Vortex Tube efficiency is typically around 0.1 to 0.2 COP (Coefficient Of Performance = Actual Cooling / Energy Supplied). Standard AC units today can have a COP as high as 3.43 or as much as 34 time the efficiency of a vortex tube. COP = SEER / 3.792 so a 13 SEER unit has a COP of 3.43.
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). Externally, 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 perpendicular 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 astonishment 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, Wirbelrohr, 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 effectively 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 escape.]
"The glimmer of a potential mechanism dawned on me. Had the incoming 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 friction between gas layers comprising the vortex would tend to establish a constant angular velocity throughout the cross-section of the chamber. In other words, each layer of gas within the vortex 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 preceding 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 circumferential 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 tubes.
"...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 requires 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, compressed 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 C.)
"...The first experimental demonstation of a vortex tube seems to have been reported in 1933 by a French engineer, Georges Ranque . by German physicist Rudolph Hilsch came to the attention of American chemist R.M. Milton... In Hilsch's hands, proper selection 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. Hilsch, who was the one to coin the term Wirbelrohr, used the tube in place of an ammonia precooling 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 mechanism, 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 tangential introduction and swirling of gas in a stationary tube. It is this pure tone that is purportedly responsible for the spectacular 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 geometry, can be on the order of a few kilohertz - influence the steady component of flow? The answer...was by 'acoustic streaming'. 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 absence of unsteady disturbances, the air flows in a 'free' vortex around the axis of the tube; the speed of the air is close to zero 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' vortex 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 whistle, 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 cylindrical 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 resonant 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 noticed 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 periphery in the manner expected for a forced vortex. Upon supprssion, however, the forced vortex was also abruptly suppressed; now quiescent at the periphery, the air rushed out close to the center-line."
"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 wondered, 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 challenge 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 ingenuity and the laws of nature, there emerge sounder knowledge and deeper understanding."
 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.
 R. Hilsch, "The Use of the Expansion of Gases in a Centrifugal Field as Cooling Process", Rev. Sci. Instrum. 18(2) (1947) 108-1113.
 M. Kurosaka, "Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (Vortex Tube) Effect", J. Fluid Mech. 124(1982)139.
 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.
J. J. Van Deemter, On the Theory of the Ranque-Hilsch Cooling Effect, Applied Science Research 3, 174-196.
Have you considered using regenerative cooling? By this I mean that the air from the compressor would first flow though a heat exchanger on the cold side before entering the vortex thereby progressively lowering the input air temperature which would lower the output temperature which would again lower the input temperature and so on. It is the same scheme used to liquefy air so I don't know why it wouldn't work with a vortex tube also+
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