Actuator Disk Model Research Articles

Simulation and analysis of flow around tilting asymmetric ducted fans mounted at the wing tips of a vertical take-off and landing unmanned aerial vehicle

Tilting ducted fans attached to the wing tips of vertical take-off and landing unmanned aerial vehicles define new applications for these types of aerial vehicles. This new configuration gives vertical take-off and landing unmanned aerial vehicles the ability to hover like helicopters and fly forward like airplanes, which results in using any arbitrary location for take-off and landing combined with increasing range and speed. Furthermore, generating additional lift using asymmetrical shape for the external body of the ducted fans can lead to reducing the wing area and related overall drag, which results in saving more energy. This research provides experimental results from wind tunnel tests in addition to computational fluid dynamics simulations to investigate the advantages of using an asymmetrical tilting ducted fan instead of a symmetrical one. “actuator disk model” combined with the assumption of “constant delivered power” to the propeller were used successfully to calculate the induced velocity to the rotor plane of the ducted fan in the computational fluid dynamics simulations. The effects of the stall and flow separation on the aerodynamic coefficients were also studied and compared for the symmetrical and asymmetrical ducted fans. Both computational fluid dynamics and experimental results showed noticeable improvement in the lift coefficient using an asymmetrical shape for the external body of the tilting ducted fans.

Effects of seabed morphology on oscillating water column wave energy converters

This paper presents a numerical model to analyse the effects of changes in the bedforms morphology on Oscillating Water Column (OWC) wave energy devices. The model was developed in FLUENT® and based on the Actuator Disk Model theory to simulate the turbine performance. The seabed forms were reproduced with the morphodynamic model XBeach-G for a series of characteristic sea states in Playa Granada (southern Spain). These bedforms were used as input bed geometries in FLUENT® and compared with a hypothetical flat seabed to analyse the effects of changes in bed level on the OWC performance. Results of the simulated sea states reveal the influence of the seabed morphology in the power take–off performance, affecting the relationship between pressure drop and air flow rate through the turbine. Energy dissipation was found to be directly dependent on the bedforms unit volume. This lead to lower mean efficiencies for the cases with evolved morphologies (up to 15%) compared to those obtained for the hypothetical flat cases (19%). The effects of seabed formations on the power take–off performance presented in this paper can be of interest in planning control strategies for OWC devices.

Effects of the Approximations Embodied in the Momentum Theory as Applied to the NREL PHASE VI Wind Turbine

This paper investigates the impact of the standard approximations embodied in the well-known Momentum Theory on its performance prediction capabilities. To this aim, the results of the momentum theory, which is still widely used in all Blade Element/Momentum codes for the analysis and/or design of wind turbines, are compared with those obtained with an actuator disk model based on Computational Fluid Dynamics techniques. In this method, the axisymmetric and steady Euler equations are solved with a classical finite volume approach, while the turbine effects are modelled through a set of axial and tangential body forces distributed over a disk shaped region representing the rotor swept surface. Since this method does not rely on the momentum theory simplifying assumptions, it can be suitably employed to verify the momentum theory validity. The analysis is carried out using the well documented experimental data of the National Renewable Energy Laboratory Phase VI wind turbine.

Validation of the actuator disc and actuator line techniques for yawed rotor flows using the New MEXICO experimental data

Experimental data acquired in the New MEXICO experiment on a yawed 4.5m diameter rotor model turbine are used here to validate the actuator line (AL) and actuator disc (AD) models implemented in the Large Eddy Simulation code EllipSys3D in terms of loading and velocity field. Even without modelling the geometry of the hub and nacelle, the AL and AD models produce similar results that are generally in good agreement with the experimental data under the various configurations considered. As expected, the AL model does better at capturing the induction effects from the individual blade tip vortices, while the AD model can reproduce the averaged features of the flow. The importance of using high quality airfoil data (including 3D corrections) as well as a fine grid resolution is highlighted by the results obtained. Overall, it is found that both models can satisfactorily predict the 3D velocity field and blade loading of the New MEXICO rotor under yawed inflow.

The Long distance wake behind Horns Rev I studied using large eddy simulations and a wind turbine parameterization in WRF

The aim of the present paper is to obtain a better understanding of long distance wakes generated by wind farms as a first step towards a better understanding of farm to farm interaction. The Horns Rev I (HR) wind farm is considered for this purpose, where comparisons are performed between microscale Large Eddy Simulations (LES) using an Actuator Disc model (ACD), mesoscale simulations in the Weather Research and Forecasting Model (WRF) using a wind turbine parameterization, production data as well as wind measurements in the wind farm wake. The LES is manually set up according to the wind conditions obtained from the mesoscale simulation as a first step towards a meso/microscale coupling.The LES using an ACD are performed in the EllipSys3D code. A forced boundary layer (FBL) approach is used to introduce the desired wind shear and the atmospheric turbulence field from the Mann model. The WRF uses a wind turbine parameterization based on momentum sink. To make comparisons with the LESs and the site data possible an idealized setup of WRF is used in this study.The case studied here considers a westerly wind direction sector (at hub height) of 270 ± 2.5 degrees and a wind speed of 8 ± 0.5 m/s. For both the simulations and the site data a neutral atmosphere is considered. The simulation results for the relative production as well as the wind speed 2 km and 6 km downstream from the wind farm are compared to site data. Further comparisons between LES and WRF are also performed regarding the wake recovery and expansion.The results are also compared to an earlier study of HR using LES as well as an earlier comparison of LES and WRF. Overall the results in this study show a better agreement between LES and WRF as well as better agreement between simulations and site data.The procedure of using the profile from WRF as inlet to LES can be seen as a simplified coupling of the models that could be developed further to combine the methods for cases of farm to farm interaction.

Effects of tilting rate variations on the aerodynamics of the tilting ducted fans mounted at the wing tips of a vertical take-off and landing unmanned aerial vehicle

Tilting ducted fans mounted at the wing tips of vertical take-off and landing unmanned aerial vehicles define new applications for these types of aerial vehicles. This new configuration gives vertical take-off and landing unmanned aerial vehicles the ability to hover like helicopters and fly forward like airplanes, which results in using any arbitrary location for take-off and landing combined with increasing range and speed. Furthermore, generating additional lift by using asymmetrical shape for the external body of the ducted fans can lead to reducing the wing area and related overall drag, which results in saving more energy. The transition between cruise mode and hovering can be done by choosing different tilting rates, which can produce instabilities in the aerodynamics of the tilting ducted fans mounted at the wing tips of the vertical take-off and landing unmanned aerial vehicles. This research provides the computational fluid dynamics simulations to investigate these instabilities and compare them for two different ducted fans. “Actuator disk model” combined with the assumption of “constant delivered power” to the propeller were used successfully to calculate the induced velocity to the rotor plane of the ducted fan in the computational fluid dynamics simulations. The effects of the flow separation on the aerodynamic coefficients were discussed and compared for both symmetrical and asymmetrical ducted fans in different tilting rates.

CFD wind turbines wake assessment in complex topography

The purpose of this work is to numerically study the wind turbine wake evolution in farm over both complex and flat terrain. The nonlinear, aerodynamic interaction between the rotor wake and the wind farm terrain is modeled using the Hybrid method combining CFD (Computational Fluid dynamics) with the actuator disk model. The rotor defined as a function of the wind speed and the thrust coefficient is applied through a source term added in Navier-Stokes equations within (RANS) decomposition. The framework is structured and resolved via an Open Source Computational fluid dynamics program based on the finite volume method. The interactions between atmospheric upwind boundary layer, downwind wake and ground effects are evaluated considering different wind farm configurations: First, simulations are conducted for flat terrain by varying the wind turbine hub height. The soil effects on the wake evolution are estimated by means of the size length of the eddy areas of low speed recorded behind the rotor. In the second configuration concerning the complex terrain, the proposed hybrid method is adapted to the local wind field significantly disturbed by the topography singularities. The flow field obtained at the hub level is then analyzed and used to define the corresponding actuator disk model. This approach is applied to a small region located in north of Algeria. However, the accuracy and performance of the proposed model to predict the near wake and the far wake are demonstrated by a comparison with wake measurement over flat terrain and are in good agreement with experimental data. Results obtained in all cases gives interesting information involved in wind farm layout.

Simulation of horizontal axis tidal turbine wakes using a Weakly-Compressible Cartesian Hydrodynamic solver with local mesh refinement

This article aims at introducing the first steps of development and validation of a CFD tool dedicated to realistic tidal turbine farm modelling. The fluid solver is presented in details, together with the actuator disc model used to represent tidal turbines. A particular attention is paid to the spatial scheme in order to limit the numerical diffusion in the wakes. Comparisons with experimental results from Mycek et al. [1] on a horizontal axis tidal turbine (HATT) are presented and discussed. For the different cases, averaged axial velocities and averaged turbulence intensity rates are compared from 1.2 to 10 tidal turbine diameters behind the device. The properties of this tool are discussed in terms of accuracy, CPU costs and applicability to industrial purpose.

A CFD study on the performance of a tidal turbine under various flow and blockage conditions

CFD simulations utilising the actuator disk model have been performed to study the effect of various parameters on the thrust produced by a tidal turbine. Instead of increasing the performance coefficients of the turbine, a turbine placed in blocked conditions is shown to experience a velocity higher than the inflow velocity using a new approach to interpret results from CFD simulations. Turbines were found to produce less thrust when boundary layers were present than when boundary layers were absent in the simulation. Also, the presence of the boundary layer results in an optimal aspect ratio where the performance of a single turbine is maximised. Besides turbulence intensity, the flow velocity is also found to affect the predicted thrust of the turbine. Thrust increases with increasing blockage ratio when channel depth is held constant, and also increases with channel depth while blockage ratio is held constant. The rate of decay of turbulence intensity in the channel is also observed to be dependent on the channel depth, which may have affected results. Thus, the effects of blockage on turbine performance should be studied by varying the channel width without changing the channel depth.

Lift calculations based on accepted wake models for animal flight are inconsistent and sensitive to vortex dynamics

There are three common methods for calculating the lift generated by a flying animal based on the measured airflow in the wake. However, these methods might not be accurate according to computational and robot-based studies of flapping wings. Here we test this hypothesis for the first time for a slowly flying Pacific parrotlet in still air using stereo particle image velocimetry recorded at 1000 Hz. The bird was trained to fly between two perches through a laser sheet wearing laser safety goggles. We found that the wingtip vortices generated during mid-downstroke advected down and broke up quickly, contradicting the frozen turbulence hypothesis typically assumed in animal flight experiments. The quasi-steady lift at mid-downstroke was estimated based on the velocity field by applying the widely used Kutta–Joukowski theorem, vortex ring model, and actuator disk model. The calculated lift was found to be sensitive to the applied model and its different parameters, including vortex span and distance between the bird and laser sheet—rendering these three accepted ways of calculating weight support inconsistent. The three models predict different aerodynamic force values mid-downstroke compared to independent direct measurements with an aerodynamic force platform that we had available for the same species flying over a similar distance. Whereas the lift predictions of the Kutta–Joukowski theorem and the vortex ring model stayed relatively constant despite vortex breakdown, their values were too low. In contrast, the actuator disk model predicted lift reasonably accurately before vortex breakdown, but predicted almost no lift during and after vortex breakdown. Some of these limitations might be better understood, and partially reconciled, if future animal flight studies report lift calculations based on all three quasi-steady lift models instead. This would also enable much needed meta studies of animal flight to derive bioinspired design principles for quasi-steady lift generation with flapping wings.

Modeling the wind circulation around mills with a Lagrangian stochastic approach

This work aims at introducing model methodology and numerical studies related to a {Lagrangian} stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian \textit{stochastic downscaling method} that we have introduced in [3] and [4] to the atmospheric boundary layer and we introduce here a Lagrangian version of the \textit{actuator disc} methods to take account of the mills. We present our numerical method and numerical experiments in the case of non rotating and rotating actuator disc models. First, for validation purpose we compare some numerical experiments against wind tunnel measurements. Second we perform some numerical experiments at the atmospheric scale and present some features of our numerical method, in particular the computation of the probability distribution of the wind in the wake zone, as a byproduct of the fluid particle model and the associated PDF method.

Aerodynamic optimization of shrouded wind turbines

An axisymmetric Reynolds averaged Navier–Stokes solver is used along with an actuator disk model for the analysis of shrouded wind turbine flowfields. Following this, an efficient blade design technique that maximizes sectional power production is developed. These two techniques are incorporated into an optimization framework that seeks to design the geometry of the shroud and rotor to extract maximum power under thrust constraints. The optimal solution is also evaluated using a full three-dimensional Reynolds averaged Navier–Stokes solver, suggesting the viability of the design. The predicted optimal designs yield power augmentations well in excess of the Betz limit, even if the normalization of the power coefficient is performed with respect to the maximum shroud area. Copyright © 2016 John Wiley & Sons, Ltd.

Actuator disc methods for open propellers: assessments of numerical methods

ABSTRACTThe paper describes the assessment of two different actuator disc models as applied to the flow around open propellers. The first method is based on a semi-analytical approach returning the solution for the nonlinear differential equation governing the axisymmetric, steady, inviscid and incompressible flow around an actuator disc. Despite its low computational cost, the method does not require simplifying assumptions regarding the shape of the slipstream, e.g. the wake contraction is not disregarded or prescribed in advance. Moreover, the presence of a tangential velocity in the wake as well as the spanwise variation of the load are taken into account. The second one is a commonly used procedure based on CFD techniques in which the effects of the propeller are synthetically described through a set of body forces distributed over the disc surface. Both methods avoid the difficulties and the computational costs associated with the resolution of the propeller blades geometrical details. The comparison is based on an in-depth error analysis of the two procedures which results in a set of reference data with controlled accuracy. An excellent agreement has been documented between the two methods while the computational complexity is obviously very different. Among other things the comparison is also aimed at verifying the accuracy of the semi-analytical approach at each point of the computational domain and at quantifying the effect of the errors embodied in the two methods on the quality of the solution, both in terms of global and local performance parameters. Furthermore, the paper provides a set of reference solutions with controlled accuracy that could be used for the verification of new and existing computational methods. Finally, the computational cost of the semi-analytical model is quantified, thus providing a valuable information to designers who need to select a cost effective and reliable analysis tool.

Impact of Neutral Boundary-Layer Turbulence on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine in a turbulent boundary layer under neutral stratification are investigated systematically by means of large-eddy simulations. A methodology to maintain the turbulence of the background flow for simulations with open horizontal boundaries, without the necessity of the permanent import of turbulence data from a precursor simulation, was implemented in the geophysical flow solver EULAG. These requirements are fulfilled by applying the spectral energy distribution of a neutral boundary layer in the wind-turbine simulations. A detailed analysis of the wake response towards different turbulence levels of the background flow results in a more rapid recovery of the wake for a higher level of turbulence. A modified version of the Rankine–Froude actuator disc model and the blade element momentum method are tested as wind-turbine parametrizations resulting in a strong dependence of the near-wake wind field on the parametrization, whereas the far-wake flow is fairly insensitive to it. The wake characteristics are influenced by the two considered airfoils in the blade element momentum method up to a streamwise distance of 14D (D = rotor diameter). In addition, the swirl induced by the rotation has an impact on the velocity field of the wind turbine even in the far wake. Further, a wake response study reveals a considerable effect of different subgrid-scale closure models on the streamwise turbulent intensity.

Validation of the Actuator Line Model with coarse resolution in atmospheric sheared and turbulent inflow

Wind energy has become cost competitive in recent years for several reasons. Among them, wind turbines have become more efficient, increasing its size, both rotor diameter and tower height. This growth in size makes the prediction of the wind flow through wind turbines more challenging. To avoid the computational cost related to resolve the blade boundary layer as well as the atmospheric boundary layer, actuator models have been proposed in the past few years. Among them, the Actuator Line Model (ALM) has shown to reproduce with reasonable accuracy the wind flow in the wake of a wind turbine with moderately computational cost. However, its use to simulate the flow through wind farms requires a spatial resolution and a time step that makes it unaffordable in some cases. The present paper aims to assess the ALM with coarser resolution and larger time step than what is generally recommended, taking into account an atmospheric sheared and turbulent inflow condition and comparing the results with the Actuator Disk Model with Rotation (ADM-R) and experimental data. To accomplish this, a well known wind tunnel campaign is considered as validation case.

CFD modelling approaches against single wind turbine wake measurements using RANS

Numerical simulations of two wind turbine generators including the exact geometry of their blades and hub are compared against a simplified actuator disk model (ADM). The wake expansion of the upstream rotor is investigated and compared with measurements. Computational Fluid Dynamics (CFD) simulations have been performed using the open-source platform OpenFOAM [1]. The multiple reference frame (MRF) approach was used to model the inner rotating reference frames in a stationary computational mesh and outer reference frame for the full wind turbine rotor simulations. The standard k — ε and k — ω turbulence closure schemes have been used to solve the steady state, three dimensional Reynolds Averaged Navier- Stokes (RANS) equations. Results of near and far wake regions are compared with wind tunnel measurements along three horizontal lines downstream. The ADM under-predicted the velocity deficit at the wake for both turbulence models. Full wind turbine rotor simulations showed good agreement against the experimental data at the near wake, amplifying the differences between the simplified models.

Mean kinetic energy transport and event classification in a model wind turbine array versus an array of porous disks: Energy budget and octant analysis

An array of model turbines with rotors is compared experimentally to an array of model turbines with stationary porous disks. The main discrepancy in the mean velocity components between the two cases is found in the out-of-plane component while the fluctuations of the out-of-plane component are found to play a dramatically different role in the vertical flux of mean kinetic energy. The study has wide implications on the use of the actuator disk model as a parametrization for a rotor in computational work.

Wake structure in actuator disk models of wind turbines in yaw under uniform inflow conditions

Reducing wake losses in wind farms by deflecting the wakes through turbine yawing has been shown to be a feasible wind farm controls approach. Nonetheless, the effectiveness of yawing depends not only on the degree of wake deflection but also on the resulting shape of the wake. In this work, the deflection and morphology of wakes behind a porous disk model of a wind turbine operating in yawed conditions are studied using wind tunnel experiments and uniform inflow. First, by measuring velocity distributions at various downstream positions and comparing with prior studies, we confirm that the non-rotating porous disk wind turbine model in yaw generates realistic wake deflections. Second, we characterize the wake shape and make observations of what is termed as curled wake, displaying significant spanwise asymmetry. The wake curling observed in the experiments is also reproduced qualitatively in Large Eddy Simulations using both actuator disk and actuator line models. Results suggest that when a wind turbine is yawed for the benefit of downstream turbines, the curled shape of the wake and its asymmetry must be taken into account since it affects how much of it intersects the downstream turbines.

Numerical prediction of the turbulent wakes generated by a row of marine turbines

Numerical simulations of the turbulent wakes generated by rows of up to five marine turbines are presented. The numerical scheme combines an actuator disk model with a non-uniform velocity distribution, and the solution to the Reynolds averaged Navier–Stokes (RANS) equations. The first computations examine the dynamics of the turbulent wakes when the stream flows perpendicular to the row. The experiments of Stallard et al. (2013) serve as the benchmark for the numerical predictions. The computations also explore the significance of turbulence intensity and yawed conditions. An increase in the ambient turbulent intensity results in a quicker wake recovery. When the fluid stream is yawed to the turbine row, the problem loses its symmetry and some turbines realize lower velocities as they become affected by the wakes generated by other turbines.

Performance of an ideal turbine in an inviscid shear flow

Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.