# How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon.

Both linked sources are scarce with information about how and why this works. Now, I have two questions:

• Why does it work, specifically why should the situation in the vortex lead to a transfer of thermal energy from the inner stream to the outer one?

• How efficient can it be?

• How do you define the efficiency of a device that may be closer to Maxwell's Demon than to a heat pump? My feeling is that any analysis should not only take into account the sum of input energy (thermal and mechanical energy instream) and sum output (thermal energies and pressures of both gas streams), but also the Temperature differential that is created - since that contains an ability to create work.*

• If course it's pointless to create heat from high grade 8mech.) energy to transform it back to mech. energy - but it gives an idea on the worth of the output.

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This is a very interesting question - I hadn't heard of these things before. –  Nathaniel May 7 '13 at 9:07

Why does it work? One needs to understand static gas temperature, total gas temperature and propulsion if a proper physical picture of the effect is to be constructed. This is an article by me with Prof. Straatman that explains the fundamental law of rotational cooling, it assumes a sophomore-level math and physics:

Polihronov, J.. Straatman, A.Thermodynamics of angular propulsion in fluids, Phys Rev Lett 109 054504 2012

Also, see this web site, I am putting together an easy-to-read explanation of the vortex tube effect

In more detail -

Consider the concept of vortex flow "discretization": let's simplify the vortex flow by introducing a simple flow system, which still exhibits the physics of temperature separation. The simple flow system comprises a rotating adiabatic duct and a tank of compressed gas attached to the inlet of the duct. The outlet of the duct is at $r=0$, while the inlet is at $r=R$, the point $0$ is the rotation center.

Set the system into uniform rotation. Let the linear speed at the inlet is $c= \omega R$. Then, in the stationary frame of reference, the total temperature of the gas at the inlet (at periphery) is $T=T_0 + c^2/2c_p$, where $T_0$ is the static temperature of the gas in the tank. From rothalpy conservation we get the total temperature at the outlet (at center) to be $T=T_0 -c^2/2c_p$, $c_p$ is the isobaric heat capacity of the gas. Thus, the total temperature separation is $\Delta T=c^2/c_p$. What happens with the static temperature $T_s$? At inlet (at periphery), $T_s=T_0$; at outlet, it is $T_0-c^2/2c_p$. Thus, the static temperature separation is $\Delta T_s=c^2/2c_p$.

Temperature separation is observed in a rectilinearly moving system as well. Consider an elemental system, comprising an adiabatic duct and a tank of compressed gas attached to the leading end of the duct. Set the system with uniform linear velocity $c$. Let gas leave the system with velocity $0$ in the stationary frame of reference, the gas comes out the trailing end of the duct.

The temperature separations $\Delta T$ and $\Delta T_s$ are exactly the same as in the rotation case; only now conservation of enthalpy needs to be applied to solve for the temperatures.

When it comes to the vortex tube effect, this analysis is a very good place to start.

I hope this helped!

-J. Polihronov

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I have performed few tests with Vortex tube to find its effeciency comparing with a refrigeration system.objective was to determine whether we can use compressed air or CO2 to replace refrigeration system.vortex tube works only with pressurised fluid.when sudden drop on pressure reduces temperature and the spiral form seperator inside the vortex tube which circulates the fluid around it causing it to seperate hot fluid and cold and directs it to 2 different direction.using cold air which got seperated i could cool water up to 2 degree centigrade in c scale.but it require high flow rate and pressure to drops down any further.its efficiency is too low compared. I used 75 psig and flow rate was .5liter per sec.

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GReat to find someone with actual experience! do you have actual figures? –  mart Sep 24 '13 at 9:50
Yes. I have temp diff between inlet and outlet.mass flow rate diff between inlet and outlet.and various temp drop at different pressure and flow rate.i could get finally at 80psig inlet pressure and mass flow rate of 260lpm.a temp drop of .2 degree C and cold outlet.i have data on doe.the noise level is higher at hot air outlet. –  nemu Oct 1 '13 at 15:03
And how is the efficiency compared to peltier elements? –  fibonatic Jan 2 at 0:28
I dint do any tests with peltier element.but I can test it.let me try and get back to you.may be in few months. –  nemu Jan 12 at 15:34
Ping! Did you get around to do your tests? I'd greatly appreciate if you can expand your answer –  mart May 26 at 10:48

The input stream does not only have a thermal energy - it also has a mechanical one. Mechanical energy can be used for work, and the gas temperature is easily changed by work - in adiabatic processes it rises when gas is pressed, and falls when gas is able to expand. This gives a general idea why this tube could work and at the same time not be a Maxwell's Demon. Though detailed picture can be very complex and ask for advanced understanding of gas dynamics.

If we calculate total thermal and mechanical energies of both output streams, we would find that some mechanical energy is lost, and total entropy has risen. Mixing those streams back in one would give us a slower and somewhat hotter gas than it was initially. This is the same effect as simple slowing down the stream on some obstacles.

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1) can you expand on, um, why part of the gas is expanding in the tube? 2) for any heat engine or heat pump $\Delta T$ plays a large role ... why not here? –  mart May 7 '13 at 9:44
1) Please think of this not only as of heat engine but also as of a mechanical system. Gas mechanics here is highly relevant. Gas has inertia, and it can hit walls, thus making regions of higher and lower pressure. Also there are other streams of gas besides walls, and possibly some acoustic phenomena. 2) $\Delta T$ plays large role here too, as in the heat pump: it poses constraints on what can be done and what cannot be done with such a device. But $\Delta T$ is not the source of the work here - at least, basically. –  firtree May 7 '13 at 10:11