[Aleksey_at_cfd]

" Air dancers–those long fabric tubes with fans blowing into the bottom "
There is a post about it here:
http://fyfluiddynamics.com/post/63468872083/air-dancersthose-long-fabric-tubes-with-fans

So we have a vertical nylon pipe and the upgoing airflow inside
The only lifting force is the force of interaction of airflow with the walls.
But this force is not exactly equal to the weight of the pipe.
It fluctuates, it is different in different parts of the pipe and at different moments of time.
I think sometimes it can be greater then the weight of the walls.
The higher the pipe the bigger can be this excess force.
So at some length of the pipe the excess force will tear away the pipe.

The problem is to determine that maximum height for certain fabric, diameter and airflow velocity.

Any ideas are welcome.

[agd]

If you were to consider a long fabric sleeve that is closed at the far end, how much pressure on the closed end would be required to carry the weight of the vertical sleeve? How much of a pressure rise can you get with a particular fan? If you allow flow out the top of the sleeve perpendicular to the sleeve but impacting on a normal surface that caps the sleeve, how much force will the momentum change produce based on the flow velocity, assuming steady flow for simplicity? How does that compare to the weight of the fabric? How much velocity rise can your fan develop?

Those are the questions I would consider in addressing this problem. They can help you narrow down what the relevant physics are in your situation.

[Aleksey_at_cfd]

Originally Posted by agd

If you were to consider a long fabric sleeve that is closed at the far end, how much pressure on the closed end would be required to carry the weight of the vertical sleeve? How much of a pressure rise can you get with a particular fan? If you allow flow out the top of the sleeve perpendicular to the sleeve but impacting on a normal surface that caps the sleeve, how much force will the momentum change produce based on the flow velocity, assuming steady flow for simplicity? How does that compare to the weight of the fabric? How much velocity rise can your fan develop?

The pipe is fully opened at the top, I think. The power of the fan is unlimited, for simplicity.

[FMDenaro]

I will start from a simple model in laminar case: Hagen-Poisueille solution in a pipe. That has a pressure decreasing along the axis. The weight substained at a certain height must be balanced by the total wall stress acting at a that height.
Actually, when the flow starts transition, you have vortical structures in the pipe that will cause the fluctuation of the pressure.

[agd]

I think you missed my point - suppose the end is covered. Then what can you get from that? Does it provide a bounds for the problem in terms of a maximum height? And in keeping with the viscous stresses, if you integrate the shear stress along the length of the material (out to a height H) where does the integrated friction force balance the weight of the material?

[Aleksey_at_cfd]

Originally Posted by agd

I think you missed my point - suppose the end is covered. Then what can you get from that? Does it provide a bounds for the problem in terms of a maximum height?

There are additional requirements.
The end cannot be fully covered, the airflow should go through the pipe.
Also the weight of the pipe can vary because of the water vapour condensation so
the lifting force should be proportional to the weight to minimize the excess force.

If we cover the end partly then that gives us the lifting force that is proportional to the airflow velocity.
Plus there will be "force of interaction of airflow with the walls" ( Fi ) that can be proportional to the weight because the airflow will be turbulent, the walls will form the waves and the amplitudes of that waves can be proportional to the weight.
So I hope that Fi will be proportional to the weight and to find the maximum height it is necessary to calculate Fi anyway.
Thus initially for simplicity we can keep the end of the pipe open. Later we can add the additional lifting force, it will be the equivalent to decreasing the weight.

Originally Posted by agd

And in keeping with the viscous stresses, if you integrate the shear stress along the length of the material (out to a height H) where does the integrated friction force balance the weight of the material?

Not sure that I understood the question. If in the laminar flow the friction force ( Ff ) is greater then weight ( W ) then it will be compensated by elastic force of the fabric ( that we want to minimize ). If Ff < W then the walls will start to collapse, they will form the waves, the amplitude of the waves can be proportional to the weight, the flow will become turbulent and we will have some Fi that is proportional to the W and Fi > Ff .

Please correct me if you see it another way.

[Aleksey_at_cfd]

Originally Posted by FMDenaro

I will start from a simple model in laminar case: Hagen-Poisueille solution in a pipe. That has a pressure decreasing along the axis. The weight substained at a certain height must be balanced by the total wall stress acting at a that height.
Actually, when the flow starts transition, you have vortical structures in the pipe that will cause the fluctuation of the pressure.

Which CFD IDE would you recommend for Hagen-Poisueille solution in a vertical pipe ?

[FMDenaro]

Originally Posted by Aleksey_at_cfd

Which CFD IDE would you recommend for Hagen-Poisueille solution in a vertical pipe ?

You have an analytical solution for the velocity, you can compute the stresses at the wall and integrate them along the surface up to the height until you get a force that substains the weight. Of course the model is valid for a steady laminar situation but could give a first insight.

[flotus1]

What a neat fluid dynamics/structural problem.
Here are my 2 cents: using only wall shear stresses will probably yield the lower boundary for the maximum sustainable height.
But there might be other factors to consider:
1) Pressure. Since you get a pressure drop along the tube, the tube will be pressurized. This creates additional stresses within the fabric that should also enable it to sustain some weight
2) The real world. The fabric won't stay a straight tube with turbulent air flowing through. It will ripple, creating additional drag and thus enabling it to sustain even more height
And if the top of the tube partially collapses and caps off the air flow, the pressure inside will rise even more, lifting the tube up again.

SCNR
https://www.youtube.com/watch?v=cvaRGiMWRaE

[Aleksey_at_cfd]

Originally Posted by flotus1

The real world. The fabric won't stay a straight tube with turbulent air flowing through. It will ripple, creating additional drag and thus enabling it to sustain even more height

Suppose that the power of the airflow is unlimited.
Then my concern here is that rippling will produce the force that is bigger then the weight and that excess force will surpass the maximum elastic force of the fabric, the pipe will be torn off and this effect will limit the maximum height of the pipe. So the height is limited by the strength of the material.

That is why I need to model that rippling. Is it "dynamic aeroelasticity" problem ?

Suppose we have unlimited power of the airflow and it can be regulated. Then even if we choose the minimum velocity at which the pipe is vertical - the viscosity stress and that turbulent rippling can produce the force that is greater then the weight so we will have excess force, etc. Or I am wrong here?

For example, I handle the fabric ribbon in the upgoing airflow. Is it possible to find the flow velocity at which the ribbon does not fall but the drag force is zero? I am not sure. The ribbon will oscillate and the lifting force will fluctuate and it cannot be always not greater then the weight. So sometimes it will be greater. Then we integrate this for 1000 meters and the ribbon is torn off. Is it right ?

Also there is a choice - keep the lowest velocity with maximum rippling or increase the velocity a little to decrease it. The excess force can be different for this two options. And I even not sure in which case it will be bigger, it is necessary to simulate this.

This abstract task is part of the proposal for the project that is not directly related to the "air dancers" but air dancer is a good sample to start with.

I also created the thread for freelancers here:
https://www.cfd-online.com/Forums/cfd-freelancers/213681-air-dancer-maximum-height-problem-step-step.html

[FMDenaro]

Originally Posted by Aleksey_at_cfd

Suppose that the power of the airflow is unlimited.
Then my concern here is that rippling will produce the force that is bigger then the weight and that excess force will surpass the maximum elastic force of the fabric, the pipe will be torn off and this effect will limit the maximum height of the pipe. So the height is limited by the strength of the material.

That is why I need to model that rippling. Is it "dynamic aeroelasticity" problem ?

Suppose we have unlimited power of the airflow and it can be regulated. Then even if we choose the minimum velocity at which the pipe is vertical - the viscosity stress and that turbulent rippling can produce the force that is greater then the weight so we will have excess force, etc. Or I am wrong here?

For example, I handle the fabric ribbon in the upgoing airflow. Is it possible to find the flow velocity at which the ribbon does not fall but the drag force is zero? I am not sure. The ribbon will oscillate and the lifting force will fluctuate and it cannot be always not greater then the weight. So sometimes it will be greater. Then we integrate this for 1000 meters and the ribbon is torn off. Is it right ?

Also there is a choice - keep the lowest velocity with maximum rippling or increase the velocity a little to decrease it. The excess force can be different for this two options. And I even not sure in which case it will be bigger, it is necessary to simulate this.

This abstract task is part of the proposal for the project that is not directly related to the "air dancers" but air dancer is a good sample to start with.

I also created the thread for freelancers here:
https://www.cfd-online.com/Forums/cfd-freelancers/213681-air-dancer-maximum-height-problem-step-step.html

The turbulence will increase the wall stress on a rigid wall but in case of ripping the issue is more complex. You could get a decreasing in the vertical component of the stress due to the change of shape while simultaneously having an increasing in the pressure contribution due to the partial obstruction.
A viscoelastic issue should depend on the type of the material, I don't know if the elastic contribution can be relevant in practice.

[flotus1]

To be honest, if you want to achieve a somewhat reliable prediction here you probably can not rely solely on simulation. Some controlled experiments should be performed in order to verify the modeling assumptions.

[Aleksey_at_cfd]

Originally Posted by flotus1

To be honest, if you want to achieve a somewhat reliable prediction here you probably can not rely solely on simulation. Some controlled experiments should be performed in order to verify the modeling assumptions.

What should be the minimum set of experiments for this case ?

For example, if we measure the vertical component of the stress at the part of real fabric pipe then how long should it be? I mean how many diameters should be in the experimental height ?

Or can it be enough to experiment with the ribbon made of real fabric ?

[Aleksey_at_cfd]

Originally Posted by FMDenaro

You have an analytical solution for the velocity, you can compute the stresses at the wall and integrate them along the surface up to the height until you get a force that substains the weight. Of course the model is valid for a steady laminar situation but could give a first insight.

Do you mean this formula:

en.wikipedia.org/wiki/Hagen–Poiseuille_equation#Poiseuille's_equation_fo r_compressible_fluids

?

[FMDenaro]

Originally Posted by Aleksey_at_cfd

Do you mean this formula:

en.wikipedia.org/wiki/Hagen–Poiseuille_equation#Poiseuille's_equation_fo r_compressible_fluids

?

yes, the velocity is quadratic and you can easily compute the stress at the wall.

[Aleksey_at_cfd]

Originally Posted by FMDenaro

yes, the velocity is quadratic and you can easily compute the stress at the wall.

What about Darcy-Weisbach Equation ? Will it also work for this case ?

[FMDenaro]

The gravity acts by means of the weight of the tissue but is not relevant for the air flow. Furthermore, the formula say the pressure loss not the force acring by the tangential stress

[Aleksey_at_cfd]

Originally Posted by FMDenaro

The gravity acts by means of the weight of the tissue but is not relevant for the air flow. Furthermore, the formula say the pressure loss not the force acring by the tangential stress

Do you mean the Darcy-Weisbach Equation would not work here?

[FMDenaro]

Originally Posted by Aleksey_at_cfd

Do you mean the Darcy-Weisbach Equation would not work here?

For laminar flow you can deduce analytically the pressure loss also for the Hagen-Poiseulle solution. But the normal stress is just a component of the total stress, you should consider also the tangential stress at the wall mu*du/dr at r=R.

[Aleksey_at_cfd]

Originally Posted by FMDenaro

For laminar flow you can deduce analytically the pressure loss also for the Hagen-Poiseulle solution. But the normal stress is just a component of the total stress, you should consider also the tangential stress at the wall mu*du/dr at r=R.

I think I need to read some scientific article about this, otherwise I cannot understand it in full.