# AN ANALYTIC THERMODYNAMIC MODEL FOR HYDRAULIC RESISTANCES BASED ON CFD FLOW PARAMETERS

## Authors

• Christian von Grabe RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany
• Christian Riedel RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany
• Christian Stammen RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany
• Hubertus Murrenhoff RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany

## Keywords:

lumped parameter, thermo-hydraulic simulation, hydraulic resistance, orifice, throttle, cavitation, CFD

## Abstract

This article illustrates the development of an analytic lumped parameter thermo-hydraulic model for a wide range of hydraulic resistance geometries based on mass flow. The relevant flow parameters such as the contraction coefficient in case of laminar flow separation are derived from CFD simulations. Furthermore, the consideration of cavitation effects can be included. State of the art in lumped parameter simulations of hydraulic circuits utilise volume-flow based equations like the orifice equation, which is extended for a wide variety of geometries and flow conditions including the transition from laminar to turbulent flow by adjusting the discharge coefficient based on empirical equations or lookup tables. The same situation persists for laminar flow description. In this case the Hagen-Poiseuille equation is often used in conjunction with correction factors based on the Reynolds number to regard the transition of laminar to turbulent flow. However, in practical applications the use of different equations for various flow conditions and geometries is cumbersome. Furthermore, in the widely used volume based flow description, the absolute pressure dependency of mass flow due to density changes and critical flow at which cavitation occurs is not accounted for until now. Without consideration of these influences a mass conservative modelling and thus high model precision is not possible. The overall goal of the proposed model is to increase accuracy of hydraulic system simulation tools and to support usability by simplifying parameterisation on basis of dimensions available from data sheets. The results of this study are obtained analytically as well as empirically by means of CFD simulations. Moreover, a large number of performed simulations support the understanding of fundamental effects in hydraulic resistance flow.

## Author Biographies

### Christian von Grabe, RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany

Christian von Grabe Dipl.-Ing. Christian von Grabe studied Mechanical Engineering at RWTH Aachen University. Since 2010 he is a member of the scientific staff at the Institute for Fluid Power Drives & Controls (IFAS) at RWTH Aachen University.

### Christian Riedel, RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany

Christian Riedel Dipl.-Ing. Dipl.-Wirt.-Ing. Christian Riedel is project manager at GHH Fahrzeuge in Gelsenkirchen since 2011. Between 2007 and 2011 he was a member of the scientific staff at the Institute for Fluid Power Drives & Controls (IFAS) at RWTH Aachen University. He studied Mechanical Engineering at RWTH Aachen University and Tsinghua University, Beijing..

### Christian Stammen, RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany

Christian Stammen PD Dr.-Ing. Christian Stammen is director of Research & Development at Fluitroncs GmbH, Krefeld. From 2001 till 2008 he worked at the Institute for Fluid Power Drives & Controls (IFAS) at RWTH Aachen University after his studies in mechanical engineering and earned his Doctorate (2005) and State Doctorate degree (2009) there.

### Hubertus Murrenhoff, RWTH Aachen University, Institute for Fluid Power Drives and Controls (IFAS), Steinbachstr. 53, 52074 Aachen, Germany

Hubertus Murrenhoff Univ.-Prof. Dr.-Ing. Hubertus Murrenhoff is director of the Institute for Fluid Power Drives & Controls (IFAS) at RWTH Aachen University. Main research interests cover hydraulics and pneumatics including components, systems, controls, simulation programs and the applications of fluid power in mobile and stationary equipment.

## References

Avva, R. K., Singhal, A. and Gibson, D. H. 1995. An

Enthalpy Based Model of Cavitation. ASME Journal

of Fluids Engineering, 226, pp. 63 - 70.

Baum, H. 2001. Einsatzpotentiale Neuronaler Netze bei

der CAE-Tool unterstützten Projektierung fluidtechnischer

Antriebe. Dissertation RWTH Aachen University,

Shaker Verlag, Aachen, ISBN 3-8265-9659-5.

Beater, P. 1999. Entwurf hydraulischer Maschinen.

VDI-Buch, Springer, Berlin

Bohn, D. 2008. Ähnlichkeitsprobleme des Maschinenbaus.

Vorlesungsumdruck, IDG RWTH Aachen

University.

Eich, O. 1979. Entwicklung geräuscharmer Ventile der

Ölhydraulik. Dissertation RWTH Aachen University,

Verlag Mainz.

Idelchik, I. E. 2007. Handbook of hydraulic resistances.

th revised and augmented edition, Begell

House, Inc., New York, ISBN: 978-1-56700-251-5.

Jungemann, M. 2005. 1D Modellierung und Simulation

des Durchflussverhaltens von Hydraulikkomponenten

bei sehr hohen Drücken unter Beachtung

der thermodynamischen Zustandsgrößen von Mineralöl.

Düsseldorf, p. 43.

Kajaste, J., Kauranne, H., Ellman, A. and Pietola,

M. 2006. Computational Models for Effective Bulk

Modulus of Hydraulic Fluid. The 2nd International

Conference on Computational Methods in Fluid

Power FPNI. Aalborg, Denmark, 7 p.

Kleppmann, W. 2008. Taschenbuch Versuchsplanung.

th edition, Hanser Verlag, Munich.

Latour, C. 1996. Strömungskraftkompensation in

hydraulischen Sitzventilen. Dissertation RWTH Aachen

University.

Li, M., Mulemane, A., Lai, M. C. and Poola, R.

Simulating Diesel Injectors Based on Different

Cavitation Modeling Approaches. ASME Paper

No. ICES2005-1030.

Lichtarowicz, A., Duggins, R. K. and Markland, E.

Discharge Coefficients for Incompressible

Non-Cavitating Flow Through Long Orifices.

Journal of Mechanical Engineering Science 1959-

Professional Engineering Publishing.

Luhmer, H. 1981. Aufbau hydraulischer Netzwerke

mit differenzierendem Verhalten und ihr Einsatz zur

Dämpfung hydrostatischer Antriebe. Dissertation,

RWTH Aachen University.

Maré, J. - C. and Attar, B. 2008. Enhanced model of

four way valves characteristics and its validation at

low temperature. International Journal of Fluid

Power. Vol.9, No. 3 pp. 35 - 4.

Merrit, H. E. 1967. Hydraulic Control Systems. John

Wiley & Sons, New York.

Murrenhoff, H. 2007. Grundlagen der Fluidtechnik –

Teil1: Hydraulik. Shaker Verlag, ISBN 3-8265-

-0.

N.N. 2004. Durchflussmessung von Fluiden mit Drosselgeräten

in voll durchströmten Leitungen mit

Kreisquerschnitt - Teil 2: Blenden. German edition

EN ISO 5167-2.

Nykänen, T., Esqué, S. and Ellman, A. 2000. Comparison

of different fluid models. Bath Workshop

on Power Transmission and Motion Control

PTMC. University of Bath, UK, pp. 151 - 165.

Riedel, C., Murrenhoff, H. and Stammen, C. 2010.

Physically Correct Hydraulic System Simulation

with Mass Conservative Approach. 7th International

Fluid Power Conference (IFK). Aachen, Germany,

Vol.1, pp. 523 - 534.

Riedel, C., Stammen, C. and Murrenhoff, H. 2009.

Fundamentals of Mass Conservative System Simulation

in Fluid Power. ASME Dynamic Systems and

Control Conference (DSCC). Hollywood, CA, 12-

September.

Riedel, H. - P. 1973. Untersuchungen von Kavitationserscheinungen

an hydraulischen Widerständen.

Dissertation RWTH Aachen University.

Roach, P. J. 1997. Quantification of Uncertainty in

Computational Fluid Dynamics. Annual Reviews of

Fluid Mechanics, Vol. 29, Palo Alto, CA, USA

Schmitt, T. 1966. Untersuchung zur stationären und

instationären Strömung durch Drosselquerschnitte in

Kraftstoffeinspritzsystemen von Dieselmotoren, Dissertation,

Technical University Munich, Forschungsberichte

Verbrennungskraftmaschinen Nr. 58.

Schröder, W. 2004. Fluidmechanik. Aachener Beiträge

zur Strömungsmechanik, 7th edition, Wissenschaftsverlag

Mainz, Aachen.

Singhal, A. K., Athavale, M. M., Li, H. and Jiang, Y.

Mathematical Basis and Validation of the

Full Cavitation Model. ASME J. Fluids Eng., 124,

pp. 617 - 624.

Truckenbrodt, E. 1996. Fluidmechanik. Band 1, 4.

Auflage, Springer, Berlin.

Watton, J. 2007. Modelling, Monitoring and Diagnostic

Techniques for Fluid Power Systems. Springer-

Verlag, London, 2007 ISBN 978-1-84628-373-4.

Will, D. 1986. Einfluß der Öltemperatur auf das

Durchflußverhalten von Drosselventilen. Dissertation

TU Dresden

Winklhofer, E., Kull, E., Kelz, E. and Morozov, A.

Comprehensive Hydraulic and Flow Field

Documentation in Model Throttle Experiments Under

Cavitation Conditions. Proceedings of ILASSEurope

Conference, Zürich.

Witt, K. 1974. Druckflüssigkeiten und thermodynamisches

Messen. Ingenieur Digest Verlag, Frankfurt

am Main.

Yang, H.Q., Singhal, A. K. and Megahed, M. 2005.

Industrial two-phase flow CFD – The full cavitation

model. von Kármán Institute for Fluid Dynamics,

Lecture Series, May 23 - 27.

2018-12-30

Original Article

1 2 > >>