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David Wood - One of the best experts on this subject based on the ideXlab platform.
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Performance analysis of wind turbines at low tip-Speed Ratio using the Betz-Goldstein model
Energy Conversion and Management, 2016Co-Authors: Jerson Rogério Pinheiro Vaz, David WoodAbstract:Abstract Analyzing wind turbine performance at low tip-Speed Ratio is challenging due to the relatively high level of swirl in the wake. This work presents a new approach to wind turbine analysis including swirl for any tip-Speed Ratio. The methodology uses the induced velocity field from vortex theory in the general momentum theory, in the form of the turbine thrust and torque equations. Using the constant bound circulation model of Joukowsky, the swirl velocity becomes infinite on the wake centreline even at high tip-Speed Ratio. Rankine, Vatistas and Delery vortices were used to regularize the Joukowsky model near the centreline. The new formulation prevents the power coefficient from exceeding the Betz-Joukowsky limit. An alternative calculation, based on the varying circulation for Betz-Goldstein optimized rotors is shown to have the best general behavior. Prandtl’s approximation for the tip loss and a recent alternative were employed to account for the effects of a finite number of blades. The Betz-Goldstein model appears to be the only one resistant to vortex breakdown immediately behind the rotor for an infinite number of blades. Furthermore, the dependence of the induced velocity on radius in the Betz-Goldstein model allows the power coefficient to remain below Betz-Joukowsky limit which does not occur for the Joukowsky model at low tip-Speed Ratio.
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Maximum wind turbine performance at low tip Speed Ratio
Journal of Renewable and Sustainable Energy, 2015Co-Authors: David WoodAbstract:Wind turbines can approach the Betz-Joukowsky limit on maximum power only at sufficiently high tip Speed Ratio: in practice, for Ratios in excess of about seven. This paper analyses the performance of a turbine with an infinite number of blades as the tip Speed Ratio decreases to zero, beginning with the two traditional ways of determining the maximum power. The first is the “Glauert” optimization of the power extracted at every radius and the second is the “Betz-Goldstein” optimization of the whole rotor with the wake represented as a rigid helicoidal sheet of constant pitch. At high tip Speed Ratio, the two methods give very similar power and both asymptote to the Betz-Joukowsky limit. As the Ratio approaches zero, the differences become significant. It is shown that Glauert's analysis does not account for effect of the varying pitch on the axial velocity. In addition, there is a large and unphysical energy extraction by a stationary rotor, and an unphysical constant circumferential velocity. Glauert's analysis, however, gives positive torque on a stationary rotor, which is necessary to start a wind turbine, but the torque at very low tip Speed Ratio seems too high. In contrast, the Betz-Goldstein analysis implies no torque on a stationary rotor but the circumferential velocity is zero on the axis of rotation. A modification is proposed to the Betz-Goldstein analysis to yield positive torque on a stationary rotor. The modified Betz-Goldstein torque coefficient never exceeds 1/2 and the power is less than the Glauert optimum. Finally, the analysis for varying pitch is corrected and the power maximized numerically. The modification applied to the Betz-Goldstein rotor is required to produce torque on the stationary rotor. The maximum torque coefficient was 0.55, and the maximum power was again less than the Glauert maximum. As tip Speed Ratio increases, the power from all methods asymptotes to the Betz-Joukowsky limit.
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Ideal wind turbine performance at very low tip Speed Ratio
Journal of Renewable and Sustainable Energy, 2014Co-Authors: David WoodAbstract:At very low tip Speed Ratios, wind turbine rotors behave similarly to stationary wings for which the well-known lifting line analysis gives the optimal loading. Lifting line analysis is applied to a stationary rotor of N blades for N = 1, 2, and 4. Analytic (for N = 1 and 2) or semi-analytic solutions (for N = 4) agree with the classical results obtained by conformal mapping. The present solutions compare well with numerical solutions for the Goldstein function for optimally loaded propeller or wind turbine rotors at low tip Speed Ratio. In all cases, the induced velocity is linear with radius. Assuming this result applies for all N, lifting line analysis is recast as a singular integral equation whose solution agrees with Goldstein's obtained using the same conformal mappings as in his general analysis for any tip Speed Ratio. The implication is that the assumed induced velocity distribution is correct, and is, therefore, fundamentally different from that at high tip Speed Ratios when the induced velocit...
Weidong Zhu - One of the best experts on this subject based on the ideXlab platform.
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Performance Analysis and Optimization of a Vertical-Axis Wind Turbine with a High Tip-Speed Ratio
Energies, 2021Co-Authors: Inderjit Chopra, Weidong ZhuAbstract:In this work, the aerodynamic performance and optimization of a vertical-axis wind turbine with a high tip-Speed Ratio are theoretically studied on the basis of the two-dimensional airfoil theory. By dividing the rotating plane of the airfoil into the upwind and downwind areas, the relationship among the angle of attack, azimuth, pitch angle, and tip-Speed Ratio is derived using the quasi-steady aerodynamic model, and aerodynamic loads on the airfoil are then obtained. By applying the polynomial approximation to functions of lift and drag coefficients with the angle of attack for symmetric and asymmetric airfoils, respectively, explicit expressions of aerodynamic loads as functions of the angle of attack are obtained. The performance of a fixed-pitch blade is studied by employing a NACA0012 model, and influences of the tip Speed Ratio, pitch angle, chord length, rotor radius, incoming wind Speed and rotational Speed on the performance of the blade are discussed. Furthermore, the optimization problem based on the dynamic-pitch method is investigated by considering the maximum value problem of the instantaneous torque as a function of the pitch angle. Dynamic-pitch laws for symmetric and asymmetric airfoils are derived.
Inderjit Chopra - One of the best experts on this subject based on the ideXlab platform.
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Performance Analysis and Optimization of a Vertical-Axis Wind Turbine with a High Tip-Speed Ratio
Energies, 2021Co-Authors: Inderjit Chopra, Weidong ZhuAbstract:In this work, the aerodynamic performance and optimization of a vertical-axis wind turbine with a high tip-Speed Ratio are theoretically studied on the basis of the two-dimensional airfoil theory. By dividing the rotating plane of the airfoil into the upwind and downwind areas, the relationship among the angle of attack, azimuth, pitch angle, and tip-Speed Ratio is derived using the quasi-steady aerodynamic model, and aerodynamic loads on the airfoil are then obtained. By applying the polynomial approximation to functions of lift and drag coefficients with the angle of attack for symmetric and asymmetric airfoils, respectively, explicit expressions of aerodynamic loads as functions of the angle of attack are obtained. The performance of a fixed-pitch blade is studied by employing a NACA0012 model, and influences of the tip Speed Ratio, pitch angle, chord length, rotor radius, incoming wind Speed and rotational Speed on the performance of the blade are discussed. Furthermore, the optimization problem based on the dynamic-pitch method is investigated by considering the maximum value problem of the instantaneous torque as a function of the pitch angle. Dynamic-pitch laws for symmetric and asymmetric airfoils are derived.
Mukka Govardhan - One of the best experts on this subject based on the ideXlab platform.
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Studies on the Outline of Flow Improvement With Speed Ratio in a Counter Rotating Turbine
Volume 1: Compressors Fans and Pumps; Turbines; Heat Transfer; Structures and Dynamics, 2019Co-Authors: Rayapati Subbarao, Mukka GovardhanAbstract:Abstract Flow through the Counter Rotating Turbine (CRT) stage is more complex due to the presence of two rotors that rotate in the opposite direction, the spacing between them and the tip clearance provided on rotors. This flow aspect may change, if we change the parameters like Speed, spacing and blade angles. Current effort contains simulation studies on the flow topology of CRT through dissimilar Speed Ratios in the range of 0.85–1.17. CRT components stator and the rotors are modelled. At nozzle inlet, stagnation pressure boundary condition is used. At the turbine stage or rotor 2 outlet, mass flow rate is specified. Skin friction lines are drawn on rotor 1 as well as rotor 2 on all over the blade. Not much variation of skin friction lines is witnessed in rotor 1 on the pressure side with exception to the position of the sepaRation line close to leading edge. On suction side, skin friction lines are more uniform when the Speed Ratio is greater than 1. Skin friction lines on rotor 2 pressure surface show the presence of re-attachment lines. The position of the nodal point of sepaRation near the hub remained same, but the strength is decreasing with Speed Ratio. On rotor 2 suction side, near the tip, all along the stream wise direction, line of re-attachment is observed that spreads from leading edge to trailing edge, whose strength is varying with Speed Ratio. Near the hub as well, line of re-attachment is observed, which is of more intensity in lower Speed Ratios. For the same region in rotor 1, there is proper reattachment as nodes are observed instead of lines, suggesting that more improved flow is occurring in rotor 1 than rotor 2. Thus, the present paper identifies the flow modification with Speed Ratio in a counter rotating turbine. Also, effort is made to see the consequence of flow change on the output of CRT.
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Computational Studies on the Effect of Speed Ratio and Stagger Angle in a Counter Rotating Turbine with Respect to Flow Field and Performance
Fluid Mechanics and Fluid Power – Contemporary Research, 2016Co-Authors: Rayapati Subbarao, Mukka GovardhanAbstract:Counter rotating turbine is an axial turbine with nozzle followed by a rotor and another rotor that rotates in the opposite direction of the first one. Studies show that Speed Ratio and stagger angle are the two important parameters that affect the performance of a turbomachine. Present work involves computationally studying the performance and flow field of CRT for different Speed Ratios and stagger angles. Turbine components nozzle, rotor 1 and rotor 2 are modeled for the cases of CRT with and without staggering. Total pressure and entropy distributions across the blade rows are used to describe the flow through CRT. Enthalpy losses and TKE are estimated at the exit of the blade rows and performance curves are plotted for all the configuRations. Results show that the flow composition in rotors varied with Speed Ratio and improved at the inlet of the second rotor in staggering cases. Due to this the performance of rotor 2 and CRT improved with Speed Ratio and staggering. Results confirm the beneficial aspect of varying Speeds and staggering of second rotor in CRT.
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Effect of Speed Ratio on the Performance and Flow Field of a Counter Rotating Turbine
Energy Procedia, 2014Co-Authors: Rayapati Subbarao, Mukka GovardhanAbstract:Abstract Counter Rotating Turbine (CRT) is an axial turbine with nozzle followed by a rotor and another rotor that rotates in the opposite direction of the first one. Studies show that Speed Ratio is one of the parameters that affect the performance of a turbomachine. Present work involves computationally studying the performance and flow field of CRT with different Speed Ratios ranging from 0.85 to 1.17. Equivalent mass flow rates of 0.091 to 0.137 are considered. Turbine components nozzle, rotor 1 and rotor 2 are modeled. Total pressure, velocity, entropy and turbulent kinetic energy distributions across the blade rows are used to describe the flow through CRT. Enthalpy, turbulent and secondary losses are estimated at the exit of the rotors. Performance curves are plotted for rotor 1, rotor 2 and CRT in all the configuRations. The performance of second rotor is improved in all the Speed Ratio cases. Overall efficiency of the CRT increased for Speed Ratios greater than 1 . Results confirm that losses vary with Speed Ratio and the performance of CRT can be enhanced by changing the rotational Speeds of the rotors.
Hirohisa Tanaka - One of the best experts on this subject based on the ideXlab platform.
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Speed Ratio control of a parallel layout double cavity half-toroidal CVT for four-wheel drive
JSAE Review, 2002Co-Authors: Hirohisa TanakaAbstract:Abstract A double cavity half-toroidal CVT has two variators, which gives a hint of a new four-wheel drive without a center differential gear unit by applying each of them to drive front and rear drive shafts independently. Torque re-circulation at cornering or different tire radii between front and rear tire is avoided by compensating the Speed Ratio of variator. The controller adjusts the attitude angle of power roller of the front variator against the rear by measuring the steering angle at cornering. This paper describes the Speed Ratio control system of the 4WD-CVT with Speed Ratio range of 1 : 8.7 and test results of vehicle motion mounted on a 3.2L RV.
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Stability of a Speed Ratio Control Servo-mechanism for a Half-Toroidal Traction Drive CVT
JSME international journal. Ser. C Dynamics control robotics design and manufacturing, 1993Co-Authors: Hirohisa Tanaka, Masatoshi EguchiAbstract:A continuously variable power transmission, CVT, has potential for the improvement of fuel economy and cruising comfort as an automotive propulsion system. A traction drive CVT changes its Speed Ratio by the control of side slip force on the Hertzian contact. This mechanism has the features of equal torque transmission of every rolling element and low wasted power for the Speed Ratio change, but sometimes falls into self-excited vibRation at higher rotating Speed. This paper describes the principle of the Speed Ratio changing mechanism of a half-toroidal traction drive CVT and offers a compensatory measure for stabilizing the electrohydraulically operated Speed Ratio control servomechanism.
