Classical Blade Element Momentum Research Articles

Towards vortex-based wind turbine design using GPUs and wake accommodation

Vortex methods are often cited as a promising alternative to the classical Blade Element Momentum (BEM) theory for wind turbine design, overcoming some of its limitations such as imposing steady-state, uniform, and aligned inflows. BEM assumptions are being questioned, especially for large rotors with very flexible blades or even floating wind turbines. However, vortex methods are not yet widespread due to their computational costs. The following work demonstrates how free vortex wake methods using filament discretizations can become an affordable and viable alternative to BEM. This is achieved by combining filament number reduction as well as graphical processing units (GPUs) computations. The efficiency and accuracy of the proposed approaches are demonstrated against simple test cases, including an elliptical wing and a rigid horizontal axis wind turbine (HAWT). Finally, the approaches are applied to the aero-hydro-servo-elastic simulation of floating horizontal axis wind turbines.

Development of a modified BEMT model for the analysis of helical bladed vertical axis tidal turbines

Development of a modified BEMT model for the analysis of helical bladed vertical axis tidal turbines 
 Mohammad Fereidoonnezhad1, Seán Leen1, Stephen Nash1, Tomas Flanagan2, Patrick McGarry1
 1 School of Engineering, University of Galway, Galway, Ireland
 2 ÉireComposites Teo., Údarás Industrial Estate An Choill Rua, Inverin, Galway, Ireland
 E-mail: patrick.mcgarry@universityofgalway.ie 
 
 Keywords: Blade element momentum theory, Helical vertical axis tidal turbine, FEA Analysis
 Classical blade element momentum theory (BEMT) formulations are not capable of accurately simulating complex blade geometries, such as spiral or helical blade geometries. In this paper, we develop a modified BEMT model to calculate hydrodynamic forces acting on the helical vertical axis tidal turbines. Our framework accounts for curved blade geometries where the leading edge is not orthogonal to the freestream velocity, and chord vectors are not in the azimuthal-radial plane. We validate the model using experimental data for a prototype VAWT. We then perform a parametric analysis of helical bladed VATT designs. Both the helix angle of the blade and the relative orientation of the chord strongly influence the power output of a turbine. Our modified BEMT model also predicts that an increase in blade helix angle results in reduced power fluctuations. Additionally, computed fluctuations in tangential and normal forces acting on blades are shown to reduce significantly with increasing blade helix angle, suggesting a reduction in risk of fatigue failure. We also uncover a complex distribution of normal and tangential forces along the length of a helical blade. Fluctuating hydrodynamic forces computed by our modified BEMT model are input into a finite element (FE) framework to compute the stress state in a fibre reinforced composite blade material for a range of blade azimuthal positions. Analyses reveal that blade deflections are three orders of magnitude lower than the turbine radius, suggesting that sufficient structural stiffness is achieved by the blade design. Results also uncover stress concentrations in the region of strut-blade connection, revealing a higher risk of fracture and fatigue failure at this location.

A BEM theory adaption for inclusion of hub ratio effects in HAWT rotor design and analysis

A large hub ratio in a horizontal axis wind turbine (HAWT) rotor can provide aerodynamic and structural design benefits, but the flow effects are not accounted for in the classical Blade Element Momentum Method (BEMM). Research into the effect of HAWT rotor hub ratio, necessitated development of an adaption to the BEMM, so that rotors with large hub ratios, could be designed to be aerodynamically efficient, and so that the flow effects could be included in performance prediction. Results from the BEMM with large-hub adaption were compared with results from using the classical BEMM and with results from CFD simulation. Two sets of rotors were analysed, one set in a viscous flow regime and the other in a turbulent flow regime. The BEMM with large-hub adaption, was found to provide rotor designs with better performance and provided a more accurate prediction of relative rotor power than the classical BEMM.

Development of blade element momentum (BEM) method for hydropower

The BEM method is extensively used for analyzing the aerodynamic performance of wind turbines and marine propellers. It is computationally fast and is easily implemented while it can give fairly accurate results. Application of the BEM method to predict the forces acting on rotor blades for a model scale axial shaft-driven Counter-Rotating Pump-Turbine (CRPT) is investigated. Some modifications have been proposed to adopt the classical BEM method for CRPT machine and the results are validated against results from Computational Fluid Dynamics (CFD). The results display that the proposed modifications can improve the loading predicted by BEM. However, the improvements are more pronounced in pump mode rather than turbine mode.

A method for preliminary rotor design – Part 1: Radially Independent Actuator Disc model

Abstract. We present an analytical model for assessing the aerodynamic performance of a wind turbine rotor through a different parametrization of the classical blade element momentum (BEM) model. The model is named the Radially Independent Actuator Disc (RIAD) model, and it establishes an analytical relationship between the local thrust loading and the local power, known as the local-thrust coefficient and the local-power coefficient respectively. The model has a direct physical interpretation, showing the contribution for each of the three losses: wake rotation loss, tip loss and viscous loss. The gradient for RIAD is found through the use of the complex step method, and power optimization is used to show how easily the method can be used for rotor optimization. The main benefit of RIAD is the ease with which it can be applied for rotor optimization and especially load constraint power optimization as described in Loenbaek et al. (2021). The relationship between the RIAD input and the rotor chord and twist is established, and it is validated against a BEM solver.

A Computational Fluid Dynamics Investigation on the Axial Induction Factor of a Small Horizontal Axis Wind Turbine

Abstract The evolution of wind and hydrokinetic turbines stimulated the development of several tools to evaluate and to predict horizontal axis rotor behavior. From this perspective, the blade element momentum methods stand out as one of the most common approaches due to its reliability and computing speed. In the classical blade element momentum, the axial induction factor is a crucial variable to compute correctly the turbine parameters. Usually, the axial induction is determined by an interactive process that balances the forces at blade sections with momentum equations. The forces are computed based on the airfoil polars evaluated at each blade section with local inlet velocity. This procedure assumes that the swirl terms are linearized, where the lateral pressure forces is neglected. In order to evaluate these tri-dimensional effects on the blade element momentum method, the present work introduces a different methodology to determine the axial induction factor employing computational fluid dynamics simulations. The method was applied for a full-scale horizontal axis rotor with three blades and 1 m of diameter, with wind tunnel experiments for validation. The axial induction factor obtained with the new technique was compared to the classical blade element momentum method. The results show axial induction factor variations along the radial and axial coordinates. An analogy with Glauert power coefficient limit was made, finding a specific limit curve for the tested turbine, and, moreover, a correlation between turbine firing speed and induction factor.

Implementation of the blade element momentum model on a polar grid and its aeroelastic load impact

Abstract. We show that the upscaling of wind turbines from rotor diameters of 15–20 m to presently large rotors of 150–200 m has changed the requirements for the aerodynamic blade element momentum (BEM) models in the aeroelastic codes. This is because the typical scales in the inflow turbulence are now comparable with the rotor diameter of the large turbines. Therefore, the spectrum of the incoming turbulence relative to the rotating blade has increased energy content on 1P, 2P, …, nP, and the annular mean induction approach in a classical BEM implementation might no longer be a good approximation for large rotors. We present a complete BEM implementation on a polar grid that models the induction response to the considerable 1P, 2P, …, nP inflow variations, including models for yawed inflow, dynamic inflow and radial induction. At each time step, in an aeroelastic simulation, the induction derived from a local BEM approach is updated at all the stationary grid points covering the swept area so the model can be characterized as an engineering actuator disk (AD) solution. The induction at each grid point varies slowly in time due to the dynamic inflow filter but the rotating blade now samples the induction field; as a result, the induction seen from the blade is highly unsteady and has a spectrum with distinct 1P, 2P, …, nP peaks. The load impact mechanism from this unsteady induction is analyzed and it is found that the load impact strongly depends on the turbine design and operating conditions. For operation at low to medium thrust coefficients (conventional turbines at above rated wind speed or low induction turbines in the whole operating range), it is found that the grid BEM gives typically 8 %–10 % lower 1 Hz blade root flapwise fatigue loads than the classical annular mean BEM approach. At high thrust coefficients that can occur at low wind speeds, the grid BEM can give slightly increased fatigue loads. In the paper, the implementation of the grid-based BEM is described in detail, and finally several validation cases are presented. Comparisons with blade loads from full rotor CFD, wind tunnel experiments and a field experiment show that the model can predict the aerodynamic forces in half-wake, yawed flow, dynamic inflow and turbulent inflow conditions.

Large Eddy Simulation of an Onshore Wind Farm with the Actuator Line Model Including Wind Turbine’s Control below and above Rated Wind Speed

As the size of wind turbines increases and their hub heights become higher, which partially explains the vertiginous increase of wind power worldwide in the last decade, the interaction of wind turbines with the atmospheric boundary layer (ABL) and between each other is becoming more complex. There are different approaches to model and compute the aerodynamic loads, and hence the power production, on wind turbines subject to ABL inflow conditions ranging from the classical Blade Element Momentum (BEM) method to Computational Fluid Dynamic (CFD) approaches. Also, modern multi-MW wind turbines have a torque controller and a collective pitch controller to manage power output, particularly in maximizing power production or when it is required to down-regulate their production. In this work the results of a validated numerical method, based on a Large Eddy Simulation-Actuator Line Model framework, was applied to simulate a real 7.7 MNW onshore wind farm on Uruguay under different wind conditions, and hence operational situations are shown with the aim to assess the capability of this approach to model actual wind farm dynamics. A description of the implementation of these controllers in the CFD solver Caffa3d, presenting the methodology applied to obtain the controller parameters, is included. For validation, the simulation results were compared with 1 Hz data obtained from the Supervisory Control and Data Acquisition System of the wind farm, focusing on the temporal evolution of the following variables: Wind velocity, rotor angular speed, pitch angle, and electric power. In addition to this, simulations applying active power control at the wind turbine level are presented under different de-rate signals, both constant and time-varying, and were subject to different wind speed profiles and wind directions where there was interaction between wind turbines and their wakes.

Tuning turbine rotor design for very large wind farms

A new theoretical method is presented for future multi-scale aerodynamic optimization of very large wind farms. The new method combines a recent two-scale coupled momentum analysis of ideal wind turbine arrays with the classical blade-element-momentum (BEM) theory for turbine rotor design, making it possible to explore some potentially important relationships between the design of rotors and their performance in a very large wind farm. The details of the original two-scale momentum model are described first, followed by the new coupling procedure with the classical BEM theory and some example solutions. The example solutions, obtained using a simplified but still realistic NREL S809 aerofoil performance curve, illustrate how the aerodynamically optimal rotor design may change depending on the farm density. It is also shown that the peak power of the rotors designed optimally for a given farm (i.e. ‘tuned' rotors) could be noticeably higher than that of the rotors designed for a different farm (i.e. ‘untuned' rotors) even if the blade pitch angle is allowed to be adjusted optimally during the operation. The results presented are for ideal very large wind farms and a possible future extension of the present work for real large wind farms is also discussed briefly.

Prediction of Aerodynamic Loads for NREL Phase VI Wind Turbine Blade in Yawed Condition

Aerodynamic loads for a horizontal axis wind turbine of the National Renewable Energy Laboratory (NREL) Phase VI rotor in yawed condition were predicted by using the blade element momentum theorem. The classical blade element momentum theorem was complemented by several aerodynamic corrections and models including the Pitt and Peters' yaw correction, Buhl's wake correction, Prandtl's tip loss model, Du and Selig's three-dimensional (3-D) stall delay model, etc. Changes of the aerodynamic loads according to the azimuth angle acting on the span-wise location of the NREL Phase VI blade were compared with the experimental data with various yaw angles and inflow speeds. The computational flow chart for the classical blade element momentum theorem was adequately modified to accurately calculate the combined functions of additional corrections and models stated above. A successive under-relaxation technique was developed and applied to prevent possible failure during the iteration process. Changes of the angle of attack according to the azimuth angle at the specified radial location of the blade were also obtained. The proposed numerical procedure was verified, and the predicted data of aerodynamic loads for the NREL Phase VI rotor bears an extremely close resemblance to those of the experimental data.

Stochastic Model for Aerodynamic Force Dynamics on Wind Turbine Blades in Unsteady Wind Inflow

The paper presents a stochastic approach to estimate the aerodynamic forces with local dynamics on wind turbine blades in unsteady wind inflow. This is done by integrating a stochastic model of lift and drag dynamics for an airfoil into the aerodynamic simulation software AeroDyn. The model is added as an alternative to the static table lookup approach in blade element momentum (BEM) wake model used by AeroDyn. The stochastic forces are obtained for a rotor blade element using full field turbulence simulated wind data input and compared with the classical BEM and dynamic stall models for identical conditions. The comparison shows that the stochastic model generates additional extended dynamic response in terms of local force fluctuations. Further, the comparison of statistics between the classical BEM, dynamic stall, and stochastic models' results in terms of their increment probability density functions (PDFs) gives consistent results.

Assessment of low-order theories for analysis and design of shrouded wind turbines using CFD

The use of a shroud around the rotor of a wind turbine has been known to augment the airflow through the rotor plane and hence result in improved performance. This work uses Computational Fluid Dynamics (CFD) to assess the validity of several simple theories which attempt to extend Betz theory to shrouded turbines. Two CFD models are employed and compared to predictions of previously published models. The first makes use of a fixed pressure-drop actuator disk, while the second incorporates the twist and chord distribution of the turbine blade as well as an airfoil polar using a technique much like the classical blade element momentum (BEM) method. Calculations are performed for a sweep of turbine loadings using the fixed pressure-drop model and a sweep of tip speed ratios using the BEM model for both an open and shrouded turbine. Power is computed using a control volume approach for the fixed pressure-drop model and by integrating tangential forces for the BEM model. Information including mass flow ratio, power coefficient ratio, axial induction, and shroud force is extracted from the solution fields and compared against the predictions of low-order theories. Finally, the blade element model is used to redesign the turbine twist distribution to achieve greater performance across a range of tip speed ratios.

Relevance of aerodynamic modelling for load reduction control strategies of two-bladed wind turbines

A new load reduction concept is being developed for the two-bladed prototype of the Skywind 3.5MW wind turbine. Due to transport and installation advantages both offshore and in complex terrain two-bladed turbine designs are potentially more cost-effective than comparable three-bladed configurations. A disadvantage of two-bladed wind turbines is the increased fatigue loading, which is a result of asymmetrically distributed rotor forces. The innovative load reduction concept of the Skywind prototype consists of a combination of cyclic pitch control and tumbling rotor kinematics to mitigate periodic structural loading. Aerodynamic design tools must be able to model correctly the advanced dynamics of the rotor. In this paper the impact of the aerodynamic modelling approach is investigated for critical operational modes of a two-bladed wind turbine. Using a lifting line free wake vortex code (FVM) the physical limitations of the classical blade element momentum theory (BEM) can be evaluated. During regular operation vertical shear and yawed inflow are the main contributors to periodic blade load asymmetry. It is shown that the near wake interaction of the blades under such conditions is not fully captured by the correction models of BEM approach. The differing prediction of local induction causes a high fatigue load uncertainty especially for two-bladed turbines. The implementation of both cyclic pitch control and a tumbling rotor can mitigate the fatigue loading by increasing the aerodynamic and structural damping. The influence of the time and space variant vorticity distribution in the near wake is evaluated in detail for different cyclic pitch control functions and tumble dynamics respectively. It is demonstrated that dynamic inflow as well as wake blade interaction have a significant impact on the calculated blade forces and need to be accounted for by the aerodynamic modelling approach.Aeroelastic simulations are carried out using the high fidelity multi body simulation software SIMPACK. The aerodynamic loads are calculated using ECN's AeroModule and NREL's BEM code Aerodynl3.

A coupled blade element momentum – Computational fluid dynamics model for evaluating tidal stream turbine performance

A modelling approach based on blade element momentum theory is developed for the prediction of tidal stream turbine performance in the ocean environment. Through the coupling of the blade element momentum method with computational fluid dynamics, the influence of upstream hydrodynamics on rotor performance is accounted for. Incoming flow onto the rotor can vary in speed and direction compared to free-stream conditions due to the presence of obstructions to the flow in the upstream, due to other devices for example, or due to the complexity of natural bathymetries. The relative simplicity of the model leads to short run times and a lower demand on computational resources making it a useful tool for considering more complex engineering problems consisting of multiple tidal stream turbines. Results from the model compare well against both measured data from flume experiments and results obtained using the classical blade element momentum model. A discussion considering the advantages and disadvantages of these different approaches is included.

Scaled ice accretion experiments on a rotating wind turbine blade

This work presents ice accretion tests of a model wind turbine blade mounted on a rotor test stand. The model test blade was scaled to reproduce local flow and icing conditions at the 95% radial station of the NREL Phase VI Rotor. A modified Ruff scaling method was implemented to scale atmospheric icing conditions that could be generated in a laboratory facility. Scaling laws allowed for reduced testing time as well as a reduced chord length of the blades compared to on-site icing events were implemented. Classical Blade Element Momentum Theory (BEMT) was utilized to correlate inflow conditions at the test facility to actual operating conditions of the NREL Phase VI Rotor. Experimentally obtained rime ice shapes are compared to LEWICE predictions and are used to validate the capability of the facility to reproduce representative icing conditions. The rime ice results matched with predictions to within 1% of both ice thickness and ice extent along the blade surfaces. The effects of angle-of-attack, temperature, liquid water content, and icing time on the final ice shapes were investigated in a parametric study. Experimentally obtained glaze ice shapes are used to demonstrate the severity of the icing events on wind turbine torque. The present work comprises testing procedures and experimental data that can be used for future efforts in ice accretion modeling and testing.

Reliability analysis for hydrokinetic turbine blades

Reliability is an important element in the performance of hydrokinetic turbines. It is also a driving factor of the system lifetime cost. In this paper, we perform time-dependent reliability analysis for the blades of a river-based horizontal-axis hydrokinetic turbine. Based on the stochastic representation of the monthly river velocity and material strength, a limit-state function is established with the classical blade element momentum method. In the limit-state function, a failure is defined as the event when the flapwise bending moment exceeds the allowable moment that corresponds to the ultimate strength of the material. The upcrossing rate method is employed to calculate the time-dependent reliability of the hydrokinetic turbine blade over its design life period. The results indicate that setting a proper cut-out river velocity is important for the reliability of the hydrokinetic turbine blade.