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Meccanica

, 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
Article

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.

Keywords

Gerotor pumps Gear pumps Aeration Cavitation Lumped parameter approach Fluid power 

List of symbols

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

Greek symbols

\(\alpha\)

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

Subscripts and abbreviations

B

Bubble

c

Condensation

ch

Characteristic velocity

e

Evaporation

H

Gas mass fraction at equilibrium given by Henry’s law

ij

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

Notes

Acknowledgements

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.

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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

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