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I am building a very simple turbine that runs on steam. I want to make it as simple as possible, thus avoiding impulse and reaction turbines.

I want to design the turbine to fit in an exhaust pipe (about 15cm diameter) so that steam would rotate it, and generate electricity.

How many blades must the turbine have? I know wind turbines are most efficient with 3 blades, does this also apply to simple steam turbines?

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The reason wind turbines use three blades is because it reduces the load fluctuations (fatigue) on the turbine shaft an bearings. Wind at high altitude is faster than the wind at low altitude. A two bladed rotor would be the most economical if it were not for the largest horizontal load being on the upper blade while simultaneously the lowest horizontal load being on the bottom blade. Three blades more evenly distributes this load, allowing the shaft and bearings to be smaller which makes it the most economical solution.

"Turbine" and "simple" are kindof oxymorons ;-) Impulse and reaction turbines are the simplest efficient turbine designs. It may initially seem easier to install an axial turbine, but there is significant amount of complex engineering involved. It would be pretty easy to extract 10% of the available power by guessing at the turbine design, but to achieve higher and higher efficiency a larger and larger amount of engineering is required.

A basic variable would be the number of blades like you mentioned. More blades generally means higher pressure differential and higher torque. There are many many more variables involved however, such as desired output rpm, flow velocity, blade shape, angle of attack, change of that angle of attack as it approaches the tip, inlet and outlet diameter, additional layers of blades as the steam expands, etc.

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