Chemical and Petroleum Engineering

, Volume 51, Issue 1–2, pp 113–121 | Cite as

Mathematical Modeling of the Working Processes in a Bicylindrical Spur Gear Pump

  • A. V. Grigor’ev
  • V. E. Shcherba
  • A. P. Bolshtyanskii
Compressors, Pumps, and Pipeline Fittings

Two approaches to mathematical modeling of the working processes of a new design, a bicylindrical spur gear pump, are considered. The first approach is based on Bernoulli’s equation, Hooke’s law, and the laws of conservation of mass, energy, and the dynamics of motion. The k–ε model of turbulence is used in the second approach to model the working processes of the pump. A comparison of the use of the two approaches is conducted. A dependence of the instantaneous delivery of the pump on the rotation angle of the rotors is established.


working process mathematical modeling positive-displacement pump 


  1. 1.
    V. P. Pashkov and G. G. Samoylov, Patent 2270922 RF, "A roller-impeller hydraulic engine," Nordiks-Metrologiya Scientific-Technical Center, No. 2004115083/06, subm. 05.19.2004, publ. 02.27.2006, Byull., No. 6.Google Scholar
  2. 2.
    A. V. Grigor’ev, V. E. Shcherba, and A. P. Bolshtyanskii, Patent 113543 RF, "A volumetric action engine," Omsk State Technical University, No. 2011109309/06, subm. 03.11.2011, publ. 02.20.2102, Byull., No. 5.Google Scholar
  3. 3.
    P. G. Frik, Turbulence: Models and Approaches, Perm State Technical University, Perm (1998).Google Scholar
  4. 4.
    A. V. Grigor’ev, V. E. Shcherba, V. V. Shalai, et al., "A mathematical model of the working processes in a rotary spur gear pump," Omsk. Nauch. Vest., No. 1(107), 166–170, Izd. OmGTU, Omsk (2012).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. V. Grigor’ev
    • 1
  • V. E. Shcherba
    • 1
  • A. P. Bolshtyanskii
    • 1
  1. 1.Omsk State Technical UniversityOmskRussia

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