Numerical investigation of internal flow in hydraulic

Numerical investigation of internal flow in hydraulic

Numerical investigation of internal flow in hydraulic valves
and dynamic interactions in hydraulic systems with CFD and
simplified simulation methods
Vom Fachbereich Maschinenbau
an der Technischen Universität Darmstadt
zur
Erlangung des Grades eines Doktor-Ingenieurs (Dr.-Ing.)
genehmigte
Dissertation
vorgelegt von
Dipl.-Ing. Qing Chen
aus Pingyao, China
Berichterstatter:
Prof. Dr.-Ing. B. Stoffel
Mitberichterstatter:
Prof. Dr. rer. nat. M. Schäfer
Tag der Einreichung:
19.11.2004
Tag der mündlichen Prüfung:
08.02.2005
Darmstadt 2004
D17
Berichte aus der Strömungstechnik
Qing Chen
Numerical investigation of internal flow
in hydraulic valves and dynamic interactions
in hydraulic systems with CFD and
simplified simulation methods
.
D 17 (Diss. TU Darmstadt)
Gedruckt mit Unterstützung des Deutschen Akademischen Austauschdienstes
Shaker Verlag
Aachen 2005
Bibliographic information published by Die Deutsche Bibliothek
Die Deutsche Bibliothek lists this publication in the Deutsche
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the internet at http://dnb.ddb.de.
Zugl.: Darmstadt, Techn. Univ., Diss., 2005
.
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To my parents Xiaoping Li, Lihu Chen, and my son Kaiyuan Hou
For all their love and understanding
V
Preface
The on hand dissertation came into being during my work as scientific researcher at Institute
of Turbomachinery and Fluid Power at Darmstadt University of Technology.
Prof. Dr.-Ing. Bernd Stoffel, chief of the institute, is the first person whom I thank especially
sincerely for the encouragement for this thesis, the valuable suggestions in many professional
discussions, the constant promotion and understanding, along with the chance to enrich my
development stage as engineer in Germany.
I would like to give my best and sincere thanks to Prof. Dr. rer. nat. Michael Schäfer, chief of
Department of Numerical Methods in Mechanical Engineering at Darmstadt University of
Technology, for the acceptance of co-reviewer and the critical review of the thesis.
My gratefulness is also brought to all colleagues of our institute, particularly to Dr.-Ing.
Gerhard Ludwig, Dipl.-Ing. Christian Beinert, Dipl.-Ing. Matevz Dular, Dipl.-Ing. Jens
Rösner and Dipl.-Ing. Christian Schaad, Dipl.-Ing. Miriam Roth and Dipl.-Ing. Valérie
Bischof for a multitude of fruitful discussions and assistance.
For the extensively grammatical and linguistic correction of this thesis, special thanks to my
Chinese friend Dr.-Ing. Yongxing Wang.
I should like to express my thankfulness further on to my parents, my brother and my
grandparents, who encourage me to study in Germany and give their endless concern and
understanding to me.
Special thanks to DAAD (Deutscher Akademischer Austausch Dienst, or in English: German
Academic Exchange Service), who has created the pre-condition for the accomplishment of
this thesis through financial support.
Last but not least, I would like to thank Dr.-Ing. Andreas Bootz and Dipl.-Ing. Bernhard
Brunn heartily for their assistance in solving the problem of dynamic simulation in the first
two years of my staying in Germany.
I affirm that I have independently finished the thesis except for the above mentioned
promotions and necessary implement.
Darmstadt, in November 2004
VI
Qing Chen
Abstract
On the basis of the introduction of theoretical fundamentals, dynamic interactions in hydraulic
pipeline systems are studied using different simplified simulation methods. Simulation results
of the concentrated parameter method, the distributed parameter method and the transfer
matrix method are represented and compared with each other as well with the help of Bode
analyses of magnitude and phase in the frequency domain.
By flow simulation, the internal flow processes in a hydraulic pressure relief valve and a
servo valve are investigated under different calculation conditions with the aid of CFD. The
analyses of turbulent flow, the cavitation phenomenon under steady and unsteady condition
and dynamic opening and closing process of the pressure relief valve are carried out using the
corresponding turbulent-, multiphase- and dynamic meshing model provided in the CFD
commercial code – FLUENT. Studies of the distributions of various parameters, e.g., static
pressure, velocity magnitude, velocity vector and volume fraction of vapor especially for the
evaluation of the cavitation are carried out under the corresponding computing conditions.
Furthermore, the offline and online coupled simulations of simple hydraulic systems are
implemented with the interfaces of 2-Level-S-Function in Matlab/Simulink and UDF (UserDefined-Function) in FLUENT. The principle of the coupled simulation using the model of
the distributed parameter-characteristic method and CFD is briefly introduced. In the case of
online coupling, the dynamic velocity profile at the inlet of the pressure relief valve, which is
obtained by the simulation with the characteristic method, is used as boundary condition for
the internal flow analysis with CFD. The online coupled simulation is realized by the
assignment of two parallel-working personal computers, which respectively implement CFD
calculation and the computation with the characteristic method. The necessary transfer of the
signal files is accomplished per TCP/IP to bring the coupled simulation to success. Hereafter,
some simulation results are represented to validate the validity of the coupling principle.
VII
Kurzfassung
Basierend auf die Einführung der theoretischen Grundlagen werden dynamische Wechselwirkungen in hydraulischen Systemen untersucht mittels verschiedener vereinfachter Simulationsverfahren. Simulationsergebnisse, die mit der Methode der konzentrierten Parameter, mit
dem Charakteristikenverfahren und mit dem Übertragungsmatrizenverfahren erzielt wurden,
werden dargestellt und miteinander verglichen an Hand von Bode-Analysen der Größe und
der Phase im Frequenz Bereich.
Bei Strömungssimulation werden die inneren Strömungsvorgänge in einem Druckbegrenzungsventil und in einem Servoventil unter verschiedenen Berechnungsbedingungen mit Hilfe
von CFD untersucht. Es erfolgen Analysen der turbulenten Strömung, des Kavitationsphänomens unter stationärer und instationärer Bedingung und des dynamischen Öffnungs- und
Schließvorgangs des Druckbegrenzungsventils unter Verwendung von entsprechenden „turbulent, multiphase und dynamic meshing" Modellen, die im kommerziellen CFD- Code
FLUENT bereitgestellt sind. Es werden Studien der Verteilungen der unterschiedlichen Parameter, z.B. des statischer Drucks, der Geschwindigkeitsgröße, des Geschwindigkeitsvektors
und des Dampfanteils speziell für die Beurteilung der Kavitation durchgeführt unter den entsprechenden Berechnungs-Bedingungen.
Darüber hinaus werden „online" und "offline" gekoppelte Simulationen für einfache hydraulische Systeme ausgeführt mit dem Interface der „2-Level-S-Function“ in Matlab/Simulink und
UDF (User-Defined-Function) in FLUENT. Das Prinzip der gekoppelten Simulation mit der
Methode des Charakteristikenverfahrens und CFD wird kurz eingeführt. Im Falle von onlineKoppelung liefert das dynamische Geschwindigkeitsprofil bei der Einströmung zum Druckbegrenzungsventil, das von der Simulation mit dem Charakteristikenverfahren erhalten wird, die
Randbedingungen für die Analyse der inneren Strömungen mit CFD. Diese online gekoppelte
Simulation wird realisiert durch den Einsatz von zwei parallel betriebenen Personal-Computern, die jeweils die CFD-Berechnungen bzw. die Rechnungen mit dem Charakteristikenverfahren ausführen. Der erforderliche Transfer der Signal-Dateien, um die gekoppelte Simulation zum Erfolg zu bringen, erfolgt mit TCP/IP. Einige Simulationsergebnisse werden präsentiert, um die Gültigkeit des Koppelungsprinzips zu bestätigen.
VIII
Contents
1 Introduction………………………………………………………………………..……....1
1.1 Objectives and methods………………………………………………………………..2
1.2 Structure……………………………………………………………………………......4
2 State-of-the-art……...………………………..…………………………………….............5
2.1 Academic overview of the problem……………………………………………...…….5
2.1.1 Dynamic pressure change………………………………………………………....5
2.1.2 Oscillating and pulsating flow…………………………………………………….6
2.1.3 Transient flow…………………………………………………………….............7
2.1.4 Dynamic performance of the pipe flow………………………………………......9
2.1.5 CFD analysis of flow behavior of hydraulic valves……..……………………....10
2.2 Simulation tools used in fluid technology………………………………………..…...12
2.2.1 Simplified modelling techniques………………………………………...............13
2.2.2 Structure analysis with FEM………………………………………………….....14
2.2.3 Flow simulation with the aid of CFD…………………………………………....14
3 Theoretical fundamentals……………………………………………………….….……17
3.1 Simplified simulation methods for oil hydraulic systems………………………….....17
3.1.1 Model of concentrated parameters..…………………………………...………...17
3.1.1.1 Derivation………………………………………………………….…….…18
3.1.1.2 Solution to the system equations……………………………..…………….19
3.1.2 Distributed parameters...…………………………………...…………………….20
3.1.2.1 Derivation……………………………….…………………….……………20
3.1.2.2 Solution to the system equations in time domain………………..………....22
3.1.2.3 Approach of wall shear stress………………..…...…………………….….27
3.1.2.4 Optimization of the friction approach……...…..…………..………………32
3.1.3 Transfer matrix method………………………………………………..………...33
3.2 CFD numerical calculation……………………………………………………………35
3.2.1 Description of turbulent flow………………………………………...………….35
3.2.1.1 Standard k- H turbulence model…………………..…….……….…………35
3.2.1.2 RNG k- H turbulence model…………...……………….....………………..36
3.2.2 Mixture multiphase model……………………………………………………….38
3.2.2.1 Continuity equation for the mixture………………...………………………39
3.2.2.2 Momentum equation for the mixture……………………………..…….…..39
3.2.2.3 Energy equation for the mixture……………….…………………..…...…..40
3.2.2.4 Relative (Slip) velocity and the drift velocity…………………………..….40
3.2.2.5 Volume fraction equation for the secondary phases…...……………..…....41
3.2.3 Dynamic mesh model……………………………………………………………41
3.2.3.1 Dynamic mesh conservation equations……………………………………..42
3.2.3.2 Dynamic mesh update methods…………………………………...………..43
4 Simulation results of hydraulic systems with simplified modelling methods….….…47
4.1 n-element concentrated parameter…………………………………………………....47
4.1.1 32-element concentrated parameter……………………………………………...47
4.1.2 Comparison of different elements concentrated parameter……………………...51
4.2 Characteristic method…………………………………………………………………53
4.3 Comparison of concentrated and distributed parameter………………………………56
4.4 Simulation with transfer matrix method………………………………………………58
4.5 Comparison of simulations with different simplified methods….…...……….....…....60
IX
4.6 Conclusions………………………………………………………………………...…63
5 Turbulent flow and cavitation of a pressure relief valve…………………………..…..65
5.1 Turbulent flow………………………………………………………………………...65
5.1.1 Valve with complex seat…………………………………………………………66
5.1.2 Valve with simple seat……………………………………………….…………..68
5.1.3 Comparison of simulation results of two simplified configurations…….…….....69
5.1.3.1 Influences of the inlet flow rate………………………………..……….…..70
5.1.3.2 Influences of the outlet pressure…………..…………………………….….71
5.2 Cavitation………………………………………………………………………..........74
5.2.1 Unsteady cavitation in the valve with complex seat……………...……………..74
5.2.1.1 Influences of the inlet flow rate………………..…………………………...77
5.2.1.2 Influences of the outlet pressure………………………………………..…..79
5.2.1.3 Influences of turbulence models…………………………………………....80
5.2.2 Cavitation in the valve with simple seat…………………………………………81
5.2.2.1 Steady cavitatin…………………………..……………………………...….81
5.2.2.2 Unsteady cavitation…………………………………………..…….……….83
5.2.3 Influence of gap on cavitation………………………...…………………………85
6 Dynamic mesh simulation……………………………………………………….…….....89
6.1 Opening process of the valve with simple seat………………………...……………..89
6.1.1 Distribution of pressure…………………….......….……………………………..90
6.1.2 Distribution of velocity…………………………………………………………..91
6.2 Closing process of the valve with simple seat………………………………………..92
6.2.1 Static pressure……………………………………………………………………92
6.2.2 Velocity magnitude………………………………………………………………93
6.3 Cavitation and closing process of the valve…………………………………………..95
6.3.1 Constant cone motion velocity…………………………………………………..95
6.3.1.1 Vapor volume fraction……………………...………………………………96
6.3.1.2 Static pressure…………………………………………………………...….97
6.3.1.3 Velocity………………………….…………………………................…….98
6.3.2 Sinusoidal cone motion velocity………………………………………………..100
7 Numerical simulation of a 3D servo valve…………………………………………..…104
7.1
7.2
7.3
7.4
Geometry and mesh…………………………………………………….....................104
Laminar flow…………………………………………………………………..….…106
Turbulent flow……………………………………………………………………….108
Cavitation………………………………………………………………………...….111
8 Coupled simulation of whole hydraulic systems……………………………………..114
8.1 Off-line-coupling…………………………………………………………………….114
8.2 On-line-coupling…………………………………………...………………………..118
8.2.1 Motivation…………………………………………………...…………………118
8.2.2 Determination of the coupling modus………………………………...………..119
8.2.3 Formulation of boundary conditions………………………………...…………119
8.2.4 Predefinition and tests…………………………..……………………….……..121
8.2.5 Coupling principle…………………………………………………..……….…122
8.2.6 Coupling results……………………………………………………………...…124
9 Summary and outlook…...………………………………………………………...…....127
10 Literature………………………………………………………..…………..….………129
X
11 Symbols and abbreviations………………………………..…….………………….….136
12 Appendices……………………………………………………………...……………....141
XI