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Heat and Mass Transfer

, Volume 45, Issue 5, pp 613–632 | Cite as

A review on design criteria for vortex tubes

  • M. YilmazEmail author
  • M. Kaya
  • S. Karagoz
  • S. Erdogan
Original

Abstract

In this study, the past investigations of the design criteria of vortex tubes were overviewed and the detailed information was presented on the design of them. Vortex tubes were classified and the type of them was described. All criteria on the design of vortex tubes were given in detail using experimental and theoretical results from the past until now. Finally, the criteria on the design of them are summarized.

Keywords

Inlet Pressure Vortex Tube Vortex Chamber Exergy Destruction Inlet Nozzle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

cross section (m2)

CFD

computational fluid dynamics

COP

coefficient of performance

cp

specific heat at constant pressure (kJ kg−1 K−1)

cv

specific heat at constant volume (kJ kg−1 K−1)

d

diameter (m)

D

diameter (m)

h

enthalpy (kJ kg−1)

k

specific heat ratio

k

Boltzmann constant (J K−1)

L

length (m)

\( \dot{m} \)

mass flow rate (kg s−1)

N

number

p

pressure (Pa)

\( \dot{Q} \)

heat transfer rate (W)

R

specific gas constant (kJ kg−1 K−1)

RHVT

Ranque–Hilsch vortex tube

S

entropy (W K−1)

T

temperature (K)

\( T_{\text{sm}}^{*} \)

temperature assumed to be \( T_{h}^{1 - \varepsilon } T_{c}^{\varepsilon } \)

\( \dot{W} \)

power (W)

X

normalised pressure drop \( \left( {X = {{\left( {p_{{\text{in}}} - p_{c} } \right)} \mathord{\left/ {\vphantom {{\left( {p_{{\text{in}}} - p_{c} } \right)} {p_{{\text{in}}} }}} \right. \kern-\nulldelimiterspace} {p_{{\text{in}}} }}} \right) \)

Greek symbols

α

angle of cone-shaped control valve

α

ratio of hot end area to tube area

β

cold orifice diameter ratio \( \left( {\beta = {{d_{\text{c}} } \mathord{\left/ {\vphantom {{d_{\text{c}} } D}} \right. \kern-\nulldelimiterspace} D}} \right) \)

ε

cold fraction

εo

Lennard–Jones potential

η

efficiency

ΔT

temperature difference

\( {{\Updelta T} \mathord{\left/ {\vphantom {{\Updelta T} {T_{\text{in}} }}} \right. \kern-\nulldelimiterspace} {T_{\text{in}} }} \)

normalised temperature drop/rise

Γ

\( {{\left( {k - 1} \right)} \mathord{\left/ {\vphantom {{\left( {k - 1} \right)} k}} \right. \kern-\nulldelimiterspace} k} \)

Θ

irreversibility parameter

\( \tau_{\text{p}} \)

pressure ratio \( \left( { = {{p_{\text{in}} } \mathord{\left/ {\vphantom {{p_{\text{in}} } {p_{\text{c}} }}} \right. \kern-\nulldelimiterspace} {p_{\text{c}} }}} \right) \)

Subscripts

atm

atmosphere

c

cold

cr

cooler

cr

critical

h

hot

hp

heat pump

in

inlet

i

irreversible

ir

irreversible

s

isentropic

Notes

Acknowledgments

The authors would like to acknowledge that this study was supported with a grant from The Scientific and Technological Research Council of Turkey, TÜBİTAK (Project No: 105M028, Project Title: Use of Vortex Tubes in Refrigeration Technique), and Atatürk University Scientific Research Foundation (Project No: BAP 2005/20, Project Title: Use of Vortex Tubes in Refrigeration Technique).

References

  1. 1.
    Gao C (2005) Experimental study on the Ranque–Hilsch vortex tube. PhD Thesis, Technische Universiteit EindhovenGoogle Scholar
  2. 2.
    Eiamsa-ard S, Promvonge P (2007) Review of Ranque–Hilsch effects in vortex tubes. Renew Sustain Energy Rev. doi: 10.1016/j.rser.2007.03.006
  3. 3.
    Ranque GJ (1933) Experiments on expansion in a vortex with simultaneous exhaust of hot air and cold air. J Phys Radium (Paris) 4:112–114, June. Also translated as General Electric Co., Schenectady Works Library 1947; T.F. 3294Google Scholar
  4. 4.
    Ranque GJ (1934) Method and apparatus for obtaining from a fluid under pressure two outputs of fluid at different temperatures. US patent 1:952,281Google Scholar
  5. 5.
    Hilsch R (1947) The use of expansion of gases in a centrifugal field as a cooling process. Rev Sci Instrum 18(2):108–113CrossRefGoogle Scholar
  6. 6.
    Westley R (1954) A bibliography and survey of the vortex tube. College of Aeronautics, Cranfield note, UKGoogle Scholar
  7. 7.
    Curley W, McGree R Jr (1951) Bibliography of vortex tubes. Refrig Eng 59(2):191–193Google Scholar
  8. 8.
    Kalvinskas L (1956) Vortex tubes (an extension of Wesley’s bibliography). Jet Propulsion Laboratory, California Inst of Technology Literature Search, 56, Part 2Google Scholar
  9. 9.
    Dobratz BM (1964) Vortex tubes: a bibliography. Lawrence Radiation Laboratory UCRL-7829Google Scholar
  10. 10.
    Nash JM (1972) The Ranque–Hilsch vortex tube and its application to spacecraft environmental control systems. Dev Theor Appl Mech, p 6Google Scholar
  11. 11.
    Hellyar KG (1979) Gas liquefaction using a Ranque–Hilsch vortex tube: design criteria and bibliography. Report for the degree of Chemical Engineer, Massachusetts Institute of TechnologyGoogle Scholar
  12. 12.
    Fulton CD (1950) Ranque’s tube. J ASRE Refrig Eng 58:473–479Google Scholar
  13. 13.
    Fulton CD (1951) Comments on the vortex tube. J ASRE Refrig Eng 59:984Google Scholar
  14. 14.
    Hartnett JP, Eckert ERG (1957) Experimental study of the velocity and temperature distribution in a high-velocity vortex-type flow. Trans ASME J Heat Transfer 79:751–758Google Scholar
  15. 15.
    Martynovskii VS, Alekseev VP (1957) Investigation of the vortex thermal separation effect for gases and vapors. Sov Phys-Tech Phys 26(2):2233–2243Google Scholar
  16. 16.
    Lay JE (1959) An experimental and analytical study of vortex flow temperature separation by superposition of spiral and axial flows: Part I. Trans ASME J Heat Transfer 81(4):202–212Google Scholar
  17. 17.
    Lay JE (1959) An experimental and analytical study of vortex flow temperature separation by superposition of spiral and axial flows: Part II. Trans ASME J Heat Transfer 81(4):213–222Google Scholar
  18. 18.
    Deissler RG, Perlmutter M (1958) An analysis of the energy separation in laminar and turbulent compressible vortex flows. Heat Transfer and Fluid Mechanics Institute, Stanford University PressGoogle Scholar
  19. 19.
    Deissler RG, Perlmutter M (1960) Analysis of the flow and energy separation in a vortex tube. Int J Heat Mass Transfer 1:173–191CrossRefGoogle Scholar
  20. 20.
    Takahama H (1965) Studies on vortex tubes. Bull Jpn Soc Mech Eng 8(31):433–440Google Scholar
  21. 21.
    Takahama H, Ikeda T, Kawamura H (1973) Japan Soc Mech Eng 77:733–734Google Scholar
  22. 22.
    Takahama H, Soga N (1966) Studies on vortex tubes 2nd report, Reynolds no. the effects of the cold air rate and partial admission of nozzle on the energy separation. Bull Jpn Soc Mech Eng 9(33):121–130Google Scholar
  23. 23.
    Takahama H, Kawamura M, Kato B, Yokosawa H (1979) Performance characteristics of energy separation in a steam operated vortex tube. Int J Eng Sci 17:735–744CrossRefGoogle Scholar
  24. 24.
    Takahama H, Yokosawa H (1981) Energy separation in vortex tubes with a divergent chamber. Trans ASME J Heat Transfer 103:196–203Google Scholar
  25. 25.
    Takahama H, Kawashima K (1966) An experimental study of vortex tubes. Bull JSME 9(33):227–245Google Scholar
  26. 26.
    Sibulkin M (1962) Unsteady, viscous, circular flow, Part III. Application to the Ranque–Hilsch vortex tube. J Fluid Mech 12:269–293CrossRefGoogle Scholar
  27. 27.
    Linderstrom-Lang CU (1964) Gas separation in the Ranque–Hilsch vortex tube. Int J Heat Mass Transfer 7:1195–1206CrossRefGoogle Scholar
  28. 28.
    Linderstrom-Lang CU (1966) Gas separation in the Ranque–Hilsch vortex tube model calculations based on flow data. Riso report, Denmark, JuneGoogle Scholar
  29. 29.
    Linderstrom-Lang CU (1971) The three-dimensional distributions of tangential velocity and total-temperature in vortex tubes. J Fluid Mech 45:161–187CrossRefGoogle Scholar
  30. 30.
    Linderstrom-Lang CU (1971) Studies on transport of mass and energy in the vortex tube. The significance of the secondary flow and its interaction with the tangential velocity distribution. Riso report, Denmark, SeptemberGoogle Scholar
  31. 31.
    Borisenko AI, Safonov VA, Yakovlev AI (1968) The effect of geometric parameters on the characteristics of a conical vortex cooling unit. J Eng Phys Thermophys 15(6):1158–1162Google Scholar
  32. 32.
    Bruun HH (1969) Experimental investigation of the energy separation in vortex tubes. J Mech Eng Sci 11(6):567–582CrossRefGoogle Scholar
  33. 33.
    Raiskii Yu D, Tunkel LE (1974) Influence of vortex-tube saturation and length on the process of energetic gas separation. J Eng Phys 27(6):1578–1581CrossRefGoogle Scholar
  34. 34.
    Soni Y (1973) A parametric study of the Ranque–Hilsch tube. PhD Thesis, University of IdahoGoogle Scholar
  35. 35.
    Soni Y, Thompson WJ (1975) Optimal design of the Ranque–Hilsch vortex tube. Trans ASME J Heat Transfer 94(2):316–317Google Scholar
  36. 36.
    Marshall J (1977) Effect of operating conditions, physical size and fluid characteristics on the gas separation performance of the Linderstrom–Lang vortex tube. Int J Heat Mass Transfer 20:227–231CrossRefGoogle Scholar
  37. 37.
    Kurosaka M (1982) Acoustic streaming in swirling flow and the Ranque–Hilsch (vortex tube) effect. J Fluid Mech 124:139–172CrossRefGoogle Scholar
  38. 38.
    Stephan K, Lin S, Durst M, Huang F, Seher D (1983) An investigation of energy separation in a vortex tube. Int J Heat Mass Transfer 26:341–348CrossRefGoogle Scholar
  39. 39.
    Stephan K, Lin S, Durst M, Huang F, Seher D (1984) A similarity relation for energy separation in a vortex tube. Int J Heat Mass Transfer 27:911–920CrossRefGoogle Scholar
  40. 40.
    Balmer RT (1988) Pressure driven Ranque Hilsch temperature separation in liquids. J Fluids Eng 110:161–164CrossRefGoogle Scholar
  41. 41.
    Nabhani N (1989) Hot-wire anemometry study of confined turbulent swirling flow. PhD Thesis, Bradford University, BradfordGoogle Scholar
  42. 42.
    Ahlborn B, Keller JU, Staudt R, Treitz G, Rebhan E (1994) Limits of temperature separation in a vortex tube. J Phys D Appl Phys 27:480–488CrossRefGoogle Scholar
  43. 43.
    Ahlborn B, Camire J, Keller JU (1996) Low-pressure vortex tubes. J Phys D Appl Phys 29:1469–1472CrossRefGoogle Scholar
  44. 44.
    Ahlborn B, Groves S (1997) Secondary flow in a vortex tube. Fluid Dyn Res 21(2):73–86CrossRefGoogle Scholar
  45. 45.
    Ahlborn B, Keller JU, Rebhan E (1998) The heat pump in a vortex tube. J Non-Equilib Thermodyn 23(2):159–165zbMATHGoogle Scholar
  46. 46.
    Ahlborn B, Gordon JM (2000) The vortex tube as a classic thermodynamic refrigeration cycle. J Appl Phys 88(6):3645–3653CrossRefGoogle Scholar
  47. 47.
    Gutsol AF (1997) The Ranque effect. Phys Uspekhi 40(6):639–658CrossRefGoogle Scholar
  48. 48.
    Gutsol AF, Bakken JA (1998) A new vortex method of plasma insulation and explanation of the Ranque effect. J Phys D Appl Phys 31:704–711CrossRefGoogle Scholar
  49. 49.
    Lewins J, Bejan A (1999) Vortex tube optimization theory. Energy J 24:931–943CrossRefGoogle Scholar
  50. 50.
    Saidi MH, Yazdi MR (1999) Exergy model of a vortex tube system with experimental results. Energy 24:625–632CrossRefGoogle Scholar
  51. 51.
    Cockerill TT (1998) Thermodynamics and fluid mechanics of a Ranque–Hilsch vortex tube. PhD Thesis, University of CambridgeGoogle Scholar
  52. 52.
    Khodorkov L, Poshernev NV, Zhidkov MA (2003) The vortex tube-a universal device for heating, cooling, cleaning, and drying gases and separating gas mixtures. Chem Pet Eng 39(7–8):409–415CrossRefGoogle Scholar
  53. 53.
    Poshernev NV, Khodorkov IL (2003) Experience from the operation of a conical vortex tube with natural gas. Chem Pet Eng 39(9–10):602–607CrossRefGoogle Scholar
  54. 54.
    Poshernev NV, Khodorkov IL (2004) Natural-gas tests on a conical vortex tube (CVT) with external cooling. Chem Pet Eng 40(3–4):212–217CrossRefGoogle Scholar
  55. 55.
    Shannak BA (2004) Temperature separation and friction losses in vortex tube. Heat Mass Transfer 40:779–785CrossRefGoogle Scholar
  56. 56.
    Singh PK, Tathgir RG, Gangacharyulu D, Grewal GS (2004) An experimental performance evaluation of vortex tube. IE(I) J-MC 84:149–153Google Scholar
  57. 57.
    Behera U, Paul PJ, Kasthurirengan S, Karunanithi R, Ram SN, Dinesh K et al (2005) CFD analysis and experimental investigations towards optimizing the parameters of Ranque–Hilsch vortex tube. Int J Heat Mass Transfer 48(10):1961–1973CrossRefGoogle Scholar
  58. 58.
    Aljuwayhel NF, Nellis GF, Klein SA (2005) Parametric and internal study of the vortex tube using a CFD model. Int J Refrig 28(3):442–450CrossRefGoogle Scholar
  59. 59.
    Skye HM, Nellis GF, Klein SA (2006) Comparison of CFD analysis to empirical data in a commercial vortex tube. Int J Refrig 29:71–80CrossRefGoogle Scholar
  60. 60.
    Promvonge P, Eiamsa-ard S (2004) Experimental investigation of temperature separation in a vortex tube refrigerator with snail entrance. ASEAN J Sci Technol Dev 21(4):297–308Google Scholar
  61. 61.
    Promvonge P, Eiamsa-ard S (2005) Investigation on the vortex thermal separation in a vortex tube refrigerator. Sci Asia J 31(3):215–223CrossRefGoogle Scholar
  62. 62.
    Eiamsa-ard S, Promvonge P (2006) Numerical prediction of vortex flow and thermal separation in a subsonic vortex tube. J Zhejiang Univ SCI Int Appl Phys Eng J 7(8):1406–1415zbMATHCrossRefGoogle Scholar
  63. 63.
    Eiamsa-ard S, Promvonge P (2007) Numerical investigation of the thermal separation in a Ranque–Hilsch vortex tube. Int J Heat Mass Transfer 50(5–6):821–832zbMATHCrossRefGoogle Scholar
  64. 64.
    Azarov AI (1993) Industrial application of the range of vortex coolers. In: Proceedings of all-union conference “Application of the Vortex Effect in Engineering”. SGAI, Samara, pp 75–79Google Scholar
  65. 65.
    Azarov AI (2004) Ways of improving commercial vortex tubes. Chem Pet Eng 40(7–8):411–416CrossRefGoogle Scholar
  66. 66.
    Azarov AI. Modular multi-chambers vortex tubes. Available at [http://www.ecoteco.ru].
  67. 67.
    Azarov AI (2000) Multipurpose vortex air coolers: examination of the scales of industrial use. Vestn. MGTY 2000;Special Issue:93–9Google Scholar
  68. 68.
    Azarov AI (2002) Reducing the specific energy consumption for obtaining cold in vortex tubes. Mezhvuz. Sb. Nauch. Tr. Probl. Ékon. Topli.-Énerg. Resurs. Prompredpr. TÉS, pp 112–117Google Scholar
  69. 69.
    Yilmaz M, Comakli O, Kaya M, Karsli S (2006) Vortex tubes: 1 Technological development (in Turkish). Eng Mach 47(553):46–54Google Scholar
  70. 70.
    Yilmaz M, Comakli O, Kaya M, Karsli S (2006) Vortex tubes: 2 Energy separation mechanism and performance characteristics (in Turkish). Eng Mach 47(554):42–51Google Scholar
  71. 71.
    Piralishvili SA, Fuzeeva AA (2006) Similarity of the energy-separation process in vortex Ranque tubes. J Eng Phys Thermophys 79(1):27–32CrossRefGoogle Scholar
  72. 72.
    Silverman MP (1982) The vortex tube: a violation of the second law. Eur J Phys 3:88–92CrossRefGoogle Scholar
  73. 73.
    Cengel YA, Boles MA (1998) Thermodynamics: an engineering approach, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  74. 74.
    Piralishvili SA, Polyaev VM (1996) Flow and thermodynamic characteristics of energy separation in a doublecircuit vortex tube-an experimental investigation. Int J Exp Therm Fluid Sci 12(4):399–410CrossRefGoogle Scholar
  75. 75.
    Singh K. Ranque–Hilsch vortex tube. Available at [http://sps.nus.edu.sg]
  76. 76.
    Westley R (1957) Vortex tube performance data sheets. Cranfield College Note 67, College of AeronauticsGoogle Scholar
  77. 77.
    Gulyaev AI (1965) Ranque effect at low temperatures. J Eng Phys 9(3):242–244CrossRefMathSciNetGoogle Scholar
  78. 78.
    Gulyaev AI (1966) Investigation of conical vortex tubes. J Eng Phys 10(3):193–195CrossRefMathSciNetGoogle Scholar
  79. 79.
    Lewellen WS (1971) A review of confined vortex flows. Space Propulsion Lab., Massachusetts Institute of Technology. Contract Report NASA-CR-1772; N71-32276Google Scholar
  80. 80.
    Amitani T, Adachi T, Kato T (1983) A study on temperature separation in a large vortex tube. Trans JSME 49:877–884Google Scholar
  81. 81.
    Saidi MH, Valipour MS (2003) Experimental modeling of vortex tube refrigerator. Appl Therm Eng 23:1971–1980CrossRefGoogle Scholar
  82. 82.
    Dincer K, Baskaya S, Uysal BZ (2007) Experimental investigation of the effects of length to diameter ratio and nozzle number on the performance of counter flow Ranque–Hilsch vortex tubes. Heat Mass Transfer. doi: 10.1007/s00231-007-0241-z
  83. 83.
    Aydın O, Baki M (2006) An experimental study on the design parameters of a counter flow vortex tube. Energy J 31(14):2763–2772CrossRefGoogle Scholar
  84. 84.
    Universal Vortex, Inc. Pilot gas heater. Available at [http://www.universal-vortex.com/]
  85. 85.
    Arizona Vortex Tube—Manufacturing Company. Vortex tubes. Available at [http://www.arizonavortex.com/vortex-tube/]
  86. 86.
    Newman Tools Inc. Vortex tubes. Available at [http://www.newmantools.com/vortex.htm]
  87. 87.
    Exair Corporation. Vortex tubes and spot cooling products. Available at [http://www.exair.com]
  88. 88.
    AiRTX The Air Research Technology Company. Vortex tubes. Available at [http://www.airtxinternational.com/index.php]
  89. 89.
    Vortec. Vortex tubes. Available at [http://www.vortec.com/]
  90. 90.
    Meech Static Eliminators Ltd. Vortex coolers. Available at [http://www.meech.com/ProductGroup.aspx?id=62]
  91. 91.
    XoAir. Vortex tube. Available at [http://www.x-air.fr/]
  92. 92.
    C. C. Steven & Associates. Vortex tubes. Available at [http://www.vortexair.biz/]
  93. 93.
    Nex Flow™ Air Products Corp. Industrial Cooling Systems. Vortex tubes. Available at [http://www.nex-flow.com/vortex_tube.htm]
  94. 94.
    Westley R (1955) Optimum design of a vortex tube for achieving larger temperature drop ratios. Cranfield College Note 30, College of AeronauticsGoogle Scholar
  95. 95.
    Reynolds AJ (1961) Energy flows in a vortex tube. J Appl Math Phys 12:343zbMATHCrossRefMathSciNetGoogle Scholar
  96. 96.
    Reynolds AJ (1961) Studies of rotating fluids: I. Plane axisymmetric flow. II. The Ranque–Hilsch vortex tube. PhD Thesis, University of LondonGoogle Scholar
  97. 97.
    Reynolds AJ (1962) A note on vortex-tube flows. J Fluid Mech 14:18CrossRefGoogle Scholar
  98. 98.
    Metenin VI (1961) Investigation of vortex temperature type compressed gas separators. Sov Phys Tech Phys 5(9):1025–1032Google Scholar
  99. 99.
    Metenin VI (1964) An investigation of counter-flow vortex tubes. Int Chem Eng 4(3):461–466Google Scholar
  100. 100.
    Parulekar BB (1961) The short vortex tube. J Refrig 4:74–80Google Scholar
  101. 101.
    Leites IL, Semenov VP, Polovinkin VA, Mure BI, Tagintsev BG, Narizhnyi VP, Kozlova MS, Poletaev AS, Murzin MI (1971) The purification of natural gas by means of the vortex effect. Int Chem Eng 11(2):195–201Google Scholar
  102. 102.
    Wu YT, Ding Y, Ji YB, Ma CF, Ge MC (2007) Modification and experimental research on vortex tube. Int J Refrigeration (in press)Google Scholar
  103. 103.
    Merkulov AP (1969) Technical applications of the vortex effect (in Russian). Mashinostroenie, MoscowGoogle Scholar
  104. 104.
    Blatt TA, Trusch RB (1962) An experimental investigation of an improved vortex cooling device. American Society of Mechanical Engineers, Winter Annual Meeting, AmericaGoogle Scholar
  105. 105.
    Schlenz D (1982) Kompressible strahlgetriebene drallstromung in rotationssymmetrischen Kanalen. PhD Thesis, Technische Fakultat Universitat, Erlangen-NurnbergGoogle Scholar
  106. 106.
    Otten EH (1958) Production of cold air—simplicity of the vortex tube method. Engineering(London) 186(4821):154–156Google Scholar
  107. 107.
    Chu JG (1982) Acoustic streaming as a mechanism of the Ranque–Hilsch effect. PhD Thesis, University of Tennessee, KnoxvilleGoogle Scholar
  108. 108.
    Kuroda H (1983) An experimental study of temperature separation in swirling flow. PhD Thesis, University of Tennessee, KnoxvilleGoogle Scholar
  109. 109.
    Özgür AE (2001) Determination of parameters influencing the operating criteria of vortex tubes and industrial applications (in Turkish). MSc Thesis, Süleyman Demirel Üniversitesi, IspartaGoogle Scholar
  110. 110.
    Ma TQ, Zhao QG, Yu J, Ye F, Ma CF (2002) Experimental investigation on energy separation by vortex tubes. In: Twelfth international heat transfer conference, Grenoble, France, 18–23 August, vol 4, pp 537–542Google Scholar
  111. 111.
    Dincer K, Başkaya Ş, Kirmaci V, Usta H, Uysal BZ (2006) Investigation of performance of a vortex tube with air, oxygen, carbon dioxide and nitrogen as working fluids (in Turkish). Eng Mach 47(560):36–40Google Scholar
  112. 112.
    Williams A (1971) The cooling of methane with vortex tubes. J Mech Eng Sci 13(6):369–375CrossRefGoogle Scholar
  113. 113.
    Collins RL, Lovelace RB (1979) Experimental study of two-phase propane expanded through the Ranque–Hilsch tube. Trans ASME J Heat Transfer 101:300–305Google Scholar
  114. 114.
    Starostin PI, Itkin MS (1968) Operation of a vortex tube on high pressure superheated steam. Teploenergetika 15(8):31–35Google Scholar
  115. 115.
    Yilmaz M, Kaya M, Karagoz S, Erdogan S (2007) Vortex tube design: I (in Turkish). Machinery 116:100–106Google Scholar
  116. 116.
    Yilmaz M, Kaya M, Karagoz S, Erdogan S (2007) Vortex tube design: II (in Turkish). Machinery 117:102–107Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Engineering FacultyAtatürk UniversityErzurumTurkey
  2. 2.Türk Hava Yolları Teknik A. Ş. HavaalanıErzurumTurkey
  3. 3.Erzurum Vocational School of Higher EducationAtatürk UniversityErzurumTurkey

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