This is a picture of a traditional vortex tube

Computational fluid dynamics simulations show, that this effect of temperature separation can be produced also by removing the pipe, or surrounding walls of the tube. All we need is the injector AND we need to apply suction at the cold exit. Then the cooling takes place just as shown above! The injector has to inject a swirl and combined with suction at the cold exit, the vortex tube effect takes place without a surrounding wall. There is no heating! However, the total temperature around the vortex rises, which means that kinetic energy from the core is imparted as propulsion to the air around the vortex. Full detail is given in the article “Vortex Tube Effect Without Walls”.

Once surrounding walls are added in the calculation, the static temperature next to them rises, even if the cylindrical wall is relatively far away from the core. This is because the rear part of the vortex tube acts as a centrifugal compressor and the confinement of the walls leads to heating. Therefore, the traditional vortex tube (shown above) is a rotorless turboexpander. The front, core portion is a rotorless radial inflow turbine while the rear section is a rotorless centrifugal compressor.

How is turbine propulsion possible without walls or rotating blades? It is possible only when the flow forms a specific spiral geometry, which acts as a turbine rotor

The middle spiral part is the flow trajectory of the air that comes out of the cold exit. The surrounding spiral branch comes from the injector, folds-in, and heads towards the cold exit. There is friction (shear) between the middle and surrounding spiral flow, which imparts propulsion to the outer layers and speeds them up. Again, this is best seen when the effect is modeled without surrounding walls. We shall call this geometry “an infolding spiral”; it is crucial in the propulsion of rotorless vortices because it fulfills the function of a turbine rotor.

Another name for this “turbine rotor” is “angular propulsion engine”, or APE. Computational fluid dynamics simulations for a traditional vortex tube (with walls) show a peak in the shear stress on the wall of the tube, which can be explained by the action of the APE in the tube. Here is a representation of the shear stress on the wall, plotted along the length of the tube:

On the left, a sharp peak is seen. This is the vortex tube injector. As we move towards the hot exit, another peak appears due to the APE in the tube. Towards the hot side, the APE is no longer found. This is because the hot end is the “compressor” side; the APE is the rotorless radial inflow turbine which acts closer to the injector. Once again, this plot confirms that there exists a rotorless radial inflow turbine, or a rotorless APE, acting in the vortex tube by extracting rotational work from the cold flow.

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

• “Thermodynamics of Angular Propulsion”
• “Vortex Tube Effect Without Walls”
• “Angular Propulsion - The Rotational Analog of Rocket Motion”
• “On the Thermodynamics of Angular Propulsion",
• Proceedings of the 10th International Conference on HEFAT, 14-16 July 2014, Orlando (2014).