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Journal articles on the topic 'Chord and twist distributions'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Tahani, Mojtaba, Ghazale Kavari, Mojtaba Mirhosseini, and Samira Ghiyasi. "Different functionalized chord and twist distributions in aerodynamic design of HAWTs." Environmental Progress & Sustainable Energy 38, no. 4 (2019): 13108. http://dx.doi.org/10.1002/ep.13108.

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Giovanetti, EliB, and KennethC Hall. "Minimum Loss Load, Twist, and Chord Distributions for Coaxial Helicopters in Hover." Journal of the American Helicopter Society 62, no. 1 (2017): 1–9. http://dx.doi.org/10.4050/jahs.62.012001.

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Tahani, Mojtaba, Ghazale Kavari, Mehran Masdari, and Mojtaba Mirhosseini. "Aerodynamic design of horizontal axis wind turbine with innovative local linearization of chord and twist distributions." Energy 131 (July 2017): 78–91. http://dx.doi.org/10.1016/j.energy.2017.05.033.

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Yang, Kyoungboo. "Geometry Design Optimization of a Wind Turbine Blade Considering Effects on Aerodynamic Performance by Linearization." Energies 13, no. 9 (2020): 2320. http://dx.doi.org/10.3390/en13092320.

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For a wind turbine to extract as much energy as possible from the wind, blade geometry optimization to maximize the aerodynamic performance is important. Blade design optimization includes linearizing the blade chord and twist distribution for practical manufacturing. As blade linearization changes the blade geometry, it also affects the aerodynamic performance and load characteristics of the wind turbine rotor. Therefore, it is necessary to understand the effects of the design parameters used in linearization. In this study, the effects of these parameters on the aerodynamic performance of a wind turbine blade were examined. In addition, an optimization algorithm for linearization and an objective function that applies multiple tip speed ratios to optimize the aerodynamic efficiency were developed. The analysis revealed that increasing the chord length and chord profile slope improves the aerodynamic efficiency at low wind speeds but lowers it at high wind speeds, and that the twist profile mainly affects the behaviour at low wind speeds, while its effect on the aerodynamic performance at high wind speeds is not significant. When the blade geometry was optimized by applying the linearization parameter ranges obtained from the analysis, blade geometry with improved aerodynamic efficiency at all wind speeds below the rated wind speed was derived.

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Tan, Chung Ming, and Mei Juan Lai. "Small Wind Turbine Design Verification by Computer Simulation." Applied Mechanics and Materials 863 (February 2017): 235–40. http://dx.doi.org/10.4028/www.scientific.net/amm.863.235.

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Rotor blade design relies heavily on the aerodynamic theory. Extensive calculations are necessary in order to determine the blade parameters such as chord and thickness distributions, twist angle distribution and taper that is matched with the selected airfoil sections. For practical purposes, the engineers need a convenient means to verify their design. Wind turbine blades must be designed to operate in desirable performance. This research proposes a computer aided method that helps the engineers to examine the design and amend it in time. The numerical example shows good applicability of the methodology proposed. The proposed methodology not only lets us verify our design scientifically but also makes us understand the associated physical insight. The numerical example demonstrated here showed the converted power by the rotor can be evaluated easily by Flow Simulation according to the aerodynamics theory.

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Tangler, J. L. "Influence of Pitch, Twist, and Taper on a Blade’s Performance Loss due to Roughness." Journal of Solar Energy Engineering 119, no. 3 (1997): 248–52. http://dx.doi.org/10.1115/1.2888027.

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The purpose of this study was to determine the influence of blade geometric parameters such as pitch, twist, and taper on a blade’s sensitivity to leading edge roughness. The approach began with an evaluation of available test data of performance degradation due to roughness effects for several rotors. In addition to airfoil geometry, this evaluation suggested that a rotor’s sensitivity to roughness was also influenced by the blade geometric parameters. Parametric studies were conducted using the PROP93 computer code with wind tunnel airfoil characteristics for smooth and rough surface conditions to quantify the performance loss due to roughness for tapered and twisted blades relative to a constant-chord nontwisted blade at several blade pitch angles. The results indicate that a constant-chord nontwisted blade pitched toward stall will have the greatest losses due to roughness. The use of twist, taper, and positive blade-pitch angles all help reduce the angle-of-attack distribution along the blade for a given wind speed and the associated performance degradation due to roughness.

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Galetuse, S. "On the Highest Efficiency Windmill Design." Journal of Solar Energy Engineering 108, no. 1 (1986): 41–48. http://dx.doi.org/10.1115/1.3268062.

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A discussion concerning the effect of profile drag on induced velocities is presented. It is concluded that Glauert’s relations for the ideal windmill are also valid for a real windmill. Using these results, the optimum conditions for induced efficiency and power coefficient are obtained. The chord distribution and the twist of the blade are then given as a function of constant K2 for highest power coefficient.

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Debbache, Mohammed, Messaoud Hazmoune, Semcheddine Derfouf, Dana-Alexandra Ciupageanu, and Gheorghe Lazaroiu. "Wind Blade Twist Correction for Enhanced Annual Energy Production of Wind Turbines." Sustainability 13, no. 12 (2021): 6931. http://dx.doi.org/10.3390/su13126931.

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Blade geometry is an important design parameter that influences global wind turbine energy harvesting performances. The geometric characteristics of the blade profile are obtained by determining the distribution of the chord and twist angle for each blade section. In order to maximize the wind energy production, implying a maximum lift-to-drag ratio for each wind speed, this distribution should be optimized. This paper presents a methodology to numerically determine the change in the twist angle by introducing a range of pitch angles for the maximum power coefficient case. The obtained pitch values were distributed from the root to the tip of blade. The results prove that the power coefficient increases for wind speeds greater than the rated point, which improves the yearly production of energy by 5% compared to the reference case.

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Purusothaman, M., T. N. Valarmathi, and S. Praneeth Reddy. "Selection of Twist and Chord Distribution of Horizontal Axis Wind Turbine in Low Wind Conditions." IOP Conference Series: Materials Science and Engineering 149 (September 2016): 012203. http://dx.doi.org/10.1088/1757-899x/149/1/012203.

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Xu, Jianhua, Zhonghua Han, Xiaochao Yan, and Wenping Song. "Design Optimization of a Multi-Megawatt Wind Turbine Blade with the NPU-MWA Airfoil Family." Energies 12, no. 17 (2019): 3330. http://dx.doi.org/10.3390/en12173330.

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A new airfoil family, called NPU-MWA (Northwestern Polytechnical University Multi-megawatt Wind-turbine A-series) airfoils, was designed to improve both aerodynamic and structural performance, with the outboard airfoils being designed at high design lift coefficient and high Reynolds number, and the inboard airfoils being designed as flat-back airfoils. This article aims to design a multi-megawatt wind turbine blade in order to demonstrate the advantages of the NPU-MWA airfoils in improving wind energy capturing and structural weight reduction. The distributions of chord length and twist angle for a 5 MW wind turbine blade are optimized by a Kriging surrogate model-based optimizer, with aerodynamic performance being evaluated by blade element-momentum theory. The Reynolds-averaged Navier–Stokes equations solver was used to validate the improvement in aerodynamic performance. Results show that compared with an existing NREL (National Renewable Energy Laboratory) 5 MW blade, the maximum power coefficient of the optimized NPU 5 MW blade is larger, and the chord lengths at all span-wise sections are dramatically smaller, resulting in a significant structural weight reduction (9%). It is shown that the NPU-MWA airfoils feature excellent aerodynamic and structural performance for the design of multi-megawatt wind turbine blades.

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Droandi, G., and G. Gibertini. "Aerodynamic shape optimisation of a proprotor and its validation by means of CFD and experiments." Aeronautical Journal 119, no. 1220 (2015): 1223–51. http://dx.doi.org/10.1017/s0001924000011222.

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AbstractThe aerodynamic shape design of a proprotor for a tiltrotor aircraft is a very complex and demanding task because it has to combine good hovering capabilities with high propeller efficiency. The aim of the present work is to describe a two-level procedure and its results for the aerodynamic shape design of a new rotor blade for a high-performance tiltwing tiltrotor aircraft taking into account the most important flight conditions in which the aircraft can operate. Span-wise distributions of twist, chord and aerofoil were chosen making use of a multi-objective genetic optimiser that worked on three objectives simultaneously. A non-linear sweep angle distribution along the blade was designed to reduce the power losses due to compressibility effects during axial flight at high speed. During the optimisation process, the aerodynamic performance of the blade was evaluated with a classical two-dimensional strip theory solver. The optimised blade was than analysed by means of a compressible Navier-Stokes solver and calculations were validated comparing numerical results with experimental data obtained from wind-tunnel tests of a scaled model of the proprotor.

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Selig, M. S., and V. L. Coverstone-Carroll. "Application of a Genetic Algorithm to Wind Turbine Design." Journal of Energy Resources Technology 118, no. 1 (1996): 22–28. http://dx.doi.org/10.1115/1.2792688.

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This paper presents an optimization method for stall-regulated horizontal-axis wind turbines. A hybrid approach is used that combines the advantages of a genetic algorithm with an inverse design method. This method is used to determine the optimum blade pitch and blade chord and twist distributions that maximize the annual energy production. To illustrate the method, a family of 25 wind turbines was designed to examine the sensitivity of annual energy production to changes in the rotor blade length and peak rotor power. Trends are revealed that should aid in the design of new rotors for existing turbines. In the second application, five wind turbines were designed to determine the benefits of specifically tailoring wind turbine blades for the average wind speed at a particular site. The results have important practical implications related to rotors designed for the Midwestern US versus those where the average wind speed may be greater.

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Rahgozar, Saeed, Abolfazl Pourrajabian, Syed Ali Abbas Kazmi, and Syed Muhammad Raza Kazmi. "Performance analysis of a small horizontal axis wind turbine under the use of linear/nonlinear distributions for the chord and twist angle." Energy for Sustainable Development 58 (October 2020): 42–49. http://dx.doi.org/10.1016/j.esd.2020.07.003.

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Chattot, Jean-Jacques. "Optimization of Wind Turbines Using Helicoidal Vortex Model." Journal of Solar Energy Engineering 125, no. 4 (2003): 418–24. http://dx.doi.org/10.1115/1.1621675.

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The problem of the design of a wind turbine for maximum output is addressed from an aerodynamical point of view. It is shown that the optimum inviscid design, based on the Goldstein model, satisfies the minimum energy condition of Betz only in the limit of light loading. The more general equation governing the optimum is derived and an integral relation is obtained, stating that the optimum solution satisfies the minimum energy condition of Betz in the Trefftz plane “in the average.” The discretization of the problem is detailed, including the viscous correction based on the 2-D viscous profile data. A constraint is added to account for the thrust on the tower. The minimization problem is solved very efficiently by relaxation. Several optimized solutions are calculated and compared with the National Renewable Energy Laboratory (NREL) rotor, using the same profile, but different chord and twist distributions. In all cases, the optimization produces a more efficient design.

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Alkhabbaz, Ali, Ho-Seong Yang, A. H. Samitha Weerakoon, and Young-Ho Lee. "A novel linearization approach of chord and twist angle distribution for 10 kW horizontal axis wind turbine." Renewable Energy 178 (November 2021): 1398–420. http://dx.doi.org/10.1016/j.renene.2021.06.077.

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Chaudhary, Manoj Kumar, and Anindita Roy. "Design & optimization of a small wind turbine blade for operation at low wind speed." World Journal of Engineering 12, no. 1 (2015): 83–94. http://dx.doi.org/10.1260/1708-5284.12.1.83.

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A small wind turbine blade was designed and optimized in this research paper. The blade plays an important role, because it is the most important part of the energy absorption system. Consequently, the blade has to be designed carefully to enable to absorb energy with its greatest efficiency. The main objective of this paper is to optimized blade number and selection of tip speed ratio corresponding to the solidity. The power performance of small horizontal axis wind turbines was simulated in detail using blade element momentum methods (BEM). In this paper for wind blade design various factors such as tip loss, hub loss, drag coefficient, and wake were considered. The design process includes the selection of the wind turbine type and the determination of the blade airfoil, twist angle distribution along the radius, and chord length distribution along the radius. A parametric study that will determine if the optimized values of blade twist angle and chord length create the most efficient blade geometry. The 3-bladed, 5-bladed and 7-bladed rotor achieved maximum values of Cp 0.46, 0.5 and 0.48 at the tip speed ratio 7, 5 and 4 respectively. It was observed that using BEM theory, maximum Cp varied with strongly solidity and weakly with the blade number. The studies showed that the power coefficient increases upto blade number B = 5, while the blade number if increased above 5 then the power coefficient decreases at operating pitch angle equal to 3°. Highest Cp would have solidity between 4% to 6% for number of blade 3 and design point tip speed ratio of about "7". Highest Cp would have solidity ranging from 5% to 10% for number of blade 5 and 7 and design point tip speed ratio of about 5 and 4 respectively.

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Jimenez-Garcia, A., M. Biava, G. N. Barakos, K. D. Baverstock, S. Gates, and P. Mullen. "Tiltrotor CFD Part II - aerodynamic optimisation of tiltrotor blades." Aeronautical Journal 121, no. 1239 (2017): 611–36. http://dx.doi.org/10.1017/aer.2017.21.

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ABSTRACTThis paper presents aerodynamic optimisation of tiltrotor blades with high-fidelity computational fluid dynamics. The employed optimisation framework is based on a quasi-Newton method, and the required high-fidelity flow gradients were computed using a discrete adjoint solver. Single-point optimisations were first performed to highlight the contrasting requirements of the helicopter and aeroplane flight regimes. It is then shown how a trade-off blade design can be obtained using a multi-point optimisation strategy. The parametrisation of the blade shape allowed the twist and chord distributions to be modified and a swept tip to be introduced. The work shows how these main blade shape parameters influence the optimal performance of the tiltrotor in helicopter and aeroplane modes, and how an optimised blade shape can increase the overall tiltrotor performance. Moreover, in all the presented cases, the accuracy of the adjoint gradients resulted in a small number of flow evaluations for finding the optimal solution, thus indicating gradient-based optimisation as a viable tool for modern tiltrotor design.

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Wang, Qing, and Qijun Zhao. "Rotor blade aerodynamic shape optimization based on high-efficient optimization method." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 2 (2019): 375–87. http://dx.doi.org/10.1177/0954410019865700.

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In order to design a high-performance rotor, a high-efficient optimization method is established by coupling Kriging model and sequential quadratic programming with high-accuracy computational fluid dynamics method. In order to obtain the global optimal design point, the initial blade shape is optimized by using the Kriging model coupled with genetic algorithm based on the baseline rotor blade (Helishape 7A rotor). After that, the modified sequential quadratic programming method is employed to search the final blade shape based on the initial blade shape deeply. In the optimal process, the regions of design variables are restricted considering rotor dynamic characteristics. As a result, a new shape of rotor blade with characters of nonlinear twist, variational chord length, complex swept, and anhedral distributions is obtained. Compared with the baseline rotor, blade-tip vortex of the final optimized rotor is significantly weakened, the figure of merit of the final optimized rotor increases about 3.42%, and the peak of sound pressure decreases about 16.9%. At the same time, it is demonstrated that the final optimized rotor has better forward flight characteristics.

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Wang, Yong Zhi, Feng Li, Xu Zhang, and Wei Min Zhang. "Composite Wind Turbine Blade Aerodynamic and Structural Integrated Design Optimization Based on RBF Meta-Model." Materials Science Forum 813 (March 2015): 10–18. http://dx.doi.org/10.4028/www.scientific.net/msf.813.10.

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An aerodynamic and structural integrated design optimization method of composite wind turbine blade based on multidisciplinary design optimization (MDO) is presented. The optimization aims to reduce the mass of blade under some constraints, including the power and deflection at the rated wind speed, and the strength and deflection under ultimate case. The design variables include parameters both in aerodynamic and structural disciplines. In order to keep the shape of blade smooth,the chord and twist distributions are controlled by the Bezier function in the optimization process. 3D parameterization of blade was carried out in Finite Element Analysis (FEA) software. Considering tip-loss and hub-loss, aerodynamic analysis was performed by using Blade Element Momentum (BEM) theory. Finite Element Method (FEM) was used in structural analysis. Multi-island Genetic Algorithm (MIGA) which has excellent exploration abilities was used to optimize wind turbine blade. RBF meta-model was construct to approximate the accurate structural analysis model by Optimal Latin Hypercube DOE sample points. An example was given to verify the method in this paper. The result shows that the optimization method has good optimization efficiency and the RBF meta-model could reduce the computational cost a lot.

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Khalil, Yassine, Lhoussaine Tenghiri, Farid Abdi, and Anas Bentamy. "Improvement of aerodynamic performance of a small wind turbine." Wind Engineering 44, no. 1 (2019): 21–32. http://dx.doi.org/10.1177/0309524x19849847.

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The aerodynamic performance of horizontal-axis wind turbines is strongly dependent on many parameters, among which the airfoil type and the blade geometry (mainly defined by the chord and the twist distributions) are considered the most critical ones. In this article, an approach giving the appropriate airfoil for a small wind turbine design was conducted by performing an aerodynamic improvement of the blade’s airfoil. First, a preliminary design of the rotor blades of a small wind turbine (11 kW) was conducted using the small wind turbine rotor design code. This preliminary approach was done for different airfoils, and it resulted in a maximum power coefficient of 0.40. Then, the aerodynamic efficiency of the wind turbine was improved by modifying the geometry of the airfoils. This technique targets the optimization of the lift-to-drag ratio (Cl/Cd) of the airfoil within a range of angles of attack. Also, a non-uniform rational B-spline approximation of the airfoil was adopted in order to reduce the number of the design variables of the optimization. This methodology determined the best airfoil for the design of a small wind turbine, and it gave an improved power coefficient of 0.42.

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Iemma, Umberto, Caterina Poggi, Monica Rossetti, and Giovanni Bernardini. "Techniques for adaptive metamodelling of propeller arrays far-field noise." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 4 (2021): 2674–86. http://dx.doi.org/10.3397/in-2021-2203.

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The fast development of Urban-Air-Mobility as well as the constant growth of the air transport have made the acoustic pollution abatement a crucial requirement for the aviation industries in order to comply with the increasingly demanding constraints for the community acceptance. The aeroacoustic characterization of arrays of electrically-powered propellers is one of the most challenging issues. The vast majority of the UAM concepts under development adopt propulsion systems based on multiple propellers, for which reliable and cost-efficient aeroacoustic models are still lacking. The present paper proposes the development of surrogate models for the description of acoustic emission of multi-propeller configurations. The numerical investigation focuses on surrogate models able to take into account the effects of the propeller blade geometry (e.g., chord and twist distributions) and global propeller-array geometric parameters (e.g., propellers clearance) on acoustic performances of the whole system. An innovative Artificial Neural Network adaptive metamodelling technique is applied on a numerical database obtained through a boundary integral formulation for the solution of incompressible potential flows around lifting/thrusting bodies, followed by the application of the Farassat 1A boundary integral formulation for the noise field evaluation.

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Stanley, Andrew P. J., and Andrew Ning. "Coupled wind turbine design and layout optimization with nonhomogeneous wind turbines." Wind Energy Science 4, no. 1 (2019): 99–114. http://dx.doi.org/10.5194/wes-4-99-2019.

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Abstract. In this study, wind farms were optimized to show the benefit of coupling complete turbine design and layout optimization as well as including two different turbine designs in a fixed 1-to-1 ratio in a single wind farm. For our purposes, the variables in each turbine optimization include hub height, rotor diameter, rated power, tower diameter, tower shell thickness, and implicit blade chord-and-twist distributions. A 32-turbine wind farm and a 60-turbine wind farm were both considered, as well as a variety of turbine spacings and wind shear exponents. Structural constraints as well as turbine costs were considered in the optimization. Results indicate that coupled turbine design and layout optimization is superior to sequentially optimizing turbine design, then turbine layout. Coupled optimization results in an additional 2 %–5 % reduction in the cost of energy compared to optimizing sequentially for wind farms with turbine spacings of 8.5–11 rotor diameters. Smaller wind farms benefit even more from coupled optimization. Furthermore, wind farms with closely spaced wind turbines can greatly benefit from nonuniform turbine design throughout the farm. Some of these wind farms with heterogeneous turbine design have an additional 10 % cost-of-energy reduction compared to wind farms with identical turbines throughout the farm.

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Ding, Jiao Jiao, Hao Wang, Li Ping Sun, and Bing Ma. "Optimal Design of Wind Turbine Blades with Wilson and BEM Method Integrated." Applied Mechanics and Materials 404 (September 2013): 286–91. http://dx.doi.org/10.4028/www.scientific.net/amm.404.286.

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This paper presented a new dynamic optimal design method of wind turbine blade which combined the Wilson model with the BEM aerodynamic model. Considering the wind energy utilization coefficient as the target function, the Wilson theory was used to optimize a 1.5MW blades aerodynamic shape. The revised distribution of chord and twist angle was nearly of linear change in the main output power section of blade. The optimized wind energy utilization coefficient can reach 0.552, which is very closed to the Betz limitation. In the part of the calculation of aerodynamic performance, considering both the effect of solidity and eddy current loss on the aerodynamic performance calculation, and also considering the sensitivity of the initial value in a nonlinear equation, it utilized the blade element momentum theory (BEM) which was a classical method on the aerodynamic performance of blade to calculate the aerodynamic performance.The results shows the optimized power output can be up to 1.3426MW, and compared with the rated power, the efficiency reached 89%.

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Bir, Gunjit S. "Computerized Method for Preliminary Structural Design of Composite Wind Turbine Blades." Journal of Solar Energy Engineering 123, no. 4 (2001): 372–81. http://dx.doi.org/10.1115/1.1413217.

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A computerized method has been developed to aid preliminary design of composite wind turbine blades. The method allows for arbitrary specification of the chord, twist, and airfoil geometry along the blade and an arbitrary number of shear webs. Given the blade external geometry description and its design load distribution, the Fortran code uses ultimate-strength and buckling-resistance criteria to compute the design thickness of load-bearing composite laminates. The code also includes an analysis option to obtain blade properties if a composite laminates schedule is prescribed. These properties include bending stiffness, torsion stiffness, mass, moments of inertia, elastic-axis offset, and center-of-mass offset along the blade. Nonstructural materials—gelcoat, nexus, and bonding adhesive—are also included for computation of mass. This paper describes the assumed structural layout of composite laminates within the blade, the design approach, and the computational process. Finally, an example illustrates the application of the code to the preliminary design of a hypothetical blade and computation of its structural properties.

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Encarnacion, Job Immanuel, Cameron Johnstone, and Stephanie Ordonez-Sanchez. "Design of a Horizontal Axis Tidal Turbine for Less Energetic Current Velocity Profiles." Journal of Marine Science and Engineering 7, no. 7 (2019): 197. http://dx.doi.org/10.3390/jmse7070197.

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Existing installations of tidal-stream turbines are undertaken in energetic sites with flow speeds greater than 2 m/s. Sites with lower velocities will produce far less power and may not be as economically viable when using “conventional” tidal turbine designs. However, designing turbines for these less energetic conditions may improve the global viability of tidal technology. Lower hydrodynamic loads are expected, allowing for cost reduction through downsizing and using cheaper materials. This work presents a design methodology for low-solidity high tip-speed ratio turbines aimed to operate at less energetic flows with velocities less than 1.5 m/s. Turbines operating under representative real-site conditions in Mexico and the Philippines are evaluated using a quasi-unsteady blade element momentum method. Blade geometry alterations are undertaken using a scaling factor applied to chord and twist distributions. A parametric filtering and multi-objective decision model is used to select the optimum design among the generated blade variations. It was found that the low-solidity high tip-speed ratio blades lead to a slight power drop of less than 8.5% when compared to the “conventional” blade geometries. Nonetheless, an increase in rotational speed, reaching a tip-speed ratio (TSR) of 7.75, combined with huge reduction in the torque requirement of as much as 30% paves the way for reduced costs from generator downsizing and simplified power take-off mechanisms.

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Modarres, Ramin, and David A. Peters. "Optimum Actuator-Disk Performance in Hover and Axial Flight by a Compact Momentum Theory with Swirl." Journal of the American Helicopter Society 60, no. 1 (2015): 1–10. http://dx.doi.org/10.4050/jahs.60.012003.

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A new compact form of momentum theory is introduced for actuator disks including swirl. The new form unifies both the axial and angular momentum balances into a single momentum equation, applicable over the entire range of thrust and power coefficients. While completely consistent with earlier momentum theories, such as that of Glauert with swirl, the compact form allows analytic expressions for the parameters of a Betz actuator disk and reveals additional insight into the limiting efficiency of rotors, propellers, and wind turbines. The compact form also allows a completely closed form for the truly optimum Glauert rotor. We will also present results from the Betz hypothesis as practically optimum. Closed-form results presented here include the practically optimum values of induced flow, inflow angle, thrust, induced power, and efficiency. Closed-form expressions are also given for practically optimum twist, chord distribution, and solidity in the presence of profile drag (along with the resulting overall efficiencies). This report also gives a closed-form solution for the truly optimum rotor in hover, based on the Glauert optimality criterion.

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Ma, Yong, Aiming Zhang, Lele Yang, Chao Hu, and Yue Bai. "Investigation on Optimization Design of Offshore Wind Turbine Blades based on Particle Swarm Optimization." Energies 12, no. 10 (2019): 1972. http://dx.doi.org/10.3390/en12101972.

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Offshore wind power has become an important trend in global renewable energy development. Based on a particle swarm optimization (PSO) algorithm and FAST program, a time-domain coupled calculation model for a floating wind turbine is established, and a combined optimization design method for the wind turbine’s blade is developed in this paper. The influence of waves on the power of the floating wind turbine is studied in this paper. The results show that, with the increase of wave height, the power fluctuation of the wind turbine increases and the average power of the wind turbine decreases. With the increase of wave period, the power oscillation amplitude of the wind turbine increases, and the power of the wind turbine at equilibrium position decreases. The optimal design of the offshore floating wind turbine blade under different wind speeds is carried out. The results show that the optimum effect of the blades is more obvious at low and mid-low wind speeds than at rated wind speeds. Considering the actual wind direction distribution in the sea area, the maximum power of the wind turbine can be increased by 3.8% after weighted optimization, and the chord length and the twist angle of the blade are reduced.

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Serré, Ronan, Hugo Fournier, and Jean-Marc Moschetta. "A design methodology for quiet and long endurance MAV rotors." International Journal of Micro Air Vehicles 11 (January 2019): 175682931984593. http://dx.doi.org/10.1177/1756829319845937.

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Over the last 10 years, the use of micro air vehicles has rapidly covered a broad range of civilian and military applications. While most missions require optimizing the endurance, a growing number of applications also require acoustic covertness. For rotorcraft micro air vehicles, combining endurance and covertness heavily relies on the capability to design new propulsion systems. The present paper aims at describing a complete methodology for designing quiet and efficient micro air vehicle rotors, ranging from preliminary aerodynamic prediction to aeroacoustic optimization to experimental validation. The present approach is suitable for engineering purposes and can be applied to any multirotor micro air vehicle. A fast-response and reliable aerodynamic design method based on the blade-element momentum theory has been used and coupled with an extended acoustic model based on the Ffowcs Williams and Hawkings equation as well as analytical formulations for broadband noise. The aerodynamic and acoustic solvers have been coupled within an optimization tool. Key design parameters include the number of blades, twist and chord distribution along the blade, as well as the choice of an optimal airfoil. An experimental test bench suitable for non-anechoic environment has been developed in order to assess the benefit of the new rotor designs. Optimal rotors can maintain high aerodynamic efficiency and low acoustic signature with noise reductions in the order of 10 dB(A).

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., Sutrisno, Prajitno ., Purnomo ., and B. W. Setyawan. "The Performance & Flow Visualization Studies of Three dimensional (3-D) Wind Turbine Blade Models." Modern Applied Science 10, no. 5 (2016): 132. http://dx.doi.org/10.5539/mas.v10n5p132.

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The researches on the design of 3-D wind turbine blades have been received less attention so far even though 3-D blade products are widely sold. In the opposite, advanced researches in 3-D helicopter blade have been studied rigorously. Researches in wind turbine blade modeling are mostly assumed that blade span wise sections behaves as independent two dimensional (2-D) airfoils, implying that there is no exchange of momentum in the span wise direction. Further more flow visualization experiments are infrequently conducted.The purpose of this study is to investigate the performance of 3-D wind turbine blade models with backward-forward swept and verify the flow patterns using flow visualization. In this research, the blade models are constructed based on the twist and chord distributions following Schmitz’s formula. Forward and backward swept are added to the wind turbine blades. It is hoped that the additional swept would enhance or diminish outward flow disturbance or stall development propagation on the span wise blade surfaces to give better blade design.The performance of the 3-D wind turbine system models are measured by a torque meter, employing Prony’s braking system, and the 3-D flow patterns around the rotating blade models are investigated applying “tuft-visualization technique”, to study the appearance of laminar, separated and boundary layer flow patterns surrounding the 3-dimentional blade system.For low speed wind turbines, Dumitrescu and Cardos (2011) have identified that stall spreads from the root of the rotating blade. In this study, it is found that for blades with (i) forward swept tip and backward swept root, the initial stall at the blade bottom would be amplified by concurrent strengthening flow due to the backward swept root to create strong stall spreading outward, and therefore the blades gives lower performance. For blades with (ii) backward swept tip and forward swept root, the initial stall at the blade bottom would be weakened by opposite weakening flow due to the forward swept root, generate weak stall that tend to deteriorate. These blades have better performance.

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Burger, C., and W. Ruland. "Analysis of chord-length distributions." Acta Crystallographica Section A Foundations of Crystallography 57, no. 5 (2001): 482–91. http://dx.doi.org/10.1107/s0108767301005098.

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Pons, Marie-Noëlle, Kim Milferstedt, and Eberhard Morgenroth. "Modeling of chord length distributions." Chemical Engineering Science 61, no. 12 (2006): 3962–73. http://dx.doi.org/10.1016/j.ces.2006.01.036.

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Barron, Nicholas R., Shawn D. Ryan, and Thijs Heus. "Reconciling Chord Length Distributions and Area Distributions for Fields of Fractal Cumulus Clouds." Atmosphere 11, no. 8 (2020): 824. http://dx.doi.org/10.3390/atmos11080824.

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While the total cover of broken cloud fields can in principle be obtained from one-dimensional measurements, the cloud size distribution normally differs between two-dimensional (area) and one-dimensional retrieval (chord length) methods. In this study, we use output from high-resolution Large Eddy Simulations to generate a transfer function between the two. We retrieve chord lengths and areas for many clouds, and plot the one as a function of the other, and vice versa. We find that the cloud area distribution conditional on the chord length behaves like a gamma distribution with well-behaved parameters, with a mean μ=1.1L and a shape parameter β=L−0.645. Using this information, we are able to generate a transfer function that can adjust the chord length distribution so that it comes much closer to the cloud area distribution. Our transfer function improves the error in predicting the mean cloud size, and is performs without strong biases for smaller sample sizes. However, we find that the method is still has difficulties in accurately predicting the frequency of occurrence of the largest cloud sizes.

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Northum, Jeremy D., and Stephen B. Guetersloh. "The Application of Microdosimetric Principles to Radiation Hardness Testing." Science and Technology of Nuclear Installations 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/828921.

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Chord length distributions for rectangular parallelepipeds of various relative dimensions were studied in relation to radiation hardness testing. For each geometry, a differential chord length distribution was generated using a Monte Carlo method to simulate exposure to an isotropic radiation source. The frequency and dose distributions of chord length crossings for each geometry, as well as the means of these distributions, are presented. In every case, the dose mean chord length was greater than the frequency mean chord length with a 34.5% increase found for the least extreme case of a cube. This large increase of the dose mean chord length relative to the frequency mean chord length demonstrates the need to consider rare, long-chord-length crossings in radiation hardness testing of electronic components.

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Gille, Wilfried. "Chord Length Distributions of the Hemisphere." Journal of Mathematics and Statistics 1, no. 1 (2005): 24–28. http://dx.doi.org/10.3844/jmssp.2005.24.28.

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Gates, J. "Some properties of chord length distributions." Journal of Applied Probability 24, no. 4 (1987): 863–74. http://dx.doi.org/10.2307/3214211.

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The chord length distributions of planar convex sets are discussed, particularly the density values at the extremes of the range; there is a qualitative distinction between polygons and sets with smooth boundaries. The distance between convex sets is related to the distance between distribution functions.

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Gates, J. "Some properties of chord length distributions." Journal of Applied Probability 24, no. 04 (1987): 863–74. http://dx.doi.org/10.1017/s0021900200116742.

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Ren, Delin. "Random chord distributions and containment functions." Advances in Applied Mathematics 58 (July 2014): 1–20. http://dx.doi.org/10.1016/j.aam.2014.05.003.

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Быстров, В., V. Bystrov, В. Андреев, et al. "Innovative manufacturing technology of billets of wide-chord blades of gas turbine engines." Science intensive technologies in mechanical engineering 1, no. 2 (2016): 12–18. http://dx.doi.org/10.12737/17797.

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The method of design of wide-chord billets for blades of aircraft gas turbine engines, deliberately fabricated without twist of the airfoil profile, is described. The feasible options of manufacturing sequence of their processing are considered. The stamp structure for pen twist of the blade billets and stabilizing the obtained geometric dimensions are described.

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Vidovic, Zoran. "Limit Distributions of Maximal Random Chord Length." Journal of Statistics Applications & Probability 5, no. 2 (2016): 213–20. http://dx.doi.org/10.18576/jsap/050202.

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Gille, W. "Chord length distributions and small-angle scattering." European Physical Journal B 17, no. 3 (2000): 371–83. http://dx.doi.org/10.1007/s100510070116.

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van Rooij, R. P. J. O. M., and J. G. Schepers. "The Effect of Blade Geometry on Blade Stall Characteristics." Journal of Solar Energy Engineering 127, no. 4 (2005): 496–502. http://dx.doi.org/10.1115/1.2037090.

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The effect of rotation has been investigated with emphasis on the impact of blade geometry on the “correction factor” in stall models. The data used came from field tests and wind tunnel experiments performed by the National Renewable Energy Laboratory and were restricted to the steady-state nonyawed conditions. Three blade layouts were available; a blade with constant chord without twist (phase II), a blade with constant chord and twist (phases III and IV), and a tapered blade with twist (phase VI). Effects due to twist and taper were determined from comparison of c n between the different blade layouts. The formulation of the stall model was rewritten so that the measured c n values could be used without reference to 2D airfoil performance. This enabled a direct comparison of the normal force characteristics between the four blade stations of the selected blade configurations. In particular, the correction term f used in stall models for rotational effects was analyzed. The comparison between the test results with a straight and a twisted blade showed that a relation for twist + pitch is required in f . In addition, a dependency offon the angle-of-attack was identified in the measurements and it is recommended that this dependency be incorporated in the stall models.

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Nagel, W. "Orientation-dependent chord length distributions characterize convex polygons." Journal of Applied Probability 30, no. 3 (1993): 730–36. http://dx.doi.org/10.2307/3214779.

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It is shown that the convex polygons are uniquely determined (up to translation and reflection) by their covariograms. The covariogram can be represented by the ‘orientation-dependent chord length distribution', i.e. the distribution of the length of chords which are generated by random lines parallel to fixed directions. Thus the result contributes to answer Blaschke's question about the content of information comprised in chord length distributions.

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Nagel, W. "Orientation-dependent chord length distributions characterize convex polygons." Journal of Applied Probability 30, no. 03 (1993): 730–36. http://dx.doi.org/10.1017/s0021900200044442.

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Clark, N. N., and R. Turton. "Chord length distributions related to bubble size distributions in multiphase flows." International Journal of Multiphase Flow 14, no. 4 (1988): 413–24. http://dx.doi.org/10.1016/0301-9322(88)90019-5.

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Burkardt, Matthias. "Higher-twist parton distributions in QCD2." Nuclear Physics B 373, no. 3 (1992): 613–29. http://dx.doi.org/10.1016/0550-3213(92)90268-g.

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Simmons, M. J. H., P. A. Langston, and A. S. Burbidge. "Particle and droplet size analysis from chord distributions." Powder Technology 102, no. 1 (1999): 75–83. http://dx.doi.org/10.1016/s0032-5910(98)00197-1.

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Gille, Wilfried. "Chord length distributions of infinitely long geometric figures." Powder Technology 123, no. 2-3 (2002): 292–98. http://dx.doi.org/10.1016/s0032-5910(01)00455-7.

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Mazzolo, Alain, Benoı̂t Roesslinger, and Wilfried Gille. "Properties of chord length distributions of nonconvex bodies." Journal of Mathematical Physics 44, no. 12 (2003): 6195. http://dx.doi.org/10.1063/1.1622446.

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Hansen, Steen. "Estimation of chord length distributions from small-angle scattering using indirect Fourier transformation." Journal of Applied Crystallography 36, no. 5 (2003): 1190–96. http://dx.doi.org/10.1107/s0021889803014262.

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It is shown that it is possible to estimate the chord length distribution from small-angle scattering data by indirect Fourier transformation. This is done for several examples of scatterers varying in structure from globular to elongated as well as scatterers consisting of separated parts. The presented examples suggest that the chord length distribution may give additional information about the scatterer. Therefore it may be relevant to consider estimation of the chord length distribution as an additional tool for analysis of small-angle scattering data.

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Phillips, W. F., and D. F. Hunsaker. "Designing Wing Twist or Planform Distributions for Specified Lift Distributions." Journal of Aircraft 56, no. 2 (2019): 847–49. http://dx.doi.org/10.2514/1.c035206.

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