A NUMERICAL APPROACH FOR THE EVALUATION OF THE EFFECTS OF AIR RELEASE AND VAPOUR CAVITATION ON EFFECTIVE FLOW RATE OF AXIAL PISTON MACHINES
Keywords:numerical models, cavitation, axial piston pumps, fluid properties
This work illustrates a numerical methodology for the description of effective flow rate of axial piston pumps and motors. The presented mathematical model is similar to classical lumped parameter approaches that are commonly used to simulate hydraulic units; however, this work uniquely utilises a mathematical formulation for compressible flows based on an original description of fluid density. Assuming the behaviour of typical mineral oil, the model can evaluate fluid density for all possible values of pressure while considering the ccurrence of gas cavitation (due to the release of air normally dissolved into liquid) below saturation pressure, and of vapour cavitation (due to liquid change of phase) below vapour pressure. The developed simulation model allows a description of several characteristics of the machine (i.e. instantaneous cylinder pressure and density, delivery and inlet flow rates, etc.) in its whole field of operation taking into account conditions of insufficient flow due to cavitation at the low pressure port. Tests were carried out on a swash plate type axial piston pump for open circuit applications to verify potentials of the developed numerical model. Experiments were conducted to test the pump under typical operating conditions as well as situations critical from the point of view of cavitation (high shaft speed, low values of inlet pressure), thus permitting the comparison between the prediction given by the developed model and experimental results over a wide range of data. Results highlight how fluid density changes can be used to characterize effective flow rate but also to justify, in particular operating conditions, the utilization of the approach for compressible flows. Results show that the developed model uniquely allows the calculation of effective flow rate through the pump at fair and extreme conditions, thus permitting the ability to predict limitations of the machine. Furthermore, the realistic prediction of pressures throughout the machine in these conditions leads the accurate predictions of pressure forces and of flow through the lubricating gaps that may be critical in other models.
Casoli, P., Vacca, A., Franzoni G. and Berta, G. L.
Modelling of fluid properties in hydraulic
positive displacement machines. Elsevier - Simulation
Modelling Practice and Theory, Vol. 14, pp.
Delannoy, Y. and Kueny, J. L. 1990. Two Phase Flow
Approach in Unsteady Cavitation Modeling. Cavitation
and Multiphase Flow Forum, ASME FED,
Vol. 98, pp. 153-158.
Edge, K. A. and Darling, J. 1989. The Pumping Dynamics
of Swash Plate Piston Pumps. Journal of
Dynamic Systems, Measurement and Control,
Trans. of ASME, Vol. 11, pp. 307-311.
Hoffman, J. D., 1992, Numerical methods for engineers
and scientists, Mc Graw Hill.
Hyman, J. M. 1984. Numerical Methods for Tracking
Interfaces. Los Alamos Natl. Lab. Rep. LA-9917-
Imagine, S. A. 2007. HYD Advanced Fluid Properties.
Technical Bulletin n° 117, Rev 7, May 2007.
Ivantysyn, J. and Ivantysynova, M. 2000. Hydrostatic
Pumps and Motors, Principles, Designs, Performance,
Modelling, Analysis, Control and Testing.
New Delhi. Academia Books International.
Ivantysynova, M., Grabbel, J. and Ossyra, J. C.
Prediction of swash plate moment using the
simulation tool CASPAR. ASME Int. Mech. Eng.
Congress, Nov. 17-22, 2002, New Orleans, USA.
Kim, S. D., Cho, H. S. and, Lee, C. O. 1987. A Parameter
Sensitivity Analysis for the Dynamic
Model of a Variable Displacement Axial Piston
Pump. IMechE Proc, Instn Mech Engrs, Vol. 201,
Klop, R. and Ivantysynova, M. 2008. Investigation of
Noise Source Reduction Strategies in Hydrostatic
Transmissions. Proc. of the 5th FPNI PhD Symposium,
Cracow, Poland, pp. 63 - 76.
Lamb, W. S. 1987. Cavitation and aeration in hydraulic
systems. Bedfordshire, UK. BHRGroup. 114.Manring, N. D. 2000. The Discharge Flow Ripple of
an Axial-Piston Swash-Plate Type Hydrostatic
Pump. Journal of Dynamic Systems, Measurement,
and Control, Vol. 122 pp. 263-268.
Palmberg, J. O. 1989. Modelling of flow ripple from
fluid power piston pumps. In 2nd Bath Int. Fluid
Power Workshop, Univ. of Bath, UK, Sept 1989.
Schmidt, D. P. and Corradini, M. L. 1997. Analytic
Prediction of the Exit Flow of Cavitating Orifices.
Atomization and Sprays, Vol. 7 pp. 603-616.
Schmidt, D. P., Rutland, C. J. and Corradini, M. L.
A fully compressibile, two-dimensional
model of Small, High-Speed, Cavitating Nozzles.
Atomization and Sprays, Vol. 9. pp. 225-276.
Schoenau, G. J., Burton, R. T. and Kavanagh, G. P.
Dynamic Analysis of a Variable Displacement
Pump. Journal of Dynamic System, Measurement,
and Control. Vol. 112, pp.122-132.
Seeniraj, G. and Ivantysynova, M. 2008. Noise Reduction
in Axial Piston Machines Based on Multi-
Objective Optimization. Proc. of the 5th FPNI PhD
Symposium, Cracow, Poland, pp. 111 - 123.
Shaughnessy, E. J., Katz, I. M. and Schaffer, J. P.
Introduction to Fluid Mechanics. Oxford
University Press, New York, USA.
Singhal, A. K., Athavale, M. M., Li, H. and Jiang, Y.
Mathematical Basis and Validation of the
Full Cavitation Model. Journal of Fluid Engineering,
Vol. 124 pp. 617-624.
Takahashi, S., Washio, S., Uemura, T. and Okazaki,
A. 2003. Experimental Study on Cavitation Starting
at and Flow Characteristics Close to the Point of
Separation. 5th Int. Symposium on Cavitation,
Osaka, Japan November 1-4, 2003.
Tillner, W., Fritsch, H., Kruft, R., Lehman, W. and
Masendorf, D. G. 1993. The avoidance of cavitation
damage. MEP, London.
Washio, S., Takahashi, S., Uda, Y. and Sunahara, T.
Study on cavitation inception in hydraulic oil
flow through a long two-dimensional constriction.
IMechE - Proc Instn Mech Engrs. Vol. 215 Part J,
Wieczorek, U. and Ivantysynova, M. 2000. CASPAR
- A Computer Aided Design Tool for Axial Piston
Machines. Proc. Bath Workshop on Power transmission
and Motion Control PTMC 2000, Bath,
UK, pp. 113 - 126.
Wieczorek, U. and Ivantysynova, M. 2002. Computer
Aided Optimization of Bearing and Sealing Gaps in
Hydrostatic Machines - The Simulation Tool CASPAR.
International Journal of Fluid Power, Vol. 3,
No.1, pp. 7-20.