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I have been reading about the Ranke-Hilsch vortex tube. Details of the explanation tend to differ somewhat among different sources, but it got me thinking about the following thought experiment.
Air enters a tube of about 0.5 x 4 cm cross section. It passes through a section that is channelized into narrower passages in order to achieve a degree of laminarity. Then it immediately enters a bend with an inner radius of 1 to 1.5 cm. This section is partitioned as shown, such that you have one air stream following a smaller radius and one following a larger radius. The partition wall however has a slit running along it, such that the centrifugal pressure difference can allow some of the inner radius air to expand into the outer channel, thus compressing it.
To some degree of approximation, the air in the inner channel is thus doing work to compress the outer air. The process is approximately adiabatic and isenthalpic if we consider the ( inner + outer ) air as our system. To the extent that these statements are true, we should get cold and hot air from the two outlets.
I did a very rough calculation that shows that the extra centrifugal pressure on the outer air can be of the order of 0.2 atm when the velocity is 150 m/s, so that the temperature can rise by around 50 deg. C, with a similar drop on the cold side..
Questions:
Just as a thought experiment, is it plausible? What can cause it to fail (i.e. to produce not even say 5 deg of a cooling effect)?
Air enters a tube of about 0.5 x 4 cm cross section. It passes through a section that is channelized into narrower passages in order to achieve a degree of laminarity. Then it immediately enters a bend with an inner radius of 1 to 1.5 cm. This section is partitioned as shown, such that you have one air stream following a smaller radius and one following a larger radius. The partition wall however has a slit running along it, such that the centrifugal pressure difference can allow some of the inner radius air to expand into the outer channel, thus compressing it.
To some degree of approximation, the air in the inner channel is thus doing work to compress the outer air. The process is approximately adiabatic and isenthalpic if we consider the ( inner + outer ) air as our system. To the extent that these statements are true, we should get cold and hot air from the two outlets.
I did a very rough calculation that shows that the extra centrifugal pressure on the outer air can be of the order of 0.2 atm when the velocity is 150 m/s, so that the temperature can rise by around 50 deg. C, with a similar drop on the cold side..
Questions:
Just as a thought experiment, is it plausible? What can cause it to fail (i.e. to produce not even say 5 deg of a cooling effect)?
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