To break the vortex into bits, we create a very simple flow system - the building block of a vortex, or its discrete element.

The building block of a vortex

Consider a duct with compressed gas tank mounted to the inlet:

We shall move from simple to more complex concepts. For this reason, let's first study the behavior of the above duct system when the system is in rectilinear motion; then, we can study its rotational motion.

The duct has adiabatic walls - no heat comes in or goes out through them. The same applies to the tank. The gas in the tank is stored at some high pressure and has room (static) temperature.

Linear Motion:

The observer in the stationary frame of reference F will see total temperature difference

(let c = 330 m/s, just below sonic. For air, c_p=1006 J/(kg.K) --> 108.25K separation in total temperature) and static temperature difference

(let c = 330 m/s, just below sonic. For air, c_p=1006 J/(kg.K) --> 54.1K maximum cooling of air, not counting any expansion effects when the gas may be injected from the tank into the duct inlet, similarly to the injection done in vortex tubes, where the maximum cooling may be somewhat larger due to nozzle expansion)

This means since the gas at the exit has been stopped adiabatically, it exhibits a drop in thermodynamic temperature compared to the tank (all friction is neglected).  Therefore cooling is observed F. Not just cooling, but "temperature separation" is also observed. The leading end of the duct system appears hot, while its trailing end appears cold. This conclusion comes from the values of the total/static temperatures at the two ends of the system.
 

Where did the energy go?

The observer in the stationary frame F sees a gas parcel with high initial kinetic energy and room (static) temperature. Upon exiting the moving system, not only has the parcel stopped, it has also been cooled! This goes against intuition. Usually, when a moving parcel is forced to stop adiabatically, its static temperature goes up. The conclusion is:

The energy of the gas parcel was delivered as propulsion to the moving system!

Rotational Motion

The discrete vortex element (the duct) rotates about an axis with uniform angular velocity:

The rotation axis is perpendicular to the duct; the rotation axis is at the duct outlet. Gas from the tank flows towards the center of rotation.

The observer in the stationary frame sees this total temperature difference between inlet and outlet! (let c = 330 m/s, just below sonic. For air, c_p=1006 J/(kg.K) --> 108.25K separation in total temperature).

What is the static temperature difference? At inlet,

Express the static temperatures at inlet/outlet through the total temperatures at inlet/outlet and take the difference:

precisely as in the case of rectilinear motion!
The stationary observer sees

in both static and total temperature! (let c = 330 m/s, just below sonic. For air, c_p=1006 J/(kg.K) --> 54.1K maximum cooling of air, not counting any expansion effects when the gas may be injected from the tank into the duct inlet, similarly to the injection done in vortex tubes, where the maximum cooling may be somewhat larger due to nozzle expansion)

In total temperatures, there is HEATING at periphery and COOLING at center! Air trajectories are SPIRALS! No doubt, the physics of this system is highly relevant to the vortex tube effect.

Where did the energy go?

The observer in the stationary frame F sees a gas parcel with high initial kinetic energy and room temperature (at periphery). Upon exiting the rotating system, not only has the parcel stopped, it has also been cooled! This goes against intuition. Usually, when a moving parcel is forced to stop adiabatically, its static temperature goes up. The conclusion is:

The energy of the gas parcel was delivered as propulsion to the rotating system! This is ANGULAR PROPULSION.

Ansys FLUENT simulation results:

The information contained in this site is based on the following research articles written by Jeliazko G Polihronov and collaborators:

• “Thermodynamics of Angular Propulsion”
• Physical Review Letters 109, 054504, 2012.
• “Vortex Tube Effect Without Walls”
• Canadian Journal of Physics, doi:10.1139/cjp-2014-0227 (2015).
• “Angular Propulsion - The Rotational Analog of Rocket Motion”
• Canadian Journal of Physics, doi:10.1139/cjp-2014-0297 (2014).
• “On the Thermodynamics of Angular Propulsion",
• Proceedings of the 10th International Conference on HEFAT, 14-16 July 2014, Orlando (2014).