Newsgroups: sci.physics.fusion
From: (W. Robert Bernecky)
Subject: Wirbelrohr or vortex tube
Sender: scott@zorch.SF-Bay.ORG (Scott Hazen Mueller)
Date: Sat, 1 Jul 1995 23:11:02 GMT

The following may be relevant to the Potapov device.

It contains excerpts from "And yet it moves...strange systems &
subtle questions in physics," by Mark P. Silverman, Cambridge
University Press, 1993; Chpt 6 "The Wirbelrohr's Roar".

  [BILL B. NOTE:  also see Scientific American, November 1958 for a
  Hilsch-tube construction article in  Stong's THE AMATEUR SCIENTIST]

"It was a Wirbelrohr, he explained; you blew into the stem, and
out one end of the cross-tube flowed hot air, while cold air
flowed out the other. I laughed; I was certain he was teasing me.
Although I had never heard of a Wirbelrohr, I recognised a
Maxwell demon when it was described."

"...he machined in his basement workshop a working model which I
received from him shortly afterwards. The exterior was more or
less just as he had described it: two identical long thin-walled
tubes (the cross-bar of the T), were connected by cylindrical
collars screwed into each end of a short section of pipe that
formed the central chamber; a gas inlet nozzle (the stem of the
T), shorter than the other two tubes but otherwise of identical
construction, joined the midsection tangentially (Fig. 6.1). Ex-
ternally, except for a throttling valve at the far end of one
output tube to control air flow, the entire device manifested bi-
lateral symmetry with respect to a plane through the nozzle per-
pendicular to the cross-tubes.

"Only someone with the lung capacity of Hercules could actually
blow into the stem.  Instead, the nozzle was meant to be attached
to a source of compressed air.  Taking the Wirbelrohr into my
laboratory, I looked sceptically for a moment at its symmetrical
shape before opening the valve by my work table that started the
flow of room-temperature compressed air. Then, with frost forming
on the outside surface of one tube, I yelped with pain and aston-
ishment when, touching the other tube, I burned my fingers!"

"...With the few parts of the Wirbelrohr laid out on my table, I
understood better the significance of the German name, Wirbel-
rohr, or vortex tube. The heart of the device is the central
chamber with a spiral cavity and offset nozzle. Compressed gas
entering this chamber streams around the walls of the cavity in a
high-speed vortex.  But what gives rise to spatially separated
air currents at different temperatures? ...the placement in one
cross-tube (the cold one) of a small-aperture diaphragm effec-
tively blocked the efflux of gas along the walls of the tube,
thereby forcing this part of the air flow to exit through the
other arm whose cross-section was unconstrained.

  __                 |-----------|
 |  \  --------------|           |------------------
 |   \                          |   "COLD" PIPE
 |    |       "HOT" PIPE
 |   /                           | <--- diaphragm 
 |__/  --------------|           |------------------
                     |---|   |---|
                 /       |   |
          CENTRAL        |   |
          CHAMBER        |   |
             |           |   | <- INLET
         /      \			Fig 6 - Schematic of Wirbelrohr or 
       /   __     \                vortex tube.
      /   /        \
     |   /          |  Top View
     |   |          |       
      \  | |       /
       \ | |      /
         | |    /
         | |--- 
         | |
         | | <- INLET
         | |
          Room-temperature compressed air enters the inlet tube,
          spirals around the central chamber, and exits through
          the 'hot' pipe with unconstrained cross-section or
          through the 'cold' pipe whose aperture is restricted 
          by a diaphragm.
[BILLB: the 'hot' tube should be partially blocked, with either a valve,
or even better, a narrow ring-slot that lets air near the inner surface

"The glimmer of a potential mechanism dawned on me. Had the in-
coming air conserved angular momentum, the rotational frequency
of air molecules nearest the axis of the central chamber would be
higher - as would also be the corresponding rotational kinetic
energy - than peripheral layers of air. However, internal fric-
tion between gas layers comprising the vortex would tend to es-
tablish a constant angular velocity throughout the cross-section
of the chamber. In other words, each layer of gas within the vor-
tex would exert a tangential force upon the next outer layer,
thereby doing work upon it at the expense of its internal energy
(while at the same time receiving kinetic energy from the preced-
ing inner layer). Energy would consequently flow from the center
radially outward to the walls generating a system with a low-
pressure, cooled axial region and a high-pressure, heated circum-
ferential region.  Because of the diaphragm, the cooler axial air
had to exit one tube (the cold side), whereas a mixture of axial
and peripheral air exited the other (the hot side).

"The presence of the throttling valve on the hot side now made
sense. If the low pressure of the air nearest the axis of the
tube fell below atmospheric pressure, the cold air would not exit
at all...By throttling the flow, pressure within the central
chamber was increased sufficiently so that air could exit both

"...with some simplifying assumptions I was able to calculate the
entropy change... Under what is termed adiabatic conditions -
i.e. with no heat exchange with the environment - the 2nd Law re-
quires that the entropy change of the gas, alone, be >= zero.
The resulting mathematical expression, augmented by the equation
of state of an ideal diatomic gas and the conservation of energy
(1st Law) yields an inequality:

 (x^f)[(1-fx)/(1-f)]^(1-f) >= (Pf/Pi)^(2/7)

 where x= Tc/Ti
       Tc  is temperature of cold air
       Ti  is initial temperature
       Pf  is the final pressure
       Pi  is the initial pressure
       f is the fraction of gas directed thru the cold side

"By setting the expression for the entropy change equal to zero,
I could calculate the lowest temperature that the cold tube
should be able to reach if the gas flow were an ideal reversible
process. The result was astonishing.  With an input pressure of
10 atmospheres and the throttling set for a fraction f= 0.3, com-
pressed air at room temperature (20 C) could in principle be
cooled to about -258 C, a mere 15 degrees above absolute zero!
(The corresponding temperature of the hot side would have been 80

"...The first experimental demonstation of a vortex tube seems to
have been reported in 1933 by a French engineer, Georges Ranque
[1].  by German physicist Rudolph Hilsch came to the attention of
American chemist R.M. Milton... In Hilsch's hands, proper selec-
tion of the air fraction f (~ .33) and an input pressure of a few
atmospheres gave rise to an amazing output of 200 C at the hot
end and -50 C at the cold end[2]. Hilsch, who was the one to coin
the term Wirbelrohr, used the tube in place of an ammonia pre-
cooling apparatus in a machine to liquify air.

"...Milton was not satisfied with the interpretation of Hilsch
and Ranque that frictional loss of kinetic energy produced the
radial temperature distribution...."

M Kurosaka et al[3,4], in 1982, proposed a far different mecha-
nism, supported by experiment.

"With a loud roar air rushes turbulently thru the Wirbelrohr,
just as it does thru a jet engine or a vacuum cleaner.  Buried
within that roar, however, is a pure tone, a "vortex whistle" as
it has been called...the vortex whistle can be produced by tan-
gential introduction and swirling of gas in a stationary tube. It
is this pure tone that is purportedly responsible for the spec-
tacular separation of temperature in a vortex tube.

"The Ranque-Hilsch effect is a steady-state phenomenon - i.e. an
effect that survives averaging over time. How can a high-pitch
whistle - a sound that, depending on air velocity and cavity ge-
ometry, can be on the order of a few kilohertz - influence the
steady component of flow? The answer...was by 'acoustic stream-
ing'.  As a result of a small nonlinear convection term in the
fluid equation of motion, an acoustic wave can act back upon the
steady flow and modify its properties substantially. In the ab-
sence of unsteady disturbances, the air flows in a 'free' vortex
around the axis of the tube; the speed of the air is close to ze-
ro at the center (like a hurricane), increases to a maximum at
mid-radius, and drops to a small value near the walls. Acoustic
streaming, however, deforms the free vortex into a 'forced' vor-
tex where the air speed increases linearly from the center to the
periphery.  Acoustic streaming and the production of a forece
vortex, rather than mere static centrifugation, engender the
Ranque-Hilsch effect.

"The experimental test could not be more direct. Remove the whis-
tle, and only the whistle, and see whether the radial temperature
distribution remains. To do this [Kurosaka] monitored the entire
roar with a microphone and ...decomposed it into frequencies of
which the discrete component of the lowest frequency and largest
amplitude was identified as the vortex whistle. Next, he enclosed
the Wirbelrohr inside a tunable acoustic suppressor: a cylindri-
cal section of Teflon with radially drilled holes serving as
acoustic cavities distributed uniformly around the circumference.
Inside each hole was a small tuning rod that could be inserted
until it touched the outer shell of the Wirbelrohr to close off
the cavity, or withdrawn incrementally to make the cavity reso-
nant at the specified frequency to be suppressed.

"To simplify the experimental test, he sealed off one output of
the vortex tube and monitored with thermocouples the temperatuare
difference between the center and periphery. In the absence of
the suppressor, an increase in pressure produced, as I had no-
ticed when experimenting with my own vortex tube, a louder roar
and greater temperature difference. When, however, the acoustic
cavity was adjusted to suppress only the frequency of the vortex
whistle (leaving unaffected the rest of the turbulent noise), the
temperature difference plunged precipitously at the instant the
corresponding input air pressure was reached. In one such trial,
the centerline temperature jumped 33 C, from -50 C to -17 C. With
further increase in pressure, the frequency of the whistle rose,
and as it exceeded the narrow band of the acoustic suppressor,
the temperature difference increased again.

"Additional evidence came from a striking transformation in the
natuare of the flow...Before the vortex whistle was suppressed,
the exhaust air swirled rapidly near and outside the tube periph-
ery in the manner expected for a forced vortex. Upon supprssion,
however, the forced vortex was also abruptly suppressed; now qui-
escent at the periphery, the air rushed out close to the center-

"For all I know, the case of the mysterious Wirbelrohr is largely
closed although, science being what it is, future version of that
device may yet hold some suprises in store. I have sometimes won-
dered, for example, what would result from supplying a vortex
tube, not with room-temperature air, but with a quantum fluid,
like liquid helium, free of viscosity and friction.

The exorcism of the demon in the Wirbelrohr will not, I suspect,
dampen one bit the ardour of those whose passion it is to chal-
lenge the 2nd Law. Despite the time and effort that has been
frittered away in the past, others will undoubtedly try again.
On the whole such schemes are bound to fail, but every so often,
as in the case of Maxwell's own whimsical creation, this failure
has its positive side: when, from the clash between human ingenu-
ity and the laws of nature, there emerge sounder knowledge and
deeper understanding."


[1] G. Ranque, "Experiences sur la Detente Giratore avec Productions Simultanees d'un Echappement d'air Chaud et d'un Echappement d'air Froid", J. de Physique et Radium 4(7)(1933) 112 S.

[2] R. Hilsch, "The Use of the Expansion of Gases in a Centrifugal Field as Cooling Process", Rev. Sci. Instrum. 18(2) (1947) 108-1113.

[3] M. Kurosaka, "Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex Tube) Effect", J. Fluid Mech. 124(1982)139.

[4] M. Kurosaka, J.Q. Chu, & J.R. Goodman, "Ranque-Hilsch Effect Revisited: Temperature Separation Traced to Orderly Spinning Waves or Vortex Whistle", conference of Am Inst. of Aero & Astro 1982.



C. L. Stong, The "Hilsch" Vortex Tube, The Amateur Scientist, Scientific American, 514-519.

A Universe of Atoms, an Atom in the Universe, Ch 1, " The Wirbelrohr's Roar" (google books)

J. J. Van Deemter, On the Theory of the Ranque-Hilsch Cooling Effect, Applied Science Research 3, 174-196.
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