Tangential Induction Factors Research Articles

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.

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.

Study on Typical Aerodynamic Faults of Variable Pitch Wind Turbine

The variable-speed variable-pitch wind turbine is an important part of China's power and energy systems, and is also the main conversion form of wind energy utilization. Aiming at the problem that the traditional blade element-momentum theory cannot achieve the modeling and simulation of wind turbine plane wind unbalance caused by wind shear and tower shadow effect, the modeling and simulation numerical calculation method of aerodynamic load of wind turbine actuation disk with different blade wind unbalance pitch angles is proposed, This method can derive the analytical expressions for solving the key variables of load calculation, axial induction factor and tangential induction factor, and realize the aerodynamic load solution. At the same time, it is also verified that the characteristic vibration component of 3 times the low speed shaft rotation frequency (3P) is a typical dynamic load feature of tower shadow effect, and is also the most important aerodynamic load fluctuation feature of variable-speed variable-pitch wind turbine, However, under normal conditions, the wind shear effect has little effect on the wind turbine load fluctuation.

How to extrapolate 3D aerodynamic coefficients from HAWT CFD simulations: an inverse BEM approach

In the present work the authors developed a methodology based on an inverse BEM method, to easily extrapolate 3D aerodynamic coefficients from HAWT CFD 3D simulation results. Specifically, since the BEM method was based on the solution of a discrete number of blade radial sections, the CFD model was implemented in Ansys Fluent in such a way to split the surface of one of the blades in a certain number of sections already at the CAD level. Therefore, the normal and tangential aerodynamic forces were calculated for each radial section and subsequently provided directly within the modified BEM code developed in Matlab. Thus, the BEM code iterated for the axial and tangential induction factors and calculated the lift and drag coefficients, the related local angle of attack, the torque, the power and the power coefficient for each specific operating condition simulated. The methodology proposed here was validated using the NREL Phase VI rotor geometry for which a very good agreement between numerical and experimental data was found. Furthermore, this allowed for an insight into the 3D effects over the blade since it was possible to compare the experimental 2D and the 3D lift and drag coefficients section by section.

Experimental investigation of the effect of blade solidity on micro-scale and low tip-speed ratio wind turbines

It is well-established that micro-scale wind turbines require high blade solidity in order to overtake friction torque of all mechanical parts and starts operating. Therefore, multi-bladed micro-scale rotors with a low design tip-speed ratio λ are advocated. However, no consensual blade solidity is admitted by the scientific community at low Reynolds number and low tip-speed ratio because the reliability of the airfoil data, used in the blade element momentum theory, is questionable. The vast majority of the open literature has focused on the number of blades rather than varying blade chord length to increase the solidity. This experimental study carried out in a wind tunnel serves two purposes: to examine blade solidity effect on the power Cp and torque coefficients Cτ vs. tip-speed ratio curves at a fixed number of blades and to investigate its effects on the velocity distributions using stereoscopic particle image velocimetry (SPIV) for three tip-speed ratio λ=0.5, λ=1 and λ=1.4. Six 200mm diameter runners with 8 blades and various blade solidity from σ=1.5 to σ=0.5 were designed at λ=1 without using airfoil data. The results emphasise that the maximum power coefficient increases with blade solidity up to a maximum value Cp,max=0.29 reached for σ=1.25. High-solidity rotors have a very low cut-in wind speed V0=3.8 m s−1 and their torque coefficient Cτ decreases drastically and linearly while increasing the tip-speed ratio λ. These specificities could be of particular interest for energy harvesting of low speed air flow in order to power low-energy appliances. However, for low-solidity rotors, the Cτ vs. λ curves present a similar trend than the lift coefficient vs. angle of attack polar plots of isolated airfoil which is characterised by a significant drop in Cτ illustrating stall effect. An increase in blade solidity postpones and attenuates the stall effects due to greater mutual blade interactions. The SPIV recordings reveal that for high-solidity rotors the magnitude and radial profiles of axial and tangential induction factors and the flow deflection were close to the design settings. Moreover, the analysis exhibits that an increase in the blade solidity and tip-speed ratio leads to higher axial and tangential induction factors. The investigation of the wake highlights that the aerodynamic torque generated by a wind turbine is not produced in a same way as changing the blade solidity or the tip-speed ratio. To conclude, the best compromise between the maximum power coefficient, the cut-in wind speed, the mass of filament and the stability of the wake is achieved for the rotor with a blade solidity of σ=1.25.

Generalized aerodynamic models for crosswind kite power systems

This paper presents two novel semi-analytical models for predicting the aerodynamic performance of crosswind kite power systems (CKPSs), where the kite induction effects on the oncoming flow are taken into account. The blade element momentum theory forms the backbone of the models. The effects of reel-out ratio, solidity factor, rotor incidence angle, side-slip angle and tether drag are included in the formulation for the axial induction factor and power output. For simplicity, the wake rotation and the tangential induction factor are neglected. Aerodynamic model 1 is developed for predicting the reel-out power with uniform inflow assumption, and it is suitable for CKPSs with ground-based power generation. Aerodynamic model 2, on the other hand, can predict both the reel-out and torque powers with either uniform or non-uniform inflow assumption, and the model can be used for CKPSs with ground-based, or on-board power generation, or with the combination of the two. Some parametric studies have been conducted for a generic kite system with pre-defined aerodynamic efficiency parameters to highlight the effects of incidence and side-slip angles. In addition, a particular CKPS and its variants are examined to show the individual and combined effects of incidence angle, side-slip angle, tether drag and airfoil shape on the induction factor and power output.

Aerodynamic Rotor Performance of a 3300-kW Modern Commercial Large-Scale Wind Turbine Installed in a Wind Farm

Abstract Wind turbine technology in the world has been developed by continuously improving turbine performance, design, and efficiency. Over the last 40 years, the rated capacity and dimension of the commercial wind turbines have increased dramatically, so the energy cost has declined significantly, and the industry has moved from an idealistic position to an acknowledged component of the power generation industry. For this reason, a thorough examination of the aerodynamic rotor performance of a modern large-scale wind turbine working on existing onshore wind farms is critically important to monitor and control the turbine performance and also for forecasting turbine power. This study focuses on the aerodynamic rotor performance of a 3300-kW modern commercial large-scale wind turbine operating on an existing onshore wind farm based on the measurement data. First, frequency distributions of wind speeds and directions were obtained using measurements over one year. Then, wind turbine parameters such as free-stream wind speed (U∞), far wake wind speed (UW), axial flow induction factor (a), wind turbine power coefficient (CP), tangential flow induction factor (a′), thrust force coefficient (CT), thrust force (T), tip-speed ratio (λ), and flow angle (ϕ) were calculated using the measured rotor disc wind speed (UD), atmospheric air temperature (Tatm), turbine rotational speed (Ω), and turbine power output (P) parameters. According to the results obtained, the maximum P, CP, CT, T, and Ω were calculated as approximately 3.3 MW, 0.45, 0.6, 330 kN, and 12.9 rpm, respectively, while the optimum λ, ϕ, U∞, and Ω for the maximum CP were determined as 7.5–8.5, 6–6.3°, 5–10 m/s, and 6–10 rpm, respectively. These calculated results can contribute to assessing the economic and technical feasibility of modern commercial large-scale wind turbines and supporting future developments in wind energy and turbine technology.

Optimization Technique for Hydrokinetic Turbine Blades: Pressure Minimization Approach

Everyday rise in world population push for more energy demand. The dependence and usage of fossil fuel in an uncontrolled manner has triggered environmental imbalance. A need to discourage the use of fossil fuel birth renewable energy is a form of energy which is not just environmentally friend but relatively cheap. Hydrokinetic turbine is a device which extracts kinetic energy from moving water to generate power. Hydrokinetic blade is an integral part of hydrokinetic turbine which is one of the components that determines the output power. There is power loss during the operation of the turbine and there is need to reduce this loss. This gives rise to a need to develop an optimization technique that can optimize turbine blade in addition to the existing models. Parameters concentrated on include pressure coefficient, axial induction factor, tangential induction factor, local tip speed ratio and angle of flow

Design and Optimization of Wind Turbine with Axial Induction Factor and Tip Loss Corrections

The aerodynamic modeling of an HAWT (horizontal axis wind turbine) is an essential step in the design of this machine. Generally, the Blade Element Momentum theory (BEM) theory is used. It consists of combining Momentum theory and Blade Element Momentum theory, which makes it possible to solve the equations of aerodynamic forces by an iterative method. This method does not lead to a concordance with the experience. Several studies have tried to introduce corrections to improve the model. The purpose of this study is the design of wind turbine blade by taking into account the corrections of the axial and tangential induction factors. To that end, an iterative method based on Blade Element Momentum theory (BEM) is used and simulations are conducted for NACA airfoil with 5-digit. The study examined blade constructed with only one profile, and blade constructed with two different profiles. Their aerodynamic forces were compared and were shown to increase with the use of the blade built with two different profiles ( NACA63421+NACA63215).

The aerodynamic coupling design and wind tunnel test of contra-rotating wind turbines

The performance of contra-rotating wind turbines (CRWTs) is highly dependent on aerodynamic design. However, flow interaction between two rotors hasn't been fully understood. In this paper, flow interaction was considered in theoretical model based on actuator disc theory with wake rotation. As a consequence, a coupling design method was formulated. Simultaneous blade design of both rotors was originally expressed by a global optimization problem. The input variables include axial and tangential velocity induction factors of both rotors. The output is energy efficiency of CRWT at the annular disc. As a result, chord length and blade section pitch distribution were determined synchronously. This method was applied on the 500W cases of a CRWT and a single rotor wind turbine (SRWT) with identical radius. Wind tunnel test were carried out on the prototypes, with rotating speed and pitch of both rotors controlled independently under various wind velocity. Result validated the effectiveness of design method. At rated wind velocity, the maximum power coefficients of CRWT and SRWT were 0.426 and 0.373. Despite a slightly high start-up wind speed, CRWT demonstrated a higher power coefficient than single turbine at wind velocity 8–14 m/s, with power coefficient relative increment 5.3–28.9%.

A new perspective on the aerodynamic performance and power limit of crosswind kite systems

In this paper, a new perspective on the aerodynamic performance modelling of crosswind kite power systems (CKPSs) is provided, where the effects of the induction factor or flow retardation by the kite are taken into account. For simplicity, only CKPSs in straight downwind configuration are considered, where the kites sweep an area perpendicular to the wind direction. Moreover, the in-plane or tangential induction factor is neglected. It is argued that the concept of the swept-area-normalized power coefficient, which is commonly used for conventional wind turbines, is not practically important for CKPSs. Instead, a kite-area-normalized power coefficient concept is adopted and is shown to be a more appropriate metric of performance of kite systems. The kite-area-normalized useful and wasted power coefficients for both a lift and a drag mode CKPS are plotted at different values of solidity factor and aerodynamic efficiency. Moreover, it is shown that the two modes of power generation, i.e. lift and drag modes, yield the same amount of useful power when the kite system solidity factor is essentially zero – this is in agreement with the underlying assumption in the crosswind kite power principle. For non-zero solidity factors, thus non-zero induction factors, however, our results suggest that the drag mode has higher power generation potential than the lift mode.

Prediction of the Wind Turbine Performance by Using a Modified BEM Theory with an Advanced Brake State Model

Abstract: A mathematical model for fluid dynamics wind turbine design and rotor performance prediction (based on the blade element momentum theory) has been implemented and enhanced. Particular attention was paid to the brake state model to correctly determine axial and tangential induction factors for different wind speed ranges, to the stall delay model in order to consider the centrifugal pumping effects caused by the radial flow along the blades (Himmelskamp effect), and to the models for the representation of the aerodynamic coefficients in pre-stall and post-stall regions. With the numerical codes given in this work, the aerodynamic forces and the power for a NREL wind rotor were predicted. The mathematical simulations results have been compared with experimental data and mathematical models considered in the literature, and are found to be reliable and satisfactory.

A revised theoretical analysis of aerodynamic optimization of horizontal-axis wind turbines based on BEM theory

This article presents a revised theoretical analysis of aerodynamic optimization of horizontal-axis wind turbines, including drag effects, based on Blade Element-Momentum theory. It is demonstrated that horizontal-axis wind turbines can never reach Betz limit, even in the absence of drag effects. Formulating the optimization problem as a nonlinear programming problem with equality and inequality constraints, it is confirmed that, in order to reach maximum performance, all blade sections have to operate under maximum lift-to-drag ratio condition. This condition has been adopted in the literature, but without a mathematical proof that is indeed true. The optimal distributions of axial and tangential induction factors are determined adopting a different approach from those found in the literature. The results include a diagram where both, the optimal operating tip speed ratio and the maximum power coefficient, can be quickly found as functions of the maximum airfoil lift-to-drag ratio.

Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes

A simple unsteady blade element analysis is used to account for the effect of the trailing wake on the induced velocity of a wind turbine rotor undergoing fast changes in pitch angle. At sufficiently high tip speed ratio, the equation describing the thrust of the element reduces to a first order, nonlinear Riccti's equation which is solved in a closed form for a ramp change in pitch followed by a constant pitch. Finite tip speed ratio results in a first order, nonlinear Abel's equation. The unsteady aerodynamic forces on the NREL VI wind turbine are analyzed at different pitch rates and tip speed ratio, and it is found that the overshoot in the forces increases as the tip speed ratio and/or the pitch angle increase. The analytical solution of the Riccati's equation and numerical solution of Abel's equation gave very similar results at high tip speed ratio but the solutions differ as the tip speed ratio reduces, partly because the Abel's equation was found to magnify the error of assuming linear lift at low tip speed ratio. The unsteady tangential induction factor is expressed in the form of first order differential equation with the time constant estimated using Jowkowsky's vortex model and it was found that it is negligible for large tip speed ratio operation.

A case study on optimum tip speed ratio and pitch angle laws for wind turbine rotors operating in yawed conditions

The values of the tip speed ratio and blade pitch angle that yield maximum power coefficient are calculated for a rotor operating in yawed conditions. In a first step, the power coefficient is determined using a model based on the blade element momentum theory (BEMT) which includes a Prandtl-Glauert root-tip losses correction, a non-uniform model for the axial and tangential induction factors, and a model of the rotational augmentation effects. The BEMT model is validated with the experimental data from the NREL-UAE. The maximum values of the power coefficient are determined for different yaw angles and the corresponding values of the tip speed ratio and blade control angle are obtained. The maximum power coefficient using these optimum laws is compared to the maximum power coefficient using the optimum laws of the non-yawed case and it is shown that there is a gain in the power coefficient. For the case study presented in this paper it has been found that for yaw angles of 30° about 10% of the power coefficient can be recovered.

Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow

The mean wake of a three-bladed horizontal axis tidal stream turbine operating at maximum power coefficient has been investigated experimentally in a wide flume with width 11 times the depth, providing minimal restriction to transverse wake development and behaviour of large-scale horizontal turbulence structures. This is an important first stage for understanding wake interaction in turbine arrays and hence large-scale power generation. The rotor diameter has a typical value of 60% of the depth and the thrust coefficient is representative of a full-scale turbine. The shear layers originating from the rotor tip circumference show classic linear expansion downstream, with the rate of a plane shear layer vertically and 1.5 times that horizontally. These shear layers merge by around 2.5 diameters downstream forming a self-similar two-dimensional wake beyond eight diameters downstream with a virtual origin at two diameters downstream of the rotor plane. The spreading rate is somewhat less than that for solid bodies. The detailed velocity measurements made in the near wake show rotation and vorticity similar to that measured previously for wind and marine turbines although with asymmetry associated with bed and surface proximity. The longitudinal circulation in a transverse plane is conserved at about 1% of the swept circulation from the blade tip within two diameters downstream, the extent of detailed measurement. Turbines are usually designed using blade element momentum theory in which velocities at the rotor plane are characterised by axial and tangential induction factors and it is now possible to see how this idealisation relates to actual velocities. The axial induction factor corresponds to velocity deficits at 0.4–0.8 radii from the rotor axis across the near wake while the tangential induction factor at the rotor plane corresponds to velocities at 0.4–0.6 radii between 1–2 diameters downstream, indicating some general correspondence. For the two-dimensional self-similar far wake the two parameters defining the centreline velocity deficit and the transverse velocity profiles are likely to be insensitive to Reynolds number in turbulent conditions.

A simple solution method for the blade element momentum equations with guaranteed convergence

ABSTRACTThe blade element momentum (BEM) equations, though conceptually simple, can be challenging to solve reliably and efficiently with high precision. These requirements are particularly important for efficient rotor blade optimization that utilizes gradient‐based algorithms. Many solution approaches exist for numerically converging the axial and tangential induction factors. These methods all generally suffer from a lack of robustness in some regions of the rotor blade design space, or require significantly increased complexity to promote convergence. The approach described here allows for the BEM equations to be parameterized by one variable—the local inflow angle. This reduction is mathematically equivalent, but greatly simplifies the solution approach. Namely, it allows for the use of one‐dimensional root‐finding algorithms for which very robust and efficient algorithms exist. This paper also discusses an appropriate arrangement of the equation and corresponding bounds for the one‐dimensional search—intervals that bracket the solution and over which the function is well behaved. The result is a methodology for solving the BEM equations with guaranteed convergence and at a superlinear rate.Copyright © 2013 John Wiley & Sons, Ltd.

A New Method for Horizontal Axis Wind Turbine Angle of Attack Determination

This paper proposes a new method for horizontal axis wind turbine (HAWT) angle of attack (AOA) determination. Despite common circular planes for data extraction, here, data is extracted on rectangular planes. NREL Phase VI is used for validation of the method. Results show that even in a high velocity wind the proposed plane can be an appropriate choice. Furthermore, the average radial distributions of axial and tangential induction factors are calculated based on the velocity values at the planes. Moreover, local normal force coefficients are calculated and then, the local AOA are compared with 2D results and other 3D values for different wind speeds.

Advanced brake state model and aerodynamic post-stall model for horizontal axis wind turbines

Abstract In scientific literature, when the aerodynamic design of a horizontal axis wind turbine is discussed, different brake state models are presented. The brake state models are implemented within a BEM code which is a 1-D numerical code, based on Glauert propeller theory, and able to predict HAWT performance. This code provides reliable results only if a proper brake state model and aerodynamic post-stall model are implemented. In this research, the authors have produced a numerical code based on BEM theory in conjunction with an aerodynamic post-stall model, indispensable for taking into account radial flow along the wind turbine blades (Himmelskamp Effect), and the brake state models by Buhl, combined with the calculation of Jonkman's tangential induction factor. In scientific literature, Shen's brake state model is commonly implemented within 1-D numerical codes, based on BEM theory. Subsequently, a comparison with Shen's brake state models was carried out. With the numerical code presented in this work, the power for an NREL wind rotor was predicted. With the numerical simulation, it was possible to notice when these different brake state model furnish results close to experimental data.

Simulation and Test of the Blade Models’ Output Characteristics of Wind Turbine

This electronic document is a “live” template. Based on the momentum-element theory, mathematical model of numerical simulation of the output characteristics is set up for resemble models of MW-scale wind turbine blades, which is under a test system with three different setting angles of 10.5°, 30.5°and 50.5°. The initial values of axial and tangential induction factors are determined by Newton-Raphson method, the powers P, power coefficients CP and torque coefficients CM of the three model test systems are simulated by programming in Matlab and Visual Basic. At the same time, characteristic output tests are carried out by in-truck test method of the three model test systems. The results show that each relative error of simulation and testing results of the model test systems is less than 10%; it proves that the simulation method is reliable and the testing results are reasonable.