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.

 

[piercas]

I would like to clarify that Bernoulli's equation is a simplified form of the conservation of energy equation, specifically for incompressible fluids. It states that the total energy in a fluid system remains constant, meaning that the sum of kinetic energy, potential energy, and pressure energy must remain constant. In the case of a wind turbine, the incoming wind has kinetic energy, which is converted into mechanical energy by the blades, and then into electrical energy by the generator.

In regards to your question about the pressure differential near the plane of the swept area, it is important to note that the pressure differential is a result of the change in the velocity of the air. As the air passes through the blades, it experiences a decrease in velocity and an increase in pressure. This pressure differential is small and can be ignored for most practical purposes, but it is still a factor to consider in the overall energy conversion process.

Turbulence can affect the performance of a wind turbine by causing variations in the wind speed and direction, which can affect the efficiency of the blades. However, the principles of conservation of energy still apply, and the total energy in the system remains constant.

To ensure that this is a conservation problem, you can check if all the energy inputs and outputs are accounted for. In the case of a wind turbine, the energy input is the kinetic energy of the wind, and the energy output is the electrical energy generated. As long as there are no other significant energy losses, the conservation of energy should hold true.

I hope this helps clarify some of your conceptual questions. Good luck with your presentation!