How Does Solid Body Rotation Affect Vortex Tube Functionality?

[nickisverygoo]

this is written in wiki:
"There are different explanations for the effect and there is debate on which explanation is best or correct.

What is usually agreed upon is that the air in the tube experiences mostly "solid body rotation", which simply means the rotation rate (angular velocity) of the inner gas is the same as that of the outer gas. This is different from what most consider standard vortex behavior — where inner fluid spins at a higher rate than outer fluid. The (mostly) solid body rotation is probably due to the long time which each parcel of air remains in the vortex — allowing friction between the inner parcels and outer parcels to have a notable effect.

It is also usually agreed upon that there is a slight effect of hot air tending to "rise" toward the center, but this effect is negligible — especially if turbulence is kept to a minimum.

One simple explanation is that the outer air is under higher pressure than the inner air (because of centrifugal force). Therefore the temperature of the outer air is higher than that of the inner air.

Another explanation is that as both vortices rotate at the same angular velocity and direction, the inner vortex has lost angular momentum. The decrease of angular momentum is transferred as kinetic energy to the outer vortex, resulting in separated flows of hot and cold gas.
"


can anyone explain it for me?

i can't understand the first explanation, i knew the the air tempreture will get higher when being compressed， but while the compressed air be released into normal pressure won'it cool down the surrounding air? In the other way, when the low-pressure air that located in the center be released, won't it affect the air near by and let the tempreture become higher?

i totally can't understand the second explanation, i don't know how can the lost angular momentum been transferred to kinetic energy ...

THANK U :)

 

[Valerie Park]

The first explanation is that the outer air is under higher pressure than the inner air due to centrifugal force. This causes the temperature of the outer air to be higher than that of the inner air. This is because when air is compressed, its temperature increases. When the air is released into normal pressure, it will cool down the surrounding air. However, when the low-pressure air located in the center is released, it can affect the nearby air and cause the temperature to become higher. The second explanation is that as both vortices rotate at the same angular velocity and direction, the inner vortex has lost angular momentum. The decrease of angular momentum is transferred as kinetic energy to the outer vortex, which then separates the flows of hot and cold gas. This means that the inner vortex is losing energy due to friction with the outer vortex, which is then transferred to the outer vortex in the form of kinetic energy. This kinetic energy causes the separation of the hot and cold gas flows.