NUMERICAL FLOW ANALYSIS OF GEAR PUMP
by
Yogendra M. Panta
Submitted in Partial Fulfillment ofthe Requirements
for the Degree of
Master ofScience in Engineering
in the
Mechanical Engineering
Program
YOUNGSTOWN STATE UNIVERSITY
August, 2004
NUMERICAL FLOWANALYSIS OF GEAR PUMP
Yogendra M. Panta
I hereby release this thesis to the public. I understand that this thesis will be made
available from the OhioLINK ETD Center and the Maag Library Circulation Desk for
public access. I also authorize the University or other individuals to make copies ofthis
thesis as needed for scholarly research.
Signature: ot- O~ -0lt
Yogendra M. Panta, Student Date
Date
...
Dr. H / W. Kim, Thesis Advisor
Approvals:
Dr. Daniel H. Suchora, Committee Member
~~~cCa----=----? ??~ __8-+---+-&A_,t/
Date
Dr. Hazel Pierson, Committee Member Date
Date
11
ABSTRACT
The objective ofthis study was to develop a numerical solution method for flow analysis
of a gear pump with various boundary conditions and rotational speeds of gears. Flow
variable contours and plots were obtained for fluid flow inside a gear pump subject to
pressure inlet and pressure outlet conditions using the numerical control volume method
in the commercial package FLUENT. Gears with different magnitudes ofpressure outlets
and rotational speeds were analyzed. Currently, no solutions that report the numerical
turbulent flow analysis ofgear pumps are available in the literature.
It is important to the design engineer that accurate methods are available to determine
various flow parameters such as pressure, velocity, turbulence, flow rate etc. for the flow
analysis of the gear pump. The method developed in this work was compared with the
general data ofP3l5 external gear pump manufactured by Parker Hannifin Corporation,
as a validation ofthe numerical model.
An engineer will be able to use the solution method developed in this work for the
analysis of flow parameters inside a gear pump in order to achieve its optimum design.
Another benefit ofthis work is to demonstrate to practicing engineers that FLUENT has
the capability of solving turbulent flow analysis of gear pumps by using its Moving
Dynamic Mesh method. Students can follow this thesis to solve the dynamic mesh
problem step by step. This work should be considered a small subset of numerical
analysis of flow in gear pumps. It is expected that the results presented in this research
provide important information for the extension to a three dimensional analysis of a
similar problem.
III
Dedicated to my Parents
Mr. Gehendra M. Panta & Mrs. Bed Kumari Panta
IV
ACKNOWLEDGMENTS
I would like to thank my advisor Dr. Hyun W. Kim for his guidance and insight
throughout this thesis. His own work motivated some of the questions studied here and
helped me to organize the results in a more logical manner. I would also like to thank him
for his help in proofreading.
I would like to thank Dr. Daniel H. Suchora and Dr. Hazel Pierson for being in my thesis
committee, helping me in proofreading, and providing important suggestions. I would
like to thank Mr. Thomas Calko for doing most of the modeling of the gear pump. I
would also like to thank Mr. Ashish Sudhakar Watve of FLUENT Inc., who gave me
valuable guidance during the simulation work in FLUENT. In addition, I am grateful to
Parker Hannifin Corporation, Gear Pump Division, Youngstown, OH, for providing
physical data ofthe P315 Gear Pump.
During the work, I received very encouraging suggestions and help from my dear friends
Manju and Narayan. I would like to thank my brothers Nagendra and Purushottam for
their support ofme as I completed this work. I would like to express my deepest gratitude
to my fellow graduate students and friends, Ankur and Nassib. Finally, I would also like
to thank Lois Romito, Administrative Assistant of the Graduate School, and especially
Department Secretary Karen Pomponio, for their unwavering strength and friendship.
v
VITA
1995................................ Bachelor of Science, Physics, Mathematics and Statistics,
Tribhuvan University, Kathmandu, Nepal.
2000 Bachelor of Engineering, Mechanical Engineering, Tribhuvan
University, Kathmandu, Nepal.
2004................................ Master ofScience, Mechanical Engineering, Youngstown State
University, Youngstown, Ohio.
2002- 2004 Graduate Assistant, Department of Mechanical & Industrial
Engineering, Youngstown State University, Youngstown,
Ohio.
FIELDS OF STUDY
Major: Mechanical Engineering
Minor: Physics, Mathematics, and Statistics
UNDERGRADUATE SENIOR PROJECT
Detail Design ofPelton Turbine for 500 kW (with Pattern)
VI
TABLE OF CONTENTS
Page
Abstract iii
Dedication iv
Acknowledgements v
Vita vi
List ofFigures ix
List ofTables xi
List ofSymbols xii
CHAPTERl
INTRODUCTION ~ 1
CHAPTER 2
PHYSICAL MODEL OF GEAR PUMP
2.1 Description ofModel 5
2.2 General Data ofP 315 External Gear Pump 7
2.3 Working fundamental ofGear Pump 8
CHAPTER 3
MATHEMATICAL MODELING OF GEAR PUMP
3.1 Governing Equations ofFluid Flow for Gear Pump 10
3.2 The Turbulence Kinetic Energy k-E Equations 11
CHAPTER 4
NUMERICAL MODELING OF GEAR PUMP
4.1 Numerical Simulation 12
4.2 CFD Analysis in FLUENT 13
4.2.1 GAMBIT, the Preprocessor 13
4.2.2 FLUENT, the CFD Solver 14
4.2.3 Problem Solving Steps 16
VB
4.4 Solution Approach in FLUENT 17
4.4.1 Segregated Solution Method 18
4.4.2 Linearization: Implicit 19
4.4.3 Discretization: First Order Upwind Scheme .20
4.4.4 Under-Relaxation Factors .21
4.4.5 Improving the Grid by Smoothing and Swapping .22
4.4.6 Judging Convergence .22
4.5 Judging Convergence 22
4.6 Dynamic Mesh Modeling: Moving Dynamic Mesh 22
CHAPTERS
SOLUTION OF 2-D GEAR PUMP FLOW USING BY FLUENT
5.1 Two Dimensional Gear Pump Model .25
5.2 Case Studies 25
5.3 Geometry Setup and Mesh Generation in GAMBIT 27
5.4 Dynamic Mesh Setting and Calculating Results in FLUENT .37
CHAPTER 6
RESULTS &INTERPRETATIONS
6.1 Results for Various Rotational Speed 66
6.2 Comparative Graphics for Various Flow Parameters 70
6.3 Comparison: Results ofFlow Parameters 84
6.4 Interpretation ofResults 85
CHAPTER 7
CONCLUDING REMARKS 87
BIBLIOGRAPHY 88
Appendix 1: User Defined Function Syntax 91
Appendix 2: Moving Dynamic Mesh: DEFINE_CG_MOTION 93
Appendix 3: Geometry andpumping action ofan externalgearpump 94
Vlll
LIST OF FIGURES
Figure 2.1 Middle Casing 3D-view 5
Figure 2.2 Driving Gear 3D-view 5
Figure 2.3 Driven Gear 3D-view 5
Figure 2.4 Wire frame View ofthe Assembled Gear Pump 6
Figure 2.5 Shaded View ofthe Assembled Gear Pump 6
Figure 2.6 Top View ofthe Assembled Gear Pump 7
Figure 3.1 2-D Gear Pump Model 9
Figure 4.1 Basic Program Structure in Numerical Simulation 12
Figure 4.2 Convergence in Segregated Solution Method 19
Figure 4.3 Rigid Body Rotation Coordinates ~ 24
Figure 5.1 Translation, Rotation, and Scaling down offaces in gear pump model.. 30
Figure 5.2 Graphics ofgear pump showing groups 31
Figure 5.3 Meshes on the gear pump's fluid face 33
Figure 5.4 Initial grid displayed by FLUENT 40
Figure 5.5 Mesh Motion Preview 54
Figure 5.6 Static Pressure Contours at t = as 59
Figure 5.7 Velocity Vectors at t = as 61
Figure 5.8 Iterations until time t = 1.15 sec for N = 2000 rpm & Pout = 3500 psi 62
Figure 5.9 Static Pressure Contours at t = 4.4965 s 63
Figure 5.10 Velocity Vectors at time t = 4.4965 s 63
Figure 5.11 Exact Graphic ofVelocity Vectors at t = 4.4965 s 64
Figure 6.1 Flow Contours for gears at 3000 rpm; Pout = 3500 psi 66
Figure 6.2 Flow Contours for gears at 2000 rpm; Pout = 1000 psi 67
Figure 6.3 Flow Contours for gears at 2000 rpm; Pout = 2500 psi, 67
Figure 6.4 Flow Contours for gears at 2000 rpm; Pout = 3000 psi 68
Figure 6.5 Flow Contours for gears at 2000 rpm; Pout = 3500 psi 68
Figure 6.6 Flow Contours for gears at 2000 rpm; Pout = 3500 psi (Modified casing) 69
Figure 6.7 Static Pressure Contours for gears rotating at 2000 rpm 70
Figure 6.8 Dynamic Pressure Contours for gears rotating at 2000 rpm 71
IX
Figure 6.9 Total Pressure Contours for gears rotating at 2000 rpm 72
Figure 6.1 0 Velocity Magnitude Contours for gears rotating at 2000 rpm 73
Figure 6.11 X- Velocity Contours for gears rotating at 2000 rpm 74
Figure 6.12 Y- Velocity Contours for gears rotating at 2000 rpm 75
Figure 6.13 Velocity Vectors colored by Velocity Magnitude for gears at 2000 rpm 76
Figure 6.14 Velocity Vectors colored by Static Pressure for gears at 2000 rpm 77
Figure 6.15 Contours ofWall Shear Stress for gears rotating at 2000 rpm 78
Figure 6.16 Path Lines colored by Static Pressure 79
Figure 6.17 Path Lines colored by Velocity Magnitude 79
Figure 6.18 Velocity Vectors at the inlet port 80
Figure 6.19 Velocity Vectors at the outlet port 81
Figure 6.20 Pressure Vs. curved length ofgears ...............................................?...............82
Figure 6.21 Velocity magnitudes vs. position ofgears and default interior 83
Figure 6.22 Turbulent Kinetic Energy vs. position ofgears and default interior 83
Figure A 3.1 Pumping action in an external gear pump 94
Figure A 3.2 Gear Type Rotary Pump 94
Figure A 3.3 Geometry ofan external gear pump 95
x
LIST OF TABLES
Table 5.1 Case studies 26
Table 6.1 Comparison: Pressure and Velocity 84
Table 6.2 Comparison: Mass Flow Rate 84
Xl
LIST OF SYMBOLS
p: Density
Il: Viscosity
V:Velocity Vector
Vs : Velocity Vector on the gear surfaces
P : Pressure Vector
Pi: Pressure at the inlet port
Po: Pressure at the outlet port
i, j, k: The unit vectors
Ilt: The turbulent viscosity
A : Surface Area Vector
r? :Diffusion Coefficient for ?
V' ? : Gradient of<D
V' : Del Operator
k: Kinetic Energy
E: Kinetic Energy Dissipation Rate
Gk: The generation ofturbulence kinetic energy the mean velocity gradients
Gb: The generation ofturbulence kinetic energy due to buoyancy
YM: The fluctuating dilatation in compressible turbulence to the overall dissipation rate
(J'K: Turbulent Prandtl number for k
(J'E: Turbulent Prandtl number for E
S<I>, SK and SE : User-defined source terms.
ak: Turbulent Prandtl number for k
aE": Turbulent Prandtl number for E
CIE' C2E ,C3E , CJL: Constants
Nfaces : Number offaces enclosing cell
cf>f: Value cf> of convected through face f
P f vf?Af : Mass flux thorugh the face
XlI
Af : Area of face, f!AI(= IA) + AyJI)in 2D
(V??n :Magnitude of V?> nonnal to f
V: Cell volume
X;;l : Position ofthe center ofgravity
(je~;l : Orientation ofthe center ofgravity
Ve,g, : Linear velocity and ofthe center ofgravity
Qe,g, : Angular velocity ofthe center ofgravity
G : The transfonnation matrix that defines the choice of (j
(u, v, w): Linear velocity as a function oftime
(w x, wy, wz) : Angular velocity as a function oftime
er , ea : The unit vectors
Xlll
CHAPTER 1
INTRODUCTION
The pump is the heart ofthe hydraulic system. Like a heart in a human body, a hydraulic
pump generates a flow by moving the fluid from a low-pressure region to a higher 
pressure region. The pump does not create system pressure, although the pump is often
described in terms ofits limitation ofpressure. The pressure that exists at the outlet port
of the pump is a result of system load that was created by a resistance to the flow.
Therefore, the outlet flow rate (or the displacement) and the pressure are proper terms to
characterize and describe the pump. The pumps are generally categorized in two distinct
groups, positive-displacement pumps and kinetic pumps. All pumps used in hydraulic
systems are ofthe positive displacement type that includes gear, vane, and piston pumps.
This means that the fluid will be pushed forward from the inlet to the outlet by the direct
motion of solid bodies in a positive displacement action. The gear pump is the most
robust and rugged type of all positive displacement pumps and is one of the simplest
hydraulic pumps [1]. The kinetic type pumps transfer the mechanical power input to
kinetic energy and transforms the kinetic energy into static pressure. These pumps are
mainly used to generate a high rate offluid flow and include centrifugal pumps [2].
Two years ago, Youngstown State University began to develop a collaborative research
and educational programs in hydraulics with Parker Hannifin Corporation and established
the Center for Hydraulics Research and Education in Fall 2003 [3]. Parker Hannifin,
headquartered in Cleveland, Ohio, is a world class business and manufacturing leader in
hydraulics. Two ofits divisions, Gear Pumps and Mobile Cylinders, are at local plants in
Youngstown. As part of that development, the Mechanical Engineering Program is
working toward establishing a state-of-the-art computational laboratory that includes
solid modeling, computational fluid dynamics analysis, interactive flow and stress
analysis, interactive motion control, and simulation. Computational fluid dynamics can
help to optimize the design of the pump and improve the efficiency of the pump, other
components, and the entire hydraulic system. A flow analysis for an external gear pump
1
by FLUENT, one ofthe most versatile CFD software packages currently available in the
market, was selected as one ofthe initial research projects in the developmental effort.
The flow pattern created inside an external gear pump by the motion oftwo gears rotating
in opposite directions is deceptively complex despite the simple geometry of the gear
pump. The flow cannot be analyzed, based on a steady-state assumption that is usually
employed to analyze turbo-machinery despite the fact that the flow is essentially steady.
Only the time-dependent, unsteady, dynamic meshing can predict the motion ofthe fluid
flow against the very high adverse pressure distribution. Although the complexity of
analysis is inherent in all positive displacement pumps, gear pumps pose an exceptional
challenge due to the fact that there are two rotating components which must be in contact
with each other all the time housed within a stationary three-dimensiona1-casing. The
study and analysis presented in this thesis will deal with those problems to make an
acceptable preliminary investigation on the gear pump flow and document the step by
step procedure from the description of a physical model to the results of the numerical
analysis.
The hydraulic pump has been used for a long time. The Ancient Egyptians invented water
wheels with buckets mounted on them to move water for irrigation. In the 200's B.c.
Ctesibius, a Greek inventor, made a reciprocating pump for pumping water. Around the
same time, Archimedes, a Greek mathematician, invented a screw pump made ofa screw
rotating in a cylinder, now known as an Archimedes screw. Thousands of years later,
pumps still operate in the same basic way. The modem day development of the gear
pump began in 1588. In 1588, Ramelli, an Italian engineer invented a water pump which
continues to be used in oil pumps and compressors. In 1636, Pappenheim, a German
engineer invented the gear pump used to lubricate engines. In 1799, one ofJames Watt's
co-workers, Murdock, adapted Pappenheim's gear pump to create a rotary piston steam
engine. In 1859, Jones, modified Pappenheim's gear pump and produced a double rotor
with only two teeth per gear [5].
Since the introduction of the gear pump in the 1930s, gear pump technology has been
steadily improved. Gear pumps have been widely used in polymer manufacturing plants
2
and transportation industries. Thus, research of the gear pump is one of the older fluid
power research fields and is considered as a mature technology. More recent classical
research activity, initiated by Professor Borghi at the end ofthe 1980's, is still active and
includes major industrial research in cooperation with the CASAPPA Fluid Power (1995
- present), one ofthe important Italian manufacturers in this field [6].
Luc Machiels (1997) performed research on different randomly forced turbulent systems,
by direct numerical simulation. Luc showed the high degree of randomness produced
intrinsically in three-dimensional incompressible Navier-Stokes turbulence and the
numerical method for the simulation of randomly forced turbulent systems [7]. Spyros
Gavrilakis found the effects ofrotation on the turbulent field inside a straight square duct
in his research on numerical simulation of turbulent flows. He included the decay of
turbulence even at low Reynolds numbers [8].
Noah D. Manring and Suresh B. Kasaragadda have done research on the theoretical
flow ripple of an external gear pump of similar size, using different numbers ofteeth on
the driving and driven gears. According to them, an external gear pump design with a
large number ofteeth on the driven gear and a fewer number ofteeth on the driving gear
would be better for high performance. The results showed that the driving gear dictates
the flow ripple characteristics of the pump while the driven gear dictates the pump size
[9]. Jaakko MyllykyHi, Tampere University of Technology, Tampere, Finland has done
research on the suction capability of an external gear pump. He showed that higher
rotational speeds can lead to cavitations. His research collected data on a number ofgear
pumps to study the suction characteristics. He formulated a theory for suction ofexternal
gear pumps with two gears. According to his research, he mentioned that the biggest
uncertainty factor is the mathematical expression for the effect of the housing shape on
the suction characteristics [10]. Lev Nelik, used the basic equations of pump flow and
volumetric efficiency and verified the results with experiments. He found three important
things: volumetric efficiency is lower at higher differential pressures, viscous fluids result
in higher volumetric efficiency, and volumetric efficiency appears higher at higher speeds
[11]. Y.P. Marx as the chief of research team for Faculty of Engineering Sciences and
3
Techniques (ST!) at the Swiss Federal Institute of Technology - Lausanne (EPFL),
developed numerical tools for simulating generalized Newtonian flows in gear-pumps.
The computer program code SAGARMATHA, developed by Marx, with contributions
from T. Jongen, O. Byrde and M.L. Sawley, was applied on several gear pump inlets for
the simulation ofgeneralized Newtonian flows at very low Reynolds numbers. With the
proposed formulation, a numerical principle was used to solve the Stokes and the
potential equations. This was demonstrated by the ease in transforming a Stokes solver
into a potential flow solver. The code incorporates modem numerical methods and
computational techniques for the numerical simulation of large-scale incompressible
flows. The code is also used for the simulation of flows involving both stationary and
rotating sub domains. Computational meshes with blocks that slide across each other can
be employed [12]. Using the Mesh Superposition Technique in POLYFLOW software,
Fluent Inc. has done a simulation for the molten polymer flow analysis ofthe gear pump.
A research result obtained by the company's internal team showed that a high pressure
region is formed where the gear teeth are closing in the outlet port [13].
Despite its long history ofusage and numerous researches on gear pumps related subjects
[14-39], no work has been reported in the literature that examined the numerical turbulent
flow analysis ofgear pump. Therefore, this research has been initiated using FLUENT, a
commercial finite volume CFD software package, to investigate two dimensional
turbulent flow analysis of a gear pump. It is expected that the results obtained in this
report provide important information for the extension to a three dimensional analysis.
4
CHAPTER 2
PHYSICAL MODEL OF GEAR PUMP
2.1 Description ofModel
P300 senes pumps are the production of Parker Rannifin Corporation, Gear Pump
Division, Youngstown, OR. The physical model for the fluid flow analysis was chosen
from Parker Corporation's existing product; P315 external gear pump (refer to Figures
2.1,2.2,2.3,2.4,2.5).
Figure 2.1 Middle Casing 3D View
Figure 2.2 Driving Gear 3D View
5
Figure 2.3 Driven Gear 3D View
Figure 2.4 Wire Frame View ofthe Assembled Gear Pump
Figure 2.5 Shaded View ofthe Assembled Gear Pump
6
Figure 2.6 Top View ofthe Assembled Gear Pump
2.2 General Data ofP 315 External Gear Pump
After careful study of the general data of the P315 gear pump in PGP/PGM300 Series
available and published by Parker Hannifin Corporation, the following data are taken for
the analysis ofgear pump:
Pump Type
External gear pump, heavy duty
Solid Material:
Cast iron for gear housing
Stainless steel for gear rotors
Hydraulic Fluid:
Mineral oil, water glycol, HFC; water oil emulsions 60/40, HFB
Gear Drives
Clockwise, counterclockwise, double
Speed Range
From 400 to 3000 rpm
Pump Inlet Pressure
30 psil 0.8 to 2.0 bar at operating temperature
7
Outlet Pressure Range
Continuous 2500-3500 psi, intermittent 4000 psi
Fluid Temperature
Mineral oil with standard seals: 0? to 180? F (-20?C to +80?C)
Basic Dimensions ofGear Pump:
Weight: 18 lbs
Gear widths: 0.5 to 2.5 in.
Total no. ofgear teeth in each rotor: 12
Center to center distance ofgears: 0.98 in.
Gear outside diameter: 1 in.
Gear inside diameter: 0.75 in.
Inlet port size: 0.25 in. curved
Outlet port size: 0.75 in. curved
2.3 Working Fundamentals ofthe Gear Pump
The gear pump is made oftwo or more gears rotating inside a closed casing (Figure 2.4).
The driver gear motion is produced by a motor, while the driven gear motion occurs
through the meshing ofthe teeth ofthe two gears. As the gears start to rotate, the teeth are
in and out ofcontact with each other (refer to Appendix 3). As a tooth leaves the contact
region, a vacuum is created. The liquid that runs into this space to fill this vacuum has to
be supplied through the pump's inlet port. Once filled with the fluid, the fluid follows in
pockets between the teeth, trapped in place because ofthe sealed housing, until it reaches
the pump's outlet port. The fluid stays in place between the teeth until it passes to the
other open chamber of the gear mesh, on the outlet side. At this point, the teeth of the
gears continue rotating and thus come back into contact, and the liquid there is forced
out. Since there are sealed bushing around the gears, the displaced liquid must move
forward to the pump's outlet port. The pump works like a rotating conveyor belt, with a
lot of pockets of liquid between the teeth of the gears moved forward by the rotating
motion.
8
CHAPTER 3
MATHEMATICAL MODELING OF GEAR PUMP
The gear pump problem to be considered is shown schematically in Figure 3.1. Low
pressure oil enters through the inlet port and rotates with the rotational motion of gears,
creating pockets of fluid, and finally discharges from the outlet port with high pressure.
Creation ofa 2D gear pump model, setup parameters, and solution procedure to solve the
flow inside a gear pump is presented in the following sub topics.
Out/~(
Or/lien Cffllr rClocJ:lVlsel
HOUSIng
inlet
Grid (Time=1.1500e+00)
Gear Pump Design by Yogen
Aug 03, 2004
FLUENT 6.1 (2d, dp. segregated, dynamesh, ske, unsteadl)
Figure 3.1 2D Gear Pump Model
9
3.1 Governing Equations ofFluid Flow for Gear Pump
The fluid motion generated by two fast rotating gears inside a gear pump can be
described by the Navier-Stokes equation; however, the flow is expected to be highly
turbulent. Therefore, the fluid motion and transport characteristics are governed by not
only three conservation equations, but also by two additional equations for the turbulent
kinetic energy and the rate ofdissipation ofkinetic energy.
Assumptions incurred on this flow analysis may be stated as follows:
1. The fluid is a Newtonian, incompressible fluid.
2. The fluid is originally stationary.
3. The flow is two dimensional.
4. Body forces are negligible.
5. Viscous heating is considered.
The coordinate system is chosen such that the origin ofthe Cartesian coordinate is at the
center of the driven gear. Upon imposing the above stated conditions, the governing
equations, boundary conditions, and initial conditions can be expressed as follows:
Continuity Equation
V? V=0 Equation 3.1
Momentum Equation
(8V - -I - 2 - ?P 8t + V .V V) =-V.P + JiV V EquatIOn 3.2
Initial condition:
At timet :::; 0: V=0
With boundary conditions ofvelocity:
On the casing wall: V= 0
On the gear surfaces: V=Vs
Also, the boundary conditions ofpressure:
At the inlet port: P = Pi
At the outlet port: P = Po
10
Energy Equation
a(pcT)+V. (pVcT)= V(kVT)+ S? Equation 3.3at
Where,
a~ a ~ a ~V = Del operator = -i+-j+-k
ax 8y 8y
Boundary conditions oftemperatures:
At the inlet port: T = Tj
At the outlet port: T = To
aTOn the gear surfaces: - =0
an
3.2 The Turbulence Kinetic Energy k-f Equations
As previously stated, two additional equations are necessary in order to characterize the
turbulent flow.
~ (pK) +V'(p..v) = V'[(~+ ~JV'k] +G, +G, - pc-YM +S, Equation 3.4
The turbulent (or eddy) viscosity, Ill, is computed by combining k and f as follows:
k 2 ?f.1t = pCJ.i - EquatIon 3.6
&
Generally, these values are initially set to:
11
CHAPTER 4
NUMERICAL MODELING OF GEAR PUMP
4.1 Numerical Simulation
Computational fluid dynamics (CFD) performs numerical analysis of a fluid flow field
once a finite volume grid has been created. Setting boundary conditions, defining fluid
properties, executing the solution, refining the grid, and viewing and post processing the
results are generally performed within the chosen CFD code. For this research, Solid
Works was used for model construction, GAMBIT was used for preprocessing & grid
generation, and FLUENT was used for the CFD solver.
Solid Works
? Geometry construction for the gears and the casing
GAMBIT
? Geometry set up from Solid Works
? 2D mesh generation
\11
FLUENT
? Mesh import and adaption from
GAMBIT
? Physical models selection
? Boundary conditions set up
? Material properties database
? Moving dynamic domains set up
? Calculation
? Postprocessing
Figure 4.1 Basic Program Structure in Numerical Simulation
12
4.2 CFD Analysis in FLUENT
FLUENT uses an unstructured algorithm for mesh generation in order to simplify the
geometry and mesh generation process, model more complex geometries and adapt the
mesh to resolve the flow-field features. FLUENT can also use body-fitted, block 
structured meshes. The software is capable of handling triangular and quadrilateral
elements in 2D, and tetrahedral, hexahedral, pyramid, and wedge elements (or a
combination ofthese) in 3D. The initial mesh is first generated using GAMBIT, and then
it can be adapted in FLUENT in order to resolve large gradients in the flow field.
4.2.1 GAMBIT, the Preprocessor for Geometry Modeling and Mesh Generation,
Postprocessor for Results Viewing
GAMBIT is a software package designed to build, import and mesh models for
computational fluid dynamics (CFD) and other scientific applications. GAMBIT gets
user input by graphical user interface (GUI). Then the GUI performs the fundamental
steps of building, meshing, and creating zone types in a model. The most important
operations are associated with the Geometry, Mesh, Zones, and Exporting files for
Postprocessing command buttons, which will be described here.
(i) Creating Geometry in Solid Works and Importing it into GAMBIT
File -7 Import -7 IGES ....the files were imported from Solid Works source files.
(ii) Meshing ofthe Model
Mesh command button on the Operation tool pad in GAMBIT opens the Mesh sub pad
which contains command buttons that performs mesh operations involving boundary
layers, edges, faces, volumes, and groups. In the particular problem of 2D gear pump
model, this was used for face meshing (refer to section 5.3/step 7/page 32)
13
(iii) Specifying Zone Types
The domains ofthe model at its boundaries and in some specific regions can be defined
by using zone-type specifications. There are two classes ofzone-type specifications:
? Boundary types: Wall for gears and casing; Pressure Inlet for the inlet and
Pressure Outlet for the outlet.
? Continuum types: Fluid for the meshed face.
(iv) Exporting Results Files from GAMBIT
To display post processing results for any given solution, two files must be imported into
GAMBIT:
? A results database
? A neutral file
The results-database file contains the results data for the solution. The neutral file
contains coordinate and connectivity information for the model.
4.2.2 FLUENT, the CFD Solver
FLUENT is a finite volume based code for the simulations and modeling offluid flow as
well as heat transfer. Since FLUENT is written in the C computer language, it makes full
use ofthe flexibility and power offered by the language. FLUENT is ideally appropriate
for incompressible and compressible fluid flow simulations in complex geometries. The
following considerations are intricate in order to solve a gear pump problem in FLUENT:
? Modeling Goals: One must identify the expected specific results and the degree
ofaccuracy required from the model.
? Geometrical Parameters Processing: This addresses the computational domain,
where one must specify boundary conditions used at the boundaries ofthe model,
dimension of the model (2D or 3D), type of grid topology best suited for the
model.
14
? Flow and Dynamic Data Processing: The flow type of viscous model must be
specified: inviscid, laminar, or turbulent, unsteady or steady flow over the time,
heat transfer, incompressible or compressible fluid.
? Solution Procedure: The solver formulation, solution parameters and the result
convergence need to be decided upon and specified.
For the Moving Dynamic Mesh (MDM), user-defined functions (UDFs) were used to
control the dynamic mesh of two rotating gears and a stationary casing. Smoothing and
re-meshing were used for the rotating gears and casing. The rotation of the gears was
defined and controlled by UDF as a rigid body type that utilizes a macro specific to the
dynamic mesh model while the casing was taken as a stationary type boundary.
Previously created gear pump housing with two gears was imported into GAMBIT from
a Solid Works 2D source file to create the 2D geometry for the gear pump. A fine mesh
was generated (refer to Figure 5.4). Finally, the mesh file was exported to FLUENT for
the further flow analysis. Once the meshed model was in FLUENT, the following major
steps are summarized for the flow analysis:
1. Dynamic mesh capability of FLUENT was used to solve rotating gears rigid body
motion problem.
2. A compiled user-defined function (UDF) was used to specify the rigid body motion
ofrotating gears.
3. The dynamic mesh was previewed before starting the flow computation.
4. A solution using segregated solver was calculated.
Program Capabilities ofFLVENT
The FLUENT solver has capabilities of solving the following model. Note that the bold
type indicates the features utilized in this work.
? 2D planar, 2D axisymmetric, 2D axisymmetric with swirl and 3D flows.
? Quadrilateral, triangular, hexahedral (brick), tetrahedral, prism (wedge),
pyramid, and mixed element meshes.
? Steady-state or transient flows.
15
? Incompressible or compressible flows.
? Inviscid, laminar, and turbulent flows.
? Newtonian or non-Newtonian flows.
? Heat transfer ofall kinds and radiation.
? Chemical species mixing and reaction, including homogeneous and heterogeneous
combustion models and surface deposition/reaction models.
? Free surface and multiphase models for gas-liquid, gas-solid, & liquid-solid flows.
? Lagrangian trajectory calculation for dispersed phase (particles/dropletslbubbles),
including coupling with continuous phase.
? Cavitation model.
? Phase change model for melting/solidification applications.
? Porous media with non-isotropic permeability, inertial resistance,- solid heat
conduction, and porous-face pressure jump conditions.
? Lumped parameter models for fans, pumps, radiators, and heat exchangers.
? Inertial (stationary) or non-inertial (rotating or accelerating) reference frames.
? Multiple reference frame (MRF) and sliding mesh options for modeling multiple
moving frames.
? Mixing-plane model for modeling rotor-stator interactions, torque converters, and
similar turbo machinery applications with options for mass conservation and swirl
conservation.
? Dynamic mesh model for modeling domains with moving and stationary
mesh (MDM).
? Volumetric sources ofmass, momentum, heat, and chemical species.
? Material property database.
? Extensive customization capability via user-defined functions (UDF).
4.2.3 Problem Solving Steps
Once after determining the important features ofthe particular problem ofgear pump, the
following basic procedural steps were taken.
Geometrical Modeling and Meshing (in Solid Works and GAMBIT)
1. Create the model the geometry and grid.
16
Preprocessing (in FLUENT)
2. Start the appropriate solver ofFLUENT for 2ddp modeling.
3. Import the grid: File Menu
4. Check the grid : Grid Menu
5. Select the solver formulation: Define Menu
6. Choose the basic equations: laminar or turbulent (or inviscid) etc. : Define Menu
7. Specify material properties: Define Menu
Dynamic Mesh Zones: Moving Dynamic Mesh
8. Specify dynamic mesh zones & boundary conditions: Define Menu
9. Adjust the solution control parameters: Solve Menu
10. Initialize the flow field: Solve Menu
Calculation:
11. Calculate a solution: Solve Menu
12. Examine the results: Display, Plot, Report Menu
Postprocessing:
13. Save the results: File Menu
4.4 Solution Approach in FLUENT
The approach involves a numerical modeling to assess the use of CFD to model and
predict the flow patterns ofthe flow inside the gear pump. FLUENT is used to complete a
series ofsimulations for flow from the pump's intake to its outlet.
For the gear pump model, a segregated solver was used. Using this method, FLUENT
solves the governing equations of Navier-Stokes for the conservation of mass and
momentum, and (when appropriate) for energy and other scalars such as turbulence. In
segregated solver method, a control-volume-based technique is used which consists of:
? Division ofthe domain into discrete control volumes using a computational grid.
? Integration of the governing equations on the individual control volumes to
construct algebraic equations for the discrete dependent variables such as
velocities, pressure, temperature, and conserved scalars.
17
? Linearization of the discretized equations and solution of the resultant linear
equation system to yield updated values ofthe dependent variables.
FLUENT is also capable of a coupled solution numerical method which employs a
similar discretization process (finite-volume); but the approach used to linearize and
solve the discretized equations is different than the segregated solver. Since all of the
simulations were done using the segregated solver, the coupled solution method is not
included.
4.4.1 Segregated Solution Method
Using this approach, the governing equations are solved sequentially (i.e., segregated
from one another). As the governing equations are non-linear, several iterations of the
solution loop must be done before a converged solution is achieved.
1. Fluid properties are updated each iteration based on the current solution.
2. The u, v, and w momentum equations are solved individually using the current
iterative values for pressure and face mass fluxes to update the velocity field.
3. Since the velocities obtained may not satisfy the continuity equation locally, the
pressure correction equation is then solved to get the corrections for the pressure and
velocity fields that do satisfy the continuity equation.
4. Equations for scalars, e.g. turbulence, are solved using the updated values ofthe other
variables.
5. Ifinter phase coupling is to be included, the source terms in the appropriate continuous
phase equations are updated with a discrete phase trajectory calculation.
6. Convergence for the equation set is checked each iteration until the convergence
criteria is met.
18
I Update Properties !
~
Solve momentum equations
1
Solve continuity equation.
Update pressure, face mass flow rate
1
Solve energy, turbulence and other
scalar equations.
1 -
STOP r Converged? 1L
J
Figure 4.2 Program Algorithm in Segregated Solution Method
4.4.2 Linearization: Implicit
In the segregated solution method, the governing equations are linearized to create a
system ofequations for all dependent variables in each computational cell. The resultant
linear system is then solved for an updated flow-field solution. The implicit option is the
only one available in the segregated solver, thus it was the solution method for the gear
pump. In the segregated solution, each discrete governing equation is linearized
implicitly with its dependent variables. A point implicit (Gauss-Seidel) linear equation
solver is used with an algebraic multi-grid (AMG) simultaneously to solve the resultant
scalar system of equations for the dependent variable in each and every cell. So, the
segregated approach solves a single variable field (e.g., v) by considering all cells at
once. Then it continues to solve for the next variable field again by considering all cells
at once, and so on.
19
4.4.3 Discretization: First Order Upwind Scheme
FLUENT uses a Control Volume (CV) Technique to convert the governing equations
into algebraic equations. The control volume technique is the integration ofthe governing
equations in each control volume, yielding discrete equations which conserve each
quantity on a control-volume basis.
Integral form for a control volume V:
1p?v.dA = 1r?V?.dA + JS?dV Equation 4.1
Where,
p = Density
v= Velocity vector (ul + v) =in 2D)
A = Surface area vector
r? = Diffusion coefficient for <P
V? = Gradient of<p = (8%x) +(8%)J in 2D
Sq, is source of<P per unit volume.
This is applied in each control volume, or cell, in the computational domain.
Discretization ofthe above equation on a given cell yields
Nraces Nfaces
Ipfvf?f'Af = Ir?{v?t.Af +S?V Equation4.2
f f
20
Where,
Nfaces = Number offaces enclosing cell
CPf = Value cI> ofconvected through face f
Pf vf .Af = Mass flux through the face
(VcjJ) n = Magnitude of VcjJ nonnal to face f
V = Cell volume
The first-order discretization generally yields better convergence than the second-order
scheme, although it generally will yield less accurate results, especially on triangular and
tetrahedral grids. This is because the flow is never aligned with the grid. More accurate
results could be obtained by using the second-order discretization. However, for moving
dynamic meshes, first order upwind is used, and thus used in the gear pump model, as the
moving dynamic mesh will be more stable.
4.4.4 Under-Relaxation Factors
As the nonlinearity ofthe equations is solved by FLUENT, it needs to control the change
ofa variable CP, which can be achieved by under-relaxation. This reduces the change ofcP
generated during an iteration. So, the new cP within a cell depends upon the old, cP old and
only a portion, Ci., ofthe L\<I> occurring during an iteration.
cP = cP old + a L\ <D ??????...?...?.?.................?.?????.?.?.?.??????????.?.?............?.?.???.?.?.?.???...?. Equation 4.3
21
4.4.5 Improving the Grid by Smoothing and Swapping
Smoothing and face swapping are basic tools to complement grid adaption, usually
increasing the quality of the final numerical mesh. Smoothing relocates the nodes and
face swapping modifies the cell connectivity to achieve these improvements in quality.
4.4.6 Judging Convergence
? Crude initial guesses for mean and turbulence quantities can cause the solution to
diverge. The iteration solution was started from inlet pressure conditions in this
problem. Since the inlet boundary conditions are given in FLUENT, it
automatically shows the initial guess for the iteration.
? Reasonable initial guesses for the k and E fields can give a quick convergence.
Here, the default criterion was changed from 10-3 to 10-6 for the precision.
4.5 Dynamic Mesh Modeling: Moving Dynamic Mesh
The dynamic mesh model in FLUENT can be used to model flows where the shape ofthe
domain is continuously changing with time due to motion on the domain boundaries. The
motion can either be a prescribed motion (e.g., in this research, angular velocities are
specified about the center ofgravity oftwo gears with time) or an un-prescribed motion
where the subsequent motion is determined through a user-defined function [38]. The
volume mesh updating is done automatically by FLUENT at every time step based
on the new positions created in the boundaries. In order to use the dynamic mesh model,
it is needed to provide an initial volume mesh and the details of the motion of any
moving domains.
As stated previously, the unsteady flow created by two rotating gears inside a gear pump
is complex and can be analyzed only by properly accommodating constantly changing
boundaries. FLUENT can perform such tasks through its Moving Dynamic Mesh
capability.
The motion of the rigid body was specified by the linear and angular velocity of the
center ofgravity. Velocities can be specified by profiles or user-defined functions (UDF).
22
UDF can be written for linear velocity (u, v, w) as a function oftime or angular velocity
(w x, wy, wz) as a function oftime or both as needed. UDFs were used to specify angular
velocities ofgears for gear pump. For this problem, UDF code written in "C" has angular
velocity inputs for the rotating gears. The starting location of the center of gravity and
orientation ofthe rigid body must also be specified. FLUENT automatically updates the
center ofgravity position and orientation at every time step (refer to Figure 4.3) such that:
xn+1 =xn +v I:1t Equation 4.4e.g. e.g. e.g.
iJ n+1 =iJ n + GO I:1t Equation 4.5e.g. e.g. e.g.
Where,
X;;1 and iJe~;.1 are the position and orientation of the center of gravity, veg . and
0c.g. are the linear and angular velocities ofthe center ofgravity, and G is the transformation matrix
that defines the choice of e. By default, G is taken to be the identity matrix. Typically, eis chosen to
be an appropriate set ofEuler angles. In this case, the rigid-body motion must be specified using a
user-defined function (DEFINE_CG_MOTION) where the appropriate form ofG can be speficied.
The position vectors 0e.g. on the rigid body are updated based on rotation about the
instantaneous angular velocity vector. For a finite rotation anglel:1B =IOe.g.ll:1t, the final
position of a vector xr on the rigid body with respect to xe.g . can be expressed as:
-n+l -n A:;; . 6x
r =xr + L.U EquatIon 4.
Where,
I:1X =Ix; I[sin(1:1 B)eo + (cos(1:1 B) -l)er] Equation 4.7
23
- .. -- --- -- ~ - ......--- ---
I
f
/,.
---
Figure 4.3 Rigid Body Rotation Coordinates
The unit vectors er and ee are defined as
n xxe = e.g. r
r Inc.g . x Xr I
_ Equation 4.8e
xQ~ e e.g.ee = _
lee x Qc.g.1
If the solid body is also translating with, vc.g . the n+1 position vector on the rigid body
b d -n+! -n - A -n+! E . 49c.g. +vc.gut + xr quatlOn .
Where, x;+! is given by above Equation 4.6. In the gear pump problem, however, the
solid body only underwent rotation not translation.
24
CHAPTERS
SOLUTION OF 2D GEAR PUMP FLOW USING BY FLUENT
5.1 Two Dimensional Gear Pump Model
For the flow analysis inside the gear pump, two dimensional (2D) gear pump model was
used for the purpose of computational analysis in FLUENT. A three dimensional (3D)
model was not considered, due to the complexity ofa 3D moving mesh, the run time, and
the size of files created after the simulation. The 2D simplification in the modeling,
however, is expected to produce a reasonably accurate numerical analysis that will
provide vital information for 3D modeling work in the future. A full sectional-view ofthe
gear pump is as shown in Figure 3.1.
5.2 Case Studies
A 2D gear pump model is proposed for flow analysis, and the commercial CFD software
FLUENT is used to analyze the flow inside the gear pump. Using FLUENT, numerous
parameters were found for different cases. The velocity vector, pressure contours,
turbulence and flow rate are some of them. Among the issues deserving further
investigation is the emulation ofother camera functions like zooming and rotation as well
as the rendering ofperspective.
Over six different cases were examined for flow analysis in FLUENT (refer to Table 5.1)
and two more cases were used for simulation to test the flow pattern with some geometry
change in the casing. The computational analysis includes pressure contours, velocity
vectors, and XY plot animation. From each case, the variables were analyzed and were
compared with the other cases. The results are presented in Tables 6.1, and 6.2. The
following cases were examined in FLUENT for the flow analysis.
25
Table 5.1 Case studies
Case Rotational Pout (psi) Pin (psi) Casing geometry
speed (rpm)
1 3000 3500 30
2 2000 1000 30
3 2000 2500 30 Original
4 2000 3000 30
5 2000 3500 30
6 2000 3500 30 Modified
The following variables were analyzed from model:
I.Grid motion
2. Contours ofvelocity
(a) Stream function
(b) Velocity magnitude
3. Contours ofpressure
(a) Static pressure
(b) Dynamic pressure
(c) Total pressure
4. Path lines
5. Contours ofwall fluxes ( Wall shear stress)
6. XYplot:
(a) Static pressure vs. position of interior
(b) Velocity magnitude vs. position ofinterior
(c) Static and dynamic pressure vs. curve length ofdriven gear
(d) Static and dynamic pressure vs. curve length ofdriving gear
(e) Velocity vs. curve length ofboth gears
(f) Static pressure vs. direction vector ofcasing
7. Mass flow rate
26
5.3 Geometry Setup and Mesh Generation in GAMBIT
Step 1: Start GAMBIT with ID as sub initial by using DOS command.
Step 2: Import IGES files from Solid Works source file for gears and casing.
File ->Import ->IGES ..... then browsing the right location for the IGES file and
accept the three Solid Works IGES files of two rotors and casing to upload in
GAMBIT.
Import IGES File '" ~
File Name: Un:\Gear\solid Works 2-D Case lUGS Browse...I
Summary:
Product 10 Solid Works 2-D Case II
System 10 SolidWorks 2001 Plus by SolidWorks Corporation
Model Space SCale Units IN
Date 040319 Time 200633
Distance Tolerance 1e-006
Maximum Coordinate 19665.039
ImpOrt OptionS:
Translator: v Native. Spatial
Model Scale Factorp
Stand-alone Geometry:
.J No stand-alone vertices
.J No stand-alone edges
.J No stand- alone faces
Import Source Generic .... I
.JHealGeometry
? Make Tolerant
.J Virtual aeanup:
..." V(-dU.~ II
? SlIort<.s1 Ellge % 1;.;-1:-:::----
M"'9i> Tol"ranc" p
27
... Rotate
v Scale
Step 3: Selecting a Solver.
Choosing the solver for CFD calculation by selecting the following from the main menu
bar:
Solver ->FLUENT 5/6
The solver currently selected can be seen at the top ofthe GAMBIT GU!.
Step 4: Scaling down, Rotating and translating faces.
GEOMETRY .-!:.l->FACE nJ 1->Move/cOpy Faces I~"~
Move I Copy Faces
Faces Pick...J IIface.: ~
... Move v Copy W- 
Operation:
v Translate
v Reflect
Angle 1~
Axis Define
Active Coord. Sys. Vectol
(0,0,0) -> (0,0,1)
..J Connected geometry
Apply I Reset I aose I
28
First, the mesh file (from GAMBIT) and the C file (specifying dynamic mesh) were
uploaded in the FLUENT to see whether the geometry of the gear pump needed
revisions. Once the UDF was compiled, the geometry appeared acceptable. However,
during the mesh motion preview, it was noticed that after some time steps, the gear teeth
contacted each other. This is invalid as far as CFD simulation is concerned. This is due to
fact that when gear teeth touch each other, there is no space left between the two gears to
put mesh in it. Thus, for gear pump dynamic mesh simulations, it is recommended to
avoid contact between gear teeth. There are two possible ways to achieve this:
1. Increase the center to center distance between the two gears. This is only possible in
GAMBIT or any CAD package, where the geometry is created.
2. Keep the center to center distance constant but reduce the addendum, pitch circle
diameters ofthe gears by some factor. This also is only possible in GAMBIT or any CAD
package, where the geometry is created.
The second method was chosen in this research to avoid the gear teeth contact. First,
driven gear face was translated to the origin of the axis and was rotated 15? about the
origin. The faces ofboth rotors were then scaled down to 0.96 to create more clearance
between the gear teeth. Finally, the driven gear was translated back to its original
position. This is shown in Figure 5.1.
29
Figure 5.1 Translation, Rotation, and Scaling down of Faces in Gear Pump Model
Step 5: Subtracting faces to specify the fluid face
GEOMETRY Iij 1-> FACE FD L> Subtract Real Faces Is:r)1
Subtract Real Faces
Face IIrace.1
..J Retain
Subtract
Faces l]"ace.z 13
..J Retain
Apply I Reset I COse
30
The faces of the two gears were subtracted from the face of casing to specify the space
enclosed between the inside the casing and the outside the gears. After subtracting, there
was only one face enclosed between gears and casing, the fluid zone.
Step 6: Creating groups ofedges
lit I [Biiiil IfBi~
GEOMETRY ~->GROUP ~> Create Group ~
Five Groups were created to specify Inlet, Outlet, Casing, Driven Gear and Driving Gear
using the edges. The respective group were named as in, out, cas, pos and neg as shown
in Figure 5.2.
Figure 5.2 Graphics ofGear Pump showing Groups
31
Step 7: Creating meshes on fluid face
MESH ~-> FACE Ft] 1-> MESH FACES ~ I
This command sequence opens the Mesh Faces fonn. The interval size of the mesh was
taken as the default value and the mesh was tn-pave meshing scheme for the moving
dynamic mesh (MDM) setting up. This is shown in Figure 5.3.
Mesh Faces
Faces IIrace.' .:!I
Scheme: ? Apply Default
Elements: Tri -JI
Type: Pave -J I
Spacing:
~,
Options:
? Apply Default
Interval size
? Mesh..J
Remove old me!
..J Ignore size func
~p1y I Reset I Qose I
32
Figure 5.3 Meshes on the Gear Pump's Fluid Face
Step 8: Set Boundary Types
1. Hiding the mesh from the display before setting the boundary types makes it easier to
see the edges and faces of the geometry. The mesh is not deleted, but rather removed
from the graphics window.
EllClick the SPECIFY DISPLAY ATTRIBUTES command button ...!!lJat the bottom of
the Global Control tool pad.
b) Select the Offradio button to the right ofMesh near the bottom ofthe form.
c) Click Apply and close the form.
2. Set boundary types for the entire gear pump.
ZONES - L> SPECIFY BOUNDARY TYPES -I
33
Specify Boundary Types
FlUENT5JG
Action:
..., Add
..., Delete
.. Modify
..., Delete all
Name Type
ill - - - .liI:I.?'II=
Jrout PRESSUREcas WALLpos WALLneg WALL t7
I?:l ll"":lo oCl.--...J I>
..J Show labels ..J Show colon
Name: Ilin
Type:
PRESSURE_INLET
Entity:
Groups ..J II]n ~ Editl
label Type
ill iiI!W"- j
tv
Kl I""" ,"?
Remove Edit I
Apply I Reset Oose I
3. Set continuum zone types:
ZONES -I->SPECIFY CONTINUUM TYPES 1-1-
This opens the specify continuum window:
34
::;llCClly Uliltmuum Iypcs
flUENT 516
Action:
v Add
v Dolata
.. Mo~ify
v 0019ta all
Nwne Typ.
IWi r.c
~
..J Show tab. ..J ShOW cob
Name: I;
Type:
FLUID .... 1
Entity:
Faces .... 1If.!I
Remove I Edit I
IWIY I Reset I 0GSe
Here, "f'was specified which was taken as fluid flowing in the face1.
Step 9: Exporting the Mesh and Saving the Session
1. Export a mesh file for the gear pump.
File ->Export ->Mesh...
This command sequence opens the Export Mesh File for providing that the File Type is
Structured FLUENT 5/6 Grid.
35
File Type: UNS I RAMPANT I FLUENT 5JG
File Name: ~_t_he_S_is_Im_S_h 1Browse...I
? Export 2-D(X-V) Mesh
Accept I aose I
a) Enter the File Name for the file to be exported (2 -D thesis.GRD).
b) Click Accept.
The file will be written to the working directory.
2. Saving the GAMBIT session and exiting GAMBIT.
File->Exit
GAMBIT will ask whether to save the current session before you exit.
I]J
Save the current session
(thesis)
before exit?
No I cancelI
Click Yes to save the current session and exit GAMBIT.
In summary, the IGES files from Solid Works source were imported to GAMBIT and
manipulated using the necessary steps for mesh generation in the fluid face, including
boundary types set up, and specification ofthe Fluent 5/6 solver. A final mesh file ready
for CFD processing was the outcome.
36
5.4 Dynamic Mesh Setting and Calculating Results in FLUENT
1. Make sure that the user-defined function (UDF) syntax file to define the rigid-body
motion ofgear is included in the same working directory. This function was already
named as "motion.c". This file will be needed to compile it within FLUENT.
2. Start the 2ddp version ofFLUENT either using DOS command prompt from the
working directory or simply going through the start menu.
Step 1: Grid
1. Read the grid file "thesis.msh".
File -tRead -tCase... browsing the right location ofmesh file in the working
directory.
Welcome to Fluent 6.1.22
Copyright 2003 Fluent Inc.
All Rights Reserued
Loading "C:\Fluent.Inc\fluent6.1.22\lib\fl_s117.dmp"
Done.
Loading "H:\/.cxlayout..
Done.
> Reading ..H:\Thesis1\Thesis.msh.....
2382 nodes.
200 mixed wall faces, zone 3.
198 mixed wall faces, zone 4.
198 mixed wall faces, zone 5.
6 mixed pressure-outlet faces, zone 6.
30 mixed pressure-inlet faces, zone 7.
5885 mixed interior faces, zone 9.
4134 triangular cells, zone 2.
Building...
grid,
materials,
interface,
domains,
zones,
default-interior
in
out
cas
pos
neg
f
shell conduction zones,
Done.
37
2. Check the grid.
Grid -+Check
While checking grids, just make sure that the cell volume does not detect negative
volumes, as FLUENT can not do a calculation for a negative cell volume. If a negative
volume is found, it would need to be re-meshed in order to make it non negative.
Checking the grid shows the following display in the FLUENT window screen:
Grid Check
1.729073e-01
8.153766e-01
1.926298e+03
-3.174464e+01. max (m)
-6.040756e+01. max (m)
Domain Extents:
x-coordinate: min (m)
y-coordinate: min (m)
Uolume statistics:
minimum uolume (m3):
maximum uolume (m3):
total uolume (m3):
Face area statistics:
minimum face area (m2): 5.114121e-01
maximum face area (m2): 1.63889ge+00
Checking number of nodes per cell.
Checking number of faces per cell.
Checking thread pointers.
Checking number of cells per face.
Checking face cells.
Checking bridge faces.
Checking right-handed cells.
Checking face handedness.
Checking element type consistency.
Checking boundary types:
Checking face pairs.
Checking periodic boundaries.
Checking node count.
Checking nosolue cell count.
Checking nosolue face count.
Checking face children.
Checking cell children.
Checking storage.
Done.
3. Scale the grid.
Grid -+Scale...
38
3.730625e+01
2.230755e+01
Scale Grid \,~
Scale Factors Units Conversion
Grid Was Created In lin 3XIO.0254
YIO.0254 Change Length Units I
Domain Extents
Xmin (in) 1-31.11111611
Ymin (in) 1-66.11I155 >
Xmax pn) 131.31625
Ymax pn) 122.31155
Scale I UnScale I Close I Help
(a) "in" was selected under Units Conversion from the drop-down list for Grid
Was Created In in (inches).
(b) Click Scale to scale the grid.
(c) Click Change Length Units as the working units for length now becomes
inches, and then click close.
n must be noted that the numbers shown in the Domain Extents reflect the size of
magnified model drawn in Solid Works. Therefore, the numbers should be further
scaled down by the geometric scale factor of39.18.
4. Display the grid [Figure 5.4].
Display -tGrid...
axis
clip-surf
exhaust-fan
fan
Outline , InteriorI
Ed To . lae Iype
r Nodes r- All
po Edges ("" Featurer
Faces ("" Outliner
Partitions
Shrink Fador Feature Angle
10 120
S=.,u::.:rf.::,:a:::ce:::...:..:N..=am:::.::..e..:..Pa..=tt::.:ce:,:,rn::--__ Surface TypesII
Match II
Display I Colors... I Close I Help I
39
Outlet --
/ Housing (Cast Iron)
:-Inlet
Meshing of Grid done in GAMBIT
Grid
Full Section of.gear Pump 20 Model by Yogen imported from GAMBIT
JuI22,2004
FLUENT 6.1 (2d. dp. segregated. lam)
Figure 5.4 Initial grid displayed by FLUENT
Step 2: Units
1. For convenience, define new units for pressure and mass flow.
Pressure, length, and temperature are specified in psi, inch, and Fahrenheit
respectively. The units for length were already changed while scaling the grid.
Define ~ Units...
Set Units '~;'lf '
SetAl. To...---------,
defaultI
si I
.:::.J british I
cgs I
torr.J
Iblft2
Factor 1689_.757
Offset I"
mass-per-volume---time
mass-transfer-rate
mole-specific-energy
mole-specific-entropy
molec-wt
moment
particles-cone
percentage
ower
Quantities
New... I List I Close I Help I
40
(a) Select pressure under Quantities, and psi under Units.
(b) Select temperature under Quantities, and click f under Units.
The Define Unit panel will be displayed as:
Set All Tor::---------
defaultI
si I
british I
cOs I..J Factor 1"?5555556
Offset1 .67
soot-formati0 n-constant-unit ....
soot-Iimiting-nucIei-rate
soot-linear-termination
soot-pre-exp0 nentiaI-constanl
specific-energy
specific-heat
stefan-b0 Itzmann-constant
surface-tension
surface-tension-
Quantities
New... I List I Close I Help I
Step 3: Models
1. Enable a 2D time-dependent calculation.
Define -tModels -tSolver...
Solver
(:' Segregated
(" Coupled
Formulation
(:' Implicit
(" Explicit
Flux Formulation?
l'
(:' 20 (" Steady
(" Axisymmetric (:' Unsteady
(" Axisymmetric Swirl r Use Frozen
(" 30
Velocity Formulation
(:' Absolute
(" Relative
UnsteadY Formulation
(" Explicit
(:' 1st-Order Implicit
(" 2nd-Order Implicit
Gradient Option
(:' Cell-Based
(" Node-Based
Porous Formulation
(:' Superficial Velocity
(" Physical Velocity
OK Cancel I Help I
41
(a) Under Space, click on 2D.
(b) Click on Unsteady under Time.
(c) Keep the default Unsteady Formulation option of1st-Order Implicit.
Keep in mind that dynamic mesh simulations work only with first order time
variant for tri/tetra mesh, re-meshing, and smoothing.
(d) Click on OK.
2. Turn on the Energy Equation for viscous heating properties for oil.
Define -.Models -.Energy...
Energy
IP' Energy Equation I
OK Cancel I Help I
3. Turn on the standard k- f turbulence model.
Define -.Models -.Viscous?..
CUtIBl!I!.;;abll:l?t!t!!I?III- IlI1??
Model Constants
TKE Prandtl Number
Inone
TOR Prandtl Number
11.44
C2-Epsilon
emu ~
10009
Cl-Epsilon
11.92 ~I
TKE Prandtl Number
11 ?
Turbulent Viscosity
I Inone
I
i Energy Prandtl Number
Inone
ModelI('
InYlscid I
i (' Laminar Ii('
SpalalhUlmaras (1 eqn) I!
Co' k-epsilon (2 eqn) i
I (' t-omega (2 eqn) II('
Reynolds Slress (5 eqn) I
t-epsilon Model
'I Co' Standard i(' RNG I
I (' Realizable i
N",ea,.,""-"W""a",II..!CTr",ealm"""",en!,-t ~ lJlO",,"Defirle"'?IlIl~n~ _I
Co' Standard Wall FunctionsI('
Non-Equllibrium Wall Functionsi('
Enhanced Wall Treatment
Options
42
(a) Check on k-epsilon as the Model, and use the default setting of Standard
under k-epsilon Model.
(c) Check on Viscous Heating under Options.
(d) Click on OK.
Step 4: Materials
A new material called cast iron was created for housing material. Engine oil and
steel were loaded from the FLUENT database for the fluid and solid material
properties used to represent the fluid face and the gears.
Define -.Materials
-------~--- --------- ---cast-iron (fe)
Name Material Type
l-ca-s-t---i-ro-n-------Isolid
Chemical Formula Solid MaterialsI-fe--------
Order MaterialsOJ
r. Name
r Chemical Formula
Database..? I
Mixture
Inone
Properties
0:1 EdiLIDensity (kg/m3) Iconstant,...---------==-==
17106.9
0:1 EdiLICp UJkg-k) Iconstantr----------==-==
1545 ?77
0:1 Edit... IThermal Conductivity (wlm-kJ Iconstant
-~------==-==132.427
ChangelCreate I Delete Close Help
The physical and thermal properties ofcast iron were taken from ALGOR database.
43
(a) In the Material Type field, select solid fonn the drop down list.
(b) In the Name field, enter cast iron and type fe in Chemical Formula field.
(c) Specify 7160.9 for the Density.
(d) Specify 545.77 for Cpo
(e) Click Change/Create.
(1) Click No for not to overwrite steel on aluminum.
(J) Change/Create mixture and Overwrite steel?
I Yes I No
Two other materials engine oil as fluid and steel as solid were uploaded from the
FLUENT Database.
Step 5: Operating Conditions
Set the operating pressure to 0 psi.
Define --.Operating Conditions...
Operating Conditions ~"" .
Operating Pressure [psi)
10
Reference Pressure location
X [in) 10
Y [in) 10
Pressure Gravity
Ir Gravity I
OK I cancell Help I
44
Step 6: Boundary Conditions
Dynamic mesh motion and all related parameters are specified using the items in the
Define/Dynamic Mesh submenu, not through the Boundary Conditions panel. Here,
Pressure inlet at "in" zone and pressure outlet at "out" zone were set up as well as "steel"
was chosen as the material for the driving and driven gears. "Cast iron" was picked up as
the material for the housing and "engine oil" for the fluid meshed face. Inlet zone
temperature was assumed as 77? F (25?C) and back flow total temperature from the outlet
zone was assumed as 113? F (45? C). Turbulence intensity (%) and turbulent viscosity
ratio for inlet zone were assumed 2% and 2 respectively. For the outlet zone, backflow
turbulence intensity (%) and backflow turbulent viscosity ratio were taken as 10 % and
10 respectively. The pressure inlet and pressure outlet were used 30 psi and 2000 to 3500
psi respectively.
Define -..Boundary Conditions...
Set the conditions for the pressure inlet ( inlet) as shown in the following figure.
Pressure Inlet .. "~ '!}t ?
Zone Name
liIi1
Gauge Total Pressure (psi) 1 I :::J
SupersoniC/lnitial Gauge Pressure (psi) 1r-3-0------Ir-c-on-s-ta-n-t-----:::J
Total Temperature (f) In Ir-c-on-s-t-an-t-----:::J
Direction Specification MethodI Vector :::J
X-Component of Flow Direction 1-1 Ir-~-o-ns-t-a-n-t-----:::J
V-Component of Flow Direction 10 Iconstant 3
Turbulence Specification Method I and Viscosity Ratio :::J
Turbulence Intensity l"J 12
Turbulent Viscosity Ratio 12
OK I Cancel I Help I
2. Click OK.
45
3. Set the conditions for the exit boundary (outlet) as shown in the following figure.
Zone Name
Gauge Pressure (psi) 1 I :3
Backflow Total Temperature (f) 1113 Il""'c-o-ns-t-a-nt-----:3
Backflow Direction Specification Method INormal to Boundary ::::I
Turbulence Specification Method Il""'ln-t-e-n-si-ty-a-n-d-V-iS-C-O-S-ity-R-a-t-io------::::I
Backflow Turbulence Intensity l")11?
Backflow Turbulent Viscosity Ratio 11o
OK I Cancel I Help I
4. Click OK.
5. Set the fluid material "engine oil" for the grid face as shown below:
Zone Name
1[1
Material Name Iengine-oil
r Source Terms
r Fixed Values
r Laminar Zone
r Porous Zone
::J Edit... I
Rotation-Axis On in
X (in) 10
Y (in) 10
Motion Type I ::J ....
OK I Cancel I Help I
6. Get engine oil selecting from the drop down list in Material Name. Click OK.
46
Zone Name
Adjacent Cell ZoneIf
Thermal IDPM IMomentum ISpecies IRadiation IUDS
Thermal Conditions
I
Heat Aux(wIm2) 10 I
Wall Thickness pn) I~o------ ------
Heat Generation Rate (w/m3) 10
c: Heat Flux
r Temperaturer
Convection
r Radiation
r Mixed
Material Name
Isteel
OK I Cancel I Help I
7. Choose steel as the material for driven gear "pos" as shown above and similarly
for driving gear "neg" too. Choose cast iron as the material for housing "cas" in
the similar way. Click OK for every three wall windows.
Step 7: Mesh Motion
1. Read in and compile the user-defined function (UDF).
Define ----+ User-Defined ----+ Functions ----+ Compiled...
(ompded UOfs i~ ~lW
I-S;;';;FU;~---~~--H;;ie;A~~---~:!J.;J1
I II !I~~ I~~
I
L1bra'Y Name IlibUdf Build I
~ Cancell~
(a) click Add... under Source Files,
A Select File panel will show up. ( Appendix 1)
(b) Choose the source code motion.c in the Select File panel, and click on OK.
(c) Click on Build in the Compiled UDFs panel,
47
The user-defined function was already been defined. Compiling the UDF in
FLUENT creates a library with the default name "libudf' in the working
directory.
1 fil~(s) copi~d.
(syst~1lI "1lI0U~ us~r_nt.udf libudf\ntx86\2ddp")0
(syst~1lI "copy C:\Flu~nt.Inc\flu~nt6.1.22\src\llIak~fil~_nt.udf libudf\ntx86\2ddp\llIak~fil~")o
(chdir "libudf") 0
(chdir "ntx86\2ddp")()
llIotion .c
UG~n~rating udf_nal1l~s.c b~caus~ of llIak~fil~ llIotion.obj
udf nalll~s.c
ULInking libudf.dll b~caus~ of llIak~fil~ us~r_nt.udf udf_nalll~s.obj llIotion.obj
Microsoft (R) Incr~llI~ntal Link~r U~rsion 6.00.8447
Copyright (C) Microsoft Corp 1992-1998. All rights r~s~ru~d.
Cr~ating library libudf.lib and obj~ct libudf.~xp
Don~.
1 fil~(s) copi~d.
(d) Click on OK in the dialog box which will show up as shown below. It is just a
warning to remove any other "libudf' directory existing in the working
directory.
Information ' /"ci!;"
Make sure that UOF source files are in the directory
that contains your case and data files. If you have an
existing Iibudf directory. please remove this directory
to ensure that the latest files are used.
OK I
(e) Click on Load to upload the user-defined function library for the iteration.
Opening library ..libudf.....
Library "libudf\ntx86\2ddp\libudf.dU" opened
clock wise
anticlock wise
Done.
48
2. Activate dynamic mesh motion and specify the associated parameters.
Define -+Dynamic Mesh -+Parameters...
Dynamic Mesh ~: t,!tjfi
'e>'
Model
P' Dynamic Meshr
In-Cylinder
Mesh Methods
P' Smoothingr
Layering
P' Remeshing
Smoothing ILayering I Remeshing Iin-Cylinder I
Spring Constant factor 10. 1
Boundary Node Relaxation 11"'"0-.3----
Convergence Tolerance 10. 001
Number of Iterations Is 0 :3
OK I Cancel I Help I
(a) Select Dynamic Mesh under Model.
(b) Under Mesh Methods, select Smoothing and Re-meshing.
FLUENT automatically re-meshes and smoothes the existing mesh zones for use of the
different dynamic mesh methods where applicable.
(c) Setting up the parameters under Smoothing as follows:
i. Specifying 1 for the Spring Constant Factor.
ii. Specifying 0.3 for the Boundary Node Relaxation.
iii. Keeping up the default specification of0.001 for the Convergence Tolerance.
iv. Specifying 50 for the Number ofIterations.
(d) Setting up the parameters under Re-meshing as follows:
49
Model
P' Dynamic Meshr
In-Cylinder
Mesh Methods
P' Smoothingr
layering
P' Remeshing
Smoothing Ilayering Remeshing Iin-CylinderI
Options
r Sizing Function
P' Must Improve Skewness
Minimum Cell Volume [m3) 11 .1e-15
Maximum Cell Volume [m3) 11 . 2e-08
Maximum Cell Skewness 10 . 9
Size Remesh Interval 11"'"1---- ~
OK I Cancel I Help I
i. Under Options, be sure that the Must Improve Skewness option is selected.
ii. Specify 1.le-15 m3 for the Minimum Cell Volume.
iii. Specify 1.2e-08 m3 for the Maximum Cell Volume.
iv. Keeping up the default value of0.9 for the Maximum Cell Skewness.
v. Specify 1 for the Size Re-mesh Interval.
Any cells exceeding these limits will be re-meshed and smoothed automatically.
(e) Click on OK.
3. Specify the motion ofthe gears and the housing.
The motion of two gears and the stationary wall "housing" were specified by
usingUDFs.
Define ~ Dynamic Mesh ~ Zones...
(a) Specify the motion ofthe stationary housing named as 'cas'.
50
Dynamic Zones ~' ill
Zone Names
Icas
Type
r. Stationary
r Rigid Bodyr
Deforming
r User-Defined
Dynamic Zones0:]
Motion Attributes IGeometry Definition Meshing Options I
Adjacent Zone If Cell Height (in) 10? 005
Adjacent Zone Ir---------- Cell Height (in) 10
Create I Draw I Delete I Update I Close I Help
i. Selecting housing 'cas' in the Zone Names drop-down list.
ii. Selecting Stationary under Type.
iii. Click the Meshing Options tab.
vi. Specify 0.005 in for Cell Height.
vii. Click on Create.
(b) Specify the rigid body motion ofthe driving gear
i. Select the driving gear named as "pos" in the Zone Names drop-down list,
ii. Under Type, keep the default selection ofRigid Body.
iii. Under Motion Attributes, select anticlock_wise in the Motion UDF/Profile
drop-down list.
iv. Keep the default values of (0, 0) m for e.G. Location, and 0 for C.G.
Orientation. The position of the CG will be updated automatically by
FLUENT based on the input ofmotion.
v. Click on the Meshing Options tab.
vi. Specifying 0.005 in for Cell Height.
51
vii. Click Create.
Zone Names
'pos
Type
(' Stationary
r. Rigid Body
(' Deforming
(' User-Defined
Dynamic Zones:::I
cas
I I
Motion Attributes IGeometry Definition IMeshing Options I
Motion UDF/Profile
'anticlock_wise
C.G. location C.G. Orientation
'-X-(-in-)1-0--,------,ITheto~Z IdegJ I"
V (in) 10
Create I Draw I Delete I Update I Close I Help I
(c) Specify the motion ofthe driven gear
All of the steps were taken in the similar way as of the driving gear. There was a
change in CG location; the CG location ofthe driven gear "neg" was taken as (0,  
38.4 in.). Since the geometry is magnified in Solid Works as stated on page 39, the
CG location ofthe driven gear ofthe model used in this research is (0, -38.4 in.). In
fact, the CG location ofthe driven gear in the actual physical model is (0, -0.98 in.).
All other settings were unchanged from that ofthe driving gear "pos". The Dynamic
Zones panel for the driven gear "neg" is as follows:
52
Dynamic 20nes , }!Jilll, ,
Zone Names
Ineg
Type
r Stationaryc:
Rigid Bodyr
Deformingr
User-Defined
Dynamic Zones4:]
cas
pos
Motion Attributes IGeometry Definition IMeshing Options I
Motion UDFtprofileI
clock_wise
C.G. location C.G. Orientation
,.:..x:..=.(.:....:in~) 1---0-----------,IThela_Z [degllo
V (in) 1-38 ?4
Create I Draw I Delete I Update I Close I Help I
(d) Preview ofMesh Motion
Solve -tMesh Motion...
Time Display Options
Current Mesh Time (s) 10 P' Display Gridr
Save Hardcopy
Time Step Size (s) 10.0001 Display Frequencyr ~
Number of Time Steps Is ~
PreviewI Close I Help I
(i) Type 0.0001 in Time Step Size and 5 in the Number ofTime Steps.
(ii) Check Display Grid under Display Options to see the mesh motion in grid.
53
(iii)Click on Preview to view the mesh motion in gear pump model with rotational
motions in both gears. The graphics window of mesh motion in the grid was
displayed with the following message in the FLUENT window screen. Also the
stretching, skewing, and collapsing of cells were seen in grid graphics (refer to
Figure 5.5)
Updating mesh to time 2.63500e-01 (step
This is Anti Clockwise Gear
CG_Omega for anticlock wise: 0, 0, 210
02635)
CG Position for anticlock_wise: 0, 0, 1.32136e-306
CG Orientation for anticlock_wise: 0, 0, 1.32136e-306
This is Clockwise Gear
CG Position for clock_wise: 0, -0.97536, 1.32136e-306
CG Orientation for clock_wise: 0, 0, 1.32136e-306
Mesh Statistics:
Min Uolume 1.78291e-05
Max Uolume 1.04916e-03
Max Cell Skew = 9.23842e-01 (cell zone 2) Done.
Gear Pump Model by Yogen (Mesh Motion Preview)
Ju130,2004
FLUENT 6.1 (2d, dp. segregated, dynamesh, ske, unsteady)
Figure 5.5 Mesh Motion Preview
54
Step 9: Solution
1. Set the solution parameters.
Solve - Controls- Solution.?.
Equ2ltions
Flow
Turbulence
Ener
..!I.=J Under-Relaxation Factors
Pressure I".3
Density1
Body Forces 11"""1--
Momentum I"-
Discretization
Autosave Case/'Data ' "!'J'
Pressure IStandard :::J ?
Pressure-Velocity CouplingIS-IM-P-LE-------:::J
MomentumIFirst Order Up.wind :::J
Turbulence Kinetic EnergyI Order Upwind :::J ?
OK I Default I Cancel I Help I
(a) Keep all default discretization methods and values for under-relaxation factors.
(b) Click on OK.
2. Request that case and data files are automatically saved every 50 time steps.
File -+ Write -+ Autosave...
lEI
Autosave Case File Frequency 11"""5-0-- :3
Autosave Data File Frequency 15 0 :3
Filename
1~:\The5i51\The5i5
OK Cancel I Help I
(a) Set both Autosave Case File Frequency & Autosave Data File Frequency to 50.
(b) In the Filename field, enter thesis.
(c) Click OK.
55
3. Enable the plotting ofresiduals during the calculation.
Solve ---+ Monitors ---+ ResiduaI...
Residual Monitors ~i'
PI tf
P' Print Iterations 11000 it Window ro- it
P' Plot
Iterations 11 000 itNormalization
Ir Normalize P' Scale I Axes... ICurves... I
Check Convergence .:.
!Residual Monitor Convergence Criterion
Icontinuity P' P' 11e-06
'x-uelocity P' P' 1 - 06 -
~-uelocity P' P'
'
1e
-
06
energy P' P' 1 - 06 r
Ik P' P' 11e- 06 ?-
o .
OK Plot I Renorm I Cancel I Help I
4. Initialize the solution.
Initializing the flow field at this point will display contours and vectors that can be used
to define animations.
Solve ---+ Initialize ---+ Initialize...
(a) In Solution Initialization panel, select "in" from the drop down lists of
Compute from menu. Then, FLUENT will automatically set up the following
parameters from the inlet "in" boundary conditions as shown below:
(i) Gauge Pressure to 30 psi.
(ii) X Velocity to -15.25349 mls
(iii) Y Velocity to 0 mls.
(iii) Turbulence Kinetic Energy to 0.1396014.
(iv) Turbulence Dissipation Rate to 16.8147.
(v) Click Init, Apply and Close.
56
Solution Initialization ,
"
Compute From
Initial Values
Reference Frame0:1 (:
Relative to Cell Zoner
Absolute
...
Gauge Pressure [psi) 1 ?
X Velocity [mls) 1-15 _25349
Y Velocity [mls) 1
Turbulence Kinetic Energy [m2/s2) 10.1396014
lnit I ResetI Apply I Close I Help
....
5. Create animation sequences for the static pressure contour plots and velocity vectors
plots in the gear pump.
Solution animation features ofFLUENT were used to save contour plots ofthe particular
animation sequence in every 5 time steps. After completing the calculation, solution
animation playback feature could be used to view the animated sequence plots over time.
Basically, there are five types ofanimation sequence displays over the time; they are grid,
contours, vectors, XY plot etc. For this problem, grid animation, velocity and pressure
contours, velocity and pressure direction vectors were picked for animation sequences
over 5 time steps.
Solve -+Animate -+ Define...
Solution AmnlatlOn ~ J"
Animation Sequences r ~
Active Name Every When
r Ir-gr"""'i-d---r :~H .... -Ste-P-::oJ Define I
r Ipressure r ~ ITime Step :::I Define I
r IUelOCity r ~ 'Time Step :::I Define I
r Ipress_dir r ~ ITime Step :::I Define I
r Iuel_dir r ~ ITime Step :::I Define I
57
(a) Increase the number ofAnimation Sequences to 5.
(b) Under Name, enter grid for the first animation, and pressure for the second one,
velocity for the third, pressure_dir and vel_dir for the latter two.
(c) Under Every, increase the number to 5 for all five sequences.
(d) In the When drop-down list, select Time Step.
(e) Define the animation sequence for the second animation sequence pressure.
i. Click Define... on the line for pressure to set the parameters for the sequence.
The Animation Sequence panel will open as:
Animation Sequence ,1 ''li~I:;
Sequence Parameters Display Type
Storage Type Name r Grid
r In ....emory Ipressure (: Contours
(: ....etafile r Vectors
r PP.... lmage Window 11 3~ r X'( Plotr ....onitor
Storage Directory Monitor Type
I IReSidualS 0:1
Properties... I
OK I Cancel I Help I
ii. Below the Storage Type, keep the default selection ofMetafile.
iii. Increase the Window number to 1 and click Set.
Graphics window number 1 will be displayed.
iv. Under the Display Type, select Contours.
The Contours panel will be displayed.
58
o tions
po Filled
po Node Values
po Global Range
po Auto Ranger
Clip to Ranger
Draw Profilesr
Draw Grid
Contours Of
IPressure... :::I
IStatic Pressure :::I
Min (psi) Max [psi}
129.99999 13500
Surfaces ..s.I...:J
?Levels Setup -
default-interior[203[13
in
neg -
Surface Name Pattern out .::J
1 Surface Types , ..s.I.=Jaxis =J
Match I clip-surf
exhaust-fan
fan .::J
Display I Compute I Close I Help
v. Under Options, tum on Filled.
vi. In the Contours Ofdrop-down lists, select Pressure... and Static Pressure.
vii. Click Display (refer Figure 5.6)
C,: fjt ;?'Jr. : t ;;1'j1'1: l'r.:.-'H _ IF .-11 ITlr".=O 1.1001.1?. +00 I JIJJ ":4, .:.(11)4-
G, -.If l'urHt-:, D..19r,llt''':':''jd' nDDofT r=, 11';'d.,Jot:' :'_3r'_'3-J1' _~ ,J','r,:.r,,,.:'t,,:l '_ 'Jrl.':1"."J 3',11
Figure 5.6 Static Pressure Contours at t = 0 s
59
viii. Click OK in the Animation Sequence panel.
The Animation Sequence panel will close, and the checkbox in the Active column next
to pressure in the Solution Animation panel will become selected.
ix. Click OK in the Solution Animation panel.
(f) Define the animation sequence for the velocity vectors.
i. Click Define.?. on the line for vel_dir to set the parameters for the sequence.
The Animation Sequence panel will open. It is same as pressure contour panel.
ii. Under Storage Type, keep the default selection ofMetafile.
iii. Increase the Window number to 2 and click Set.
Graphics window number 2 will open.
iv. Under Display Type, select Vectors.
v. Type lOin the Scale panel to see the velocity vectors distinctive.
The Vectors panel will open and it will show Min(m/s) and Max (m/s) 15.25349
when clicking on Display.
Options
r Node Values
17 Global Range
17 Auto Ranger
Clip to Range
17 Auto Scaler
Draw Grid
Style larrow
Scale 1
Skip 1'--0-3
Vector Options I
Custom Vectors I
Surface Name Pattern
Match
Vectors Of
IVelocity .:1
Color By
cas
default-interior
in
neg
out
pos
Surface Types
axis
clip-surf
exhaust-fan
fan
Display I Compute I Close I Help
60
v. Click on Display in the Vectors panel (refer Figure 5.7)
~.?.I .11:" '.' ""t"1 C _.I_f .j:tll '.' 1_ rt'.' }(-~qrlrt'Jj Ir",' I ITlr" _1111111 II, +11111 .r'JI .... J. .... 11114
C Jrl'JI,,"F Ii. 1._rll"?.J.?,_.~,rl? nor::r,fTt",11 .... J dp, - =If 3,t d, j"r.Jr" __ l,, -~ ,IH,,"'_':!'.'I
Figure 5.7 Velocity Vectors at t = 0 s
vi. Click OK in the Animation Sequence panel.
The Animation Sequence panel will be closed, and the checkbox in the Active column
next to vel_dir in the Solution Animation panel will become selected.
vii. Click OK in the Solution Animation panel.
6. Set the time step parameters for the calculation.
Solve -+ Iterate...
(a) Set the Time Step Size to 0.0001 s.
(b) Increase the Max Iterations per Time Step to 200.
(c) Click Apply.
7. Save the initial case and data files (thesis.cas and thesis.dat).
File -+ Write -+ Case & Data...
8. Request 100 time steps. For better results at total time t = 1 s, 10,000 time steps were
set up.
Solve -+Iterate.?.
61
Time
Time Step Size (s) 10.0001
Number of Time Steps 1 ~
Time Ste in Method
r. Fixedr
Adaptive
Options
Iteration
Max Iterations per Time Step 1 ~
Reporting Interval 1 ~
UDF Profile Update Interval 1 ~
Iterate I Apply I Close I Help
Max Iterations per time step, reporting interval & UDF profile update interval can be
changed. The following graphics window ofiteration (refer to Figure 5.8) was after time t
=1.15 sec for the case ofgear pump with N = 2000 rpm and Pin = 30 psi, Pout = 3500 psi.
Residuals
-continuity
-x-velocity
.- y-velocity
-energy
Ik
-ensilon
1e+00
1e-01
1e-02
1e-03
1e-04
1e-05
1e-07
1e-08
1e-09
1e-10 +--~---~~-----~---~~
9900OCB90500091 000091500092000092500093000093500094000094500095000
Iterations
Scaled Residuals (Time=1.1500e+00)
Gear Pump Design by Yogen
Ju131.2004
FLUENT 6.1 (2d. dp. segregated. dynamesh. ske. unsteady)
Fig 5.8 Iterations until time t = 1.15 sec for the case: N = 2000 rpm & Pout = 3500 psi
62
Step 10: Postprocessing
1. Inspect the solution at the final time step.
(a) Observe the contours ofstatic pressure in the gear pump (Figure 5.9).
I. :f:::::2718+03
16303... 03
1088+03
5418+02
-1758+00
-5448+02
~10ge+03
-1638+03
-2178+03
-2718+03
-3268+03
-3808+03
-4348+03
-4888+03
-5428+03
-5.978+03
-6518+03
Contours of Static Pressure (psi) <Time-4.496Se+OO) Ju125. 2004
Gear Pump Design by Yag." FLUENT 6.1 (2d, dp. segregated. dynamesh. ske, unsteady)
Fig 5.9 Static Pressure Contours at t = 4.4965 s
(b) Observe the velocity vectors in the gear pump (Figure 5.10).
2. Optionally, inspect the solution at different intermediate time steps.
(a) Read in the corresponding case and data files ( thesis.cas and thesis.dat).
File -4Read -4Case & Data...
(b) Display the desired contours and vectors.
I2.888+022738+022598+022.448+022308+02
2168+02
2018+02
1878+02
1.738+02
1588+02
1448+02
1298+02
1.158+02
1.0103+02
8638+01
7198+01
5.75e+01
4,318+01
2.888+01
1448+01
74Se-03
Velocity Vectors Colored By Velocity Magnitude (m/s) (Time-4.4965e+OO) Jul 25. 2004
Gear Pump Design by Yogen FLUENT 6.1 (2d, dp, segregated, dynamesh, ske, unsteady)
Fig 5.10 Velocity Vectors at time t = 4.4965 s
63
3. Play back the animation ofthe pressure contours. A plot at time t = 4.4965 s is shown
in Figure 5.11.
Solve -tAnimate -tPlayback...
Fig 5.11 Exact Graphic ofVelocity Vectors shown at t = 4.4965 s
(a) In the Sequences list, select pressure.
The playback control buttons will become active.
(b) Set the slider bar above Replay Speed about halfway between Slow and Fast.
(c) Keep the default settings in the rest ofthe panel and click the play button (the
second from the right in the group ofbuttons under Playback).
64
velocity
press_vir
vel dir
~~~r;-~~~ .!.I ------=---W
Slow Replay Speed Fast Delete IDelete Alii
Write/Record FormatIAnimation Frames 0:1 __H_a_r_d_c_op_y_O_p_ti_o_ns_"_".---..I
Write I Read... I Close I Help I
4. Play back the animation ofthe velocity vectors"
Solve -+Animate -+ Playback...
(a) In the Sequences list, select vel_dir.
(b) Keep the default settings in the rest ofthe panel and click the play button.
Results ofgraphs and plots are included in chapter 6.
65
CHAPTER
6
RESULTS
AND
INTERPRETATIONS
6.1
ResultsforVariousRotationalSpeed,N
I
85494
81219
76944
7267068395
64.120
59846
55571
51296
47.022
42747
38472
34198
29923
25.648
213731709912824
8549
4,275
0,000
I
565473547493823834029
2918,676
2003,324
1087971
172618
-742735
-1858088
-2573.441
-3488.794
-4404,147-5319,500
-6234853
-7150,206
-8065559
-8980911-9896265-10811617-11726970
-12642,323
Contours
of
Wall
Sheat
Stress
(psi)
(Time=5.5900e-02)Ju12S.2004
Gear
Pump
Design
by
Vogen
FLUENT
6.1
(2d.
dp.
segregated,
dynamesh.
ske.
unsteady)
Contours
of
Static
Pressure
(psi)
(Time=5.5900e-02)
Jul
28.
2004
Gear
Pump
Design
by
YogenFLUENT
6.1
(2d.
dp.
segregated.
dynames-h.
ske,
unsteady)
Contours
of
Velocity
Magnitude
(mk:)
(Time=5.5900e-02)Jul2S.2004Gear
Pump
Design
by
YogenFLUENT
6.1
(2d.
dp.
segregated.
clynamesh.
ske.
unsteady)
15800032
4156188
3060,292
,,,,J
1964395
868.499
-227,397
-1323294
-2419,190
-3515086
-46D.982
-5705879
-6802.775-1898.671
-/\\--'j
-8994.567-10090.464-11186,360-12282.257-13378.153
~
-~.
..~.~
.~
Velocity
Vectors
Colored
By
Static
Pressure
(psi)
(Time=5.5900e-02)Ju128.2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.
dynamesh.
ske.
unsteady)
I
384.192
364982345773326563
307,354288.144268.934
249725230515211306
192096
172.886
153677134467
115258
96048
76838
57629
38.419
19210
0000
Figure6.1FlowContoursforrotationalspeed
of
gears=3000rpm;
Pout
=3500psi,
Pin
=30psi
66
f"
23976
227,14
21452
20190
1892817666
164,05
15143
13881
126,19
113.57
10095
8833
7571
6309
50.48
3786
2524
1262
0.00
~
-~
Idriver/opengliWin+'NOlinnerltextlright
ContoursofVelocityMagnitude
(m/s)
(Time=2.0400e-02)Ju128.2004Gear
pum~~~~~_i~:_~,~~~~_n
FLUENT
6.1
(2d.dp.segregated.dynamesh.
ske.
unsteady)
210111
174371
1386.31
102890
671.50
314.09
-4331 -40071
-75812
-111552
"147293
-1830.33
-218773
-254514-290254
-325995
-3617.35
-397476
-4332,16
-468956
-5046.97
I
~
-~.
Idriver/opengllwin+wOlinnerltextlright
Contours
of
StaticPressure(psi)(Time=2.0400e-02)Ju128.2004
Ge:~~_u_~p
~esign
by
YogenFLUENT
6.1
(2~~~~
segregated.dynamesh.
ske.
unsteady)
Figure6.2Flow
Contours
forrotationalspeed
of
gears
=
2000
rpm;
Pout
=
1000psi,
Pin
=
30psi
I,m
..
2837.21
238656
1935.91
148527
1034.62
58397
13332
-317,33
-76798
-121863-166928-211992-257057-302122-347187-392252-437317-482382
-5274.47-572511
I
27414
260.43246,72
23302
219,31
20560
19189
178,19
1644815077
13707
1233610965
9595
8224
6853
5483
4112
2741
1371
0.00
Contours
of
StaticPressure(psi)(Time=l.1500e+00)Jul28.2004GearPumpDesignbyYoegnFLUENT
6.1
(2d,dp.segregated.dynamesh.
ske,
unsteady)
-------_
..
_--~
_._-----
Contours
of
VelocityMegnitude(mls)(Time=1.1500e+OO)Jul28.2004GearPumpDesignbyYoegnFLUENT6.1(2d,dp,segregated.dynamesh.ske.
unste8dy~
Figure6.3Flow
Contours
forrotationalspeed
of
gears
=
2000
rpm;
Pout
=
2500psi,
Pin
=
30psi
67
I
382870334133
2853.95
236657
187919139182
90444
417.06
?70,31-557.69
-104507
-153245
-201982-250720-299458
?348196
-396933
-445671
-494409
-5431.47
-591884
I::::
25575
24154
22733
21312
19891
184
71
170.50
15629
14208
127.87
11367
9946
8525
7104
5683
4262
2842
1421
000
Contours
of
StaticPressure(psi)(Time=1.1500e+OO)
Jul
28.
2004GearPumpDesignbyYogen
flUENT
6.1
(2d.dp.segregated.
c1ynamesh.
ske.
unsteady)Contours
of
VelocityMagnitude
(mIs)
(Time=1
.1500e+OO)
Jul
28,
2004GearPumpDesign
by
YogenFLUENT
6.1
(2d,dp.segregated.dynamesh.ske.unsteady)
---------~_
..
~-_._~.--
Figure
6.4Flow
Contours
for
rotational
speed
of
gears
=
2000
rpm;
Pout
=
3000psi,
Pin
=
30psi
Contours
of
StaticPressure(psi)(Time=1.1500e+00)
Jul
28.
2004GearPumpDesignbyYogan
FlUENT
6.1
(2d,dp.segregated.dynamesh.ske.unsteady)
I
Contours
of
VelocityMagnitude(m/s)(Time=1.1500e+OO)Ju128.2004GearPumpDesign
by
YogenFLUENT
6.1
(2d.dp.segregated,dynamesh,ske.unsteady)
287,68
27329
25891244,53
23014
21576
20137
186,99172,61
15822
143,84
12946
11507
10069
8630
71,925754 
4315
2877
1438
0.00
I
4239,58
376433328908
281384
233859
1863,34
1388,10
91265
437.60
-37.64
-512.89
-988.14
-146338-193663
-2413.88
-288912
-336437-383962-431486
-479011-5265,36
I
Figure
6.5Flow
Contours
for
rotational
speed
of
gears
=
2000
rpm;
Pout
=
3500psi,
Pin
=
30psi
68
I
481960
417218
352475
287733
222991
1582.48
9350628764
-35979
-100721
-165464-230206
-2949.48
-3596.91
-424433
-4891.75
-553918-618660
-683402
-748145-812887
I'?"
467.94
443.31
418.69
3940636943 34480
32017
29554
270.91
24629 22166
1970317240 14777
123.14
9851
7389
49.2624.63
000
Contours
of
StaticPressure(psi)(Time=2.7900e-02)
Jut
28.
2004
GearPumpDesignbyYogenFLUENT
6.1
(2d.dp,segregated.dynamesh,ske.unsteady)
ContoursofVelocityMagnitude
(m/s)
(Time=2.7900e-02)
Jut
28,
2004
GearPumpDesign
by
rogen
FlUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
Figure6.6Flow
Contours
forrotationalspeed
of
gears
=
2000
rpm;
Pout
=
3500psi,
Pin
=
30psi(Modifiedcasing)
69
6.2ComparativeGraphicsforVariousFlowParameters
I
o~
fDUI
-"
25tJtJ
psi
-1669-2120
-2571
-3021-3472-3923-4373-4824-5274-5725
I
382933412654
2367
18791392
904
417-70-558-1045-1532-2020
-2507
-2995-3482-3969
-4457
-4944-5431-5919
Pout
0=
3000
ContoursofStaticPressure(psi)(Time=1.1500e+00)Ju129.2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
Contours
of
Static
Pressure
(psi)
(Time=1.1500e+OO)
Jul
29.2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.
dynamesh.
ske.
unsteady)
482041723525
2877
22301582935286-360-1007-1655-2302-2949-3597-4244-4892-5539-6187-6834-7481-8129
I
I""
37643269
2814
233916631368913
436
-38-513-988
Poul"
3500
psi
-1463-1939-2414-2889-3364-3840-4315-4790-5265
Contours
of
Static
Pressure(psi)(Time=1.1500e+OO)
Jul
29.2004Gear
Pump
Design
by
Yogan
FLUENT
6.1
(2d.
dp.
segregated,
dynamesh.
ske.
unsteady)
Contours
of
StaticPressure(psi)(Time=2.7900e-02)
Gear
Pump
Design
by
Yogen
Ju129.2004FLUENT
6.1
(2d,
dp.
segregated.dynamesh.
ske.
unsteady)
Figure6.7StaticPressureContours*forgearsrotatingat2000rpm(atTimet
=
1.15s)
70
1'""
I
""
4734
5294
4485
5016
4236
4737
3987
4458
3738
4180
348839013239
3622
29903344
2741
3065
24922786
Pout?
?!iB8
psi
Pout-lODO
2243
25081993222917441950
14951672
1246
1393
997
1115
748
836
498
557249
279
0
Contours
of
DynamicPressure(psi)(Time=1.1500e+OO)
Jul
29.
2004GearPumpDesignbyVogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)Contours
of
DynamicPressure(psi)(Time=1.1500e+OO)Jul29.2004GearPumpDesignbyVogenFLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady;
7076
6722
6368
6015
56615307
4953
4600
4246
3892
3538318428312477
2123
1769
1415
1062
708354
Contours
of
DynamicPressure(psi)(Time=2.7900e-02)
Ju129.
20~
GearPumpDesignbyVogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
I
I
""
47094395
40813767
3453
313928252511
2197
1883
15701256
942
628
3140
Contours
of
DynamicPressure(psi)(Time=1.1500e+OO)Jul
29.
2004GearPumpDesignbyVogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
Figure6.8DynamicPressureContours*forgearsrotating
at
2000
rpm
(at
Timet
=
1.15s)
71
1
""
3726340230782754
2430
2106178214571133809
485
161
-163-487-811-1135
?1460
-1784-2108
1=
4733436840043639327529112546218218171453
Pout
=
3000
1088724360
-5
-369-734-1098-1463-1827
ContoursofTotolPressure(psi)(Time=1.1500e+00)
Jul
29.
2004
GearPumpDesign
by
YoganFLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
Contours
of
TotalPressure(psi)(Time=1.1500e+OO)
GearPumpDesign
by
Yogen
Ju129.2004FLUENT
6.1
(2d,
dp.
segregated,dynamesh.
ske.
unsteady)
I'?'
7177666261465630
5114
4599
4083
35673051253620201504988
473
-43-559-1075-1590-2106-2622
1
~"::
.,60095567512446824239
3797
335529122470202715851143700258-185-627-1070-1512-1954
Contours
ofT
01,1
Pressure(psi)
(Time=1.1500e+OO)
Jul
29.
2004
GearPumpDesign
by
YoganFLUENT
6.1
(2d.dp.segregated.dynamesh,ske.unsteady)
ContoursofTotalPress.re(psi)(Time=2.7900e-02)Ju129.2004FLUENT
6.1
(2d,
dp,
segregated.dyn,mesh.ske.unsteady)
Figure6.9TotalPressureContours*forgearsrotating
at
2000
rpm
(at
Timet
=
1.15
s)
72
1
~~
1
~~
247256233242219227206213192199178185164170
151
156137142
Pout
".?5~1J
psi
Pout~3000
1231281101149699828569
71
5557
41
43
2728141400
ContoursofVelocity
Magn~ude
(m/s)(Time=1.1500e+00)Ju129.2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)ContoursofVelocity
Magn~ude
(m/s)(Time=1.1500e+00)
Jul
29.
2004
Gear
Pump
Design
by
YogenFLUENT
6.1
(2d.
dp.
segregated,
dynamesh,
ske,
unsteady)
1
'"
I"
273
468
259
443
245
419
230394216369
201
345187320173296158
271
144246129
Pout~3S00psi
22211519710117286148721235899
43
7429
49
142500
Contours
of
Velocity
Magn~ude
(m/s)(Time=1.1500e+00)Ju129.2004GearPumpDesign
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
-~-~~,-~~~~-
ContoursofVelocity
Magn~ude
(m/s)(Time=2.7900e-02)Ju129.2004Gear
Pump
Design
by
YogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh,ske.
unstea<!y)
Figure6.10VelocityMagnitudeContours*forgearsrotatingat2000rpm(atTimet
=
1.15s)
73
1-
209190
171
15213311495
76
57
38
19
Poul~3000
-0
-19
.38
-57-76-95
-115
-134
-153
I'"
199182165148
131114
98
81
64
47
fout
~
?SdlJ
psi
30
13
-4-21-38-55
-72
-89-106
-123
Contours
of
XVelocity(mls)(Time=I.1500e+00)GearPumpDesignbyYogenJu129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)Contours
of
XVelocity(mls)(Time=I.1500e+00)GearPumpDesign
by
YogenJu129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
I-
n
1~1~
m
1n
1~
~ ~
41
21
1
~-3S00p~
~~~~
-101
-121
-141
-162-182
I
247213
178
144110
75
41
6
-28-62-97-131-165-200-234-269-303-337
-372-406-441
Contours
of
XVelocity(mls)(Time=I.1500e+00)GearPumpDesign
by
YogenJu129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)Contours
of
XVelocity
(l\'1/s)
(Time=2.7900e-02)GearPumpDesignbyYogenJu129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
Figure6.11X-VelocityContours*forgearsrotatingat2000rpm(atTimet
=
1.15s)
74
I'"
I"
11917710315988140
72
122
57
1034285
26
66
11
47-5
29
-20
10
Poui
~
25M
pSI
Pout=)OOO
-35-8
-51
-27-66
-45
-82
-64
-97-82
-112
-101-128-120
-143
-138
-159-157-174-175
Contours
of
YVelocity
(m/s)
(Time=1_1500e+OO)
GearPumpDesignbyYogen
Ju129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)Contours
of
YVelocity
(m/s)
(Time=1.1500e+OO)
GearPumpDesignbyYogen
Ju129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
225203
181
159136114
92
70
48
26
3
-19
-41
-63-85-108-130-152-174-196-219
I
I""
248225203
181
158136113
91
6846
24
Pout-3500psi
1
-21
-44-66-88-111-133-156-178
Contours
of
YVelocity(mls)(Time=1.1500e+OO)GearPumpDesignbyYogenJu129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)Contours
of
YVelocity(mls)(Time=2.7900e-02)
GearPumpDesign
by
Yogen
Ju129.2004FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
Figure6.12Y-VelocityContours*forgears
rotating
at
2000
rpm
(at
Timet
=
1.15
s)
75
I~
I~:
269255310240293226276212258198
241
184224170207156189
141
172
127
155
Poui=3001J
113138
99
12185103
71
86
57
694252
28
34
14
17
00
VelocityVectorsColored
By
VelocityMognijude(mls)
(Time=1.1500e-+<J0)
Jul
29.
2004
Gear
Pump
Dasign
by
Yogan
FLUENT
6.1
(2d.
dp.
segregatad.
dynamesh.
ske.
unsteady)VelocityVactorsColored
By
VelocityMagnijude(mls)(Time=1.1500e+00)
Jul
29.
2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamash.ske.unsteady)
--~-----------
I'"
I
""
439598416566393535370503347472324440300409277378254346231315208
Pout-3500psi
283185252
Pout-
3500
psi
162220139189116158921266995
46
63
23
32
0
0
VelocityVectorsColored
By
VelocityMognijude(mls)(Time=1.1500e+00)
Jul
29.
2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp,
segregated,
dynamesh.
ske.
unsteady)
VelocityVectorsColored
By
VelocityMagnijude(mls)(Time=2.7900a-02)Ju129.2004GearPumpDesign
by
YogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.ske.unsteady)
Figure6.13VelocityVectors*coloredbyVelocityMagnitudeforgearsrotatingat2000rpm(atTimet
=
1.15s)
76
I
""
I'M
2911347724492952198624281524190310611378599853136328-326-197-789
-721
-1251-1246
Pout
~
251M
p
Pout=)OOO
-1714-1771-2176-2296-2639-2821-3101-3346-3564-3871-4026-4395-4489-4920-4951-5445
-5414
-5970-5876-6495
VelocityVectorsColored
By
Static
Pressure(psi)(Time=1.1500e+00)Ju129.2004Gear
Pump
Design
by
YogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
--~-_.----
VelocityVectorsColored
By
Static
Pressure(psi)(Time=1.1500e+00)Ju129.2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated,
dynamesh.
ske.
unsteady)
I""
I""
3952416634543494295528232456
2152
195714811458809959138460-533-39-1204-537
-1875
-1036
Pout~3S00psi
-2547-1535-3218
Pout~]500psi
-2034
p~
-3889-2533-4560
'S/
lJ
-3032-5232-3531-5903-4030-6574-4528-7245
....
,:>(:
-5027-7917
.~
I
-5526-8588
VelocityVectorsColored
By
StaticPressure(psi)(Tima=1.1500e+00)
Jul
29.
2004GearPumpDesign
by
YogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)VelocityVectorsColored
By
Static
Pressure(psi)(Time=2.7900e-02)Ju129.2004Gea,PumpDesign
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.ske.unsteady)
Figure6.14VelocityVectors*coloredbyStaticPressureforgearsrotatingat2000rpm(atTimet=1.15s)
77
I"
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37
41
35
39
33
36
31
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31
2629
24
27
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25M
psi
Pout-30DO
20
22
181915
17
13
14
11
12
9107745220
0
Contours
of
Wall
Shear
Stress(psi)
(Time=1.1500e+OO)
Jul
29.
2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.
dynamesh.
ske.
unsteady)
Contours
of
Wall
Shear
Stress(psi)(Time=1.1500e+OO)Ju129.2004Gear
Pump
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FLUENT
6.1
(2d.
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WallShearStress(psi)(Time=1.1500e+OO)Jul
29.
2004GeerPumpDesignbyYogenFLUENT
6.1
(2d.
dp.
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ske.
unsteady)Contours
of
WallShearStress(psi)(Time=2.7900e-02)Ju129.2004GearPumpDesignbyYogenFLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
Figure6.15Contours
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ShearStress*forgearsrotatingat2000rpm(atTimet
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Jul
29.
2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.ske.unsteady)
Path
LinesColored
by
Slabc
Pressure(psi)(Time=I.1500e+OO)
Jul
29.
2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.dynamesh.
ske.
unsteady)
Figure6.16PathLines*coloredbyStaticPressureforinlet,drivengear,drivinggear,andoutlet
1
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Jul
29.
2004GearPumpDesign
by
YogenFLUENT
6.1
(2d.
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segregated.dynamesh.
ske.
unsteady)
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LinesColored
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VelocityMagnitude(mls)(Time=2.7900e-02)Ju129.2004Gear
Pump
DesignbyYogenFLUENT
6.1
(2d.
dp.
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79
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(2d,
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Ju131.
2004
GearPumpDesign
by
YogenFLUENT
6.1
(2d,
dp.
segregated.
dynamesh.
51(8.
unsteady)
VelocityVectorsColored
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VelocityMagnitude(mls)(Time=2.7900e?02)Pout=3500psiJu131.2004
GearPumpDesign
by
YogenFLUENT
6.1
(2d.
dp,
segregated.
dynamesh.~ke.
unsteady)
Figure6.18VelocityVectors*attheinletport:80
I-I-
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ill
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0VelocityVectorsColored
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(mls)(Time=1.1500e.oO)Pout=2500psi
Jul
31,
2004
Gear
Pump
Design
by
YogenFLUENT
6.1
(2d,
dp.
segregated,dynamesh.
ske.
unsteady)
VelocityVectorsColored
By
Velocity
M.gn~de
(mIs)
(Time=1.1500e.oO)Pout=3000psiJul
31.
2004
GearPumpDesign
by
YogenFLUENT
6,1
(2d.
dp,
segregated.dynamesh.
ske.
unsteady)
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(mls)(Time=1.1500e.oO)Pout=3500psiJu131.2004
GearPumpDesign
by
YogenFLUENT
6.1
(2d,
dp,
segregated.
dynamesh,
ske.
unsteady)
VelocityVectorsColored
By
Velocity
M.gn~de
(mls)(Time=2,7900e-02)Pout=3500psiJul
31.
2004
GearPumpDesign
by
YogenFLUENT
6.1
(2d.
dp,
segregated.
dynamesn.
ske,unsteady)
---_._-
Figure6.19VelocityVectors*attheoutletport:
81
..
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.
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??
?
100125150175200225
75
50
25
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1_
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,
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.
3.000+030.000+002.000+031.000+035.000+034.000+03-3.000+03-4.000+03.-5.000+03-6.000+03
~~,~~~~~~~~~~~~~~~~~~
StaticPressure
-1,000+03
(psi)
-2.000+03
!?
neo
?
..
.
..
100125150175200225755025
?
V'\,,4vV".
~Vt~
I?
pos
I
5.000+034.000+033.000+032.000+031.000+030.000+00
StaticPressure
?1.000+03
(psi)
-2.000+03-3_000+03?4.000+03?5.000+03-6.000+030
CurveLength(in)CurveLength(in)
Static
Pressure
vs.
Curve
Length
(Time::1.1500e+OO)N
::::
2000
rpm,
Pin::::
30
psi,
Pout::3500
psi
Ju131,
2004Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d.
dp.
segregated.
dynamesh,
ske.
unsteacfr)
StaticProssuro
vs.
CurvoLongth(Timo=1.15000+00)N=2000
rpm.
Pin
=30psi.Pout=3500psi
Jul
31.
2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d,
dp,
segregated,
dynamesh,
ske,
unsteady)
-
-_
...
_
...
_~---,~~~~-
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200225175
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8.00e+03
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(psi)
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Total
2.000+03
Pressure(psi)
1.000+030.000+00?1.000+03-2.000+030TotalProssuro
vs.
Curvo
Longth(Timo=1.15000+00)N=2000
rpm.
Pin
=30psi,Pout=3500psi
Ju131.
2004
Gear
Pump
Design
by
Yogen
FLUENT
6.1
(2d,
dp.
segregated,
dynamesh,
ske.
unsteady)
TotalProssuro
vs.
CurvoLongth(Timo=1.1500e+00)N=2000
rpm.
Pin
=30psi.Pout=3500psi
Ju131,
2004
Gear
Pump
Design
by
Yogan
FLUENT
6.1
(2d.
dp,
segregated,
dynamesh,
ske,
unsteady)
Figure6.20PressureVs.curvedlength
of
gears
82
40
3020-10010
Position(in)
-20-305.00e+Ol
O.OOe+OO
~
-403.00e+02
,
..
2.50e+02
~
..
..
.
.
.
'-
2.00e+02
~
#.
,
.....
..
1.50e+021
?.
Velocity
.
...
.
Magnitude
?.
(mls)
..
1.00e+02VelocityMagnitude(Time=1.1500e+OO)
GearPumpDesign
by
Yogen
N=2000rpm.
Pin
=30psi.Pout=3500psiJu131.2004
FLUENT
6.1
(2d.dp.segregated.dynamesh.ske.unsteady)
-.,_._-~-,
..
~._._~-"_._--,"----,--",,--,,-,-
Figure6.21Velocitymagnitude*vs.position
of
gearsanddefaultinterior
5.00e+03
4.50e+034.00e+033.50e+03
3.00.+03
Turbulent
2.50.+03
KineticEnergy
2.00.+03
(kl
1.50e+03
(m2/s2
1.00e+03
5.00.+020.00.+00-40-30
??
-20
??
..
...
'.
-10
0
10
Position(in)
20
30
40
Turbulent
Kinetic
Energy
(k)
(Time=1.1500e+OO)Gear
Pump
Design
by
Yogan
N
=2000
rpm.
Pin
=30
psi,
Pout
=3500
psi
Jul
31.2004FLUENT
6.1
(2d.
dp.
segregated.
dynamesh,
ske.
unsteady)
Figure6.22TurbulentKineticEnergy*vs.position
of
gearsanddefaultinterior
83
6.3Comparison:Results
of
FlowParametersTable
6.1
PressureandVelocity
RotationalSpeedPressureOutletVelocityRangeStaticPressureRangeDynamicPressureRange
of
gears
Pout.
psi
V,m/s
pst.t.
psiP
dyn.,
psi(N),rpmScalingdownfactor=
39.18
(fromthemagnifiedDynamicScalingdownfactor=
1535.36
(Page
39)
geometrymodel)
2000*
3500
0-12.58
-81294820
0-4.61
3000
3500
0-9.80
-126425665
0-6.19
2000
3500
0-7.35
-52654240
0-4.09
3000
0-7.25
-59193829
0-3.63
2500
0-6.99
-57253288
0-2.59
1000
0-6.43
-50462101
0-2.11
Table6.2MassFlowRate
PressureOutletMassflowrateMassflowrate
N,rpm
Pout.
psikg/sNetmass-flow,kg/sgpmInletOutletInletOutlet
2000*
3500
3.7-3.7
68
-6802000
3500
1.5
-
1.5
27
-27
0
3000
1.9
-
1.9
35-350
2500
2.4
-2.4
44-440
1000
3.8-3.870-700
Negativeandpositivesigninmassflowrateindicatesthemass
of
fluidcorninginandgoingoutfromthegearpump.*ModifiedCasingDesignatt
=
2.27ge-2
s.
84
6.4 Interpretation ofResults
The figures exhibiting velocity distributions show a slight change in velocity magnitude
as the outlet pressure increases for the same rotational speed. However, when the
rotational speed is changed from 2000 rpm to 3000 rpm, the maximum velocity increases
significantly from a 7.35 m/s to 9.84 m/s (refer to Table 6.1) at the identical pressure
boundary conditions. As noted on page 39, the velocity and the dynamic pressure
distributions shown in the figures must be reduced by the geometric scaling factor of
39.18 and the dynamic scaling factor of 1535.36, respectively. The velocity is about zero
close to the stationary casing wall as the fluid becomes stationary. The velocity contours
show the patterns that were expected around the gears. As clearly seen in the figures
showing the velocity vectors, the fluid is pushed forward to the outlet port as _the teeth of
two gears close. The graphs also show almost symmetrical recirculation flows forming
near the outlet port. When each gear pushes the fluid towards the outlet port by force, the
fluid in the region near the highly curved portions of the outlet pocket tends to stay in
place and become separated from the main outlet flow. Subsequently, the fluid flows in a
nearly circular motion that can be seen more clearly in the figure showing velocity
vectors. There can be small recirculation flows even in the inlet port due to the similar
mechanism.
The X-Y plots for the velocity components show very reasonable results. The magnitudes
of X-component of the velocity are larger near the top of the gear since the tangential
component is in phase of X coordinate. A similar conclusion can be drawn on the Y 
component ofthe velocity showing the large magnitude in the right side ofthe gear. The
magnitude of velocity vectors changes with respect to time domain. As the differential
pressure (difference between inlet and outlet pressure) decreases, recirculation flows
become more distinct. On the contrary, ifthe differential pressure increases, the flow rate
will decrease due to added resistances to the outgoing flow and the reverse flow through
the gap existing between two gears. Typically, fluids seek the path of least resistance;
consequently, the higher the differential pressure, the more fluid that will be forced back
through the clearances, resulting in decreased flow rate.
85
The wall shear stress is due to the velocity gradient offlow; as expected due to the same
reason already mentioned, the highest wall shear stress was found in the high velocity
region where teeth oftwo gears meet.
As seen in the figures, the pressure distributions are significantly different in magnitude,
but show similar patterns as the outlet pressure changes for the cases with constant
rotational speed and inlet pressure. The static and dynamic pressures increase as the
outlet pressure increases. Static pressure contours inside the gear pump have four regions
roughly, the first one is in the inlet port side, the second includes almost two identical
contours around the top and the bottom of two gears close to the casing, the third is in
between the gear meshes where the cavitation occurs and the fourth is in the high
pressure side close to the outlet. The high values of negative static pressur~ in a very
small region near the suction side where the gear teeth come out of the mesh shows
cavitation effect in the gear pump. This phenomenon is created by the local pressure
being lower than the vapor pressure, resulting in vaporization of the liquid to vapor
bubbles. The subsequent collapse of the vapor bubbles forms a liquid jet flowing into
collapsing bubble. This implosion results in highly negative values of pressure. M.S.
Plesset and R.B. Chapman were able to observe and measure up to 30,000 psi of the
bubble collapse pressure [39]. It should be noted that the cavitation may not happen in
actual flows in gear pumps. The cavitation effects shown in this analysis are probably due
to the high velocities ofthe fluid passing through the narrow gap between the two gears.
The dynamic pressure is due to the velocity of fluid. Almost the concentric contour of
pressure around the gear teeth is the main feature of dynamic pressure, which confirms
the uniform velocity profiles. Total pressure contours show the combined effect of the
static pressure and the dynamic pressure. In all of the cases, the high pressure region
starts from the outlet port. The pressure is the maximum at the closing ofgear teeth, and
decreases toward the inlet port.
86
CHAPTER 7
CONCLUDING REMARKS
A method ofnumerical analysis for gear pump flows was developed. A two dimensional,
unsteady, turbulent flow model was selected for the analysis by FLUENT. FLUENT has
the capability of solving problems that are needed a moving dynamic meshing scheme.
This scheme is used to analyze the gear pump flow. Several cases ofthe gear pump flows
with various boundary conditions and different rotational speed ofgears were analyzed.
A detailed step by step process ofnumerical modeling and analysis are presented in order
to facilitate modeling for future problems. The results ofthe analysis showed-reasonably
expected distribution of the velocity and pressure except the region of a narrow gap
between the two gears. The gap was created larger in order to avoid collapsing the
moving dynamic meshes that will cause the termination ofcomputing. In future analysis,
this gap must be closed to better represent actual models.
A number ofgraphical outputs for the velocity and pressure distributions versus time for
each case study were presented. The maximum time allowed was 5 seconds. The
convergence ofthe numerical integration was obtained fairly quickly. The results showed
qualitatively anticipated outcome for a variety of flow characteristics. The results should
be used carefully for the purpose ofpreliminary investigations only since the accuracy of
the analysis is low due to the simplification of flow and the modification ofthe dynamic
mesh model. The reverse flow existing between two gears and the subsequent cavitation
shown in this analysis may not occur in the same location in an actual flow.
However, despite all shortcomings, this study provides reasonable outcomes and
substantial information on modeling and executing FLUENT for solving gear pump
flows. A further refining in modeling and analysis will surely produce better results that
will be used for design and performance improvements.
87
BIBLIOGRAPHY
[1] Sullivan, James A., Fluid Power, Theory and Applications, Prentice Hall, 4th
Edition, 1998.
[2] Wright, T., Fluid Machining, Performance, Analysis and Design, CRC Press, 1999.
[3] Kim, H.W., Development of Fluid Program in Engineering & Technology,
Proceedings ofthe ASEE Annual Conference, Salt Lake City, Utah, 2004.
[4] Neff, Darby R, High Pressure Pumps and Their Controls, American Brake Shoe
Company, Columbus, Ohio.
[5] Novak, Julia and Gates, Kimberly, The World of Pumps, Civil Engineering
Department, Virginia Tech University, Blacksburg, VA, 2002.
[6] Borghi, Massimo, Fluid Power Research Group, DIMEC, Department of
Mechanical and Civil Engineering, Faculty ofEngineering in Modena, University
ofModena and Reggio Emilia, Modena - Italy, International Journal ofFluid Power
jointly published by FPNI and TuTech, Vol. 3, No.1, April 2002.
[7] Machiels, Luc, Simulation and theory ofrandomly forced turbulence, These No.
1724, Ecole Polytechnique Federale de Lausanne (EPFL scientific report), 1997.
[8] Gavrilakis, Spyros, Direct Numerical Simulation of Turbulence, Laboratoi re
d'Ingenierie Numerique (LIN) Projet No 1998.1, Ecole Polytechnique Federale de
Lausanne (EPFL scientific report), 2000.
[9] Manring, Noah D& Kasaragadda, Suresh B, The Theoretical Flow Ripple of an
External Gear Pump, Journal of Dynamic Systems, Measurement, and Control,
Volume 125, Issue 3, pp. 396-404, September 2003.
[10] MyllykyHi, Jaakko , Semi-Empirical Model from the Suction Capability of an
External Gear Pump, thesis 271, Tampere University ofTechnology 1999.
[11] Nelik, Lev, Operating conditions and comparisons between chemical duty pumps
and specialized high pressure gear pumps, World Pumps, Dec 200l.
[12] Marx, YP., Numerical simulation of gear-pump flows, Laboratoire d'ingenierie
numerique (LIN) Projet No 1999.2, Ecole Polytechnique Federale de Lausanne
(EPFL scientific report), 2000.
[13] FLUENT Solutions: Gear pump Solution, Example X 219, FLUENT inc., USA.
88
[14] Panta, Yogendra M., Adhikari, S., Panthee, P., Bhattarai, R.and Gyawali, P., Detail
Design ofPelton Turbine for 500 kW (with Pattern), Undergraduate Senior Project
in Mechanical Engineering submitted to Mechanical Engineering Department,
Pulchowk Campus, Tribhuvan University, 2000.
[15] Panta, Yogendra M., Rural Energy Technology, E-Vision, Mechanical Engineering
Department, Pulchowk Campus, Tribhuvan University, 2nd Edition, 1999.
[16] Murakami, Kobayashi, Yoshizawa, Kato, S., Taniguchi N., Hamba E, Kato C.,
Oshima M., Ooka R., Numerical Simulation of Turbulent Flow Research
Commemorative Symposium, Numerical Simulation of Turbulence (NST), Institute
of Industrial Science, University of Tokyo & TSFD(Turbulence Simulation and
Flow Design) Research Group in lIS, 2003.
[17] Roy, Trina M., Physically-Based Fluid Modeling using Smoothed Particle
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[18] Lal, Jagdish, Hydraullic Machines, Metropolitan Book Co. Pvt. Ltd., 6th Ed., 1997.
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89
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90
APPENDIX 1
User Defined Function (UDF) Syntax for "motion.c" for gears at N = 2000 rpm
/*This code is written in "C"*/
/*UDF starts for both the gears*/
#inc1ude "udf.h"
#inc1ude "dynamesh_tools.h"
/*UDF starts for Rotational Speed of2000 rpm for Driving Gear*/
DEFINE_CG_MOTION(antic1ock_wise, dt, vel, omega, time, dtime)
{
NY_S (vel, =, 0.0);
NY_S (omega, =,0.0);
/*Linear Velocity for Driving Gear*/
vel[O] = 0.0;
vel[l] = 0.0;
vel[2] = 0.0;
/*Angular Velocity for Driving Gear */
omega[O] = 0;
omega[l] = 0;
omega[2] = 210;
/*Messages for Display*/
Message("\nThis is Anti Clockwise Gear\n");
Message("\nCG_Omega for antic1ock_wise: %g, %g, %g\n", omega[O],omega[I],
omega[2]);
Message("\nCG Position for antic1ock_wise: %g, %g, %g\n", NV_LIST(DT_CG(dt)));
Message("\nCG Orientation for antic10ck_wise: %g, %g, %g\n",
NY_LIST(DT_THETA(dt)));
}
/*UDF ends for Rotational Speed of2000 rpm for Driving Gear*/
Continued...
91
/*UDP starts for Rotational Speed of2000 rpm for Driven Gear*/
/*Rotational Speed of2000 rpm for Driven Gear*/
DEPINE_CG_MOTION(clock_wise, dt, vel, omega, time, dtime)
{
NY_S (vel, =, 0.0);
NY_S (omega, =, 0.0);
/*Linear Velocity for Driven Gear*/
vel[O] = 0.0;
vel[l] = 0.0;
vel[2] = 0.0;
/*Angular Velocity for Driven Gear */
omega[O] = 0;
omega[l] = 0;
omega[2] = -210;
/*Messages for Display*/
Message("\nThis is Clockwise Gear\n");
Message("\nCG_Omega for clock_wise: %g, %g, %g\n", omega[O], omega[I],
omega[2]);
Message("\nCG Position for clock_wise: %g, %g, %g\n", NY_LIST(DT_CG(dt)));
Message("\nCG Orientation for clock_wise: %g, %g, %g\n", NY_LIST(DT_THETA(dt)));
}
/*UDP ends for Rotational Speed of2000 rpm for Driven Gear*/
/* UDP ends for both the gears*/
92
APPENDIX 2
Moving Dynamic Mesh: DEFINE_CG_MOTION
DEFINE_CG_MOTION macro is used to specify the motion of a particular dynamic
domain in FLUENT to provide linear and angular velocities at every time step.
Macro: DEFINE_CG_MOTION (name, dt, vel, omega, time, dtime)
Argument types: Dynamic_Thread *dt
real vel[]
real omega[]
real time real
dtime
Function returns: void
93
3
APPENDIX 3
2 1
Figure A 3.1 Pumping action in an external gear pump
r>a IV.NO Of"I
1
I ?D
Figure A 3.2 Gear Type Rotary Pump
94
"~I:::tc--I OUTLET
Root diameter circle
00diameter circle (Oa)
center distance
Pitch diameter (gear contact) circle
Addendum = radial distance from the pitch circle
f. O?Dand 00circle \a - ~ P)
Dedendum::;: radial distance from the pitch circle
I D -D )to the root circle \ b _ ~ r
Figure A 3.3 Geometry ofan external gear pump
95