thheerrmmaall lhhyyddrraauuliicc aannaallyyssiiss ooff

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: _____________________

v

Dedicated

To My Sweetest

M. Wasif and S. Fatima

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 ‎6.5: Axial wall pressure distribution at higher back pressure ............. 73

Figure ‎6.6: Axial static temperature profile for SJP1 geometry of SJP .......... 74




Figure ‎6.10: 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


............................................................................................................... 82

xiv


............................................................................................................... 83


............................................................................................................... 84

Figure ‎6.16: Mass ratio curves for SJP1 geometry of SJP ............................ 85




Figure ‎6.20: Suction lift curves for geometry SJP1 of SJP............................ 88




Figure ‎6.24: Void fraction distribution in the mixing section for SJP1 geometry

of SJP...................................................................................................... 92


of SJP...................................................................................................... 93


of SJP...................................................................................................... 94


of SJP...................................................................................................... 95

Figure ‎6.28: Steam jet in the mixing section of SJP2 geometry of SJP ......... 96


xv


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 ‎4.9: 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




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 ‎C1.5: 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 D1.3: Void fraction data for SJP4 geometry at 𝑃𝑠 = 1.8 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 𝛼𝑞𝜌𝑞𝑕𝑞 + 𝛻. 𝛼𝑞𝜌𝑞𝒗𝑞𝑕𝑞 = −𝛼𝑞

𝜕𝑃𝑞

𝜕𝑡+ 𝝉𝑞 ∶ 𝛻𝒗𝑞 − 𝛻𝒒𝑞

+𝑆𝑞 + 𝑄𝑝𝑞 +𝑚 𝑝𝑞𝑕𝑝𝑞 −𝑚 𝑞𝑝𝑕𝑞𝑝

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

http://en.wikipedia.org/wiki/Thallium

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



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



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



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



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.


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.


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.


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.


76


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].


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.


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.


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


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.


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.


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



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


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).


91


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


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.

94


95


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


97


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).

99

Figure ‎6.31: Contours of mass transfer for SJP2 geometry of SJP

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.

101

Figure ‎6.32: Contours of volume fraction for SJP2 geometry of SJP

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.

103

Figure ‎6.33: Centerline steam velocity for SJP2 geometry of SJP

104

Figure ‎6.34: Mach number contours for SJP2 geometry of SJP

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

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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)

117

A3: DCC model validation

128

9 Appendix B

B1:Data tables for geometry SJP1

Table B1.1: Void fraction data for SJP1 geometry at 𝑃𝑠 = 1.4 𝑏𝑎𝑟


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



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


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



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



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




𝑚 𝑤 ,𝑖𝑛

(𝐾𝑔

𝑠)

𝑚 𝑠,𝑖𝑛

(𝐾𝑔

𝑠)


(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


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



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



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



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



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




𝑚 𝑤 ,𝑖𝑛

(𝐾𝑔

𝑠)

𝑚 𝑠,𝑖𝑛

(𝐾𝑔

𝑠)


(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


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



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



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



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



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




𝑚 𝑤 ,𝑖𝑛

(𝐾𝑔

𝑠)

𝑚 𝑠,𝑖𝑛

(𝐾𝑔

𝑠)


(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

137

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