I Centrifugal separation into hot & cold air streams?

AI Thread Summary
The discussion centers on a thought experiment involving the Ranke-Hilsch vortex tube, where air flows through a channelized tube and experiences centrifugal forces in a bend, potentially creating temperature separation. The setup includes a partition with a slit that allows inner radius air to compress outer radius air, theoretically resulting in cold and hot air outputs. A rough calculation suggests that significant temperature changes could occur, with a potential rise of 50 degrees Celsius on the hot side. Concerns are raised about the feasibility of achieving effective cooling, particularly regarding the design complexity and the efficiency of heat separation in just half a turn. The conversation also suggests exploring existing vortex tube products for practical experimentation.
Swamp Thing
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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)?
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I expect it would work, but I don't think half of one turn would generate sufficient heat separation. The rectangular section would be more difficult to manufacture than a tube.
Get a vortex tube to experiment with. Vortex tubes for cooling cutting tools are now cheap. https://www.ebay.com.au/itm/383502848138
A waistcoat, with a vortex tube air cooler, costs less than $100 on eBay.
https://www.ebay.com.au/itm/134353374282
 
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