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).

 

[pmacias]

Hello,

Designing a wind turbine can be a complex process, but there are some equations that can help you determine the power output based on the number and angle of the blades. Let's break down the equation you mentioned and see how it relates to these variables.

The equation you mentioned, P = (0.5 x mass x area x velocity^3), represents the theoretical maximum power output of a wind turbine. This equation assumes that all of the wind's kinetic energy is converted into electrical energy, which is not always the case in real-world situations.

To incorporate the number of blades into the equation, you can use the concept of blade solidity. Blade solidity is the ratio of blade area to the swept area of the rotor. This can be calculated by dividing the total blade area by the area of a circle with a diameter equal to the rotor's diameter. The equation for blade solidity is:

σ = (number of blades x blade width x blade length)/(π x rotor diameter)^2

To account for the angle of the blades, you can use the concept of tip speed ratio (TSR). TSR is the ratio of the speed of the blade tip to the wind speed. A higher TSR typically results in a higher power output. The equation for TSR is:

λ = (tip speed x rotor diameter)/(wind speed)

Combining these equations, we can modify the original equation to include the number of blades and the angle of the blades:

P = (0.5 x mass x σ x λ^3 x wind speed)

Keep in mind that this is still a theoretical maximum and may not accurately reflect the actual power output of a wind turbine. Factors such as wind turbulence and blade efficiency also play a role in determining the power output.

I hope this helps with your project. Good luck with your wind turbine design!