Calculating the Entry Area for a Funnel to Increase Air Speed

[BenGoble]

Hello!
I've attached an image below that shows a simple diagram of my question. I would like to know how to work out the area that I would need for a funnel to increase the air speed from 4.8m/s to 12m/s. The exit would measure 25 by 25, how big would the entrance need to be?

I've done my own calculation and believe that the opening should be 31.45 m x 31.45m. I'd like to see what you all think.

 

[Cyrus]

Just use the Bernoulli Equation. Should take a whole 5 mins to calculate. Also, its not called a 'funnel' but a converging nozzle.

Also, 25x 25 what: inches? cm? m? ft?

 

[BenGoble]

Alright, Another question then. If I funnel air and increase its speed from 4.8m/s to 12m/s will it turn a wind turbine with increased force or will the resultant loss of pressure energy mean that the turbine will only turn as fast as if it were a 4.8m/s wind?

 

[0xDEADBEEF]

Not even Bernulli... volume stream (volume per second) Vdot = speed * area. Vdot is the same as entrance and exit. so you have to solve the complicated equation "speed1 * area1 = speed2 * ?"
If you don't want to use the ideal liquid approximation there be dragons.

 

[Cyrus]

Why would you want to do this? You're not going to extract more energy out of the air by doing this, in fact you will extract less energy.

 

[BenGoble]

I thought, that if you increased the wind speed by funneling it then potentially the greater proportion of kinetic energy might i.e. since the air is now oving at 12m/s could turn my turbine more rapidly. Though I wasn't sure how the loss of potential energy would affect this. So, The increased wind speed gained from tunnelling air will not in any way help me?

My intended use for this was that I would have a wider opening on one side of an obstruction and that the negative pressure created on the sheltered side would draw the air through this funnel and turn my turbine more rapidly?

 

[0xDEADBEEF]

I see you want to funnel wind... this is more complicated, and will really require at least Bernulli. There is the possibility that you will not gain much, because the "Bernulli pressure" stays the same, I'll do a quick check and pressure measurement, but with wind I think the answers are not very simple.

 

[Cyrus]

I was considering that as I typed my response to you. Basically, any nozzle will be nonisentropic, which means it has losses as it speeds up (converging nozzle) or slows down (diverging nozzle) the flow.

Let's think about this from an idealized standpoint, and I will discuss why this idea won't work in actuality later.

Let's assume a uniform wind speed ([1]this is not true) entering into your nozzle. There is a fixed amount of energy coming into the nozzle. No matter what, the same amount of energy will come out the other end but at a faster speed ([2]this is not true either). That wind, while faster, still has the same amount of energy. The wind turbine, therefore, will still generate, the *same* amount of energy because the total energy in the airflow did not change.

What you could do, though, is have an entrance much bigger than the exit; *but* the exit is the size of the rotor of the wind turbine. Then you are taking more energy and pushing it through a smaller area at the exit. You're still pushing the same *amount* of energy - but its now higher because the area at the entrance is much larger than the turbine itself ([3,4]again, not true).



[1]Wind turbines operate near the ground where they are inside the boundary layer of the earth. The velocity profile is not constant, and the direction changes depending on which way the wind is blowing. So, the equation 0xDEADBEEF gave you is no longer valid, and the nozzle would have to turn with the wind turbine into the wind as the wind changes direction.

[2] All nozzles are nonisentropic, which means they have losses, so the energy coming out will be slightly less than the energy coming in due to losses in heat/friction/noise.

[3] Wind Turbines are HUGE. The size of this nozzle would be prohibitively large.

[4] Wind Turbines cannot operate when the wind speed is too slow, or too *fast*. So if the wind is strong, you don't want to over speed the blades on the wind turbine with your nozzle, they will fail and fly off.

 

[0xDEADBEEF]

Ok I just checked and I think the total pressure will stay the same. When your turbine starts, then the pressure on the blades is equal to the total pressure since the speed on the surface is 0 (same argument as with the pitot tube) and in laminar flow this number is constant. Inside the funnel the static pressure will decrease for a gain in dynamic pressure. Your total torque should stay the same but the turbine might go faster when it is unloaded.

 

[Cyrus]

Ok I just checked and I think the total pressure will stay the same. When your turbine starts, then the pressure on the blades is equal to the total pressure since the speed on the surface is 0 (same argument as with the pitot tube) and in laminar flow this number is constant. Inside the funnel the static pressure will decrease for a gain in dynamic pressure. Your total torque should stay the same but the turbine might go faster when it is unloaded.

This statement is wrong. The power is the torque times the RPM. If the torque is constant (as your claiming) and the turbine goes faster when unloaded - it would generate more power. Why do you claim the total torque will stay the same?

If the free stream velocity increases, the torque goes down as it spins faster.
If the free stream velocity decreases, the torque goes up as it spins slower.

The net power is the same.

 

[BenGoble]

Firstly, I understand all of your points and totally agree with them. I am however, doing a project for masters and testing theoretical potentials of energy systems.

In this case I was studying how I might encompass a vertical axis turbine into a new urban form based around solely wind energy as an extreme! Thus, I was considering incorporating a VAWT inbetween wedge form buildings that would be 29m tall due to the 29m diameter of the turbine, at the exit of the funnel end and much larger on the opening side.

This is a study based in Manchester England where 80% of the wind comes from the South West which gives a reasonable basis for positioning a structure in that direction.

I also realize there will be losses so I have tried to build in some manner of compensation since the specific turbine I was considering could produce 500MW-750MW at winds of 7.5m/s rather than the 12m/s I was quoting and the cut-out speed approximately 30m/s.

With all of this in mind, I would never claim this to be a solution but it's an interesting concept to see if in an ideal situation this form of exaggerated local energy production could be done. The answer would typically be, probably not, but examples exist of similar things, just not ground based like this for examplee I've attached three images, one of a constructed project which vaguely uses these concepts and the other of a building that use vertical axis and pressure differences to suck wind through its turbines.

 

[Cyrus]

These are not questions a masters student should be asking.

You really need to do more background research on this topic: Journals, textbooks, websites.

Is your masters not in engineering?

 

[BenGoble]

hehe, no it's not in engineering unsurprisingly. I'm an architect and urbanist looking at peak oil, so sadly my knowledge of air flow, torque and that are a little lacking but that's exactly why I'm asking so when someone asks me, "Does this fantastic concept actually work?" I can say... "No, but it almost works! and wouldn't it be nice" haha Anyhow thank you very much for your help guys.

 

[Cyrus]

hehe, no it's not in engineering unsurprisingly. I'm an architect and urbanist looking at peak oil, so sadly my knowledge of air flow, torque and that are a little lacking but that's exactly why I'm asking so when someone asks me, "Does this fantastic concept actually work?" I can say... "No, but it almost works! and wouldn't it be nice" haha Anyhow thank you very much for your help guys.

Your masters topic really requires a complex understanding of fluid dynamics. I really don't know what to say here. I think your doing some very wishful thinking.

 

[0xDEADBEEF]

This statement is wrong. The power is the torque times the RPM. If the torque is constant (as your claiming) and the turbine goes faster when unloaded - it would generate more power.[...]

I don't claim that the torque stays the same one the turbine is spinning, only the starting torque when the blades don't move yet. The pressure that pushes the blades is the static pressure not the dynamic one. Once the blades have the same speed as the gas, there is no more torque. Your comments about the losses in the funnel are correct of course. But as a physicist all my funnels are ideal ;)

 

[BenGoble]

as a physicist all my funnels are ideal ;)

Haha, Quality

 

[Cyrus]

I don't claim that the torque stays the same one the turbine is spinning, only the starting torque when the blades don't move yet. The pressure that pushes the blades is the static pressure not the dynamic one. Once the blades have the same speed as the gas, there is no more torque. Your comments about the losses in the funnel are correct of course. But as a physicist all my funnels are ideal ;)

Why are you talking about starting torques? This isn't relevant to our conversation.

This is again wrong. There is always a net torque on the blades. Thats *how* they extract energy from the air.

 

[0xDEADBEEF]

Ok I believe you I am using second semester Prandel tube pictures as my guide if you know your hydrodynamics better since you seem do do aircraft propulsion or something similar go ahead and preach the truth.
I don't know how turbines are designed but I didn't find it unlikely that they are in some kind of "creeping" speed as compared to the involved wind velocities, which would move us close to the static case.
I don't see what you were calling false again, maybe because I didn't define well what I called speed of the blades, but I am convinced that the gas will not act with a force on the blades if the comoving derivative of the blades' position is zero.

 

[Cyrus]

Read:

http://books.google.com/books?id=nM...rontcover&dq=helicopter+aerodynamics+lieshman

I don't know what your calling a 'comoving derivative'. But there absolutely is a force on the blades - its extracting energy from the air. There *has* to be a force on the blades - otherwise you have a perpetual motion machine.

 

[rcgldr]

In real life the pressure of a fluid flowing in a pipe decreases with distance, because of friction and viscosity effects (exit pressure has to be lower in order to induce the flow). The main advantage of a large intake is that it captures more air. Tapering the pipe in a turbine so that parameters such as pipe diameter versus flow speed can make the turbine more efficient. This is why fighter jet engines have an adjustable exit nozzle size.

 

[sterlingpeter]

I think the idea is to use a smaller less expensive turbine propeller, vs the expected low cost of a long large funnel. the air is free...

 

[Cyrus]

Why are you talking about starting torques? This isn't relevant to our conversation.

This is again wrong. There is always a net torque on the blades. Thats *how* they extract energy from the air.

I need to revise what I said here to be clear. The net torque on the blades is zero. But there is a torque on the blades due to the air. This torque is equal and opposite to that due to the electric generator applying a load to the system. The net torque equal to zero simply means the system speeds at constant rotational velocity.

 

[xxChrisxx]

This is a study based in Manchester England where 80% of the wind comes from the South West which gives a reasonable basis for positioning a structure in that direction.

Why don't you come up with an idea that draws energy from ****ty weather. We've had enough of that recently to jump start a star.