Actuator Disk Method Research Articles

Analysis of the sweeped actuator line method

The actuator line method made it possible to describe the near wake of a wind turbine more accurately than with the actuator disk method. Whereas the actuator line generates the helicoidal vortex system shed from the tip blades, the actuator disk method sheds a vortex sheet from the edge of the rotor plane. But with the actuator line come also temporal and spatial constraints, such as the need for a much smaller time step than with actuator disk. While the latter one only has to obey the Courant-Friedrichs-Lewy condition, the former one is also restricted by the grid resolution and the rotor tip-speed. Additionally the spatial resolution has to be finer for the actuator line than with the actuator disk, for well resolving the tip vortices. Therefore this work is dedicated to examining a method in between of actuator line and actuator disk, which is able to model the transient behaviour, such as the rotating blades, but which also relaxes the temporal constraint. Therefore a larger time-step is used and the blade forces are swept over a certain area. The main focus of this article is on the aspect of the blade tip vortex generation in comparison with the standard actuator line and actuator disk.

Analysis of long distance wakes of Horns Rev I using actuator disc approach

The wake recovery behind the Horns Rev wind farm is analysed to investigate the applicability of Large Eddy Simulations (LES) in combination with an actuator disc method (ACD) for farm to farm interaction studies. Periodic boundary conditions on the lateral boundaries are used to model the wind farm (as infinitely wide), using only two columns of turbines. The meteorological conditions of the site are taken into account by introducing wind shear and pre-generated synthetic turbulence to the simulation domain using body forces. Simulations are carried out to study the power production and the velocity deficit in the farm wake. The results are compared to the actual power production as well as to wind measurements at 2 km and 6 km behind the wind farm. The simulated power production inside the farm shows an overall good correlation with the real production, but is slightly overpredicted in the most downstream rows. The simulations overpredict the wake recovery, namely the wind velocity, at long distances behind the farm. Further studies are needed before the presented method can be applied for the simulation of long distance wakes. Suggested parameters to be studied are the development of the turbulence downstream in the domain and the impact of the grid resolution.

Comparison of wind turbine wake properties in non-uniform inflow predicted by different rotor models

The wake of the 2MW NM80 wind turbine subject to non-uniform and laminar inflow conditions is simulated using CFD with a fully resolved rotor geometry, an actuator line method and actuator disc method, respectively and in all simulations the wake properties are compared. Based on the comparison the strengths and limitations of the models are pointed out.

Performance analysis of open and ducted wind turbines

In this paper the analysis of the aerodynamic performance of ducted wind turbines is carried out by means of a nonlinear and semi-analytical actuator disk model. It returns the exact solution in an implicit formulation as superposition of ring vortices properly arranged along the duct surface and the wake region. In comparison with similar and previously developed models, the method can deal with ducts of general shape, wake rotation and rotors characterised by radially varying load distributions. Moreover, the nonlinear mutual interaction between the duct and the turbine, and the divergence of the slipstream, which is particularly relevant for heavily loaded rotors, are naturally accounted for. Present results clearly show that a properly ducted wind turbine can swallow a higher mass flow rate than an open turbine with the same rotor load. Consequently, the ducted turbine achieves a higher value of the extracted power. The paper also presents a detailed comparison between the aforementioned nonlinear and semi-analytical actuator disk method and the widely diffused CFD actuator disk method. The latter is based on the introduction of an actuator disk model in a CFD package describing the effects of the rotor through radial profiles of blade forces distributed over a disk surface. A set of reference numerical data, providing the inviscid axisymmetric velocity and pressure field distributions, are generated with controlled accuracy. Owing to an in-depth analysis of the error generated by the semi-analytical method and to the exactness of the solution in its implicit form, the collected data are well-suited for code-to-code validation of existing or newly developed computational methods.

Minimizing Axial Energy Loss by Using Vane Turbine in the Propeller Slipstream

The paper describes the results of analytical investigation on the application of vane-turbine in the propeller slipstream. The vane-turbine is attached on single-and twin-screw ships with total number of investigated ships are 20. Performance of the turbine was analyzed by actuator disc method. The effect of vane-turbine on ship performance is investigated. Discussions are focused on two main topics, namely speed loss and power efficiency gain. Final result finds out that the ratio of the thrust-power producing by vane turbine and thrust-power producing by propeller will influence the efficiency gain.

Numerical Study of Helicopter Rotors in a Ship Airwake

Operating helicopters in a naval environment is challenging because it imposes a pilot workload significantly higher than that during land-based operations. The aerodynamic interaction between the aircraft and the ship wake is known to play an important role in increasing the pilot workload, hence reducing the aircraft capability as a result of maintaining safety. As a further step toward numerical prediction of ship/helicopter operational limitations, computational-fluid-dynamics simulations are conducted for the Canadian Patrol Frigate. The effect of the rotor is included in the simulation, first using an actuator-disc method together with steady calculations, then using rotor blades and the unsteady Reynolds-averaged Navier–Stokes equations. Results using the actuator-disc method demonstrate the importance of coupling effects on the wake and rotor inflow when the rotor is operating close to the ship and therefore the invalidity of superposition methods. The case of a Sea King helicopter main rotor hovering above the deck just before touchdown is reproduced to overcome the limitations of steady calculations and the actuator-disc method. Predictions of rotor thrust compare well with the experimental data available and give confidence in the results. The findings highlight the differences in rotor loading between forward flight and near-deck operation. The possibility of using such simulations for determining safe flight envelopes is discussed as part of the future work.

A CFD code comparison of wind turbine wakes

A comparison is made between the EllipSys3D and SnS CFD codes. Both codes are used to perform Large-Eddy Simulations (LES) of single wind turbine wakes, using the actuator disk method. The comparison shows that both LES models predict similar velocity deficits and stream-wise Reynolds-stresses for four test cases. A grid resolution study, performed in EllipSys3D and SnS, shows that a minimal uniform cell spacing of 1/30 of the rotor diameter is necessary to resolve the wind turbine wake. In addition, the LES-predicted velocity deficits are also compared with Reynolds-Averaged Navier Stokes simulations using EllipSys3D for a test case that is based on field measurements. In these simulations, two eddy viscosity turbulence models are employed: the k-ϵ model and the k-ϵ-fp model. Where the k-ϵ model fails to predict the velocity deficit, the results of the k-ϵ-fP model show good agreement with both LES models and measurements.

Airfoil data sensitivity analysis for actuator disc simulations used in wind turbine applications

To analyse the sensitivity of blade geometry and airfoil characteristics on the prediction of performance characteristics of wind farms, large-eddy simulations using an actuator disc (ACD) method are performed for three different blade/airfoil configurations. The aim of the study is to determine how the mean characteristics of wake flow, mean power production and thrust depend on the choice of airfoil data and blade geometry. In order to simulate realistic conditions, pre-generated turbulence and wind shear are imposed in the computational domain. Using three different turbulence intensities and varying the spacing between the turbines, the flow around 4-8 aligned turbines is simulated. The analysis is based on normalized mean streamwise velocity, turbulence intensity, relative mean power production and thrust. From the computations it can be concluded that the actual airfoil characteristics and blade geometry only are of importance at very low inflow turbulence. At realistic turbulence conditions for an atmospheric boundary layer the specific blade characteristics play an minor role on power performance and the resulting wake characteristics. The results therefore give a hint that the choice of airfoil data in ACD simulations is not crucial if the intention of the simulations is to compute mean wake characteristics using a turbulent inflow.

The role of conservative forces in rotor aerodynamics

AbstractThe theory to predict the performance and loads on rotors (propellers, screws, windmills) has a history of more than a century. Apart from modern computational fluid dynamics and vortex panel models taking the true blade geometry into account, most other models proceed from an infinitely thin actuator disc or line. These models assume an externally defined force field distributed at the disc or line, representing the loads on the real rotor. Given this force field, the flow is solved by momentum balances or by the equations of motion. The use of external force fields was discussed in textbooks of the first decades of the 20th century, but has received little attention since then. This paper investigates the higher-order effect of adding thickness to the actuator disc or changing the actuator line to a blade with cross-sectional dimensions. For the generation of a Rankine vortex by a force field acting on an actuator disc with thickness, an exact solution has been found in which not only the thrust and torque determine the flow, but also a radial force. This force is conservative, in contrast to the other force components. For rotor blades, a conservative normal and radial force acting on the chordwise bound vorticity is present. This explains the experimentally observed inboard motion of the tip vortex of model wind turbine rotors before the wake induction field drives it outboard. Simulations by computational fluid mechanics and a vortex panel code reproduce the inboard motion, but an actuator line analysis, in which the chordwise vorticity is absent, does not. The conservative load is only $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}1\mbox{--}2\, \%$ of the thrust on the entire blade but ${\approx }10\, \%$ of the thrust at the tip ($r/R>0.9$). Conservative forces at the disc and rotor blade vanish for vanishing disc thickness or blade cross-section, so play no role in any of the infinitely thin actuator disc or line methods. However, if higher-order effects of non-zero dimensions are to be modelled, the conservative force field has to be included.

Comparison of wind turbine wake properties in non‐sheared inflow predicted by different computational fluid dynamics rotor models

AbstractThe wake of the 5MW reference wind turbine designed by the National Renewable Energy Laboratory (NREL) is simulated using computational fluid dynamics with a fully resolved rotor geometry, an actuator line method and an actuator disc method, respectively. Simulations are carried out prescribing both uniform and turbulent inflows, and the wake properties predicted by the three models are compared. In uniform inflow, the wake properties predicted by the actuator disc and line methods are found to be in very close agreement but differ significantly from the wake of the fully resolved rotor, which is characterized by much higher turbulence levels. In the simulations with turbulent inflow, the wake characteristics predicted by the three methods are in close agreement, indicating that the differences observed in uniform inflow do not play an important role if the inflow is turbulent. Copyright © 2014 John Wiley & Sons, Ltd.

Large‐eddy simulations of the Lillgrund wind farm

AbstractThe power production of the Lillgrund wind farm is determined numerically using large‐eddy simulations and compared with measurements. In order to simulate realistic atmospheric conditions, pre‐generated turbulence and wind shear are imposed in the computational domain. The atmospheric conditions are determined from data extracted from a met mast, which was erected prior to the establishment of the farm. In order to allocate most of the computational power to the simulations of the wake flow, the turbines are modeled using an actuator disc method where the discs are imposed in the computational domain as body forces which for every time step are calculated from tabulated airfoil data. A study of the influence of imposed upstream ambient turbulence is performed and shows that higher levels of turbulence results in slightly increased total power production and that it is of great importance to include ambient turbulence in the simulations. By introducing ambient atmospheric turbulence, the simulations compare very well with measurements at the studied inflow angles. A final study aiming at increasing the farm production by curtailing the power output of the front row turbines and thus letting more kinetic energy pass downstream is performed. The results, however, show that manipulating only the front row turbines has no positive effect on the farm production, and therefore, more complex curtailment strategies are needed to be tested. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical CFD Comparison of Lillgrund Employing RANS

The following article will validate the results obtained using the actuator disc method in the state of the art numerical Computational Fluid Dynamic (CFD) tool WindSim using on-site measurements from the offshore wind farm Lillgrund. WindSim solves the mass, momentum and energy conservation equations using the Reynolds Average Navier Stokes (RANS) method. Emphasis will be put here on investigating how the choice of different parameters influences the results, and comparisons will be performed with experimental data. The quantity that will be compared is the individual energy production of the wind turbines for different grid resolutions, inflow angles, thrust radial distributions and turbulence closure models.

Ducted Propeller Flow Analysis by Means of a Generalized Actuator Disk Model

The paper presents a generalized semi-analytical actuator disk model as applied to the analysis of the flow around ducted propellers at different operating conditions. The model strongly couples the non-linear actuator disk method of Conway[1] (J. Fluid Mech. 1998; 365: 235-267) and the vortex element method of Martensen[2] (Arch. Rat. Mech. 1959; 3: 235-270) and it returns the exact solution, although in an implicit formulation, for incompressible, axisymmetric and inviscid flows. The solution is made explicit through a semi-analytical procedure developed and validated by Bontempo and Manna[3] (J. Fluid Mech. 2013;728:163-195). Moreover the method duly accounts for non-uniform load radial distribution, slipstream contraction, mutual non-linear interaction between duct and propeller, wake rotation, and ducts of general shape. Thanks to its extremely reduced computational cost it can easily be integrated into design systems based on the repeated analysis scheme of hierarchical type. A comparison between open and ducted rotors is carried out in order to quantify the effects of the duct on the overall performance of the device. Emphasis is given to the appropriate matching between the duct geometry and the propeller load to exploit the benefits that could arise ducting the propeller.

Design of a Novel Experimental Facility for Testing of Tidal Arrays

In order to obtain the maximum amount of energy from tidal stream extraction devices, deployment in large arrays should be studied. The area of seabed with favorable conditions is fairly limited; therefore layout spacing has to be optimized. In this paper a feasibility study for a novel experimental facility, suitable for the testing of an array of tidal devices, is presented. To avoid space and scale limitations of towing tanks, testing is proposed to be performed in large lakes or calm seas using a self-propelled vessel, which will carry an array of devices with variable spacing, creating relevant speed differences and measuring their performance and loading. Using hydrodynamic scaling laws, an appropriate size for test turbines and the range of vessel speed was determined to fulfill experimental requirements. Computational fluid dynamic simulations, using the actuator disc method, have suggested a suitable turbine array configuration to resemble real application conditions. A simplified model of the vessel was analyzed using the finite elements method to determine the main scantlings. The hull resistance calculated by empirical formulae was found to be negligible compared to the resistance of the tested turbine. It was confirmed that turbine size and speed determined by scaling laws are also reasonable from a propulsion point of view.

Aerodynamic optimization of wind turbine rotors using a blade element momentum method with corrections for wake rotation and expansion

ABSTRACTThe blade element momentum (BEM) method is widely used for calculating the quasi‐steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now be obtained in the blade root and tip sections. It is expected that this will lead to small changes in optimum blade designs. In this work, has been implemented, and the spanwise load distribution has been optimized to find the highest possible power production. For comparison, optimizations have been carried out using BEM as well. Validation of shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using , and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM. In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd.

Modeling of lifting‐device aerodynamics using the actuator surface concept

AbstractThe actuator surface (AS) concept and its implementation within a differential, Navier–Stokes control volume finite‐element method (CVFEM) are presented in this article. Inspired by vortex and actuator disk methods, the AS concept consists of using porous surfaces carrying velocity and pressure discontinuities to model the action of lifting surfaces on the flow. The underlying principles and mathematics associated with AS are first reviewed, as well as their implementation in a CVFEM. Results are presented for idealized 2D cases with analytical solutions, as well as for the 3D cases of a finite wing and an experimental wind turbine. In the case of the finite wing, wake induction is well handled by the model with accurate predictions of induced angles and drag when compared with the Prandtl lifting line model. Comparisons with volume force approaches, often used to model the action of propellers or wind turbine blades in a simplified analysis, show that the AS concept has some interesting advantages in terms of accuracy and respect of flow physics. This new approach is easy and rapid to embed in most computational fluid dynamics (CFD) methods. It is applicable to a wide range of problems involving thin lifting devices like finite wings, propellers, helicopter or wind turbine blades. Copyright © 2009 John Wiley & Sons, Ltd.

1412 旋回キャビテーションの抑制に関する一考察(GS-5 キャビテーション)

This paper shows a possibility of passive or active control of the rotating cavitation by using an actuator disk method. A device which can change the amplitude and phase difference of the velocity disturbance is assumed. It was found that, (1) A stable region appeared dependent on the amplitude and phase. (2)For large value of mass flow gain factor, it is not possible to completely supress rotating cavitation. (3) However, entirely stable region apperes, if mass flow gain factor is relatively small.

1831 アクチュエータディスク法による不始動超音速翼列の安定解析

1831 アクチュエータディスク法による不始動超音速翼列の安定解析

NUMERICAL INVESTIGATIONS OF THE AERODYNAMICS AND THE AEROELASTIC STABILITY OF OSCILLATING ANNULAR WINGS

The nacelles of modern aeroengines are constantly increasing in size. Thus, engine air-loads are becoming more powerful and their importance for the aeroelastic stability is becoming more significant. The principal goal of this study is to answer the question of how unsteady airloads vary while shifting to transonic Mach numbers. The investigations are carried out by applying a finite volume Euler method to a harmonically oscillating annular wing. The results show that transonic effects in the case of an annular wing are essentially weaker than in the case of an airfoil. The order of magnitude of the variations is around 10%. Possible consequences for the aeroelastic stability are examined with the example of an elastically mounted annular wing in transonic flow. The shifts of the stability curves also remain within a range of 10%. In addition, an actuator disk method, which is frequently used for the simulation of the fan jet, is expanded in such a way that unsteady flows can be treated. Some unsteady air-loads are strongly dependent on the pressure jump across the fan.

Stability Analysis of Supersonic Cascade Flow by Actuator Disk Methods.

In recent years, the rotational speed of gas turbines is increasing more and more to increase the pressure ratio per one stage and hence to reduce the total number of stages. Accordingly, it is becoming more common that the relative inflow is supersonic near the tip of the fan and the first stage compressor cascades. At higher speeds, it is well-known that stable operating range becomes extremely narrow due to surge and choke. In this circumstances, it is important to understand the characteristics of the supersonic compressor in the off-design region as well as at the design point.