Wind generator turbine blades

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The generator project was started in 1985 when I tested out some fluid dynamics equations at home on my ZX81! I generated 32 aerofoil sections for the 32 stations along the length of a blade and hand plotted the computer co-ordinates I had calculated onto graph paper, joined up the dots and stuck them onto balsa wood to make up the 32 physical sections of the blade. The 32 sections were then mounted onto a wire through each sections 0,0 co-ordinate and glued together at the correct blading angle to make a 12 inch blade. This was obviously too small to be of any significant power generation use. Since the design needed about 16 blades on one rotor I decided to shelve the project and start again at a later date with a larger design.
23 years later I noticed a B+Q offering of a wind generator. This had arrived two years after easier planning permission had come into effect. Most of the designs seem to be based upon Met office predictions about wind speeds. However these are taken at an elevation of 20 metres and do not reflect the fickle winds around a housing estate and nearby tall buildings. In any case on inspection of more recent designs I noticed that the blade shape seems to be for catching 'indident wind where the 'weight' of wind (i.e. it's momentum change imparts a force on a deflecting surface). I dont know how much design went into the blade sectional shaping but I suspect it was based on more or a wing and a prayer than fluid flow equations.
Another aspect to the design of house mounted blades (apart from the lack of available wind most of the time), is the amount of available energy which may by captured by a set of blades rotating on a windmill tower. The energy available in wind is dependant directly on the volume of air passing through the 'energy recovery system' see figure. Someone who sold wing generators for a living told me that designs were limited to 3 blades for for balancing purposes and that more blades would present too much of a problem. I believe myself that is a car wheel can be balanced with a weight then so can a fairly small roof mounted system with lots of blades.

Maybe the real reason is that with a 'full compliment' of blades the scenery behind the windmill would be blotted out and therefore produce an unacceptable environmental impact. There might also be engineering hazzards with rapidly varying wind direction and overall 'windage' of the mill.

On the other hand it might be simple economics regarding the production and maintenance of a many bladed generator versus the percentage return in the form of energy. Maybe for some reason the energy recovery falls off exponentially with extra addition of blades. We will see !

With an incident air flow system of 'momentum' energy recovery it can be shown that the maximum air recovery requires that the downstream velocity of air has to be 1/3 of the upstream velocity. Equations show that for a bernoulli recovery system (not dependant on momentum change but on pressure changes around the blade section e.g. an aircraft wing) there are no such restrictions (at least in the equations). Whether practical reasons apply will be discovered.

The second blade was produced in the same manner as the first using paper stuck on balsa wood but this time scaled up a bit with 64 stations, a 100mm chord length and a designed swept area diameter of 1m. I plotted the blades through a dot-matrix printer as I could control the scaling of the x and y plotting more accurately using the raster codes for an Epson FX100.

The idea was to generate electricity using power extracted from the wind. After researching the nominal wind velocities recorded at diferent locations within the UK, I quickly decided that they were very optomistic average values indeed. The average wind speed near my village of Boreham in Essex definitely does not average 15 knots.

I decided to 'listen' to the wind and get a general feel for what it was doing (shifting, gusting strength etc) and derive my own 'magical' figures based on no scientific measurements at all. I decided that the generator would be better designed to pick up very light average air movements using an aero-foil (airfoil) shape bladed in such a way as to also make best use of any gusts impinging on the blade surface rather than just the designed aero-dynamic lift of the blade. A diagram is shown of the proposed generator in diagram 1 (to follow)
The general idea therefore was to use lift at low wind speeds and the impinging wind momentum of higher wind speeds. The blading angle of the blades changes from root to tip to account for the difference in rotational velocity of the blade at these two and intermediate points. The larger angular incidence of the blade to the wind diraction at the tip would pick up the wind momentum, as described by Newton's laws of motion, while at lower wind speeds, Bernoulli's equations would describe the pressure difference at each side of the blade resulting in a rotational force (lift) being generated creating enough energy of a constant type based on average wind speeds of 1 to 4 knots, which could be used to say trickle charge a lead acid battery.
However, designing the generator blades for optimum low wind speeds performance means either converting Bernoulli's equations to make them apply to a relatively mathematically complicated airfoil shape, or using a transform to convert the airfoil shape to a less complicated mathematical shape for easy Bernoulli analysis. To cut a long story short there is just such a transform called a Joukowski transform (which I will refer to as a J-transform) which converts mathematical sets from one mapping to another. The derivation is complicated, but generally it can be made to convert simple circles into airfoil shapes. The only problem being that the circles and the air flow around them have to be mathematically described in some way. This is done using traditional 'ideal' fluid flow analysis methods. (to be continued)
So the two energy regimes are: 1) The wind's mass momentum and 2) It's kinetice energy. These two regimes will have different significance and wieghting on the main derivation of power over the operating speeds of the mill, one of which should be easy to determine from Newtons laws of momentum. While the other will require belief in the the flow dynamics equations or actual measurements in practice of a working windmill.
To be continued