Comments on: Can we Overcome the Betz Limit in Windpower Extraction?

By: Anthony Morris

Anthony Morris — Fri, 09 Sep 2011 03:11:55 +0000

The proposal violates the second law of thermodynamics. It is only possible to convert heat energy to work by harnessing the flow of heat from the source to a colder sink. The heat source in your calculations is at 15 degrees C and even if you had a sink at 0 deg C the maximum possible efficiency (Carnot) for a heat engine operating between these limits is 15/(15+273) = 5.2%

Of course no such sink exists and the extraction of thermal energy as described is impossible.

By: Horia Nica

Horia Nica — Thu, 06 Jan 2011 16:17:25 +0000

Due to financial struggles we have difficulties to build a proper prototype to validate our theory.

More than a year ago I asked the editors to make some corrections in the article as it seemed to be a mix-up between Energy and Power.
At that point in time put the error on the shoulders of the editors as the article was re-edited a bit from our original document.
I apologize for my mistake.

Recently, a young student, Philipp Jablonski, I believe from Germany (Ökumenisches Gymnasium zu Oberneuland ), pointed out that there still seem to be a confusion between the Energy and the Power in our calculations, more specifically in the unit of measures.
We checked again our paper and it turns out that he was right, as well as the initial comments made back in 2009.

The error was in the portion of thermal calculation as we considered that to be Power when in fact it was the energy.
The new document is much cleaner, the power does not intervene so we eliminated the confusion created by using the power and the energy in our calculations.

The corrections does not change the conclusion or the order of magnitude of Thermal energy extraction vs Kinetic energy extraction.

We are very grateful for all these comments that helped us improve our document.

By: Paul Dvorak

Paul Dvorak — Thu, 18 Nov 2010 17:02:22 +0000

Mr. Sadiq:
Thanks for your comment. The Betz limit suggests about 59% maximum possible power extraction by a wind turbine. The posted article’s subject was how to get more than that maximum and the proposed method was to extract heat from the passing as well as mechanical energy. When the researcher in the article presents a working prototype of such a turbine, I will be glad to write a story on it.
Paul Dvorak

By: mohammad sadiq

mohammad sadiq — Thu, 18 Nov 2010 10:38:16 +0000

Nothing is impossible being with in the energy coservation one can improvise means and way for brakethrough

By: WindPower Engineering

WindPower Engineering — Tue, 08 Dec 2009 13:56:47 +0000

Windpower Engineering Note:

It has come to our attention that some of the equations above were edited incorrectly. As we re-wrote the equations from Horia Nica, we failed to observe the difference between power and energy. We apologize for any misinformation provided and have made the necessary changes.

By: Horia Nica

Horia Nica — Mon, 07 Dec 2009 22:32:10 +0000

We all agree that Betz Limit cannot be violated in terms of kinetic energy extraction. And this is valid for all current wind technologies which extract only the kinetic energy from the wind. The article talks about the possibility to extract the thermal energy in addition to the kinetic energy. The fact that current wind technologies (with or without augmenters) cannot tap into that portion of wind energy does not invalidate that possibility.

By: Lawrence Willey

Lawrence Willey — Mon, 07 Dec 2009 19:46:34 +0000

Augmented wind turbines are not new and are well known in the industry. They are limited in terms of cost effective up-scaling and economical COE, and as a result are a fringe sector. Stating that they “beat” the Betz limit is an eye-catching headline, but at the same time an unfortunate technical mistake that’s easily debunked by taking a closer look. When Alfred Betz formulated his theorem for an open rotor, he recognized that the rotor diameter (and hence the swept area) was a convenient parameter for characterizing all of the energy entering the turbine system. The free-streamtube control volume is straight forward to draw and the theorem readily confirmed. The shrouded (augmented) rotor diameter is not an equivalent parameter for characterizing all of the incoming energy for an augmented wind turbine. That’s because projecting this area forward to the incoming freestream flow does not account for all the energy actually engaged in the augmented wind turbine energy balance; i.e., a larger “effective diameter” must be projected forward to account for all the energy entering the augmented wind turbine control volume. The important new energy exchange accounted using this new control volume (where the free-streamtube control volume is drawn further outboard then the physical limits of the outer shroud) is for the entrainment enhanced diffuser. This is where some of the incoming energy external to the rotor core flow is exchanged for further depressed pressure behind the rotor (beyond what can be expected for a non-enhanced diffuser). The Betz limit is properly observed once the correct streamtube and energy accounting are applied. In the spirit of the original Betz energy balance, augmented wind turbines DO NOT beat the Betz limit.

By: Shy Baratz

Shy Baratz — Mon, 07 Dec 2009 19:45:57 +0000

It is important to understand why such a limit has to exist. The following is a simplified explanation.

Let us assume that there is no such limit and we can build a turbine that captures ALL the wind energy.
The wind hits this turbine at a certain speed, loaded with energy. The air flows through the turbine and comes out at the other side with no energy as ALL the energy has been captured by this fantastic turbine.
However, air with no energy does not move because if it moved – it had some energy in it. So we have this amazing turbine – air flows in but does not flow out. It’s not just the energy that is captured by the turbine, but the air too.

The air has to flow out, and in order to do so it has to keep some energy with it. This is why a turbine will never be able to capture all the energy. It has to leave some for the air to be able to flow out.

Betz simply calculated the minimum energy that has to be left in the air in order to allow all the air to flow out.
By Shy Baratz CTO at WIndextra Ltd.

By: Lawrence Willey

Lawrence Willey — Mon, 07 Dec 2009 19:45:22 +0000

No — The Betz limit simply can’t be violated. Every time someone claims this, look closer. There’s always a problem with the energy balance or control volume assumptions. In short — Energy can never be created or destroyed in a closed system, and the free-stream tube control volume forms the proper “closed system” reference for assessing any type of wind energy converter. All forms of energy including sound, chemical, radiant/thermal, electrical, atomic, and mechanical/potential can theoretically interplay to varying degrees within the overall energy balance that witnesses the energy conversion process going from wind to electricity — But there’s no way to beat the Betz limit. To do so would mean that continuity or conservation of energy or both would be violated and thus cause us to completely re-write physics as we know it — Making such a discovery on par with the likes of Galileo, Newton, and Einstein combined.

By: Horia Nica

Horia Nica — Tue, 03 Nov 2009 03:30:52 +0000

The pressure recovery will take place after the rotor, so it has no impact on the energy extracted/transferred to the rotor.
The possibility of ice throw is a hazard of the HAWT design.
Ice will not be created by the extraction of thermal energy from the airflow.
Moreover, even if ambient conditions are favorable for icing, the device mentioned in the article prevents any throw away of the ice.