The Flutter of a Helicopter Rotor Blade in Forward Flight

1970 ◽  
Vol 21 (1) ◽  
pp. 18-48 ◽  
Author(s):  
C. W. Stammers
Keyword(s):  
Equations Of Motion ◽  
Approximate Solutions ◽  
Speed Ratio ◽  
Forward Speed ◽  
Forward Flight ◽  
Helicopter Blade ◽  
Integer Multiple ◽  
Tip Speed Ratio ◽  
Half Integer ◽  
Helicopter Rotor Blade

SummaryThe nature of flapping torsion flutter of a helicopter blade in forward flight is discussed. The essential complication in the analysis is the presence of periodic coefficients in the equations of motion; approximate solutions are obtained by use of a perturbation procedure. An unusual behaviour of the flutter equations which occurs when the fundamental frequency of flutter is a half-integer multiple of rotational speed is studied. Two different instability mechanisms can be distinguished and are related to the two energy sources in the system, namely the rotation of the rotor and the forward speed of the helicopter. It is found that forward flight can have a significant stabilising influence on flutter and that, as the tip speed ratio increases, flutter occurs predominantly at half-integer frequencies. The results are confirmed by the use of a numerical method.

Dynamic Stall: The Case of the Vertical Axis Wind Turbine

1986 ◽  
Vol 108 (2) ◽  
pp. 140-145 ◽  
Author(s):  
A. Laneville ◽  
P. Vittecoq
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Leading Edge ◽  
Vertical Axis ◽  
Dynamic Stall ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Airfoil Surface ◽  
Helicopter Blade ◽  
Tip Speed Ratio

This paper presents the results of an experimental investigation on a driven Darrieus turbine rotating at different tip speed ratios. For a Reynolds number of 3.8 × 104, the results indicate the presence of dynamic stall at tip speed ratio less than 4, and that helicopter blade aerodynamics can be used in order to explain some aspects of the phenomenon. It was observed that in deep stall conditions, a vortex is formed at the leading edge; this vortex moves over the airfoil surface with 1/3 of the airfoil speed and then is shed at the trailing edge. After its shedding, the vortex can interact with the airfoil surface as the blade passes downstream.

Dynamics of a Wheeled Cart Driven by a Savonius Rotor

2021 ◽  
Vol 22 (5) ◽  
pp. 254-261
Author(s):  
A. P. Holub ◽  
A. F. Zubkov ◽  
A. A. Masterova ◽  
Y. D. Selyutskiy
Keyword(s):  
Wind Turbines ◽  
Equations Of Motion ◽  
Aerodynamic Characteristics ◽  
Speed Ratio ◽  
Aerodynamic Load ◽  
Rectilinear Motion ◽  
Tip Speed Ratio ◽  
Savonius Rotor ◽  
Wind Speeds ◽  
Analysis Of Dynamics

Savonius rotor is one of relatively wide-spread type of wind turbines. The rotation rate of this rotor is considerably lower than that of horizontal axis wind turbines and Darrieus wind turbines. However, it starts rotating at small wind speeds, doesn’t require any additional devices to ensure its re-orientation in case of change of the wind direction, and generates a rather large torque. Therefore, it is suitable for use as a drive in different mechanical and electromechanical systems. In the present paper, dynamics of rectilinear motion of a wheeled cart is studied, which is driven by Savonius rotor installed on it. It is assumed that the wind makes a certain constant angle with the line, along which the cart moves. The aerodynamic load upon the rotor is described with an empirical model, in the context of which the aerodynamic characteristics (aerodynamic torque, drag and lateral force coefficients) are represented as Fourier series with respect to the rotor revolution angle, the coefficients of the series being functions of the rotor tip speed ratio (dimensionless angular speed). Experiments were performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University intended to measure aerodynamic characteristics of the rotor at different wind speeds and rotor angular speeds. Based on experimental data, functions were proposed that approximately describe the dependence of the above mentioned coefficients upon the tip speed ratio. The obtained dependences were used for analysis of dynamics of the cart driven by the Savonius rotor. The equations of motion are averaged with respect to the angle of revolution of rotor. Steady solutions of this averaged system are studied. It is shown that, for certain values of parameters, there exist two attracting steady motions corresponding to different directions of the cart velocity. Cart dynamics in the context of the full system of equations of motion is compared with its dynamics in the context of the averaged system.

scholarly journals Performance assessment and optimization of a helical Savonius wind turbine by modifying the Bach’s section

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
M. Niyat Zadeh ◽  
M. Pourfallah ◽  
S. Safari Sabet ◽  
M. Gholinia ◽  
S. Mouloodi ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Performance Assessment ◽  
Turbulent Flows ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Tip Speed Ratio ◽  
Basic Model ◽  
Turbine Performance ◽  
Primary Model ◽  
Savonius Wind Turbine

AbstractIn this paper, we attempted to measure the effect of Bach’s section, which presents a high-power coefficient in the standard Savonius model, on the performance of the helical Savonius wind turbine, by observing the parameters affecting turbine performance. Assessment methods based on the tip speed ratio, torque variation, flow field characterizations, and the power coefficient are performed. The present issue was stimulated using the turbulence model SST (k- ω) at 6, 8, and 10 m/s wind flow velocities via COMSOL software. Numerical simulation was validated employing previous articles. Outputs demonstrate that Bach-primary and Bach-developed wind turbine models have less flow separation at the spoke-end than the simple helical Savonius model, ultimately improving wind turbines’ total performance and reducing spoke-dynamic loads. Compared with the basic model, the Bach-developed model shows an 18.3% performance improvement in the maximum power coefficient. Bach’s primary model also offers a 12.4% increase in power production than the initial model’s best performance. Furthermore, the results indicate that changing the geometric parameters of the Bach model at high velocities (in turbulent flows) does not significantly affect improving performance.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Numerical Research on the Characteristics of Lift-Drag Type Vertical Axis Wind Turbine

2012 ◽  
Vol 189 ◽  
pp. 448-452
Author(s):  
Yan Jun Chen ◽  
Guo Qing Wu ◽  
Yang Cao ◽  
Dian Gui Huang ◽  
Qin Wang ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Vertical Axis ◽  
Chord Length ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Tip Speed Ratio ◽  
Middle Range ◽  
Parabolic Form ◽  
Cfd Method

Numerical studies are conducted to research the performance of a kind of lift-drag type vertical axis wind turbine (VAWT) affected by solidity with the CFD method. Moving mesh technique is used to construct the model. The Spalart-Allmaras one equation turbulent model and the implicit coupled algorithm based on pressure are selected to solve the transient equations. In this research, how the tip speed ratio and the solidity of blade affect the power coefficient (Cp) of the small H-VAWT is analyzed. The results indicate that Cp curves exhibit approximate parabolic form with its maximum in the middle range of tip speed ratio. The two-blade wind turbine has the lowest Cp while the three-blade one is more powerful and the four-blade one brings the highest power. With the certain number of blades, there is a best chord length, and too long or too short chord length may reduce the Cp.

scholarly journals Implementation of Control System for Hydrokinetic Energy Converter

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Katarina Yuen ◽  
Senad Apelfröjd ◽  
Mats Leijon
Keyword(s):  
Control System ◽  
Laboratory Tests ◽  
Vertical Axis ◽  
Load Control ◽  
Speed Ratio ◽  
Energy Converter ◽  
Hydrokinetic Energy ◽  
Tip Speed Ratio ◽  
The Town ◽  
Design Construction

At Uppsala University, a research group is investigating a system for converting the power in freely flowing water using a vertical-axis turbine directly connected to a permanent magnet generator. An experimental setup comprising a turbine, a generator, and a control system has been constructed and will be deployed in the Dalälven river in the town of Söderfors in Sweden. The design, construction, simulations, and laboratory tests of the control system are presented in this paper. The control system includes a startup sequence for the turbine and load control. These functions have performed satisfactorily in laboratory tests. Simulations of the system show that the power output is not maximized at the same tip-speed ratio as that which maximizes the turbine power capture.

scholarly journals Effects of tip speed ratio on the performance of an H-Darriues wind turbine with NACA 4415 air foil

2020 ◽  
Author(s):  
Yogie P. Sibagariang ◽  
Indro Pramono ◽  
Koki Kishinami ◽  
Himsar Ambarita
Keyword(s):  
Wind Turbine ◽  
Speed Ratio ◽  
Tip Speed Ratio
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