No, even Betz limit is not possible to achieve in actual scenario because its an ideal case of infinitely thin rotor.

Sure it is, but only by doing things that may look like "cheating" and add an exorbitant cost.

Use two rotors, one in front of the other. There are many variations of this. They could both act as turbines, in which case you can get just a bit over Betz. Note that this is based on frontal area, not total swept area. Some may call this cheating. Another method: Have the rear turbine act like a normal turbine, and the front one only extracts power from the tip area. That air goes around the outside of the rear turbine, and hence extracting power from it is all gain. The best you can do is Betz limit based on active swept area, but based on frontal area, that gets you to about 0.79.

Use the front rotor as a propeller. This can increase the size of the captured stream tube, and hence power output. The problem here is there is circulating power: Some of the turbine's power is used to run the propeller. Excess losses in the system can pile up to the point you do not make a profit.

A well designed duct can easily beat Betz based on rotor area, and can even do so on duct exit area.

I worked on a configuration called "dynamic inducer" that added winglets to the tips of a wind turbine. It could also exceed Betz based on frontal area.

Altough all of this can let you beat Betz based on frontal area, they all add extra blade area and cost. If you instead used that extra area and money to make a larger single rotor, you would get more power. That is why none of these ideas are actually used.

Sorry for the late response,

Thank you Joseph Nyangon ,

SO, can we increase the Cp more than 0.59?

Thanks Zeashan Khan

Could we increase the Cp to be higher than 59%?

Thank you very much M. Mohamed Sajeer

Don't you think there there are alternative methods to estimate the Cp ?

I think Betz theory is only one theory to describe it.....

Thanks anyway....

Dear Bart Hibbs

Your reply is very interesting, I like it.

Please think about this: is the maximum Cp the same for laminar or turbulent flow?

Thank you very much....

Nazaruddin Sinaga : There are different methods to calculate this value, but finally you will end up with the same value only. For example, from axial induction factor

𝐶𝑃=4𝑎(1−𝑎)2

For maximum 𝐶𝑃

𝑑𝐶𝑃/𝑑𝑎=0 which gives 𝑎=1/3

𝐶𝑃=16/27=0.5926

Thank you M. Mohamed Sajeer

What do you think about the turbulence level, will it change the maximum Cp?

Dear Nazaruddin Sinaga

In my understanding it will reduce, because it is the ratio of rotor power and wind power. For adjusting fluctuation in the grid, the wind turbines are set to rated speed. Therefore, rotor power is constant for above rated speed while wind power is increasing with respect to velocity.

Dear M. Mohamed Sajeer and all scholars,

Please have a look precisely on the derivation of the Cp. There are 4 assumptions, at least, and the use of Bernoulli equation. In Bernoulli equation there are 4 assumptions, at least. And please look carefully that Betz did not say anything about the flow regimes, laminar or turbulent. If you remember, is there any difference between laminar and turbulent Bernoulli equations? I hope this will guide us to the more accurate calculation of Cp, I hope....

Dear scholars,

Please give your reply.

Thank you very much.

Dear respected colleagues and scholars. Please participate in the discussion and give your comments.

Thank you very much.

Dear respected scholars, please join our important and interesting discussion at:

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Best regards.

Hello colleagues

CP is defined as the overall turbine efficiency.

CP= Aerodynamic Efficiency * Mechanical Efficiency * Electric Efficiency

As you may know every turbine has some losses such as (bearing, gear tooth, windage, and electrical resistance) losses. So, there is no Ideal turbine (CP=1) in real life situation. This means that all of the power (kinetic energy converted per unit of time) would be converted to electrical power. No wind coming out of the downwind side of the turbine and no mechanical or electrical losses in the system.

Hoping this helps you mate.

Many Thanks

Dear Ali Alhelal , thanks for your reply.