# Wind turbines in tunnels

## Main Question or Discussion Point

Hi everyone….

I’m trying to evaluate the feasibility of putting what is essentially a wind turbine inside a horizontal exhaust shaft. I have a feeling that this would affect the volume flow rate through the shaft, but am having difficulty proving it. I have found plenty of textbook examples showing pressure and velocity changes through a turbine in the open air, with a small ‘envelope’ upstream changing to a larger ‘envelope’ downstream, but because my case is in a confined space, I am not sure that they apply.

By applying conservation of energy theory, Ein = Eout + Eelec, where Ein & Eout is that of the air, and Eelec is the power generated by the turbine.

If Ein & Eout = (Pressure/density)+(velocity^2/2)+(gravity*height), the height term will go, because it is constant, but what changes and how with respect to the pressure and velocity. My gut feeling is that the velocity changes…but I’m not sure.

Maybe I’m on the completely wrong track though, so any help that you can offer would be much appreciated.

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FredGarvin
What you should be looking for is ducted fans. They have better performance characteristics than regular fans do.

Astronuc
Staff Emeritus
In addition to what Fred mentioned,
Ein = Eout + Eelec
would not be correct, since Eelec is the result of conversion from mechanical to electrical energy.

Ein = Eout + Emech would be better, but there are still losses associated with the turbine to consider.

russ_watters
Mentor
You'll need to know the pressure drop through the tunnel, across the fan, and across the turbine at various speeds. You can match the curves....

Thanks for the help guys; your points have been noted.

At this stage I’m not really concerned about the exact type of fan/turbine though (that will come later), I’m mainly interested in the effect that having the fan in the middle of the tunnel will have on the air flow rate through the tunnel…although maybe different fans will have very different effects on the flow rate – time for some more research.

Also, at this stage I’m not after any definitive numbers, just trying to figure out the theory!

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Some more info that people may find useful - the flow through the tunnel is actually driven by fans that are downstream of the turbine. Sounds like an inefficient way to generate power I know, but that's the whole point - I want to be able to show why.
Especially if the flow rate throught the tunnel is affected, because then to maintain the required flow, with a turbine in place, the exhaust fans will require more power => which means you consume more power to make some power. But that gets me back to my main problem at this point - how do I show that the flow is affected!?!

russ_watters
Mentor
Ehh, it seems like a really weird thing. By the first law of thermodynamics alone, you know that you lose more speeding up the fan to keep the airflow constant with a new obstruction than you gain by having that obstruction be a turbine. If you have good specs on the turbine and fan and the velocity in the duct is low (so the loss is low), you can calculate the loss simply by multiplying the efficiencies together. Ie, if your turbine and fan are both 60% efficient, your generator is 90%, and you get 100W out of the generator, that's 100/(.6*.6*.9)=308 watts of input.

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FredGarvin
I can't imagine a fan putting out enough for a turbine to extract work from.

Ehh, it seems like a really weird thing. .... Ie, if your turbine and fan are both 60% efficient, your generator is 90%, and you get 100W out of the generator, that's 100/(.6*.6*.9)=308 watts of input.
Yep, a weird thing it is. I get what you have said, however, if I can't somehow show that the volume flow through the tunnel is affected by the turbine, then there is essentially no reason to increase the power to the exhaust fans. So in that respect, you kind of would be getting energy for nothing:surprised I realise that in this situation that is impossible - I'd just like to be able to show it, ie through the decrease in flow.

I can't imagine a fan putting out enough for a turbine to extract work from.
Fair point, but this is a number of fans, and the air often moves through the tunnel at pretty quick velocities - right now it's at 15m/s, and moving about 800cubic metres of air, which I believe is plenty fo a wind turbine. Not that you'd get a proper wind turbine in the tunnel, but I'm just using my imagination a little bit here....

AlephZero
Homework Helper
if I can't somehow show that the volume flow through the tunnel is affected by the turbine, then there is essentially no reason to increase the power to the exhaust fans
Assume everything is horizontal, for simplicity.

Consider a control volume round your complete turbine. If you are taking some energy out of the air flow, then the pressure and/or momentum of the air will change as it passes through the control volume.

If the mass flow is unchanged by the turbine, the downstream pressure and momentum must be the same as they were without the turbine, because the tunnel presumably discharges into the atmosphere. Therefore the conditions upstream will change. Therefore the exit conditions for the fan will change. Therefore the fan will be doing a different amount of work to deliver the same mass flow as before.

A similar argument applies if the mass flow is changed because the turbine partly blocks the tunnel.

FredGarvin
Fair point, but this is a number of fans, and the air often moves through the tunnel at pretty quick velocities - right now it's at 15m/s, and moving about 800cubic metres of air, which I believe is plenty fo a wind turbine. Not that you'd get a proper wind turbine in the tunnel, but I'm just using my imagination a little bit here....
Cool. As Joe Dirt would say: "Keep on keepin' on."

Consider a control volume round your complete turbine. If you are taking some energy out of the air flow, then the pressure and/or momentum of the air will change as it passes through the control volume.
Something that always confuses me is how the pressure affects the flow rate....
If the pressure drops after the turbine, then does the fluid become less dense leading to a change in flow rate?

Ahh, hang on...if the mass flow rate is constant, a change in pressure will lead to a change in density which will lead to a change in the volume flow rate, right?

So then if the pressure is increased after the turbine, the volume flow rate will decrease.
(Given that Volume flow rate = velocity * area,
and mass flow rate = volume flow rate * density)

Assuming that is all correct, I’m kind of back to square one – why does/would/could the turbine cause an increase in pressure downstream?

Thanks for helping me out and being a bit of a sounding board everyone – it is very much appreciated.

Hi everyone, another question for you….

I have attached something that I’m calling a ‘flow power analysis’, which just states the power at each point of the air flow through the tunnel, and also the power in to the fan and out of the turbine. There are three situations – the first with no turbine, second with a turbine and no extra power to the fan, and the third is with a turbine and also extra power to the fan. I just want to double check that this is a reasonable (although very simplified) explanation of what would happen in these situations. I know it’s probably a little weird to talk about the ‘power’ of airflow, but I don’t think that it’s necessarily wrong, is it?

Anyway – if anyone has a spare moment to have a look, that would be tops. I think the diagrams are pretty self-explanatory, if not, I’m happy to clarify things

#### Attachments

• 28.5 KB Views: 110
russ_watters
Mentor
Sorry I missed this before:
Something that always confuses me is how the pressure affects the flow rate....
If the pressure drops after the turbine, then does the fluid become less dense leading to a change in flow rate?

Ahh, hang on...if the mass flow rate is constant, a change in pressure will lead to a change in density which will lead to a change in the volume flow rate, right?
For the velocities and pressures we're talking about, the change in density is insignificant, so both the volumetric and mass flow rates are constant. [/quote] So then if the pressure is increased after the turbine, the volume flow rate will decrease.
(Given that Volume flow rate = velocity * area,
and mass flow rate = volume flow rate * density)

Assuming that is all correct, I’m kind of back to square one – why does/would/could the turbine cause an increase in pressure downstream?

Thanks for helping me out and being a bit of a sounding board everyone – it is very much appreciated.[/QUOTE] The turbine does not cause an increase in pressure downstream. Inserting the turbine into an already functioning system will give you a different pressure gradient than you had before, but it'll still be decreasing through the duct - in addition to a sharp drop through the turbine.

russ_watters
Mentor
I know it’s probably a little weird to talk about the ‘power’ of airflow, but I don’t think that it’s necessarily wrong, is it?
It looks ok to me.

Thanks for the replies russ....

Sorry I missed this before: For the velocities and pressures we're talking about, the change in density is insignificant, so both the volumetric and mass flow rates are constant.
Bugger, so that puts a hole in my assumption that putting a turbine in will reduce the amount of air extracted. Hang on, you mean that they are constant throughout the tunnel, but the flow rate for the case with the turbine will be lower than the case without the turbine.

The turbine does not cause an increase in pressure downstream. Inserting the turbine into an already functioning system will give you a different pressure gradient than you had before, but it'll still be decreasing through the duct - in addition to a sharp drop through the turbine.
So I think I'm getting confused a bit here...if we select a point, say, 100m downstream of the 'proposed' turbine position, with a turbine in place the pressure will be significantly lower at this point compared to without a turbine?

Ok, I think I have it figured out now.
Placing a turbine in the tunnel creates essentially a blockage, which means that the volume and mass flow rates will be less than without the blockage.
The airflow after the turbine loses energy due to a pressure drop, not a change in air velocity or density.
Obviously we can't extract more energy than we put in, and due to the inefficiencies of mechanical devices we actually get out significantly less than we put in - a net gain in energy is impossible. In fact the turbine would mean that the system consumes more power than a system without the turbine.
All seems very straight forward - I'm not quite sure what all my confusion was about

russ_watters
Mentor
Hang on, you mean that they are constant throughout the tunnel, but the flow rate for the case with the turbine will be lower than the case without the turbine.
Yes. You seemed to be saying previously that due to the pressure drop across the turbine, the flow rates on either side of the turbine would be different (lower pressure means lower density, means high volumetric flow). They wouldn't for this type of turbine, but high pressure power turbines (ie, gas turbine engines) have large diffusers on them and large changes in volume inside the engine.
So I think I'm getting confused a bit here...if we select a point, say, 100m downstream of the 'proposed' turbine position, with a turbine in place the pressure will be significantly lower at this point compared to without a turbine?
Yes.
Ok, I think I have it figured out now.
Placing a turbine in the tunnel creates essentially a blockage, which means that the volume and mass flow rates will be less than without the blockage.
The airflow after the turbine loses energy due to a pressure drop, not a change in air velocity or density.
Yes. Pressure is force. Work is force times distance, so pressure times volume is work (and times time for power).
Obviously we can't extract more energy than we put in, and due to the inefficiencies of mechanical devices we actually get out significantly less than we put in - a net gain in energy is impossible. In fact the turbine would mean that the system consumes more power than a system without the turbine.
Yes.

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