Blade Element Momentum Theory Research Articles

Fast CFD methodology for accurate prediction of wind turbine airfoil polars by means of Generalized k-omega turbulence model

Abstract Design and optimization of wind turbine blades still relies on 1D numerical codes such as the ones based on the Blade Element Momentum Theory (BEM). These simplified models, require accurate aerodynamics polars as input, for a wide range of Reynolds number conditions, in order to provide reliable predictions. Wind tunnel experimental measurements of lift and drag coefficients is very time consuming and expensive therefore the data available in the scientific literature are generally quite limited. Moreover, the data are often related to few limited operative conditions. On the other hand, the increase of computational power as well as the recent progresses of Computational Fluid Dynamics (CFD) in terms of accuracy and calculation speed have led to an ever wider use of CFD tools for the calculation of the airfoil polars. In this context, the authors developed a fast and accurate CFD methodology based on the use of the recently developed Generalized k-omega (GEKO) RANS turbulence model available in the Ansys Fluent solver. The new procedure to generate a suitable computational domain, the spatial discretization methods as well as Fluent solver settings and GEKO model calibration and optimization are described in detail. The methodology was validated on the basis of experimental data of the widely known S809 wind turbine airfoil, at different Reynolds numbers. Despite the use of a steady RANS turbulence modelling, the proposed CFD methodology demonstrated to accurately predict lift and drag coefficients in fully stalled conditions as well. Moreover, thanks to the automation of the entire CFD process, the methodology allowed to obtain full polars in very short times on a small HPC workstation. Thus, the results of the present work may represent an important step ahead to develop accurate databases of aerodynamic polars by means of a fast and easy but at the same time accurate approach.

A Simplified Model for Propeller Thrust in Oblique Flow

New aircraft architectures are being proposed for unmanned aerial vehicles and air taxis, which include tilt-able motor and propellers. These propulsive units operate with a propeller axis at an angle oblique to the flight direction, and thus it is important to understand and model how thrust is produced by a propeller operating under these conditions. Propellers in oblique flow have been modeled using Blade Element Momentum Theory coupled to an inflow model, and the Vortex Lattice Method. In the present work, we develop a much simpler approach that neglects the crossflow component of the incoming air velocity. An advance ratio is developed based on the parallel inflow component, and is coupled to existing propeller data collected in axial flow conditions. The proposed model is evaluated using existing experimental data collected under oblique flow conditions, and is predicts thrust to within \(5\,\%\) of experimental values for most conditions. The greatest discrepancy between the model and experiments occurs in the pure crossflow case, which is of lesser importance in the application to unmanned aerial vehicles and air taxis.

Investigation of motion response suppression characteristics in floating platforms equipped with novel spiral side plates

AbstractTo enhance the stability of floating wind turbine platforms, this study combines the structural characteristics of helical side plates and proposes the installation of serrated helical side plates on Spar wind turbine platforms. Based on potential flow theory, the present study employs blade element momentum theory and radiation‐diffraction theory. Upon establishing a dynamic data link library, wind‐wave coupling was implemented, and the dynamic response characteristics of platforms with different helical side plates were compared. The results indicate that in the frequency domain analysis, the platform with serrated helical side plates demonstrates reduced sensitivity to waves, with a particularly notable increase in added mass in the heave direction, suggesting excellent hydrodynamic performance. In the time domain analysis, improvements in the platform's surge and heave stability performances were observed, measuring 10.99% and 10.64%, respectively, in extreme conditions. Owing to the unique features of the serrated structure, the tension in the mooring chains on the wave‐facing side is reduced, thereby effectively lowering the fatigue load on the mooring chains.

A rapid aerodynamic noise prediction model for multi-rotor unmanned aircraft systems with inclusion of wake effect

In this work, the effect of wake on the rotor aerodynamics and aeroacosutics is studied based on an efficient rapid prediction model, which incorporates the induced effects of tip vortex on the blades into the blade element momentum theory. The tip vortex model is estimated using the free vortex wake method. The aerodynamic flow variables, as well as the unsteady loadings due to the radial flow and induction of tip vortices, are employed to model to equivalent sources and, therefore, noise emission, using Goldstein's acoustic analogy. The comparison between the hybrid algorithm and blade element momentum theory shows that the wake effect is not significant in the case of axial flow only. During forward flight conditions, the wake vortex correction greatly affects high frequency harmonics. In addition, a preliminary case study of a quad-rotor vehicle is also discussed, demonstrating the proposed low-fidelity computational framework is helpful for low-noise design and operation of the multi-rotor UAS vehicles.

Blade Surface Pressure Measurements in the Field and Their Usage for Aerodynamic Model Validation

ABSTRACTThis study presents results from a long‐term measurement campaign on a research wind turbine in the field. Pressure measurements are conducted at 25% blade radius over several months. Together with inflow measurements provided by a LiDAR system, they form an extensive dataset, which is used in the validation of numerical aerodynamic models. The model validation is conducted based on both ten‐minute average data as well as time‐resolved unsteady data. Initially, it is investigated how representative ten‐minute average pressure measurements are of the underlying unsteady aerodynamics. Binned ten‐minute average pressure distributions are then analysed together with their numerical counterpart, consisting of a combination of rotor and airfoil level aerodynamic/aeroelastic simulation results using average environmental and operating conditions as input. Finally, time‐resolved measurements and simulation results are compared, validating the aeroelastic tools' capability to reproduce unsteady aerodynamics.Overall, reasonable agreement is found between numerical simulations and field experiment data showcasing two aspects: Numerical tools based on blade element momentum theory and panel methods with viscous‐inviscid interaction remain relevant for simulating modern multi‐megawatt wind turbines, and long‐term pressure measurements provide invaluable means for validating such tools.

Technical Note: Analytical Estimate of Rotor Controls Required for a Propeller Wake Disturbance Rejection

During helicopter air-to-air refueling, the aircraft propeller’s jet can engage with the helicopter rotor. The impact on the helicopter rotor thrust and aerodynamic hub moments is solved analytically for the first time, based on blade element momentum theory. The collective and cyclic blade pitch controls needed for disturbance rejection are computed for a typical air-to-air refueling scenario. A propeller jet affecting the retreating side of the rotor requires much more pilot controls to retrim than an impingement on the advancing side.

Compensation Algorithm for Wind Turbine Main Shaft Loads Based on LSTM

Abstract For wind turbine development, load size is the core and critical factor. Currently, most companies employ Bladed software for load calculations, which enjoys widespread use in engineering applications due to its efficiency and ease of use. However, constrained by the limitations of blade element theory and momentum theory, there still exist discrepancies between the simulation results and actual conditions. This paper aims to combine simulation algorithms with the application of an LSTM (Long Short-Term Memory) neural network to develop a compensation algorithm for the main shaft loads of wind turbines. By doing so, it endeavors to realize real-time monitoring of the main shaft loads, thereby providing a foundation for achieving high-precision control in wind turbine systems.

Performance Estimation of Fixed-Wing UAV Propulsion Systems

The evaluation of propulsion systems used in UAVs is of paramount importance to enhance the flight endurance, increase the flight control performance, and minimize the power consumption. This evaluation, however, is typically performed experimentally after the preliminary hardware design of the UAV is completed, which tends to be expensive and time-consuming. In this paper, a comprehensive theoretical UAV propulsion system assessment is proposed to assess both static and dynamic performance characteristics via an integrated simulation model. The approach encompasses the electromechanical dynamics of both the motor and its controller. The proposed analytical model estimates the propeller and motor combination performance with the overarching goal of enhancing the overall efficiency of the aircraft propulsion system before expensive costs are incurred. The model embraces an advanced blade element momentum theory underpinned by the development of a novel mechanism to predict the propeller performance under low Reynolds number conditions. The propeller model utilizes XFOIL and various factors, including post-stall effects, 3D correction, Reynolds number fluctuations, and tip loss corrections to predict the corresponding aerodynamic loads. Computational fluid dynamics are used to corroborate the dynamic formulations followed by extensive experimental tests to validate the proposed estimation methodology.

Physics-guided federated learning as an enabler for digital twins

Digital twins bring the potential to increase the efficiency of assets, systems, and processes by building virtual replicas through real-time data and modeling. However, data are often confidential and distributed, high-fidelity models based on physical principles tend to be slow and require detailed knowledge about the asset design that may not be available, simplified models lack accuracy, and data-driven models are not interpretable and limited to their training space. We demonstrate the interplay of two enabling technologies, namely federated learning and hybrid analysis and modeling, to combine the strengths of physics-based and data-driven models on distributed data sets that are kept confidential by different stakeholders. Throughout the work, an ensemble of physics-guided neural networks is designed, optimized, and validated to infer the parameters of digital twin components. The physics-guided neural network is injected with output from a simplified physics-based model in intermediate layers for increased performance, and the injection layer is optimized through weight regularization. The model is then integrated into a simulation of the digital twin asset and validated there. It is shown that the model outperforms the simplified physics-based and the data-driven models both on component and on asset level. In the final step, the physics-guided neural network is trained using federated methods, which allows training on confidential data owned by different stakeholders without requiring the stakeholders to share their data. We show that federated hybrid models can – with the right training strategy – by design achieve results that are always identical and potentially superior to models trained on a central data set. The problem chosen for this demonstration is the prediction of airfoil lift and drag coefficients based on the airfoil shape and the angle of attack, which is a task crucial for simulating wind turbines. Using the physics-guided neural network, the estimation of the airfoil coefficients experiences a speedup of several orders of magnitude compared to the high-fidelity simulation, and integration into blade element momentum theory shows that the turbine thrust, torque, and mechanical power can be accurately calculated. The federated approach makes it possible to extend the training of the model to any number of distributed confidential data sets from both simulations and experiments to further increase the model’s accuracy.

An XAI Framework for Predicting Wind Turbine Power under Rainy Conditions Developed Using CFD Simulations

Renewable energy sources are essential to address climate change, fossil fuel depletion, and stringent environmental regulations in the subsequent decades. Horizontal-axis wind turbines (HAWTs) are particularly suited to meet this demand. However, their efficiency is affected by environmental factors because they operate in open areas. Adverse weather conditions like rain reduce their aerodynamic performance. This study investigates wind turbine power prediction under rainy conditions by integrating Blade Element Momentum (BEM) theory with explainable artificial intelligence (XAI). The S809 airfoil’s aerodynamic characteristics, used in NREL wind turbines, were analyzed using ANSYS FLUENT and symbolic regression under varying rain intensities. Simulations at a Reynolds number (Re) of 1 × 106 were performed using the Discrete Phase Model (DPM) and k–ω SST turbulence model, with liquid water content (LWC) values of 0 (dry), 10, 25, and 39 g/m3. The lift and drag coefficients were calculated at various angles of attack for all the conditions. The results indicated that rain led to reduced lift and increased drag. The innovative aspect of this research is the development of machine learning models predicting changes in the airfoil coefficients under rain with an R2 value of 0.97. The proposed XAI framework models rain effects at a lower computational time, enabling efficient wind farm performance assessment in rainy conditions compared to conventional CFD simulations. It was found that a heavy rain LWC of 39 g/m3 could reduce power output by 5.7% to 7%. These findings highlight the impact of rain on aerodynamic performance and the importance of advanced predictive models for optimizing renewable energy generation.

Evaluation of LM 43.8P blade performance at different hub height wind speeds using blade element momentum theory

Abstract An investigation was conducted on a three-bladed rotor similar to AVANTIS AV908. The rotor blade is appropriate for a Class I wind turbine generator and consists of three LM 43.8P blades. The 2.5 MW gearless wind turbine generator has a rated rotational speed of 16 rpm. An analysis of the LM 43.8P blade’s aerodynamics was carried out using the Blade Element Momentum (BEM) Theory to assess the turbine’s performance at different hub height wind speeds. The study employed three BEM models, including the original BEM concept without correction factors, the BEM Theory by DNV/Ris0, and the BEM Theory obtained from GH Bladed. The rotor radius is 45.1 m, and the blade comprises five different airfoils with a design tip speed ratio of 7.557. The axial and tangential induction factors, lift and drag coefficients, aerodynamic forces, and torque profiles as a function of the nondimensional rotor blade were calculated and compared with the numerical solutions obtained from the BEM models at varying upstream wind speeds. The calculation results revealed that with the original BEM concept, the axial induction factor for this particular blade became larger than 0.5 when the upstream wind speed was less than 7.45 m/s. This suggests that the Momentum Theory becomes invalid for lower wind speeds. However, the thrust force, driving force, and torque may be considerably over-predicted with hub height wind speeds larger than 9.50 m/s. It was found that out of the three models considered, the GH Bladed BEM model bears a striking resemblance with the actual power curve of AV908 with a confidence level above 95%, as indicated by a correlation coefficient of 0.99915 and a t-value of 0.51606 using Student’s t-test, implying that the two power curves have no significant difference.

A method for fast and accurate prediction of wind turbine thrust coefficients using classical momentum theory and power curve

Abstract The planning and development of windfarms require accurate prediction of the thrust coefficient (cT ) of wind turbines, which significantly affects the downstream wake. Traditional methods, such as blade element momentum theory (BEMT), often necessitate detailed geometric information of wind turbines for cT computation, information that is not frequently available, especially in the early stages of windfarm planning. This paper aims to address this challenge by presenting a novel and efficient approach to predict cT for horizontal-axis wind turbines (HAWTs). The proposed method integrates classical momentum theory with power curve data to estimate the average axial induction factor (a), thereby enabling the calculation of cT without requiring detailed geometric information of HAWTs. The method was validated against thirty-five existing pitch-controlled HAWTs, with R2 values ranging from 0.9604 to 0.9989. This validation confirms the accuracy of the method, making it a viable alternative to traditional techniques that demand comprehensive wind turbine geometric details. The method has demonstrated both rapidity and precision in cT computation for turbine wake analysis, ensuring high levels of prediction accuracy and potentially lowering the barrier to entry for windfarm development. Unlike existing models predominantly focused on wind turbine power curves, cT modelling has largely been overlooked. This study makes a unique contribution to the field by proposing a novel method for cT prediction, thereby filling a critical gap in windfarm planning and development. However, while the study shows promising results, further research is warranted to explore its applicability in diverse windfarm scenarios and turbine configurations.

Helicopter rotor in a propeller slipstream: Aerodynamic and rotor blade flapping responses

During helicopter air-to-air refueling the helicopter's rotor can engage the tanker aircraft's wing and flap end tip vortices and the slipstream of its propellers. The tip vortices represent a swirl around an axis that is essentially parallel to the rotor longitudinal axis. The slipstream of the propellers includes a strong air jet downstream that can cover a significant amount of the helicopter's main rotor. This phenomenon was recently treated analytically for a rigid rotor by means of blade-element momentum theory and the rotor control angles required to reject the disturbance were computed. In this article, the rotor blade flapping is introduced as degree of freedom. It is shown that the rotor coning is affected by the slipstream position with respect to the rotor hub. Without retrim, the largest amount of coning and cyclic flapping occurs for slipstream positions on the retreating side of the rotor.

Use of Dampers to Improve the Overspeed Control System with Movable Arms for Butterfly Wind Turbines

To reduce the cost of small wind turbines, a prototype of a butterfly wind turbine (6.92 m in diameter), a small vertical-axis type, was developed with many parts made of extruded aluminum suitable for mass production. An overspeed control system with movable arms that operated using centrifugal and aerodynamic forces was installed for further cost reduction. Introducing this mechanism eliminates the need for large active brakes and expands the operating wind speed range of the wind turbine. However, although the mechanism involving the use of only bearings is simple, the violent movement of the movable arms can be a challenge. To address this in the present study, dampers were introduced on the movable arm rotation axes to improve the movement of the movable arms. To predict the behavior of a movable arm and the performance of the wind turbine with the mechanism, a simulation method was developed based on the blade element momentum theory and the equation of motion of the movable arm system. A comparison of experiments and predictions with and without dampers demonstrated qualitative agreement. In the case with dampers, measurements confirmed the predicted increase in the rotor rotational speed when the shorter ailerons installed perpendicularly to the movable arms were used to achieve the inclination. Field experiments of the generated power at a wind speed of 6 m/s (10 min average) showed relative performance improvements of 11.4% by installing dampers, 91.3% by shortening the aileron length, and 57.6% by changing the control target data. The movable arm system with dampers is expected to be a useful device for vertical-axis wind turbines that are difficult to control.

Aerodynamic Characterization of the IEA 15 MW Reference Wind Turbine by Code-to-Code Comparison

The consistency of different aerodynamic formulations applied to the analysis of a modern multi-megawatt horizontal axis wind turbine rotor is investigated. The proposed code-to-code comparison involves specific implementations of a hierarchy of solvers based on Blade Element Momentum Theory (AEOLIAN), Actuator Line Modelling (OpenFOAM), free-wake Panel Method (FUNAERO) and blade-resolved Computational Fluid Dynamics (OpenFOAM ). The analysis addresses local and integral aeroloads and flow physical quantities concerning the state-of-the-art IEA 15 MW reference wind turbine in axial uniform flow conditions. The proposed solvers predict consistent rotor performance and blade aeroloads (also in line with data from of IEA Task 47). However, differences emerge close to blade root, where blade-resolved CFD reveals a significant flow separation on the suction side. Furthermore, scattering of induction factors computations is observed, especially in the axial direction. Different methodologies and numerical setup used in blade-resolved simulations allow achieving physically-consistent induction values, especially at blade tip. Finally, flow-field predictions by Computational Fluid Dynamics (CFD) and Panel Method are consistent upstream and close to the disk downstream (except where significant flow separation occurs), whilst a more detailed study on the effect of extending wake refinement zone in CFD simulation is advisable.

Effect of Induction and Blade Elasticity Modelling on Wind Turbine Rotor Performance Predictions

This study investigates the impact of blade induction modelling on the accuracy of wind turbine rotor aeroelastic predictions. It extends the capabilities of AEOLIAN (AErOeLastic sImulAtioN), a Fluid Structure Interaction (FSI) solver based on Blade Element Momentum Theory (BEMT) coupled with a Lumped Mass approach to represent the blade structure. Herein, AEOLIAN’s analytical wake induction engineering model is replaced with the outcomes of a physically-consistent three-dimensional Free-Vortex Wake (FVW) formulation initially employed in AeroROTOR. This versatile aeroelastic simulation tool is implemented within the framework of MATLAB Simulink/Simscape-Multibody©, a modular environment suitable for industry analysts, researchers, and academic users focusing on wind turbine aero-servo-elastic applications. Furthermore, it serves to lay the groundwork for the development of advanced control laws for multi-megawatt rotors, fostering innovation in the design and optimization of the next-generation wind turbines. The presented analyses focus on predicting the aeroelastic behavior of the bottom-fixed NREL 5MW rotor in uniform axial flow over the operating range, complemented by more detailed investigations at the rated condition undergoing inflow with/without wind misalignment (yaw). The study on key performance parameters is conducted by comparing with the higher-fidelity data from available Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) coupled with CFD.

Determination of annual energy production loss due to erosion on wind turbine blades

Increasing size of the modern wind turbines amplifies the issues of leading-edge erosion, especially on the outboard sections of the blades, impacting both their structural integrity and aerodynamic efficiency. Predicting and detection of the aerodynamic losses which occurs before a noticeable structural degradation on the blade can be crucial for operational predictive maintenance strategies to avoid significant loss production. This paper presents the results from the collaborative study between DTU and CENER in order to investigate the influence of leading-edge erosion on wind turbine aerodynamic performance. For this purpose, three distinct erosion scenarios are analyzed by means of computational fluid dynamics (CFD), both 2D and 3D, blade-element momentum theory (BEM) based solver (OpenFAST) and a Simplified Aerodynamic Loss Tool (SALT). The results from previous studies are used as an input for these tools, with outputs from each tool complementing and reinforcing one another. Furthermore, annual energy production (AEP) reductions due to leading-edge erosion across these tools are compared and validation of the SALT tool is presented. It is observed that the thrust and power losses from both CFD and OpenFAST exhibit comparable results and for a severe erosion case, spanning the last third of the blade, results in a 4.3 % reduction in the annual energy production.

On the role of induced power in turbine wake scaling: bridging 100-m to 0.1-m rotors

A wake scaling methodology is proposed in which turbine power is separated into its induced and profile power components. It is shown that preserving induced power as a function of thrust coefficient in conjunction with the radial circulation distribution are sufficient conditions for wake scaling. This work demonstrates the primary role of induced power in scaling turbine wakes over three orders of magnitude from full-scale down to model-scale rotors. The extended theory is verified using blade-element momentum theory (BEMT) and large-eddy simulation (LES), and an example set of model-scale turbine wake experiments is proposed for known wind tunnel facilities around the world.

Validating low- and high-fidelity simulations of a yawed 8 MW wind turbine against measurements

This paper presents a comparison study of the aerodynamic behavior of an 8 MW wind turbine operating under yawed conditions using field measurements, Blade Element Momentum (BEM) theory and Computational Fluid Dynamics (CFD). Turbulent inflow wind field measurements are used to generate an IEC-compliant turbulence box upstream of the wind turbine that is used within the BEM tool MoWiT and the CFD tool chain by IWES in OpenFOAM. Both simulation approaches take into account blade flexibility using modal reduced, anisotropic beam elements in BEM and Geometrically Exact Beam Therory (GEBT) in CFD. While the focus is being set towards the CFD approach, turbine power output, blade root bending moments and blade tip deflections are analyzed. It is shown that both modeling approaches react differently towards the generated wind field.

Development of a numerical model for floating Vertical Axis Wind Turbines

Vertical Axis Wind Turbines (VAWTs), which are primarily used in small-scale applications, such as in remote or urban areas, could be particularly promising for floating offshore wind projects, where they offer benefits like increased stability, lower maintenance costs, and the potential for closer spacing due to lesser aerodynamic wake effects. However, to be competitive with floating HAWTs, scaling up VAWTs size is an urgent necessity to facilitate large-scale industrialization. To achieve this goal, the development of tools capable of assessing VAWT performance in challenging offshore environments is crucial. This work aims to introduce a time domain model of a floating VAWT, developed within the Matlab-Simscape environment. The model comprises a floating platform, a wind turbine, and a mooring system. The aerodynamics is simulated using the Double Multiple Stream Tube method, which relies on Blade Element Momentum (BEM) theory. Hydrodynamics is modelled using WEC-Sim, a Simscape library developed by NREL and SANDIA. Among the main advantages of the model are the flexibility and low computational time. The article presents a case study involving a semi-sub foundation, the OC4-DeepCwind, supporting a Darrieus H-rotor VAWT. The results obtained are compared with those from QBlade Ocean, an open-source tool developed by TU Berlin, demonstrating a good agreement between the two codes.