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Air moving in long tube


Danijel Gorupec

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Probably I should know the answer, but I have doubts...

There is a very long tube (pipe), say 2 km long and 3 meters in diameter. The tube is open at one end and there is a stationary air inside and outside the tube at normal pressure and temperature. At the other end of the tube there is a piston.

piston.png.362fb8ab4a380658fcf829fa4f48f5d1.png

At one moment the piston starts moving with some constant velocity (much lower than the speed of sound) something like 5m/s. My question is how long does it take that the air at the open end of the tube starts moving at speed comparable to the piston speed? My guess is that this would happen quickly (comparable to the time sound needs to travel the distance). Am I right? Will there be oscillations of air speed at the open tube end (if yes, on what will oscillation frequency depend)?

More difficult question for me to guess... There is the same setting as above but the piston is not moving at constant velocity, but is pressing the air with some constant force (that is, it creates constant local pressure of the air). How will now look the air-speed curve (speed-vs-time) at the open end of the tube? Will it lag significantly to the air-speed curve near the piston?

No need to make actual calculations - I am only trying to qualitatively understand what is happening. No need to consider high piston velocities either. Thanks.

 

Edited by Danijel Gorupec
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Since no one else want to answer this here goes.

 

When the piston initially starts to move it will generate a pressure pulse immediately in front of it.

This pulse will move away from the piston at the speed of sound in the gas and eventually expel a pulse of air at the open end.

If the piston continues to move smoothly and evenly it will generate a succession of such pulses which will coalesce into a region of increased pressure air between the travelling initial pulse and the piston face.
So once the air has commenced exiting the open end the pressure between the piston and the open end will be increased all the way but will not rise further.

Waves or pulses will only be generated if the piston moves jerkily.

Edit

As a matter of interest you cannot apply Bernoulli's theorem directly here as there is an energy input to the fluid.
The setup is effectively the inside of a pump.

 

Edited by studiot
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Thanks Studiot... In my application there is a 3MW fan pushing air into tubes that feeds the air toward tunnel boring machines (TBM). I was puzzled because there was a claim that an air-speed sensor nearer to the fan will be able to sense air-flow changes much sooner (faster response regarding the fan speed) than if it is placed at the far end of the tube. I however tend to believe there will be no relevant difference (it is a slow regulation process anyway), and you seem to confirm this.

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41 minutes ago, Danijel Gorupec said:

Thanks Studiot... In my application there is a 3MW fan pushing air into tubes that feeds the air toward tunnel boring machines (TBM). I was puzzled because there was a claim that an air-speed sensor nearer to the fan will be able to sense air-flow changes much sooner (faster response regarding the fan speed) than if it is placed at the far end of the tube. I however tend to believe there will be no relevant difference (it is a slow regulation process anyway), and you seem to confirm this.

In any feedback control system the sensor should be as close as possible to the business end of the device.

Having the sensor up by the fan is counterproductive as it will respond to changes close to the fan before these have any effect on the boring machine end.
So any desired change in airflow at the boring machine end will effectively be short circuited.

You said your tubes were a couple of kilometres long so the latency in the control system will need to be designed to prevent this happening.

3MW is a big fan.

:o

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In any case, I will have sensors at both ends so it is only the matter of weighting factors. Normally the regulation will be agonizingly slow, but there might be situations (after power interruption, for example) when a quick re-establishment of air flow will be needed - and this is when latency could be an issue.

(There are 4 fans of 0.8MW always working in parallel as a single unit - it would be cumbersome to transport a single 3MW unit and it would lack redundancy. I however think that not even half of the installed power will ever be needed.)

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