Physical Principles in Wind Turbine Operation & Design Hints For Energy Efficiency in Power Generation
The wind turbine is a much underutilised method of power generation by governments, corporates & home owners. As government public service becomes weaker & more expensive, it becomes necessary for communities & home owners to secure their own power. While solar power is more popular, wind power is also a potentially valuable resource for power generation. This is particularly true in windy areas, higher lattitudes & areas heavily shadowed by trees, mountains, valley slopes & high rise buildings etc.. The design of the wind turbine is important to maximise the conversion of wind velocity to wind turbine rotor rotation & then maximuise rotor rotation to electricity production. This article has the aim of generating ideas for better designs for research, governments, & corporations, as well as give the home owner an idea of wind power potential, & wind turbine physics & workings, to encourage the building & installation of domestic wind turbines to access this free for all energy.
The idea of domestic wind turbines is a possibility for us all, ranging from a generous to small budget. For those with $ but limited time, information will help determine the best types of wind turbines from & installed from the best people, as well as help with the monitoring & maintenance of the system. For those with more time & less $ , there is the potential learn the system thoroughly, in order to diy manufacture & install your own system, as well as manage all system monitoring & maitenance. The advantage of the latter option is that you can save alot of money & tailor make your own design to suit your own situation & preferences.
How Wind Turbines Operate
Wind turbines simply convert some of the kinetic energy of the wind (or speed of air at atmospheric pressure), from the air to rotor blade rotation, which rotates a shaft connected to a generator, which in turn converts the rotational energy to electrical energy.
The three basic parts of any wind turbine are:
The rotor blades which convert wind energy into rotational energy in the form of angular momentum.
The shaft transfers this rotational energy to the generator.
The generator converts the rotational energy into electrical energy by means of electromagnetic induction.
The generator consists of a series of magnets attached to the shaft, so that they rotate with the rotor blades around a conductor, which is connected to the power generation electric circuit. The generator works on the principle of electromagnetic induction, which means as the electromagnetic field of the conductor changes with the rotating of the magnets, an electric field (ie. voltage & current) is induced in the conductor according to Lenz’s Law.
Lenz’s Law di/dl = – dB/dt
where i = current (amps), l=length of conductor & B = magnetic field strength (Tesla),& t=time
This is the production of electricity, which then moves around the power generation circuit usually to charge up a battery in a domestic system.
The Rotor Blades and Tail Fin
The rotor blades are tilted at an angle in the same direction for all blades like an aircraft propeller. In the presence of wind, a portion of the wind resistance will then turn each of the blades in the same direction creating the angular momentum of the rotor & shaft. Then assuming the rotational resistance of the rotor piece and the shaft & generator to be small, the rotors speed up nearly to the speed of the wind passing through it, in much the same way as an aircraft’s speed is nearly proportional to the rotor speed (except for air resistance).
Better wind turbines also have a tail fin, which has dual purposes of;
Maintaining the plane of the rotor perpendicular to the wind direction as it changes, thus maximising the available wind to power the rotation of the rotor piece.
Balancing the rotor piece so that the net weight of the wind turbine is on top of its suport, meaning the structural stress on the support is balanced & thereby minimised (ie. so that the centre of mass is directly over the support or slightly on the rotor side to allow some adjustment to average wind force).
Physical Principles of Rotor Rotation
It is important to note that modern wind turbines are based on the concept of speed of roration rather than the amount of work done by the rotation of the rotor. This is evident in the difference seen between the wind turbine & windmill, whereas the former is designed for speed, the latter is designed for work. It must therefore be concluded that the relative physical load of modern wind turbines is light.
The physcal principles affecting the speed of rotor rotation can be summarised as follows;
The surface area, number of, & angle of the rotors to the wind direction.
The angular momentum of the rotor piece, which is dependent on the design & weight distribution of the rotor piece.
Air resistance to rotation (ie. drag when the rotors are rotating faster than the wind).
Internal friction & electromagnetic force resistance to magnet rotation in the generator.
Wind Power Torque on the Rotor Piece
Rotational force (ie. torque) on the rotor piece for a set wind speed increases with the radius, number, and surface area of blades. The angle of the blades is also important in rotational force, which is maximised at 45 degrees to wind direction.
Considering one blade at radius r & angle of Ø to the rotor with wind force F, then the torque on the blade at radius r from the shaft can be expressed per unit area of blade as follows;
T = r X F = r F sinØ = rF (for wind turbine rotors since Ø=90°)
where T = torque (Nm), F = Force (N), W = force due to wind, A = area (m^2) & r = radius of rotor blade (m),
also X = cross-product of vector terms (ie. magnitude & direction).
Now considering the nature of the rotor blade, assuming a constant slope of blade to the wind direction (W), the lateral force on the blade can be expressed as follows;
F = W A cosð * sinð where ð = the angle of blade to the wind direction
cos ð = force perpendicular to the blade,
& sinð = that component of force on the blade effective in generating torque.
It is easily shown the maximum torque occurs at an angle of 45°.
Therefore in the case of a load on the torque of rotation, such as with a windmill, steeper angles are required to meet the work requirement (ie. nearer 45°).
However where the load is light, the speed of rotation of the blades can reach a significant proportion of the speed of the wind, assuming the wind speed is relatively constant. A shallow blade angle in such a case mutiplies the rotor piece rotation, but also decreases the effective torque.
The torque on the rotor blades is also proportional to the area which intersects the wind, & therefore increases proportionally with the number of blades. Therefore the windmill has most of the wheel covered by rotor blades.
As for the wind turbine, for speed of rotors, the number of rotors is not so important, only in so far as the angular acceleration to reach wind speed as it changes. In design for speed, the strength & drag of the rotor blades is important with respect to maximum speed able to be attained before the blades break. To increase speed ability, a design that could be considered is the wheel, because it both strengthens the rotor piece and reduces drag. Drag can be further decreased if the blade angle is spung to return to vertical when wind ceases, or at least can be varied according to wind & rotor speed.
Angular Momentum (L)
Angular momentum is a mass & radial property that keeps the rotor piece turning, when the wind ceases or decreases. This is important because it determines the rate of angular deceleration of the rotor piece in opposing angular motion resisting forces such as drag, friction & electromagnetic forces in the generator.
dL = m * dr where m = mass / unit length of rotor blade & dr = incremental radius of the blade
L = m §dr = m*r = M*R where r=radius of blade, M = mass of blade & R = radius of centre of mass
Now for an evenly weighted blade R = r/2. So wind turbines sometimes have a weight within the blades which can be adjusted to optimise angular momentum.
Angular acceleration also increases proportionally with the number of blades.
Angular momentum can be improved by increasing the area of the wheel covered by blades, but also by using the configuration of the wheel, with significant weight on the circumference (ie. maximum r). Such a configuration also has the advantage of strengthening the rotor piece (ie. increasing safety rotor speed) & reducing drag.
Load of the Wind Turbine with respect to Other Design Possibilities
The typical wind turbine by its design, is very inefficient in harnessing the energy of the wind, in terms of energy produced per unit radius of rotor wheel. In order to improve wind energy efficiency a larger load should be incorporated into the generator part, which would translate into larger scale magnets & solenoids being used. This would mean that one well designed wind turbine would produce the same amount of power as many of the current designs combined. The extra load would require the wheel area of the rotor piece to have more blades, & a wheel configuration. Other design improvements would be the capability of the blade angle to be varied in order to maximise torque, momentum, as well as act as a brake by increased drag, & reduce resistance of the blades to the wind (ie. stop blades breaking), when the wind is too strong. Also in light winds, a gearing system could improve results.
DIY Home Design
Quite surprisingly, it is quite easy to plan & build your own wind turbine system. Planning is very important though, but can now be managed via information available on the internet. It is obviously easier & simpler to construct a simple miniture 3 blade type similar to the modern wind turbine, however there is scope to improve power output & energy efficiency by 1) using more blades & 2) having a wheel configuration. There is plenty of scope for the experimenter, also, to try different blade angles & DC electric motors etc. A domestic wind turbine system may be sufficient to power your home, or supplement your solar power system. The main concern with wind turbines is charging up the battery with less wind time, typically than solar time for a solar panel system. Therefore it is a good idea to be familiar with the wind patterns & climate in your area, & use this as part of planning. However typically in coastal areas, commonly there is a cold frontal system with windy conditions lasting a day or two once a week or more often, particularly during the winter months. It would therefore be preferable to be able to charge your battery(s) with each wind event that occurs. Information will go along way towards the planning, monitoring & maitenance of your system, & even the construction & installation. If you have the time, you can definately save alot of $ & yet design a good system, & be capable of managing it yourself. If you lack the time, then learning as much as you can is important for planning & managing the system, but research the avaiable products & installers well before you invest. All the best in harnessing this free for all energy.