Search results for: Pitching airfoil

Authors: Marco Raciti Castelli, Stefano De Betta, Ernesto Benini

Abstract:

A two-dimensional numerical simulation of the contribution of both inertial and aerodynamic forces on the blade loads of a Vertical-Axis Wind Turbine (VAWT) is presented. After describing the computational model and the relative validation procedure, a complete campaign of simulations - based on full RANS unsteady calculations - is proposed for a three-bladed rotor architecture characterized by a NACA 0021 airfoil. For each analyzed angular velocity, the combined effect of pressure and viscous forces acting on every rotor blade are compared to the corresponding centrifugal forces, due to the revolution of the turbine, thus achieving a preliminary estimation of the correlation between overall rotor efficiency and structural blade loads.

Keywords: CFD, VAWT, NACA 0021, aerodynamic forces, inertial loadings.

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Authors: M-J. Huang, C-J. Huang, L-C. Chen

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In a previously developed fast vortex method, the diffusion of the vortex sheet induced at the solid wall by the no-slip boundary conditions was modeled according to the approximation solution of Koumoutsakos and converted into discrete blobs in the vicinity of the wall. This scheme had been successfully applied to a simulation of the flow induced with an impulsively initiated circular cylinder. In this work, further modifications on this vortex method are attempted, including replacing the approximation solution by the boundary-element-method solution, incorporating a new algorithm for handling the over-weak vortex blobs, and diffusing the vortex sheet circulation in a new way suitable for high-curvature solid bodies. The accuracy is thus largely improved. The predictions of lift and drag coefficients for a uniform flow past a NASA airfoil agree well with the existing literature.

Keywords: Resurrected core-spreading vortex method, Boundaryelement method, Vortex sheet, Over-weak vortex blobs.

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Authors: Hemant Kumawat

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Axial flow fans, while incapable of developing high pressures, they are well suitable for handling large volumes of air at relatively low pressures. In general, they are low in cost and possess good efficiency, and can have blades of airfoil shape. Axial flow fans show good efficiencies, and can operate at high static pressures if such operation is necessary. Our objective is to model and analyze the flow through AXIAL FANS using CFD Software and draw inference from the obtained results, so as to get maximum efficiency. The performance of an axial fan was simulated using CFD and the effect of variation of different parameters such as the blade number, noise level, velocity, temperature and pressure distribution on the blade surface was studied. This paper aims to present a final 3D CAD model of axial flow fan. Adapting this model to the available components in the market, the first optimization was done. After this step, CFX flow solver is used to do the necessary numerical analyses on the aerodynamic performance of this model. This analysis results in a final optimization of the proposed 3D model which is presented in this article.

Keywords: ANSYS CFX, Axial Fan, Computational Fluid Dynamics (CFD), Optimization.

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Authors: S. A. Ahmadi, S. Sharif, R. Jamshidi

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In this article, the flow behavior around a NACA 0012 airfoil which is oscillating with different Reynolds numbers and in various amplitudes has been investigated numerically. Numerical simulations have been performed with ANSYS software. First, the 2- D geometry has been studied in different Reynolds numbers and angles of attack with various numerical methods in its static condition. This analysis was to choose the best turbulent model and comparing the grids to have the optimum one for dynamic simulations. Because the analysis was to study the blades of wind turbines, the Reynolds numbers were not arbitrary. They were in the range of 9.71e5 to 22.65e5. The angle of attack was in the range of -41.81° to 41.81°. By choosing the forward wind speed as the independent parameter, the others like Reynolds and the amplitude of the oscillation would be known automatically. The results show that the SST turbulent model is the best choice that leads the least numerical error with respect the experimental ones. Also, a dynamic stall phenomenon is more probable at lower wind speeds in which the lift force is less.

Keywords: Dynamic stall, Numerical simulation, Wind turbine, Turbulent Model

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Authors: Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

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A dynamic stall-corrected Blade Element-Momentum algorithm based on a hybrid polar is validated through the comparison with Sandia experimental measurements on a 5-m diameter wind turbine of Troposkien shape. Different dynamic stall models are evaluated. The numerical predictions obtained using the extended aerodynamic coefficients provided by both Sheldal and Klimas and Raciti Castelli et al. are compared to experimental data, determining the potential of the hybrid database for the numerical prediction of vertical-axis wind turbine performances.

Keywords: Darrieus wind turbine, Blade Element-Momentum Theory, extended airfoil database, hybrid database, Sandia 5-m wind turbine.

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Authors: Paul Okonkwo, Howard Smith

Abstract:

A study to estimate the size of the cabin and major aircraft components as well as detect and avoid interference between internally placed components and the external surface, during the conceptual design synthesis and optimisation to explore the design space of a BWB, was conducted. Sizing of components follows the Bradley cabin sizing and rubber engine scaling procedures to size the cabin and engine respectively. The interference detection and avoidance algorithm relies on the ability of the Class Shape Transform parameterisation technique to generate polynomial functions of the surfaces of a BWB aircraft configuration from the sizes of the cabin and internal objects using few variables. Interference detection is essential in packaging of non-conventional configuration like the BWB because of the non-uniform airfoil-shaped sections and resultant varying internal space. The unique configuration increases the need for a methodology to prevent objects from being placed in locations that do not sufficiently enclose them within the geometry.

Keywords: Packaging, Optimisation, BWB, Parameterisation, Aircraft Conceptual Design.

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Authors: Marco Raciti Castelli, Stefano De Betta, Ernesto Benini

Abstract:

This paper presents a mean for reducing the torque variation during the revolution of a vertical-axis wind turbine (VAWT) by increasing the blade number. For this purpose, twodimensional CDF analysis have been performed on a straight-bladed Darreius-type rotor. After describing the computational model, a complete campaign of simulations based on full RANS unsteady calculations is proposed for a three, four and five-bladed rotor architecture characterized by a NACA 0025 airfoil. For each proposed rotor configuration, flow field characteristics are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade number on flow geometric features and dynamic quantities, such as rotor torque and power. Finally, torque and power curves are compared for the analyzed architectures, achieving a quantification of the effect of blade number on overall rotor performance.

Keywords: CFD, VAWT, NACA 0021, blade number

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Authors: Cristian P. Topa, Esteban A. Valencia, Victor H. Hidalgo, Marco A. Martinez

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Wind tunnel experiments for aerodynamic profiles display numerous advantages, such as: clean steady laminar flow, controlled environmental conditions, streamlines visualization, and real data acquisition. However, the experiment instrumentation usually is expensive, and hence, each test implies a incremented in design cost. The aim of this work is to select and implement a low-cost static pressure data acquisition system for a NACA 2412 airfoil in an open cycle wind tunnel. This work compares wind tunnel experiment with Computational Fluid Dynamics (CFD) simulation and parametric analysis. The experiment was evaluated at Reynolds of 1.65 e⁵, with increasing angles from -5° to 15°. The comparison between the approaches show good enough accuracy, between the experiment and CFD, additional parametric analysis results differ widely from the other methods, which complies with the lack of accuracy of the lateral approach due its simplicity.

Keywords: Wind tunnel, low cost instrumentation, experimental testing, CFD simulation.

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Authors: Etsuo Morishita

Abstract:

In this paper, we show shallow water in a tin box as an analogous simulation tool for high-speed aerodynamics education and research. It is customary that we use a water tank to create shallow water flow. While a flow in a water tank is not necessarily uniform and is sometimes wavy, we can visualize a clear supercritical flow even when we move a body manually in stationary water in a simple shallow tin box. We can visualize a blunt shock wave around a moving circular cylinder together with a shock pattern around a diamond airfoil. Another interesting analogous experiment is a hydrodynamic shock tube with water and tea. We observe the contact surface clearly due to color difference of the two liquids those are invisible in the real gas dynamics experiment. We first revisit the similarities between high-speed aerodynamics and shallow water hydraulics. Several educational and research experiments are then introduced for engineering students. Shallow water experiments in a tin box simulate properly the high-speed flows.

Keywords: Aerodynamics compressible flow, gas dynamics, hydraulics, shock wave.

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Authors: Ich Long Ngo, Dinh Tai Dang, Ngoc Tu Nguyen, Minh Duc Nguyen

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This paper describes an investigation on designing and enhancing the performance of H-Darrieus Wind Turbine (HDWT) of 10 kW at the medium wind speed. The aerodynamic characteristics of this turbine were investigated by both theoretical and numerical approaches. The optimal design procedure was first proposed to enhance the power coefficient under various effects, such as airfoil type, number of blades, solidity, aspect ratio, and tip speed ratio. As a result, the overall design of the 10 kW HDWT was well achieved, and the power characteristic of this turbine was found by numerical approach. Additionally, the maximum power coefficient predicted is up to 0.41 at the tip speed ratio of 3.7 and wind speed of 8 m/s. Particularly, a generalized correlation of power coefficient with tip speed ratio and wind speed is first proposed. These results obtained are very useful for enhancing the performance of the HDWTs placed in a country with high wind power potential like Vietnam.

Keywords: Computational Fluid Dynamics, double multiple stream tube, H-Darrieus wind turbine, renewable energy.

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Authors: S. Daneshmand, A. Ahmadi Nadooshan, C. Aghanajafi

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Traditional wind tunnel models are meticulously machined from metal in a process that can take several months. While very precise, the manufacturing process is too slow to assess a new design's feasibility quickly. Rapid prototyping technology makes this concurrent study of air vehicle concepts via computer simulation and in the wind tunnel possible. This paper described the Affects layer thickness models product with rapid prototyping on Aerodynamic Coefficients for Constructed wind tunnel testing models. Three models were evaluated. The first model was a 0.05mm layer thickness and Horizontal plane 0.1μm (Ra) second model was a 0.125mm layer thickness and Horizontal plane 0.22μm (Ra) third model was a 0.15mm layer thickness and Horizontal plane 4.6μm (Ra). These models were fabricated from somos 18420 by a stereolithography (SLA). A wing-body-tail configuration was chosen for the actual study. Testing covered the Mach range of Mach 0.3 to Mach 0.9 at an angle-of-attack range of -2° to +12° at zero sideslip. Coefficients of normal force, axial force, pitching moment, and lift over drag are shown at each of these Mach numbers. Results from this study show that layer thickness does have an effect on the aerodynamic characteristics in general; the data differ between the three models by fewer than 5%. The layer thickness does have more effect on the aerodynamic characteristics when Mach number is decreased and had most effect on the aerodynamic characteristics of axial force and its derivative coefficients.

Keywords: Aerodynamic characteristics, stereolithography, layer thickness, Rapid prototyping, surface finish.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

This paper presents a means for reducing the torque variation during the revolution of a vertical-axis water turbine (VAWaterT) by increasing the blade number. For this purpose, twodimensional CFD analyses have been performed on a straight-bladed Darrieus-type rotor. After describing the computational model and the relative validation procedure, a complete campaign of simulations, based on full RANS unsteady calculations, is proposed for a three, four and five-bladed rotor architectures, characterized by a NACA 0025 airfoil. For each proposed rotor configuration, flow field characteristics are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade number on flow geometric features and dynamic quantities, such as rotor torque and power. Finally, torque and power curves are compared for the three analyzed architectures, achieving a quantification of the effect of blade number on overall rotor performance.

Keywords: Vertical-Axis Water Turbine, rotor solidity, CFD, NACA 0025

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Authors: M. Ismail, Cao Yihua, Zhao Ming, Abu Bakar

Abstract:

Heavy rainfall greatly affects the aerodynamic performance of the aircraft. There are many accidents of aircraft caused by aerodynamic efficiency degradation by heavy rain. In this Paper we have studied the heavy rain effects on the aerodynamic efficiency of cambered NACA 64-210 and symmetric NACA 0012 airfoils. Our results show significant increase in drag and decrease in lift. We used preprocessing software gridgen for creation of geometry and mesh, used fluent as solver and techplot as postprocessor. Discrete phase modeling called DPM is used to model the rain particles using two phase flow approach. The rain particles are assumed to be inert. Both airfoils showed significant decrease in lift and increase in drag in simulated rain environment. The most significant difference between these two airfoils was the NACA 64-210 more sensitivity than NACA 0012 to liquid water content (LWC). We believe that the results showed in this paper will be useful for the designer of the commercial aircrafts and UAVs, and will be helpful for training of the pilots to control the airplanes in heavy rain.

Keywords: airfoil, discrete phase modeling, heavy rain, Reynolds

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Authors: M. Elkhoury

Abstract:

A recently developed one-equation turbulence model has been successfully applied to simulate turbulent flows with various complexities. The model, which is based on the transformation of the k-ε closure, is wall-distance free and equipped with lagging destruction/dissipation terms. Test cases included shockboundary- layer interaction flows over the NACA 0012 airfoil, an axisymmetric bump, and the ONERA M6 wing. The capability of the model to operate in a Scale Resolved Simulation (SRS) mode is demonstrated through the simulation of a massive flow separation over a circular cylinder at Re= 1.2 x106. An assessment of the results against available experiments Menter (k-ε)1Eq and the Spalart- Allmaras model that belongs to the single equation closure family is made.

Keywords: Turbulence modeling, complex flow simulation, scale adaptive simulation, one-equation turbulence model.

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Authors: Altab Hossain, Ataur Rahman, Jakir Hossen, A.K.M. P. Iqbal, SK. Hasan

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The measurement of aerodynamic forces and moments acting on an aircraft model is important for the development of wind tunnel measurement technology to predict the performance of the full scale vehicle. The potentials of an aircraft model with and without winglet and aerodynamic characteristics with NACA wing No. 65-3- 218 have been studied using subsonic wind tunnel of 1 m × 1 m rectangular test section and 2.5 m long of Aerodynamics Laboratory Faculty of Engineering (University Putra Malaysia). Focusing on analyzing the aerodynamic characteristics of the aircraft model, two main issues are studied in this paper. First, a six component wind tunnel external balance is used for measuring lift, drag and pitching moment. Secondly, Tests are conducted on the aircraft model with and without winglet of two configurations at Reynolds numbers 1.7×105, 2.1×105, and 2.5×105 for different angle of attacks. Fuzzy logic approach is found as efficient for the representation, manipulation and utilization of aerodynamic characteristics. Therefore, the primary purpose of this work was to investigate the relationship between lift and drag coefficients, with free-stream velocities and angle of attacks, and to illustrate how fuzzy logic might play an important role in study of lift aerodynamic characteristics of an aircraft model with the addition of certain winglet configurations. Results of the developed fuzzy logic were compared with the experimental results. For lift coefficient analysis, the mean of actual and predicted values were 0.62 and 0.60 respectively. The coreelation between actual and predicted values (from FLS model) of lift coefficient in different angle of attack was found as 0.99. The mean relative error of actual and predicted valus was found as 5.18% for the velocity of 26.36 m/s which was found to be less than the acceptable limits (10%). The goodness of fit of prediction value was 0.95 which was close to 1.0.

Keywords: Wind tunnel; Winglet; Lift coefficient; Fuzzy logic.

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Authors: Vatasta Koul, Vaibhav Sharma, Ayush Gupta, Rajesh Yadav

Abstract:

Exploratory missions to Mars and Titan have increased recently with various endeavors to find an alternate home to humankind. The use of surface rovers has its limitations due to rugged and uneven surfaces of these planetary bodies. The use of aerial robots requires the complete aerodynamic characterization of these vehicles in the atmospheric conditions of these planetary bodies. The dynamic stall phenomenon is extremely important for rotary wings performance under low Reynolds number that can be encountered in Martian and Titan’s atmosphere. The current research focuses on the aerodynamic characterization and exploration of the dynamic stall phenomenon of two different airfoils viz. E387 and Selig-Donovan7003 in Martian and Titan’s atmosphere at low Reynolds numbers of 10000 and 50000. The two-dimensional numerical simulations are conducted using commercially available finite volume solver with multi-species non-reacting mixture of gases as the working fluid. The k-epsilon (k-ε) turbulence model is used to capture the unsteady flow separation and the effect of turbulence. The dynamic characteristics are studied at a fixed different constant rotational extreme of angles of attack. This study of airfoils at different low Reynolds number and atmospheric conditions on Mars and Titan will be resulting in defining the aerodynamic characteristics of these airfoils for unmanned aerial missions for outer space exploration.

Keywords: Aerodynamic, dynamic stall, low Reynolds, Mars, Titan.

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Authors: P. Booma Devi, Dilip A. Shah

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This paper seeks the potentials of studying aerodynamic characteristics of inward cavities called dimples, as an alternative to the classical vortex generators. Increasing stalling angle is a greater challenge in wing design. But our examination is primarily focused on increasing lift. In this paper, enhancement of lift is mainly done by introduction of dimple or cavity in a wing. In general, aircraft performance can be enhanced by increasing aerodynamic efficiency that is lift to drag ratio of an aircraft wing. Efficiency improvement can be achieved by improving the maximum lift co-efficient or by reducing the drag co-efficient. At the time of landing aircraft, high angle of attack may lead to stalling of aircraft. To avoid this kind of situation, increase in the stalling angle is warranted. Hence, improved stalling characteristic is the best way to ease landing complexity. Computational analysis is done for the wing segment made of NACA 0012. Simulation is carried out for 30 m/s free stream velocity over plain airfoil and different types of cavities. The wing is modeled in CATIA V5R20 and analyses are carried out using ANSYS CFX. Triangle and square shapes are used as cavities for analysis. Simulations revealed that cavity placed on wing segment shows an increase of maximum lift co-efficient when compared to normal wing configuration. Flow separation is delayed at downstream of the wing by the presence of cavities up to a particular angle of attack.

Keywords: Lift, square and rectangle dimples, enhancement of stall angle, cavity.

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Authors: Vatasta Koul, Ayush Gupta, Vaibhav Sharma, Rajesh Yadav

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Today we are unmarking the secrets of the universe by exploring different stars and planets and most of the space exploration is done by unmanned space robots. In addition to our planet Earth, there are pieces of evidence that show other astronomical objects in our solar system such as Venus, Mars, Saturn’s moon Titan and Uranus support the flight of fixed wing air vehicles. In this paper, we take forward the concept of presence of large rounded tubercles along the leading edge of a wing and use it as a passive flow control device that will help in improving its aerodynamic performance and maneuverability. Furthermore, in this research, aerodynamic measurements and performance analysis of wavy leading tubercles on the fixed wings at 5-degree angle of attack are carried out after determination of the flow conditions on the selected planetary bodies. Wavelength and amplitude for the sinusoidal modifications on the leading edge are analyzed and simulations are carried out for three-dimensional NACA 0012 airfoil maintaining unity AR (Aspect Ratio). Tubercles have consistently demonstrated the ability to delay and decrease the severity of stall as per the studies were done in the Earth’s atmosphere. Implementing the same design on the leading edges of Micro-Air Vehicles (MAVs) and UAVs could make these aircrafts more stable over a greater range of angles of attack in different planetary environments of our solar system.

Keywords: Amplitude, NACA0012, tubercles, unmanned space robots.

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Authors: Julio C. Gómez-Mancilla, Luis M. Palacios-Pineda, Yunuén López-Grijalba

Abstract:

A new mechanism responsible for structural life consumption due to resonant fatigue in turbine blades, or vanes, is presented and explained. A rotating blade or vane in a gas turbine can change its contour due to erosion and/or material build up, in any of these instances, the surface pressure distribution occurring on the suction and pressure sides of blades-vanes can suffer substantial modification of their pressure and temperatures envelopes and flow characteristics. Meanwhile, the relative rotation between the blade and duct vane while the pressurized gas flows and the consequent wake crossings, will induce a fluctuating thrust force or lift that will excite the blade. An actual totally used up set of vane-blade components in a HP turbine power stage in a gas turbine is analyzed. The blade suffered some material erosion mostly at the trailing edge provoking a peculiar surface pressure envelope which evolved as the relative position between the vane and the blade passed in front of each other. Interestingly preliminary modal analysis for this eroded blade indicates several natural frequencies within the aeromechanic power spectrum, moreover, the highest frequency component is 94% of one natural frequency indicating near resonant condition. Independently of other simultaneously occurring fatigue cycles (such as thermal, centrifugal stresses).

Keywords: Aeromechanic induced vibration, potential flowinteraction, turbine unsteady flow, rotor/stator interaction, turbinevane-blade aerodynamic interaction, airfoil clocking

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Authors: C. Amer, M. Sahin

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The design of an optimised horizontal axis 5-meter-long wind turbine rotor blade in according with IEC 61400-2 standard is a research and development project in order to fulfil the requirements of high efficiency of torque from wind production and to optimise the structural components to the lightest and strongest way possible. For this purpose, a research study is presented here by focusing on the structural characteristics of a composite wind turbine blade via finite element modelling and analysis tools. In this work, first, the required data regarding the general geometrical parts are gathered. Then, the airfoil geometries are created at various sections along the span of the blade by using CATIA software to obtain the two surfaces, namely; the suction and the pressure side of the blade in which there is a hat shaped fibre reinforced plastic spar beam, so-called chassis starting at 0.5m from the root of the blade and extends up to 4 m and filled with a foam core. The root part connecting the blade to the main rotor differential metallic hub having twelve hollow threaded studs is then modelled. The materials are assigned as two different types of glass fabrics, polymeric foam core material and the steel-balsa wood combination for the root connection parts. The glass fabrics are applied using hand wet lay-up lamination with epoxy resin as METYX L600E10C-0, is the unidirectional continuous fibres and METYX XL800E10F having a tri-axial architecture with fibres in the 0,+45,-45 degree orientations in a ratio of 2:1:1. Divinycell H45 is used as the polymeric foam. The finite element modelling of the blade is performed via MSC PATRAN software with various meshes created on each structural part considering shell type for all surface geometries, and lumped mass were added to simulate extra adhesive locations. For the static analysis, the boundary conditions are assigned as fixed at the root through aforementioned bolts, where for dynamic analysis both fixed-free and free-free boundary conditions are made. By also taking the mesh independency into account, MSC NASTRAN is used as a solver for both analyses. The static analysis aims the tip deflection of the blade under its own weight and the dynamic analysis comprises normal mode dynamic analysis performed in order to obtain the natural frequencies and corresponding mode shapes focusing the first five in and out-of-plane bending and the torsional modes of the blade. The analyses results of this study are then used as a benchmark prior to modal testing, where the experiments over the produced wind turbine rotor blade has approved the analytical calculations.

Keywords: Dynamic analysis, Fiber Reinforced Composites, Horizontal axis wind turbine blade, Hand-wet layup, Modal Testing.

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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