scholarly journals An impulse-based derivation of the Kutta–Joukowsky equation for wind turbine thrust

2021 ◽  
Vol 6 (1) ◽  
pp. 191-201
Author(s):  
Eric J. Limacher ◽  
David H. Wood
Keyword(s):  
Wind Turbine ◽  
Control Volume ◽  
Finite Thickness ◽  
Speed Ratio ◽  
Near Wake ◽  
Vortex Sheets ◽  
Wide Range ◽  
Uniform Case ◽  
Control Volumes ◽  
Classical Derivation

Abstract. Using the concept of impulse in control volume analysis, we derive general expressions for wind turbine thrust in a constant, spatially uniform wind. The absence of pressure in the impulse equations allows for their application in the near wake, where the flow is assumed to be steady in the frame of reference rotating with the blades. The assumption of circumferential uniformity in the near wake – as applies when the number of blades or the tip speed ratio tends to infinity – is needed to reduce these general expressions to the Kutta–Joukowsky (KJ) equation for blade-element thrust. The present derivation improves upon the classical derivation based on the Bernoulli equation by allowing the flow to be rotational in the near wake. The present derivation also yields intermediate expressions for thrust that are valid for a finite number of blades and trailing vortex sheets of finite thickness. For the circumferentially uniform case, our analysis suggests that the magnitudes of the radial velocity and the axial induction factor must be equal somewhere on the plane containing the rotor, and we cite previous studies that show this to occur near the rotor tip across a wide range of thrust coefficients. The derivation reveals one further complication; when deriving the KJ equations using annular control volumes, the existence of vorticity on the lateral control surfaces may cause the local blade loading to differ from the KJ equation, but the magnitude of these deviations is not explored. This complication is not visible to the classical derivation due to its neglect of vorticity.

Modeling and Simulation of a Supercharger

1988 ◽  
Vol 110 (3) ◽  
pp. 316-323 ◽  
Author(s):  
Raymond Merala ◽  
Mont Hubbard ◽  
Takashi Miyano
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Design Parameters ◽  
Graph Models ◽  
Side Plate ◽  
Predicting Performance ◽  
Wide Range ◽  
Time Histories ◽  
Energy Equations ◽  
Control Volumes

A dynamic model is developed for simulating and predicting performance for superchargers of relatively arbitrary geometric configuration. A thermodynamic control volume approach and bond graph models are used to derive continuity and energy equations linking the various control volumes. Bond graphs also serve to study and understand the causal implications of laws governing flows between control volumes and system dynamics. Heat transfer is neglected. Simulation outputs include time histories of pressure, temperature, mass, and energy associated with each control volume, time histories of the various flows in the supercharger, and overall volumetric efficiency. Volumetric efficiencies are predicted over a wide range of speed/pressure ratio combinations and are within three percent of experimentally measured values. The simulation is used to investigate the sensitivity of supercharger performance to several key design parameters, including rotor-rotor separation, and rotor-housing and side plate clearance distances.

The Starting Behavior Analysis of a Micro Horizontal Axis Wind Turbine

2014 ◽  
Vol 1079-1080 ◽  
pp. 543-546 ◽  
Author(s):  
Zhi Kui Wang ◽  
Yi Bao Chen ◽  
Gwo Chung Tsai
Keyword(s):  
Wind Turbine ◽  
Renewable Energy Sources ◽  
Point Of View ◽  
Horizontal Axis ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Horizontal Axis Wind Turbine ◽  
Operational Characteristics ◽  
Start Up ◽  
Wide Range

The wind turbines have gained a wide range of applications in Renewable Energy Sources (RES) by virtue of its dominant advantages, and it has achieved almost the state-of-the-art from the engineering point of view. Nevertheless, the starting behavior which plays a prominent role in wind power generation has achieved few studies up to this moment. We conducted this analysis of a micro horizontal axis wind turbine (MHAWT) on its starting behavior to give insight into its start-up torque as well as its start-up speed on an assumption that it is rigid body, and some relative simplification on its structure are adopted meanwhile. The wind turbine's power coefficient CP, tip-speed-ratio l along with torque coefficient CT were taken into consideration and discussed to a large extent in order to having a relative clear cognition of its operational characteristics.

scholarly journals Determination of the Angle of Attack on a Research Wind Turbine Rotor Blade Using Surface Pressure Measurements

2020 ◽  
Author(s):  
Rodrigo Soto-Valle ◽  
Sirko Bartholomay ◽  
Joerg Alber ◽  
Marinos Manolesos ◽  
Christian Navid Nayeri ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Turbine Rotor ◽  
Speed Ratio ◽  
Horizontal Axis Wind Turbine ◽  
Turbine Rotor Blade ◽  
Wide Range ◽  
Wind Turbine Rotor

Abstract. In this paper, a method to determine the angle of attack on a wind turbine rotor blade using a chordwise pressure distribution measurement was applied. The approach uses a reduced number of pressure taps data located close to the blade leading edge. The results were compared with three 3-hole probes located at different radial positions and analytical calculations. The experimental approaches are based on the 2-D flow assumption; the pressure tap method is an application of the thin airfoil theory and the 3-hole probe method uses external probe measurements and applies geometrical and induction corrections. The experiments were conducted in the wind tunnel at the Hermann Föttinger Institut of the Technische Unversität Berlin. The research turbine is a three-bladed upwind horizontal axis wind turbine model with a rotor diameter of 3 m. The measurements were carried out at rated condition with a tip speed ratio of 4.35 and different yaw and pitch angles were tested in order to compare both methods over a wide range of conditions. Results show that the pressure taps method is suitable with a similar angle of attack results as the 3-hole probes for the aligned case. When a yaw misalignment was introduced the method captures the same trend and feature of the analytical estimations. Nevertheless, it is not able to capture the tower influence. Regarding the influence of pitching the blades, a linear relationship between the angle of attack and pitch angle was found.

scholarly journals Development of a Computational System to Improve Wind Farm Layout, Part I: Model Validation and Near Wake Analysis

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 940 ◽  
Author(s):  
Rafael Rodrigues ◽  
Corinne Lengsfeld
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Wind Farm ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Near Wake ◽  
Tip Speed Ratio ◽  
Wind Farm Layout

The first part of this work describes the validation of a wind turbine farm Computational Fluid Dynamics (CFD) simulation using literature velocity wake data from the MEXICO (Model Experiments in Controlled Conditions) experiment. The work is intended to establish a computational framework from which to investigate wind farm layout, seeking to validate the simulation and identify parameters influencing the wake. A CFD model was designed to mimic the MEXICO rotor experimental conditions and simulate new operating conditions with regards to tip speed ratio and pitch angle. The validation showed that the computational results qualitatively agree with the experimental data. Considering the designed tip speed ratio (TSR) of 6.6, the deficit of velocity in the wake remains at rate of approximately 15% of the free-stream velocity per rotor diameter regardless of the free-stream velocity applied. Moreover, analysis of a radial traverse right behind the rotor showed an increase of 20% in the velocity deficit as the TSR varied from TSR = 6 to TSR = 10, corresponding to an increase ratio of approximately 5% m·s−1 per dimensionless unit of TSR. We conclude that the near wake characteristics of a wind turbine are strongly influenced by the TSR and the pitch angle.

scholarly journals Development of a Computational System to Improve Wind Farm Layout, Part II: Wind Turbine Wakes Interaction

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1328 ◽  
Author(s):  
Rafael Rodrigues ◽  
Corinne Lengsfeld
Keyword(s):  
Wind Turbine ◽  
Pitch Angle ◽  
Wind Farm ◽  
Wake Flow ◽  
Design Parameters ◽  
Speed Ratio ◽  
Near Wake ◽  
Wind Farm Layout ◽  
Wake Effects ◽  
Far Wake

The second part of this work describes a wind turbine Computational Fluid Dynamics (CFD) simulation capable of modeling wake effects. The work is intended to establish a computational framework from which to investigate wind farm layout. Following the first part of this work that described the near wake flow field, the physical domain of the validated model in the near wake was adapted and extended to include the far wake. Additionally, the numerical approach implemented allowed to efficiently model the effects of the wake interaction between rows in a wind farm with reduced computational costs. The influence of some wind farm design parameters on the wake development was assessed: Tip Speed Ratio (TSR), free-stream velocity, and pitch angle. The results showed that the velocity and turbulence intensity profiles in the far wake are dependent on the TSR. The wake profile did not present significant sensitivity to the pitch angle for values kept close to the designed condition. The capability of the proposed CFD model showed to be consistent when compared with field data and kinematical models results, presenting similar ranges of wake deficit. In conclusion, the computational models proposed in this work can be used to improve wind farm layout considering wake effects.

scholarly journals Determination of the angle of attack on a research wind turbine rotor blade using surface pressure measurements

2020 ◽  
Vol 5 (4) ◽  
pp. 1771-1792
Author(s):  
Rodrigo Soto-Valle ◽  
Sirko Bartholomay ◽  
Jörg Alber ◽  
Marinos Manolesos ◽  
Christian Navid Nayeri ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Angle Of Attack ◽  
Turbine Rotor ◽  
Speed Ratio ◽  
Horizontal Axis Wind Turbine ◽  
Turbine Rotor Blade ◽  
Wide Range ◽  
Wind Turbine Rotor

Abstract. In this paper, a method to determine the angle of attack on a wind turbine rotor blade using a chordwise pressure distribution measurement was applied. The approach used a reduced number of pressure tap data located close to the blade leading edge. The results were compared with the measurements from three external probes mounted on the blade at different radial positions and with analytical calculations. Both experimental approaches used in this study are based on the 2-D flow assumption; the pressure tap method is an application of the thin airfoil theory, while the probe method applies geometrical and induction corrections to the measurement data. The experiments were conducted in the wind tunnel at the Hermann Föttinger Institut of the Technische Universität Berlin. The research turbine is a three-bladed upwind horizontal axis wind turbine model with a rotor diameter of 3 m. The measurements were carried out at rated conditions with a tip speed ratio of 4.35, and different yaw and pitch angles were tested in order to compare the approaches over a wide range of conditions. Results show that the pressure tap method is suitable and provides a similar angle of attack to the external probe measurements as well as the analytical calculations. This is a significant step for the experimental determination of the local angle of attack, as it eliminates the need for external probes, which affect the flow over the blade and require additional calibration.

RANS Computations of MEXICO Rotor in Uniform and Yawed Inflow

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Christina Tsalicoglou ◽  
Samira Jafari ◽  
Ndaona Chokani ◽  
Reza S. Abhari
Keyword(s):  
Wind Turbine ◽  
Wind Farms ◽  
Computational Effort ◽  
Navier Stokes ◽  
Speed Ratio ◽  
Flow Properties ◽  
Horizontal Axis Wind Turbine ◽  
Near Wake ◽  
Measured Flow ◽  
Rans Simulations

Full Reynolds-averaged Navier–Stokes (RANS) simulations of the flow in the near wake of a three-bladed horizontal-axis wind turbine are presented. The simulations, which are based on the model experiments in controlled conditions (MEXICO) experiment and include the complete rotor, nacelle, and tower show good agreement with experimental data, with 4% difference relative to measured flow properties. The flow properties in the near wake are detailed for both uniform and nonuniform flow conditions. The effects of increasing tip-speed ratio and a yawed inflow of 30 deg are studied. The full RANS simulations are used to support the development of an immersed wind turbine model at ETH Zurich. This model allows for modeling of the wake evolution and interactions in wind farms, for multiple turbines, with substantially reduced computational effort.

scholarly journals Derivation of an Impulse Equation for Wind Turbine Thrust

2019 ◽  
Author(s):  
Eric J. Limacher ◽  
David H. Wood
Keyword(s):  
Radial Velocity ◽  
Wind Turbine ◽  
Control Volume ◽  
Necessary Condition ◽  
Speed Ratio ◽  
Exact Equation ◽  
Vortex Lines ◽  
New Equation ◽  
Impulse Equation ◽  
Blade Element

Abstract. Using the concept of impulse in control volume (CV) analysis, we derive a new equation for steady wind turbine thrust in a constant, spatially uniform wind. This equation contains the circumferential velocity and tip speed ratio. We determine the conditions under which the new equation reduces to the standard equation involving only the axial velocity. A major advantage of an impulse formulation is that it removes the pressure and introduces the vorticity, allowing the equation to be used unambiguously immediately behind the blades. Using two CVs with this downwind end – one rotating with the blades, and one stationary – highlights different aspects of the analysis. We assume that the vorticity is frozen relative to an observer rotating with the blades, so the vortex lines follow the local streamlines in the rotating frame and vorticity does not appear explicitly in the impulse equation for force. In the stationary frame, streamlines and vortex lines intersect, and one of the thrust terms can be interpreted as the effect of wake rotation. The impulse analysis also shows the significance of the radial velocity in wind turbine aerodynamics. By assuming both the radial and axial velocities are continuous through the rotor disk, their contributions to the final thrust expression cancel to leave an expression dependent on azimuthal velocity alone. The final integral equation for thrust can be viewed as a generalization of the Kutta–Joukowsky theorem for the rotor forces. We give a proof, for the first time, for the conditions under which the Kutta–Joukowsky equations apply. The analysis is then extended to the blade elements comprising the rotor. The new formulation gives a very simple, exact equation for blade element thrust which is the major contribution of this study. By removing the pressure partly through the kinetic energy contribution of the radial velocity, the new equation circumvents the long-standing concern over the role the pressure forces acting on the expanding annular streamtube intersecting each blade element. It is shown that the necessary condition for blade-element independence of the conventional thrust equation – that which involves the axial induction factor – is the constancy of the vortex pitch in the wake.

RANS Computations of Wind Turbine Near-Wake Aerodynamics in Uniform and Yawed Inflow

2013 ◽  
Author(s):  
C. Tsalicoglou ◽  
S. Jafari ◽  
N. Chokani ◽  
R. S. Abhari
Keyword(s):  
Wind Turbine ◽  
Wind Farms ◽  
Computational Effort ◽  
Speed Ratio ◽  
Flow Properties ◽  
Horizontal Axis Wind Turbine ◽  
Near Wake ◽  
Measured Flow ◽  
Rans Simulations ◽  
Good Agreement

Full RANS simulations of the flow in the near wake of a three-bladed horizontal-axis wind turbine are presented. The simulations, which are based on the MEXICO experiment and include the complete rotor, nacelle and tower, show good agreement with experimental data, with 4% difference relative to measured flow properties. The flow properties in the near wake are detailed for both uniform and non-uniform flow conditions. The effects of increasing tip-speed ratio and of yawed inflow of 30° are studied. The full RANS simulations are used to support the development of an immersed wind turbine model at ETH Zurich. This model allows for modeling of the wake evolution and interactions in wind farms, for multiple turbines, with substantially reduced computational effort.

scholarly journals Research on Zero-Voltage Ride Through Control Strategy of Doubly Fed Wind Turbine

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2287
Author(s):  
Kaina Qin ◽  
Shanshan Wang ◽  
Zhongjian Kang
Keyword(s):  
Wind Turbine ◽  
Wind Power ◽  
Control Strategy ◽  
Large Scale ◽  
Sliding Mode ◽  
Stable Operation ◽  
Wide Range ◽  
Dc Bus ◽  
Doubly Fed ◽  
Zero Voltage

With the rapid increase in the proportion of the installed wind power capacity in the total grid capacity, the state has put forward higher and higher requirements for wind power integration into the grid, among which the most difficult requirement is the zero-voltage ride through (ZVRT) capability of the wind turbine. When the voltage drops deeply, a series of transient processes, such as serious overvoltage, overcurrent, or speed rise, will occur in the motor, which will seriously endanger the safe operation of the wind turbine itself and its control system, and cause large-scale off-grid accident of wind generator. Therefore, it is of great significance to improve the uninterrupted operation ability of the wind turbine. Doubly fed induction generator (DFIG) can achieve the best wind energy tracking control in a wide range of wind speed and has the advantage of flexible power regulation. It is widely used at present, but it is sensitive to the grid voltage. In the current study, the DFIG is taken as the research object. The transient process of the DFIG during a fault is analyzed in detail. The mechanism of the rotor overcurrent and DC bus overvoltage of the DFIG during fault is studied. Additionally, the simulation model is built in DIgSILENT. The active crowbar hardware protection circuit is put into the rotor side of the wind turbine, and the extended state observer and terminal sliding mode control are added to the grid side converter control. Through the cooperative control technology, the rotor overcurrent and DC bus overvoltage can be suppressed to realize the zero-voltage ride-through of the doubly fed wind turbine, and ensure the safe and stable operation of the wind farm. Finally, the simulation results are presented to verify the theoretical analysis and the proposed control strategy.

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