Abstract

Currently, the wind generator is gradually increased recently according to new status, so the dynamic and kinematic equation is needed to use to them as well. In this paper the power with speed and mass in wind turbine blades is discussed in detail. It is observed that in the low rotation the power will increase with the long wind blade. This paper will express the all kinds of these respects to adopt curve to explain the relation of them. It is observed that if the wind speed is 10.8m/s to 6.8m/s the average power will decrease from 300kW m/s to 50kW under the mass of wind turbine blades are from 3.3tons to 1.6tons at 40° that becomes cosine distribution. The decreasing α and β is the way from 0 to 83° to increase them. When α increases from 83° to 180° the power and force increase too. There is a certain power changes in power with 150kW and force with 15kN with β changing from 0 to 20°. Only rotating speed reaching a certain value can the maximum effect be.

Keywords: Wind generator; Dynamics; Wind speed; Equation; Turbine blades; α and β; angle

Introduction

The wind turbines are the latest to enter the market. To build wind turbines for environmental protection is an inevitable trend in the world. Although it is not as powerful or as efficient as other conventional thermal and hydro-electric generators, it is replacing them with abundance and sustainability. In places like Yantai city in Shandong province, huge wind turbines are set up in groups on hillsides to bring freshness and wind energy utilization, and even appear in the game world of some large cities. These huge structures have an unexpected power generation effect by slowly rotating the same huge impeller. Therefore, this paper discusses its energy utilization status from its efficiency and quantity to evaluate its physical significance. Here processing is the most important link, and then transportation and erection costs, but its use is not low. In 15 to 20 years since a wind turbine could be used, the calculations are low. In this time it would spin 2.16 million times and calculate energy up to 100 million Joules and 10 million Watts of power. That’s 50 times the size of a small city in the 70s and 80s. With 500 such generators, the total power would be 5 gWs and 50 gJs, about one-fifth of the 22,000 mWs of installed capacity of the three gorges reservoir. On the other hand the strong winds can quickly make up for their use, filling the countryside with the energy from wind turbines. At present, the number of wind turbines used by European and American countries is increasing year by year. China also is needed to catch up and keep in line with the international developed level. Therein 2,000 such turbines would be comparable to the Three Gorges Reservoir, China’s biggest generator. This means that an average medium-sized city can have nearly a quarter of the power generated by the Three Gorges Reservoir. Because these generators run 24 hours a day, there is a constant supply and quantity of electricity to these big cities without the interruption of power supply. Perfect storage function will really bring energy effect. Storing energy from strong winds for later use is an urgent problem for wind turbines. If you put it on a windy mountain, it will continue to generate electricity. At this time to set the number of more engines, in order to prepare for sporadic scattered wind brings the problem of insufficient wind power. The wind and water hybrid power generation is needed to solve the problem of energy shortage and continuity. Seawater utilization should also be included in the plan such as the use of tide and high tide, etc… In the case of typhoons and tsunamis, their strength, especially fatigue strength, is needed to guarantee. Some typhoons can even pull up some trees. Therefore, the bending strength of the ground and straight head of the generator should be guaranteed to avoid economic losses. If the broken parts fly to buildings or roadside facilities, they can cause a second damaging effect, causing damage to public facilities and causing problems for the country such as repair. On the other hand, if there are energy reserved devices and methods to absorb this big source into them the abundant source will be maintained for us to use month by month. We can transform it into another style like wide water reservoir within leisure and abundant time and use it in necessity [1-12].

Model Establishment

The parameters of German Nordex N60, S70 and S77 models are shown in Table 1. The wind generator has the overall layout of the wind turbine with blade length l and it rotates at the speed of ω. From Figure 1 the wind speed v and force F and the wind speed and direction. The pitch angle β which is angle of blade chord and rotational plane obtains x-y direction of velocity and force of component, is the inlet air speed v in generator blade vxˎ vy and force Fxˎ Fy. Angle of attack α which convergence speed being the angle of inlet air and rotational relative synthesis speed and blade chord obtains x’-y’ direction of velocity and force of component is the main speed in turbine blade slope area. Flow angle f which is the angle of convergence speed and rotational relative synthesis speed. Since the uniform wind speed acts on the blade, then

dvL = dv (cosf)

Here, according to the law of conservation of energy

Here I is the inertia product, and m is the mass of the blade of the

Table 1: Data of Nordex wind turbine.

N60	N60	S70	S77
P, MW	1.3	1.5	1.5
V, m/s	60	70	77
L, m	29	34	37.5
Vrate ,m/s	15	13	13
Mrate ,tons	5	5.6	9.9
N r/m	12.8	19	17
Vin ,m/s	3	3	3
Vout ,m/s	25	25	25/20

Figure 1: schematic of wind speed and force resolution.

Here I is the inertial product, omega is the angular velocity, m is the blade mass, and v is the blade velocity.

P is blade power, Q is kinetic energy, and t is time, because

Therefore,     the     calculation    formula     of     acceleration    is

Here n is rotation r/m; vL is the wind speed m/s; vn is the rotation speed m/s; f is angle.

The calculated results are shown in Figure 2 and 3. Figure 2 (a~e) is the dynamic simulation relationship of the rotating a cycle of the wind turbine blade. The power & force and α angle attack are shown in Figure 2 (a~d) and Figure 3(a~d) respectively under the wind speed of 10.8 m/s and 6.8m/s at 40° amplitude. The Figure 2 and Figure 3 forms into cosine distribution, between speed and angle of attack is a cosine amplitude. Figure 2 is the power with the increase of angle of attack α becomes cosine curve. The average force is from 25kN to 7.5kN. In order to improve the efficiency, the three blades are taken together so that they act continuously with a difference of 120° to produce energy and output energy like a three-phase star generator. The most effective way to increase power is to increase speed, so high speed is the main factor to improve efficiency. As shown in Figure 2, the corresponding power generation energy increases with the increase of rotating speed. So we think the requirement is to wind speed. The second is blades mass. The more wind speed and blades mass, the more energy. Therefore, the speed and mass greater than the specified value is the necessary condition to obtain high power. In Figure 2(a~d) and Figure 3(a~d) the power and force decreases with the increasing α changes 0-80°& β changes 5-20°. The power and force becomes periodical cosine curve. The maximum average power is 300kW and force is 25kN at α is 40° and β is 5°. There is a certain power changes in power with 150kW and force with 15kN. It is known that the decreasing α and β is the way from 0 to 83° to increase them. When α increases from 83° to 180° the power and force increase too.

a) P, β is pitch angle, v=10.8m/s, m1=3.3tons

b) P, β is pitch angle, v=10.8m/s, m1=1.6tons

c) P, β is pitch angle, v=6.8 m/s, m1=3.3tons

 d) P, β is pitch angle, v=6.8 m/s, m1=1.6tons

Figure 2: Relations of power and angle of attack α in a cycle under v=6.8~10.6m/s and m1=1.6~3.3tons.

a) F, β is pitch angle, v=10.8m/s, m1=3.3tons

 b) F, β is pitch angle, v=10.8m/s, m1=1.6tons

 c) F, β is pitch angle, v=6.8m/s, m1=3.3tons

d) F, β is pitch angle, v=6.8m/s, m1=1.6tons

Figure 3: Relations of force and angle of attack α in a cycle under v=6.8~10.6m/s and m1=1.6~3.3tons.

Figure 3 shows the data between force and angle of attack with a blade mass of 3.3 tons and 1.6 tons at a speed of 10.8m/s and 6.8m/s at the blade length is 34m. It can be seen that in the first 80° the force drops sharply to 0kN, then it gradually increases. This indicates that the moment of inertia Jc is at work, that is, the huge blades with a mass of 9.9 tons~4.8 tons are slowly driven by the large start-up energy. It can be seen from Figure 3 (a &b) that the force increases near linearly with the increase of the speed of arrival. It indicates that a large amount of force is needed at the beginning of the drive, and the greater the mass, the greater the speed, the greater the force required. The rotation energy consumption is too large to meet the requirement of conversion to dynamic energy. In this way, power consumption and efficiency will be lower, which is not conducive to power generation. So the right amount of speed is the basic to ensure the maximum power. Too much speed requires more force, too little speed does not play its due role. From the above analysis, it can be seen that only if the rotating speed reaches a certain value can the maximum effect be guaranteed.

Figure 4: Relations of rotation and angle f with turbine blade radius R=29m~42m under v=3.8m/s.

In Figure 4 the rotation will become maximum 62 r/m at the angle f=83° with radius 29m under v=3.8m/s, then decreases with the increasing and decreasing angle. With the increasing radius R to 42m the rotation has decreased gradually to 42 r/m at the angle f=83°. It explains that the lower rotation transforms into the bigger power with the longer blade length.

Conclusions

It is found that the lower rotation transforms into the bigger power with the longer blade length in this paper. When the wind speed is 10.8m/s and 6.8m/s under the pitch angle at 40° the maximum average power will become cosine distribution with 300kW and 100kW. The decreasing α and β is the way from 0 to 83° to increase them. When α increases from 83° to 180° the power and force increase too. There is a certain power changes in power with 150kW and force with 15KN with β changing from 0 to 20°. The power consumption and efficiency will be low then. Only rotating speed reaching a certain value can the maximum effect be.

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