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# Vortex tube

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### Vortex tube

For the term 'vortex-tube' used in fluid dynamics please see: vorticity
Separation of a compressed gas into a hot stream and a cold stream

The vortex tube, also known as the Ranque-Hilsch vortex tube, is a mechanical device that separates a compressed gas into hot and cold streams. The air emerging from the "hot" end can reach temperatures of 200 °C, and the air emerging from the "cold end" can reach -50 °C.[1] It has no moving parts.

Pressurized gas is injected tangentially into a swirl chamber and accelerated to a high rate of rotation. Due to the conical nozzle at the end of the tube, only the outer shell of the compressed gas is allowed to escape at that end. The remainder of the gas is forced to return in an inner vortex of reduced diameter within the outer vortex.

## Contents

• Method of operation 1
• Fundamental Approach: The Physics of Vortex Tubes 1.1
• Phenomenological Approach 1.2
• History 2
• Efficiency 3
• Applications 4
• Current applications 4.1
• References 6

## Method of operation

To explain the temperature separation in a vortex tube, there are two main approaches:

### Fundamental Approach: The Physics of Vortex Tubes

This approach is based on first-principles physics alone and is not limited to vortex tubes only, but applies to moving gas in general. It shows that temperature separation in a moving gas is due only to enthalpy conservation in a moving frame of reference.

The main physical phenomenon of the vortex tube is the temperature separation between the cold vortex core and the warm vortex periphery. The "vortex tube effect" is fully explained with the work equation of Euler,[2] also known as Euler's turbine equation, which can be written in its most general vectorial form as:[3]

T - \frac{ \vec v \cdot \vec \omega \times \vec r}{c_p}=\mbox{const} ,

where T is the total, or stagnation temperature of the rotating gas at radial position \vec r, the absolute gas velocity as observed from the stationary frame of reference is denoted with \vec v; the angular velocity of the system is \vec \omega and c_p is the isobaric heat capacity of the gas. This equation has been published in 2012; it explains the fundamental operating principle of vortex tubes. The search for this explanation began in 1933 when the vortex tube was discovered and continued for more than 80 years.

The above equation is valid for an adiabatic turbine passage; it clearly shows that while gas moving towards the center is getting colder the peripheral gas in the passage is "getting faster". Therefore, vortex cooling is due to angular propulsion. The more the gas cools by reaching the center, the more rotational energy it delivers to the vortex and thus the vortex rotates even faster. This explanation stems directly from the law of energy conservation. Compressed gas at room temperature is expanded in order to gain speed through a nozzle; it then climbs the centrifugal barrier of rotation during which energy is also lost. The lost energy is delivered to the vortex, which speeds its rotation. In a vortex tube, the cylindrical surrounding wall confines the flow at periphery and thus forces conversion of kinetic into internal energy, which produces hot air at the hot exit.

Therefore, the vortex tube is a rotorless turboexpander.[4] It consists of a rotorless radial inflow turbine (cold end, center) and a rotorless centrifugal compressor (hot end, periphery). The work output of the turbine is converted into heat by the compressor at the hot end.

### Phenomenological Approach

This approach relies on observation and experimental data. It is specifically tailored to the geometrical shape of the vortex tube and the details of its flow and is designed to match the particular observables of the complex vortex tube flow, namely turbulence, acoustic phenomena, pressure fields, air velocities and many others. The earlier published models of the vortex tube are phenomenological. They are:

(1) Radial pressure difference: centrifugal compression and air expansion

(2) Radial transfer of angular momentum

(3) Radial acoustic streaming of energy

More on these models can be found in recent review articles on vortex tubes,.[5][6]

The phenomenological models were developed at an earlier time when the turbine equation of Euler was not thoroughly analyzed; in the engineering literature, this equation is studied mostly to show the work output of a turbine; while temperature analysis is not performed since turbine cooling has more limited application unlike power generation, which is the main application of turbines. Phenomenological studies of the vortex tube in the past have been useful in presenting empirical data. However, due to the complexity of the vortex flow this empirical approach was able to show only aspects of the effect but was unable to explain its operating principle. Dedicated to empirical details, for a long time the empirical studies made the vortex tube effect appear enigmatic and its explanation - a matter of debate.

## History

The vortex tube was invented in 1933 by French physicist Rudolf Hilsch improved the design and published a widely read paper in 1947 on the device, which he called a Wirbelrohr (literally, whirl pipe).[7] The vortex tube was used to separate gas mixtures, oxygen and nitrogen, carbon dioxide and helium, carbon dioxide and air in 1967 by Linderstrom-Lang.[8] [9] Vortex tubes also seem to work with liquids to some extent, as demonstrated by Hsueh and Swenson in a laboratory experiment where free body rotation occurs from the core and a thick boundary layer at the wall. Air is separated causing a cooler air stream coming out the exhaust hoping to chill as a refrigerator.[10] In 1988 R.T.Balmer applied liquid water as the working medium. It was found that when the inlet pressure is high, for instance 20-50 bar, the heat energy separation process exists in incompressible (liquids) vortex flow as well. Note that this separation is only due to heating; there is no longer cooling observed since cooling requires compressibility of the working fluid.

## Efficiency

Vortex tubes have lower efficiency than traditional air conditioning equipment.[11] They are commonly used for inexpensive spot cooling, when compressed air is available.

## Applications

### Current applications

Commercial vortex tubes are designed for industrial applications to produce a temperature drop of up to 71 °C (127 °F). With no moving parts, no electricity, and no Freon, a vortex tube can produce refrigeration up to 6,000 BTU/h (1,800 W) using only filtered compressed air at 100 PSI (6.9 bar). A control valve in the hot air exhaust adjusts temperatures, flows and refrigeration over a wide range.[12]

Vortex tubes are used for cooling of cutting tools (lathes and mills, both manually-operated and CNC machines) during machining. The vortex tube is well-matched to this application: machine shops generally already use compressed air, and a fast jet of cold air provides both cooling and removal of the "chips" produced by the tool. This completely eliminates or drastically reduces the need for liquid coolant, which is messy, expensive, and environmentally hazardous.

## References

1. ^ Walker, Jearl (1975). "The madness of stirring tea". The Flying Circus of Physics. John Wiley & Sons, Inc. p. 97.
2. ^ [7] - Z.S. Spakovszky. Unified: thermodynamics and propulsion (Lecture notes), Massachusetts Institute of Technology, Cambridge, Mass. 2007. ch. 12.3.
3. ^ [8] - J. Polihronov et al, "Thermodynamics of angular propulsion in fluids", Physical Review Letters 054504, 2012.
4. ^ [9] - J. Polihronov et al, "Vortex tube effect without walls", Canadian Journal of Physics, DOI: 10.1139/cjp-2014-0227(2015).
5. ^ [10] - Y. Xue et al, "A critical review of temperature separation in a vortex tube", Exper. Therm. Fluid Sci.34, 1367 (2010).
6. ^ [11] - S. Eiamsa-ard et al, "Review of Ranque–Hilsch effects in vortex tubes", Renewable and Sustainable Energy Reviews 12 (2008) 1822–1842
7. ^ *Rudolf Hilsch, The Use of the Expansion of Gases in A Centrifugal Field as Cooling Process, The Review of Scientific Instruments, vol. 18(2), 108-1113, (1947). translation of an article in Zeit. Naturwis. 1 (1946) 208.
8. ^ Chengming Gao, Experimental Study on the Ranque-Hilsch Vortex Tube, (2005) page 2
9. ^ Vortex tubes are constructed of stainless steel and use a generator and valve made of brass and sealed with viton o-rings to allow their use in the widest range of environments.
10. ^ R.T. Balmer. Pressure-driven Ranque-Hilsch temperature separation in liquids. Trans. ASME, J. Fluids Engineering, 110:161–164, June 1988.
11. ^ [12] - J. Polihronov et al, "The maximum coefficient of performance (COP) of vortex tubes", Canadian Journal of Physics, DOI: 10.1139/cjp-2015-0089(2015).
12. ^ Newman Tools Inc. http://www.newmantools.com/vortex.htm

• G. Ranque, Expériences sur la Détente Giratoire avec Productions Simultanées d'un Echappement d'air Chaud et d'un Echappement d'air Froid, J. de Physique et Radium 4(7)(1933) 112S.
• H. C. Van Ness, Understanding Thermodynamics, New York: Dover, 1969, starting on page 53. A discussion of the vortex tube in terms of conventional thermodynamics.
• Mark P. Silverman, And Yet it Moves: Strange Systems and Subtle Questions in Physics, Cambridge, 1993, Chapter 6
• Samuel B. Hsueh and Frank R. Swenson,"Vortex Diode Interior Flows," 1970 Missouri Academy of Science Proceedings, Warrensburg, Mo.
• C. L. Stong, The Amateur Scientist, London: Heinemann Educational Books Ltd, 1962, Chapter IX, Section 4, The "Hilsch" Vortex Tube, p514-519.
• J. J. Van Deemter, On the Theory of the Ranque-Hilsch Cooling Effect, Applied Science Research 3, 174-196.
• Saidi, M.H. and Valipour, M.S., "Experimental Modeling of Vortex Tube Refrigerator", J. of Applied Thermal Engineering, Vol.23, pp. 1971–1980, 2003.
• Valipour MS, and Niazi N, "Experimental modeling of a curved Ranque–Hilsch vortex tube refrigerator", International Journal of Refrigeration, vol.34(4),1109-1116, 2011.(http://dx.doi.org/10.1016/j.ijrefrig.2011.02.013)
• M. Kurosaka, Acoustic Streaming in Swirling Flow and the Ranque-Hilsch (vortex-tube) Effect, Journal of Fluid Mechanics, 1982, 124:139-172
• M. Kurosaka, J.Q. Chu, J.R. Goodman, Ranque-Hilsch Effect Revisited: Temperature Separation Traced to Orderly Spinning Waves or 'Vortex Whistle', Paper AIAA-82-0952 presented at the AIAA/ASME 3rd Joint Thermophysics Conference (June 1982)
• Gao, Chengming. Experimental Study on the Ranque-Hilsch Vortex Tube. Eindhoven : Technische Universiteit Eindhoven.
• R. Ricci, A. Secchiaroli, V. D’Alessandro, S. Montelpare. Numerical analysis of compressible turbulent helical flow in a Ranque-Hilsch vortex tube. Computational Methods and Experimental Measurement XIV, pp. 353–364, Ed. C. Brebbia, C.M. Carlomagno, ISBN 978-1-84564-187-0.
• A. Secchiaroli, R. Ricci, S. Montelpare, V. D’Alessandro. Fluid Dynamics Analysis of a Ranque-Hilsch Vortex-Tube. Il Nuovo Cimento C, vol.32, 2009, ISSN 1124-1896.
• A. Secchiaroli, R. Ricci, S. Montelpare, V. D’Alessandro. Numerical simulation of turbulent flow in a Ranque-Hilsch vortex-tube. Int. J. of Heat and Mass Transfer, Vol. 52, Issues 23-24, November 2009, pp. 5496–5511, ISSN 0017-9310.
• N. Pourmahmoud, A. Hassanzadeh, O. Moutaby. Numerical Analysis of The Effect of Helical Nozzles Gap on The Cooling Capacity of Ranque Hilsch Vortex Tube. Int. J. of Refrigeration, Vol. 35, Issue 5, 2012, pp. 1473–1483, ISSN 0140-7007.
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