thheerrmmaall lhhyyddrraauuliicc aannaallyyssiiss ooff
Post on 07-Apr-2022
6 Views
Preview:
TRANSCRIPT
TThheerrmmaall HHyyddrraauulliicc AAnnaallyyssiiss ooff
SStteeaamm JJeett PPuummpp
AAjjmmaall SShhaahh
PPaakkiissttaann IInnssttiittuuttee ooff EEnnggiinneeeerriinngg aanndd AApppplliieedd SScciieenncceess
IIssllaammaabbaadd PPaakkiissttaann
JJaannuuaarryy 22001122
ii
This work is submitted as a thesis in partial fulfillment for the award of the
degree of
DOCTOR OF PHILOSOPHY
in the Department of Nuclear Engineering Pakistan Institute of Engineering
and Applied Sciences Islamabad, Pakistan
iii
Declaration
I hereby declare that all the material and intellectual content contained in this
thesis is the product of my own work. The work which is not my own has
been identified and that no material has previously been submitted and
approved for the award of a degree by this or in any other university.
Signature: ______________
Author’s Name: Ajmal Shah
Date: __________________
Place: _PIEAS (Islamabad)_
iv
Certificate of Approval
It is certified that the work contained in this thesis titled "Thermal Hydraulics
Analysis of Steam Jet Pump" was carried out by Ajmal Shah under the
supervision of Dr. Mansoor Hameed Inayat and Dr. Nasim Irfan and that in
our opinion, it is fully adequate in scope and quality, for the degree of doctor
of philosophy in the Department of Nuclear Engineering (DNE).
Approved by:
Signature: _________________________
Dr. Mansoor Hameed Inayat (Supervisor)
Deputy Chief Engineer & Head of Department of Chemical Engineering Pakistan Institute of Engineering and Applied Sciences
Islamabad, Pakistan.
Head, DNE: _____________________
vi
Acknowledgements
All praises and thanks to Almighty ALLAH, the most Merciful, Compassionate,
Gracious and Beneficent WHO has created this world and is the entire source
of knowledge and wisdom endowed to mankind.
I am greatly thankful to my supervisor, Dr. Mansoor Hameed Inayat, Head
DChE and Co-Supervisor Dr. Nasim Irfan, Head DNE for their supervision,
keen interest, technical advices and support during the research,
experimentation, publications and preparation of thesis. I am really grateful to
Dr. Imran Rafiq Chughtai, PE DChE (PIEAS) for his sincere guidance, support
and advices.
I am thankful to my colleagues and friends who ensured a creative and good
working environment and helped me in technical and non-technical matters.
My special thanks are due to Mr. Shozab Mehdi and Mr. Asif Hussain Malik. I
am also thankful to the technical staff in the mechanical workshop and
mechanical lab of PIEAS, for their help and support in developing the
experimental setup and performing experiments. I am grateful to HEC for
their financial support for the completion of this work.
I am also thankful to my family who has been missing me during my long
working hours at PIEAS. I would like to express my dearest feelings and
respect towards my parents for their endless prayers and support under
which I always feel secure. At the end, I am grateful to all those who have
always wished to see me glittering on the skies of success, may ALLAH bless
them with healthy, happy and long lives. With my deepest gratitude,
Ajmal Shah
vii
Thesis Reviewers
1. Prof. Dr. Ruben Avila, Thermofluids Department, Engineering Faculty,
Universidad Nacional Autonoma de Mexico (UNAM).
2. Ass. Prof. Dr. Rehan Sadiq, School of Engineering, Okanagan Campus,
The University of British Columbia, Canada.
3. Prof. Dr. Wei Wang, Institute of Process Engineering, Chinese Academy
of Sciences.
4. Prof. Dr Asad Majid, Department of Mechanical Engineering, Pakistan
Institute of Engineering and Applied Sciences (PIEAS).
5. Prof. Dr Hafeez ur Rehman Memon, Mehran University of Engineering
and Technology, Jamshoro, Pakistan.
6. Prof. Dr A. K. Salariya, Dean Wah Engineering College, Wah Cantt.,
Pakistan.
viii
Research Work Publications
Shah, A., I.R. Chughtai, and M.H. Inayat, Numerical Simulation of Direct-
contact Condensation from a Supersonic Steam Jet in Subcooled Water.
Chinese Journal of Chemical Engineering, 2010. 18[1]: p. 577-587.
Shah, A., I.R. Chughtai, and M.H. Inayat, Experimental and numerical
analysis of steam jet pump. International Journal of Multiphase Flow, 2011.
37(10): p. 1305-1314.
Malik, A.H., M.S.I. Alvi, S. Khushnood, F.M. Mahfouz, M.K.K. Ghauri, A. Shah,
Experimental study of conjugate heat transfer within a bottom heated vertical
concentric cylindrical enclosure, International journal of Heat and Mass
Transfer, 2012. 55 (4): p. 1154-1163.
Malik, A.H., M.S.I. Alvi, S. Khushnood, F.M. Mahfouz, M.K.K. Ghauri, A. Shah,
Numerical study of conjugate heat transfer within a bottom heated cylindrical
enclosure, in: Applied Sciences and Technology (IBCAST), 2012 9th
International Bhurban Conference on, 2012, pp. 213-220.
ix
Table of Contents
ACKNOWLEDGEMENTS .................................................................................................................... VI
THESIS REVIEWERS .......................................................................................................................... VII
RESEARCH WORK PUBLICATIONS ................................................................................................... VIII
TABLE OF CONTENTS .........................................................................................................................IX
LIST OF FIGURES ...............................................................................................................................XII
LIST OF TABLES ............................................................................................................................... XVI
NOMENCLATURE .......................................................................................................................... XVIII
ABSTRACT .......................................................................................................................................... 1
CHAPTER 1 ........................................................................................................................................ 3
1 INTRODUCTION ......................................................................................................................... 3
1.1 INTRODUCTION TO STEAM JET PUMP (SJP) ....................................................................................... 3
1.2 PRINCIPLE OF SJP ...................................................................................................................... 4
1.2.1 Steam nozzle ................................................................................................................ 4
1.2.2 Water nozzle ................................................................................................................ 5
1.2.3 Mixing section .............................................................................................................. 5
1.2.4 Diffuser ........................................................................................................................ 5
1.3 PROBLEM DEFINITION ................................................................................................................. 5
1.4 RESEARCH OBJECTIVES ................................................................................................................ 6
1.5 THESIS ORGANIZATION ................................................................................................................ 7
CHAPTER 2 ...................................................................................................................................... 10
2 LITERATURE REVIEW ............................................................................................................... 10
2.1 JET PUMP .............................................................................................................................. 10
2.1.1 Jet ejector .................................................................................................................. 11
2.1.2 Jet injector ................................................................................................................. 15
2.2 DIRECT-CONTACT CONDENSATION (DCC)...................................................................................... 18
2.3 GAMMA-RAY DENSITOMETRY ..................................................................................................... 21
CHAPTER 3 ...................................................................................................................................... 23
3 MATHEMATICAL MODELING ................................................................................................... 23
3.1 INTRODUCTION TO TWO-PHASE FLOW MODELING ............................................................................ 23
x
3.2 EULER-EULER TWO-PHASE FLOW MODEL ....................................................................................... 24
3.2.1 Mass balance equation .............................................................................................. 25
3.2.2 Momentum balance equation .................................................................................... 26
3.2.3 Energy balance equation ............................................................................................ 27
3.3 MATHEMATICAL MODELING OF DCC ............................................................................................ 28
3.3.1 Assumptions of DCC model ......................................................................................... 28
3.3.2 The Direct-Contact Condensation (DCC) model ........................................................... 29
3.4 TURBULENCE MODEL ................................................................................................................ 34
3.5 INTERFACIAL DRAG MODEL ......................................................................................................... 35
3.6 1D SUPERSONIC NOZZLE DESIGN .................................................................................................. 36
CHAPTER 4 ...................................................................................................................................... 41
4 EXPERIMENTAL SETUP AND DATA........................................................................................... 41
4.1 INTRODUCTION TO EXPERIMENTAL SETUP ....................................................................................... 41
4.2 STEAM JET PUMP GEOMETRY ...................................................................................................... 42
4.2.1 Steam and water nozzles ............................................................................................ 43
4.2.2 Mixing section and diffuser ........................................................................................ 45
4.3 PRESSURE AND TEMPERATURE MEASURING SYSTEMS......................................................................... 48
4.3.1 Pressure transmitters ................................................................................................. 48
4.3.2 Data acquisition systems ............................................................................................ 50
4.4 VOID FRACTION MEASURING SYSTEM ............................................................................................ 50
4.5 FLOW VISUALIZATION SYSTEM ..................................................................................................... 53
4.6 EXPERIMENTAL DATA ................................................................................................................ 54
CHAPTER 5 ...................................................................................................................................... 58
5 CFD SIMULATIONS .................................................................................................................. 58
5.1 INTRODUCTION AND AIMS OF CFD SIMULATIONS ............................................................................. 58
5.2 A SUPERSONIC STEAM JET INJECTED INTO A SUBCOOLED WATER TANK .................................................... 59
5.2.1 Geometry and mesh ................................................................................................... 60
5.2.2 Boundary conditions .................................................................................................. 61
5.2.3 CFD Models applied.................................................................................................... 62
5.3 FLOW THROUGH STEAM JET PUMP................................................................................................ 63
5.3.1 Geometry and mesh ................................................................................................... 63
5.3.2 Boundary conditions .................................................................................................. 64
5.3.3 CFD models applied .................................................................................................... 65
xi
CHAPTER 6 ...................................................................................................................................... 66
6 RESULTS AND DISCUSSION ...................................................................................................... 66
6.1 INTRODUCTION ....................................................................................................................... 66
6.2 STATIC PRESSURE ..................................................................................................................... 66
6.2.1 Axial wall static pressure in steam nozzle.................................................................... 67
6.2.2 Axial wall static pressure in mixing section ................................................................. 70
6.2.3 Axial wall pressure distribution in diffuser................................................................... 72
6.2.4 Back pressure investigation ........................................................................................ 72
6.3 TEMPERATURE DISTRIBUTION ...................................................................................................... 74
6.3.1 Axial temperature distribution .................................................................................... 75
6.3.2 Radial temperature distribution.................................................................................. 78
6.4 OPERATIONAL CHARACTERISTICS OF SJP ........................................................................................ 80
6.4.1 Mass flow rate ........................................................................................................... 81
6.4.2 Mass Ratio ................................................................................................................. 85
6.4.3 Suction lift .................................................................................................................. 88
6.5 VOID FRACTION DISTRIBUTION AND FLOW VISUALIZATION................................................................... 91
6.6 CFD RESULTS .......................................................................................................................... 97
6.6.1 Contours of mass transfer .......................................................................................... 98
6.6.2 Contours of volume fraction ..................................................................................... 100
6.6.3 Centerline flow velocity and contours of mach number ............................................. 102
CHAPTER 7 .................................................................................................................................... 105
7 CONCLUSIONS AND FUTURE RECOMMENDATIONS............................................................... 105
7.1 CONCLUSIONS ....................................................................................................................... 105
7.2 FUTURE RECOMMENDATIONS.................................................................................................... 107
REFERENCES ................................................................................................................................... 108
APPENDIX A ................................................................................................................................... 115
APPENDIX B.................................................................................................................................... 128
APPENDIX C .................................................................................................................................... 131
APPENDIX D ................................................................................................................................... 134
PUBLISHED RESEARCH PAPERS ....................................................................................................... 137
xii
List of Figures
Figure 1.1: Schematic diagram of a typical SJP showing its different parts ..... 4
Figure 2.1: Constant area and constant pressure designs of ejector [18] ..... 11
Figure 3.1: A typical vapor-liquid interface ................................................. 29
Figure 3.2: A typical converging-diverging nozzle ....................................... 37
Figure 4.1: The experimental setup ........................................................... 41
Figure 4.2: Schematic diagram of the experimental setup ........................... 42
Figure 4.3: SJP made of brass .................................................................. 43
Figure 4.4: Drawing of steam and water nozzles ........................................ 44
Figure 4.5: Fabricated steam and water nozzles made of brass ................... 44
Figure 4.6: Mixing section and diffuser made of perspex ............................ 46
Figure 4.7: Mixing section and diffuser combinations for SJP1, SJP2, SJP3 and
SJP4 geometries of SJP (dimensions in mm) .............................................. 47
Figure 4.8: Circuit to linkup pressure transmitter to DAC channel ................ 49
Figure 4.9: Various systems installed on the experimental setup ................. 49
Figure 4.10: Schematic diagram of densitometry system ............................ 51
Figure 4.11: The densitometry setup, detector and counter ........................ 52
Figure 4.12: Transparent geometry of SJP installed on the experimental setup
............................................................................................................... 53
Figure 5.1: Nozzle fitted water tank geometry being simulated ................... 59
xiii
Figure 5.2: Meshed geometry of water tank and steam nozzle .................... 60
Figure 5.3: Meshed plane at the exit of steam nozzle ................................. 61
Figure 5.4: Meshed geometry of SJP, A: Full geometry with surface mesh, B:
enlarged and sectioned view showing surface meshes ................................ 64
Figure 6.1: Axial wall static pressure profile for SJP1 geometry of SJP ......... 67
Figure 6.2: Axial wall static pressure profile for SJP2 geometry of SJP ......... 68
Figure 6.3: Axial wall static pressure profile for SJP3 geometry of SJP ......... 69
Figure 6.4: Axial wall static pressure profile for SJP4 geometry of SJP ......... 70
Figure 6.5: Axial wall pressure distribution at higher back pressure ............. 73
Figure 6.6: Axial static temperature profile for SJP1 geometry of SJP .......... 74
Figure 6.7: Axial static temperature profile for SJP2 geometry of SJP .......... 75
Figure 6.8: Axial static temperature profile for SJP3 geometry of SJP .......... 76
Figure 6.9: Axial static temperature profile for SJP4 geometry of SJP .......... 77
Figure 6.10: Steam jets showing periodic compression-expansion [65] ........ 78
Figure 6.11: CFD results of radial temperature distribution for SJP1 geometry
of SJP at six different axial locations (x) .................................................... 79
Figure 6.12: Entrained water mass flow rate curves for SJP1 geometry of SJP
............................................................................................................... 81
Figure 6.13: Entrained water mass flow rate curves for SJP2 geometry of SJP
............................................................................................................... 82
xiv
Figure 6.14: Entrained water mass flow rate curves for SJP3 geometry of SJP
............................................................................................................... 83
Figure 6.15: Entrained water mass flow rate curves for SJP4 geometry of SJP
............................................................................................................... 84
Figure 6.16: Mass ratio curves for SJP1 geometry of SJP ............................ 85
Figure 6.17: Mass ratio curves for SJP2 geometry of SJP ............................ 86
Figure 6.18: Mass ratio curves for SJP3 geometry of SJP ............................ 87
Figure 6.19: Mass ratio curves for SJP4 geometry of SJP ............................ 87
Figure 6.20: Suction lift curves for geometry SJP1 of SJP............................ 88
Figure 6.21: Suction lift curves for geometry SJP2 of SJP............................ 89
Figure 6.22: Suction lift curves for geometry SJP3 of SJP............................ 90
Figure 6.23: Suction lift curves for geometry SJP4 of SJP............................ 91
Figure 6.24: Void fraction distribution in the mixing section for SJP1 geometry
of SJP...................................................................................................... 92
Figure 6.25: Void fraction distribution in the mixing section for SJP2 geometry
of SJP...................................................................................................... 93
Figure 6.26: Void fraction distribution in the mixing section for SJP3 geometry
of SJP...................................................................................................... 94
Figure 6.27: Void fraction distribution in the mixing section for SJP4 geometry
of SJP...................................................................................................... 95
Figure 6.28: Steam jet in the mixing section of SJP2 geometry of SJP ......... 96
Figure 6.29: Steam jet in the mixing section of SJP3 geometry of SJP ......... 96
xv
Figure 6.30: Steam jet in the mixing section of SJP4 geometry of SJP ......... 97
Figure 6.31: Contours of mass transfer for SJP2 geometry of SJP................ 99
Figure 6.32: Contours of volume fraction for SJP2 geometry of SJP ........... 101
Figure 6.33: Centerline steam velocity for SJP2 geometry of SJP ............... 103
Figure 6.34: Mach number contours for SJP2 geometry of SJP .................. 104
xvi
List of Tables
Table 4.1: Geometric and material specification of SJP geometries used in the
experiments............................................................................................. 46
Table 4.2: Configurations of SJP geometries used in experimentation.......... 47
Table 4.3: Axial distance of measurement points for SJP geometries ........... 48
Table 4.4: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟 ................. 54
Table 4.5: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟 ................. 55
Table 4.6: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟 ................. 55
Table 4.7: Void fraction data for SJP2 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟 ................. 56
Table 4.8: Void fraction data for SJP2 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟 ................. 56
Table 4.9: Flow rates, mass ratio and suction lift data at different steam inlet
and water suction pressures for SJP2 geometry ......................................... 57
Table 5.1: Boundary conditions used for nozzle fitted water tank geometry . 62
Table 5.2: Boundary conditions used for SJP geometries ............................ 65
Table B1.1: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟 ............. 128
Table B1.2: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟 ............. 128
Table B1.3: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟 ............. 129
Table B1.4: Void fraction data for SJP1 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟 ............. 129
Table B1.5: Void fraction data for SJP1 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟 ............. 129
xvii
Table B1.6: Flow rates, mass ratio and suction lift data at different steam inlet
and water suction pressures for SJP1 geometry ....................................... 130
Table C1.1: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟 ............. 131
Table C1.2: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟 ............. 131
Table C1.3: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟 ............. 132
Table C1.4: Void fraction data for SJP3 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟 ............. 132
Table C1.5: Void fraction data for SJP3 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟 ............. 132
Table C1.6: Flow rates, mass ratio and suction lift data at different steam inlet
and water suction pressures for SJP3 geometry ....................................... 133
Table D1.1: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟 ............. 134
Table D1.2: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟 ............. 134
Table D1.3: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟 ............. 135
Table D1.4: Void fraction data for SJP4 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟 ............. 135
Table D1.5: Void fraction data for SJP4 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟 ............. 135
Table D1.6: Flow rates, mass ratio and suction lift data at different steam
inlet and water suction pressures for SJP4 geometry ................................ 136
xviii
Nomenclature
1-D One dimensional
2-D Two dimensional
3-D Three dimensional
BWR Boiling water reactor
CFD Computational fluid dynamics
D1,D2 Different geometries of diffuser
DCC Direct-contact condensation
M1,M2,M3,M4 Different geometries of mixing section
MP1 to MP8 Data measurement points along axis of SJP
PWR Pressurized water reactor
SJP Steam jet pump
SJP1,SJP2,SJP3,SJP4 Different geometries of SJP
SN Steam nozzle
VOF Volume of fluid
WN Water nozzle
A Cross-sectional area
𝐴𝑓𝑔 Interfacial area per unit volume
𝐶𝐷 Drag coefficient
𝐶𝑝 Specific heat capacity at constant pressure
𝑭𝑙𝑖𝑓𝑡 ,𝑞 Lift force for phase q
𝑭𝑞 External body force for phase q
𝑭𝑣𝑚 ,𝑞 Virtual mass force for phase q
𝐻𝑓 Liquid side volumetric heat transfer coefficient
𝐻𝑓𝑠 Saturation liquid enthalpy
𝐻𝑔 Vapor side volumetric heat transfer coefficient
𝐻𝑔𝑠 Saturation vapor enthalpy
𝐼𝑚𝑖𝑥 Average counts of gamma-ray across mixture
𝐼𝑠 Average counts of gamma-ray across steam phase
𝐼𝑤 Average counts of gamma-ray across water phase
𝐾𝑓𝑔 Liquid-vapor exchange coefficient
𝑀 Mach number
𝑁𝑢𝑓 Nusselt number for liquid phase
𝑃 Fluid pressure
𝑃𝑟 Prandtl number
𝑷𝒔 Steam inlet pressure
xix
𝑷𝒔𝒖𝒄 Water suction pressure
𝑄𝑓 Heat flux from interface to liquid phase
𝑄𝑔 Heat flux from vapor to interface
𝑄𝑝𝑞 Intensity of heat transferring from phase p to phase q
𝑅 Universal gas constant
𝑅𝑒 Relative Reynolds number
𝑹𝑝𝑞 Phases interaction force for phase q
𝑇 Fluid temperature
𝑇𝑓 Local liquid temperature
𝑇𝑔 Local vapor temperature
𝑇𝑠 Local saturation temperature
𝑈𝑔 − 𝑈𝑓 Absolute relative velocity between the two phases
𝑉𝑞 Volume of phase q
𝑎 Speed of sound
𝑑 Diameter
𝑑0 Bubble diameter at reference liquid subcooling 𝜃0
𝑑1 Bubble diameter at reference liquid subcooling 𝜃1
𝑑𝑔 Vapor bubble diameter
𝑓𝑑 Drag function
𝒈 Body force due to gravity
𝑓 Liquid side heat transfer coefficient
𝑔 Vapor side heat transfer coefficient
𝑝𝑞 Enthalpy of phase p converting to phase q
𝑞𝑝 Enthalpy of phase q converting to phase p
𝑞 Specific enthalpy for phase q
𝑘𝑓 Thermal conductivity for liquid phase
𝑚 Mass flow rate
m pq Mass transfer from phase p to phase q
m qp Mass transfer from phase q to phase p
𝒎 𝒔,𝒊𝒏 Steam mass flow rate at inlet of SJP
𝒎 𝒘,𝒊𝒏 Water mass flow rate at inlet of SJP
𝒎 𝒘,𝒐𝒖𝒕 Water mass flow rate at outlet of SJP
𝑞𝑓 Rate of energy transfer from interface to liquid phase
𝑞𝑔 Rate of energy transfer from vapor to interface
𝒒𝑞 Heat flux for phase q
Sq Source term for phase q
xx
𝑣 Fluid velocity
vq Velocity of phase q
𝑥 Distance along x-coordinate
𝛼 Volume fraction/void fraction
αq Volume fraction of phase q
ρq Density of phase q
𝜌 𝑞 Effective density of phase q
𝝉𝒒 Stress-strain tensor for phase q
𝜃 Local liquid subcooling
𝜃0 Reference liquid subcooling = 13.5 𝐾
𝜃1 Reference liquid subcooling = 0 𝐾
𝜌𝑓 Density for liquid phase
𝜇𝑓 Viscosity for liquid phase
𝜏𝑓𝑔 Particulate relaxation time
𝜌 Density of fluid
𝛾 Specific heat ratio for vapor phase
Abstract
Steam jet pump (SJP) is a non-conventional pumping device for pumping
radioactive and hazardous fluids or slurries. It is also used for producing
vacuum in various chemical and process industries. Comparing to
conventional pumps, its main advantage is that it has no moving parts and
hence is maintenance free. However, the transport phenomena occurring in
SJP is highly complicated because of the direct-contact condensation (DCC) of
steam. The present knowledge of SJP is limited mostly to experimental data,
1-D modeling and empirical correlations. In this study, the transport
phenomena of DCC are studied theoretically, experimentally and numerically
with particular focus on SJP. A mathematical model of DCC is developed and
used to study, numerically, the transport phenomena across steam-water
interface in SJP and in a supersonic steam jet injected into a subcooled water
tank. The DCC model is validated by comparing the numerical simulation
results with the experimental results. The experiments are performed on
different geometries of SJP, designed, fabricated and assembled into an
experimental setup in this research work. The experimental data is translated
into characteristic curves to study the performance of SJP under different
operating and geometric conditions. To rigorously validate the DCC model and
study the two-phase flow in the mixing section of SJP, void fraction is
measured by gamma-ray densitometry and the steam jet is visualized through
high speed photography.
The experimental results of axial static pressure, axial static temperature and
void fraction are compared with the computational results. A close agreement
between the two results validates the DCC model and CFD simulations. These
results also explain the flow behavior and transport phenomena in SJP. The
characteristic curves of SJP in terms of entrained water mass flow rate, mass
ratio and suction lift are generated as a function of steam inlet pressure and
water nozzle suction pressure. These curves help in understanding the
performance of SJP at different operating conditions. The suction lift,
2
calculated from experimental data using Bernoulli's equation, gives the idea of
the depth from which the SJP is able to suck and pump water under different
operating conditions. The maximum value of mass ratio and suction lift
recorded in these experiments are 64.63 and 2.2 m respectively for the
geometries studied. The computational results of volume fraction, mass
transfer and axial steam velocity provide important information about the
steam-water interface and the transport phenomena occurring in SJP. The
results of flow visualization also explain the behavior of steam jet and validate
the DCC model and gamma-ray densitometry results. A new concept named
as interface vibration phenomena related to DCC of SJP was introduced and
explained. It was shown that transport phenomena in SJP are strongly
dependent on the interface vibration phenomena and the length of the
converging part of the mixing section plays an important role in improving the
interface vibration phenomena in DCC of SJP. It is believed that the
mathematical modeling based on the physics of the transport phenomena and
3-D numerical simulation of complex phenomena of DCC in SJP are valuable
addition to the previously available 1-D, 2-D modeling and empirical
correlations.
3
CHAPTER 1
1 INTRODUCTION
1.1 Introduction to steam jet pump (SJP)
Steam jet pump (SJP) is a unique type of pumping device used for specific
industrial applications. Unlike conventional pumps, the pumping action in SJP
is produced by high pressure steam called the motive medium. The medium
to be pumped may be gasses, liquids and/or solids in suspension and is called
the entrained medium. One of the features which make this device very
attractive is its passive nature provided that high pressure steam is available.
Similarly, the absence of any moving part in such pumps makes them
attractive for pumping hazardous liquids. There are other numerous
advantages of using SJP like: no maintenance, easy control, negligible
leakages, noise free, easy installation, economical and compact system.
However, the direct interaction between motive and entrained mediums in
SJP is highly complex. Therefore, modeling of SJP still represents an
incompletely solved problem. There are some other disadvantages of SJP, like
the steam is mixed with the liquid to be pumped, thus increasing the total
bulk of the pumped liquid. Similarly, the transfer of heat from the motive
steam to the entrained liquid rises the liquid temperature.
In this work an effort is made to carry out thermal hydraulics analysis of SJP
by studying the flow phenomena and performance characteristics of SJP while
pumping against a certain depth. The work done includes: experimentation,
numerical simulation, flow visualization, gamma-ray densitometry and,
foremost, development of a mathematical model for direct-contact
condensation (DCC) of steam into subcooled water [2-3].
4
1.2 Principle of SJP
In SJP the high pressure motive medium (steam) is passed through a
converging-diverging nozzle to create sonic or supersonic flow. This flow will
create a negative pressure around the exit of steam nozzle and facilitate the
suction of the entrained medium. The two fluids then come in direct contact
with each other and exchange mass, energy and momentum while flowing
through the pump. The steam condenses completely to water and is mixed in
the entrained liquid. The discharge of the SJP is liquid at relatively high
pressure. A schematic diagram of SJP is shown in Figure 1.1. The steam jet
pump geometry can be divided into four parts as discussed below.
Figure 1.1: Schematic diagram of a typical SJP showing its different parts
1.2.1 Steam nozzle
It has a typical converging-diverging shape and its function is to accelerate
the motive steam to sonic or supersonic speed. The steam expands nearly
isentropically through the steam nozzle and its enthalpy is partly converted
into the kinetic energy, resulting in high speed flow.
5
1.2.2 Water nozzle
The space around the steam nozzle leading to the mixing section is called the
water nozzle. Its function is to produce moderate acceleration and distribute
the water all around the exit of the steam nozzle.
1.2.3 Mixing section
This section has two parts; the converging part and the throat part. The two
streams (motive and entrained) come in direct contact with each other in this
section. The mixing section may be considered as the heart of SJP, because,
the suction and pumping action depend on the transport phenomena
occurring in this section. An interface is developed between the two streams
in the mixing section and the mass, momentum and energy transfer between
them occurs across this interface. The process of condensation takes place
within this section.
1.2.4 Diffuser
The last section of steam jet pump is called the diffuser and its function is to
increase the pressure of outgoing liquid. It has a diverging shape.
1.3 Problem definition
Mechanically, SJP is the simplest type of all the vacuum pumps and
compressors. However, the hydrodynamic phenomena which produce the
suction and pumping action are highly complex and technically sophisticated.
In a typical SJP the flow is compressible, two-phase, supersonic and
turbulent. An interface is developed between the two phases involved and
heat, mass and momentum transfer between the phases occur across this
interface [3]. Due to the above mentioned complexities the previously
published work related to flow process within SJP is limited mostly to
empirical correlations and simplified approaches [4-16]. With the rapid
6
advancement in the field of computing and numerical techniques it is now the
time to understand the physics of the flow phenomena within SJP.
The aim of the present research is to study the transport phenomena and
suggest a more realistic model for DCC with particular focus on SJP. To
achieve these targets, a lab-scale experimental setup of SJP is required to
generate experimental data for parametric analysis and validation of CFD
simulations. A mathematical model is required to be developed and validated
for DCC of steam into water. To perform numerical simulations of the flow
phenomena of SJP, using DCC model and CFD software. Flow visualization
and gamma-ray densitometry measurements will provide additional support to
validate the CFD simulations and to better understand the phenomena of SJP.
1.4 Research objectives
The specific objective of this research is to understand the physics of the
phenomena occurring in SJP by studying its characteristics through
experimental and numerical techniques. To accomplish this task, a point wise
description of research objectives is given below:
To design, fabricate and develop a lab scale experimental setup for the
measurement and calculation of the following parameters related to
different geometries of SJP.
i. Axial variation of static pressure.
ii. Axial variation of static temperature.
iii. Steam and water flow rates at inlets and outlet of SJP.
iv. Volume fraction of steam and water in the mixing section of SJP.
v. Suction pressure at the exit of water nozzle.
vi. Suction lift.
7
To study the characteristics of different geometries of SJP at various
steam inlet and water suction pressures.
To develop a mathematical model for DCC of steam into subcooled
water.
To validate the DCC model by numerically simulating the condensation
of steam in water using this model.
Simulating the flow through SJP using the DCC model.
To study the two phase region of SJP using gamma-ray densitometry
and by flow visualization through high speed photography.
To make a comparison of the experimental and numerical results.
To have a better understanding of the transport phenomena in DCC
with particular focus on SJP.
1.5 Thesis organization
Chapter 1 - Introduction
This chapter deals with the introduction of SJP and its merits and
complications as compared to conventional pumps. The importance of steam
jet pump in specialized application has been highlighted. A brief review of the
complexities involved in SJP, along with an indication towards the areas of
research and main objectives of the research have been defined. Finally an
organization chart of the thesis has been given.
Chapter 2 – Literature review
In order to have a complete picture of the issues related to jet pumps, DCC
and gamma-ray densitometry a comprehensive literature review is carried
out. The experimental and computational work of the past researchers and
different models used related to jet pump, DCC and gamma-ray densitometry
8
are discussed. The main emphasis has been made on the work related to SJP
and DCC process.
Chapter 3 – Mathematical modeling
The phenomena occurring in the mixing section of SJP is highly complex
because it is compressible, two-phase, supersonic and highly turbulent and
involves the transfer of heat, mass and momentum. In this chapter it is tried
to present the models which are necessary for simulating the flow in SJP.
Foremost is the theory of DCC model which is developed and used in the
numerical analysis during this research work.
Chapter 4 – Experimental setup and data
This chapter explains the specifications of different SJP geometries used
during the experimentations performed in this study. The SJP geometries are
fabricated of brass and Perspex material and are explained in this chapter.
The various systems installed to measure different flow parameters are also
described in this chapter. The systems described are the pressure measuring
system, temperature measuring system, void fraction measuring system and
the flow visualization system. It also includes the tables of experimental data
generated in this study.
Chapter 5 – Numerical analysis
This chapter includes the details of the numerical simulations which are
carried out in this project. The numerical analyses of a ‘supersonic steam jet
injected into subcooled water tank’ and ‘flow through SJP’ are carried out
using commercial CFD software Fluent 6.3 and the DCC model developed
during this work.
9
Chapter 6 – Results and discussion
The experimental and numerical results of static pressure, static temperature
and void fraction are compared and discussed. Characteristic curves of SJP
are plotted and discussed. The results of flow visualization and numerical
simulations are plotted to study the flow phenomena through SJP.
Chapter 7 – Conclusions and future recommendations
In this chapter the work done during this research work is highlighted. The
main conclusions made by the author during this study are provided. At the
end the recommendations for future study in this field are provided.
10
CHAPTER 2
2 LITERATURE REVIEW
2.1 Jet pump
The technology of jet pump is known for more than a century. It has been
used in chemical and process industry for producing vacuum. It has been
used as a feedwater supply device in locomotives and ships. For the last four
decades it has been used as a jet ejector in the refrigeration cycle. In recent
years it is studied as a proposed system for emergency core cooling and as
feedwater heater and used as jet air ejector to remove non condensable
gasses from the condenser in steam power plants. It has also been used in
food, paper, oil exploration, district heating and water desalination industry.
The jet pump is a general name and there are various names given to it
depending upon the flow, operating conditions and/or fluid type as given
below:
Ejector: It generally describes all types of jet pumps that discharge at
a pressure intermediate between motive and suction pressures.
Injector: It describes all types of jet pumps that use a condensable
gas to entrain a liquid and discharge against a pressure higher than
either motive or suction pressure. It is also called as boiler injector.
Eductor: It is a jet pump that uses liquid as the motive fluid to pump
liquids.
Jet compressor: It is a jet pump used to boost the pressure of gases.
Siphon: It is a jet pump utilizing a condensable vapor, as the motive
fluid, to pump liquids.
11
In the last three to four decades the jet pump has been studied, mainly, as
jet ejector or injector, therefore, this literature review will focus on the
research work done in the past related to jet ejector and injector.
2.1.1 Jet ejector
The review by [17] outlined the developments in mathematical modeling and
design of jet ejectors. The review shows that there are two basic approaches
for ejector analysis. These include mixing of the motive and entrained
mediums, either at constant pressure or at constant area as shown in Figure
2.1 [18].
Figure 2.1: Constant area and constant pressure designs of ejector [18]
Design models of stream mixing at constant pressure are more common in
literature because the performance of the ejectors designed by this method is
more superior to the constant area method and it compares favorably against
experimental data. The constant pressure design procedure was initially
developed by [19]. Subsequently, several investigators have used this model
for designing and evaluating the performance of various types of jet ejectors.
This involved a number of modifications in the model, especially losses within
the ejector and mixing of the motive and entrained streams. In this research
work the constant pressure design was used.
12
Several theoretical models have been suggested and experimental work
carried out to study the performance of jet ejectors [19-23]. Most of these
were applied to cooling and refrigeration systems operating at low
temperature ranges.
Keenan and his coworkers [19, 23] presented a model for analyzing air jet
ejectors. They presented a 1-D model of jet ejector based on ideal gas law in
conjunction with the principles of the conservation of mass, momentum, and
energy.
Gupta and his coworkers [22] developed a theoretical model for steam-vapor
system in a single-stage ejector. The model is used to estimate the motive
steam requirements over an extended range of ejector load.
Eames et al. [21] modified the 1-D model of Keenan and his coworkers [19,
23] by introducing the irreversibilities associated with the nozzle, mixing
section, and diffuser in the model. They also performed experimentation on a
steam jet refrigeration system.
Aphornratana and Eames [24] performed experiments on a small scale steam
ejector refrigerator using ejector with adjustable primary nozzle and showed
that a single optimum primary nozzle position cannot be defined to meet all
operating conditions.
Chen and Sun [25] performed experiments to investigate the characteristics
of the steam ejector refrigeration cycle. It was found that changing the
operating conditions greatly affects both the critical entrainment ratio and the
critical back pressure. They also claimed that the performance characteristics
of steam ejector are better than those ejectors operated with refrigerant
R114.
The review of literatures by [19-23, 26], shows that the design and
development of a steam jet refrigeration system requires a thorough
13
understanding of the flow inside the jet pump, especially, in the mixing
section. In the past, ejectors were designed based on a classical 1-D theory
developed by Keenan and Neumann [19]. However, this theory is applicable,
when the ejector is operated at its critical back pressure and does not include
the effects of the ejector’s geometries. Recently, with the evolution of
computers and numerical solution methods, researchers are attempting to
apply numerical techniques in modeling the flow within ejectors. Their
contributions are discussed below.
Riffat and Omer [27] predicted the performance of a jet ejector using
numerical simulations. The ejector was methanol driven. They did not validate
their results with any experimental data.
Rusly et al. [28] simulated the flow through a jet ejector operated with
refrigerant R141b. They investigated the geometric parameters of ejector
through numerical simulation and validated there results with experimental
data of [29].
Grazzini and Mariani [30] developed a computer program in QuickBasic to
simulate a multi-stage classical one-dimensional system with constant-area
mixing. The results are validated using the experimental results of [21].
Aly et al. [31] presented two different models for simulating the flow through
steam jet ejector. The first model calculates the pressure and velocity by
applying steady-state equations of energy, momentum, and continuity at the
steam nozzle, mixing section and diffuser. The second model assumes the
flow inside the ejector as an ideal gas, and uses the model of a steam-vapor
ejector presented by Eames and his coworkers [21]. The results of these
models are compared with the results of [32].
El-Dessouky et al. [33] presented a semi-empirical model for steam jet ejector
to study the entrainment ratio as a function of the expansion ratio and the
pressures of the entrained vapor, motive steam and compressed vapor. They
14
developed correlations for motive steam pressure at the nozzle exit as a
function of the evaporator and condenser pressures and the area ratios as a
function of the entrainment ratio and the stream pressures.
Rusly et al. [34] developed a one-dimensional model, based on constant
pressure mixing, to determine the constant area section diameter of jet
ejector. The model satisfies the fluid dynamics constraints of constant
pressure mixing and a normal shock in the ejector.
Eames [35] presented a new theoretical model by assuming a constant rate
of momentum change within the diffuser of a supersonic jet pump. As
compared to conventional methods used for the design of jet pump, this new
approach brought a significant improvement in both entrainment ratio and
pressure lift ratio. The results are also validated with experimental results.
Sriveerakul et al. [13-14] used Fluent code to simulate a steam ejector,
equipped in an experimental steam jet refrigeration cycle. The effects of
operating conditions and geometric parameters on the performance of steam
jet ejector are investigated both numerically and experimentally.
Alexis and Rogdakis [36] developed a numerical model for jet pump based on
the theory of [37]. They validated the results of their model with various
experimental results available in literature.
Khattab and Barakat [38] developed a theoretical model for analyzing solar
steam jet cooling cycles for air conditioning. They studied the performance of
solar steam jet cooling system under different design and operating
conditions using this model.
Sun [39] developed a computer program for studying the performance of
ejector refrigeration system. The study is focused on comparing various
refrigerants used in jet ejector refrigeration system.
15
Pianthong and his coworkers [12] studied ejector refrigeration system,
operated on water as the working fluid. They conducted CFD simulations
using Fluent code. The model used is the one used in Chunnanond’s study
[40]. The numerical results are also compared with experimental ones.
2.1.2 Jet injector
Jet injector has been studied by several researchers in the past 20-30 years
and proposed several systems for use in nuclear industry. Injector is getting
more and more attention because of its ability to generate a high back
pressure, even higher than the motive medium inlet pressure, and transfer of
heat to entrained medium. However, the flow phenomenon through the
injector is highly complex. Therefore a lot more effort is required to fully
understand the heat, mass and momentum transfer occurring in the mixing
section of jet injector. With the evolution of computers and development of
numerical techniques, the CFD application to the flow phenomena in jet
injector is becoming an effective tool to understand the physics of the
problem. The experimental and computational efforts of some of the
researchers, related to steam jet injectors, are presented below.
Cattadori and his coworkers [8] performed experiments on steam injector.
The high pressure safety injection system for BWR is considered as the
reference application of this injector. They also presented and applied a
simple one-dimensional mathematical model, called the global model, to this
injector. In this model the mass, momentum and energy balance equations
are applied at the inlet and outlet of each section of the steam injector. The
results calculated with this model are in good agreement with the
experimental one. An important outcome of these experiments is that the
back water pressure is about 10% higher than the inlet steam pressure.
Deberne et al. [10] also applied the one-dimensional global model to simulate
the flow through steam injector. They considered security water injection in
16
steam generators of nuclear reactors as the reference application. They
performed experiments on a 1/12 scaled test facility, designed and built to
represent the desired system of nuclear reactor. Deberne and his co-workers
[10] studied the influence of the mixing section outlet diameter, the inlet
steam pressure and inlet liquid temperature. They reported that accuracy of
the model is about 15%.
Deberne et al. [41] performed experiments to understand the physical laws
driving the flow in the mixing section of a steam injector. They measured void
fraction in the mixing region with Gamma-ray attenuation method and also
visualized the flow in the mixing section with an analog camera. They
reported that at the entrance of the mixing section the flow is characterized
by a strong non-equilibrium of temperatures and velocities and is strongly
dissipative with high production of irreversibilities. Quickly the flow becomes
homogeneous and follows a quasi-isentropic evolution.
Beithou and Aybar [4-7] developed a one-dimensional, steady state, control
volume based computer program to simulate the flow through steam injector.
The geometry of steam injector selected is similar to that experimented by [8]
and the reference application is passive core injection system of a BWR. The
results of the model are validated with the experimental results of Cattadori
and his co-workers [8].
The authors of [42-47] have developed a two-dimensional, two-phase flow
model and embed it in PHOENICS and Star-CD software. They also performed
experiments on a 1/2, 1/5, and 1/7 scaled visualized steam injector models.
The model is used to simulate steam injector-driven passive core injection
system, steam injector-driven primary loop recirculation system and multi-
stage steam injectors driven feedwater heaters of advance BWR. They
claimed that the conventional core coolant injection systems and feedwater
heating systems of nuclear power plant can be replaced efficiently with multi-
17
stage steam injector systems and additional benefits of reduced space, weight
and maintenance of these systems can also be achieved.
Yan et al. [16, 48] studied, experimentally and theoretically, steam injector
for developing a district-heating system and showing the effect of swirling
vanes on the performance of steam jet injector. A simple, 1-D, global model,
used by [8, 10] is employed for theoretical analysis. Experiments are
performed to validate the analysis results. The analysis and experimental data
agree with each other within 15%.
Dumaz and his coworkers [49] studied steam injector with reference to steam
generator emergency feed water system of PWR. They used three different
experimental facilities: a lab-scale facility (IMP-PAN) in Poland, an industrial
scale facility (CLAUDIA) in France and another industrial scale facility (IETI) in
Italy. For CFD simulation CATHARE code is used by modifying it by
introducing heat and momentum transfer correlations based on the results of
CLUDIA tests. This new model is used in a complex WWER plant (Czech
Dukovany Power Plant) input data deck and a quit satisfactory behavior is
obtained calculating a blackout accident.
Shah et al. [3] performed experiments on a lab-scale steam jet pump to study
its suction characteristics. The phenomena of direct-contact condensation in
the mixing region are explored by performing 3-D, steady state CFD
simulations using Fluent 6.3 code and the DCC model developed by the same
authors.
The above literature survey indicates that the past research related to jet
pump is limited to experimental data, empirical correlations, 1-D or 2-D
modeling and simulation. Furthermore, there is no reported study related to
the suction characteristics of steam jet pump. Therefore, in this study it is
aimed to work on the modeling of transport phenomena and suction
characteristics of steam jet pump.
18
2.2 Direct-Contact Condensation (DCC)
In the mixing section of a steam-driven, water-entrained jet pump the two
streams come into direct contact with each other. As a result direct-contact
condensation of saturated steam into subcooled water takes place. The
process of heat, mass and momentum transfer in DCC is highly complicated.
It has been studied extensively in the last two-three decades because of its
importance in a variety of industrial operations such as: underwater
propulsion systems, steam jet pumps, direct feedwater heaters and nuclear
reactor systems (e.g., depressurization system of PWR and pressure
suppression system of BWR). There are many experimental and theoretical
works on the flow involving the process of direct-contact condensation. Some
of them are reported here.
A number of previous investigators [50-52] proposed empirical heat transfer
correlations for DCC of vapor jets into subcooled water. These correlations
are obtained by using a simplified steam-water interfacial area. These results
show that the DCC heat transfer is very efficient heat transport mechanism.
Sonin [53] studied the turbulent intensity near the steam-water interface
using a special apparatus to understand the transport mechanisms across the
interface.
Simpson and Chan [54] experimentally studied DCC in subsonic steam jets.
They observed that the dynamics of subsonic steam jets are quite different
from those of sonic jets and found that the average heat transfer for subsonic
jets is about one-fifth to one-tenth of the sonic jet values.
Weimer et al. [55] developed a theoretical expression for the penetration
length of vapor jets injected into quiescent subcooled liquids of the same
fluid. They assumed vapor jet as axisymetric free jet in which the vapor
bubbles and liquid are dispersed throughout the jet plume.
19
Chen and Faeth [56] presented simplified theoretical models for the
penetration length of the steam jet. They assumed an idealized plume shape
and a homogenous two-phase flow.
Cumo et al. [51] and Tin et al. [57] studied stable and unstable vapor plumes
by presenting stability lines based on the pool temperature and the steam
mass flow rate. The reported that steam mass flux provides a measure of the
driving force exerted on the liquid side of the interface and the pool
temperature represents the magnitude of the thermal driving potential.
Chun et al. [9] presented a steam-water DCC regime map and developed
correlations for an average steam-water DCC heat transfer coefficient and
dimensionless steam plume penetration length for high mass flux of steam.
Chun and his co-workers performed 346 different experiments on steam-
water DCC to perform the above mentioned study.
Kim et al. [11] presented three different models to investigate the DCC heat
transfer, occurring around a stable steam plume, in subcooled water. That is,
the interfacial transport model due to the turbulent intensity, the surface
renewal model’, and the shear stress model’. They validated the results of
these models with experimental results.
Petrovic [58] presented a simple analytical model to trace the interface
between steam and water in direct-contact condensation for four different
shapes of steam plumes. The model is based on the mass, momentum and
energy balance equations and the jump conditions. However, the heat
transfer coefficient and steam plume penetration length are calculated using
semi-empirical equations.
The authors of [59] presented a new three-dimensional condensation regime
diagram for DCC of steam injected into stagnant water and validated the
results with experimental results.
20
Gulawani et al. [60] performed numerical analysis of the DCC of steam into
subcooled water and the results are compared with the published
experimental data. Thermal phase change model of CFX 5.7 is used to model
the heat and mass transfer across the interface.
The authors of [61] used the holographic interferometer and high speed
camera for studying DCC heat transfer coefficients around steam bubbles on
the gravity injection of core makeup tanks. They also investigated
condensation regime maps associated with the downward injection of steam
into water.
Kang and Song [62] simulated the DCC of high pressure steam jet into a
subcooled water tank, with so-called the steam condensation region model
using CFX 4.4. The computational results are validated with the test data.
Wu et al. [15, 63-65] performed experiments on DCC of sonic and supersonic
steam jets in subcooled water tank and studied the plume shape, penetration
length, heat transfer coefficient, condensation regime diagram and axial and
radial temperature profiles. Wu et al. [15] studied supersonic steam jet
condensation phenomena for the first time and presented correlations for
penetration length and condensation heat transfer coefficient.
Shah et al. [2] presented a DCC model to simulate the experimental model of
[15] using Fluent 6.3 code. They compared the 3-D numerical simulation
results of penetration length, condensation heat transfer coefficient and
average heat transfer coefficient with the experimental results of [15] and
validated the DCC condensation model.
The above literature survey related to DCC indicates that the past research is
limited to experimental data and empirical correlations. Therefore, in this
work it is aimed to study the physics of transport phenomena in DCC of steam
jet in subcooled water and develop an analytical model for DCC.
21
2.3 Gamma-Ray Densitometry
In SJP, a steam-water interface is formed in the mixing section. Transfer of
heat, mass and momentum between the phases occur across this interface.
The void fraction in this two-phase region is an important parameter and can
be measured by gamma-ray attenuation technique known as gamma-ray
densitometry. This technique is used worldwide for measurement of void
fraction and density in the field of medical science, chemical and process
industry and for measuring soil bulk density. However, here we restrict
ourselves to its use for the measurement of void fraction in multiphase flow
problems.
Kim et al. [66] used gamma attenuation principle to measure void fraction in
liquid hydrogen which is used as moderator in HANARO research reactor.
Abro and johansen [1] and Tjugum et al. [67] carried out experiments using
multi-beam gamma-ray densitometry to measure void fraction in hydrocarbon
multiphase oil, water and gas pipelines and in oil and gas pipelines,
respectively.
Dong-hui et al. [68] developed a dual-energy gamma-ray attenuation system
to measure the volume fractions of static oil, water and gas multiphase
mixtures. They performed experiments on horizontal pipe flow by using two
different gamma-ray sources of Americium (𝐴𝑚) and Cesium (𝐶𝑠). They
reported that the measurements have acceptable accuracy.
Aslina et al. [69] measured the void fraction in two phase flow with vertical
gamma-ray beam. They used a traversing beam gamma-ray densitometer to
perform the experiments. They studied the cross-sectional phase distribution
of water and kerosene in a horizontal stainless steel section, using gamma-
ray beam.
22
The study of void fraction in the mixing section of SJP is carried out by
Deberne et al. [41], using gamma-ray attenuation method. Using these
experimental results they presented two empirical models for solving the rest
of the parameters (mass flow rates and velocities of the two phases involved)
in the mixing section of SJP.
The above literature related to void fraction measurement in multiphase flow
by gamma-ray densitometry shows that this technique provides an efficient
mean to study the transport phenomena in SJP.
23
CHAPTER 3
3 MATHEMATICAL MODELING
3.1 Introduction to two-phase flow modeling
The steam jet vacuum pumps have no rotating or reciprocating parts, no
lubrication or oil problems, nor extremely close tolerances. It is mechanically
the simplest of all the present-day types of vacuum pumps and compressors.
However, the thermodynamics and fluid-dynamics phenomena producing the
suction and pumping action within the simple converging-diverging nozzles is
highly complex. The flow through steam-jet, water-entrained pump is two-
phase, compressible, supersonic and highly turbulent. The two phases are
separated by a steam-water interface between the fluids. The transfer of
mass, momentum and energy between the phases occur across this interface.
Therefore, the mathematical modeling of SJP, especially of the phenomena
occurring in the mixing section, requires high level of technical skill and
experience [2-3, 5-8, 10, 43-47, 49].
Two approaches are very common while modeling two-phase flows: the
Euler-Lagrangian approach and the Euler-Euler approach [5, 8, 10, 16, 49].
The Euler-Lagrange approach is suitable for flows in which the dispersed
phase occupies a low volume fraction. In this approach the continuous phase
is treated as a continuum by solving the time-averaged Navier-Stokes
equations (Euler approach) and the dispersed phase is solved by tracking a
large number of particles, bubbles or droplets through the calculated flow
field (Lagrange approach). This model is appropriate for modeling of spray
dryers, coal and liquid fuel combustion, and some particle-laden flows, but
inappropriate for modeling of liquid-liquid mixtures, fluidized beds, or any
application where the volume fraction of the second phase is not negligible.
The second formulation, the Euler-Euler approach, provides a more general
method of modeling two-phase flows. In this model the two phases are
24
treated as interpenetrating continua and the volume fractions are assumed to
be continuous functions of space and time and their sum is equal to one.
Each phase has a separate set of conservation equations and these equations
are closed by empirical relations. The above mentioned complexities in the
flow through SJP suggest the application of two-fluid model from an Euler-
Euler point of view.
Modeling of DCC is a hot topic, because there is no direct-contact
condensation model available which can be used universally and accurately
for all types of flows involving DCC. In this study a mathematical model of
DCC is developed and used for numerical simulation of SJP. The realizable
𝑘 − 휀 model is used for capturing the characteristics of flow turbulence and
symmetric model is used for drag calculations. The details of these models
are given below.
3.2 Euler-Euler two-phase flow model
Three different Euler-Euler two-phase flow models are generally used. These
models are:
The Volume of fluid Model (VOF)
The Mixture model
The Eulerian model
The Volume of fluid model is a surface tracking model and is applied to flows
involving two or more immiscible phases. It is applied to flows where the
position of the interface between the phases is of interest. A single
momentum equation is shared by the phases, and the volume fraction of each
phase in each computational cell is tracked throughout the computational
domain.
25
The Mixture model is applied to flows where two or more phases are mixed to
form a homogeneous mixture. The mass, momentum and energy
conservation equations are solved for the mixture.
The Eulerian model is the most complex model and, theoretically speaking,
can be applied to all sort of two or multiphase flows. Computationally, it is the
most expensive model because a separate set of mass, momentum and
energy equations is solved for each phase. Coupling between the phases is
achieved through pressure and interphase exchange coefficients.
In this study, the two phases involved (steam and water) have higher
gradients of temperature and velocity and accompanies the mass transfer
(condensation) across the interface; therefore, the Eulerian model is selected
for CFD analysis.
A detailed derivation of this model is available in literatures [70-71]; however
the summary of its main equations is given below:
3.2.1 Mass balance equation
In Eulerian two-phase flow model two separate mass balance equations, one
for each phase, are required to keep track of the mass of the flow inventory
in a thermal hydraulics system. For a multiphase flow system with 𝑛 phases,
the mass balance equation for phase 𝑞 is given by:
𝜕
𝜕𝑡 𝛼𝑞𝜌𝑞 + 𝛻. 𝛼𝑞𝜌𝑞𝒗𝑞 = 𝑚 𝑝𝑞 −𝑚 𝑞𝑝
𝑛
𝑝=1
+ 𝑆𝑞 (3.1)
Where 𝛼𝑞 , 𝜌𝑞 , 𝒗𝑞 and 𝑆𝑞 are the volume fraction, physical density, flow
velocity and source terms for phase 𝑞 and 𝑚 𝑝𝑞 and 𝑚 𝑞𝑝 describe the mass
transfer from phase 𝑝 to 𝑞 and from phase 𝑞 to 𝑝, respectively.
26
The Eq. 3.1 is similar to its counterpart in single phase flow except for the
volume fraction and mass transfer terms. The volume fraction accounts for
the fact that each computational cell is occupied by different phases in their
respective fraction. Thus, in multiphase flows volume fraction is also an
unknown like temperature or velocity. The volume of phase 𝑞, 𝑉𝑞 is defined
as:
𝑉𝑞 = 𝛼𝑞𝑑𝑉𝑉
(3.2)
and
𝛼 = 𝛼𝑞
𝑛
𝑞=1
= 1 (3.3)
The effective density of phase 𝑞, 𝜌 𝑞 , is:
𝜌 𝑞 = 𝛼𝑞𝜌𝑞 (3.4)
The mass transfer terms represent the mass gained or lost across the
interface by evaporation or condensation of phase 𝑞. They depend strongly
on the interfacial heat transfer and dispersed phase particle diameter and will
be discussed later on in this chapter.
3.2.2 Momentum balance equation
Like mass balance equation, the Eulerian two-phase flow model solves two
equations for momentum balance, one for each phase. The momentum
balance equation for phase 𝑞, in a multiphase mixture of different phases is
given by:
27
𝜕
𝜕𝑡 𝛼𝑞𝜌𝑞𝒗𝑞 + 𝛻. 𝛼𝑞𝜌𝑞𝒗𝑞𝒗𝑞 = −𝛼𝑞𝛻𝑃 + 𝛻. 𝝉𝑞 + 𝛼𝑞𝜌𝑞𝒈
+ 𝑹𝑝𝑞 +𝑚 𝑝𝑞𝒗𝑝𝑞 −𝑚 𝑞𝑝𝒗𝑞𝑝
𝑛
𝑝=1
+ 𝑭𝑞 + 𝑭𝑙𝑖𝑓𝑡 ,𝑞 + 𝑭𝑣𝑚 ,𝑞
(3.5)
Where 𝑃, 𝝉𝒒 and 𝒈 are the pressure of the flow field, stress-strain tensor of
phase 𝑞 and the body force. While, 𝑭𝑞 , 𝑭𝑙𝑖𝑓𝑡 ,𝑞 , 𝑭𝑣𝑚 ,𝑞 and 𝑹𝑝𝑞 are the
external body force, lift force, virtual mass force and phases interaction force
on phase 𝑞.
3.2.3 Energy balance equation
There are two separate energy balance equations, one for each phase, in
two-phase Eulerian model. The energy balance equation for phase 𝑞, in a
multiphase flow of n phases is given by:
𝜕
𝜕𝑡 𝛼𝑞𝜌𝑞𝑞 + 𝛻. 𝛼𝑞𝜌𝑞𝒗𝑞𝑞 = −𝛼𝑞
𝜕𝑃𝑞
𝜕𝑡+ 𝝉𝑞 ∶ 𝛻𝒗𝑞 − 𝛻𝒒𝑞
+𝑆𝑞 + 𝑄𝑝𝑞 +𝑚 𝑝𝑞𝑝𝑞 −𝑚 𝑞𝑝𝑞𝑝
𝑛
𝑝=1
(3.6)
Where 𝑞 and 𝒒𝑞 are the specific enthalpy and heat flux of phase 𝑞, and
𝑝𝑞 , 𝑞𝑝 and 𝑄𝑝𝑞 are the enthalpy of phase 𝑝 converting to phase 𝑞,
enthalpy of phase 𝑞 converting to phase 𝑝 and the intensity of heat
transferring from phase 𝑝 to phase 𝑞 respectively. The above mentioned
equations of Eulerian model and other multiphase flow models are given in
many literatures like [70-71].
28
3.3 Mathematical modeling of DCC
In the mixing section of SJP saturated steam and subcooled water come into
direct contact with each other. The steam forms a cone in the central region
of the mixing section and this cone of steam is surrounded by the entrained
subcooled water. The two phases are separated by an interface between
them. Beside mass transfer, there occurs a transfer of heat and momentum
across the interface. In other word the phenomena of DCC in SJP is highly
complex and require a suitable steam condensation model to properly
simulate the flow through SJP. The DCC model which is developed in this
work is validated in [2-3]. It is used to simulate the DCC between steam and
water. An introduction of the DCC model is given below.
3.3.1 Assumptions of DCC model
The DCC model is applied to determine the heat, mass and momentum
transfer across the interface. A typical vapor-liquid interface is shown in
Figure 3.1. The condensation model, used in this study, is based on the
following assumptions:
Vapor bubbles are assumed of spherical shape.
The heat entering and leaving the interface balance each other.
The interface is assumed to be at saturation conditions at the local
pressure.
Vapor is assumed superheated or at least saturated.
Liquid is assumed subcooled or at the most saturated.
Condensation is assumed to occur at saturation conditions.
Evaporation of liquid phase is negligible.
29
Figure 3.1: A typical vapor-liquid interface
3.3.2 The Direct-Contact Condensation (DCC) model
The rate of condensation across the interface is determined by performing an
energy balance at the vapor-liquid interface. That is the rate of energy
transferred from vapor to the interface must be equal to the rate of energy
transferred from the interface to the liquid phase, under steady state
conditions. Key parameters affecting the rate of energy transfer across the
interface are: interfacial area, interfacial heat transfer coefficients and
interfacial mass transfer. The DCC model developed and used in this study is
based on these three parameters. These are discussed below.
30
3.3.2.1 Interfacial area
The contact area between the continuous liquid phase and the dispersed
vapor bubbles (interfacial area) is an important parameter in DCC to estimate
the rate of mass transfer. Estimation of volumetric heat transfer coefficients
on the vapor and liquid sides of the interface requires an estimate of the
interfacial area per unit volume (𝐴𝑓𝑔 ), across which heat transfer takes place.
For spherical vapor bubbles of diameter 𝑑𝑔 and volume fraction 𝛼𝑔 in a liquid,
the interfacial area per unit volume of the vapor phase is estimated by;
𝐴𝑓𝑔 =6𝛼𝑔
𝑑𝑔 (3.7)
Eq. (3.7) shows that the interfacial area is dependent on the vapor bubble
diameter 𝑑𝑔 . Thus vapor bubble diameter is an important parameter in
estimating the heat, mass and momentum transport across the interface. The
mean bubble diameter is modeled as a linear function of local liquid
subcooling (𝑇𝑠 − 𝑇𝑓) and its relation is given in Eq. (3.8). 𝑇𝑠 and 𝑇𝑓 are the
local saturation and liquid temperatures respectively.
𝑑𝑔 =𝑑1 𝜃 − 𝜃0 + 𝑑0(𝜃1 − 𝜃)
𝜃1 − 𝜃0
(3.8)
Where 𝑑0 and 𝑑1 are the bubble diameters at the reference liquid subcoolings
𝜃0 and 𝜃1 respectively. Outside this subcooling range the vapor bubble
diameter is assumed constant and equal to 10−3 𝑚. The reference subcoolings
and bubble diameters used are 𝑑0 = 1.5 × 10−4 𝑚 at 𝜃0 = 13.5 𝐾 and
𝑑1 = 1.5 × 10−3 𝑚 at 𝜃1 = 0 𝐾. The bubble diameter model given in Eq.
(3.8) is originally presented in [72] and also used in CFX 4.2.
31
3.3.2.2 Interfacial heat transfer
To perform the heat and mass transfer calculations across the interface the
heat transfer coefficients between fluids are required. To calculate the heat
transfer at the interface two-resistance model is used. In this model the heat
transfer across the interface is modeled in two steps: (i) heat transfer from
vapor to the interface and (ii) heat transfer from interface to the liquid. Thus
the heat transfer phenomena in DCC is characterized by two heat transfer
coefficients one on the vapor side and the other on the liquid side of the
interface.
At the vapor side of the interface it is assumed that the heat generated is
completely transferred to the interface. This treatment may be called as zero
resistance model. Thus a large heat transfer coefficient on the vapor side of
the interface 𝑔 is assumed to bring the vapor temperature quite close to the
saturation temperature [2, 73].
𝑔 = 104 𝑊
𝑚2 −𝐾 (3.9)
𝐻𝑔 = 𝑔𝐴𝑓𝑔 (3.10)
Where 𝐻𝑔 represent the volumetric heat transfer coefficient on the vapor side
of the interface.
On the liquid side of the interface the heat transfer coefficient, which is
known as condensation heat transfer coefficient, is generally related to the
Nusselt number of the liquid phase 𝑁𝑢𝑓, thermal conductivity of the liquid 𝑘𝑓
and vapor bubble diameter 𝑑𝑔 as given below.
𝑓 =𝑘𝑓𝑁𝑢𝑓
𝑑𝑔 (3.11)
32
The 𝑁𝑢𝑓 is calculated using the correlation of [74] as given below.
𝑁𝑢𝑓 = 2.0 + 0.6𝑅𝑒0.5𝑃𝑟0.33; 0 ≤ 𝑅𝑒 < 776.06, 0 ≤ 𝑃𝑟 < 250
2.0 + 0.27𝑅𝑒0.62𝑃𝑟0.33 ; 776.06 ≤ 𝑅𝑒, 0 ≤ 𝑃𝑟 < 250 (3.12)
𝑅𝑒 is the relative Reynolds number based on the diameter of the vapor
bubble 𝑑𝑔and the relative velocity of the two phases 𝑈𝑔 − 𝑈𝑓 .
𝑅𝑒 =𝜌𝑓 𝑈𝑔 − 𝑈𝑓 𝑑𝑔
𝜇𝑓 (3.13)
𝑃𝑟 is the Prandtl number of the liquid phase and is defined as;
𝑃𝑟 =𝐶𝑝𝜇𝑓
𝑘𝑓 (3.14)
The volumetric heat transfer coefficient 𝐻𝑓 for liquid phase is;
𝐻𝑓 = 𝑓𝐴𝑓𝑔
(3.15)
Where 𝑘𝑓 is the thermal conductivity, 𝜇𝑓 is the coefficient of viscosity, 𝐶𝑝 is
the specific heat, 𝐻𝑓 is the volumetric heat transfer coefficient on the liquid
side and 𝑓 is the condensation heat transfer coefficient of the liquid phase.
An upper limit has been placed on the liquid side volumetric heat transfer
coefficient 𝐻𝑓 . This limit is called umbrella restriction and is used to force the
coefficient to small values as the void fraction of the vapor phase approaches
0 or 1 [75]. The expression is:
33
𝐻𝑓 = min[𝐻𝑓 , 17539 max{4.724,472.4𝛼𝑔 1− 𝛼𝑔 }
× max{0, min 1,𝛼𝑔 − 1.0 × 10−10
0.1 − 1.0 × 10−10 }]
(3.16)
According to Koncar and Mavko [75] this umbrella restriction has no physical
basis, but is used to avoid code failure due to errors in water property caused
by high condensation rates. However, this umbrella restriction may reduce the
condensation heat transfer coefficient considerably, causing independence of
the calculation results on the type of correlations used.
3.3.2.3 Interfacial mass transfer
In DCC phenomena the location of the interface depends on the condensation
rate. Therefore, to accurately locate the interface an accurate modeling of the
mass transfer mechanism is required. On the other hand, the transfer of mass
accompanies the transfer of heat and momentum therefore the model should
be able to incorporate their effects. As mentioned earlier the condensation
rate is determined by performing an energy balance at the interface. The rate
of energy transfer from vapor phase to the interface 𝑞𝑔 is given by;
𝑞𝑔 = 𝑔(𝑇𝑠 − 𝑇𝑔) (3.17)
Where 𝑇𝑔 represents the local temperature of vapor phase. Similarly the rate
of energy transfer from interface to liquid phase 𝑞𝑓 is assumed to be a
function of local liquid subcooling (𝑇𝑠 − 𝑇𝑓).
𝑞𝑓 = 𝑓(𝑇𝑠 − 𝑇𝑓) (3.18)
34
The heat fluxes from the vapor phase to interface 𝑄𝑔 and from the interface
to the liquid phase 𝑄𝑓 are estimated by the following relations.
𝑄𝑔 = −𝑞𝑔 +𝑚 𝑓𝑔𝐻𝑔𝑠 (3.19)
𝑄𝑓 = −𝑞𝑓 −𝑚 𝑓𝑔𝐻𝑓𝑠 (3.20)
The interphase mass transfer 𝑚 𝑓𝑔 is derived from the total heat balance at
the interface i.e., the heat entering the interface is equal to the heat leaving
the interface. As a result of this energy balance the mass transfer rate is
calculated by the following relation.
𝑚 𝑓𝑔 =𝑞𝑓 + 𝑞𝑔
𝐻𝑔𝑠 − 𝐻𝑓𝑠 (3.21)
𝐻𝑔𝑠 and 𝐻𝑓𝑠 are the local saturation enthalpies of vapor and liquid phases.
3.4 Turbulence model
Various turbulence models are available to model the turbulence
characteristics of fluid flows. In this study the flow is highly turbulent at the
vapor-liquid interface and, therefore, the realizable 𝑘 − 휀 turbulence model is
used. The term realizable means that the model satisfies certain mathematical
constraints on the Reynolds stresses, consistent with the physics of turbulent
flows. Neither the standard 𝑘 − 휀 model nor the RNG 𝑘 − 휀 model is
realizable. As compared to standard 𝑘 − 휀 turbulence model, this model has
the following two modifications.
It has a new formulation for calculating the turbulence viscosity.
35
It has a new formulation for calculating the dissipation rate 휀 derived
from an exact equation for the transport of the mean-square vorticity
fluctuation.
This model provides more accurate results to predict the spreading rate of
both planar and round jets. It is likely to provide more accurate results to
model the flows involving rotation, boundary layers under strong adverse
pressure gradients, separation, and recirculation [70].
One of the weaknesses of the standard 𝑘 − 휀 model or other traditional 𝑘 − 휀
models lies with the modeled equation for the dissipation rate 휀. The well-
known round-jet anomaly is considered to be mainly due to the modeled
dissipation equation. The realizable 𝑘 − 휀 model proposed by [76] is intended
to address these deficiencies of traditional 𝑘 − 휀 models. One limitation of the
realizable 𝑘 − 휀 model is that it produces non-physical turbulent viscosities in
situations when the computational domain contains both rotating and
stationary fluid zones (e.g., multiple reference frames, rotating sliding
meshes). This is due to the fact that the realizable 𝑘 − 휀 model includes the
effects of mean rotation in the definition of the turbulent viscosity [70]. The
mathematical equations of multiphase realizable 𝑘 − 휀 model are very
complex and lengthy and are, therefore, not produced here. However, they
are mentioned in [70, 76].
3.5 Interfacial drag model
The interfacial drag is modeled using a model known as the symmetric model.
In Eulerian multiphase flow model the coupling between the phases is
achieved by interphase exchange coefficients. The fluid-fluid exchange
coefficient 𝐾𝑓𝑔 is calculated using the following expression to incorporate the
symmetric model of interfacial drag.
36
𝐾𝑓𝑔 =𝛼𝑔(𝛼𝑓𝜌𝑓 + 𝛼𝑔𝜌𝑔)𝑓𝑑
𝜏𝑓𝑔 (3.22)
𝜏𝑓𝑔 =(𝛼𝑓𝜌𝑓 + 𝛼𝑔𝜌𝑔)𝑑𝑔
2
18(𝛼𝑓𝜇𝑓 + 𝛼𝑔𝜇𝑔) (3.23)
𝑓𝑑 =𝐶𝐷𝑅𝑒
24 (3.24)
𝐶𝐷 =
24 1 + 0.15𝑅𝑒0.687 𝑅𝑒
; 𝑅𝑒 ≤ 1000
0.44; 𝑅𝑒 > 1000
(3.25)
Where 𝑓𝑑 is the drag function, 𝜏𝑓𝑔 is the particulate relaxation time and 𝐶𝐷 is
the drag coefficient. The symmetric model is generally used for flows in which
the secondary (dispersed) phase in one region of the domain becomes the
primary (continuous) phase in another. Further details of this model are given
in [70].
3.6 1D supersonic nozzle design
In SJP the motive steam passes through a converging-diverging nozzle. At the
exit of steam nozzle the flow should be sonic or supersonic to create suction
in the vicinity of steam nozzle exit. In this study a steam nozzle is designed
based on 1-D, isentropic compressible flow theory. It is assumed that the
steam passing through the steam nozzle behaves like a perfect gas. Figure
3.2 shows a converging-diverging nozzle in which the nozzle inlet section is
named as section 1, the throat as the sonic throat and the exit section as
section 2. The sonic values are represented with a superscript ‘*’ and the
stagnation values are represented with subscript ‘o’. The known and unknown
parameters and the algorithm for designing this 1-D nozzle are given below.
37
Figure 3.2: A typical converging-diverging nozzle
The know parameters are;
𝑃1=fluid pressure at nozzle inlet
𝑇1=fluid temperature at nozzle inlet
𝑚 =mass flow rate at an average inlet pressure
𝑑1=steam nozzle inlet diameter
𝑃2=flow pressure at nozzle exit (An assumed vacuum)
The unknown parameters are;
𝑑∗=sonic throat diameter
𝑑2=nozzle exit diameter
The steps of algorithm are;
The density, cross-sectional area, velocity, speed of sound and Mach
number at inlet of the nozzle are calculated by the following equations.
𝜌1 =𝑃1
𝑅𝑇1
(3.26)
38
𝐴1 =𝜋
4𝑑1
2
(3.27)
𝑣1 =𝑚
𝜌1𝐴1
(3.28)
𝑎1 = 𝛾𝑅𝑇1 (3.29)
𝑀1 =𝑣1
𝑎1
(3.30)
The total temperature, total pressure, total density and total speed of
sound at inlet of the nozzle are calculated by the following equations.
𝑇𝑜 = 𝑇1(1 +𝛾 − 1
2𝑀1
2) (3.31)
𝑃𝑜 = 𝑃1(1 +𝛾 − 1
2𝑀1
2)𝛾
(𝛾−1) (3.32)
𝜌𝑜 =𝑃𝑜
𝑅𝑇𝑜 (3.33)
𝑎𝑜 = 𝛾𝑅𝑇𝑜 (3.34)
The sonic values of throat cross-sectional area, diameter, temperature,
pressure density and speed of sound are calculated by the following
equations.
𝐴∗ =𝐴1
1𝑀2
[ 2
𝛾 + 1 1 +
𝛾 − 12
𝑀12 ]
(𝛾+1)2(𝛾−1)
(3.35)
39
𝑑∗ = 𝐴∗4
𝜋 (3.36)
𝑇∗ = 𝑇𝑜2
𝛾 + 1 (3.37)
𝑃∗ = 𝑃𝑜 (2
𝛾 + 1)𝛾𝛾−1 (3.38)
𝜌∗ = 𝜌𝑜(2
𝛾 + 1)
1𝛾−1 (3.39)
𝑎∗ = 𝑎𝑜(2
𝛾 + 1)
12 (3.40)
The sonic mach number, velocity, temperature, speed of sound, mach
number, cross-sectional area and diameter at nozzle exit are calculated
by the following equations.
𝑀2∗ =
𝛾 + 1
𝛾 − 1(1−
𝑃2
𝑃𝑜)𝛾−1𝛾 (3.41)
𝑣2 = 𝑀2∗𝑎∗
(3.42)
𝑇2 = 𝑇∗(𝑃2
𝑃∗)𝛾−1𝛾 (3.43)
𝑎2 = 𝛾𝑅𝑇2 (3.44)
𝑀2 =𝑣2
𝑎2
(3.45)
40
𝐴2 = 𝐴∗1
𝑀2
[ 2
𝛾 + 1 1 +
𝛾 − 1
2𝑀2
2 ](𝛾+1)
2(𝛾−1) (3.46)
𝑑2 = 𝐴2
4
𝜋 (3.47)
The nozzle designed, based on the above algorithm, will be able to accelerate
the inlet fluid to a supersonic speed.
41
CHAPTER 4
4 EXPERIMENTAL SETUP AND DATA
4.1 Introduction to experimental setup
Experiments have been performed to study the transport phenomena
occurring in SJP. Besides generating valuable data about SJP the
experimentation also helped to validate the DCC model developed during this
study. The experiments were conducted at different operating conditions of
the motive steam and entrained water, using different geometries of SJP. The
parameters measured during the experimentation include axial static
pressure, axial static temperature, inlet and outlet mass flow rates and
volume fraction. Some of the geometries were made of transparent material
to visualize the two phase flow in the mixing section, using high speed
photography. The experimental setup and its schematic diagram are shown in
Figure 4.1 and Figure 4.2 respectively. SJP geometry and various systems
installed to measure different parameters are discussed in the subsequent
articles.
Figure 4.1: The experimental setup
42
Figure 4.2: Schematic diagram of the experimental setup
4.2 Steam jet pump geometry
As mentioned in § 1.2, SJP consists of four parts namely:
Steam nozzle
Water nozzle
Mixing section
Diffuser
These parts were made of either brass or perspex material and there
geometric configurations and other details are given below. Figure 4.3 shows
a complete SJP geometry made of brass and fitted in the experimental
system.
43
Figure 4.3: SJP made of brass
4.2.1 Steam and water nozzles
The steam and water nozzles used in this research work have been made of
brass. The steam nozzle was designed according to the 1-D compressible
model algorithm described in § 3.6. The steam nozzle has been used to
accelerate the saturated steam, entering it, to supersonic speed at the exit.
The water nozzle was designed to circulate the entrained water uniformly
around the steam nozzle. The steam nozzle (SN)and water nozzle (WN) have
been fabricated according to the drawing shown in Figure 4.4. The
geometries of steam and water nozzles were kept unchanged during the
experimentation. The fabricated brass geometries of steam and water nozzles
were assembled into a single geometry as shown in Figure 4.5. The pressure
and temperature have been measured at three different locations along the
axis of steam nozzle and at a single location (exit point) in the water nozzle.
Some of the details of steam and water nozzles (SN, WN) are mentioned in
Table 4.1.
44
Figure 4.4: Drawing of steam and water nozzles
Figure 4.5: Fabricated steam and water nozzles made of brass
45
4.2.2 Mixing section and diffuser
The mixing section may be called as the heart of SJP, because, the pumping
action is produced due to the processes occurring in this section. The flow in
the mixing section of SJP is, generally, two-phase, compressible and
supersonic. The transport of mass, momentum and energy occur across the
steam-water interface in this section. To study the transport process in detail,
the mixing section has been fabricated in different dimensions. The diffuser
has the role to convert velocity head into pressure head and increase the
back pressure in SJP.
Four different mixing sections named as M1, M2, M3 and M4 and two
different diffusers D1 and D2 were used in the experiments. The details of the
dimensions and materials of mixing sections and diffusers are given in Table
4.1. The mixing section M1 and the Diffuser D1 were made as a single
geometry i.e., they are integral parts. However, the other geometries of
mixing section (M2, M3 and M4) and diffuser (D2) were made in parts to
simplify their fabrication. Moreover, the converging and throat parts of the
mixing section were also made separately and joined through flanges. The
mixing sections (M2, M3 and M4) and diffuser (D2) have been made of
perspex to visualize the two-phase flow occurring in this section through high
speed photography. Figure 4.6 shows the coupled geometry of mixing section
and diffuser made of perspex. In total there were four complete geometries
of SJP (SJP1, SJP2, SJP3 and SJP4), whose configurations are given in Table
4.2. The geometries and dimensions of four different combinations of mixing
sections and diffusers are shown in Figure 4.7.
46
Figure 4.6: Mixing section and diffuser made of perspex
Table 4.1: Geometric and material specification of SJP geometries used in the
experiments
SJP
Length (mm) Diameter (mm)
Material Converging
section
Throat Diverging
section
Inlet Throat Outlet
Steam
nozzle (SN) 37.3 0.0 12.7 15.87 6.1 7.12 Brass
Mix
ing
sect
ion
M1 100.0 10.0 - 24.00 15.5 15.50 Brass
M2 80.0 30.0 - 24.00 15.0 15.00 Perspex
M3 100.0 30.0 - 26.00 15.0 15.00 Perspex
M4 120.0 30.0 - 27.50 15.0 15.00 Perspex
Dif
fuse
r D1 - - 100.0 15.50 - 30.00 Brass
D2 - - 110.0 15.00 - 30.65 Perspex
Water
nozzle (WN) 77.4 24.00 - - Brass
47
Table 4.2: Configurations of SJP geometries used in experimentation
Geometry Of SJP Steam nozzle Water nozzle Mixing section Diffuser
SJP1 SN WN M1 D1
SJP2 SN WN M2 D2
SJP3 SN WN M3 D2
SJP4 SN WN M4 D2
Figure 4.7: Mixing section and diffuser combinations for SJP1, SJP2, SJP3 and SJP4
geometries of SJP (dimensions in mm)
48
4.3 Pressure and temperature measuring systems
The static pressure and temperature of the fluid have been measured
experimentally at various locations along the axis of SJP. The pressure was
measured using pressure transmitters and pressure gauges, while the
temperature was measured using K-type thermocouples. Within the SJP
geometry the static pressure and temperature were measured at nine
different locations. For all geometries, the pressure and temperature were
measured at three points along the axis of steam nozzle (MP1, MP2 and
MP3), one point at the exit of water nozzle, three points along the axis of
mixing section (MP4, MP5 and MP6) and two points along the axis of diffuser
(MP7 and MP8). The details of the axial distances (𝑥) of the measurement
points along the axis of different geometries of SJP are given in Table 4.3.
The details of different systems are given below.
Table 4.3: Axial distance of measurement points for SJP geometries
Geometry Of SJP MP1
(mm)
MP2
(mm)
MP3
(mm)
MP4
(mm)
MP5
(mm)
MP6
(mm)
MP7
(mm)
MP8
(mm)
SJP1 0 17.8 37.3 85 120 155 205 260
SJP2 0 17.8 37.3 77 104 145 215 270
SJP3 0 17.8 37.3 84 118 165 235 290
SJP4 0 17.8 37.3 90 130 185 255 310
4.3.1 Pressure transmitters
The suction pressure at the exit of water nozzle was measured by pressure
transmitter Dwyer® model, 626-00C-CH-P1-E5-S1-LED. It measures the
suction pressure in inches of mercury. It has his own display and can also be
connected to an external display unit. Its accuracy is 0.25%. The pressure at
other eight locations along the length of SJP was measured by pressure
transmitters Aplisens® model PCE-28. Its accuracy is 0.2%. The current
produced by the flow pressure is converted to voltage in the outer measuring
49
circuit as shown in Figure 4.8. The pressure transmitters and other systems
installed on the experimental setup are shown in Figure 4.9.
Figure 4.8: Circuit to linkup pressure transmitter to DAC channel
Figure 4.9: Various systems installed on the experimental setup
50
4.3.2 Data acquisition systems
Two different data acquisition systems were used; one for measuring the
static pressure and the other for measuring the temperature along the axis of
the SJP. Iotech® data acquisition system, model Personnel DAQ 3000 series
was used for measuring the pressure and Pico® data logger was used for
measuring the temperature. These data acquisition systems are shown in
Figure 4.1 and Figure 4.9. The data acquisition systems were interfaced to a
personal computer to record the pressure and temperature data at run time.
4.4 Void fraction measuring system
The void fraction in the mixing section of steam jet pump has been measured
by gamma-ray densitometry technique. The principle of gamma-ray
densitometry is based on the fact that the intensity of gamma rays, passing
through matter, decreases exponentially. Based on this principle, the void
fraction 𝛼 of two-phase flow in a pipe can be calculated with the following
equation.
𝛼 =𝑙𝑛(𝐼𝑚𝑖𝑥 /𝐼𝑤 )
𝑙𝑛(𝐼𝑠/𝐼𝑤 ) (4.1)
Where 𝐼𝑤 and 𝐼𝑠 correspond to 100% water and steam, respectively and
𝐼𝑚𝑖𝑥 is the measured intensity which depends on the amount of water and
steam across the x-section of the two-phase region. The contribution of
scattered photons detected is assumed to be negligible in the above equation.
The contribution of scattered photons depends on several parameters, like
pipe material, pipe thickness and the presence of a collimator etc.
The schematic diagram of densitometry setup, used in this study, is shown in
Figure 4.10. A gamma densitometer consists of two principal components; a
gamma source and a detector unit. These were placed on a supporting plate
51
on opposite sides of the mixing section of SJP. The supporting plate was
bolted to a universal table which was placed on an iron table specially
designed and fabricated for this setup. The universal table and thus the
supporting plate were able to move 20 cm in horizontal direction along the
axis of SJP. Collimator structures were used to ensure the production of a
narrow gamma-ray beam. The source side collimator was fan-type in the
vertical direction only to allow the gamma-ray photons to pass through the
whole x-section of the mixing section as shown in the side view of Figure
4.10. The detector side collimator was placed such that to allow only the
gamma-rays passing through a specific x-section to reach the detector.
Figure 4.10: Schematic diagram of densitometry system
Gamma source used for these experiments was Caesium-137 (Cs-137) having
half-life of about 30.17 years and strength of 5 mille-curies to provide beam
of gamma photons. The source was contained in lead brick (8″×4″×2″) with
tapered hole in it to produce fan-type collimated gamma-ray beam. The
52
individual gamma photons were detected by NaI (Tl) (Sodium iodide doped
with thallium) scintillation detector (2″×2″) and a photomultiplier. NaI
detector was used in this study due to its high detection efficiency for gamma
radiation. The whole setup was properly shielded with lead bricks to minimize
the effect of scattered photons being detected by the detector. The
experimental setup, detector and counting system are shown in Figure 4.11.
The counter was set to measure the number of gamma-ray photons detected
per 10 seconds.
Figure 4.11: The densitometry setup, detector and counter
53
4.5 Flow visualization system
As mentioned before, the flow in the mixing section for a steam-driven water-
entrained SJP is two-phase. The two phases are separated by an interface
between them. The flow phenomena in the mixing section are highly complex
due to direct transfer of heat, mass and momentum across the interface
between the two phases involved. Three geometries of mixing section are
made of perspex so as to visually observe the steam-water interface and
steam jet in this section. A high speed camera is used for flow visualization. A
snap shot of the transparent mixing section of SJP is shown in Figure 4.12.
Figure 4.12: Transparent geometry of SJP installed on the experimental setup
54
4.6 Experimental data
Experiments were performed on SJP to generate experimental data as per
research objectives described in chapter-1. The steam inlet pressure and
temperature and water nozzle suction pressure and temperature are the
independent variables. While the steam inlet mass flow rate, water inlet mass
flow rate, water outlet mass flow rate, static pressure and temperature along
the axis of SJP and the gamma-ray counts for void fraction calculations along
the mixing section are the dependent (measured) variables. As mentioned
earlier, four different SJP geometries were experimented. The experimental
data for geometry SJP2 related to gamma-ray counts, void fraction and the
uncertainty in void fraction at axial distance (𝑥) along SJP is mentioned in
Table 4.4 to Table 4.8. Similarly the experimental data for steam and water
mass flow rates, mass ratio and suction lift for geometry SJP2 of SJP is
mentioned in Table 4.9. The same data for other three geometries (SJP1,
SJP3, and SJP4) is given in the Appendix B-D. The procedures adopted for
calculating the uncertainty in void fraction and the suction lift are mentioned
in Appendix A.
Table 4.4: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 108620±385 104845±434 123044±411 0.22 3.0
65 107856±465 104029±539 120505±433 0.25 4.0
80 94607±501 92392±428 100133±532 0.29 8.0
95 105610±378 102243±544 115300±482 0.27 4.5
110 110637±454 109472±535 120423±436 0.11 6.3
125 113238±487 112980±322 125873±498 0.02 4.7
140 114394±567 114198±512 127865±529 0.01 5.9
155 116394±399 116265±437 129657±465 0.01 4.6
170 117313±471 117285±525 130457±519 0.00 5.6
55
Table 4.5: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 108929±401 104845±434 123044±411 0.24 3.1
65 108124±425 104029±539 120505±433 0.26 3.8
80 94649±471 92392±428 100133±532 0.30 7.6
95 106859±478 102243±544 115300±482 0.37 4.8
110 113094±351 109472±535 120423±436 0.34 4.9
125 115286±411 112980±322 125873±498 0.19 4.0
140 114456±471 114198±512 127865±529 0.02 5.3
155 116291±457 116265±437 129657±465 0.00 5.0
170 117288±510 117285±525 130457±519 0.00 5.9
Table 4.6: Void fraction data for SJP2 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 108954±399 104845±434 123044±411 0.24 3.1
65 109628±447 104029±539 120505±433 0.36 3.8
80 94846±462 92392±428 100133±532 0.33 7.5
95 105312±398 102243±544 115300±482 0.25 4.7
110 112902±513 109472±535 120423±436 0.32 6.0
125 116662±501 112980±322 125873±498 0.30 4.5
140 115309±478 114198±512 127865±529 0.09 5.2
155 116273±428 116265±437 129657±465 0.00 4.8
170 117289±485 117285±525 130457±519 0.00 5.7
56
Table 4.7: Void fraction data for SJP2 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 108965±457 104845±434 123044±411 0.24 3.3
65 109915±587 104029±539 120505±433 0.37 4.3
80 95262±521 92392±428 100133±532 0.38 8.1
95 105875±501 102243±544 115300±482 0.29 5.1
110 112456±486 109472±535 120423±436 0.28 5.9
125 115654±399 112980±322 125873±498 0.22 3.9
140 116458±475 114198±512 127865±529 0.17 4.9
155 116401±387 116265±437 129657±465 0.01 4.6
170 117298±409 117285±525 130457±519 0.00 5.3
Table 4.8: Void fraction data for SJP2 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 108969±426 104845±434 123044±411 0.24 3.2
65 109916±523 104029±539 120505±433 0.37 4.0
80 95676±541 92392±428 100133±532 0.43 8.3
95 106834±411 102243±544 115300±482 0.36 4.4
110 112670±458 109472±535 120423±436 0.30 5.7
125 116609±321 112980±322 125873±498 0.29 3.3
140 118939±399 114198±512 127865±529 0.36 4.1
155 119606±426 116265±437 129657±465 0.26 4.2
170 117385±512 117285±525 130457±519 0.01 5.8
57
Table 4.9: Flow rates, mass ratio and suction lift data at different steam inlet and
water suction pressures for SJP2 geometry
𝑃𝑠 (𝐾𝑃𝑎)
𝑃𝑠𝑢𝑐 (𝑖𝑛 𝑜𝑓 𝐻𝑔)
𝑚 𝑤 ,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑠,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑜𝑢𝑡
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑖𝑛
𝑚 𝑠,𝑖𝑛
Suction
Lift (𝑚)
140 -2.5 0.1445 0.0060 0.1505 24.08 1.15
140 -3.0 0.1102 0.0060 0.1162 18.37 1.33
140 -3.5 0.0818 0.0060 0.0878 13.63 1.51
160 -2.5 0.2923 0.0069 0.2992 42.36 1.13
160 -3.0 0.2207 0.0069 0.2276 31.99 1.32
160 -3.5 0.1659 0.0069 0.1728 24.04 1.50
160 -4.0 0.1220 0.0069 0.1289 17.68 1.67
160 -4.5 0.0918 0.0069 0.0987 13.30 1.85
180 -2.5 0.4182 0.0081 0.4263 51.63 1.09
180 -3.0 0.3277 0.0081 0.3358 40.46 1.29
180 -3.5 0.2219 0.0081 0.2300 27.40 1.49
180 -4.0 0.1679 0.0081 0.1760 20.73 1.67
180 -4.5 0.1317 0.0081 0.1398 16.26 1.85
180 -5.0 0.1018 0.0081 0.1099 12.57 2.02
180 -5.5 0.0700 0.0081 0.0781 8.64 2.20
200 -3.0 0.5008 0.0092 0.5100 54.43 1.24
200 -3.5 0.4621 0.0092 0.4713 50.23 1.42
200 -4.0 0.3505 0.0092 0.3597 38.10 1.63
200 -4.5 0.2610 0.0092 0.2702 28.37 1.83
200 -5.0 0.2046 0.0092 0.2138 22.24 2.01
200 -5.5 0.1500 0.0092 0.1592 16.30 2.19
220 -4.0 0.6592 0.0102 0.6694 64.63 1.51
220 -4.5 0.4903 0.0102 0.5005 48.07 1.76
220 -5.0 0.4300 0.0102 0.4402 42.16 1.95
220 -5.5 0.3800 0.0102 0.3902 37.25 2.14
58
CHAPTER 5
5 CFD SIMULATIONS
5.1 Introduction and aims of CFD simulations
In the past three to four decades, the rapid development of numerical
techniques and computer hardware has made the numerical simulation of
thermal hydraulics problems more and more convenient and attractive. A
number of CFD codes are now available in the market, like; Fluent, CFX, Star-
CD, PHOENICS, and many others. These codes are capable of simulating the
transient and steady state fluid dynamics problems in 3-D coordinates. In this
study a mathematical model of DCC of steam into water has been presented.
The model is able to study two-phase steam-water flow in which the two
phases are separated by an interface between them. To validate the model
and simulate the complex phenomena of DCC, in 3-D, the framework of
Fluent 6.3 code was used. Fluent 6.3 provide the option of adding a user
defined model to the simulation. The main aims of conducting CFD
simulations are listed below.
To study the heat, mass and momentum transfer phenomena in DCC.
To simulate the process of DCC of supersonic steam jet into subcooled
water.
To validate the DCC model developed during this research and
explained in § 3.3.
To study the characteristics of SJP by simulating the flow through it
using DCC model.
To study different flow parameters in DCC problems.
Due to complicated nature of the transport phenomena involved, the 3-D
simulations of DCC of supersonic steam jet into subcooled water is a difficult
task to achieve. To validate the DCC model and study the transport
59
phenomena in problems related to DCC two different problems have been
simulated. They are a supersonic steam jet injected into a subcooled water
tank and pumping of subcooled water using SJP. The CFD simulations of
these problems include many steps which have been discussed below in
detail.
5.2 A supersonic steam jet injected into a subcooled water
tank
The problem of a supersonic steam jet injected into a subcooled water tank
has been numerically simulated to validate the DCC model, developed during
this study. The results of the CFD simulations have been compared with the
experimental results of Wu et al. [15] and critically analyzed against the
compressible flow theory of supersonic flows. These results are shown in
appendix A. The geometry of nozzle fitted water tank being simulated has
been shown in Figure 5.1. The steps performed to conduct CFD simulations
have been discussed below.
Figure 5.1: Nozzle fitted water tank geometry being simulated
60
5.2.1 Geometry and mesh
The geometry of the nozzle fitted water tank, shown in Figure 5.1, was
constructed in 3-D coordinates because, the DCC phenomena are very
complex and 2-D assumption is not valid. Gambit 2.2 has been used as a pre-
processor to construct the geometry and mesh. The water tank and steam
nozzle geometries, generated and meshed in Gambit software, are shown in
Figure 5.2.
Figure 5.2: Meshed geometry of water tank and steam nozzle
A tetrahedral mesh was used to mesh the nozzle as well as the water tank.
Along the axis of the steam nozzle (x-direction) there were 913 grid points
and near the exit of steam nozzle the mesh was relatively finer. Along the
outer boundaries of the tank there were 67 grid points in the x-direction. In
61
the y-direction the maximum and minimum numbers of grid points were 228
and 34 and in the z-direction the corresponding grid points were 201 and 35
respectively. In the y and z-directions the maximum grid points were along
the plane passing perpendicularly through the exit of steam nozzle. The
meshed plane passing perpendicularly through the exit of steam nozzle is
shown in Figure 5.3. This mesh is finer near the exit of the steam nozzle and
is coarser towards the outer boundaries.
Figure 5.3: Meshed plane at the exit of steam nozzle
5.2.2 Boundary conditions
To obtain a converged and correct solution from a CFD simulation, proper
boundary conditions must be applied. After generating geometry and mesh
the boundary conditions were applied. The inlet section of the steam nozzle
was selected as the pressure boundary by specifying the value of pressure at
this section. The outer surface of steam nozzle was selected as the adiabatic
wall boundary. The outer surface of the simulated tank is far away from
steam jet therefore, it was assumed that the pressure at the outer surface is
equal to ambient pressure to allow free entrainment across this surface. With
62
this setting of boundary conditions the tank may be assumed to be an infinite
tank. The numerical values of different parameters used as boundary
conditions are given in [2] and mentioned in Table 5.1.
Table 5.1: Boundary conditions used for nozzle fitted water tank geometry
Steam pressure at nozzle inlet, 𝑃𝑠/𝑀𝑃𝑎
Steam temperature at nozzle inlet, 𝑇𝑠/𝐾
Water Temperature in tank, 𝑇𝑤/𝐾
Ambient pressure, 𝑃𝑎/𝑀𝑃𝑎
Throat diameter of nozzle, 𝑑𝑡/𝑚𝑚
Exit diameter of nozzle, 𝑑𝑒/𝑚𝑚
0.3
Saturated
293-343
0.099
2.0
3.0
5.2.3 CFD Models applied
After setting the boundary conditions, the meshed geometry file was exported
to Fluent for applying different models and carrying out the CFD simulations.
The following settings were made in Fluent before starting the simulations.
Three dimensional steady state analyses were carried out.
Eulerian Multiphase model was selected for simulations.
Realizable 𝑘 − 휀 turbulence model was selected.
Steam and water were selected as the two phases involved.
Steam was treated as a compressible fluid using the ideal gas law and
water as incompressible fluid
The drag force between the phases was modeled by selecting the
symmetric model.
DCC model was embedded in the Fluent code as User Defined
Function.
DCC model was selected for modeling the mass transfer
(condensation) across the interface.
SIMPLE coupled-implicit solver was selected for solving the non-linear
governing equations.
63
Upwind and power law schemes were selected for the discretization of
different equations.
The algebraic multigrid solver was selected. It performs computations
on finer mesh and no coarse meshes have to be constructed or stored,
and no fluxes or source terms need to be evaluated on the coarse
levels.
After setting the above mentioned models, the simulations were started. The
above mentioned models involve a lot of computations to be performed at
each computational cell. The mesh selected was tetrahedral and total number
of computational cells was more than 0.3 million. Therefore obtaining a
converged solution took three-four weeks on a core2Duo PC system having
speed of 2.66 GHz.
5.3 Flow through steam jet pump
After validating the DCC model with the simulation of a supersonic steam jet
injected into subcooled water tank, the model was used to simulate the flow
through SJP. The results of these simulations have been compared with the
experimental data on SJP, generated during this research work. Besides
further validating the DCC model, the results of these simulations helped to
understand the transport phenomena in SJP. The steps involved in these
simulations have been discussed below.
5.3.1 Geometry and mesh
Four Different geometries of SJP (SJP1, SJP2, SJP3 and SJP4), mentioned in §
4.2, were generated and meshed using the same pre-processor (Gambit) as
used in the previous problem. However, instead of tetrahedral mesh, this time
a combination of tetrahedral and hexahedral mesh was used to mesh the flow
domain. The meshed geometry of one of the SJP geometries used in this
study has been shown in Figure 5.4. The total number of cells, generated in
64
SJP geometries, was around 70,000 with a minimum cell volume of 0.1 𝑚𝑚3
and the maximum cell volume of 24.3 𝑚𝑚3.
Figure 5.4: Meshed geometry of SJP, A: Full geometry with surface mesh, B:
enlarged and sectioned view showing surface meshes
5.3.2 Boundary conditions
Four geometries of SJP have been numerically simulated at different
operating conditions. The steam nozzle inlet section was selected as inlet
pressure boundary. The water nozzle inlet section was also selected as the
inlet pressure boundary. The walls of steam nozzle, water nozzle, mixing
section and diffuser were taken as adiabatic wall boundaries, while the outlet
section of the diffuser was selected as the outlet pressure boundary. The
65
numerical values of different parameters used as boundary conditions have
been given in Table 5.2.
Table 5.2: Boundary conditions used for SJP geometries
Steam inlet pressure, 𝑃𝑠𝑎/𝐾𝑃𝑎 140, 160, 180, 200, 220
Steam inlet temperature, 𝑇𝑠𝑎/𝐾 Saturated
Water nozzle pressure, 𝑃𝑤𝑐 /𝐾𝑃𝑎 93.56,92.92, 91.87, 90.38, 89.30
Water nozzle temperature, 𝑇𝑤𝑐 /𝐾 290
Water exit pressure, 𝑃𝑤𝑓 /𝐾𝑃𝑎 96-115
5.3.3 CFD models applied
After setting the boundary conditions, the meshed geometry files of SJP were
exported to Fluent for applying different models and carrying out the 3-D
steady state simulations. The same CFD models and settings have been used
in the simulations of SJP as used in the previous problem, given in § 5.2.3.
The mesh was a combination of hexahedral and tetrahedral cells in the SJP
problem and the total number of computational cells was below 0.1 million.
The simulations are performed on a core2Duo PC system having speed of
2.66 GHz. Each simulation took five-seven days in the simulation of SJP
problem.
66
CHAPTER 6
6 RESULTS AND DISCUSSION
6.1 Introduction
In this research work a mathematical model has been developed to study,
model and simulate the transport phenomena in direct-contact condensation
of steam into subcooled water. Two different problems of DCC have been
simulated in this study. The first problem, a supersonic steam jet injected into
subcooled water tank, was simulated to validate the DCC model developed
during this research work. The parameters studied were the dimensionless
plume length, condensation and average heat transfer coefficients, radial and
axial temperature distributions and the steam plume shape. The results of the
CFD simulations have been compared with the experimental results of [15]
and critically analyzed against the compressible flow theory of supersonic
flows. The results of these simulations have been mentioned in [2] and
appendix A. However, the results of simulations of second problem, pumping
of subcooled water using SJP, have been mentioned and discussed here.
These results further validate the DCC model and provide a good insight of
the flow phenomena occurring in SJP. The results of simulations of various
parameters in SJP have been compared with the experimental data obtained
in this work. These results are given and discussed in the subsequent articles.
6.2 Static pressure
Fluid static pressure in SJP is an important parameter because the suction
and pumping action is produced only when a certain pressure difference is
created between the water tank and the exit of water nozzle. The axial static
pressure for all geometries of SJP (SJP1, SJP2, SJP3 and SJP4) was measured
experimentally and computed numerically through 3-D CFD simulations and
has been shown in Figure 6.1-Figure 6.44. The study was conducted at steam
67
inlet pressure range of 140-220 KPa, due to lab safety protocol and design
limitations. The experimental and CFD results (Figure 6.1-Figure 6.44)
matched closely with each other for all geometries of SJP (SJP1, SJP2, SJP3
and SJP4) studied in this work. The behavior of fluid static pressure in
different sections of SJP has been discussed below.
Figure 6.1: Axial wall static pressure profile for SJP1 geometry of SJP
6.2.1 Axial wall static pressure in steam nozzle
According to 1-D compressible flow theory [77-78] if the flow through
converging-diverging nozzle is subsonic the fluid will expand in the converging
section and compress in the diverging part resulting in a decrease in pressure
in the converging section and increase in pressure in the diverging section. In
this case the nozzle will operate more like an incompressible flow nozzle and
68
the diverging part will behave like a diffuser. However if the nozzle is
supersonic the fluid will expand and pressure will decrease in the converging
section to attain sonic conditions. In the diverging section the fluid continues
to expand and as a result the fluid pressure decreases and the flow is
supersonic. However, shock wave may occur at the exit to compensate for
the difference between the exit and back pressures. In this case, due to the
presence of sonic throat, maximum mass flows through the nozzle for the
given fixed upstream conditions. Under such conditions the nozzle is said to
be choked.
Figure 6.2: Axial wall static pressure profile for SJP2 geometry of SJP
In Figure 6.1-Figure 6.4 the pressure decreased in the steam nozzle (0-50
mm length) in the converging as well as diverging section. At the exit of
steam nozzle (Figure 6.1-Figure 6.4) an abrupt increase in the pressure was
69
observed. According to the above discussion on compressible flows it might
be concluded that the steam nozzle was supersonic and choked for the
operating steam inlet pressure range (140-220 KPa). A sudden change
observed in axial pressure at the steam nozzle exit indicates the presence of
shock wave at this location. This phenomenon has also been reported by [3,
5-7] for such type of flows. The experimental and CFD results in the steam
nozzle Figure 6.1-Figure 6.4 are in good agreement with each other.
Therefore, besides validating the DCC model, these results also validates the
design of supersonic steam nozzle for the operating flow conditions used in
this study.
Figure 6.3: Axial wall static pressure profile for SJP3 geometry of SJP
The behavior of axial pressure in different geometries of SJP (SJP1, SJP2,
SJP3 and SJP4) has similar trends, provided the steam inlet pressure was kept
70
constant. The reason is that a single steam nozzle was used in all the
experiments related to SJP.
Figure 6.4: Axial wall static pressure profile for SJP4 geometry of SJP
6.2.2 Axial wall static pressure in mixing section
The flow in the mixing section of SJP is highly complex due to the reason that
the flow here is two-phase, compressible, supersonic and highly turbulent.
The experimental and numerical results of the axial fluid pressure in this
section are shown in Figure 6.1-Figure 6.4 for all the SJP geometries (SJP1,
SJP2, SJP3 and SJP4) studied. At the exit of steam nozzle or entrance of
mixing section an abrupt pressure change can be observed in Figure 6.1-
Figure 6.4. According to the supersonic compressible flow theory [77-78] this
might be due to the normal shock wave at this location to account for the
71
pressure difference between the steam nozzle and the mixing section. The
pressure stabilizes quickly to sub atmospheric pressure due to sudden
expansion of the supersonic steam in the mixing section as shown in Figure
6.1-Figure 6.4.
The pressure in the mixing section is almost constant due to continuous
condensation. At the completion of condensation again an abrupt pressure
increase can be observed in the mixing section that might be due to
condensation shock [79]. A stronger condensation shock has been observed
at high steam inlet pressures in geometry SJP2 (Figure 6.2) as compared to
other geometries studied.
The transport of heat, mass and momentum in the mixing section of SJP
takes place across the steam-water interface surrounding the steam plume
(steam jet). At high steam inlet pressures (200 and 220 KPa) the
condensation shock occurs at the exit of mixing section in all the geometries
studied. This indicates that the steam plume at high steam pressures extends
the whole length of the mixing section. The surface area of the steam-water
interface at high steam inlet pressures (200 and 220 KPa) is smaller for
geometry SJP2 due to its minimum length of the mixing section (80+30 mm,
mixing section of SJP2) among all the geometries studied. To accomplish the
same rate of heat, mass and momentum transfer across the smaller surface
area (interface) in the mixing section of SJP2 geometry there are two
possibilities that either:
The steam plume expands in radial direction to acquire greater surface
area.
The entrained water mass flow rate is increased.
These complicated phenomena can be explained that initially the steam
plume expands in radial direction to acquire greater surface area (interface).
As a result of excessive expansion, a greater suction pressure is achieved in
72
the mixing section. In response to greater suction in the mixing section, the
entrained water mass flow rate increases. The increased mass flow rate, of
the entrained water, improves the condensation rate which again reduces the
surface area of the steam-water interface. The interface continues to vibrate
in and out till equilibrium is reached as a result of a compromise between the
above mentioned two possibilities. This argument is also supported by more
negative pressure, observed, in the mixing section of SJP2 geometry at high
steam inlet pressures (Figure 6.2 (D and E)) as compared to other
geometries. This phenomenon may be called as the interface vibration
phenomenon in DCC of SJP.
For geometries SJP1 and SJP3 the length of the converging part of the mixing
section was same (100 mm) and the inlet and outlet diameters and the length
of throat section were different. But no major difference in the axial pressure
profiles was observed for these two geometries (Figure 6.1 andFigure 6.3).
This might be due to the strong dependence of condensation process on the
length of the converging part of the mixing section.
6.2.3 Axial wall pressure distribution in diffuser
The axial static pressure distribution in the diffuser section has the same
trend for all the geometries (SJP1, SJP2, SJP3 and SJP4) as shown in Figure
6.1-Figure 6.4. Along this section the flow is incompressible and due to
diverging shape the pressure head increases at the cost of velocity head.
6.2.4 Back pressure investigation
The pressure at the exit of SJP is called the back pressure. The back pressure
or the exit mass flow rate of SJP can be varied with the help of back pressure
valve. In different experiments the back pressure valve was adjusted to have
a constant mass flow rate at the exit. The exit mass flow rate was kept
constant to be able to compare and investigate the back pressure behavior of
73
different geometries. The experimental results of axial pressure distribution
have been obtained for different geometries (SJP2, SJP3 and SJP4) at a
steam inlet pressure of 220 KPa and at a constant exit mass flow rate (0.3
Kg/s, arbitrary value). The numerical results were obtained, for the same
geometries of SJP, by enforcing the experimentally measured values of back
pressures at the outlet boundaries. The experimental and computational
results are shown in Figure 6.5. It was observed that, for the same outflow,
geometry SJP2 can develop higher back pressure as compared to SJP3 and
SJP4 geometries. The suction pressure in the mixing section and
condensation shock were also stronger in geometry SJP2 as compared to
other geometries. These results also support the interface vibration
phenomenon in DCC of SJP.
Figure 6.5: Axial wall pressure distribution at higher back pressure
74
6.3 Temperature distribution
Like pressure, temperature is also an important parameter in the thermal
hydraulics of SJP. As mentioned earlier, the flow in the mixing section of SJP
is two-phase, compressible and condensing which further increases the
importance of temperature in this section. The fluid temperature was
measured experimentally at selected axial locations of SJP as mentioned in
Table 4.3 and computed numerically throughout the flow domain. The axial
and radial temperature distributions for different geometries of SJP are
discussed below.
Figure 6.6: Axial static temperature profile for SJP1 geometry of SJP
75
6.3.1 Axial temperature distribution
The fluid temperature was measured experimentally at selected axial
locations for all four geometries of SJP (SJP1, SJP2, SJP3 and SJP4). These
experimental results were compared with the cross-section averaged axial
temperatures obtained from CFD simulations of the same geometries and
shown in Figure 6.6-Figure 6.9.
Figure 6.7: Axial static temperature profile for SJP2 geometry of SJP
76
Figure 6.8: Axial static temperature profile for SJP3 geometry of SJP
The temperature in the steam nozzle (Figure 6.6-Figure 6.9) was observed to
decrease due to expansion in the converging as well as diverging part. This
behavior is in agreement with the supersonic compressible flow theory [77-
78] mentioned earlier. The temperature of the fluid was seen to increase at
the start and then decreases towards the end of the mixing section. As
mentioned earlier a shock wave can occur at the junction of steam nozzle and
mixing section. This shock might have caused the temperature to increase
initially, however at the same time, mixing with subcooled water and
condensation of steam produces cooling effect which decreases the fluid
temperature. At high steam inlet pressure the periodic increase and decrease
in temperature has been observed. According to the supersonic compressible
flow theory and the past research work [2-3, 15, 64] the supersonic steam jet
submerged into subcooled water undergoes a series of periodic compression
77
and expansion. These periodic compression and expansion cause the steam
temperature to increase and decrease periodically. This phenomenon was
studied and observed experimentally by [15, 63-65], while injecting steam jet
into subcooled water tank. Figure 6.10 shows the corresponding experimental
results of [65].
Figure 6.9: Axial static temperature profile for SJP4 geometry of SJP
78
Figure 6.10: Steam jets showing periodic compression-expansion [65]
At the exit of mixing section (entrance of diffuser) condensation has
completed and the flow is single phase and incompressible. Therefore, the
temperature of the flow remains constant in the diffuser (Figure 6.6-Figure
6.9). The comparison of experimental and computational results of axial
temperature shows a close agreement between them, thus supporting the
DCC model and CFD simulations.
6.3.2 Radial temperature distribution
Radial temperature was not measured experimentally in this research work.
However, the simulation results have been presented here to explain the flow
phenomena in the mixing section of SJP. The radial temperature distribution
at various steam inlet pressures and different axial locations (x) along the
length of SJP are shown in Figure 6.11 for SJP1 geometry. The temperature,
towards the outer radial direction at x=50 mm, first increases and then
decreases as shown in Figure 6.11 (A). The reason might be the expansion of
the steam in the diverging part of the steam nozzle. This expansion causes
the pressure and temperature along the axis of SJP to decrease at the exit of
steam nozzle. The same behavior of radial temperature has previously been
reported for supersonic steam jets experimentally by [15]. Figure 6.11 also
shows that the temperature of the steam decreases rapidly with axial distance
79
(x) due to steam condensation and expansion of steam jet in the mixing
section.
As mentioned before, the supersonic steam jet submerged into subcooled
water undergoes a series of periodic compression and expansion. These
periodic compression and expansion cause the steam temperature to increase
and decrease periodically. In Figure 6.11 (A-D) the effect of these periodic
compression and expansion can be seen. For example in Figure 6.11 (D) the
maximum value of steam temperature belongs to the case with Ps=180 KPa
instead of Ps=220 KPa.
Figure 6.11: CFD results of radial temperature distribution for SJP1 geometry of SJP
at six different axial locations (x)
80
Another important observation related to Figure 6.11 is that the radial
temperature is asymmetric over the axis of SJP. The asymmetric behavior is
probably due to the periodic compression and expansion waves in the steam
flow. Due to this asymmetric behavior such type of flows cannot be accurately
simulated in two-dimensional axisymmetric domain.
6.4 Operational characteristics of SJP
Mass ratio, entrained water mass flow rate and suction lift are important
parameters to study the performance and suction characteristics of SJP. The
mass ratio is defined as the ratio of mass flow rate of entrained water and
motive steam. It represents the amount of sucked water per unit of steam
consumed. The suction lift is defined as the theoretical maximum depth from
which the SJP is able to suck water under different operating conditions.
Suction lift has been calculated using the Bernoulli’s equation as mentioned in
appendix A. The characteristic curves related to entrained water mass flow
rate, mass ratio and suction lift are plotted in Figure 6.12-Figure 6.23 for all
four SJP geometries (SJP1, SJP2, SJP3 and SJP4) studied.
During the experimentation the water tank at the suction side was kept at
atmospheric pressure (measured to be 96 KPa) and the water level in the
tank was maintained at a depth of one foot from the axis of SJP. The water
nozzle exit pressure was controlled by a valve between the water tank and
the water nozzle. It was observed during the experiments that at a constant
steam pressure, closing the valve gradually, the water mass flow rate
decreases and the negative pressure at the water nozzle exit increases. In
this study, the negative pressure in the water nozzle was varied by adjusting
the valve position to simulate the suction lift. It was also observed that
increasing the steam inlet pressure causes the negative pressure in the water
nozzle to increase, provided the valve position is not changed. Keeping the
81
above discussion in mind it will now be tried in the subsequent articles to
throw light on the performance and operational characteristics of SJP.
6.4.1 Mass flow rate
Entrained water mass flow rate variation as a function of steam inlet pressure
and water nozzle suction pressure (negative pressure) are shown in Figure
6.12-Figure 6.15 for all four SJP geometries (SJP1, SJP2, SJP3 and SJP4)
studied.
Figure 6.12: Entrained water mass flow rate curves for SJP1 geometry of SJP
It was observed (Figure 6.12-Figure 6.15) that the water mass flow rate
increases with increasing the steam inlet pressure, provided the water nozzle
negative pressure (suction lift) is kept constant. The reason is that, while
82
increasing the steam pressure, constant suction pressure at water nozzle can
be maintained only by opening the valve. On the other hand the water flow
rate decreases with increasing the negative suction pressure (suction lift),
provided the steam inlet pressure is kept constant. The reason is obvious that
the negative pressure increases by closing the valve at constant steam
pressure.
Figure 6.13: Entrained water mass flow rate curves for SJP2 geometry of SJP
The rate of increase of entrained water mass flow rate for geometry SJP1
shown in Figure 6.12 increases with increasing the steam pressure at lower
values of suction pressure (suction lift). However, this rate of increase in
mass flow rate with steam pressure decreases at higher values of suction
pressure. In terms of performance of SJP this behavior of SJP1 geometry can
be stated as it has better performance while pumping against shallow depths.
83
In case of geometry SJP2 (Figure 6.13) the behavior of entrained water mass
flow rate is somewhat opposite to geometry SJP1. At low suction pressure
(suction lift) and low steam pressure the rate of increase in mass flow rate
decreases with steam pressure. However, at high values of suction pressure
Figure 6.14: Entrained water mass flow rate curves for SJP3 geometry of SJP
and high values of steam pressure the entrained water mass flow rate
increases sharply. Unlike geometry SJP1, higher suction pressure values (-2.5
to -5.5 inch of Hg) are achieved with geometry SJP2 while operating in the
same range of steam inlet pressure (140-220 KPa). This implies that
geometry SJP2 is able to suck water against greater depth (suction lift) as
compared to geometry SJP1. Also it might give better performance when
pumping against higher depths. The length and inlet diameter of the mixing
section for geometry SJP1 and SJP2 are same (110 mm and 24 mm).
84
However, the shorter length of the converging part in geometry SJP2 (80
mm) as compared to SJP1 (100 mm) forces an efficient and quick
condensation (mass transfer) of the steam especially at high steam pressure.
This results in speedy transfer of energy and momentum from motive steam
to entrained water in the mixing section.
Figure 6.15: Entrained water mass flow rate curves for SJP4 geometry of SJP
The entrained water mass flow rate curves for geometries SJP3 and SJP4 are
shown in Figure 6.14 and Figure 6.15. The mixing sections of these two
geometries have greater lengths and inlet diameters as compared to SJP1 and
SJP2 geometries. Therefore, within the operated range of steam inlet
pressure (140-220 KPa) they don't exhibit sharp increase in mass flow rates
with steam pressure. However, the trend of these curves at high steam
85
pressure indicates that these geometries may show better performance when
operated at steam pressure higher than 220 KPa.
6.4.2 Mass Ratio
Mass ratio, also known as jet coefficient, is an important performance index
to describe the discharge mass flux of SJP. The characteristic curves of mass
Figure 6.16: Mass ratio curves for SJP1 geometry of SJP
ratio as a function of steam nozzle inlet pressure and water nozzle suction
pressure (suction lift) for geometries SJP1, SJP2, SJP3 and SJP4 are shown in
Figure 6.16-Figure 6.19. It is seen in these figures that mass ratio is directly
proportional to steam inlet pressure, provided that water suction pressure is
kept constant, and is inversely proportional to water nozzle suction pressure
86
(suction lift) provided that steam inlet pressure is kept constant. The same
behavior was reported previously by [7, 16] for steam jet injector.
Figure 6.17: Mass ratio curves for SJP2 geometry of SJP
For geometry SJP1 the maximum mass ratio was 62.08 at water suction
pressure of -3.0 inch of Hg, whereas for geometry SJP2 its maximum value
was 64.63 at water suction pressure of -4.0 inch of Hg. The water suction
pressure of – 4.0 inch of Hg corresponds to a greater depth (suction lift) as
compared to -3.0 inch of Hg. It indicates that geometry SJP2 has a higher
value of mass ratio while pumping against a greater depth as compared to
geometry SJP1.
87
Figure 6.18: Mass ratio curves for SJP3 geometry of SJP
Figure 6.19: Mass ratio curves for SJP4 geometry of SJP
88
Maximum values of mass ratio for geometry SJP3 and SJP4 are smaller and
correspond to smaller values of water nozzle suction pressure (suction lift) as
compared to SJP3 and SJP4 geometries.
6.4.3 Suction lift
Suction lift is defined as the theoretical maximum depth from which the SJP is
able to suck water under different operating conditions. In order to calculate
the suction lift the Bernoulli’s equation was applied between the water tank
and the exit of water nozzle. The water tank was at atmospheric pressure
(measured to be 96 KPa) and the exit pressure of water nozzle was measured
during the experiments at different steam pressures for geometries SJP1,
SJP2, SJP3 and SJP4.
Figure 6.20: Suction lift curves for geometry SJP1 of SJP
89
Figure 6.21: Suction lift curves for geometry SJP2 of SJP
The values of suction lift calculated for different SJP geometries are tabulated
in chapter-4 and appendix B. Figure 6.20-Figure 6.23 show the suction lift
curves as a function of steam inlet pressure and water suction pressure. It
was observed in these figures that increasing the negative suction pressure of
water, increases the suction lift provided the steam pressure is kept constant.
This indicates that at higher values of water suction pressure the pump is able
to suck water from a greater depth. However, increasing the steam pressure
causes the suction lift to decrease slightly, provided the suction pressure is
kept constant. The reason is that experimental values of water flow rate are
90
used to calculate the velocity at water nozzle exit which includes the effect of
friction losses (proportional to square of velocity). Since the flow rate
increases with steam pressure, therefore, at high steam pressure the suction
lift decreases. This behavior is quite prominent in Figure 6.20 andFigure 6.21
(for geometries SJP1 and SJP2) as compared to Figure 6.22 andFigure 6.23
(for geometries SJP3 and SJP4).
Figure 6.22: Suction lift curves for geometry SJP3 of SJP
91
Figure 6.23: Suction lift curves for geometry SJP4 of SJP
The reason is that higher flow rates are achieved with geometries SJP1 and
SJP2 as compared to SJP3 and SJP4, which increases the friction losses in
these geometries at high steam pressure. Since maximum water nozzle
suction pressure (-5.5 inch of Hg) and the maximum suction lift (2.2 m) have
been produced by geometry SJP2, therefore, this geometry is able to operate
against higher depths as compared to geometries SJP1, SJP3 and SJP4. The
above discussion also supports the interface vibration phenomenon in DCC of
SJP, mentioned previously.
6.5 Void fraction distribution and flow visualization
As mentioned earlier the flow in the mixing section of SJP is highly
complicated being compressible, two-phase, supersonic and turbulent.
Therefore, the flow in this region was studied with more attention to
92
rigorously validate the DCC model and study the transport phenomena. The
void fraction in the mixing section is measured by gamma-ray densitometry
technique and visualized using high speed photography. The experimental
results of void fraction are compared with the CFD simulation results for
geometries SJP1, SJP2, SJP3 and SJP4 as shown in Figure 6.24-Figure 6.27.
The uncertainty in experimental values of void fraction was calculated and
plotted in these figures. The void fraction variation in the mixing section of
SJP also indicates the periodic expansion and compression of the steam jet.
These periodic compression and expansion increases with the steam inlet
pressure. At low steam pressure the steam jet condenses quickly and a short
steam plume is formed. However, at high steam pressure the steam plume
extends the whole length of the mixing section.
Figure 6.24: Void fraction distribution in the mixing section for SJP1 geometry of SJP
93
Figure 6.25: Void fraction distribution in the mixing section for SJP2 geometry of SJP
The values of void fraction in the mixing section of geometry SJP2 (Figure
6.25) are relatively high as compared to geometry SJP1 (Figure 6.24). Thus
the steam jet in geometry SJP2 exhibits a greater radial expansion as
compared to geometry SJP1. Similarly geometry SJP1 has higher values of
void fraction as compared to geometries SJP3 and SJP4 (Figure 6.24Figure
6.26 and Figure 6.27). These results also support the interface vibration
phenomenon in DCC inside SJP. These results also support the higher values
of suction lift and water flow rates for geometry SJP2 as compared to other
geometries of SJP. Similarly geometry SJP1 has better performance than
geometries SJP3 and SJP4.
95
Figure 6.27: Void fraction distribution in the mixing section for SJP4 geometry of SJP
For geometries SJP2, SJP3 and SJP4 of SJP the mixing section and diffuser
have been made of perspex to visualize the flow in the two-phase region.
Flow visualization was made in the converging part of the mixing section only,
because, the flow in the throat part of the mixing section was not visible due
to coupling arrangement. Similarly the flow in the diffuser section was not
visualized because it was single phase. A high speed camera was used for this
purpose.
96
Figure 6.28: Steam jet in the mixing section of SJP2 geometry of SJP
Figure 6.29: Steam jet in the mixing section of SJP3 geometry of SJP
97
Figure 6.30: Steam jet in the mixing section of SJP4 geometry of SJP
The visualized steam jets for geometries SJP2, SJP3 and SJP4 are shown in
Figure 6.28-Figure 6.30, at different steam inlet pressures. These figures
show that at low steam inlet pressure the steam jet condenses quickly within
the converging part of the mixing section. However, at high steam pressure
the steam jet (steam plume) extends beyond the converging part of the
mixing section. The periodic compression and expansions are also visible in
these steam jets. Thus flow visualization results also support the DCC model,
numerical simulations and gamma ray densitometry results qualitatively.
6.6 CFD results
Four different geometries (SJP1, SJP2, SJP3 and SJP4) of SJP were simulated
numerically, using Fluent code and DCC model. Some of these CFD results
have been presented in [3], whereas some are presented here. The
comparison and matching of experimental and numerical results of various
flow parameters discussed in the above articles strongly validate the DCC
98
model. Moreover, the CFD results provide great insight of the transport
phenomena occurring in SJP.
6.6.1 Contours of mass transfer
The DCC model developed and used in the CFD simulations takes care of the
mass transfer across the steam-water interface in the mixing section of SJP.
The transfer of mass accompanies the transfer of momentum and energy
across the interface, which complicates the transport phenomena. Therefore,
an accurate calculation of the mass transfer was required to properly model
the transport phenomena across the interface. The contours of mass transfer
in x-y plane, modeled with DCC model, are shown in Figure 6.31 for geometry
SJP2 at different steam inlet pressures. This figure shows that mass transfer
takes place along the whole interface between the two phases. However, the
mass transfer rate is high due to the low pressure (compression wave) near
the exit of steam nozzle. The contours of mass transfer also indicate the
location of interface between the two phases. The periodic compression and
expansion are also clearly visible in Figure 6.31. At low steam inlet pressure
the steam inlet mass flow rate is low and, therefore, condenses quickly as
compared to high steam pressure (Figure 6.31).
100
6.6.2 Contours of volume fraction
The two-phase flow in the mixing section of SJP is studied in more detail in §
6.5. However, the contours of volume fraction obtained from numerical
computations provide additional information to study the two-phase flow in
this region. Figure 6.32 shows the contours of volume fraction for geometry
SJP2 at different steam inlet pressures. In the mixing section the flow is two-
phase in such a way that there is a steam jet in the central part surrounded
by water in the outer annulus. The two-phases are separated by an interface.
The process of steam condensation takes place across this interface. The
condensation of steam extends more in the mixing section at high steam inlet
pressure as shown in Figure 6.32. Again the periodic compression and
expansion are visible in Figure 6.32. The phenomena of suction and pumping
can be explained from the contours of volume fraction. As the steam enters
the mixing section, at a low steam pressure, it creates suction in the water
nozzle. At the same time the steam jet expands laterally creating a narrow
converging annulus at the outer surface of the steam jet for the entrained
water. The entrained water accelerates through this converging annulus,
forming an interface between the steam and water. On one side of the
interface saturated steam is present which has a high velocity (of the order of
sonic velocity) and temperature while on the other side it has subcooled
water which has very low velocity and temperature. High velocity gradient
across the interface drags and accelerates the water in the mixing section and
thus creating the pumping action. The process of pumping is further
enhanced by condensation of high velocity steam into water.
102
6.6.3 Centerline flow velocity and contours of mach number
In SJP the steam velocity and mach number are very important parameters.
The steam nozzle in SJP is designed in such a way to accelerate the steam to
sonic or supersonic speed to create suction and pumping action. The
centerline velocity of steam for geometry SJP2 at different steam inlet
pressures is shown in Figure 6.33. The steam velocity at the exit of steam
nozzle is higher than 550 m/s for higher steam inlet pressure as shown in
Figure 6.33. The maximum steam velocity achieved at the exit of steam
nozzle increases with steam inlet pressure. This results in stronger suction
and high water mass flow rate at high steam inlet pressure.
The steam velocity decreases sharply in the mixing section due to the
interaction with water across the interface. The decrease in steam velocity in
the mixing section is not uniform, especially at high steam inlet pressure, due
to the periodic compression and expansion in the steam jet. The contours of
mach number for SJP2 are shown in Figure 6.34 for three different steam
inlet pressures. The maximum mach number at steam inlet pressure of 140
KPa is just below sonic value, however, at higher steam inlet pressure its
value is above the sonic value. The results of Figure 6.34 also support the
design of steam nozzle based on 1-D compressible theory to accelerate the
motive steam to sonic or supersonic value.
105
CHAPTER 7
7 CONCLUSIONS AND FUTURE
RECOMMENDATIONS
7.1 Conclusions
The technology of SJP has been known for more than a century but due to
the flow complexities involved the mathematical modeling and, therefore, the
3-D numerical simulation of transport phenomena through SJP is still an
unresolved issue. In this study, the transport phenomena of direct-contact
condensation have been studied theoretically, experimentally and numerically
with particular focus on steam jet pump. The previous work on the
mathematical modeling of transport phenomena in DCC has many
discrepancies like, 1-D modeling, axisymmetric flow assumption, empirical
correlations etc. Mathematical modeling of DCC in this research work is based
on the physics of the transport phenomena across steam-water interface,
with minimum assumptions. 3-D numerical simulation of the flow phenomena
through SJP has been made for the first time up to the best of the author's
knowledge. In light of the objectives set in chapter-1, the accomplished work
and main conclusions are summarized below.
The DCC model is validated by simulating a supersonic steam jet
injected into subcooled water tank [2-3]. The results of these
simulations provide valuable information about the steam jet length,
condensation and average heat transfer coefficients, axial steam
temperature, radial temperature and the steam jet shape.
The experimental results of static pressure, temperature and void
fraction are in close agreement with the computational results, and
thus validate the DCC model and support the numerical simulations.
The characteristic curves of SJP are plotted and it is concluded that the
characteristics of SJP are dependent on the transport phenomena in
106
the mixing section. Whereas, the transport phenomena are dependent
on the interface vibration phenomena in DCC of SJP. It is established
that the length of the converging part of the mixing section plays an
important role in improving the interface vibration phenomena in DCC
of SJP.
The two-phase nature of the flow in the mixing section of SJP is further
studied by measuring the void fraction through gamma-ray
densitometry technique. The densitometry results of void fraction
matched closely with the CFD results which not only validate the
simulations but also endorse the application of gamma-ray
densitometry for void fraction measurement.
The flow visualization results of steam jet in the mixing section support
the CFD simulations, DCC model and gamma-ray densitometry
qualitatively.
The CFD results of mass transfer, volume fraction, steam centerline
velocity and mach number validate the modeling of steam nozzle and
provide important information related to DCC across a steam-water
interface.
The CFD results and its comparison with experimental results strongly
validate the different models and assumptions used in DCC model (§
3.3). For example steam bubble diameter calculation model presented
by [72], two resistance model on both sides of the interface,
assumption of constant heat transfer coefficient on the vapor side,
condensation of steam at saturation conditions etc are validated. The
DCC model developed in this study is considered to be a valuable
contribution in understanding the transport phenomena across a
steam-water interface.
107
7.2 Future recommendations
In order to enhance the research work further, the following
recommendations are suggested.
PIV study of the DCC is recommended to have a better understanding
of the transport phenomena across the interface, and further validate
the DCC model.
It is recommended to study SJP characteristics for pumping liquids
other than water and solids in suspension to access the characteristics
of SJP while pumping high density liquids.
Air can also be used as the motive medium to pump liquids. The
comparison of jet pump characteristics can be made based on using
different motive mediums (air and steam).
108
References
1. Abro, E. and G.A. Johansen, Void Fraction and Flow Regime Determination
by Low-Energy Multi-Beam Gamma-Ray Densitometry. 1st World Congress
on Industrial Process Tomography, Buxton, Greater Manchester, April 14-17,
1999.
2. Shah, A., I.R. Chughtai, and M.H. Inayat, Numerical Simulation of Direct-
contact Condensation from a Supersonic Steam Jet in Subcooled Water.
Chinese Journal of Chemical Engineering, 2010. 18(4): p. 577-587.
3. Shah, A., I.R. Chughtai, and M.H. Inayat, Experimental and numerical
analysis of steam jet pump. International Journal of Multiphase Flow, 2011.
37(10): p. 1305-1314.
4. Aybar, H.S. and N. Beithou, Passive core injection system with steam driven
jet pump for next generation nuclear reactors. Annals of Nuclear Energy,
1999. 26(9): p. 769-781.
5. Beithou, N. and H.S. Aybar, A mathematical model for steam-driven jet pump.
International Journal of Multiphase Flow, 2000. 26(10): p. 1609-1619.
6. Beithou, N. and H.S. Aybar, High-Pressure Steam-Driven Jet Pump---Part I:
Mathematical Modeling. Journal of Engineering for Gas Turbines and Power,
2001. 123(3): p. 693-700.
7. Beithou, N. and H.S. Aybar, High-Pressure Steam-Driven Jet Pump---Part II:
Parametric Analysis. Journal of Engineering for Gas Turbines and Power,
2001. 123(3): p. 701-706.
8. Cattadori, G., et al., A single-stage high pressure steam injector for next
generation reactors: Test results and analysis. International Journal of
Multiphase Flow, 1995. 21(4): p. 591-606.
9. Chun, M.-H., Y.-S. Kim, and J.-W. Park, An investigation of direct
condensation of steam jet in subcooled water. International Communications
in Heat and Mass Transfer, 1996. 23(7): p. 947-958.
10. Deberne, N., et al., A model for calculation of steam injector performance.
International Journal of Multiphase Flow, 1999. 25(5): p. 841-855.
109
11. Kim, Y.S., J.W. Park, and C.H. Song, Investigation of The Steam-Water
Direct Contact Condensation Heat Transfer Coefficients Using Interfacial
Transport Models. Int. Comm. Heat Mass Transfer, 2004. 31 (3): p. 397-408.
12. Pianthong, K., et al., Investigation and improvement of ejector refrigeration
system using computational fluid dynamics technique. Energy Conversion and
Management, 2007. 48(9): p. 2556-2564.
13. Sriveerakul, T., S. Aphornratana, and K. Chunnanond, Performance
prediction of steam ejector using computational fluid dynamics: Part 1.
Validation of the CFD results. International Journal of Thermal Sciences,
2007. 46(8): p. 812-822.
14. Sriveerakul, T., S. Aphornratana, and K. Chunnanond, Performance
prediction of steam ejector using computational fluid dynamics: Part 2. Flow
structure of a steam ejector influenced by operating pressures and geometries.
International Journal of Thermal Sciences, 2007. 46(8): p. 823-833.
15. Wu, X.-Z., et al., Experimental study on the condensation of supersonic steam
jet submerged in quiescent subcooled water: Steam plume shape and heat
transfer. International Journal of Multiphase Flow, 2007. 33(12): p. 1296-
1307.
16. Yan, J.-j., et al., Experiment and analysis on performance of steam-driven jet
injector for district-heating system. Applied Thermal Engineering, 2005. 25(8-
9): p. 1153-1167.
17. Sun, D.W. and I.W. Eames, Recent developments in the design theories and
applications of ejectors-A review. Fuel and Energy Abstracts, 1995. 36(5): p.
361-361.
18. Watanawanavet, S., Optimization of a high efficiency jet ejector by
computational fluid dynamics software. ,MSc Thesis, Texas A&M University,
2005.
19. Keenan, J.H. and E.P. Neumann, A simple air ejector. Journal of Applied
Mechanics, 1942. 64: p. 85–91.
20. Chunnanond, K. and S. Aphornratana, An experimental investigation of a
steam ejector refrigerator: the analysis of the pressure profile along the
ejector. Applied Thermal Engineering, 2004. 24(2-3): p. 311-322.
21. Eames, I.W., S. Aphornratana, and H. Haider, A theoretical and experimental
study of a small-scale steam jet refrigerator. International Journal of
Refrigeration, 1995. 18(6): p. 378-386.
110
22. Gupta, S.K., R.P. Singh, and R.S. Dixit, A comparative parametric study of
two theoretical models of a single-stage, single-fluid, steam jet ejector. The
Chemical Engineering Journal, 1979. 18(1): p. 81-85.
23. Keenan, J.H., E.P. Neumann, and F. Lustwerk, An investigation of ejector
design by analysis and experiment. 1948: Massachusetts Institute of
Technology, Guided Missiles Program.
24. Aphornratana, S. and I.W. Eames, A small capacity steam-ejector
refrigerator: experimental investigation of a system using ejector with
movable primary nozzle. International Journal of Refrigeration, 1997. 20(5): p.
352-358.
25. Chen, Y.-M. and C.-Y. Sun, Experimental study of the performance
characteristics of a steam-ejector refrigeration system. Experimental Thermal
and Fluid Science, 1997. 15(4): p. 384-394.
26. Chunnanond, K. and S. Aphornratana, Ejectors: applications in refrigeration
technology. Renewable and Sustainable Energy Reviews, 2004. 8(2): p. 129-
155.
27. Riffat, S.B. and S.A. Omer, CFD modelling and experimental investigation of
an ejector refrigeration system using methanol as the working fluid.
International Journal of Energy Research, 2001. 25(2): p. 115-128.
28. Rusly, E., et al., Ejector CFD modelling with real gas model. 16th Conference
of the Mechanical Engineering Network Thailand (ME-NETT), 14-16 October
2002: p. 150-155.
29. Huang, B.J., et al., A 1-D analysis of ejector performance. International
Journal of Refrigeration, 1999. 22(5): p. 354-364.
30. Grazzini, G. and A. Mariani, A simple program to design a multi-stagejet-
pump for refrigeration cycles. Energy Conversion and Management, 1998.
39(16-18): p. 1827-1834.
31. Aly, N.H., A. Karameldin, and M.M. Shamloul, Modelling and simulation of
steam jet ejectors. Desalination, 1999. 123(1): p. 1-8.
32. Power, R.B., Steam jet ejectors for the process industries. McGraw-Hill, 1994.
33. El-Dessouky, H., et al., Evaluation of steam jet ejectors. Chemical
Engineering and Processing: Process Intensification, 2002. 41(6): p. 551-561.
111
34. Rusly, E., et al., CFD analysis of ejector in a combined ejector cooling system.
International Journal of Refrigeration, 2005. 28(7): p. 1092-1101.
35. Ian W, E., A new prescription for the design of supersonic jet-pumps: the
constant rate of momentum change method. Applied Thermal Engineering,
2002. 22(2): p. 121-131.
36. Alexis, G.K. and E.D. Rogdakis, A verification study of steam-ejector
refrigeration model. Applied Thermal Engineering, 2003. 23(1): p. 29-36.
37. Munday, J.T. and D.F. Bagster, A New Ejector Theory Applied to Steam Jet
Refrigeration. Industrial & Engineering Chemistry Process Design and
Development, 1977. 16(4): p. 442-449.
38. Khattab, N.M. and M.H. Barakat, Modeling the design and performance
characteristics of solar steam-jet cooling for comfort air conditioning. Solar
Energy, 2002. 73(4): p. 257-267.
39. Da-Wen, S., Comparative study of the performance of an ejector refrigeration
cycle operating with various refrigerants. Energy Conversion and
Management, 1999. 40(8): p. 873-884.
40. Chunnanond, K., A study of Steam Ejector Refrigeration Cycle, Parameters
Affecting Performance of Ejector. , Ph.D. Thesis, Sirindhorn International
Institute of Technology University, 1994.
41. Deberne, N., J.-F. Leone, and A. Lallemand, Local measurements in the flow
of a steam injector and visualisation. International Journal of Thermal
Sciences, 2000. 39(9-11): p. 1056-1065.
42. Goto, S., S. Ohmori, and M. Mori, Analysis of Heat Balance on Innovative-
Simplified Nuclear Power Plant Using Multi-Stage Steam Injectors. JSME
International Journal Series B Fluids and Thermal Engineering, 2006. 49(4): p.
1266-1271.
43. Narabayashi, T., W. Mizumachi, and M. Mori, Study on two-phase flow
dynamics in steam injectors. Nuclear Engineering and Design, 1997. 175(1-2):
p. 147-156.
44. Narabayashi, T., et al., Study on two-phase flow dynamics in steam injectors:
II. High-pressure tests using scale-models. Nuclear Engineering and Design,
2000. 200(1-2): p. 261-271.
112
45. Narabayashi, T., et al., Development of Multi-Stage Steam Injector for
Feedwater Heaters in Simplified Nuclear Power Plant. JSME International
Journal Series B Fluids and Thermal Engineering, 2006. 49(2): p. 368-376.
46. Ohmori, S., T. Narabayashi, and M. Mori, Scale Model Test and Transient
Analysis of Steam Injector Driven Passive Core Injection System for
Innovative-Simplified Nuclear Power Plant. Journal of Power and Energy
Systems, 2008. 2(2): p. 492-500.
47. Ohmori, S., et al., Development of Technologies on Innovative-Simplified
Nuclear Power Plant using High-Efficiency Steam Injectors System Outline
and Endurance Test of Low-Pressure Steam Injectors. Journal of Power and
Energy Systems, 2007. 1(1): p. 99-110.
48. Yan, J., D. Chong, and X. Wu, Effect of swirling vanes on performance of
steam-water jet injector. Applied Thermal Engineering, 2010. 30(6-7): p. 623-
630.
49. Dumaz, P., et al., The DEEPSSI project, design, testing and modeling of steam
injectors. Nuclear Engineering and Design, 2005. 235(2-4): p. 233-251.
50. Young, R.J., K.T. Yang, and J.L. Novotny, Vapor-Liquid Interaction in a
High Velocity Vapor Jet Condensing in a Coaxial Water Flow. ASME Journal
of Heat Transfer, 1974. 3: p. 226-230.
51. Cumo, M., G.E. Farello, and G. Ferrari, Direct Heat Transfer in Pressure-
Suppression Systems. Proc. of 6th International Heat Transfer Conference,
Toronto, 1978(5): p. 101-106.
52. Aya, I. and H. Nariai, Evaluation of Heat-Transfer Coefficient at Direct-
Contact Condensation of Cold Water and Steam. Nuclear Engineering Design,
1991. 131: p. 17-24.
53. Sonin, A.A., Suppression Pool Dynamics Research at MIT. , NUREG/CP-
0048, 1984: p. 400-421.
54. Simpson, M.E. and C.K. Chan, Hydrodynamics of a Subsonic Vapor Jet in
Subcooled Liquid. Journal of Heat Transfer, 1982. 104(2): p. 271-278.
55. Weimer, J.C., G.M. Faeth, and D.R. Olson, Penetration of vapor jets
submerged in subcooled liquids. AIChE Journal, 1973. 19(3): p. 552-558.
56. Chen, L.D. and G.M. Faeth, Condensation of Submerged Vapor Jets in
Subcooled Liquids. Journal of Heat Transfer, 1982. 104(4): p. 774-780.
113
57. Tin, G.D., E. Lavagno, and M. Malandrone, Pressure and Temperature
Measurements in a Vapor Condensing Jet. Proc. of 7th International Heat
Transfer Conference, Munchen, 1982. 6: p. 159-164.
58. Petrovic, A., Analytical Study of Flow Regimes for Direct Contact
Condensation Based on Parametrical Investigation. Journal of Pressure
Vessel Technology, 2005. 127(1): p. 20-25.
59. Petrovic de With, A., R.K. Calay, and G. de With, Three-dimensional
condensation regime diagram for direct contact condensation of steam
injected into water. International journal of Heat and Mass Transfer, 2007.
50(9-10): p. 1762-1770.
60. Gulawani, S.S., et al., CFD analysis of flow pattern and heat transfer in direct
contact steam condensation. Chemical Engineering Science, 2006. 61(16): p.
5204-5220.
61. Hun Ju, S., H. Cheon No, and F. Mayinger, Measurement of heat transfer
coefficients for direct contact condensation in core makeup tanks using
holographic interferometer. Nuclear Engineering and Design, 2000. 199(1-2):
p. 75-83.
62. Kang, H.S. and C.H. Song, CFD analysis for thermal mixing in a subcooled
water tank under a high steam mass flux discharge condition. Nuclear
Engineering and Design, 2008. 238(3): p. 492-501.
63. Wu, X.-Z., et al., Experimental study on sonic steam jet condensation in
quiescent subcooled water. Chemical Engineering Science, 2009. 64(23): p.
5002-5012.
64. Wu, X.-Z., et al., Experimental investigation of over-expanded supersonic
steam jet submerged in quiescent water. Experimental Thermal and Fluid
Science, 2010. 34(1): p. 10-19.
65. Wu, X.-Z., et al., Condensation regime diagram for supersonic/sonic steam jet
in subcooled water. Nuclear Engineering and Design, 2009. 239(12): p. 3142-
3150.
66. Kim, M.-S., et al., Application of gamma densitometer for measurement of
void fraction in liquid hydrogen moderator of HANARO cold neutron source.
Physica B: Condensed Matter, 2009. 404(12-13): p. 1695-1700.
67. Tjugum, S.A., B.T. Hjertaker, and G.A. Johansen, Multiphase flow regime
identification by multibeam gamma-ray densitometry. Measurement Science
and Technology, 2002. 13(8): p. 1319.
114
68. Dong-hui, L., et al., Volumetric fraction measurement in oil-water-gas
multiphase flow with dual energy gamma-ray system. Journal of Zhejiang
University - Science A, 2005. 6(12): p. 1405-1411.
69. Siti Aslina, et al., Water Local Volume Fraction on Oil in Water Dispersion.
Journal of Applied Fluid Mechanics, ,2008. 1(2): p. 57-63.
70. Fluent, Fluent 6.3 user guide. 2006, Fluent Inc.
71. Ranade, V.V., Computational Flow Modeling for Chemical Reactor
Engineering. 2002: Academic Press.
72. Anglart, H. and O. Nylund, CFD application to prediction of void distribution
in two-phase bubbly flows in rod bundles. Nuclear Engineering and Design,
1996. 163(1-2): p. 81-98.
73. Brucker, G.G. and E.M. Sparrow, direct contact condensation of steam
bubbles in water at high pressure. International journal of Heat and Mass
Transfer, 1977. 20: p. 11.
74. Hughmark, G.A., Mass and heat transfer from a rigid sphere. AIChE, 1967.
13: p. 3.
75. Koncar, B. and B. Mavko, Modelling of low-pressure subcooled flow boiling
using the RELAP5 code. Nuclear Engineering and Design, 2003. 220(3): p.
255-273.
76. Shih, T.-H., et al., A new k-ϵ eddy viscosity model for high reynolds number
turbulent flows. Computers & Fluids, 1995. 24(3): p. 227-238.
77. White, F.M., Fluid Mechanics. McGraw-Hill, 2002. 5th edition.
78. Maurice J. Zucrow and Joe D. Hoffman, Gas Dynamics. Wiley, 1976. volume
1.
79. Sherif, S.A., A. United States. National, and A. Space, Analysis and modeling
of a two-phase jet pump of a thermal management system for aerospace
applications. 1998, Washington, DC; Springfield, Va.: National Aeronautics
and Space Administration ; National Technical Information Service,
distributor.
115
8 Appendix A
A1: Suction lift calculation
Suction lift is defined as the theoretical maximum depth from which the SJP is
able to suck water under different operating conditions. In order to calculate
the suction lift the Bernoulli’s equation is applied between the water tank and
the exit of water nozzle. The Bernoulli’s equation applied between the water
tank and the exit of water nozzle, neglecting the friction losses in the piping,
is given below.
𝑃𝑤
𝜌𝑤𝑔+ 0.5
𝑣𝑤2
𝑔+ 𝑧𝑤 =
𝑃𝑤𝑐
𝜌𝑤𝑐𝑔+ 0.5
𝑣𝑤𝑐2
𝑔+ 𝑧𝑤𝑐 (3.48)
𝑧𝑤𝑐 =𝑃𝑤 − 𝑃𝑤𝑐
𝜌𝑤𝑔− 0.5
𝑣𝑤𝑐
𝑔
2
+ 𝑧𝑤 (3.49)
𝑣𝑤𝑐 =𝑚𝑤
𝜌𝑤𝐴𝑤𝑐 (3.50)
Where, the first subscript of the parameters used in the above equations, ‘𝑤’
represents water and the second subscript ‘𝑐’ represents the section 𝑐
mentioned in Figure 1.1. ‘𝑧’ is the potential head.
116
A2: Uncertainty calculation technique
If ±𝑥1, ±𝑥2 ,… , ±𝑥𝑛 are the uncertainties in parameters 𝑥1, 𝑥2 ,… , 𝑥𝑛
respectively, then the uncertainty propagating into a function 𝑔 =
𝑓(𝑥1, 𝑥2,… , 𝑥𝑛) is given by the following relation.
±𝛿𝑔 = (𝜕𝑔
𝜕𝑥𝑖𝛿𝑥𝑖)
2
𝑖=𝑛
𝑖=1
(3.51)
128
9 Appendix B
B1:Data tables for geometry SJP1
Table B1.1: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 79245±655 77313±434 86445±411 0.22 8.4
65 72553±575 70869±539 77978±433 0.25 10.3
80 66168±605 63255±428 73704±532 0.29 6.9
95 58548±478 56522±544 64412±482 0.27 8.3
110 63933±454 62771±535 74054±436 0.11 6.3
125 77999±647 77615±322 98094±498 0.02 3.9
140 95103±567 94775±512 118999±529 0.01 3.5
155 125655±679 125442±437 148231±465 0.01 3.8
170 128855±571 128812±525 149762±519 0.00 4.0
Table B1.2: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 79237±635 77313±434 86445±411 0.22 8.2
65 72763±565 70869±539 77978±433 0.28 10.1
80 65717±571 63255±428 73704±532 0.25 6.7
95 58497±78 56522±544 64412±482 0.26 8.4
110 65002±484 62771±535 74054±436 0.21 6.1
125 79937±637 77615±322 98094±498 0.13 3.7
140 95407±597 94775±512 118999±529 0.03 3.6
155 125851±689 125442±437 148231±465 0.02 3.9
170 128867±591 128812±525 149762±519 0.00 4.1
129
TableB1.3: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 79387±665 77313±434 86445±411 0.24 8.5
65 72802±565 70869±539 77978±433 0.28 10.1
80 65323±571 63255±428 73704±532 0.21 6.8
95 58882±498 56522±544 64412±482 0.31 8.4
110 65546±554 62771±535 74054±436 0.26 6.4
125 82352±687 77615±322 98094±498 0.25 3.8
140 96812±580 94775±512 118999±529 0.09 3.4
155 125669±729 125442±437 148231±465 0.01 4.0
170 128992±671 128812±525 149762±519 0.01 4.4
Table B1.4: Void fraction data for SJP1 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 79331±657 77313±434 86445±411 0.23 8.4
65 73420±635 70869±539 77978±433 0.37 10.6
80 66347±581 63255±428 73704±532 0.31 6.6
95 58606±508 56522±544 64412±482 0.28 8.6
110 66304±554 62771±535 74054±436 0.33 6.2
125 81507±687 77615±322 98094±498 0.21 3.9
140 99064±667 94775±512 118999±529 0.19 3.5
155 125896±769 125442±437 148231±465 0.02 4.2
170 128863±751 128812±525 149762±519 0.00 4.7
Table B1.5: Void fraction data for SJP1 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 79349±655 77313±434 86445±411 0.23 8.4
65 74385±695 70869±539 77978±433 0.51 10.9
80 67154±641 63255±428 73704±532 0.39 7.0
95 59648±568 56522±544 64412±482 0.41 8.8
110 66575±594 62771±535 74054±436 0.36 6.5
125 83461±487 77615±322 98094±498 0.31 2.9
140 98341±687 94775±512 118999±529 0.16 3.7
155 126921±798 125442±437 148231±465 0.07 4.2
170 128871±721 128812±525 149762±519 0.00 4.6
130
Table B1.6: Flow rates, mass ratio and suction lift data at different steam inlet and
water suction pressures for SJP1 geometry
𝑃𝑠 (𝐾𝑃𝑎)
𝑃𝑠𝑢𝑐 (𝑖𝑛 𝑜𝑓 𝐻𝑔)
𝑚 𝑤 ,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑠,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑜𝑢𝑡
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑖𝑛
𝑚 𝑠,𝑖𝑛
Suction
Lift (𝑚)
140 -1.5 0.1497 0.006 0.1557 2496 0.82
140 -2.0 0.1191 0.006 0.1251 19.85 0.99
140 -2.5 0.0950 0.006 0.101 12.50 1.17
160 -1.5 0.2507 0.0069 0.2576 36.34 0.80
160 -2.0 0.1935 0.0069 0.2004 28.04 0.98
160 -2.5 0.1505 0.0069 0.1574 18.91 1.16
160 -3.0 0.1088 0.0069 0.1157 14.49 1.34
160 -3.5 0.0791 0.0069 0.086 10.05 1.51
180 -1.5 0.4266 0.0081 0.4347 52.67 0.77
180 -2.0 0.3387 0.0081 0.3468 41.81 0.96
180 -2.5 0.2817 0.0081 0.2898 34.77 1.14
180 -3.0 0.2259 0.0081 0.234 25.42 1.33
180 -3.5 0.1795 0.0081 0.1876 17.72 1.50
180 -4.0 0.1216 0.0081 0.1297 12.54 1.68
180 -4.5 0.0850 0.0081 0.0931 10.49 1.86
200 -2.0 0.5819 0.0092 0.5911 62.08 0.89
200 -2.5 0.5227 0.0092 0.5319 56.82 1.08
200 -3.0 0.4314 0.0092 0.4406 46.89 1.28
200 -3.5 0.3926 0.0092 0.4018 42.67 1.47
200 -4.0 0.3098 0.0092 0.319 33.67 1.66
200 -4.5 0.2500 0.0092 0.2592 27.17 1.84
220 -3.0 0.6807 0.0102 0.6909 61.90 1.20
220 -3.5 0.6316 0.0102 0.6418 55.92 1.39
220 -4.0 0.4803 0.0102 0.4905 47.08 1.62
220 -4.5 0.3990 0.0102 0.4092 39.12 1.81
131
10 Appendix C
C1:Data tables for geometry SJP3
Table C1.1: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 149785±487 146371±426 164695±388 0.19 3.4
65 146219±420 140211±414 159785±412 0.32 2.8
80 135545±577 131481±411 151532±453 0.21 3.5
95 126872±599 125731±508 133430±400 0.15 9.8
110 134886±478 133814±467 142343±476 0.13 7.6
125 141690±212 141602±449 145201±491 0.02 13.7
140 143803±601 143782±525 149786±381 0.00 13.5
155 144341±485 144340±362 150987±427 0.00 9.3
170 145155±469 145155±388 155582±466 0.00 6.0
Table C1.2: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 149595±563 146371±426 164695±388 0.18 3.8
65 145357±509 140211±414 159785±412 0.28 3.2
80 137711±486 131481±411 151532±453 0.33 3.0
95 127670±606 125731±508 133430±400 0.26 9.5
110 135261±349 133814±467 142343±476 0.17 6.3
125 142225±276 141602±449 145201±491 0.17 13.2
140 144161±369 143782±525 149786±381 0.06 10.4
155 144340±408 144340±362 150987±427 0.00 8.4
170 145155±548 145155±388 155582±466 0.00 6.7
132
Table C1.3: Void fraction data for SJP3 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 150376±537 146371±426 164695±388 0.23 3.6
65 145618±482 140211±414 159785±412 0.29 3.1
80 136450±357 131481±411 151532±453 0.26 2.5
95 127541±461 125731±508 133430±400 0.24 8.1
110 136062±514 133814±467 142343±476 0.27 7.5
125 142166±219 141602±449 145201±491 0.16 12.5
140 144261±372 143782±525 149786±381 0.08 10.4
155 144411±468 144340±362 150987±427 0.01 9.1
170 145248±419 145155±388 155582±466 0.00 5.6
Table C1.4: Void fraction data for SJP3 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 149567±507 146371±426 164695±388 0.18 3.5
65 145331±472 140211±414 159785±412 0.27 3.0
80 136427±500 131481±411 151532±453 0.26 3.1
95 128376±427 125731±508 133430±400 0.35 7.3
110 136106±458 133814±467 142343±476 0.27 7.0
125 142459±321 141602±449 145201±491 0.24 13.5
140 144143±489 143782±525 149786±381 0.06 11.8
155 144340±406 144340±362 150987±427 0.00 8.4
170 145155±455 145155±388 155582±466 0.00 5.9
Table C1.5: Void fraction data for SJP3 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 150172±472 146371±426 164695±388 0.22 3.3
65 146325±603 140211±414 159785±412 0.33 3.6
80 137536±515 131481±411 151532±453 0.32 3.1
95 127487±377 125731±508 133430±400 0.23 7.3
110 136758±510 133814±467 142343±476 0.35 7.3
125 142498±331 141602±449 145201±491 0.25 13.7
140 144434±527 143782±525 149786±381 0.11 12.0
155 144345±379 144340±362 150987±427 0.00 8.1
170 145155±464 145155±388 155582±466 0.00 6.0
133
Table C1.6: Flow rates, mass ratio and suction lift data at different steam inlet and
water suction pressures for SJP3 geometry
𝑃𝑠 (𝐾𝑃𝑎)
𝑃𝑠𝑢𝑐 (𝑖𝑛 𝑜𝑓 𝐻𝑔)
𝑚 𝑤 ,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑠,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑜𝑢𝑡
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑖𝑛
𝑚 𝑠,𝑖𝑛
Suction
Lift (𝑚)
140 -1.5 0.2393 0.0060 0.2453 39.88 0.81
140 -2.0 0.1709 0.0060 0.1769 28.48 0.99
140 -2.5 0.1191 0.0060 0.1251 19.85 1.16
160 -1.5 0.3411 0.0069 0.3480 49.43 0.79
160 -2.0 0.3011 0.0069 0.3080 43.64 0.97
160 -2.5 0.2617 0.0069 0.2686 37.93 1.15
160 -3.0 0.2169 0.0069 0.2238 31.43 1.33
160 -3.5 0.1791 0.0069 0.1860 25.96 1.50
180 -1.5 0.4301 0.0081 0.4382 53.1 0.77
180 -2.0 0.3664 0.0081 0.3745 45.23 0.96
180 -2.5 0.3282 0.0081 0.3363 40.52 1.14
180 -3.0 0.2606 0.0081 0.2687 32.17 1.32
180 -3.5 0.2135 0.0081 0.2216 26.36 1.50
180 -4.0 0.1722 0.0081 0.1803 21.26 1.68
180 -4.5 0.1205 0.0081 0.1286 14.88 1.85
200 -2.0 0.4504 0.0092 0.4596 48.96 0.94
200 -2.5 0.3843 0.0092 0.3935 41.77 1.13
200 -3.0 0.3325 0.0092 0.3417 36.14 1.31
200 -3.5 0.2815 0.0092 0.2907 30.6 1.49
200 -4.0 0.2153 0.0092 0.2245 23.4 1.67
200 -4.5 0.1601 0.0092 0.1693 17.4 1.85
220 -2.0 0.5608 0.0102 0.5710 54.98 0.91
220 -2.5 0.4975 0.0102 0.5077 48.77 1.10
220 -3.0 0.4317 0.0102 0.4419 42.32 1.29
220 -3.5 0.3700 0.0102 0.3802 36.27 1.48
220 -4.0 0.3158 0.0102 0.3260 30.96 1.66
220 -4.5 0.2851 0.0102 0.2953 27.95 1.84
134
11 Appendix D
D1: Data tables for geometry SJP4
Table D1.1: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 98491±435 96100±434 110353±325 0.18 4.2
65 95556±405 92032±315 104519±337 0.29 3.9
80 89833±502 88142±359 102643±385 0.12 4.4
95 82431±479 80772±368 93822±412 0.14 4.7
110 75553±511 75222±391 86123±436 0.03 6.2
125 86774±471 86746±408 99073±475 0.00 5.4
140 95285±614 95281±376 104726±455 0.00 8.0
155 96317±452 96313±345 105573±465 0.00 6.4
170 98770±573 98754±326 106128±376 0.00 9.3
Table D1.2: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.6 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 98323±543 96100±434 110353±325 0.16 4.8
65 94711±401 92032±315 104519±337 0.23 4.0
80 91562±421 88142±359 102643±385 0.25 3.7
95 83886±472 80772±368 93822±412 0.25 4.4
110 77330±508 75222±391 86123±436 0.20 5.8
125 88208±466 86746±408 99073±475 0.13 5.1
140 95727±603 95281±376 104726±455 0.05 7.8
155 96320±455 96313±345 105573±465 0.00 6.4
170 98774±512 98754±326 106128±376 0.00 8.5
135
Table D1.3: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.8 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 98396±465 96100±434 110353±325 0.17 4.4
65 95240±389 92032±315 104519±337 0.27 3.8
80 91452±514 88142±359 102643±385 0.24 4.2
95 84143±520 80772±368 93822±412 0.27 4.7
110 76518±625 75222±391 86123±436 0.13 6.9
125 88646±438 86746±408 99073±475 0.16 4.8
140 95848±442 95281±376 104726±455 0.06 6.3
155 96477±528 96313±345 105573±465 0.02 7.1
170 98820±506 98754±326 106128±376 0.01 8.4
Table D1.4: Void fraction data for SJP4 geometry at 𝑃𝑠 = 2.0 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 98034±451 96100±434 110353±325 0.14 4.4
65 95566±380 92032±315 104519±337 0.30 3.7
80 91592±472 88142±359 102643±385 0.25 4.0
95 83233±437 80772±368 93822±412 0.20 4.3
110 77834±495 75222±391 86123±436 0.25 5.6
125 89568±538 86746±408 99073±475 0.24 5.3
140 96712±573 95281±376 104726±455 0.16 7.2
155 97847±622 96313±345 105573±465 0.17 7.7
170 98941±533 98754±326 106128±376 0.02 8.7
Table D1.5: Void fraction data for SJP4 geometry at 𝑃𝑠 = 2.2 𝑏𝑎𝑟
𝑥 (𝑚𝑚) Average number of counts 𝛼 𝛿𝛼(%) 𝐼𝑚𝑖𝑥 ± 𝛿𝐼𝑚𝑖𝑥 𝐼𝑤 ± 𝛿𝐼𝑤 𝐼𝑠 ± 𝛿𝐼𝑠
50 97993±513 96100±434 110353±325 0.14 4.7
65 96017±455 92032±315 104519±337 0.33 4.2
80 91547±492 88142±359 102643±385 0.25 4.1
95 82625±501 80772±368 93822±412 0.15 4.8
110 78812±486 75222±391 86123±436 0.34 5.4
125 88529±511 86746±408 99073±475 0.15 5.3
140 96458±534 95281±376 104726±455 0.13 6.9
155 98113±521 96313±345 105573±465 0.20 6.6
170 99687±464 98754±326 106128±376 0.13 7.6
136
Table D1.6: Flow rates, mass ratio and suction lift data at different steam inlet and
water suction pressures for SJP4 geometry
𝑃𝑠 (𝐾𝑃𝑎)
𝑃𝑠𝑢𝑐 (𝑖𝑛 𝑜𝑓 𝐻𝑔)
𝑚 𝑤 ,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑠,𝑖𝑛
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑜𝑢𝑡
(𝐾𝑔
𝑠)
𝑚 𝑤 ,𝑖𝑛
𝑚 𝑠,𝑖𝑛
Suction
Lift (𝑚)
140 -1.0 0.1788 0.0060 0.1848 29.80 0.64
140 -1.5 0.1513 0.0060 0.1573 25.22 0.81
140 -2.0 0.1006 0.0060 0.1066 16.77 0.98
160 -1.0 0.3176 0.0069 0.3245 46.03 0.62
160 -1.5 0.2743 0.0069 0.2812 39.75 0.80
160 -2.0 0.1911 0.0069 0.1980 27.70 0.98
160 -2.5 0.1387 0.0069 0.1456 20.10 1.15
180 -1.0 0.4149 0.0081 0.4230 51.22 0.61
180 -1.5 0.3385 0.0081 0.3466 41.79 0.79
180 -2.0 0.2535 0.0081 0.2616 31.30 0.97
180 -2.5 0.1954 0.0081 0.2035 24.12 1.15
180 -3.0 0.1683 0.0081 0.1764 20.78 1.32
180 -3.5 0.1425 0.0081 0.1506 17.59 1.49
180 -4.0 0.1201 0.0081 0.1282 14.83 1.66
180 -4.5 0.0912 0.0081 0.0993 11.26 1.84
200 -1.5 0.4986 0.0092 0.5078 54.20 0.76
200 -2.0 0.4607 0.0092 0.4699 50.08 0.94
200 -2.5 0.3889 0.0092 0.3981 42.27 1.13
200 -3.0 0.3073 0.0092 0.3165 33.40 1.31
200 -3.5 0.2422 0.0092 0.2514 26.33 1.48
200 -4.0 0.1973 0.0092 0.2065 21.45 1.66
200 -4.5 0.152 0.0092 0.1612 16.52 1.83
220 -2.0 0.6204 0.0102 0.6306 60.82 0.91
220 -2.5 0.5643 0.0102 0.5745 55.32 1.09
220 -3.0 0.5026 0.0102 0.5128 49.27 1.27
220 -3.5 0.3747 0.0102 0.3849 36.74 1.47
220 -4.0 0.2928 0.0102 0.3030 28.71 1.65
220 -4.5 0.1948 0.0102 0.2050 19.10 1.83
top related