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In order to harness wind energy with high coefficients, horizontal axis wind turbines (HAWT), like propeller-type wind turbines, have an advantage in terms of practical utilization because of their scale merit. However, large size and high tip-speed ratio are inherently related to material strength problems and low frequency noise emissions to the environment. In contrast to HAWT, we will discuss a flapping-type turbine driven at low speed. The flapping turbine works using lift force like the HAWT, but employs a new wind turbine concept in the present report. The concept involves the unique flapping motion of a wind blade mounted on a Chebyshev-dyad linkage by which the wing transforms wind energy into mechanical rotation. Both static and dynamic numerical estimates are developed to optimize all fundamental parameters of this linkage in order to obtain the desired torque. In this paper, the results of primitive optimization for determining the fundamental characteristics of motion and the trajectory of the wind turbine blade are demonstrated in order to obtain smooth rotation of the generator-driving shaft. It is also shown that the present turbine can be driven at low speed with a suitable energy conversion rate. Moreover, the practicality of operating slow flapping-type wind turbines is demonstrated, focusing on usage near residential areas or, e.g., on rooftops owing to lower noise. The feasibility of “figure eight” trajectory diversity is discussed along with geometrical parameters. Assuming one-blade motion with a variable trajectory for optimization, the smooth motion and required torque at slow rotation speeds are studied.

To develop reliable wind power technology among the various renewable sources, a considerable amount of research has been conducted. Currently, it is possible to harness around 7.5 MW from a single unit whose size is larger than a Boeing 747 [

In this paper, we advocate a third category of wind turbines―a flapping type. The flapping wind turbine is a relatively new concept. We propose a novel wind turbine moving along a unique trajectory fabricated with the Chebyshev-dyad linkage. The blade flaps are controlled through various geometrical parameters for a given attack angle and wind velocity; the wing then produces unsteady lift and drag forces to generate rotational torque. Whereas preceding research related to HAWT focused on relatively higher tip speed ratios for optimum driving conditions of about 3 to 4 [

In order to find a suitable flapping motion, we must optimize several geometric parameters. In the present research, a Chebyshev-dyad linkage is connected to a single blade composed of a NACA 0012 airfoil mounted vertical to the flow direction, as shown in

path generation and b) continuous path generation. Point-to-point generation is concerned with a varying number of points on the path where the trajectory between these points is not important, whereas optimal synthesis methods are used for continuous path generation. In other words, the latter method focuses on minimizing constraints such as link-length ratios, transmission angles, and crank existence conditions [

The aim of the present research is to design a prototype wind turbine by optimizing various parameters to obtain sufficient torque under smooth flapping movement at low speed, producing lower turbine noise and mechanical vibrations while reducing the avian mortality rate. The simplicity of these kinematic linkage pairs in a planar layout without gears makes the design simpler, utilizing the unique trajectory of the blade. A schematic view is shown in

As shown in

ter of gravity of the wing was fixed at point K, i.e., it was fixed with ABK. The links AO and BC are connected with a deltoid, ABK, at points A and B, respectively. Points A, B, and C are free. The points O and C are the centers of revolution of links AO and BC, respectively. On rotating point A, point B moves in a rocking motion; path B and point K transform along path K as figure eight. In the succeeding section, the link length ratio

In order to estimate the efficiency of the resultant torque for the assumed parameters, the inner product between the direction of force generated at the nodal point K and its trajectory direction is important, detailed in

In this section, we describe the fundamental geometry for the reader’s convenience. According to the geometric relationship in

Coordinates of point A:

Coordinates of point B:

where the angle

Here, the angle

The value of

Point C is fixed at

The locus of point K is calculated as

The angle of attack of the wing is determined using the following relation with

Specification | Value |
---|---|

Airfoil | NACA 0012 |

Chord length, c | 0.2 m |

Wing span, b | 0.3 m |

Typical length, L_{1} | 0.05 m |

Additional linkage conditions | L_{2} = L_{4}, AB = BK |

the mounting angle,

where,

The fundamental specifications are listed in

Let us consider the balances of forces and moments at each linkage as shown in

Balancing link OA,

For link BC,

Balancing the plate ABK,

The lift and Drag forces are

Here,

As the trajectory analysis describes in the following section, a large angle of attack inevitably appears in a certain region. In this case, the wing enters a stall but maintains a large lift coefficient. On the other hand, the drag coefficient also becomes large owing to the stall. By designing a suitable trajectory, we can obtain an effective driving force; this is discussed in the following direction.

Note that the thirteen equations from Equations (11) to (23) include thirteen variables, so the set of equations is closed. These can be solved analytically to determine the torque

During this condition, the resultant force does not increase, so motion only eases on its track in the moving direction. Subsequently, forces cause acceleration and a gain in moment in the same direction as the continuous motion. When_{1} = 0˚ to 180˚, whe-

reas the remaining portion of movement is in the anti-clockwise direction depending upon the inner product of the forces.

The lift, drag, and torque of the system depend on the velocity of the wing relative to the free stream; hence, the relative velocity must be considered in the simulation. Through these simulations, we aim to design a suitable, relatively slow rated speed. Both static and dynamic numerical simulation has been conducted using MATLAB programming code.

In the previous section, we described the equations for static analysis. Here, we represent the equations for estimating the driving speed and describe modifications for the relative velocity when the turbine is in motion. In order to monitor the wing force, i.e., the lift and drag forces, a simulation model was developed to evaluate the forces produced at the node at any time step with the following assumptions:

・ The gravity force is not considered in the model.

・ The friction force in the mechanism is ignored.

・ The forces developed in the wind affect only the nodes without considering the moment.

・ The analysis model developed in the simulation is two-dimensional for all the cross-sectional views of the blade in its width direction.

The relative velocity is calculated with wing velocity as follows:

In the present system, the rotor speed is variable; therefore, the wing velocity should be calculated as indicated in the following equations:

Here, the number i represents the calculated nodal number. Using

The temporal angle of attack is evaluated with the mounting angle

and

where I, r, and M are the moment of inertia of the rotating disk, its radius, and its mass, respectively, which are tentatively assumed the rotor of the generator. Here, we supposed that M = 5 kg and r = 0.05 m. The mass has a significant influence in the simulation where a more realistic approach for angular velocity development is considered. The calculation was started at

Several geometrical parameters are considered, such as the deltoid angle,

The advantage and uniqueness of the present system involve the wide variation of the orbit of the blade. The trajectory K is obtained with Equations (8) and (9). The variation of the trajectory depends on the deltoid angle

care must be taken to avoid an abrupt change of the orbit. As shown in

To obtain the desired results in performance and higher values of torque, several values of

The variation of generated torque in each case strongly depends on the trajectory. The maximum value of the average torque determines the optimum condition for the design. The maximum average torque of 0.037 N.m was achieved for Ψ = 80˚ at a wind velocity of 5 m/s, as shown in

Furthermore, the direction of the resultant force of the wing and the orbital direction are consistent in each phase; a cosine value close to unity determines

the characteristics favorable for the design condition. In order to confirm the optimum coupler angle, on viewing the relation between the trajectories, the average torque value and the cosine value determine the fundamental characteristics of the mechanism. Even though the higher value of torque and the cosine value obtained at Ψ = 80˚ appear to present a more favorable condition for design, the shape of the trajectory is that of a figure eight with two different sizes of curves, breaking the symmetry of the path. Because of this, the optimum value at Ψ = 70˚ develops a more symmetric trajectory shape of a figure eight with relatively high average torque in comparison with other cases.

The mounting angle (

for a wind velocity of 5 m/s. Maximum average force is developed at around 80˚, which is considered as the optimum condition for the design.

1) Linear optimization

In this study, the link length of the dyad is an important variable parameter for transferring the generated resultant force from the wing to the shaft as torque. The trajectory and torque vary with even a small variation of the link length in the Chebyshev dyad mechanism. In other words, the length of each link and the position and distance of the frame support must be optimized for the best performance. The link lengths

consideration better performance and higher coefficient values. Furthermore, the negative torque generated at the end of an azimuth angle signifies a change in the direction of motion of the wind blade, where inertia governs the continuation of the motion.

Subsequently, _{2}, L_{3}, and L_{4} with individual variation to obtain the maximum torque as a linear change in the individual link lengths. Moreover, while considering the results of the torque value for optimization, the maximum torque was calculated for L_{2} and L_{3} lengths of 0.11 m and 0.09 m, respectively.

Furthermore, a higher value of torque is considered for optimizing the link length without accounting for the nature of its trajectory, leading to a higher torque. However, there might be a sharp bend in the trajectory motion owing to rapid change direction with an asymmetric trajectory as shown in

By considering static linear optimization, the optimized parameter determined up to now was the link length ratio of _{1} = 0.05 m and the rest of the link lengths equal to 0.1 m, the coupler angle

2) Optimization by changing parameters randomly

Instead of linear optimization, these parameters can be considered randomly to obtain a greater orbital direction component with the largest wing force with the average cosine value approaching unity, which is the optimal combination of parameters. For the optimal condition, the variable parameters obtained for the link length ratio _{1} = 0˚ to 90˚ and θ_{1} = 270˚ to 360˚ has a greater travel distance compared to the remaining azimuth angles.

The static optimum condition for the various parameters before dynamic analysis calculation for the internal coupler angle _{1} = 0.05 m and the rest of the link lengths are equal to 0.1 m. Hence,

Further dynamic analysis is conducted based on the optimum conditions obtained from static analysis to determine realistic results under various load conditions and wind speeds. The dynamic analysis gives the concept of performance and the characteristics of the new flapping-type wind turbine. In the relative wind velocity approach, the starting torque concept, extraction of a certain percentage of the developed torque after gaining some momentum, the mass of the rotating disc of radius 0.05 m, and angular velocity make the simulation model a conceptual design.

80% of the generated torque is transformed to overcome the load, whereas any remaining torque is used for the development of motion.

Angular velocity varies depending on time owing to the acceleration of the system, which starts from the rest condition and attains the full-load operating condition. At the beginning of the motion, a no-load condition is assumed, and after the rotor has accelerated, the full-load operating condition is taken into account.

The torque values obtained from both static and dynamic analysis are compared

for wind velocities of 5 m/s, 7 m/s, and 10 m/s for a full period (

Aiming to operate wind turbines in multi-use zones such as neighboring residential areas and to reduce noise annoyance, we performed design and development of a small vertical axis flapping wind turbine using a Chebyshev-dyad linkage. In order to confirm the feasibility of this system, we considered both static and dynamic numerical analyses. Different variable parameters for the flapping-type wind turbine were also analyzed to determine the optimum parameters for better performance.

The optimal Chebyshev-dyad link length ratio (

Considering the correlation of the inner product between the forces and the locus along the trajectory defines maximum forces along the slope of the trajectory to improve the characteristics of the wind turbine for different combinations of geometrical parameters. A simulation model was developed in order to quantify the force and the momentum in each phase of movement to improve the performance of the design. The torque developed from static analysis was compared with that from the dynamic analysis for verification of the simulation model, and the results showed good agreement. Although torque is generated within a cyclic rotation, it was found to vary owing to the variation of movement along a unique path with varying angles of attack; this makes the design more complicated when minimizing the fluctuations in each cycle. In future, authors would like to focus on experimental investigation for the present flapping wind turbine, which has a great influence to judge the turbine performance for practical utilization.

Alam, M.S. and Hirahara, H. (2017) Numerical Performance Assessment of a Flapping-Type Vertical Axis Wind Turbine with Chebyshev-Dyad Linkage. Smart Grid and Renewable Energy, 8, 53-74. https://doi.org/10.4236/sgre.2017.82004

Simplify all Equations (11)-(19), we get

By solving equations (36 & 39), we get

Therefore,

Finally, Torque value obtained as: