Wind turbine calculation. Scheme, description

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Wind turbine calculation. Encyclopedia of radio electronics and electrical engineering

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Encyclopedia of radio electronics and electrical engineering / Alternative energy sources

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The main part of the wind turbine is the wind wheel. Through it, the kinetic energy of the wind is converted into mechanical energy.

Recall wind turbines are divided into two groups - with a horizontal and vertical axis of rotation. We will consider a wind turbine with a horizontal axis of rotation. It may have one or more blades, which are installed at some angle to the plane of rotation.

The wind wheel can be fast or slow. Depending on the diameter and number of blades, the speed of the wind wheel at the same wind speed will be different. This indicator is called the speed of the wind wheel and is determined by the ratio of the circumferential speed of the end of the blade to the wind speed:

Z = L * W / 60 / V,

where: W - wind turbine rotation frequency (rpm); V - wind speed (m/s); L - circumference (m).

But initially we do not know the speed of the wind turbine, which depends on its design. When air passes through the blades, a "perturbed" trace remains, which slows down the rotation of the wind wheel. And therefore, the more blades, the speed becomes less. In order to roughly calculate the speed of the wind wheel, we take the speed (Z) as a basis. established in a practical way for wind turbines with different numbers of blades:

1 - bladed wind wheel Z = 9,0;
2 - bladed wind wheel Z = 7,0;
3 - bladed wind wheel Z = 5,0;
6-bladed wind wheel Z = 3,0;
12-bladed wind wheel Z = 1,2.

Using the formula below, we calculate the speed of the wind wheel:

W=V/L*Z*60.

The performance of the entire structure and the safe operation of the plant depend on the design of the wind turbine.

Multi-blade designs are low-speed and, therefore, centrifugal and gyroscopic forces are much less than those of high-speed ones. Considering that wind turbine manufacturing technologies in amateur conditions leave much to be desired, multi-bladed wind turbines with at least five blades are recommended - such designs are not so critical to balancing errors, are not demanding on the aerodynamic design of the blade profile, and concave blades can be successfully used.

Blade installation

If you place a plywood sheet at an angle to the oncoming air flow, then the maximum lifting force at the same air speed will be at an installation angle of 45 °. As the angle decreases or increases, the lift force will also decrease, and the resistance to flow will decrease or increase, respectively. Therefore, we take an angle of 45 ° as a starting point. But in order for the wind wheel to make the most efficient use of wind energy and not have braking zones, the wheel must have a curved shape: the farther the blade element is from the axis of rotation, the smaller the installation angle is required

Screw pitch

One of the indicators for calculating the blade is the pitch of the screw - the distance that the mass of air will move in one revolution, if we imagine this mass of air in the form of a nut whose diameter is 2R, and the angle of the thread is equal to the angle between the chord of the taken section and the plane of rotation of the screw. The screw pitch is determined by the formula:

H = 2πR*tgα,

where: H = step of the selected section (m.); R = section radius (m); α = angle of installation of the section (deg.).

The installation angle of the section of the wind turbine blades is determined by the transformed formula:

α (installation angle) = Arctg (H/2πA).

Blade twist calculation example

Blade pitch = 1 meter, wind wheel diameter = 3 meters.

With these settings, ideally, without taking into account the resistance of the wind wheel, at a wind speed of 3 m / s, the wind wheel should make 3 revolutions per second or 3 * 60 = 180 rpm.

But this is ideal. In fact, the speed of rotation of the wind wheel is affected by the turbulence of the flow from the previous blade, the friction created by the blades themselves, the response of the generator depending on the applied electrical load. And in reality, the speed of the wind wheel will tend to the calculated indicators, but in fact they will turn out to be much lower.

Wind flow power

The next indicator in the calculation of the wind wheel is the power of the wind flow passing through the sweeping area of the wind wheel. It is calculated quite accurately according to the generally accepted method:

P \u0,5d XNUMX * Q * S * V³,

where P - power (W); Q - air density (1,23 kg/m3); S - rotor sweeping area (m:); V - wind speed (m/s).

Since one hundred percent conversion of one type of energy into another is impossible, we will begin to subtract losses. The wind wheel has a certain coefficient of use (conversion) of wind energy. The maximum value of the theoretical use of wind energy for ideal high-speed paddle wind turbines is 0,593. For the best samples of high-speed wind wheels with an aerodynamic profile, this figure ranges from 0,42 to 0,46. For multi-bladed low-speed wind turbines, this indicator ranges from 0,27 to 0,35, depending on the quality of workmanship, and is denoted in calculations by the symbol Ср. To match the speed of a low-speed wind wheel and a generator, it is necessary to use a step-up gearbox and its efficiency ranges from 0,7 to 0,9, depending on the transmission ratio and design.

When converting mechanical energy into electrical energy, we also incur losses. Therefore, we reflect them in the generator efficiency Ng from 0,6 (for autotractor generators with an excitation winding) to 0,8 (for generators with excitation from permanent magnets).

P \u0,5d 3 * Q * S * VXNUMX * Cp * Ng * Nb,

where P - power (W); Q - air density (1,23 kg/m3); S is the sweeping area of the rotor (m2); V - wind speed, (m/s); CP - wind energy utilization factor (0,35 is a good design); Ng - generator efficiency (0,6 for automobiles, 0,8 for permanent magnets); Nb - efficiency of the step-up gearbox (0,7-0,9).

Let's substitute the data for a 6-blade 3-meter wind wheel and find out what power can be obtained on a wind turbine with a permanent magnet generator and a gearbox with an efficiency factor of 0.9 at an average speed of 5 m/s:

P \u0,5d 1,23 * 3,14 * (1,5 * (1,5 * 5)) * (5 * 5 * 0,35) * 0,8 * 0,9 * 136 \uXNUMXd XNUMX watts.

In this case, the revolutions of the wind wheel will be.

W = V / L * Z * 60 = 5 / 9,42 * 3 * 60 = 95,5 rpm.

It remains to choose the gear ratio of the gearbox, depending on the speed of the generator.

Author: Evgeny Boyko

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