What happens if cooled air passes back over a Ranque-Hilsch vortex tube?

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Nolgosphere
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To anyone familiar with the Ranque-Hilsch vortex tube:

Say if the cooled air is allowed to pass over the vortex section of this tube, what would happen?

Would the effect of cooling be the destruction of the vortex? or would it act to further decrease the temperature of the cold exhaust?
 
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My engineering sense tells me that it would just aid in cooling. However, I don't know how vortex tubes actually work nor have I seen a sound theory that can explain them. They are very mysterious devices.

BTW, welcome to the forum.