I already asked this question on July 6, 2015 but I got no answer, so I repeat it.
Let us take a rubber (or plastic) pipe that discharges water into the atmosphere.
If we squeeze the pipe wall on two opposite sides a couple of diameters ahead of its free end, but without closing it (i.e., in principle by letting the flow free to go), an instability phenomenon will occur.
At the squeezed site, the water pressure goes under the atmospheric one (because afterwards the cross section increases), so the pipe tends to close up and no flow occurs. But then, the pressure before the squeezed site builts up (because no flow is occurring) and the flow starts up again. This behaviour turns out to be recurring.
Therefore, the flow at the pipe exit keeps pulsating in an unsteady fashion.
I wonder if anyone studied this phenomenon.
Yes you can find below the link for published research:
https://ieeexplore.ieee.org/document/7979250
@ Curro - In a peristaltic pump ypu add work from outside. This is not the case.
Dear professor Carlomagno,
I am afraid I can't provide an answer to your question i.e. whether or not this problem has been ever tackled. However, I think it is a very fascinating one and I would like to speculate a little bit, looking forward for your feedback.
First of all, I assume that the hose is infinitely long upstream and that wave reflections upstream play a minor role in the phenomenon (I am aware it is a strong assumption...).
Being the restriction close to the open end, it makes sense that the pressure at the restriction may be smaller than the atmospheric one. However, the pressure outside the hose (and, of course, at the open end) is atmospheric, thus the fluid downstream is abruptly "sucked out" (and not anymore only "pushed out"). As a consequence, the restriction closes if the elasticity of the hose allows enough deformation under the forces in play. It makes sense, at this stage, that the upstream pressure builds up until, eventually reaching a critical value which re-opens the restriction.
I could guess that, among other parameters, the distance of the restriction from the open end, the velocity of the fluid and the material parameters of the hose play important roles in the definition of the critical value of the pressure (mentioned above) and in the determination of the frequency of the pulsations.
It would be interesting to see the differences which might occur when a compressible flow is involved.
My best regards.
PS: I could not get any conceptual correlation between the problem in object and the paper suggested by Mr. Harsh Jindal, which seems to be related to numerical instabilities in simulations. However, I might be wrong and I might have missed some crucial aspect of his suggestion.
S9rry for my late answer, but I was very busy.
First of all, I assume that the hose is infinitely long upstream and that wave reflections upstream play a minor role in the phenomenon (I am aware it is a strong assumption...).
This is a not necessary assumption even if it allows to neglect reflected pressure waves from the initial cross section of the pipe.
Being the restriction close to the open end, it makes sense that the pressure at the restriction may be smaller than the atmospheric one. However, the pressure outside the hose (and, of course, at the open end) is atmospheric, thus the fluid downstream is abruptly "sucked out" (and not anymore only "pushed out"). As a consequence, the restriction closes if the elasticity of the hose allows enough deformation under the forces in play. It makes sense, at this stage, that the upstream pressure builds up until, eventually reaching a critical value which re-opens the restriction.
There is no sucking or pushing. Let us assume that friction losses are not very important, which is quite the case. Without squeezing of the tube, towards its end, we practically have the atmospheric pressure because this is the boundary condition at the outlet. When the tube is squeezed a couple of diameters ahead of its free end, its cross section decreases, the velocity increases and the pressure decreases, so it goes below the atmospheric one. Beeing the pipe wall not too rigid, the pipe wall collapses so closing the fluid passage. But then, the pressure before the squeezed site builts up (because no flow is occurring) and the flow starts up again. This is an experiment very easy to be run at home.
I could guess that, among other parameters, the distance of the restriction from the open end, the velocity of the fluid and the material parameters of the hose play important roles in the definition of the critical value of the pressure (mentioned above) and in the determination of the frequency of the pulsations.
I do agree. The material parameter of the hose is its rigidity (geometry and Young modulus).
It would be interesting to see the differences which might occur when a compressible flow is involved.
If the flow is subsonic, I do not expect major differences.
PS: I could not get any conceptual correlation between the problem in object and the paper suggested by Mr. Harsh Jindal, which seems to be related to numerical instabilities in simulations.
So do I. Probably it is a way to increase his activity.
Best regards
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