Wind Turbine Design - Help w/Equations for Power Output

[endac]

Hi, I'm currently trying to design a wind turbine for a college project. I know the ideal equation for power is (mass x area x velocity cubed)divided by 2. Is there anyone who could help with equations relating the power output to the number of blades and angle of the blades. Thanks

 

[mender]

One thing to remember is that the turbine influences the stream of air passing through the turbine disc, not just the air that is directly in contact with the blades. More blades means more form drag, possibly without a corresponding increase in performance. The pitch of the blades will affect the speed that the blades move through the air as well as the torque on the turbine shaft. Also, Betz' law defines the upper limit of efficiency.

Hope that helps.

 

[malay_555]

You can directly use the energy eq here

upstream air energy = downstream air energy + your turbine power

in wind turbines generally potential energy change is negligible so you can directly use the kinetic energy
power = upstream KE - downstream KE
here mass low rate(m) is also const so it can be
P=(m*v^2)/2

 

[DyslexicHobo]

If you're still working on this project, send me a PM. I was tasked with designing a horizontal axis wind turbine for my sophomore college project. We were required to write a simulation in Matlab and I found my code to be accurate within ~35% (hopefully most of this discrepancy comes from error within the motor efficiency).

The model we used was basically conservation of energy. The air speed was calculated as it was approaching the blade, and then after it left the blade. Because we were limited to using only foam-board as the blades, the values of lift and drag coefficients were approximated as rectangular prisms. The lift force was integrated (in the code we just broke each blade into ~1000 small rectangles using for loops instead of using numerical integration) along each blade and converted to torque. The total torque was summed and there we have our power curve! Now to optimize it we just adjust the load of the turbine so that it reaches its peak power.

The hardest part was definitely calculating 'a' and 'a prime', two values that determine the wind speeds (I'm not sure if these are just random variables assigned by our professors to help us understand it more easily or if they're actually used in aerodynamics). I don't remember the equations off the top of my head, but in order to calculate the wind velocities there was two pretty complicated equations that were required to converge. I spent hours on end trying to find the requirements for convergence, but I never did. I ended up just tossing out the divergent solutions and the final product wasn't too bad.

Let me know if you'd like any more specific details, or if you want a copy of the code we used (you must have Matlab to view it).