Blade Element Momentum Theory 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.

Validation of a BEM correction model for swept blades using experimental data

This study validates a correction model, which extends standard blade element momentum theory to swept blades and, by doing so, enhances wind turbine simulation predictability for these advanced geometries. This correction model addresses limitations in BEM algorithms, accommodating the complexities of swept blades by considering the sweep-induced tip vortex displacement and curved bound vortex self-induction. The validation is based on previously published results from wind tunnel experiments on a horizontal axis wind turbine with straight and swept blades, providing blade-level aerodynamic data for comprehensive numerical comparisons. In both blade configurations (straight and swept), good agreement is found between experimental and numerical results, validating the numerical approach. For the swept blade case, an additional comparison to a BEM algorithm assuming a straight blade and to one accounting for crossflow is drawn, underscoring the former’s inadequacy for swept blades. Comparably minor differences between the fully-corrected and only crossflow-corrected algorithms render the assessment of the proposed BEM correction model’s added benefit uncertain. Using the validated BEM algorithm, the experimental results are corrected for twist deformations of individual blades, enabling a direct comparison of the campaigns with straight and swept blades. Results align with expectations, indicating sweep-induced reductions in axial induction and blade loads in the swept blade section.

Numerical analysis of aerodynamic performance of the Ram Air Turbine in an aircraft

A rotor design of a Ram Air Turbine (RAT) for a commercial aircraft was created taking three sections with different airfoils along the blade; those sections were assessed to evaluate their performance at different critical velocities (41, 81 and 251 m/s) and choose the best profile configuration generating a new proposal to increase the glide ratio by reducing the drag, which is helpful in emergency cases. The Blade Element Momentum (BEM) theory and Computational Fluid Dynamics (CFD) were used to analyze an initial design, then validating these results with the open software QBlade. For the BEM theory a program was created for the design and performance of the RAT adding the Viterna methodology for airfoil analysis. 16 designs were proposed by strategically interchanging wing profiles in different blade sections. These designs were analyzed by CFD, using the complete rotor and the SSTk−ω turbulence model. An optimal geometry was found, presenting a significant drag reduction of 25% generating an increase in the glide ratio and improving aircraft control in addition to maintaining the power generation above the desired values; therefore, it recommends using different airfoils for each section of a RAT's rotor blade.

Technical, Economical, and Marketing Analyses of Corotating Dual‐Rotor Wind Turbines

In this study, a comprehensive analysis is done on a dual rotor wind turbine (DRWT) in co‐rotating arrangement. First, a co‐rotating dual rotor is designed and its performance is analyzed by blade element momentum theory simulation. Later, the designed co‐rotating DRWT is manufactured and then tested in the field by mounting the wind turbine on a truck. Running the truck steadily at different speeds while logging the performance parameters of the wind turbine, the power curve of the DRWT is obtained. Then, using the power curve of the co‐rotating DRWT and the actual wind measurement data from Çatalca Istanbul, the annual electricity generation of the designed turbine is calculated. The present techno‐economic analysis states that the co‐rotating DRWTs are more efficient compared to single rotor wind turbines (SRWTs), in accordance with the literature. Analyses show that with DRWT, around 22% higher power generation can be achieved. Additionally, the payback period for DRWT was found to be less than 1 year. The marketing strategy for introducing the product emphasizes identifying and targeting early adopters and influencers within the market. The present techno‐economic analysis states that the co‐rotating DRWTs are more efficient compared to SRWTs, in accordance with the literature.

Low-Order Modeling of Stacked Rotor Performance in Hover

Coaxial, corotating (stacked) rotors have shown improved performance compared to conventional rotors, but the optimum configuration is highly sensitive to the rotor parameters. This paper reports the development of a low-order model, blade interaction prediction (BLIP), to efficiently predict the thrust and power of closely spaced rotor blades and quantify the effects of rotor geometry on total and individual stacked rotor performance. BLIP couples a vortex panel method and blade element momentum theory to combine the effects of bound circulation and rotor inflow. A cascade effect in the two-dimensional vortex panel method was implemented to incorporate the effect of airfoils rotating in a circle. Validation was performed with measurements of a 1.108-m-radius fixed-pitch stacked rotor with variable axial and azimuthal spacing, and excellent correlation was observed. It was found that small azimuthal angles and axial spacings are most effective in varying total thrust. The variation of thrust and power with azimuthal spacing was found to be a result of bound circulation, while the variation with axial spacing is due to rotor inflow interactions.

Verification of Euler–Bernoulli beam theory model for wind blade structure analysis

This paper presents a computational tool for analyzing the structural response of wind turbine blades using the advanced Euler–Bernoulli Beam theory. The objective is to achieve efficient computation of blade structural response under aerodynamic loading without sacrificing computational accuracy. This study involves the development of a Python-based computer program as a numerical tool, which utilizes inputs such as blade geometry and aerodynamic loading from Blade Element Momentum theory. The program outputs axially varying moments of inertia, spatial deflections of the blade, and stress distributions within the blade. The numerical tool is verified by comparing the results with both analytical solutions and far more time-consuming commercial finite element solvers. One of the key contribution of this research is the application of the polygon algorithm, which efficiently calculates the moments of inertia of web-stiffened turbine blades along the blade length. It is shown herein that this algorithm significantly reduces computational time while maintaining numerical accuracy as compared to the results obtained from commercially available finite element codes. The study confirms that the advanced Euler–Bernoulli beam theory, when combined with the polygon algorithm, is capable of accurately predicting the structural response of cambered and twisted wind turbine blades during the initial design phase.

A function improving tip loss correction of blade-element momentum theory for wind turbines

ABSTRACT Tip loss correction is necessary for all aerodynamic computations based on the blade-element momentum theory (BEMT) that plays an essential role in wind turbine design. Glauert tip-loss correction, which is most widely used, assumes the rotor is lightly loaded and thus lose some accuracy for modern wind turbines that are highly loaded. In the present work, a new g-function involving the rotor’s thrust-coefficient is introduced, which connects the tip loss correction with the rotor’s load condition and reduces the error of the tip loss correction. Computational tests are performed on two rotors that are distinct in size and tip shape. The new g-function results in good consistency between the computed forces and the reference data, exhibiting excellent role in improving the accuracy of the BEMT computations. In general, the new g-function combines good effectiveness and applicability, and thus has great potential for engineering applications.

Going beyond BEM with BEM: an insight into dynamic inflow effects on floating wind turbines

Abstract. Blade element momentum (BEM) theory is the backbone of many industry-standard wind turbine aerodynamic models. To be applied to a broader set of engineering problems, BEM models have been extended since their inception and now include several empirical corrections. These models have benefitted from decades of development and refinement and have been extensively used and validated, proving their adequacy in predicting aerodynamic forces of horizontal-axis wind turbine rotors in most scenarios. However, the analysis of floating offshore wind turbines (FOWTs) introduces new sets of challenges, especially if new-generation large and flexible machines are considered. In fact, due to the combined action of wind and waves and their interaction with the turbine structure and control system, these machines are subject to unsteady motion and thus unsteady inflow on the wind turbine's blades, which could put BEM models to the test. Consensus has not been reached on the accuracy limits of BEM in these conditions. This study contributes to the ongoing research on the topic by systematically comparing four different aerodynamic models, ranging from BEM to computational fluid dynamics, in an attempt to shed light on the unsteady aerodynamic phenomena that are at stake in FOWTs and whether BEM is able to model them appropriately. Simulations are performed on the UNAFLOW 1:75 scale rotor during imposed harmonic surge and pitch motion. Experimental results are available for these conditions and are used for baseline validation. The rotor is analyzed in both rated operating conditions and low wind speeds, where unsteady aerodynamic effects are expected to be more pronounced. Results show that BEM, despite its simplicity, can adequately model the aerodynamics of FOWTs in most conditions if augmented with a dynamic inflow model.

Tidal turbine blade design optimization based on coupled deep learning and blade element momentum theory

The practical design optimization of blade structures is crucial for enhancing the power capture capability of tidal turbines. However, the significant computational costs required for directly optimizing turbine blades through numerical simulations limit the practical application of blade structure optimization. This paper proposes a framework for tidal turbine blade design optimization based on deep learning (DL) and blade element momentum (BEM). This framework employs control points to parameterize the three-dimensional geometric shape of the blades, uses convolutional neural networks to predict the hydrodynamic performance of each hydrofoil section, and couples BEM to forecast the performance of tidal turbine blades. The multi-objective non-dominated sorting genetic algorithm II is employed to optimize the geometric parameters of turbine blades to maximize the power coefficient and minimize the thrust coefficient, aiming to obtain the optimal trade-off solution. The results indicate that the prediction of the DL-BEM model agrees well with experimental data, significantly improving optimization efficiency. The optimized tidal turbine blades exhibit excellent power coefficients and reduced thrust coefficients, achieving a more balanced structural solution. The proposed optimization framework based on DL accurately and rapidly predicts the performance of tidal turbines, facilitating the design optimization of high-performance tidal turbine blades.

Numerical Calculation of 1P Aerodynamic Loads on Aviation Propellers

To accurately predict the 1P aerodynamic loads of aviation propellers, this paper established a mathematical model of aviation propeller 1P aerodynamic loads based on the coupling method of blade element theory and momentum theory. Correction methods such as the Prandtl tip correction method and the propeller root correction method were implemented to further improve calculation accuracy. A 1P aerodynamic load calculation procedure was developed based on the mathematical model by using the Matlab software. 1P aerodynamic loads of a three-blade propeller were predicted for three different angles including 3 °, 9 °, and 12°. The numerical calculation results show that the calculated aerodynamic characteristic parameters of individual propeller blades obtained based on the propeller 1P aerodynamic load mathematical model deviate less than 6% from the CFD simulation results, and regular periodic pulsations are observed. The numerical calculations in this paper show that the propeller 1P aerodynamic load calculation procedure developed based on this model can accurately predict the propeller 1P aerodynamic load, which can provide some reference for the study of aviation propeller aerodynamic characteristics.

Research on the Calculation Method of Propeller 1P Loads Based on the Blade Element Momentum Theory

Aircraft propellers produce relatively large in-plane loads, called propeller 1P loads, during maneuvers such as turning, diving, and lifting, and these loads can negatively affect the flight and control of the aircraft. In order to study the change rule of 1P aerodynamic loads, in this paper, a mathematical model of the propeller 1P aerodynamic loads has been developed based on the blade element momentum theory. This mathematical model was then corrected using the Pitt–Peters incoming flow correction method, the Prandtl tip correction method, and the propeller root flow correction method. Based on this mathematical model, a calculation procedure for the propeller 1P aerodynamic loads was developed using MATLAB software, and the accuracy of the procedure was verified by comparing the results with CFD simulation results. Numerical simulations show that the results calculated based on the proposed mathematical model for the coefficients of thrust, power, bending moment, and the tangential force of the propeller have an error of less than ±6.00% compared to the CFD simulation results. For a small inflow angle, the coefficients of bending moment and tangential force of the whole propeller fluctuate in a small range. But, as the inflow angle increases, the fluctuation range of the aerodynamic characteristic parameters of the propeller increases and the fluctuation becomes more complicated. Through numerical calculations, it has been shown that the mathematical model presented herein is reliable and accurate. In addition, it greatly shortens the calculation time and improves the calculation efficiency. It is expected that the proposed model can provide a certain help for the strength design of the propeller structure and the study of the aerodynamic performance of the whole aircraft.

Deep learning enhanced fluid-structure interaction analysis for composite tidal turbine blades

A precise and cost-effective prediction tool for fluid-structure interaction (FSI) analysis is crucial for optimizing the structural design of tidal turbine blades. However, the high computational costs associated with fluid dynamic analysis pose a significant challenge, as the current lack of efficient FSI prediction methods hinders the advancement of cutting-edge tidal turbine designs. To address this issue, this paper proposes a novel consolidated framework that integrates deep learning convolutional neural networks (CNN) with blade element momentum (BEM) theory and finite element method (FEM) to perform deformation analysis of turbine blade structures. The proposed CNN-BEM-FEM integrated framework efficiently identifies the geometric features and predicts the hydrodynamic parameters of turbine blades and thus, achieving accurate assessments of the structural behavior of tidal turbines. The study applies two-step verification procedures to validate the prediction accuracy of the CNN-BEM-FEM framework and the result demonstrates excellent agreement with experimental tests for hydrodynamic performance and blade deformation. When compared with the static one-way FSI calculated by Ansys Workbench software, the computational efficiency of CNN-BEM-FEM framework increases by more than 18 times, with discrepancies in blade deformation and equivalent stress calculations generally less than 5 %. By applying the proposed method to predict the FSI performance of tidal turbine blades with various shear web structures, the practical applicability for composite turbine blade design is successfully demonstrated. The results underscore the potential of the CNN-BEM-FEM framework as an efficient and accurate prediction tool for optimizing the structural design of tidal turbine blades.

Wind Tunnel Investigation of Transient Propeller Loads for Non-Axial Inflow Conditions

Recent developments in electrical Vertical Take-off and Landing (eVTOL) vehicles show the need for a better understanding of transient aero-mechanical propeller loads for non-axial inflow conditions. The variety of vehicle configurations conceptualized with different propellers in terms of blade geometry, number of blades, and their general integration concept results in aerodynamic loads on the propellers which are different from those on conventional fixed-wing aircraft propellers or helicopter rotors. Such varying aerodynamic loads have to be considered in the vehicle design as a whole and also in the detailed design of their respective electric propulsion systems. Therefore, an experimental approach is conducted on two different propeller blade geometries and a varying number of blades with the objective to explore the characteristics at non-axial inflow conditions. Experimental data are compared with calculated results of a low-fidelity Blade Element Momentum Theory (BEMT) approach. Average thrust and side force coefficients are shown to increase with inflow angle, and this trend is captured by the implemented numerical method. Measured thrust and in-plane forces are shown to oscillate at the blade passing frequency and its harmonics, with higher amplitudes at higher angles of inflow or lower number of blades.

Effect of Turbulent Wind Conditions on the Dynamic Characteristics of a Herringbone Planetary Gear System of a Wind Turbine

Due to complex environmental factors, the gear transmission systems of wind turbines are continuously affected by large torque load excitation with periodic and random properties. This paper shares the load-sharing and dynamic characteristics of a herringbone planetary gear system applied in a wind turbine. The gear dynamic model is established using a typical lumped parameter method, in which the nonlinear transmission errors of the gear pairs and left and right-side coupling stiffness of the herringbone gears are included. With the help of the blade element momentum theory, the precise calculation of the hub load of the wind turbine, which is the external excitation of the gear system, is implemented, in which the wind shear, tower shadow, turbulent effect, and tip loss correction are taken into consideration. The nonlinear dynamic characteristics of the system are obtained using the Runge-Kutta method and then discussed. The results show that the turbulent effect plays a major role in the impact on the load-sharing characteristics, and a reasonable set of the support stiffness of rotational components can improve the load-sharing characteristics of the system. The purpose of this research is to provide some useful references in numerical modelling and methods for designers and researchers of wind turbine transmission systems.

An improved B-L model for dynamic stall prediction of rough-surface airfoils

The Beddoes-Leishman (B-L) semi-empirical model is a classical method for predicting the dynamic stall of wind turbine airfoils. However, the model performs poorly for rough-surface airfoils due to the premature entry of turbulence and stall condition under the roughness effect. In this study, an improved dynamic stall model is developed for rough-surface airfoils. Two corrections are involved in the modifications. First, the calculation of flow separation points is corrected considering the difference between the normal and tangential separation points, and then an attenuation coefficient is introduced for the effective angle of attack to account for the rough-surface effect. Subsequently, the proposed model is extensively verified by experimental data of S-series airfoils with rough surfaces. Results show that the proposed model can well predict the dynamic stall characteristics of rough-surface airfoils with a higher accuracy than that of the original B-L model under various mean angle of attacks, oscillating amplitudes and reduced frequencies. At last, the model is utilized to predict the operating loads of a wind turbine using the Blade-Element Momentum theory. Significant difference between the dynamic loads predicted by smooth and rough models is observed. This indicates that the roughness effect on the dynamic stall model as well as the prediction of the operating loads on wind turbines cannot be ignored.

A Comprehensive Investigation of Linear and Nonlinear Beam Models on Flexible Wind Turbine Blade Load Calculations

This study was performed to investigate the effects of structural nonlinearity and large deformations on the aeroelastic loads of flexible wind turbine blades. First, a blade structural analysis model was established using the geometrically exact beam (GEB) theory. Subsequently, the blade element momentum (BEM) theory was corrected using the geometrically exact method leading to the development of a geometrically exact blade element momentum (GE-BEM) model. The results from the GE-BEM model indicated that flapwise deformations always reduce blade fatigue loads, while torsional deformations decrease fatigue loads under low wind speeds but increase them under high wind speeds. Finally, the linear Euler–Bernoulli beam and the GEB were compared to explore the influence of geometric nonlinearity on the blade aeroelastic loads, which revealed that the Euler beam model underestimates the blade loads. The simulations that used the GEB model produced torsional root twist fatigue loads that were 57.49% greater than those generated when the Euler beam model was used. Furthermore, the flapwise bending moment fatigue loads at the root were 8.24% greater than those obtained by the Euler beam model. The smallest discrepancy between the results of the two models was 7.26%, and it corresponded to the edgewise fatigue load.

A hybrid numerical framework of potential and viscous flows for simulations of free running surface ship maneuvering in waves

This study presents a hybrid numerical framework for the accurate and efficient simulation of free-running surface ship maneuvering in waves. The proposed hybrid framework combines the MOUM (Modified Osaka University Method) body-force method to model the propeller and a hybrid approach of potential and viscous flows for wave-ship interactions. The MOUM body-force method, based on BEMT (Blade Element Momentum Theory), considers the three-dimensional viscous effects of propellers. The hybrid approach of potential and viscous flows decomposes the total physical field into the incident field and the complementary field, where the incident wave is solved by the potential flow theory to ensure the accuracy of wave propagation with coarse grids, and viscous and nonlinear effects are incorporated through the adapted URANS (Unsteady Reynolds Averaged Navier-Stokes) with refined grids. The 6DOF (Degrees of Freedom) motion equations of the rigid body and the dynamic structured grid with the overset technology are adopted to simulate the 6DOF motions of ship maneuvering in waves. Firstly, the applicability of the computational domain, domain-moving strategy, and ship motion-solving method for effectively simulating ship maneuvering in wave conditions are thoroughly examined. Then the reliability of present hybrid approach is validated using turning benchmark model tests of KCS model in regular waves. Simulations of turning circle and zig-zag maneuvers in regular waves are carried out by the traditional viscous CFD (Computational Fluid Dynamics) based on the boundary wave-generation approach and the proposed hybrid framework. The trajectories, motions and forces of ship maneuvering in waves predicted by both methods, as well as the computational efficiency, are compared. Numerical results indicated that the proposed method offers high accuracy and efficiency for predicting ship maneuvering in waves and could serve as a highly credible alternative to existing methods.

Rotor Performance Predictions for Urban Air Mobility: Single vs. Coaxial Rigid Rotors

This work details the development and validation of a methodology for high-resolution rotor models used in hybrid Blade Element Momentum Theory Unsteady Reynolds Averaged Navier–Stokes (BEMT-URANS) CFD. The methodology is shown to accurately predict single and coaxial rotor performance in a fraction of the time required by conventional CFD methods. The methodology has three key features: (1) a high-resolution BEMT rotor model enabling large reductions in grid size, (2) a discretized set of momentum sources to interface between the BEMT rotor model and the structured URANS flow solver, and (3) leveraging of the first two features to enable highly parallelized GPU-accelerated multirotor CFD simulations. The hybrid approach retains high-fidelity rotor inflow, wake propagation, and rotor–rotor interactional effects at a several orders of magnitude lower computational cost compared to conventional blade-resolved CFD while retaining high accuracy on steady rotor performance metrics. Rotor performance predictions of thrust and torque for both single and coaxial rotor configurations are compared to test the data that the authors obtained at the NASA Langley 14- by 22-ft. Subsonic Tunnel Facility. Simulations were run with both fully turbulent and free-transition airfoil performance tables to quantify the associated uncertainty. Single rotor thrust and torque were predicted on average within 4%. Coaxial thrust and power were predicted within an average of 5%. A vortex ring state (VRS) shielding phenomenon for coaxial rotor systems is also presented and discussed. The results support that this hybrid BEMT-URANS CFD methodology can be highly parallelized on GPU machines to obtain accurate rotor performance predictions across the full spectrum of possible UAM flight conditions in a fraction of the time required by conventional higher-fidelity methods. This strategy can be used to rapidly create look-up tables with hundreds to thousands of flight conditions using a three-dimensional multirotor CFD for UAM.

Quantifying the impact of modeling fidelity on different substructure concepts for floating offshore wind turbines – Part 1: Validation of the hydrodynamic module QBlade-Ocean

Abstract. To realize the projected increase in worldwide demand for floating offshore wind, numerical simulation tools must capture the relevant physics with a high level of detail while being numerically efficient. This allows engineers to have better designs based on more accurate predictions of the design driving loads, potentially enabling an economic breakthrough. The existing generation of offshore wind turbines is reaching a juncture, where traditional approaches, such as the blade element momentum theory, are becoming inadequate due to the increasing occurrence of substantial blade deflections. QBlade is a tool that includes a higher-fidelity aerodynamic model based on lifting-line theory, capable of accurately modeling such scenarios. In order to enable the simulation of offshore conditions in QBlade and to make use of this aerodynamic capability for novel offshore wind turbine designs, a hydrodynamic module called QBlade-Ocean was developed. In the present work, this module is validated and verified with two experimental campaigns and two state-of-the-art simulation frameworks on three distinct floating offshore wind turbine concepts. The results confirm the implementation work and fully verify QBlade as a tool to be applied in offshore wind turbine simulations. Moreover, a method aimed to improve the prediction of non-linear motions and loads under irregular wave excitation is analyzed in various conditions. This method results in a significant improvement in the surge and pitch degrees of freedom in irregular wave cases. Once wind loads are included, the method remains accurate in the pitch degree of freedom, while the improvements in the surge degree of freedom are reduced. A code-to-code comparison with the industry-designed Hexafloat concept highlights the coupled interactions on floating turbines that can lead to large differences in motion and load responses in otherwise identically behaving simulation frameworks.

Comparative study on dynamic responses of integrated installation process of a 5-MW and a 15-MW offshore wind turbine considering a pre-installed foundation

The integrated installation method for offshore wind turbines has the characteristics of high efficiency and low economic cost due to the small amount of construction work. However, the complexity of the entire system is exacerbated by environmental loads and mechanical couplings. Hence, it is urgent to investigate the dynamic response of OWTs during integrated installation procedures. This work compares the dynamic responses between NREL 5 MW and IEA 15 MW OWT installation systems. The hydrodynamics are calculated using the potential flow theory and the Morison equation, while the aerodynamics under wind turbine parked conditions are computed using the blade element momentum theory. Time domain simulations, considering various wind and wave conditions, are conducted via SIMA. This paper discusses the effects of wind and wave loads on the motion responses of catamaran installation vessel and spar, the relative motion at the mating point, and the sliding gripper forces, respectively. The results reveal that both the surge motions of the catamaran and the spar and the pitch motion of the spar exhibit sensitivity to wind loads. During installation, the motion response of the IEA 15 MW model is more dramatic than that of the NREL 5 MW system. Under wave-only conditions, the radial distances of the mating points for both NREL 5 MW and IEA 15 MW systems reach 1.65 m and 2.51 m, respectively. However, the influences of wind loads and wave incident angle are limited.