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Post Info TOPIC: Does Betz apply to turbines moving through the air?
meirus


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RE: Does Betz apply to turbines moving through the air?
 

so you mean you wanne make a air to air transmission with turbines ..

 



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brother paul


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Does Betz apply to turbines moving through the air?
 

imho Yes.

what you obtain is a 'magnum effect' VAWT.

compare it with a fractilizing of a bigger concept in little subparts.

http://salientwhiteelephant.wordpress.com/category/wind-turbine/vertical-axis-wind-turbine-vawt/page/2/

 

look voor madaras

http://www.nrel.gov/docs/legosti/old/469.pdf

page 45



-- Edited by brother paul on Tuesday 24th of July 2012 03:59:18 AM

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JeffD


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Does Betz apply to turbines moving through the air?
 

In 1919 a Russian  scientist by the name of Nickolay Zhukovsky(Joukowski) wondered the same thing.  He came up with the same maximum limit as Betz did at about the same time without knowing about Betz work.

  In his derivation he does consider a device that moves through the air.  If you exclude the energy used to move the device then the limit is the same as the stationary device if moving in a linear motion.  If the device moves in a circular motion with the axis of rotation of the device being perpendicular to the fluid flow then the max limit is significantly less.

There are some good articles in " Journal of Energy Resources Technology" dating around 2000, 2001, that discuss the same thing.  Although these articles are based on computer simulations, they found the same thing that Zhukovsky did.  Efficiency drops when moving through a curved flow field.

Oh, and this was the guy that proposed the circulation theory to explain lift back in 1906.  Today it is known as the Kutta -Joukowski theorem.



-- Edited by JeffD on Sunday 22nd of July 2012 07:00:51 PM

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vegasjetskier


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RE: Does Betz apply to turbines moving through the air?
 

I think this design would probably offer a very low efficiency due to the constantly changing angle of attack of the HAWT blades. As the HAWTs spin around the circle the angle of attack will be changing from very low to stalled out and back again with every revolution (of the VAWT).

As far as power/$ go, I imagine that the additional materials needed to support the weight of the HAWTs and the complexity of getting the power to the ground will cost more than just buying a regular alternator for a VAWT or getting a conventional HAWT, even if the new design should prove to be somewhat more efficient. HAWT power output can be increased very easily by just increasing rotor diameter.

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sjh7132


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RE: Does Betz apply to turbines moving through the air?
 

itsandbits1 wrote:

yes, on a theoritical level it may be an interesting mind puzzle but don't get it confused with reality.

 the economics of it make as much sense as putting a windmill on a car to generate energy to run the car. 

No it's really not like that at all.   It might be like that if you could move your car with out gas, or you mounted a turbine on a sail boat.

The idea is if you have a large VAWT it probably spins farily slowly and an alt to generate power from it will either be very expensive or require gearing or belts.

The idea of the aerodynamic transmission is to make the large turbine push little turbines through the air.  The little turbines turn much faster so an alt for them would be cheaper.

I agree that the overall efficiency of the system probably wouldn't be as good as with a normal alt, but what are we trying to maximize?  Is it efficiency or power / $.  This approach might have some promise on the power / $ scale.

 

 



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Steve
fluitic


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RE: Does Betz apply to turbines moving through the air?
 

Here's one for an airplane.

http://www.greatplainsas.com/scgennipod.html



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Dan
itsandbits1


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RE: Does Betz apply to turbines moving through the air?
 

yes, on a theoritical level it may be an interesting mind puzzle but don't get it confused with reality.

 the economics of it make as much sense as putting a windmill on a car to generate energy to run the car. 



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fluitic


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Does Betz apply to turbines moving through the air?
 

sjh7132 wrote:

Well Peter's argument goes something like this....

3) With the HAWT moving through the air, the lower energy air is accelerated to follow the HAWT, and blocks the stationary air from coming through.

4) However if the HAWT is traveling in circles, that air following the HAWT will tend to go in straight lines, and not be behind the HAWT for very long due to centripical force.   It is replaced by more stationary air, which to the moving HAWT looks like moving air.

 

 

 Kind of fun thinking about this.

 I would think that the higher energy air in front of the HAWT is also accelerated while forming a dynamic pressure bubble.

However with the HAWT moving in a circle the pressure bubble would also slip off to the outside of the circle.



-- Edited by fluitic on Saturday 21st of July 2012 09:38:41 PM

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Dan
sjh7132


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RE: Does Betz apply to turbines moving through the air?
 

Well Peter's argument goes something like this....

1) The aerodynamic transmission is moving in circles.

2) Normally on a stationary HAWT Betz comes into play because after you take energy from the air it is moving slower, and is stuck behind the turbine preventing (or reducing) more air from flowing through.

3) With the HAWT moving through the air, the lower energy air is accelerated to follow the HAWT, and blocks the stationary air from coming through.

4) However if the HAWT is traveling in circles, that air following the HAWT will tend to go in straight lines, and not be behind the HAWT for very long due to centripical force.   It is replaced by more stationary air, which to the moving HAWT looks like moving air.

I think the argument makes sense.

 

 



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Steve
fluitic


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RE: Does Betz apply to turbines moving through the air?
 

sjh7132 wrote:

 

The question is, does Betz limit apply to a small HAWT being dragged in a circular pattern or does the circular motion somehow help get the slowed air out of the way and reduce the back pressure that is the cause of Betz limit?

 

 Just my thoughts:

The back pressure that causes the Betz limit is the same pressure that drives the turbine, so if the circular motion reduces the pressure then the power of the turbine would be reduces as well.

Also a pitot tube that indicates dynamic pressure works just as well in a wind tunnel as it does on an aircraft, so I would think that relative air speed is all that maters.



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