity profiles and power produced from the offshore wind farm. Furthermore, the effect of the wind–wave interactions on the mean velocity profiles, power production, and kinetic energy budget is quantified.

An actuator line method for performance prediction of HAWTs at urban flow conditions: A case study of rooftop wind turbines

Blade-resolved numerical modeling of wind turbines at complex flow conditions are resource expensive due to large computational domains and extra-fine grid requirements. The Actuator Line Method (ALM) can significantly boost the simulation speed, providing acceptable accuracy and flow details. This study investigates the performance of NREL Phase VI wind turbine mounted over a high-rise building at nine different locations, providing practical illustrations of complicated flow situations. To demonstrate the superior capabilities of this method compared to the actuator disk model, two hub-heights are considered for mounting the wind turbine. Results showed that the power coefficient of the turbines with higher hub-height are close to the corresponding bare wind turbine. However, up to 52 % reduction was observed for the low hub-heights. Furthermore, variations of the bending moment experienced by the turbine's blade in a complete revolution are presented, which is a crucial factor affecting the fatigue life and structural stability of the wind turbine. Eventually, more in-depth discussions on the time-evolution of rotor performance at various locations are presented by illustrating the spanwise distributions of Angle-of-Attack histogram and its PSD diagram for the blade-1 of the wind turbine.

Implementation of a New Actuator Disk Model based on BEM Theory in SU2 CFD SOFTWARE

Implementation of a New Actuator Disk Model based on BEM Theory in SU2 CFD SOFTWARE

Implementation of a new actuator disc model based on BEM theory in SU2 CFD software

Implementation of a new actuator disc model based on BEM theory in SU2 CFD software

An Unsteady Reynolds–Averaged Navier–Stokes–Large Eddy Simulation Study of Propeller–Airframe Interaction in Distributed Electric Propulsion

A conceptual framework is presented to determine the improvement in the aerodynamic performance of a canard aircraft fitted with distributed propellers along its main wing. A preliminary study is described with four airframe–propeller configurations predominantly studied in academic and commercial designs. The leading edge–based tractors and trailing edge–based pushers are identified as configurations of interest for the main study. Subsequently, a Navier–Stokes solver is used to simulate the flow using two numerical approaches–a modified steady-state actuator disk and an unsteady rotating propeller profile. Moving meshes with rotating sub-domains are used with a hybrid RANS-LES-based turbulence model while the actuator disks are modified to include viscous swirl effects. The preliminary study shows a local minimum in the change in CL and CD at 10∘ for the pusher and tractor configurations. The main study then demonstrates the outperformance of the pushers over tractors quantified using CL and CL/CD. There is a clear preference for the pushers as they increase the lifting capacity of the aircraft without disproportionately increasing the drag due to the flow smoothening by the suction of the pusher propellers over the main wing. The pushers also delay the separation of the boundary layer whereas the tractors are unable to prevent the formation of the separation bubble despite injecting momentum through their slipstreams into the flow. The results from the two numerical approaches are then compared for accuracy in designing DEP configurations for an airframe.

Extensive design and aerodynamic performance investigation of diffuser augmented wind turbine (DAWT) guided by generalized actuator disc theory

Shrouding a turbine boosts power, lowers cut-in speed, but raises installation costs, and limits adaptability to wind shifts. A compact, wide-angle DAWT with competitive capacity is crucial for practical installations. Small turbines, often in fluctuating wind sites, necessitate thorough off-design performance analysis. A relatively short, wide-angle GOE431 diffuser is optimized by an efficient response surface method. Inverse blade element method, combined with actuator disc DAWT CFD considering wake swirl, shapes 90 cm-diameter rotor blade with minimal iterations. Implications of Generalized Actuator Disc Theory on DAWT design and performance are addressed with three-dimensional CFD for the first time. This approach unveiled substantial room for improving DAWT efficiency and uncovered key factors causing deviations from ideal performance. Tip leakage and diffuser losses constituted 9.5% of overall energy losses, with wake rotation, blade efficiency, and blade drag at 9.2%. Tip-hub losses, finite blade number, rotor-diffuser interaction, suboptimal rotor, and turbulence contributed to 12.1% in three-bladed DAWT, reaching CP,max = 0.746, with tip losses about one-third of bare turbine. Six-bladed DAWT raised CP by 93%, from 0.417 to 0.805, achieving 75% of ideal DAWT. Finite blade number led to reduced attack angles, higher tip losses, and limited flow expansion, contributing significantly to energy losses. As blade number and design tip-speed-ratio increased, blade Reynolds number decreased, suggesting an optimal combination to minimize energy losses. At off-design, a strong connection existed between thrust coefficient, diffuser efficiency, and Cp increase in wide-angle diffuser DAWTs. Maintaining CT near CT,opt (0.786) at high tip-speed-ratio led to significant Cp rise.

Free-vortex models for wind turbine wakes under yaw misalignment – a validation study on far-wake effects

Abstract. Near-wake effects of wind turbine models using the free-vortex wake have been studied extensively, but there is a lack of validation for such predictions in the mid to far wake. This paper presents a novel validation study using three free-vortex wake models of increasing complexity: an actuator disc, an actuator disc with rotation, and a lifting-line model. We emphasise the application for dynamic wind farm flow control optimisation with a focus on wake redirection using yaw misalignment. For this purpose, wake models should provide sufficiently accurate power predictions at a low computational expense to enable real-time control optimisation. Three sets of wind tunnel data are used for validation: flow measurements under steady yaw misalignment, time-resolved flow measurements for a step change in yaw, and turbine output measurements with yaw control and simulated wind direction variation. Results indicate that the actuator-disc model provides the best balance between computational cost and accuracy in power predictions for the mid to far wake, which is not significantly improved upon by the addition of rotation. In the near wake, the added complexity of the lifting-line model may provide value as it models blade loading and individual tip vortices. Altogether, this study provides important validation for further studies into optimisation of wake steering under time-varying conditions and suggests that the actuator-disc model is a suitable candidate for use in a model-predictive wind farm flow control framework.

Upward Shift of Wind Turbine Wakes in Large Wind Farms

A detailed description of wake characteristics is essential for optimizing wind farm performance. Compared with the wake of a stand-alone wind turbine, less attention has been paid to wind turbine wakes in large wind farms. In this work, we investigate the vertical position of wakes for wind turbines in large wind farms with different streamwise turbine spacings and ground roughness lengths using large-eddy simulation with an actuator disk model. The simulation results reveal an upward shift of the wake center (defined as the position with the maximum velocity deficit) for the wind turbine deeply arrayed in the wind farm. Larger upward shifts of the wake center are observed for wind turbines in further downstream rows and wind turbines installed on the ground with higher roughness, for which the wake expands at a higher rate. It is conjectured that the upward shift of the wake center is caused by the upward shift of the turbulence-dominated momentum entrainment region and the constraint of ground on wake expansion. An analytical wake model incorporating the upward-shifting wake center was developed. In the proposed model, different expansion rates are employed for the lower and upper wake regions. The upward shift of the wake center is directly taken into account using the large-eddy simulation results. The comparison with the large-eddy simulation results demonstrates the importance of accounting for the upward shift of the wake center in analytical wake models.

An analytical linear two-dimensional actuator disc model and comparisons with computational fluid dynamics (CFD) simulations

Abstract. The continuous up-scaling of wind turbines enabled by more lightweight and flexible blades in combination with coning has challenged the assumptions of a plane disc in the commonly used blade element momentum (BEM)-type aerodynamic codes for the design and analysis of wind turbines. The objective with the present work is thus to take a step back relative to the integral 1-dimensional (1-D) momentum theory solution in the BEM model in order to study the actuator disc (AD) flow in more detail. We present an analytical, linear solution for a two-dimensional (2-D) AD flow with one equation for the axial velocity and one for the lateral velocity, respectively. Although it is a 2-D model, we show in the paper that there is a good correlation with axis-symmetric and three-dimensional (3-D) computational fluid dynamics (CFD) simulations on a circular disc. The 2-D model has thus the potential to form the basis for a simple and consistent rotor induction model. For a constant loading, the axial velocity distribution at the disc is uniform as in the case of the classical momentum theory for an AD. However, an important observation of the simulated flow field is that immediately downstream of the disc the axial velocity profiles change rapidly to a shape with increased induction towards the edges of the disc and less induction on the central part. This is typically what is seen at the disc in full non-linear CFD AD simulations, which is what we compare with in the paper. By a simple coordinate rotation the analytical solution is extended to a yawed disc with constant loading. Again, a comparison with CFD, now with a 3-D simulation on a circular disc in yaw, confirms a good performance of the analytical 2-D model for this more complicated flow. Finally, a further extension of the model to simulate a coned disc is obtained using a simple superposition of the solution of two yawed discs with opposite yaw angles and positioned so the two discs just touch each other. Now the validation of the model is performed with results from axis-symmetric CFD simulations of an AD with a coning of both 20 and −20∘. In particular, for the disc coned in the downwind direction there is a very good correlation between the simulated normal velocity to the disc, whereas some deviations are seen for the upwind coning. The promising correlation of the results for the 2-D model in comparison with 3-D simulations of a circular disc with CFD for complicated inflow like what occurs at yaw and coning indicates that the 2-D model could form the basis for a new, consistent rotor induction model. The model should be applied along diagonal lines on a rotor and coupled to an angular momentum model. This application is sketched in the outlook and is a subject for future research.

Wake characteristics of a balloon wind turbine and aerodynamic analysis of its balloon using a large eddy simulation and actuator disk model

Abstract. In the realm of novel technologies for generating electricity from renewable resources, an emerging category of wind energy converters called airborne wind energy systems (AWESs) has gained prominence. These pioneering systems employ tethered wings or aircraft that operate at higher atmospheric layers, enabling them to harness wind speeds surpassing conventional wind turbines' capabilities. The balloon wind turbine is one type of AWESs that utilizes the buoyancy effect to elevate the turbine to altitudes typically ranging from 400 to 1000 m. In this paper, the wake characteristics and aerodynamics of a balloon wind turbine were numerically investigated for different wind scenarios. Large eddy simulation, along with the actuator disk model, was employed to predict the wake behavior of the turbine. To improve the accuracy of the simulation results, a structured grid was generated and refined by using an algorithm to resolve about 80 % of the local turbulent kinetic energy in the wake. Results contributed to designing an optimized layout of wind farms and stability analysis of such systems. The capabilities of the hybrid large eddy simulation and actuator disk model (LES–ADM) when using the mesh generation algorithm were evaluated against the experimental data on a smaller wind turbine. The assessment revealed a good agreement between numerical and experimental results. While a weakened rotor wake was observed at the distance of 22.5 diameters downstream of the balloon turbine, the balloon wake disappeared at about 0.6 of that distance in all the wind scenarios. Vortices generated by the rotor and balloon started to merge at the tilt angle of 10∘, which intensified the turbulence intensity at 10 diameters downstream of the turbine for the wind speeds of 7 and 10 m s−1. By increasing the tilt angle, the lift force on the wings experienced a sharper increase with respect to that of the whole balloon, which signified a controlling system requirement for balancing such an extra lift force.

Numerical simulations for a parametric study of blockage effect on offshore wind farms

AbstractThe paper presents a study of the upstream influence of wind farms on the wind speed, which is called blockage effect. A Reynolds Averaged Navier–Stokes (RANS) numerical model using an actuator disc method was devised and validated using the SCADA data from a Horns Rev 1 wind farm. The maximum difference between the average power in the first row for SCADA and the numerical model was 7.8%. The model was used to determine the impact of blockage effect on the wind farm parameters and the extent to which the wind speed and the power generation were reduced. A reference wind farm was defined, with a modified size, spacing, turbine height, and diameter that were used for comparison with other wind farm configurations. The results of the investigation of the wind farm parameter effects on the upstream wind speed reduction are presented in the paper. It has been established that increasing the turbine spacing from 5D to 6.7D reduces the power loss due to blockage by two. Blockage losses are almost eliminated when the spacing is increased two times. Similarly, the wind turbine thrust coefficient (CT) has a large impact on blockage, which is more pronounced, when CT is higher. In fact, the velocity deficit due to blockage is proportional to CT. The turbine tower height has small impact on blockage effect—the power reduction was changed by 0.3% due to blockage for the investigated range. The number of turbines in a row (with a constant number of turbines in a row) does not affect blockage significantly.