Skip to main content
SpringerLink
Log in

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

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Abbreviations

A :

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

\(C_q\) :

Flow coefficient

C :

Empirical coefficient relating pressure and radius of cavitation bubble

c :

Speed of sound

E :

Bulk modulus of a phase/mixture

\(E_0\) :

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

f :

Mass fraction of a phase

\(f_H\) :

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

\(f_{g0}\) :

Mass fraction of initially dissolved gas in the solution

k :

Empirical constant

R :

Radius of the spherical cavity

\({\tilde{R}}\) :

Rate of change of mass of a phase

p :

Pressure inside a control volume

\(p_0\) :

Saturation pressure of air

\(p_v\) :

Saturation pressure of vapor

Q :

Volumetric flow rate through an orifice

T :

Time

v :

Flow velocity in an orifice

V :

Volume of a chamber/control volume

W :

Work done per unit flow of mass

w :

Weighting coefficients

\(\alpha\) :

Void fraction of a phase

\(\rho\) :

Density of a phase/mixture

\(\theta\) :

Angular position

\(\lambda\) :

polytropic constant

\(\nu\) :

kinematic viscosity of the fluid

\(\sigma\) :

Coefficient of surface tension

B :

Bubble

c :

Condensation

ch :

Characteristic velocity

e :

Evaporation

H :

Gas mass fraction at equilibrium given by Henry’s law

i, j :

Summation indices

\(g_0\) :

Initial gas mass fraction

l :

Liquid phase

g :

Non condensable gas phase

v :

Vapor phase

ge :

Gas release

gc :

Gas absorption

ve :

Liquid evaporation

vc :

Vapor condensation

in :

Inlet

out :

Outlet

\(\infty\) :

Physical quantity at a large distance from the bubble interface

CV :

Control volume

HP :

High pressure port

LP :

Low pressure port

TSV :

Tooth space volume

References

  1. Barbarelli S, Bova S, Piccione R (2009) Zero-dimensional model andpressure data analysis of a variable-displacement lubricating vanepump. Tech. rep., SAE Technical Paper

  2. Blackburn JF (1969) Fluid power control. Massachusetts Institute of Technology, The MIT Press, Cambridge

    Google Scholar 

  3. Brennen CE (2013) Cavitation and bubble dynamics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  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 101:701–709

    Article  Google Scholar 

  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 71:61–82

    Article  Google Scholar 

  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):1059–1072

    Article  Google Scholar 

  7. Dabiri S, Sirignano W, Joseph D (2010) A numerical study on the effects of cavitation on orifice flow. Phys Fluids 22(4):042102

    Article  ADS  MATH  Google Scholar 

  8. Gholizadeh H, Burton R, Schoenau G (2012) Fluid bulk modulus: comparison of low pressure models. Int J Fluid Power 13(1):7–16

    Article  Google Scholar 

  9. Imagine S (2003) Amesim user manual

  10. Ivantysyn J, Ivantysynova M (2001) Hydrostatic pumps and motors. Academic Books International, New Delhi

    Google Scholar 

  11. Manring N (2005) Hydraulic control systems. Wiley, Hoboken

    Google Scholar 

  12. McCloy D, Martin HR (1980) Control of fluid power: analysis and design. Ellis Horwood, Ltd., Chichester

    Google Scholar 

  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 47–54

  14. Merritt HE (1967) Hydraulic control systems. Wiley, Hoboken

    Google Scholar 

  15. Pearson J (2005) Easy5 user guide. Boeing Company, Huntsville

    Google Scholar 

  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. Pellegri M, Vacca A (2017) Numerical simulation of Gerotor pumps considering rotor micro-motions. Meccanica 52:1851–1870

    Article  MathSciNet  Google Scholar 

  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 power

  19. SA Imagine (2007) HYD advanced fluid properties, Technical bulletin No. 117, Rev 7. Technical report

  20. SA Imagine (2015) Hydraulic library. User manual, Rev 14

  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 1

  22. Simulink UG (2009) Version 7. The MathWorks Inc, Natick

    Google Scholar 

  23. Singhal AK, Athavale MM, Li H, Jiang Y (2002) Mathematical basis and validation of the full cavitation model. J Fluids Eng 124(3):617–624

    Article  Google Scholar 

  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):2007–2031

    Article  Google Scholar 

  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):33–45

    Article  Google Scholar 

  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 45:35–49

    Article  Google Scholar 

  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):091305

    Article  Google Scholar 

  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 152

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Maha Fluid Power Research Center, Purdue University, West Lafayette, IN, USA

    Y. G. Shah & A. Vacca

  2. Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Y. G. Shah, A. Vacca & S. Dabiri

  3. Universita’ degli Studi di Napoli Federico II, Naples, Italy

    E. Frosina

Authors
  1. Y. G. Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Vacca
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Dabiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. Frosina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. G. Shah.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shah, Y.G., Vacca, A., Dabiri, S. et al. A fast lumped parameter approach for the prediction of both aeration and cavitation in Gerotor pumps. Meccanica 53, 175–191 (2018). https://doi.org/10.1007/s11012-017-0725-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-017-0725-y

Keywords

Search

Navigation