Axial Induction Research Articles

Brief communication: A simple axial induction modification to the Weather Research and Forecasting Fitch wind farm parameterization

Abstract. We propose a modification to the Fitch wind farm parameterization implemented in the Weather Research and Forecasting (WRF) model. This modification, derived from 1D momentum theory, employs a wind-speed-dependent induction factor to correct the local grid wind speed back to freestream before computing the turbine's power and thrust. While the original implementation underestimates power, the modified version shows good agreement with the power curve. We strongly recommend employing the modification for all studies that model at maximum one turbine per WRF grid cell. For simulations with more turbines per grid cell, additional inner-cell wake losses have to be considered.

Structural Optimization of a Giant Magnetostrictive Actuator Based on BP-NSGA-II Algorithm

This study introduces an integrated structural optimization design method based on a BP neural network and NSGA-II multi-objective genetic algorithm. Initially, a two-dimensional axisymmetric finite element model of the Giant Magnetostrictive Actuator (GMA) was established, and the coupling simulation of the electromagnetic field, structural field, and temperature field was conducted to obtain the GMA’s performance parameters. Subsequently, the structural parameters of the GMA magnetic circuit, including the magnetic conducting ring, magnetic conducting sidewall, magnetic conducting body, and coil, were used as inputs, and the axial magnetic induction intensity, uniformity of axial magnetic induction intensity, and coil loss on the Giant Magnetostrictive Material (GMM) rod were used as outputs to establish a back propagation (BP) neural network model. This model delineated the nonlinear relationship between structural parameters and performance parameters. Then, the BP-NSGA-II algorithm was applied to perform multi-objective optimization on the actuator’s structural parameters, resulting in a set of Pareto optimal non-dominated solutions, from which a set of optimal solutions was obtained using the entropy weight method. Finally, simulation analysis of this optimal solution was conducted, indicating that under a 5 A power supply excitation, the maximum axial magnetic induction intensity on the optimized GMM rod increased from 0.87 T to 1.12 T; the uniformity of axial magnetic induction intensity improved from 93.1% to 96.5%; and the coil loss decreased from 7.79 × 104 W/m3 to 4.97 × 104 W/m3. Based on the optimization results, a prototype actuator was produced, and the test results of the prototype’s output characteristics proved the feasibility of this optimization design method.

On Axial Current Induction and Stability of a Pinch

On Axial Current Induction and Stability of a Pinch

A CFD Study on High‐Thrust Corrections for Blade Element Momentum Models

ABSTRACTThis paper presents a reanalysis of four axial‐flow rotor simulation datasets to study the relationship between thrust and axial induction factor. We concentrate on high‐thrust conditions and study variations in induction factor and loads across the span of the different rotor blades. The datasets consist of three different axial‐flow rotors operating at different tip‐speed ratios and, for one dataset, also at different blockage ratios. The reanalysis shows differences between the blade‐resolved CFD results and a widespread empirical turbulent wake model (TWM) used within blade element momentum (BEM) turbine models. These differences result in BEM models underestimating thrust and especially power for axial‐flow rotors operating in high‐thrust regimes. The accuracy of BEM model predictions are improved substantially by correcting this empirical TWM, producing better agreement with blade‐resolved CFD simulations for thrust and torque across most of the span of the blades of the three rotors. Additionally, the paper highlights deficiencies in tiploss modelling in common BEM implementations and highlights the impact of blockage on the relationship between thrust and axial induction factors.

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.

Comprehensive Analysis of Factors Underpinning the Superior Performance of Ducted Horizontal-Axis Helical Wind Turbines

The societal and economic reliance on non-renewable energy sources, primarily fossil fuels, has raised concerns about an imminent energy crisis and climate change. The transition towards renewable energy sources faces challenges, notably in understanding turbine shear forces within wind technology. To address this gap, a novel solution emerges in the form of the ducted horizontal-axis helical wind turbine. This innovative design aims to improve airflow dynamics and mitigate adverse forces. Computational fluid dynamics and experimental assessments were employed to evaluate its performance. The results indicate a promising technology, showcasing the turbine’s potential to harness energy from diverse wind sources. The venturi duct aided in the augmentation of the velocity, thereby increasing the maximum energy content of the wind by 179.16%. In addition, 12.16% of the augmented energy was recovered by the turbine. Notably, the integration of a honeycomb structure demonstrated increased revolutions per minute (RPM) by rectifying the flow and reducing the circular wind, suggesting the impact of circular wind components on turbine performance. The absence of the honeycomb structure allows the turbine to encounter more turbulent wind (circular wind), which is the result of the movement of the fan. Strikingly, the downwash velocity of the turbine was observed to be equal to the incoming velocity, suggesting the absence of an axial induction factor and, consequently, no back force on the system. However, limitations persist in the transient modelling and in determining optimal performance across varying wind speeds due to experimental constraints. Despite these challenges, this turbine marks a significant stride in wind technology, highlighting its adaptability and potential for heightened efficiency, particularly at higher speeds. Further refinement and exploration are imperative for broadening the turbine’s application in renewable energy generation. This research emphasizes the turbine’s capacity to adapt to different wind velocities, signaling a promising avenue for more efficient and sustainable energy production.

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.

Model predictive control of wakes for wind farm power tracking

In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows the tracking of a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows the estimation of the rotor effective wind speeds at downstream turbines, based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

Improvements to the Blade Element Momentum Formulation of OpenFAST for Skewed Inflows

In this work, we modify the blade element momentum algorithm of OpenFAST to improve its predictions under large skewed inflow conditions. We use the well-known Glauert’s skew correction and introduce continuous extension of the model for high-thrust conditions. We present the rationale behind Glauert’s empirical model and discuss the different conventions possible for the axial induction factor. We verify the model against the higher-fidelity lifting-line vortex method and blade-resolved computational fluid dynamics, and we observe that the new implementation enhances the accuracy and reliability of OpenFAST’s aerodynamic modeling capabilities in conditions involving large skew angles. For the parametric studies run using the different codes, we find that the power changes with the skew angle as cos1.7(θ skew) and the thrust as cos0.65(θ skew). An analysis of the azimuthal variation of the induced velocities in the rotor plane reveals that current redistribution models used in blade element momentum codes may need to be refined.

How do wind farm blockage and axial induction control interact?

Wake losses significantly reduce wind farm output, but wind farm flow control (WFFC) can substantially reduce these losses, using wake steering (yawing upstream turbines) and/or axial induction control (reducing turbine power and thrust to weaken their wakes). Previous work shows that ignoring wind farm blockage in traditional wake models represents a prediction bias of similar order to the gains achievable with WFFC. Axial induction control works by changing turbine thrust, which is also the cause of blockage; this raises the question of how the two effects interact. Induction control can more than compensate for any loss due to blockage, but here we investigate the relationship further. Induction control reduces turbine thrust coefficients to reduce wake losses, but this should also reduce blockage, suggesting that induction control might achieve higher gains in practice than predicted with blockage effects ignored. An engineering model for blockage effects was added to the wind farm code LongSim, and steady-state gains calculated for a well-known offshore wind farm, with and without blockage. The results confirm that the power gains are indeed higher if blockage is modelled. These results are corroborated by comparisons against RANS (Reynolds-Averaged Navier Stokes) simulations, in which blockage effects are implicitly modelled.

Enhanced Modeling of Joint Yaw and Axial Induction Control Using Blade Element Momentum Methods

Wind turbine control via concurrent yaw misalignment and axial induction control has demonstrated potential for improving wind farm power output and mitigating structural loads. However, the complex aerodynamic interplay between these two effects requires deeper investigation. This study presents a modified blade element momentum (BEM) model that matches rotor-averaged quantities to an actuator disk model of yawed rotor induction, enabling analysis of joint yaw-induction control using realistic turbine control inputs. The BEM approach reveals that common torque control strategies such as K − Ω2 exhibit sub-optimal performance under yawed conditions. Notably, the power-yaw and thrust-yaw sensitivities vary significantly depending on the chosen control strategy, contrary to common modeling assumptions. In the context of wind farm control, employing induction control which minimizes the thrust coefficient proves most effective at reducing wake strength for a given power output across all yaw angles. Results indicate that while yaw control deflects wakes effectively, induction control more directly influences wake velocity magnitude, underscoring their complementary effects. This study advances a fundamental understanding of turbine aerodynamic responses in yawed operation and sets the stage for modeling joint yaw and induction control in wind farms.

Dual Independent Rotor Axial Flux Induction Motor for Electric Vehicle Applications

This article proposes a dual independent rotor axial flux induction motor (DIR-AFIM) with two degrees of freedom as a propulsion motor for an electric vehicle (EV). The performance of this motor in different operating conditions of the vehicle is discussed and investigated. This motor has two rotors that are mechanically independent of each other, providing driving force for the EV separately and enabling the removal of any mechanical or electrical differential. The propulsion motor can play the role of differential and also reduce the cost and complexity of the entire propulsion system in some extent. The finite element modeling of the proposed motor has been performed and the performance characteristics have been evaluated in three operating scenarios: flat path, sloped path, and turning path, taking into account the dynamics of the vehicle. Additionally, the accuracy of the simulations and modeling has been confirmed by performing some practical tests on the prototype machine. The results show that the simulations and measurements are in good agreement and the proposed propulsion system can be a suitable option for lightweight electric vehicles.

Hybrid-Lambda: a low-specific-rating rotor concept for offshore wind turbines

Abstract. We introduce an aerodynamic rotor concept for an offshore wind turbine which is tailored for an increased power feed-in at low wind speeds by a substantial increase in the rotor diameter while maintaining the rated power. The main objective of the conceptual design is to limit the steady-inflow loads (blade flapwise root bending moment (RBM) and thrust) to the maximum values of a reference turbine. The outer part of the blade (i.e. outer 30 % span) is designed for a higher design tip speed ratio (TSR) and a lower axial induction than the inner part. By operating at the high TSR in light winds, the slender outer part fully contributes to the increased power capture. In stronger winds the TSR is reduced and the torque generation is shifted to the inner section of the rotor. Moreover, the blade design efficiently reduces the power losses when the flapwise RBM is limited through peak shaving, below rated wind speed. This is of high importance, given the wind speed distribution at offshore sites. The characteristics of the rotor are first investigated with stationary blade element momentum simulations and further analysed with aeroelastic simulations, considering the flexibility of blades and tower to show that a structural design is feasible even for a blade of this size and complexity. The economic revenue and the cost of valued energy of the turbine are estimated and compared to the IEA 15 MW offshore reference turbine, considering a fictitious wind-speed-dependent feed-in price. Our results for the turbine concept with an increase in rotor diameter by 36 % show that the revenue can be increased by 30 % and the cost of valued energy can be reduced by 16 % compared to the reference turbine.

An Optimal Wind Farm Operation Strategy for the Provision of Frequency Containment Reserve Incorporating Active Wake Control

This study proposes a novel operation strategy for wind farms' optimal Frequency Containment Reserve (FCR) provision that simultaneously distributes FCR and optimally controls wake formation. The power reserve allocation is dynamically decided at the wind farm supervisory control level, considering the intermittent wind power and direction, grid frequency stochasticity, and the aerodynamic complexity of the wake. A two-stage stochastic programming approach supports decision-making for an optimal contribution to day-ahead energy/FCR markets considering sub-hourly wind power and grid frequency uncertainty. Moreover, a novel method is used to reduce the computational complexity by employing a data-driven surrogate model of wake formation in the optimizer. This surrogate model consists of a neural network trained on the Gauss-Curl-Hybrid wake model in FLORIS. This deep learning approach allows fast estimation of the wake control parameters, i.e., the optimal yaw angles and axial induction factors. Then, a coevolutionary-based multi-objective particle swarm optimization searches for the optimal deloading of the WTs and maximizes the total power production and kinetic energy while minimizing wake. The performance of the proposed algorithm is evaluated on the C-Power wind farm layout in the North Sea. Simulation results demonstrate its effectiveness in improving the wind farm's overall performance for different operational conditions.

Enhancing Wind Farm Performance through Axial Induction and Tilt Control: Insights from Wind Tunnel Experiments

Static axial induction control and tilt control are two strategies that have the potential to increase power production in wind farms, mitigating wake effects and increasing the available power for downstream turbines. In this study, wind tunnel experiments are performed to evaluate the efficiency of these two techniques. First, the axial induction of upstream turbines in wind farms comprising two, three, and five turbines is modified through the tip-speed ratio. This strategy is found to be ineffective in increasing power extraction. Next, the power extraction and flow through a two-turbine wind farm are evaluated, considering different tilt angles for the upstream turbine, under two levels of incoming flow turbulence intensities and turbine spacing distances. It is shown that forward tilting increases the overall power extraction by deflecting the wake downwards and promoting the entrainment of high-speed fluid in the upper shear layer, regardless of the turbine spacing distance and turbulence intensity level. Also, the wake is seen to recover faster due to the increased shear between the wake and the outer flow. Tilting a turbine backward deflects the wake upwards and pulls low-speed flow from under the turbine into the wake space, increasing the available power for downstream turbines, but it is not enough to increase global power extraction. Moreover, since the wake deflection under backward tilting is not limited by ground blockage, it leads to larger secondary steering compared with forward tilting. Finally, it is demonstrated that the secondary steering of the downstream turbine’s wake influences the flow encountered by a turbine positioned farther downstream.

A Wind Farm Power Maximization Method Based on Multi-Strategy Improved Sparrow Search Algorithm

Abstract For large-scale constructed wind farms, reducing wake loss and improving the overall output power are the main objectives for their optimal operation. Therefore, a wind farm power maximization method based on a multi-strategy improved sparrow search algorithm (MS-ISSA) is proposed in this paper. Integrating the wake propagation mechanism of wind turbines and the characteristics of the classic Jensen wake model, the Jensen–Gaussian wake model and wake superposition model were constructed to accurately calculate the wind farm wake distribution. The constructed Jensen–Gaussian wake model and wake superposition model can accurately describe the non-uniform distribution characteristics of wake velocity. The Sin chaotic model, Cauchy distribution, and hyperparameter adaptive adjustment strategy were used to improve the sparrow search algorithm (SSA), and the optimization ability, convergence speed, and stability of the SSA were improved. Accordingly, considering the maximum output power of the wind farm as the optimization target and axial induction factor as the optimization variable, a coordinated optimization model for wind turbines based on MS-ISSA was proposed to realize the coordinated optimal operation of wind turbines with reduced wake loss. Considering the Danish Horns Rev wind farm as the research object, the results of optimization using particle swarm optimization algorithm, whale optimization algorithm, basic sparrow search algorithm, and MS-ISSA were calculated and analyzed. The calculation results revealed that under different incoming wind conditions, the MS-ISSA exhibited better optimization results than the other optimization algorithms.

The Improvement of Blade Element Momentum Theory in Horizontal Axis Wind Turbine Performance Analysis

The present work uses the blade element momentum theory method for evaluating the performance of horizontal axis wind turbine. The wind turbine performances are described in term of the thrust coefficient CT, torque coefficient CQ and the power coefficient CP. The blade element momentum theory (BEMT) represents the wind turbine performance prediction method as result of combining two methods, namely the blade element theory (BET) and the momentum theory (MT). Both theories are able to formulate the axial forces and torques which work on the blade. Equating axial force and torque formulated by BET is equal axial force and torque by MT, makes one allows the axial induction factor and the angular induction factor a^’, the unknown quantities, can be defined and furthermore the wind turbine performances can be evaluated. The BEMT method used here is the combination of BEMT. The implementation this method as the tool for predicting the wind turbine performances are work well. However, for wind turbine configuration need a little adjustment, especially in setting the hub radius rh where the blade element momentum theory starts to make calculation from the inner blade to the tip. The high pitch angle and a relatively a large chord length at rh, make the BEMT fail to converge. In addition to the present work found that the three wind turbine performance coefficients are formulated by using the momentum theory is less accurate compared with BET formulation.

Modeling and investigation of crack evaluation in metal tube based on magnetic field analysis method

In this paper, an analytical model of eddy current testing of a metal tube has been proposed to evaluate circumferential cracks from the signals of the magnetic field. First, based on Maxwell’s equations in time-harmonic form, magnetic vector potential equations for each region of space are built under two different configurations of the bobbin probe and the encircling probe respectively. Next, the magnetic vector potentials are solved by imposing conditions at the interface. Then, series expressions of the radical and axial magnetic induction intensities have been obtained. In addition, based on the proposed modeling, the influences of cracks at different locations on the surface magnetic field have been analyzed. The results have shown that the radial magnetic induction intensity increases while the axial magnetic induction intensity decreases for the internal and external cracks with the same shape and size on the surface of the metal tube. Moreover, the magnetic induction intensity has shown much more sensitive property to external cracks than it has done to internal cracks for the encircling probe. However, for the bobbin probe, the magnetic induction intensity has demonstrated almost the same sensitivity in detection for both internal and external cracks in the metal tube. The researching results have important theoretical and practical significance for understanding the physical process of eddy current testing, optimizing parameters of the experimental system and building the inversion model.

Blade optimization for hydrodynamic performance improvement of a horizontal axis tidal current turbine

This paper proposes an innovative methodology applied to blade optimization for hydrodynamic performance improvement of a horizontal axial tidal current turbine (HATCT) considering the effect of Reynolds number. Axial induction factor, tangential induction factor and angle of attack are employed for identifying the accuracy and applicability of modified Blade Element Momentum (BEM) theory. Combined with the XFoil software, the hydrofoil shape function is represented by trigonometric functions through Theodorsen method. The hydrodynamic characteristics of the hydrofoil are employed as the optimization targets, and the particle swarm optimization algorithm is used to optimize the original hydrofoil. Based on the modified BEM theory and the optimized hydrofoil, the tidal current turbine power coefficient at different tip speed ratio (TSR) is optimized according to the MATLAB function. The optimized tidal current turbine shows better performance compared with the original tidal current turbine.