Energy available to a wind turbine, Bern.'s eq

[pgunderson]

HI folks, new to this forum.I posted this on a different thread, but this seems the better location... it's a conceptual question.

I'm in a Fluid Dynamics class and need to make a presentation on Bernoulli's conservation of energy equation as it applies to wind turbines.

I think I understand the different energies involved here: kinetic(v^2/2), pressure(P/rho), potential(zg)... I want to make sure I am applying the equation right and comprehending the concepts.

It seems to me that in an airstream we've basically only got KE operating for us. The velocity entering the blade assembly is fast, energy is extracted by the turbine, and the air leaving the assembly is then slower.

But someone pointed out to me that if you think about the area really close to the plane of the swept area, there is also a pressure differential.

Is this small enough to be ignored? It seems the problem I'm to use as an example doesn't consider this possibility. The only givens are: steady windspeed of 12 m/s, blade assembly of 50m diameter, and to use air density of 1.25kg/m^3.

I'm to find the mech. energy of air/unit mass (ok) and the power generation potential (ok) and the actual power assuming 30% efficiency (ok).

Is my assumption correct that the only available energy is the KE of the wind's velocity? What happens with turbulence? If there's a pressure differential at some point, can that be causing the airstream to take on a shape that is not similar to a tube with cross-sectional area equivalent to the swept area of the blades? What rules can I apply to ensure that this really is a conservation problem?

Any conceptual help will be very much appreciated!

patti

 

[AlephZero]

I suggest you read up on how aerofoils work and how they create a lift force from a pressure difference between the two surfaces. The principle is the same for many types of aerofoil, e.g. aircraft wings, wind turbines, boat sails, etc.