, Volume 53, Issue 1–2, pp 175–191 | Cite as

A fast lumped parameter approach for the prediction of both aeration and cavitation in Gerotor pumps

  • Y. G. ShahEmail author
  • A. Vacca
  • S. Dabiri
  • E. Frosina


In this paper, a lumped parameter approach for predicting cavitation in fluid power systems is described. The modeling approach is based on the homogeneous mixture one fluid model for cavitation and takes into account the effects of compressibility of both the liquid phase and gaseous phase, related to aeration and fluid vaporization. By using the homogeneous mixture theory, equations suitable for lumped parameter models are derived, including the orifice equation to describe flow through hydraulic connections, the constitutive relations, and the pressure built up equations for hydraulic chambers. The proposed equations are then used in the paper to simulate a Gerotor pump under cavitating conditions. Results are validated experimentally for different operating conditions.


Gerotor pumps Gear pumps Aeration Cavitation Lumped parameter approach Fluid power 

List of symbols


Cross-sectional area of the orifice in a plane normal to flow direction


Flow coefficient


Empirical coefficient relating pressure and radius of cavitation bubble


Speed of sound


Bulk modulus of a phase/mixture


Bulk modulus of the oil at a pressure \(p_0\)


Mass fraction of a phase


Maximum allowable mass fraction of gas given by Henry’s law


Mass fraction of initially dissolved gas in the solution


Empirical constant


Radius of the spherical cavity


Rate of change of mass of a phase


Pressure inside a control volume


Saturation pressure of air


Saturation pressure of vapor


Volumetric flow rate through an orifice




Flow velocity in an orifice


Volume of a chamber/control volume


Work done per unit flow of mass


Weighting coefficients

Greek symbols


Void fraction of a phase


Density of a phase/mixture


Angular position


polytropic constant


kinematic viscosity of the fluid


Coefficient of surface tension

Subscripts and abbreviations






Characteristic velocity




Gas mass fraction at equilibrium given by Henry’s law


Summation indices


Initial gas mass fraction


Liquid phase


Non condensable gas phase


Vapor phase


Gas release


Gas absorption


Liquid evaporation


Vapor condensation






Physical quantity at a large distance from the bubble interface


Control volume


High pressure port


Low pressure port


Tooth space volume



The authors would like to thank Siemens for the use of the software AMESim® used to perform the simulation presented in this work.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Barbarelli S, Bova S, Piccione R (2009) Zero-dimensional model andpressure data analysis of a variable-displacement lubricating vanepump. Tech. rep., SAE Technical PaperGoogle Scholar
  2. 2.
    Blackburn JF (1969) Fluid power control. Massachusetts Institute of Technology, The MIT Press, CambridgeGoogle Scholar
  3. 3.
    Brennen CE (2013) Cavitation and bubble dynamics. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  4. 4.
    Buono D, di Cola FDS, Senatore A, Frosina E, Buccilli G, Harrison J (2016) Modelling approach on a Gerotor pump working in cavitation conditions. Energy Procedia 101:701–709CrossRefGoogle Scholar
  5. 5.
    Buono D, Siano D, Frosina E, Senatore A (2017) Gerotor pump cavitation monitoring and fault diagnosis using vibration analysis through the employment of auto-regressive-moving-average technique. Simul Model Pract Theory 71:61–82CrossRefGoogle Scholar
  6. 6.
    Casoli P, Vacca A, Franzoni G, Berta GL (2006) Modelling of fluid properties in hydraulic positive displacement machines. Simul Model Pract Theory 14(8):1059–1072CrossRefGoogle Scholar
  7. 7.
    Dabiri S, Sirignano W, Joseph D (2010) A numerical study on the effects of cavitation on orifice flow. Phys Fluids 22(4):042102ADSCrossRefzbMATHGoogle Scholar
  8. 8.
    Gholizadeh H, Burton R, Schoenau G (2012) Fluid bulk modulus: comparison of low pressure models. Int J Fluid Power 13(1):7–16CrossRefGoogle Scholar
  9. 9.
    Imagine S (2003) Amesim user manualGoogle Scholar
  10. 10.
    Ivantysyn J, Ivantysynova M (2001) Hydrostatic pumps and motors. Academic Books International, New DelhiGoogle Scholar
  11. 11.
    Manring N (2005) Hydraulic control systems. Wiley, HobokenGoogle Scholar
  12. 12.
    McCloy D, Martin HR (1980) Control of fluid power: analysis and design. Ellis Horwood, Ltd., ChichesterGoogle Scholar
  13. 13.
    Merkle CL, Feng J, Buelow PE (1998) Computational modeling of the dynamics of sheet cavitation. In: 3rd International symposium on cavitation, Grenoble, France, vol 2, pp 47–54Google Scholar
  14. 14.
    Merritt HE (1967) Hydraulic control systems. Wiley, HobokenGoogle Scholar
  15. 15.
    Pearson J (2005) Easy5 user guide. Boeing Company, HuntsvilleGoogle Scholar
  16. 16.
    Pellegri M, Vacca A, Frosina E, Buono D, Senatore A (2016) Numerical analysis and experimental validation of Gerotor pumps: a comparison between a lumped parameter and a computational fluid dynamics-based approach. In: Proceedings of the institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. SAGE Publishing. doi: 10.1177/0954406216666874
  17. 17.
    Pellegri M, Vacca A (2017) Numerical simulation of Gerotor pumps considering rotor micro-motions. Meccanica 52:1851–1870MathSciNetCrossRefGoogle Scholar
  18. 18.
    Pellegri M, Vacca A, Devendran RS, Dautry E, Ginsberg B (2016) A lumped parameter approach for Gerotor pumps: model formulation and experimental validation. In: Tenth international conference on fluid powerGoogle Scholar
  19. 19.
    SA Imagine (2007) HYD advanced fluid properties, Technical bulletin No. 117, Rev 7. Technical reportGoogle Scholar
  20. 20.
    SA Imagine (2015) Hydraulic library. User manual, Rev 14Google Scholar
  21. 21.
    Schnerr GH, Sauer J (2001) Physical and numerical modeling of unsteady cavitation dynamics. In: Fourth international conference on multiphase flow, New Orleans, USA, vol 1Google Scholar
  22. 22.
    Simulink UG (2009) Version 7. The MathWorks Inc, NatickGoogle Scholar
  23. 23.
    Singhal AK, Athavale MM, Li H, Jiang Y (2002) Mathematical basis and validation of the full cavitation model. J Fluids Eng 124(3):617–624CrossRefGoogle Scholar
  24. 24.
    Vacca A, Guidetti M (2011) Modelling and experimental validation of external spur gear machines for fluid power applications. Simul Model Pract Theory 19(9):2007–2031CrossRefGoogle Scholar
  25. 25.
    Vacca A, Klop R, Ivantysynova M (2010) A numerical approach for the evaluation of the effects of air release and vapour cavitation on effective flow rate of axial piston machines. Int J Fluid Power 11(1):33–45CrossRefGoogle Scholar
  26. 26.
    Zhou J, Vacca A, Casoli P (2014) A novel approach for predicting the operation of external gear pumps under cavitating conditions. Simul Model Pract Theory 45:35–49CrossRefGoogle Scholar
  27. 27.
    Zhou J, Vacca A, Manhartsgruber B (2013) A novel approach for the prediction of dynamic features of air release and absorption in hydraulic oils. J Fluids Eng 135(9):091305CrossRefGoogle Scholar
  28. 28.
    Zwart PJ, Gerber AG, Belamri T (2004) A two-phase flow model for predicting cavitation dynamics. In: Fifth international conference on multiphase flow, Yokohama, Japan, vol 152Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Maha Fluid Power Research CenterPurdue UniversityWest LafayetteUSA
  2. 2.Department of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  3. 3.Universita’ degli Studi di Napoli Federico IINaplesItaly

Personalised recommendations