Actuator Disk Model Research Articles

New Development of Classical Actuator Disk Model for Propellers at Incidence

The actuator disk model thrust formula was mathematically expanded in series and divided into two parts to show that propellers at incidence comprise an axial and a wing lift equivalent component. Both components share a common induced speed . This is done by considering an enhanced disk area for momentum balance, to match Glauert’s hypothesis mass flowrate. To shed light on the theoretical developments, wind tunnel tests were conducted on a two-bladed propeller at angles of incidence ranging from 0 to 90 deg. The wing component is shown to increase with airflow velocity and angle of incidence. The axial component decreases with , for all angles. The generally observed thrust increase with angle of incidence is explained, by the theory, to be mostly due to the wing component contribution. The theory also explains why at angles of incidence above 60 deg propellers inherently behave differently than at lower angles. While thrust decreases with at lower angles, it grows with airspeed at an angle of incidence of approximately 60 deg or higher. This behavioral inversion happens as the wing component positive sensitivity to overcomes the negative sensitivity of the axial component. A simplified formula is presented for predicting thrust at a given angle, based only on propellers data at an angle of incidence of 0, regardless of blade geometry.

Numerical simulation of wind turbine wake based on extended k‐epsilon turbulence model coupling with actuator disc considering nacelle and tower

The Reynolds-averaged Navier–Stokes (RANS) method coupling with the actuator disc model (ADM) is considered as a promising numerical simulation technology of wind turbine wake, and it is widely utilised in the aerodynamics of wind turbines and optimal layout of wind farms. The k − e turbulence model is widely adopted, among the RANS-based turbulence models. However, the k − e turbulence model easily overestimates the turbulence viscosity in the wake, which results in fast recovery of wake velocity and failure in wake forecasting. In addition, ADM with the oversimplified geometrical structure ignores the effects of nacelle and tower on the wind turbine wake, which further lowers the accuracy of wake simulation. Therefore, the numerical simulation of wind turbine wake based on the extended k − e turbulence model of EI Kasmi coupling with ADM considering nacelle and tower is proposed. Comparing the results of Marchwood Engineering Laboratories (MEL) ABL wind tunnel measurements and TNO wind tunnel experiments, it has been found that the proposed model improves the simulation effect for the near wake and has a certain contribution to the wake prediction accuracy overall.

Computational analysis of the indirect combustion noise generation mechanism in a nozzle guided vane in transonic operating conditions

The combustion noise in modern engines is mainly originating from two types of mechanisms. First, chemical reactions in the combustion chamber leads to an unsteady heat release which is responsible of the direct combustion noise. Second, hot and cold blobs of air coming from the combustion chamber are advected and accelerated through turbine stages, giving rise to entropy noise (or indirect combustion noise). In the present work, numerical characterization of indirect combustion noise of a Nozzle Guide Vane passage was assessed using three-dimensional Large Eddy Simulations. The present work offers an overview to the analytical, computational and experimental studies of the topic. Numerical simulations are conducted to reproduce the effects of incoming planar entropy waves from the combustion chamber and to characterize the generated acoustic power. The dynamic features of the flow are addressed by the means of frequency domain and modal analyses techniques such as Fourier Decomposition and Proper Orthogonal Decomposition. Finally, the predicted entropy noise from numerical calculations is compared with the analytical results of an actuator disk model for a stator stage. The present paper proves that the generated indirect combustion noise can be significant for transonic operating conditions. The blade acoustic response is characterized by the excitation of a latent dynamics at the forcing frequency of the planar entropy waves, and it increases as the amplitude of the incoming disturbances increases.

Numerical simulation of the Mexico wind turbine using the actuator disk model along with the 3D correction of aerodynamic coefficients in OpenFOAM

A foremost element in aerodynamic behavior analysis of wind turbines is numerical simulation. Actuator disk model is a method which enables us to simulate and analyze the flow fields and wakes behind the rotor by reducing the fluid computation around the rotor and solving the Navier-Stokes equations without considering the blade boundary layer. In addition of the need for constructing a realistic geometrical model, one also must run a simulation with very small grid spacing and time steps to resolve the blade boundary layer dynamics leading to the aerodynamic forces, which is also extremely expensive. In this paper actuator disk model along with a 3D corrected aerodynamic coefficients was implemented in the OpenFOAM software to simulate the MEXICO wind turbine rotor. The simulations were performed under three conditions: turbulent, design and stall conditions. The results of simulation including an estimation of the blade forces and the wakes velocity field were compared with the experimental results. It was found that the 3D corrected aerodynamic coefficients of airfoils led to an improved agreement between the simulation and experimental results, compared to a model implementing original aerodynamic coefficients.

Assessment of actuator disc models in predicting radial flow and wake expansion

Navier-Stokes actuator disc models have become a mature methodology for investigating wind turbine rotor performance with numerous articles published annually making use of this approach. Despite their popularity, their ability to predict near wake expansion remains questionable. The objective of this paper is to analyse the predictive ability of actuator disc models and compare results with other popular types of codes. The methodology employs the use of an actuator disc Computational Fluid Dynamics approach to model an actuator disc and a real (finite bladed) turbine case. Results are validated with existing experimental data. In addition, results from an actuator line model with and without tip corrections and a 3D vortex panel method are presented to aid the discussion. Results show that all models give a poor wake expansion prediction particularly in the inboard to mid-board areas. A good prediction is found in the outboard regions. In addition, contrary to the well known positive effects of tip corrections on load prediction, this work shows that this does not bring any particular benefit on wake expansion prediction. The conclusions from this work help to guide the use of actuator disc models in more complex flow scenarios including floating offshore wind turbine analysis.

On Stochastic Reduced-Order and LES-based Models of Offshore Wind Turbine Wakes

In this paper, the primary objective is to investigate flow structures in the wake of wind turbines based on applying a truncated Proper Orthogonal Decomposition (POD) approach. This scheme decomposes the three-dimensional velocity fields produced by the high-fidelity PArallelized LES Model (PALM) into a number of orthogonal spatial modes and time-dependent weighting coefficients. PALM has been combined with an actuator disk model with rotation to incorporate the effects of a turbine array. The time-dependent deterministic weights from applying the POD scheme are replaced by stochastic weights, estimated from two independent stochastic techniques that aim to account for unresolved small-scale features for a number of POD modes. We then reconstruct the flow field by a small number of stochastic modes to investigate how well the applied stochastic methodologies can reproduce the flow field compared to the original LES results.

Evaluation of Gaussian wake models under different atmospheric stability conditions: Comparison with large eddy simulation results

The calculation of the velocity deficit in the wake of individual wind turbines is a fundamental part of the wind farm analysis. A good approximation of the wake deficit behind a single wind turbine will improve the power estimation for downwind turbines. Large-eddy simulation (LES) is a research tool widely used in studying the velocity deficit and turbulence intensity in the wake. However, the computational cost of the LES prevents its application in wind farm performance analysis and control. Existing analytical wake models provide a fast estimation of the velocity deficit and the wake expansion rate downstream from the rotor. The Gaussian wake models use a Gaussian distribution to improve the prediction of the wake velocity deficit. With the number of analytical models available, an extensive evaluation of their performance under different flow parameters is needed. In this work, we simulate a wake of a single wind turbine using the LES code PALM (Parallelized LES Model) combined with an actuator disc model with rotation. We compare the computed flow field with the predictions made by Gaussian models and fit their parameters to obtain the best possible fit for the wake field data as computed by LES.

Validation of analytical body force model for actuator disc computations

A new analytical model for representing body forces in numerical actuator disc models of wind turbines is compared to results from a BEM model. The model assumes the rotor disc being subject to a constant circulation, modified for tip and root effects. The advantage of the model is that it does not depend on any detailed knowledge concerning the actual wind turbine being analysed, but only requires information of the thrust coefficient and tip speed ratio. The model is validated for different turbines operating under a wide range of operating conditions. The comparisons show generally an excellent agreement with the BEM model, with, however, some deviations of the tangential force in the root area and at small values of the thrust coefficient.

Power Prediction of Wind Farms via a Simplified Actuator Disk Model

This paper aims to demonstrate a simplified nonlinear wake model that fills the technical gap between the low-cost and less-accurate linear formulation and the high-cost and high-accuracy large eddy simulation, to offer a suitable balance between the prediction accuracy and the computational cost, and also to establish a robust approach for long-term wind farm power prediction. A simplified actuator disk model based on the momentum theory is proposed to predict the wake interaction among wind turbines along with their power output. The three-dimensional flow field of a wind farm is described by the steady continuity and momentum equation coupled with a k-ε turbulence model, where the body force representing the aerodynamic impact of the rotor blade on the airflow is uniformly distributed in the Cartesian cells within the actuator disk. The characteristic wind conditions identified from the data of the supervisory control and data acquisition (SCADA) system were employed to build the power matrix of these typical wind conditions for reducing the computation demands to estimate the yearly power production. The proposed model was favorably validated with the offshore measurement of Horns Rev wind farm, and three Taiwanese onshore wind farms were forecasted for their yearly capacity factors with an average error less than 5%, where the required computational cost is estimated about two orders of magnitude smaller than that of the large eddy simulation. However, the proposed model fails to pronouncedly reproduce the individual power difference among wind turbines in the investigated wind farm due to its time-averaging nature.

Wind farm layout optimization based on CFD simulations

This work shows the development of a tool for wind farm layout optimization based on computational fluid dynamics (CFD) simulations of the atmospheric wind flow and inter-turbine interference. Due to the high computational power required to simulate a whole wind farm using the complete geometry of the wind turbines, simplified models were developed to represent the turbine behavior, and the most commonly used model is the actuator disk model and its variations. The procedure for wind turbine behavior evaluation using a CFD model was implemented in the OpenFOAM software, and this model was coupled with the Dakota optimization toolkit. A genetic algorithm was selected for the optimization task due to its robustness and the characteristics of the problem solved. With this new tool in hand, three different terrain cases, with growing complexity, were tested considering different numbers of turbines on a cylindrical domain in order to achieve the best wind farm layout in terms of annual energy production that respects the imposed physical restrictions. As expected, the layout efficiency decreased as turbines were added to the domain, meaning that wake losses are introduced in this process. For the simpler domains, we observed that this efficiency decrease was approximately linear with respect to the number of turbines. Complex phenomena were captured during the optimization, such as wake deflection, different wake recoveries depending on the wind speed and interaction between the disturbances in the flow field caused by the terrain and by the turbines. These phenomena are not observed when using the tools available in the wind market and are seen as an improvement in the field of wind farm layout optimization, yielding more accurate results, and should decrease the level of uncertainty in the design of a wind farm.

Experimentally validated study of the impact of operating strategies on power efficiency of a turbine array in a bi-directional tidal channel

Flexible operation across a wide range of operating conditions is required to maximise the contribution of tidal turbine arrays to the future energy mix. This study establishes a basin efficiency range of a small array of horizontal axis turbines between 0.45 and 0.79, with dependency on turbine operating point and flow direction. This range is largely due to variation of array thrust as array power varies by less than 15% for all operating points.Analysis of array thrust, power and wakes was conducted using a RANS actuator disc model and assessed against new experimental measurements using porous discs. RANS array thrust predictions are within 10% of the experimental study. Turbine thrust differs within each array, varying by −60% to +30% compared to isolated turbines. Row-specific operating points reduce this range by a factor of two whilst also increasing the basin efficiency slightly for a given flow speed.Accounting for time variation of basin efficiency reduces the energy yield by almost 5% relative to arrays modelled with a constant net array thrust coefficient. Arrays with row-specific local thrust coefficients generate similar net power to arrays with velocity-specific array operating points but reduce the occurrences of large rates of change of power.

Aerodynamic characterization of barge and spar type floating offshore wind turbines at different sea states

AbstractThe wake dynamics behind a compliant floating offshore wind turbine (FOWT) with two alternative supporting platforms of spar buoy and barge platform are studied numerically. The computational model is based on the large eddy simulation and the use of the actuator disk model of the FOWT rotor in which the circular actuator disk is discretized with an unstructured two‐dimensional triangular mesh in a structured three‐dimensional Cartesian grid of the fluid domain. The wake dynamics and platform motions are calculated for laminar and turbulent inflow conditions. The flow solver is verified through a series of experimental wake measurements done behind a porous disk model and is also cross‐validated against previously published results. The dynamics of the floating spar and barge structures are calculated from wave–structure interaction for three distinctive sea states. The time history of power extraction and wind force for the floating offshore wind turbine are recorded and compared against a fixed horizontal axis wind turbine. The motion of the barge platform is found to induce low‐frequency modulation of the wake, whereas the spar buoy primarily displays similar wake dynamics to the fixed turbine. It is discussed how a single turbine utilizing the spar concept can be more energy efficient under the wave‐induced motion. Moreover, for both laminar and turbulent inflow conditions, due to the large axial oscillation experienced by the barge concept, the turbine wake recovers more rapidly. This suggests that for a tighter spacing of the turbines in a farm, the barge platform concept can be leveraged to obtain higher energy‐capturing efficiency over a fixed area.

Evaluation of Actuator Disk Model Relative to Actuator Surface Model for Predicting Utility-Scale Wind Turbine Wakes

The Actuator Disk (AD) model is widely used in Large-Eddy Simulations (LES) to simulate wind turbine wakes because of its computing efficiency. The capability of the AD model in predicting time-average quantities of wind tunnel-scale turbines has been assessed extensively in the literature. However, its capability in predicting wakes of utility-scale wind turbines especially for the coherent flow structures is not clear yet. In this work, we take the time-averaged statistics and Dynamic Mode Decomposition (DMD) modes computed from a well-validated Actuator Surface (AS) model as references to evaluate the capability of the AD model in predicting the wake of a 2.5 MW utility-scale wind turbine for uniform inflow and fully developed turbulent inflow conditions. For the uniform inflow cases, the predictions from the AD model are significantly different from those from the AS model for the time-averaged velocity, and the turbulence kinetic energy until nine rotor diameters (D) downstream of the turbine. For the turbulent inflow cases, on the other hand, the differences in the time-averaged quantities predicted by the AS and AD models are not significant especially at far wake locations. As for DMD modes, significant differences are observed in terms of dominant frequencies and DMD patterns for both inflows. Moreover, the effects of incoming large eddies, bluff body shear layer instability, and hub vortexes on the coherent flow structures are discussed in this paper.

A New Wind Turbine CFD Modeling Method Based on a Porous Disk Approach for Practical Wind Farm Design

In this study, the new computational fluid dynamics (CFD) porous disk (PD) wake model was proposed in order to accurately predict the time-averaged wind speed deficits in the wind turbine wake region formed on the downstream side by the 2-MW wind turbine operating at a wind speed of 10 m/s. We use the concept of forest canopy model as a new CFD PD wake model, which has many research results in the meteorological field. In the forest canopy model, an aerodynamic resistance is added as an external force term to all governing equations (Navier–Stokes equations) in the streamwise, spanwise, and vertical directions. Therefore, like the forest model, the aerodynamic resistance is added to the governing equations in the three directions as an external force term in the CFD PD wake model. In addition, we have positioned the newly proposed the LES using the CFD PD wake model approach as an intermediate method between the engineering wake model (empirical/analytical wake model) and the LES combined with actuator disk (AD) or actuator line (AL) models. The newly proposed model is intended for use in large-scale offshore wind farms (WFs) consisting of multiple wind turbines. In order to verify the validity of the new method, the optimal model parameter CRC was estimated by comparison with the time-averaged wind speed database in the wind turbine wake region with fully resolved geometries, combined with unsteady Reynolds-averaged Navier–Stokes (RANS) equations, implemented using the ANSYS(R) CFX(R) software. Here, product names (mentioned herein) may be trademarks of their respective companies. As a result, in the range from x = 5D of the near wake region to x = 10D of the far wake region, by selecting model parameter CRC, it was clarified that it is possible to accurately evaluate the time-averaged wind speed deficits at those separation distances. We also examined the effect of the spatial grid resolution using the CFD PD wake model that is proposed in the present study, clarifying that the spatial grid resolution has little effect on the simulation results shown here.

CFD simulation of helicopter rotor flow based on unsteady actuator disk model

Actuator Disks (AD) can provide characterizations of rotor wakes while reducing computational expense associated with modeling the fully resolved blades. This work presents an unsteady actuator disk method based on surface circulation distribution combined with empirical data, blade element theory and rotor momentum theory. The nonuniform circulation distribution accounts for 3D blade load effects, and in particular, tip loses. Numerical simulations were conducted for the isolated pressure sensitive paint model rotor blade in hover and forward flight using the HMB3 CFD solver of Glasgow University. Validation of CFD results in comparison with published numerical data was performed in hover, for a range of blade pitch angles using fully turbulent flow and the k-ω SST model. In forward flight, the vortex structures predicted using the unsteady actuator disk model showed configurations similar to the ones obtained using fully resolved rotor blades. Despite the reduced grid cells number, the CFD results for AD models captured well the main vortical structures around the rotor disk in comparison to the fully resolved cases.

Energy and exergy analyzing of a wind turbine in free stream and wind tunnel in CFD domain based on actuator disc technique

Abstract In this article, the effects of a wind tunnel on the MEXICO wind turbine experiment based on a generalized Actuator Disc model and the second law of thermodynamics are investigated. In this model, both Computational Fluid Dynamic (CFD) and a developed User Defined Function (UDF) code are used to simulate the wind turbine’s performance in both wind tunnel and free stream modeling. Metrological variables such as ambient pressure and temperature, velocity, and specific humidity are considered to analyze the wind turbine’s performance. The maximum relative exergy efficiency difference between the wind tunnel and free stream at the wind speed of 16 m s-1, is 7.01%. Also, pressure, temperature and relative humidity, which mainly are neglected in energy analysis, have a considerable effect on wind turbine performance in both wind tunnel and the free stream conditions. It is shown that the combination of the actuator disc and the second law of thermodynamics provides a better insight compared with the first law analysis; therefore, it provides an appropriate approach for wind power simulation.

On the potential of the ideal diffuser augmented wind turbine: an investigation by means of a momentum theory approach and of a free-wake ring-vortex actuator disk model

Diffuser-augmented wind-turbines are drawing increasing attention since they can beat the Betz-limit referred to the rotor-area. However, their diffusion is still prevented by some issues including: 1) the attainable power has not yet been shown to be larger than that of an open-turbine with the same frontal-area, 2) the classical analysis methods rely on the one-dimensional-flow and no-tip-gap assumptions whose impact has never been quantified. The paper addresses these two items investigating the potential of ideal diffuser-augmented wind-turbines using a newly-developed Axial-Momentum-Theory approach, and an extended version of a free-wake ring-vortex actuator-disk model. In comparison with similar methods, the novelty of the first approach is that it accounts for the two-dimensional effects and the tip-gap presence. Since this approach cannot evaluate the performance of a turbine for a given duct-geometry, a ring-vortex method is also developed. This is the first low-computational-cost method relying on the exact solution of the inviscid-flow through a uniformly-loaded ducted-turbine with a finite-size tip-gap. It strongly couples the flow induced by the duct and the wake which are modelled as the superposition of ring-vortices. The combined use of axial-momentum and ring-vortex methods leads to the following results. Firstly, it is clearly shown that an ideal diffuser-augmented turbine can extract more power than a Betz disk with the same frontal-area. To strengthen this statement, a new duct geometry with a remarkable value of the exit-area power-coefficient equal to 0.6098 is presented. This value is significantly higher than that of a base-line NACA5415 duct profile, i.e. 0.4800. Secondly, the impact of the one-dimensional-flow and no-tip-gap assumptions is evaluated. It is also shown that the tip-gap has negligible effects. Moreover, the one-dimensional-flow hypothesis has a low impact for high values of the rotor load, while the errors grow up decreasing the rotor thrust.

Study on interaction between the wind-turbine wake and the urban district model by large eddy simulation

Urban wind power shows a great potential and plays a significant role for a sustainable city. As a fundamental issue, the interaction between the wind-turbine wake and a building array is studied here via large eddy simulation. The standard actuator disc model is used to model the wind turbine, and 16 cube-shaped buildings are used to represent the urban district. It is found that due to the blocking effect of the downstream urban district, a high-pressure region is formed upstream, which dramatically changes the trajectory of the wind-turbine wake and results in a fast wake recovery. In addition, the wind-turbine wake suppresses the vertical momentum flux and thereby reduces the wind speed in the streamwise streets. At the top region of the urban block below the trajectory of the turbine wake, the turbulence intensity substantially increases at the entrance region of the building array, while the overall turbulence intensity is considerably reduced at the bottom of the block.

Computational investigation of multi-phase flow effects on the performance of the steam turbine exhaust hood

In this research work, a computational modeling of multi-phase flow through an asymmetric exhaust hood is presented. The three-dimensional Navier–Stokes equations along with the standard [Formula: see text] turbulent model and the Eulerian–Eulerian multi-phase equations were solved. The coupling of the last stage turbine blades and the exhaust hood has been carried out using the actuator disc model, which is less computationally demanding. The finite volume-based commercial computational fluid dynamics solver, ANSYS FLUENT, is used for the present numerical simulations. The effects of wetness on the flow structure and the pressure recovery capacity of a steam turbine exhaust hood have been investigated. One of the salient findings is that the pressure recovery capacity of a steam turbine exhaust hood enhances due to wetness effects. Wetness-induced turbulence damping is noted to be playing a crucial role in the enhancement of pressure recovery capacity of an exhaust hood.

An Alternative Numerical Model for Investigating Three- Dimensional Steam Turbine Exhaust Hood

A proper design of exhaust hood geometry is very much essential in order to improve the overall efficiency of the steam turbine plant. The geometry of the non-axisymmetric exhaust hood makes the fluid flow at the exit of the steam turbine to be radially and circumferentially non-uniform. This work involves computational simulation of steam turbine asymmetric exhaust hood flows by incorporating the actuator-disc concept. The ANSYS FLUENT, finite volume based CFD solver is used for the present computational study. In the present simulation, the implementation of actuator disc boundary conditions with and without tip leakage is described in detail. The Actuator disc model approach exhibits a similar steam turbine exhaust hood flow asymmetry and static pressure recovery compared with the results reported in the literature, highlighting the applicability of the present model in coupling the rotor tip leakage jet with the steam turbine hood flow structure with less computational effort.