Theoretical Calculation of Compressed Media Leaks in Working Bodies of Single-Rotor Screw Compressor with Circumferential Tooth Shape

  • A. F. MinikayevEmail author
  • V. A. Pronin
  • D. V. Zhignovskaya
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


In this paper, the problem of leakage of the medium being compressed in the working part of a single-rotor screw compressor (SSC) with a circumferential tooth shape is considered. The initial system of differential equations of hydro-gas dynamics in relative motion in a rotating system of cylindrical coordinates associated with a cutter tooth of a circumferential profile is shown. It was established that when considering the task, the system of differential equations of hydro-gas dynamics should relate to the thermal and caloric equations of the state of a continuous medium, the dependencies characterizing its viscosity and thermal conductivity, as well as boundary and initial conditions. Reasonably, the simplification of the obtained dependences is possible when evaluating the order of all their members, considering the specificity of the working medium flow in narrow gaps, which takes place in the engagement of the working bodies of a single-rotor screw compressor.


Single-rotor screw compressor Hydrodynamic equations A cutter tooth of a circumferential profile Leakage of a compressed medium 



The authors would like to thank the IEEE member Yerezhep Darkhan and for the financial support of ITMO University.


  1. 1.
    Pronin VA (1998) Screw single-rotor compressors for refrigeration and pneumatics. Dissertation, St. Petersburg State Academy of Cold and Food TechnologiesGoogle Scholar
  2. 2.
    Pronin VA, Zhelyabov VL, Kovalenko VV (1986) To the question of determining the geometric parameters of the cracks in the working part of a single-rotor screw compressor. Intensification Prod Use Artif Cold Abstr All-Union Sci Tech Conf 236:15–19Google Scholar
  3. 3.
    Pronin VA, Socks AN (1996) Features of the design of the working bodies of screw single-rotor compressors with a circumferential tooth profile. Compressors Pneumatics 112:60–63Google Scholar
  4. 4.
    Pronin VA, Den GN, Novikov II (1992) Single-rotor screw machine. USSR Patent 181,392,4 Nov 1992Google Scholar
  5. 5.
    Pronin VA, Kovalenko VV, Isaev YuA (1989) Cutter single rotor screw machine. USSR Patent 147,969,2 Sept 1989Google Scholar
  6. 6.
    Vimmr JA, Fryc OA (2006) Numerical simulation of leakage flow between moving rotor and housing of screw compressor engineering simulation, vol 521. Gliwice, pp 461–468Google Scholar
  7. 7.
    Reddy CG (2007) CFD studies on flow through screw compressor. Institute of Technology, RourkelaGoogle Scholar
  8. 8.
    Den GN, Pronin VA, Voevodsky AA (1990) To the calculation of leakage through the gaps between the semi-circular cutter tooth and the screw of a single-rotor oil-filled screw compressor. Res Improv Des Refrigerating Machi 214:52–59Google Scholar
  9. 9.
    Zucker R, Biblarz O (2002) Fundamentals of gas dynamics. Wiley, USAGoogle Scholar
  10. 10.
    Rathakrishnan E (2010) Applied gas dynamics. WileyGoogle Scholar
  11. 11.
    Bose TK (2014) High temperature gas dynamics. Springer Science & BusinessGoogle Scholar
  12. 12.
    Balachandran P (2006) Fundamentals of compressible fluid dynamics. PHI Learning Pvt LtdGoogle Scholar
  13. 13.
    Liepmann HW, Roshko A (2013) Elements of gas dynamics. Courier CorporationGoogle Scholar
  14. 14.
    Amosov PE (1966) Influence of the physical properties of gases on the speed of rotation of screw compressor machines. Compressor Refrigeration EngGoogle Scholar
  15. 15.
    Ginsburg IP (1953) Outflow of a viscous gas from a moving gap. Bull Leningrad State UnivGoogle Scholar
  16. 16.
    Hirschfelder JO, Curtiss CF, Bird RB (1964) The molecular theory of gases and liquids. Wiley-InterscienceGoogle Scholar
  17. 17.
    Pronin VA, Verboloz AL (2012) Estimation of the effect of the mobility of the walls of the cracks on the leakage of the medium being compressed in a single-screw screw compressor (SSC). Bull IAC 210:13–17Google Scholar
  18. 18.
    Chen N (2011) Aerothermodynamics of turbomachinery—analysis and design. WileyGoogle Scholar
  19. 19.
    Seppo A (2011) Principles of turbomachinery. Wiley, KorpelaGoogle Scholar
  20. 20.
    Murty VD (2018) Turbomachinery: concepts, applications, and design. CRC PressGoogle Scholar
  21. 21.
    Pronin VA, Prilutsky AA, Dolgovskaya OV, Podbolotova TE (2015) Investigation of the performance of the scrubber in absorbing carbon dioxide. Sci J NRU ITMO Seri Process Devices Food Prod 247:132–140Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • A. F. Minikayev
    • 1
    Email author
  • V. A. Pronin
    • 1
  • D. V. Zhignovskaya
    • 1
  1. 1.St. Petersburg National Research University of Information Technologies, Mechanics and OpticsSt. PetersburgRussia

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