Steam Condensation in the Presence of Noncondensable
Gases Under Forced Convection Conditions
by
Hisham A. Hasanein
B.S., Nuclear Engineering
Alexandria University, Egypt (1985)
M.S., Engineering Physics
Alexandria University, Egypt (1989)
Submitted to the Department of Nuclear Engineering
in Partial Fulfillment of the Requirements for the Degree of
DOCTOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 1994
Institute of Technology, 1994
(Massachusetts
All rights reserved
Signature of Author.
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of Nuclear Engineering
May 6, 1994
Certified by
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Profesol9of Nuclear Engineering
Thesis Supervisor
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Z(I-ofessor of Nuclear Engineering
Thesis Supervisor
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MASSACHUSETTS
INSTITUTE
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Steam Condensation in the Presence of Noncondensable
Gases under Forced Convection Conditions
Hisham A. Hasanein
submitted to the Department of Nuclear Engineering In May 1994in Partial Fulfilment of the
requirements for the Degree of Doctor of Science in Nuclear Engineering
ABSTRACT
An experimental and theoretical investigation has been conducted to determine the
effects of the presence of noncondensable gases on in-tube steam condensation under
forced convection conditions. The main objective of the study was to determine the
condensation heat transfer coefficientsof steam in the presence of helium and in the
simultaneous presence of air and helium. In a sensitivity analysis aimed at assessing
the effects of the coolant conditions, air was used as a noncondensable gas because of
its availabilty and low cost.
In these experiments, condensation occurred inside a 46mm internal diameter,
2.44m long vertical tube.
Steam was produced in a boiler using a set of emersion
heaters with a maximum capacity of 28kW. Air, helium or an air/helium mixture was
admitted, after being measured by calibrated rotameters, to the bottom of the boiler
to get mixed with the steam. The steam/noncondensable gas mixture flow rate was
measured by a calibtrated vortex flow meter just before it entered the vertical test
condensing tube. Cooling water flew in an annulus around the test condenser and air
was bubbled into the coolant annulus in order to promote coolant mixing. Temper-
atures of the steam/noncondensable gas mixture, the condensing tube surfaces, and
the cooling water were measured at nine stations, 0.3m apart. The local values of the
heat fluxes were calculated from the measured cooling water flowrate and the gradient
of the coolant axial temperature profile. Inlet and exit pressures and temperatures of
the cooling water and steam/noncondensable gas mixture were measured as well. The
experiments covered steam/gas mixture inlet Reynolds numbers from about 6,000 to
26,543, inlet helium mass fraction range from 0.022 up to 0.20, inlet air mass fraction
range from 0.045 up to 0.20, and mixture inlet temperature of 100 and 1300 C.
The local condensation heat transfer coefficient values were found to vary from
0.2 to 9.2kW/m 2 °C. The local mixture Nusselt numbers varied from 65 to 14,240
i
and were correlated in terms of the local mixture Reynolds number, mixture Jakob
number, and alternatively the gas mass (or mole) fractions or the mixture Schmidt
number. Correlations including the mixture Schmidt number did better in representing
the condensation process in the presence of noncondensable gases.
The ratios of the condensate film thermal resistance to the thermal resistance of
the steam/noncondensable gas mixture at the same bulk temperature were calculated.
The local values of pure steam heat transfer coefficients(or local condensate film thermal resistances) were obtained based on the well known Nusselt assumptions for film
condensation and by a correlation found in literature for annular-film condensation inside vertical tubes which incorporated the effects of interfacial shear stress, interfacial
waviness, and turbulent transport in the condensate film. Such effects were neglected
in the Nusselt treatment. In general, the condensate film thermal resistance was found
to be significant for turbulent mixture conditions (Re > 5000). The ratio of the condensate film thermal resistance to the total thermal resistance was found to increase
with steam/gas mixture Reynolds number and to decrease with noncondensable mass
(mole) fraction or steam/gas mixture Schmidt number. For laminar forced convection
the condensate film thermal resistace was found to be negligible.
On the analytical side, a diffusion steam/gas boundary layer based model was
developed. The steady state radial diffusionequations of the mixture components were
solved in order to obtain the steam mass flux at the interface between the condensate
film and the mixture. The effect of the axial flow was included in terms of an effective
boundary layer thickness which decreased with mixture Reynolds number. The model
included the effect of more than one noncondensable gas on steam condensation as
well. When the model-predicted mixture heat transfer coefficientswere compared to
the experimentally obtained mixture heat transfer coefficients, good ageement was
found for turbulent forced convection flows. For laminar forced convection flows, the
deviation of the predicted Nusselt numbers from the experimentally obtained Nusselt
numbers was found to be : +100%.
Thesis Supervisor
Title
: Michael W. Golay
: Professor of Nuclear Engineering
Thesis Supervisor
Title
: Mujid S. Kazimi
: Professor of Nuclear Engineering & Department Head
11
Achnowledgements
I would like to express my gratitude to my research advisors, Professors Golay and
Kazimi for their guidance and continued support throughout this work. The help and
guidance of Professor Griffith, my thesis reader, are greatly appreciated. His pleasant
character and kindness have made it easier for me to finish this work.
Special thanks go to Hani Sallum for his assistance in setting up the Visualisation
Experiment. His help and the help I recieved from Sarah Abdelkader in carrying out
the design for the new test section are also appreciated.
The financial support of the General Electric Company and MIT is gratefully acknowledged.
I would like also to thank my family back home in Egypt, for their love and support
throughout my entire life.
iii
Contents
Nomenclature
12
1 Introduction
16
2 The Effects of Cooling Water Conditions on In-Tube Condensation in the Presence of Noncondensables
19
2.1 Introduction ..................................
19
2.2 Experimental Setup and Data Analysis ...................
2.2.1 Description of Apparatus .
.....................
2.2.2
Experimental Procedure .......................
2.2.3
Data Analysis and Experimental
23
Errors
. . . . . . . . . . ....
2.3 Experimental Results .............................
2.3.1 Effect of Cooling Water Inlet Temperature
2.3.2
2.4
.
.
25
25
...........
................
26
26
2.3.4
27
27
Temperature Inversion ........................
Discussion of Results .............................
2.4.1
Effects
ofInlet
Cooling
Water
Temperature
............ 27
Effect of Cooling Water Flow Rate
.
................
28
2.4.3 Effect of Air Injection with Cooling Water into the Annulus . . .
28
2.4.4 Temperature Inversion ........................
Summary & Conclusions ...........................
30
31
2.6 Recommendations .............................
.
3 The Visualization Experiment
Experimental Setup
32
45
3.1 Introduction .........................
3.2
24
2.3.3 Effect of Air Injection with Cooling Water into the Annulus . . .
2.4.2
2.5
Effect of Cooling Water Flow Rate
20
20
..........
.............................
3.2.1 Description of Apparatus ......................
1
45
45
45
3.3
3.2.2 Calibration of The Pressure Transducer ..............
3.2.3 Experimental Procedure .......................
47
3.2.4
48
Data Analysis
47
. . . . .
49
Experimental Results and Discussions.
3.3.1 Flow Description . .
3.3.2 Data Correlation.
3.4 Drift Flux Correlation ............................
3.4.1 Distribution Parameter CO .....................
3.4.2
3.4.3
3.5
49
50
51
52
Average Local Drift Velocity < Vgj >...............
Annulus Characteristic Flow Dimension ..............
Concluding
Remarks
53
54
55
. . . . . . . . . . . . . . .
4 Effects of Buoyancy in the Coolant Side on In-Tube Steam Condensation in the
Presence of Noncondensables
4.1 Introduction.
68
.................
. . . . . . . . . . . ..
68
...
69
....
. . . .
69
...
. . . . . . . . ..
..
70
...
. . . . . . . . ..
. ..
70
...
. . . . . . . . . . . . .
70
...
. . . . . . . . . . . .
71
....
4.3.3 Steam/Noncondensable Gas Mixture Side of the Apparatus: . . . 78
Results and Discussions: ...........
. . . . . .. . .. .. . 78
...
4.4.1
...
4.2 Experimental Equipment: .
4.2.1 Description:.
.............
4.2.2 Experimental Procedure: ......
4.3 Data Analysis: .
4.4
4.3.1
Coolant Annulus Side:.
4.3.2
Coolant Properties' evaluation: . . .
Buoyancy Effects:.
. . . . . . . . . . . .
..
. . . ..
..
. . . . . . . . ..
..
.
.
78
4.4.2 Early Transition to Turbulence and Flow Recirculation: . . .
79
4.4.3
80
Effects on Condensation Nusselt Numbers ...........
4.5 Conclusions:.
...............................
81
5 Experimental Results for In-Tube Steam Condensation in the presence of Helium and Helium & Air
91
5.1 Introduction: .................................
91
5.2
Steam condensation in the presence of Helium: ..............
92
5.2.1
5.2.2
Comparison with Pure Steam Theory and Correlations: .....
Condensate Film Thermal Resistance ...............
92
5.2.3
Comparison with Siddique-Golay-Kazimi's Steam/Helium Cor-
relation:.
5.2.4 Steam/Helium Correlations of the Present Study: .........
2
94
95
95
99
99
5.3 Steam condensation in the presence Air/Helium mixtures: ........
5.3.1 Comparison with Pure Steam Theory and Correlations: .....
5.4
5.3.2
Condensate
Film Thermal
Resistance:
5.3.3
Steam/Air/Helium
5.3.4
Steam/Air/Helium + Steam/Helium Data-Based Correlation: . . 104
Correlations:
. . . . . . . . . . .....
101
. . . . . . . . . . . . . .....
102
Conclusions: ...................
1...............105
5.4.1 Conclusions regarding steam condensation in the presence of he-
lium..................................
5.4.2
105
Conclusions regarding steam condensation in the presence of air
.......
and helium mixture .
107
6 Modeling In-Tube Steam Condensation in the Presence of Air, Helium, and
141
Air/Helium Mixtures
6.1 Introduction:
................................
.141
6.2 Modeling: ..................
.
...............
6.2.1
Condensate
film: . . . . . . . . . . . . . . . . . . . ...
6.2.2
Steam-Noncondensables Boundary Layer: .............
6.3 Results and Discussion: ...
......
6.4 Conclusions:
...................
...............
.142
.
.........
142
143
149
151
172
7 Conclusions and Recommendations
7.1 Conclusions: .
· 172
7.1.1 Experimental findings regarding steam condensation in the presence of noncondensable gases ...................
. 172
7.1.2 Conclusions regarding modeling in-tube steam condensation in
7.1.3
7.2
the presense of noncondensables: .................
Effects of Cooling Water Conditions: ...............
· 174
. 175
7.1.4 The Visualization Experiment Findings: .............
· 175
7.1.5 Buoyancy Effects in the Coolant Side Analysis: .........
Recommendations for Future Work: ...................
. 176
. 176
References
177
Appendix A
182
A Data Reduction Procedure
A.1 Steam/Noncondensables Mixture Side ..................
A.2 The Coolant Side ..............................
3
182
. 182
. 186
Appendix B
188
B Uncertainty Analysis
B.1 Experimental Heat Transfer CoefficientError Analysis . . .
B.1.1 Coolant Flow Rate Experimental Error .......
188
B.1.2
Wall Subcooling Experimental Error.
B.1.3 Coolant Temperature Gradient Experimental Error:
B.1.4 Overall Experimental Error ..............
B.2 Correlation Predicted Nusselt Numbers' Uncertainty ....
B.3 Void Fraction Experimental Error: ..............
....
....
....
....
....
.
.
.
.
.
188
189
190
190
191
.
.
.
.
.
....
. 191
.
....
. 191
.
193
Appendix C
C Reference Composition and Reference Temperature
193
. 193
. 193
. 195
C.1 Introduction................................
C.2 Reference Composition, W, W*, and Wh*:...............
C.3 Reference Temperature, T* .......................
Appendix D
196
D Performance Model
196
Appendix E
199
E Design of New Test Facility
E.1 Introduction: ........................
E.2 Description of Apparatus: .................
E.3 Description of the Thermocouple System: ........
199
E.3.1
E.3.2
E.3.3
Thermocouple System Placement .........
Surface Thermocouple's Machining .
Surface Thermocouple's Soldering (Brazing):
. .
.........
.........
.........
.........
.........
.........
.199
.200
.201
.202
.202
.203
Appendix F
224
F Steam/Helium Reduced Data
224
Appendix G
270
G Steam/Air/Helium Reduced Data
270
4
List of Figures
2.1
2.2
2.3
2.4
2.5
Schematic of Experimental Facility .....................
Thermocouple Locations ...........................
Details of Thermocouples ...................
.......
Effect of cooling water inlet temperature on the heat flux, wall subcool-
35
36
37
ing and heat transfer coefficient .......................
38
Effect of cooling watear flow rate on the heat flux, wall subcooling and
heat transfer coefficientat atmospheric system pressure .........
2.6
39
Effect of cooling water flow rate on the heat flux, wall subcooling and
heat transfer coefficientat a system pressure of 40 psig ..........
2.7
2.8
40
Effect of injecting air with cooling water on the heat flux, wall subcooling
and heat transfer coefficientat atmospheric system pressure .......
41
Effect of injecting air with cooling water on the heat flux, wall subcooling
and heat transfer coefficient at a system pressure of 40 psig .......
42
2.9 Effect of injecting air with coolingwater on the temperature
the heat flux for the laminar and turbulent flowregimes in
2.10 Effect of injecting air with coolingwater on the temperature
the heat flux for the laminar and turbulent flow regimes in
profiles and
the annulus . 43
profiles and
the annulus
for pure steam case ..............................
44
3.1 Visualization Experiment ..........................
58
3.2
3.3
Transducer Setup ...............................
NPT Connection to Annulus for Transducer System
..........
59
60
3.4
Annulus Alignment
. . . . . . . . . .
. . . . . . . . . . . . . . . . ...
.
60
3.5 The measured air void fraction against volumetric air flow ratio in airwater systems flowing upward in an annulus for different water Reynolds
numbers ....................................
61
5
3.6 The measured air void fraction against water Reynolds number in airwater systems flowingupward in an annulus for different volumetric air
flow ratios . . . . . . . . . . . . . . . .
.
. . . . . . . . . . ......
62
3.7 Experimental against correlation predicted void fraction values .....
63
3.8 The air velocity against the total superficial velocity ..........
. 64
3.9 The experimental against correlation predicted void fraction when the
characteristic diameter is taken as (Do - Di) . ..............
65
3.10 The experimental against correlation predicted void fraction when the
characteristic diameter is taken as (Do + Di) . ..............
66
3.11 The experimental against correlation predicted void fraction when the
characteristic diameter is taken as (Do)
..................
4.1 Schematic of the Coolant Annulus ...................
..
4.2 Air-water system density and volumetric thermal expansion coefficient
against the system air void fraction for different system temperatures ..
4.3 Grq/ReR variations along the coolant annulus for the three treatments
of the air-water system properties for the same cooling water flow rate
4.4
4.5
67
82
83
and same heat flux profile ..........................
The heat flux profiles and Gr/Rel 8 variations along the coolant annulus
for three cases with the same cooling water flow rate (Reinlet - 880) ..
The heat flux profiles and Gr/Rel 8 variations along the coolant annulus for three cases with different cooling water flow ratess (Reinlet
85
880, 1373, &2780) ...............................
86
84
4.6 Grq/ReR variations along the coolant annulus for three cases with the
4.7
4.8
same cooling water flow rate (Reinlet - 880) ................
The heat flux profiles and Grq/lReR variations along the coolant annulus for three cases with different cooling water flow ratess (Reint
880, 1373,&2780) ...............................
The condenser inner wall temperature profile against theoritical predic-
87
88
tion ......................................
89
4.9 The local values of Jackob number and condensation Nusselt number
along the condensing tube length for three different experimental runs . 90
5.1 Condensation heat transfer coefficients in the presence of helium and
those of pure steam correlations against the mixture Reynolds numbers 112
6
5.2 Condensation heat transfer coefficientsin the presence of helium and
those of pure steam correlations against helium mass fraction in the
mixture ....................................
5.3 Condensation heat transfer coefficientsin the presence of helium and
those of pure steam correlations against helium mole fraction in the
mixture ....................................
5.4 Condensation heat transfer coefficientsin the presence of helium and
those of pure steam correlations against the mixture Jackob number .
5.5 Condensation heat transfer coefficientsin the presence of helium and
those of pure steam correlations against the mixture Schmidt numbers .
5.6 The ratio of steam condensation heat transfer coefficientsin the presence
of helium to those of pure steam against Reynolds numbers ......
.
5.7
5.9
5.10
5.11
5.12
114
115
116
117
The ratio of steam condensation heat transfer coefficients in the presence
of helium to those of pure steam against helium mass fraction .....
5.8
113
. 118
The ratio of steam condensation heat transfer coefficients in the presence
of helium to those of pure steam against helium mole fraction .....
.
Comparison between the experimental condensation heat transfer coefficients and those obtained using a correlation produced by Siddique, et
al [5 ..
....................................
Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/helium correlation #1 ......
Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/helium correlation #2 ......
The bulk temperature and steam, helium, and mixture dynamic viscos-
119
ity profiles along the condensing tube length ................
123
120
121
122
5.13 The bulk temperature and steam, helium, and mixture density profiles
along the condensing tube length .....................
124
5.14 The gas mixture kinematic viscosity and mass diffusivity profiles along
the condensing tube length
.........................
125
5.15 The gas mixture Schmidt number, helium mass fraction, and condensa-
tion heat transfer coefficientprofiles along the condensing tube length . 126
5.16 Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/helium correlation #3 ......
127
5.17 The condensation heat transfer coefficients in the presence of air nadhe-
lium and those of pure steam correlations against the mixture Reynolds
numbers ....................................
128
7
5.18 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against air mass fraction .. 129
5.19 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against helium mass fraction130
5.20 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against air mole fraction .. 131
5.21 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against helium mole fraction 132
5.22 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against mixture Jackob
number ....................................
133
5.23 The condensation heat transfer coefficientsin the presence of air and
helium and those of pure steam correlations against mixture Schmidt
number ....................................
134
5.24 The variations of the ratio of steam condensation heat transfer coefficients in the presence of air and helium to those of pure steam with
mixture Reynolds
numbers
. . . . . . . . . . . . . . . . . . . ......
135
5.25 The variations of the ratio of steam condensation heat transfer coefficients in the presence of air and helium to those of pure steam with air
& helium mixture mass fraction .......................
136
5.26 Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/air/helium correlation #1 . . . 137
5.27 Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/air/helium correlation #2 . . . 138
5.28 Comparison between the experimentally obtained condensation Nusselt
numbers to those obtained using steam/air/helium correlation #3
. . . 139
5.29 Comparison between the experimentally obtained condensation Nus-
selt numbers to those obtained using steam/air/helium correlation #4,
Equation
(5.19) .
. . . . . . . . . .
. . .. . . . . . . . . . . . . .
. 140
6.1 The calculated interface temperatures, the measured centerline and inner wall temperatures along the condensing tube length for a typical
steam-helium run (run# hs6 at relatively low mixture Reynolds numbers 153
6.2
The calculated interface temperatures, the measured centerline and in-
ner wall temperatures along the condensing tube length for a typical
steam-air-helium run (run# has6 at relatively low mixture Reynolds
numbers ................
..
154
8
6.3 The calculated interface temperatures, the measured centerline and inner wall temperatures along the condensing tube length for a typical
steam-helium run (run# hs24 in turbulent forced convectionflow . ... 155
6.4 The calculated interface temperatures, the measured centerline and inner wall temperatures along the condensing tube length for a typical
steam-helium run (run# has63 in turbulent forced convectionflow . . . 156
6.5 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-helium run
(run# hs31 in forced convection flows ...................
157
6.6 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-helium run (run# hs31 in forced convection flows
.................................
158
6.7 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-helium run
(run# hs24 in forced convection flows ...................
159
6.8 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-helium run (run# hs24 in forced convection flows .................................
160
6.9 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-helium run
(run# hs44 in forced convection flows ...................
161
6.10 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-helium run (run# hs44 in forced convection flows .................................
162
6.11 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-air-helium
run (run# has24 in forced convection flows ................
163
6.12 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-air-helium run (run# has24 in forced
convection flows ...................
1.............
164
6.13 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-air-helium
run (run# has41 in forced convection flows ................
165
6.14 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-air-helium run (run# has41 in forced
convection flows ................................
9
166
6.15 The calculated mixture heat transfer coefficients(HTC's), the measured
HTC's, and the condensate film HTC's for a typical steam-air-helium
run (run# has75 in forced convection flows ................
167
6.16 The calculated mixture heat transfer coefficients(HTC), the measured
HTC's, and for a typical steam-air-helium run (run# has75 in forced
convection flows ................................
168
6.17 Comparison between model-predicted steam/noncondensables mixture
Nusselt numbers and experimentally obtained mixture Nusselt numbers 169
6.18 Comparison between model-predicted steam/noncondensables mixture
Nusselt numbers and experimentally obtained mixture Nusselt numbers
for turbulent flows ..............................
170
6.19 Comparison between model-predicted steam/noncondensables mixture
Nusselt numbers and experimentally obtained mixture Nusselt numbers
for turbulent flowswith different C & n values .
E.1 New Test Section Design .
E.2 Gas/Steam Link to Test Section Entrance .
E.3
Cooling Water Inlets/Outlets.
E.4 Top End of Condenser .
E.5 Bottom End of Condenser .............
E.6 Thermocouple System .
E.7
Centerline
Thermocouple
....
. 171
.
....
....
....
....
.
.
.
.
.
.
.
.
205
206
207
208
.......209
....
Setup . . . . . . . . . .
. 210
. 211
E.8 Inner Wall Thermocouple Machining for All Stations (Except Top Station)212
E.9 Thermocouple Placement of All Stations Except 1, 2, 11, 19
.... . 213
E.10 Inner Wall Thermocouple Machining for Top Station . .
.... . 214
. 215
E.11 Top Station Thermocouple Placement .
E.12 Thermocouple Placement for Stations 2, 11, 19 .......
E.13 Details of Cooling Water Inlet/Outlet .
E.14 Fixtures on Outer Jacket for Surface TC Leads .
E.15 Probe Sealing Fixture in Outer Jacket .
E.16 Coolant TC Fixture Locations on Outer Jacket Tube
E.17 Lead Sealing Fixture in Outer Jacket .
E.18 Details of the Upper Part of the Current Design ..
E.19 Details of the Lower Part of the Current Design .
10
..
.
.
.
.
.
....
....
....
. 216
. 217
. 218
.
....
....
. 220
. 221
.
.
.219
....... 222
.223
.
.
.
.
List of Tables
2.1
2.2
2.3
2.4
Test
Test
Test
Test
Matrix
Matrix
Matrix
Matrix
for High Inlet Air Mass Fraction in Steam/Air Mixture . .
for Pure Steam Runs .
.....................
flor Low Inlet Air Mass Fraction in Steam/Air Mixture . .
for Studying the Effect of Cooling Water Inlet Temperature
3.1
Test Matrix for Visualization
Experiment
5.1
Test Matrix for Steam/Helium
Mixtures
..
. . . . . . . . . . . . . .....
5.2 Test Matrix for Steam/Air/Helium Mixture
E.1
. . . . . . . . . . . .
57
110
...............
111
Comparison between Current Test Section and New Design .......
204
11
.
33
33
34
34
Nomenclature
A
= tube inside surface area, or system parameter [see Equation (6-2)]
Co
Cp
d
= distribution parameter
= specific heat capacity
= condensing tube inner (ID)
D
= diameter or diffusion coefficient
D1 2
= bibary diffusion coefficient
ENhR
EChR
g
Gr
=
=
=
=
=
Grq
= Grashoff number based on wall heat flux and
experimental to Nusselt heat transfer coefficient[47]ratio
experimental to Chen, et al [27]heat transfer coefficientratio
acceleration of gravity
Grashoff number based on temperature difference
and hydraulic diameter of annulus
hfg
hydraulic radius of the annulus
= condensation heat transfer coefficient,or
= vertical distance between transducer measuring points in Chapter 3.
= latent heat of condensation
j
J
= local superficial velocity (volumetric flux)
= area-averaged superficial velocity (volumetric flux)
Ja
1
L
=
=
=
=
M
= molecular weight
h
= mass flowrate
mhIt
= mass flux
h
lo
Jackob number
axial location at tube length
effectivetube length
length
12
Nu
= Nusselt number
No
= dimensionless inverse viscosity number [see Equation (3-24)]
NPT
= National Pipe Thread
P
= pressure
Pl,
PVC
= critical pressure
= Poly Vinyl Chloride
Pr
= Prandtle number
Q
= volumetric flow rate
q
= heat flux
R
Re
ReR
Sc
T
TCe
=
=
=
=
=
=
U
= velocity
V
= volumetric air flow ratio to water/air mixture
VSj
= local drift velocity
W
= mass fraction
x
Y
= flow quality
= mole fraction
z
= axial position
radius
Reynolds number based on hydraulic diameter
Reynolds number based on hydraulic radius
Schmidt number
temperature
critical temerature
Greek Symbols
a
= void fraction
/3
6
= volume expansion coefficient
= condensate film thickness
AP
Ap
K
=
=
=
=
p
v
pressure differential
density difference
thermal conductivity
dynamic viscosity
= kinematic viscosity
13
p
a
= density
= surface tension
Subscripts
a, air
an
b
c
=
=
=
=
cl
con
= center line
= condensate film
f
g
= saturation liquid or fluid
= saturation vapor
g, gas
= gas
h
has
He
hs
i
in
=
=
=
=
=
=
1
= liquid, or local position along the condensing tube length
mix
= steam/noncondensable gases mixture
nc
= noncondensable
o
p
q
R
s
sat
t
ti
=
=
=
=
=
=
=
=
tot
= total
trans
= transducer
air
annulus
bulk
coolant in the annulus
hydraulic
steam/air/helium mixture
helium
steam/helium mixture
inner, interface
inlet
outer
constant pressure
based on heat flux
based on hydraulic radius
steam
saturation
tube
tube inside
14
v
w
= vapor
= cooling water; wall
Superscripts
film
= condensate film
in
lam
= condenser inlet
= laminar
lm
= Iogarithmic mean
mix
= steam/noncondensale gases mixture
N
= based on Nusselt assumptions
sat
turb
= saturation
= turbulent
v
w,x,y,z
= vapor-free basis
= correlation's coefficients
15
Chapter 1
Introduction
The presence of noncondensables in steam greatly inhibits the condensation process.
In a nuclear containment building, air and the accidental presence of hydrogen represent the main noncondensable gases. While air exists naturally in the containment
building, hydrogen can exist in case of a Loss of Coolant Accident (LOCA) or steam
line break accident. The principal sources for hydrogen production are the exothermic
fuel cladding chemical reaction with steam, radiolytic decomposition of water and corrosion of certain metallic species present in the containment. In a situation like this,
mixtures of steam, air and hydrogen will be present in the containment. Experimental assessments of the effects of air, hydrogen and the simultaneous effects of air and
hydrogen on steam condensation are therefore needed.
Many experimental and theoretical efforts have been done on the effects of noncondensables on condensation. Jensen [1] offers interesting discussions on the progress
made up to 1988. However, most of the investigations focused on the determination
of the average values of condensation heat transfer coefficients. Recently, a number
of studies investigated the effects of noncondensables on the local values of the con-
densation heat transfer coefficients. Vierow [2] performed experiments to investigate
the effects of air on local steam condensations in natural circulation in a vertical tube.
Dehbi [3] performed steam/air and steam/air/helium experiments for external condensation on a vertical wall under turbulent natural conditions. His work was done
in support of the cold wall concept for containment cooling of the Simplified Boiling
Water Reactor (SBWR) [3]. It is a common practice in experiments studying the effects of hydrogen on condensations that hydrogen is replaced by helium because of
the more demanding handling of hydrogen due to its explosive potential above certain
concentration. Both helium and hydrogen are light gases and have similar thermal and
diffusivecharacteristics. Ogg [4]ran air/steam and helium/steam experiments in order
16
to study their effectsupon local heat transfer coefficientsin a vertical tube under forced
flow conditions. Siddique [5] performed steam/air and steam/helium experiments in
a vertical tube under forced flow conditions. However,the range of the steam/helium
mixture Reynolds number and that of helium mass fraction were limited and further
experiments are needed to cover a wider range of these parameters. In addition, there
are no experiments in the literature on the simultaneous effects of air and helium on
steam condensation under forced flow conditions.
The objective of the present investigation is to study the effects of helium and the
simultaneous effects of air and helium on steam condensation in vertical tubes under
forced convection conditions.
Chapter 2 is a sensitivity analysis aimed at investigating the effects of cooling water
conditions on local heat fluxes, and consequently upon local condensation heat transfer
coefficients. The coolingwater conditions are mainly its flowrate, air (injected into the
cooling water to promote mixing) flowrate, and water inlet temperature. The effects
of cooling conditions on the previously reported wall temperature abrupt increase in
the middle of the channel have also been investigated.
Chapter 3 is an experimental and theoretical investigation of the effects of hydraulic
conditions of the coolant annulus.
A visualization experiment was constructed to
simulate the coolant side of the existing test facility. The primary objective of the
investigation was to determine the amount of air which is sufficient to achieve good
radial mixing along the length of the coolant annulus. Another objective was to observe
any secondary flows which might exist because of the annular geometry.
Chapter 4 is an analysis of the experimental data of the coolant side of the condensation experiment. The analysis aims at assessing the effects of buoyancy on the
heated upwardly flowingwater hydraulics and more specifically,to investigate the possibility of having buoyancy-driven secondary flows, early transitions to turbulence or
both within the coolant annulus. Another important objective was to assess the impact
of the effects of such phenomena on determining the local values of the condensation
heat transfer coefficients.
Chapter 5 describes in detail the experimental results of steam condensation in
the presence of helium and in the presence of both air and helium. It provides the
functional dependencies of the data on various nondimensional groups and examine the
significanceof the condensate film thermal resistance. The experimental data is then
correlated using these nondimensionalgroups for future use in predicting the behaviour
of the local steam/helium system, more precisely predicting the condensation Nusselt
numbers in vertical tubes for the range of condtitions utilized in these experiments. A
comparison with existing data in the literature has been also attempted.
17
Chapter 6 presents a simple diffusion boundary layer based model. The model
includes the effect of more than one noncondensable gas on steam condensation under
forced flow conditions. The model-predicted condensation heat transfer coefficients
have been compared to the experimentally obtained condensation heat transfer coefficients.
Chapter 7 presents the conclusionsand reccomendations.
18
Chapter 2
The Effects of Cooling Water
Conditions on In-Tube Condensation
in the Presence of Noncondensables
2.1
Introduction
Determination of local condensation heat transfer coefficientsin the presence of
noncondensables has been increasingly needed for many industrial applications. A
particular example is the Heat Exchanger (HX) of the Passive Containment Coolant
System (PCCS) in the proposed advanced boiling reactor design (Simplified Boiling
Water Reactor). This HX serves as the heat sink for the removal of the reactor coolant
system sensible heat and core heat.
During a typical postulated loss of coolant accident or steam line break, a steam/air
mixture may flow to the PCCS Heat Exchanger. The steam condenses and the condensate drains back to the reactor pressure vessel. Local values of the condensation
heat transfer coefficientsare needed for predicting the overall performance of the PCCS
and for optimizing the HX design. In order to obtain local values of the heat transfer
coefficients experimentally, determination of local heat fluxes is necessary.
However, this involves some difficulties. In most of the experimental work carried
out thus far concerning local condensation heat transfer in the presence of non noncondensables gases [2, 3, 4, 5], local values of heat fluxes were normally determined in
terms of the axial gradients of the measured coolant bulk temperatures; a technique
which is widely used in other applications as well. Thus, cooling conditions which may
affect the coolant temperature measurements eventually would affect values of the local
heat transfer coefficients.
In some situations, in order to obtain reasonably large temperature gradients in the
19
coolingmedium, the coolant flowrate is kept solow that the flowregime is laminar. In a
laminar flowa steep radial temperature gradient can exist and the thermocouple probes
in the middle of the coolant channel would not sense the correct bulk temperatures.
In order to overcome this limitation, Siddique [5] bubbled small amounts of air into
the cooling water flow in order to enhance turbulence and mixing, but a misture of
air/water flow creates a two phase flow. A sensitivity analysis is required in order to
determine the optimal amount of air to be bubbled so as to attain better mixing and
yet not to affect values of local heat fluxes. On the other hand, increasing the cooling
water flow rate such that turbulent flow conditions are achieved would provide the
mixing required for proper measurements for the coolant bulk temperatures. This may
work well at high power levels (high inlet steam fl! ow rates). However, at low power
levels, the temperature change per unit length of the condenser tube would be low and
the condensation length would be too short for any useful data to be obtained.
Also, cooling conditions may involve other associated phenomena in the cooling
channel because of the geometry. These phenomena may affect the local values of wall
or coolant temperature measurements from which local heat transfer coefficientsare
inferred. As an example of that, "temperature inversion" over the upper part of the
condensing tube was observed in measurements performed both at MIT and Berkeley
[2,3]. The cause for the inversion might be different for the two groups; however,
since the phenomenon affects the local wall temperature of the condensing tube, an
understanding of it is necessary.
Understanding the effects of cooling conditions upon local values of the condensation heat transfer coefficients is required in order for any meaningful comparison
of local values of heat transfer coefficients to be made among the results of different
experimental studies. The objective of this chapter is to provide a set of experimental
results from an investigation of the effects of cooling water conditions upon in-tube
condensation in the presence of air as a noncondensable, and thus to provide a basis
for clear phenomenological understanding.
2.2
Experimental Setup and Data Analysis
2.2.1 Description of Apparatus
Figure (2-1) shows the flow diagram of the experimental test facility used in the work
reported here. It consisted of an open cooling water circuit and an open steam/air
flow path. Four immersion type sheathed electrical heaters that can be individually
controlled (on or off) and which are rated at 7 kW each were used to generate steam
20
by boiling water in a cylindrical stainless steel vessel of 5.0 m height and 0.45 m inside
diameter. Finer control of the power level was achievedby means of a Variac connected
to one of the heaters. A pressure regulating valve, a flow control valve and a calibrated
rotameter were used to supply compressed air to the base of the steam generating
vessel. The vessel was also used as a mixing chamber where air was injected near
the vessel bottom and it mixed with the steam to form a homogeneous gas mixture
in thermal equilibrium. The steam/air mixture left the pressure vessel through an
isolation valve which was fitted to the side, near the top of the vessel.
As the gas mixture left the vessel near the top, its flow was controlled by the
isolation valve. The flow rate was measured downstream from this valve, using an
accurately calibrated vortex flow meter. The mixture pressure and temperature were
also measured before the mixture reached the inlet of the test section. The test section
used a stainless steel tube for condensation of the mixture on its inner surface. The
dimensions of the tube are 50.8 mm outside diameter (OD), 46.0 mm inside diameter
(ID) and 2.54 m in length. The stainless steel (SS) tube was also surrounded by a 62.7
mm (ID) jacket pipe. As the mixture flowed down the condenser tube, cooling water
flowed upward through the surrounding annulus. Thermal stresses were prevented by
using a sliding joint (consisting of an O ring at the bottom of the condenser) that
allowed relative motion between the tube and the jacket pipe. The liquid emerging
from the condenser was then separated in a condensate separator drum. The residual
air/steam mixture from the condenser was ven! ted to the atmosphere via the same
throttle valve. The whole apparatus including the steam generator, the test condenser
and the separator drum were thoroughly insulated with fiber glass wool to minimize
heat loss to the surroundings.
The cooling water supplied to the test condenser was not recycled, i.e., once-through
coolant flow was used. A flow control valve coupled with a calibrated rotameter were
used to control and measure the coolant flow. All cooling water exited the condenserat
the top of the test section directly to the drain. Figure (2-2) depicts the thermocouple
locations of the cooling water, the inside and outside of the tube wall, and the condenser tube centerline gases. Measurements of the above temperatures were taken at
nine locations, 0.3 meters apart, along the length of the condenser. Figure (2-3) shows
the details of the test section instrumentation. J-type (iron/constantan)thermocouples
were used for all temperature measurements. A 3.2 mm OD SS tube, horizontally in-
serted through the jacket wall and the condenser wall using compressionfittings, was
used to take gas mixture samples at each measuring station. A 1.6 mm OD SS sheathed
rigid thermocouple probe was inserted through the same tubing to measure the the centerline gas mixture temperature. Unfortunately all gas sampling had to be abandoned
21
due to blockage of the sample lines to the gas analyzer caused by steam condensation.
An attempt, in wrapping the sample line with with electrical resistance heating wiring
to overcome the condensation problem, failed. Therefore, gas composition measure-
ments along the condenser tube could not be made.
Measurements of the outer wall temperature were made by means of 0.8 mm OD
SS sheathed thermocouple probes, embedded in longitudinally machined grooves of
dimensions 0.9 mm wide x .4 mm deep x 1.7 mm long. The same kind of thermocou-
ples embedded in drilled holes filled with solder were used to measure the inner wall
temperatures.
Drilling the holes, which entered the tube wall at angle, was made such
that they would reach the inner tube surface without piercing through it. This served
as to locate the thermocouple's physical junction to less than 0.2 mm from the inner
surface of the 4.8 mm thick tube wall. In these experiments it was estimated that the
maximum error in measured wall temperature was 0.3°C. All the wall thermocouple
wires were taken out of the coolant jacket walls through compression fittings located
at the ends of the test section.
The temperatures of the cooling water were measured using 1.6 mm OD SS sheathed
rigid thermocouple probes inserted through the the coolingjacket wall to the mid point
of the annular gap. The temperatures of the coolant at the inlet and the exit (exhaust)
were also measured downstream from well insulated, 610 mm, mixing lengths in 38.0
mm OD pipe filled with wire mesh.
The pressure of the air/steam mixture at the entry of the test section was measured using a high precision calibrated pressure transducer. These measurements were
accurate to 0.1 kPa.
The inlet air mass flowrate in the condenser was determined from the measurements
of the air flowrate into the boiler vessel. A separate calculation was made of the steam
mass flow rate based upon the measured heater power input to the boiler which was
corrected for heat losses to the surroundings and the heat gained by the air in attaining
thermal equilibrium with steam. Calibration for the boiler heat losses was carried
out at all three operational temperatures of the experiments. The heat losses were
compensated for by taking the boiler to the desired temperature and then using the
Variac to adjust the heater power to account for the heat losses and hence to maintain
a steady boiler temperature.
The room temperature for these tests was the same as
when the actual experimental runs were made.
To checkthe inlet gas mixture flowrate reading, measured by the vortex flowmeter,
its reading was compared with the flowrate obtained by summing the individual steam
and air flow rates. The measured flow rate value obtained using the vortex flow meter
was found to be within 3% of that calculated value using individual flow rates. At the
22
largest discrepancy, the vortex flow meter reading was found to be greater than the
calculated value.
In preliminary tests, which were carried out using pure steam and in which all steam
is totally condensed, the total condensate flow rate was also calculated by observing
the rise in the level of the condensate separator tank over a measured time interval.
The condensate mass was calculated from the measurements of the inside diameter of
the tank and the condensate temperature. The steam mass flow rate at the inlet of
the condenser was also calculated. The two values of the flow rates obtained matched
closely showingthat the heat losses from the outer jacket were negligibleand the steam
flow measurements were quite accurate.
The mass fraction of air in the inlet stream was calculated from the individual mass
flow rates of air and steam. This value was checkedagainst that obtained by using the
measured values of inlet temperature and pressure - assuming saturation conditions and the followingGibbs-Dalton ideal gas mixture equation:
=
Ptot(- P (Tn)
(2.1)
The values of the air mass fraction determined by the two methods were found to
be in very good agreement.
The air injected with the cooling water into the annulus was taken from a compressed air supply and regulated to the desired pressure by means of a pressure reg-
ulator. The volumetric flow rate was then measured by means of a rotameter with a
built-in 16-turn precision valve for fine control of the flow. Different flow tubes were
used, depending on the air flow rate, for accurate air flow rate measurements.
A data acquisition (DA) system with fourty input channels was used to collect
data from thermocouples, pressure transducers, and vortex flow meter. The DA sys-
tem comprised of a scanner and a data processor linked to a Personnel Computer
(PC). The scanner scanned at a rate of 40 channels per second and the processor was
adjusted to record data every minute and to perform average and standard deviation
calculations. At steady state the input readings stabilized, as was manifested in the
low data standard deviation values.
2.2.2 Experimental Procedure
Before the start of each experiment the boiler was disconnected from the rest of the
system and the water level in it adjusted. Then the heater was turned on. All the
instruments were checked to ensure that they were functioning properly and initial
23
readings were recorded. Depending upon the water inventory, reaching the set temper-
ature of 2 to 40 C above the desired mixture inlet temperature required about 1 - 1.5
hours. Simultaneously,the coolant flowrate to the test condenser was adjusted to the
required value and then the boiler power was adjusted, using the Variac, to account
for heat losses and maintain the desired steam production rate.
The air flowrate for a set steam flow rate was adjusted such that it would give the
desired inlet air fraction. Air at room temperature was supplied at the desired rate
to the base of the boiler. Meanwhile, the boiler isolation valve was left fully opened.
In order to stabilize the system pressure, manual adjustments to the throttle valve
on the vent line of the condensate separator drum were made. When the boiler and
test condenser pressure and temperature readings had stabilized to a nearly constant
value for 15 minutes to ensure that the facility had reached steady-state condition, all
readings were then recorded for each channel for a period of two minutes. Coolant and
air flow rates were recorded separately. At the end of the run, the next desired inlet
volumetric air flow rate for a given water flow rate was obtained by increasing the air
flowinto the annulus and stabilizing the system pressure as before. Similarly,the next
cooling water was achieved by increasing the cooling water flow into the annulus and
then stabilizing the system pressure. Checks of the water level in the boiler and the
condensate separator drum were made before the start of each successive run by means
of a sight glass level. The separator drum was emptied by draining off the condensate.
Tests were terminated as soon as the boiler inventory was reduced to the threshold
level.
2.2.3
Data Analysis and Experimental Errors
The local values of the heat fluxes were calculated from the followingequation obtained
from a steady state energy balance on the coolant side:
q"'(z)dA= ,,,CpdT,,,,
or
q"(x) =
,,,C, dT,
W
-
(z),
(2.2)
(2.3)
with the local gradients of the cooling water temperature profile dT,/dL being determined using a least squares polynomial fit of the cooling water temperature profile.
The adjusted R2 value for the fit of the data to the polynomial was greater than 0.98
so that the error associated with curve fittings is small. Then, the local condensation
heat transfer coefficients were calculated using the following equation:
24
h(z) = q (z)
T, - Ti'
(2.4)
where Te - Ti is the local wall subcooling at position x of the condensing tube.
The errors associated with heat transfer coefficientscalculations were estimated to be
±20%. The errors associated with heat flux calculations were found to be low near the
upper part of the condensing tube ( with +6% being estimated as the highest value ),
and high near the lower end of the condensing tube ( with i15% being estimated as
the highest value ). The error analysis is detailed in Appendix B.
2.3 Experimental Results
The following results from part of a sensitivity analysis covering a range of data in which
inlet air/steam mixture temperature, inlet steam flow rate, inlet air mass fraction in
steam, cooling water flow rate, inlet air (in cooling water) flow rate and inlet cooling
water temperature were varied. The results presented in this paper are typical examples
of the full data set. The test matrices for the analysis are shown in Tables 2.1, 2.2, 2.3
and 2.4.
2.3.1
Effect of Cooling Water Inlet Temperature
Figures (2.4a) and (2.4b) show the measured distributions of air/steam mixture cen-
terline temperature, inner wall temperature and cooling water temperature for two
different inlet cooling water temperatures (Twi = 6.6&18.30 C); in both cases the inlet
steam/air mixture is .04, the inlet steam flowrate is 20 kg/hr, and no air is injected into
the cooling water. Figure (2.4c) shows the heat flux distributions along the condenser
tube for both cases. The heat fluxes display greater axial gradients for the lower inlet
cooling water temperature, convergewith those of higher cooling water inlet temperature till they meet at a certain point (around 1.6 m), and then become lower. Figure
(2.4d) shows the temperature difference (Ti - Ti) distributions.
The differences are
small at the top and they get higher as one moves down the condenser tube. Figure
(2.4e) shows the local heat transfer coefficients. Near the steam inlet, they are higher
for lower inlet cooling water temperature, come closer to those of higher inlet cooling
water temperature till they meet at a certain point below which they become lower.
25
2.3.2
Effect of Cooling Water Flow Rate
Figures (2.5a)-(2.5c) show the measured distributions of air/steam mixture center-line
temperature, inner wall temperature and cooling water temperature for three different
cooling water flowrates (,, = 3.6, 8.5 and 17 kg/min); in all cases the inlet steam/air
temperature is 100°C, the inlet air mass fraction in the steam/air mixture is 0.24, the
inlet steam flow rate is 29 kg/hr and no air is introduced in the cooling water. Figure
(2.5d) shows the heat flux distribution along the condenser tube for the three cooling
water flow rates. Figure (2.5e) shows the local temperature differences (Te - Ti) for the
three cases. They are indicative of the wall subcooling values introduced by increasing
the cooling water flow rate. The temperature differences are higher for higher cooling
water flow rates. Figure (2.5f) shows the local heat transfer coefficientsalong the
condenser tube for the three cases. They are generally lower for higher cooling water
flow rates. Figures (2.6a)-(2.6f) are repetitions of the above at inlet steam/air mixture
temperature of 1400C although at slightly different conditions. The trend of the results
observed are similar to those discussed previously.
2.3.3 Effect of Air Injection with Cooling Water into the Annulus
Figures (2.7a)-(2.7c) show the measured distributions of air/steam mixture centerline
temperature, inner wall temperature and cooling water temperature for three different
inlet volumetric flow ratios of air to the air/water mixture (%v = 0, 10 and 20); in
all cases the inlet steam/air mixture temperature 1000 C, the inlet air mass fraction
in steam/air mixture is 0.24, the inlet steam flow rate is 29 kg/hr and the cooling
water flow rate is 3.7 kg/min. Figure (2.7d) shows the heat flux distribution along the
condenser for these three cases. The heat flux values are generally lower than those
ofcases having no air injection over the upper part of the condenser, intersect and
then become higher over the rest of the condenser tube. It is interesting to observe
how air injection can greatly change the heat flux profiles as shown in Figures (2.7d),
(2.8d), (2.9c), (2.10c) and (2.10f). Figure (2.7e) shows the temperature difference (TIl
- Ti) distribution over the condenser tube. Generally these differences are higher for
higher inlet air volumetric con centration. However,the differencesbetween the three
cases are small at the top of the test section and they increase as one moves down the
condenser tube. Figure (2.7f) shows the profiles of local heat transfer coefficients along
the condenser tube. They decrease as the inlet air low rate (in coolingwater) increases.
Also, the local heat transfer coefficientsreported by Siddique [5], are plotted in the
same figure as well as in Figure (2.8d) for the same relevant conditions. Siddique [5]
stated the he had injected air into the cooling water, but failed to report the amount of
26
air injected. Figures (2.8a)-(2.8f) are repetitions of the aboveat inlet steam/air mixture
temperature of 1400C,though at slightly different conditions. Basically the data show
the same trend as noted previously. Figures (2.9a)-(2.9f), (2.10a)-(2.10f) show the
effects of the same inlet volumetric air flow ratio upon the heat flux distribution for
two different cooling water flow rates (4.5 & 17 kg/min). The two cooling water flow
rates were chos en to represent two different flow regimes in the annulus; laminar and
turbulent. It is seen that the heat flux profile is much less altered in the turbulent
regime than in the laminar regime for the same inlet air volumetric flow rate fraction
in the annulus.
2.3.4
Temperature Inversion
During the analysis of these data it was observed that the wall temperature profile
exhibits a dip near the middle of the upper part of the condenser. A similar behavior
has been also observed by Vierow [2] and Ogg [3], and termed as a "temperature inversion". Figures (2.4a), (2.4b), (2.5a), (2.5b), (2.5c), (2.6a), (2.6b), (2.6c), (2.7a), (2.7b),
(2.7c), (2.8a), (2.8b), (2.8c), (2.9a), (2.9b), (2.10a) and (2.10b) show this temperature
inversion. Figures (2.5a), (2.5b), (2.5c), Figures (2.6a), (2.6b), (2.6c), Figures (2.9a),
(2.9b), (2.9d), (2.9e), and Figures (2.10a), (2.10b), (2.10d), (2.10e) show that as the
cooling water increases, the phenomenon becomes more and more pronounced. Figures (2.7a), (2.7b), (2.7c), Figures (2.8a), (2.8b), (2.8c), Figures (2.9a), (2.9b), (2.9d),
(2.9e), and Figures (2.10a), (2.10b), (2.10d), (2.10e) show that as the inlet volumetric
are flow fraction increases, the phenomenon becomes more and more depressed. It
has also been observed that at low steam flow rates (below 10 kg/hr) and low inlet
air mass fraction in steam/air mixture (below 0.1) and cooling water flow rates above
3.7 kg/min, the phenomenon was not observed. But it was later observed when the
cooling water flow rate was reduced. It was also observed at low steam flow rate, but
with higher inlet air mass fraction in the steam/air mixture.
2.4
Discussion of Results
2.4.1 Effects of Inlet Cooling Water Temperature
Figsures 4a-4e are relevant to this discussion. As the inlet cooling water temperature
decreases, the local temperature differencesbetween the steam/air mixture centerline
and the cooling water (which along with vapor pressure differences are the driving
potentials for higher heat transfer rates) increase. Since we have the same inlet steam
flow rate, the steam/air mixture of lower inlet cooling water temperature case will dry
27
out faster than that of higher inlet cooling water temperature case thereby resulting
in a shorter condensation length. Since this is a steam rich case, at the steam inlet the
main heat and mass transfer resistance will come from the condensate film. At the very
top of the condenser tube the higher condensation rates will cause more vapor to flow
from the free stream toward the cold wall and to start to form a condensate film. The
thickness of the condensate film increases as one moves down the tube and at the same
time more of the air from the remaining steam/air mixture moves to the surface of the
condensate and attains higher concentration resulting in higher resistance to heat and
mass transfer.
Consequently the heat transfer coefficients are higher for lower inlet
water temperature over the top part of the condenser than those of higher inlet cooling
water temperature until a certain axial point (somewherebetween 0.7 and 1.0 m below
the steam inlet in this case) and then they become lower.
2.4.2
Effect of Cooling Water Flow Rate
Figures (2.5a)-(2.5f), (2.6a)-(2.6f) are relevant to this discussion. As the cooling water
flow rate increases, the flowregime inside the annulus changes from laminar to turbulent. This will lead to a more efficientheat transfer mechanism in the annulus resulting
in higher wall subcoolings (To - Ti) as shown in Figures 2.5e and 2.6e. Higher wall
subcooling will lead to high heat transfer rates (Figs. 2.5d and 2.6d). Higher heat
transfer rates imply higher rates of air moving toward the condenser wall; with steam
condensing adding to the film thickness and the air attaining higher concentration at
the interface of the condensate film. Both mechanisms contribute to higher resistance
to heat and mass transfer. At the very top of the condenser, the main heat and mass
flow resistance will come from the air and; as one moves down the condenser tube, the
resistance from the condensate film will come into play. Figures 2.5f and 2.6f show
the heat transfer coefficient decreasing as the cooling water flow rate increases for two
different system pressures; 0 & 40 psig, respectively. The trend is essentially the same
as seen previously.
2.4.3
Effect of Air Injection with Cooling Water into the Annulus
Figures (2.7a)-(2.7f), (2.8a)-(2.8f) are relevant to this discussion. Air is introduced with
cooling water into the annulus in order to promote mixing of the cooling water at low
water flowrates. Such air injection induces turbulence in the coolant annulus as can be
seem from the increase in wall subcooling with air injection (Figures (2.7e) and (2.8e)).
However,introducing air into the cooling water changes the cooling mechanism of the
condensing tube from that of a reasonably well understood single phase flow to that of
28
a somewhat more uncertain two phase flow. Thus, before we discuss the experimental
results, we first try to identify the flow regime in which the system operates. Within
the range of data taken in this work, the highest superficial air velocity was 0.08 m/s.
According to the flow regime map of Kellessidis, et al [6], for air-water concentric
annulus with an inner tube having OD of 0.051 m and outer tube with ID of 0.076 m
(exactly the same as the OD of the inner tube used in the work presented here, but
the ID of the of the outer tube in this work is different, being of 0.0627 m) the flow
regime would be identified as bubbly. However, Taitel et al [7], showed experimentally
that for very small circular channels the bubbly regime may not exist, in which case
only slug flow would exist at low liquid and gas velocities. Indeed, the system used
for the work presented here satisfies the following criterion for a small-diameter (no
bubbly regime) system [7];
1
[(Pq)a36,
-I
.
(2.5)
with the value of the left-hand side of the Inequality 2.5 being calculated to be 3.04.
The diameter D, in the above equation, is taken to be the hydraulic diameter of the
concentric annulus, namely D - Di. Because the hydraulic diameter of the system used
to produce the regime map of Kellessidiswas slightly more than twice that of the one
used in this work, we will not rule out the possibility of having either bubbly or slug
flow regimes since we do not seem to have a decisive experimental method for regime
identification. From Figures (2.7d), (2.8d), (2.9c), (2.9f), (2.10c) and (2.10f) one can
see how the introduction of air at 10% by volume of the flow rate (which is about 0.01%
by weight) in the cooling water at the annulus can bring about this great change in
the heat flux distribution over the condensingtube. In the experimental runs reported
here, with the exception of a pure steam case at high inlet steam flow rate and low
cooling water flow rate shown in Figure (2.10c), injecting air smooths the heat fluxe
profiles over the length of the condensing tube, although with differing degrees. Even
with the pure steam case mentioned earlier, injecting air decreasesthe heat fluxes over
the upper part of the condenser (where they are normally higher) and increased them
over the lowest part (where they are normally lower). By "normally" we mean in cases
using single phase cooling water flow. The reason for this might be that the pattern of
the two phase flow changes from that of bubbly flow to that of slug flow at the coolant
exit near the top of the condenser. Griffith & Synder [8]experimentally indicated that
the transition from bubble to slug flow occurs at values of the void fraction from 0.25
to 0.30. This transition can occur in a heated annulus since the pressure decreases and
29
temperature increases might lead to this limit even if the value of the void fraction
is below this limit at the inlet of the annulus. In our case, the average void fraction
value would be expected to be less than 0.25, but the narrowness of the annulus could
lead to such a regime over a portion of the annulus. In the slug flow pattern, gas flows
mainly in large bubbles called "Taylor bubbles". They are wrapped around the inner
tube. Liquid falls downwardsin the space between the Taylor bubble and the walls of
the annulus as well as in the peripheral area not occupied by the Taylor bubble. In
the latter case, the liquid carries distributed bubbles, bridging the annulus [6]. The
formation of Taylor bubbles at the upper part of the condenser tube would attenuate
the heat fluxes in this region. Even without the formation of Taylor bubbles, the
presence of air bubbles in bubbly flow will still attenuate the heat fluxes, although to
a lower degree. It should be noted that the alteration of the heat flux profile along the
channel is much less in case of high water flow rates (turbulent regime) than in case
of low cooling water flow rates (laminar regime) as shown in Figures (2.9c), (2.9f) and
Figures (2.10c), (2.10f). The reason might be that at high liquid flow rates, turbulent
forces tend to break up any large bubbles and disperse the gas phase. This results in
a finely dispersed bubble flow.
2.4.4 Temperature Inversion
There is a number of unresolved possibilities for explaining the observed wall temperature inversion. The possibility which we consider to be most applicable here is that
of having secondary flows in the coolant channel annulus. The potential for secondary
flow in annuli always exists. The shear stresses at the two walls of the annulus are
different, and the ratio between them at the walls is a function of the radii of the
tubes. This means that there is a different rate of dissipation of energy at the two
walls of the annulus. This would cause the phenomenon of secondary flow [9]. The
condition of continuity is still satisfied if we superimpose upon the basic flow a cross
flow which is also the same at all sections [10]. Since the inner tube of the annulus is
heated while the other is not, a low density layer will exist adjacent to the inner tube.
The existence of this low density layer will cause the shear stress very close to the
inner tube to increase [11]. This will make it even more likely for thesecondary flow to
occur. The existence of secondary flows in an annulus means that the fluid would have
some velocity in the radial direction. By imposing this condition on the axial velocity,
cells would develop in the gap of the annulus. These cells would bring fluid from the
colder side of the annulus to the hotter side and vice versa. This could explain the
dip in the wall temperature profile over the upper part of the tube. Increasing the
30
cooling water flowrate would increase the circulatory intensity of these cells. And this
would make the temperature inversion to be more pronounced. This occurs as one can
see from Figures (2.5a), (2.5b), (2.5c), Figures (2.6a), (2.6b), (2.6c), Figures (2.9a),
(2.9d), Figures (2.9b), (2.9e), Figures (2.10a), (2.10d) and Figures (2.10b), (2.10e).
However, increasing the inlet volumetric air flow ratio in air/water mixture seems to
be effective in damping this secondary flow as one may infer from Figures (2.7a), (2.7b),
(2.7c), Figures (2.8a), (2.8b), (2.8c), Figures (2.9a), (2.9b), Figures (2.9d), (2.9e), Figures (2.10a), (2.10b) and Figures (2.10d), (2.10e). The air bubbles would always flow
axially and tend to break down the cells created by the secondary flows. However,
increasing the air (in cooling water) flow rate will eventually cause transition from
bubbly to slug flow. Is has been observed that when the air flow rate was increased
so that the inlet volumetric air flow ratio in the air/water mixture exceeded 40%,
thermocouple readings in the vicinity of the temperature inversionstarted to oscillate,
and that this phenomenon would disappeared then reappear periodically.
2.5
Summary & Conclusions
Within the range of the data taken as shown in Tables 2.1 through 2.4, the followingare
the conclusions regarding the effect of cooling conditions on in-tube steam condensation
in the presence of air:
1. If the cooling water flow rate is kept so low that the coolant flow is laminar, local
values of condensation heat transfer coefficientsare overpredictednear the upper
part of the condensing tube.
2. If the cooling water flow rate is increased so that the flow is turbulent, the coolant
temperature rise decreases and the uncertainties associated with the local values
of condensation heat transfer coefficientsmight become high except at high power
levels (high inlet steam flowrates) where the coolant temperature change per unit
length of the condensing tube is large.
3. In situations where the coolant flow is laminar, bubbling air into the cooling
water can provide the desired amount of mixing. However,pre-analysis must be
made to determine the amount of air to be introduced with the cooling water.
The exact amount of air would depend upon the cooling water flow rate and the
power level (inlet steam flow rate) of the test.
4. Siddique did not seem to have consistently injected the amount of air which is
sufficientfor good mixing. Therefore, the local heat transfer coefficientsnear the
31
top of the condenser so obtained by him were overestimated.
5. Injecting air with the cooling water in the annulus seems to be effective in removing the "Temperature Inversion."
6. The "Temperature Inversion" seems to be a coolant side phenomenon. The cause
is unclear with the possible explanation ranging from a geometrical artifact to
thermally-induced secondary flow within the coolant.
2.6
Recommendations
Based on the conclusions of this analysis, the following steps are recomended for im-
proving the certainty of the quality of the data. The first step is necessary in order to
resume data-taking using the existing test facility:
1. Build a Visualization Experiment to simulate the coolant annulus of the existing
test section and determine the amount of air which is sufficient for good mixing,
2. Design a new test section so that it has two independent means of determining
the local heat fluxes.
32
Table 2.1: Test Matrix for High Inlet Air Mass Fraction in Steam/Air Mixture
Steam/Air
Mixture
Run
Set Inlet Temp.
#
(C)
Air (in steam)
Air (in cooling
Inlet Steam water) Volume Cooling Water
Flow Rate
Fraction
Flow Rate
(kg/hr)
(% V)
(kg/hr)
Inlet Mass
Fraction
(%w)
1
2
100
100
8
11
10.6
32
3
100
20.6
20
4
100
24
29
5
6
140
140
11
20.4
10.2
24.4
7
140
20
32
0, 10 & 20
0
10
0, 5 & 20
0
0, 10 & 20
0
0, 10 & 20
0 & 10
0
0, 10 & 20
218
270 & 1020
270 & 1020
218
510 & 1020
222
510 & 1020
219
221
510 & 1020
206
0
510 & 1020
Table 2.2: Test Matrix for Pure Steam
Steam/Air
Air (in cooling
s
Run
Mixture
Inlet Steam water) Volume Cooling Water
Set Inlet Temp. Flow Rate
Fraction
Flow Rate
#
(C)
(kg/hr)
1
2
100
100
20
41
(% V)
0, 2&4
0
10
33
(kg/hr)
218
240 & 1020
240 & 1020
Table 2.3: Test Matrix flor Low Inlet Air Mass Fraction in Steam/Air Mixture
Steam/Air
Run
Mixture
Set Inlet Temp.
#
(C)
Air (in steam)
Air (in cooling
Inlet Mass
Fraction
(%w)
Inlet Steam
Flow Rate
(kg/hr)
1
2
100
100
2.2
4.4
12
20
3
100
5.5
water) Volume Cooling Water
Fraction
Flow Rate
(% V)
(kg/hr)
22
0, 2 & 4
0, 4 & 9
0
0, 4 & 10
218
270 & 1020
270 & 1020
218
0
0, 4 & 10
0, 4, 8 & 20
510 & 1020
219
221
0
510 & 1020
0, 4, 8 & 20
0
206
510 & 1020
4
5
140
140
1.9
5
11.3
24.4
6
140
7.1
29.1
Table 2.4: Test Matrix for Studying the Effect of Cooling Water Inlet Temperature
Run
Set
#
1
2
3
Steam/Air Air (in steam)
Mixture
Inlet Mass
Inlet Temp.
Fraction
(C)
(%w)
100
100
100
2.5
2.0
4.0
Inlet Steam
Flow Rate
(kg/hr)
CoolingWater
Flow Rate
(kg/hr)
Cooling Water
Inlet Temp.
(C)
11
15
20
100
168
218
12.2 & 18.3
6.4, 10.8 & 19.3
6.6 & 18.3
34
us
ve
a
E
0
U
>0o
.
V)
Figure 2.1: Schematic of Experimental Facility
35
Steam/
noncondensable
gas mixture
Cooling
water outlet
I
.
....
..............
--..
Centerline -
--.............
4
--
Thermocouple
.......
"
30.5
cm
-------------- ....
30.5
cm
I-
·
--I
............
30.5 cm
.......
Cooling waterthermocouple
- ............. 4
o--t
---30-t-30.5 cm
2.5, 4m
.......
230.5 cm
One thermocoupleeach on the inside and
outside of tube wall
.......
30.5 cm
o-..
---.
------------- ----------...............
............
44
30.5 cm
30.5
cm
*..............
I....
a...
.................
---. t
4
I
Cooling
water inlet
Figure 2.2: Thermocouple Locations
36
Air/Steam Mixture
couples
4SS
/Constantan
}4SS
rmocouple
an
CondenserTube
Stainless Steel 304
46.0 mm ID, 50.8 mm OD
Stainless Steel 304 Pipe
62.7 mm ID
Figure 2.3: Details of Thermocouples
37
__
7(
100
90
80
70
6
U 60
5
50
4
40
3
2
30
20
1
10
10
9(
8(
0
0.00
Length (m)
Fig. 2-4a - Inlet Cooling Water Temperature
= 1.6C
--
0.50
1.00 1.50 2.00 2.50
Length (m)
Fig. 2-4b - Inlet Cooling Water Temperature
= 18.3C
42
36-
30-E 2418-
II
12
-
60.
0.00
0.50
1.00
1.50
2.00
2.50
0.0
.
.
0.5
.
1.0
.
1.5
.
2.0
I
2.5
Length (m)
Length (m)
Fig. 2-4d - Inlet Cooling Water Temperature
= 6.6 and 18.3'C
Fig. 2-4c - Inlet Cooling Water Temperature
= 6.6 and 18.3'C
3
3
2
Steam/Air Mixture Inlet Temperature = 100°C
2
Inlet Air Mass Fraction in Steam/Air Mixture
(%w) = 4
A
P1
Inlet Steam Flow Rate = 20 kg/hr
Cooling Water Flow Rate =
3.63 kg/min
I
Length (m)
Fig. 2-4e - Inlet Cooling Water Temperature
= 6.6 and 18.3'C
Figure 2-4 - Effect of Cooling Water Inlet Temperature on the Heat Flux, Wall Subcooling
and Heat Transfer Coefficient
38
I
0.0 0.5
1.0 1.5 2.0 2.5
Length (m)
Fig. 2-5a - Cooling Water
Flow Rate = 3.7 kg/min
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-5b - Cooling Water
Flow Rate = 8.5 kg/min
Length (m)
Fig. 2-5c - Cooling Water
Flow Rate = 17 kg/min
1
0-
U
,F
Xu
0
M
aI
:9
0.0 0.5
1.0 1.5 2.0 2.5
Length (m)
Fig. 2-Sd - Cooling Water
Flow Rate = variable
0.0 0.5 1.0 1.5 2.0 25
Length (m)
Fig. 2-5e - Cooling Water
Flow Rate = variable
[
0.0 0.5 1.0 15 2.0 2.5
Length (m)
Fig. 2-5f - Cooling Water
Flow Rate = variable
Steam/Air Mixture Inlet Temperature = 100'C
Inlet Air Mass Fraction in Steam/Air Mixture (%w) = 24
Inlet Steam Flow Rate = 29 kg/hr
Figure 2-5 - Effect of Cooling Water Flow Rate on the Heat Flux, Wall Subcooling, and
Condensation Heat Transfer Coefficient at Atmospheric System Pressure
39
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-6a - Cooling Water
Flow Rate = 3.43 kg/min
Fig. 2-6b - Cooling Water
Flow Rate = 8.5 kg/min
Fig. 2-6c - Cooling Water
Flow Rate = 17 kg/min
1
1
Bye
t
U
a
ru
i
a
.0
-
i0.0
0.5
1.0 1.5 2.0 2.5
Length (m)
Fig.2-6d - Cooling Water
FFlow Rate
= variable
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 10
Length (m)
Fig. 2-6e - Cooling Water
Length (m)
i
Fig. 2-6f - Cooling Water
Flow Rate = variable
Flow Rate = variable
15
2.0 2.5
Steam/Air Mixture Inlet Temperature = 140'C
Inlet Air Mass Fraction in Steam/Air Mixture (%w) = 20
Inlet Steam Flow Rate = 32 kg/hr
Figure 2-6 - Effect of Cooling Water Flow Rate on the Heat Flux, Wall Subcooling and
Condensation Heat Transfer of Coefficient at a System Pressure of 40 psig
40
pi
a
%_
I
I
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5
Length (m)
IFig.2-7a- %v (inlet
volumetricair ratio to the
I
Length (m)
Fig. 2-7b - %v (inlet
volumetric air ratio to the
Length (m)
Fig. 2-7c - %v (inlet
volumetric air ratio to the
water/air mixture) = 10
water/air mixture) = 20
water/air mixture) = 0
1.0 1.5 2.0 2.5
]I
I
:
U
or
clW
9
V
_
_
_
_
.
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-7d - %v (inlet
volumetric air ratio to the
water/air mixture = variable
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-7e - %v (inlet
volumetric air ratio to the
water/air mixture = variable
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-7f - %v (inlet
volumetric air ratio to the
water/air mixture = variable
Steam/Air Mixture Inlet Temperature = 10O'C
Inlet Air Mass Fraction in Steam/Air Mixture (%w) = 24
Inlet Steam Flow Rate = 29 kg/hr
Figure 2-7 - Effect of Injecting Air with Cooling Water on the Heat Flux, Wall Subcooling
and Condensation Heat Transfer Coefficient at Atmospheric System Pressure
41
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-8a - %v (inlet
volumetric air ratio to the
water/air mixture) = 0
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-8b - %v (inlet
volumetric air ratio to the
Length (m)
Fig. 2-8c - %v (inlet
volumetric air ratio to the
water/air mixture) = 20
water/air mixture) = 10
U
8
A
0.0 0.5
1.0 1.5 2.0 2.5
Length (m)
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-8d - %v (inlet
Fig. 2-8e - %v (inlet
volumetric air ratio to the
water/air mixture = variable
volumetric air ratio to the
water/air mixture = variable
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-8f - %v (inlet
volumetric air ratio to the
water/air mixture = variable
Steam/Air Mixture Inlet Temperature = 140'C
Inlet Air Mass Fraction in Steam/Air Mixture (%w) = 20
Inlet Steam Flow Rate = 32 kg/hr
Figure 2-8 - Effect of Injecting Air with Cooling Water on the Heat Flux, Wall Subcooling
and Condensation Heat Transfer Coefficient at System Pressure of 140 psig
42
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Fig. 2-9a - Cooling Water
Flow Rate = 4.5 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 0
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Length (m)
Fig. 2-9b - Cooling Water Fig. 2-9c - Cooling Water
Flow Rate = 4.5 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 10
100
Flow Rate = 4.5 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 0 & 10
100
90804
80-
o- l(C)
- '70
E
e 60
50
4SL)
-0-Ti1(C
a:
K40- -.&-Tw('C)
E
Me
30-
30
:20-
20
10-
10
n
0.0 0.5 1.0 1.5 2.0 2.5
V-
.
U
...-......
.
.
.
.
.
.
.
Length (m)
Fig. 2-9d - Cooling Water
Flow Rate = 17 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 0
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5
Length (m)
Fig. 2-9e - Cooling Water
Flow Rate = 17 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 10
1.0 1.5 2.0 2.5
Length (m)
Fig. 2-9f - Cooling Water
Flow Rate = 17 kg/min
%v (inlet volumetric air
ratio to the water/air
mixture) = 0 & 10
Steam/Air Mixture Inlet Temperature = 100°C
Inlet Air Mass Fraction in Steam/Air Mixture (%w) = 11
Inlet Steam Flow Rate = 32 kg/hr
Figure 2-9 - Effect of Injecting Air with Cooling Water on the Heat Flux for the Laminar
and Turbulent Flow Regimes in the Annulus
43
I
I
0.0 0.5
1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Length (m)
Length (m)
Fig. 2-10a - Cooling Water Fig. 2-10b - Cooling Water Fig. 2-10c - Cooling Water
Flow Rate = 4 kg/min
Flow Rate = 4 kg/min
Flow Rate = 4 kg/min
%v (inlet volumetric air
%v (inlet volumetric air
ratio to the water/air
mixture) = 0
ratio to the water/air
mixture) = 10
0.0 0.5 1.0 1.5 2.0 2.5
%v (inlet volumetric air
ratio to the water/air
mixture) = 0 & 10
0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5
Length (m)
Length (m)
Length (m)
Fig.: 2-10d- Cooling Water Fig. 2-10e - Cooling Water Fig. 2-10f- Cooling Water
Flov r Rate = 17 kg/min
Flow Rate = 17 kg/min
Flow Rate = 17 kg/min
%v (inlet volumetric air
%v (inlet volumetric air
%v (inlet volumetric air
ratio to the water/air
mixt ure) = 0
ratio to the water/air
mixture) = 10
ratio to the water/air
mixture) = 0 & 10
PURE STEAM
Inlet Steam Temperature = 100'C
Inlet Steam Flow Rate = 41 kg/hr
Figure 2-10 - Effect of Injecting Air on the Heat Flux for the Laminar and Turbulent
Flow Regimes for Pure Steam
44
Chapter 3
The Visualization Experiment
3.1
Introduction
The investigation carried out in Chapter 2 of the effects of cooling water conditions on
in-tube condensation in the presence of noncondensables concluded that two phase flow
(water/air mixture) pattern identification in the annulus would be helpful for clearer
understanding of the effects of cooling conditions upon local values of condensation
heat transfer coefficientsand the amount of air bubbled into the cooling water which
would provide good mixing need to be quantified.
Since the existing literature does not seem to include a decisive experimental
method for two phase regime identification and for determining the amount of air
needed for proper mixing, the development of this new visualization experiment was
necessary.
The main objective of this investigation is primarily to determine the amount of
air sufficientfor good mixing in order to resume data-taking using the existing facility.
Other objectives are to investigate the existence of secondary flows due to the annular
geometry and to correlate the data for later use in Chapter 4.
3.2 Experimental Setup
3.2.1
Description of Apparatus
The setup of the experimental facility is shown in Figure (3-1). It consisted mainly
of an annulus, air and water supplies, connecting pipe, flow measuring devices and
pressure gauges. The annulus was made of two PVC clear concentric pipes. The outer
diameter of the inner tube was 1.9" while the inside diameter of the outer tube was
45
2.469" making a gap of 0.285. The inner tube length was 102" while the length of
the outer tube was about 96". The annular dimensions were very close to those of the
actual MIT existing condensation test facility described in Chapter 2.
The lower part consisted of a PVC white pipe of 1.049" ID and 1.315" OD. A
drainage valve came out of the PVC white pipe length of 12" through a PVC Tee
connection. One end of the PVC white pipe was connected to the annulus while the
other end was connected to PVC clear pipe via a union. The PVC clear pipe was 2.067"
ID, 2.375" OD, and 6" in length. From the building main water supply, water used to
enter the lower part at a pressure between 20-60 psi depending on the water flowrate.
A flow needle valve was used to control the flow to the lower part and eventually to
the annulus. Just before the flow entered the annulus, its pressure of about 6 psig was
measured by the 0-15 psi dial pressure gauge. The building main 50 psig air supply
was used to inject air into the lower part after reducing its pressure to the desired value
using a pressure regulator. A rotameter with a 16-turn precision flow valve was used
to measure the volumetric air flow rate into the system. Depending on the desired fl
ow rate, an appropriate flow tube was selected from among a wide range of flow tubes.
This step was taken to maximize the flow rate measurement accuracy.
A 1/16" OD SS sheathed J-type thermocouple was placed through a compression
fitting in the middle of the annular gap halfway along the length of the annulus. The
upper part consisted of a PVC clear pipe from which the water/air flow was vented to
the drainage at atmospheric pressure.
A pressure transducer was connected via 1/2" OD Polyflo tubing to two 84" apart
NPT fixtures placed one at the top and the other at the bottom of the annulus. Figure
(3-2) shows in detail the pressure measurement system. The Polyflo tubing had two
bleed valves; one on each section coming from the annulus in order to remove air
bubbles which might otherwise give rise to erroneous pressure measurements. The
differential transducer had a range of 0-25" of water and it was connected to a highly
accurate digital display. Bypass valves were used to cut off the pressure transducer
from the annulus and divert the flow to a 100" dial differential gauge for a wider range
of data. In order to avoid tap error in the transducer readings, the two NPT fixtures
were made flush to the inside of the outer tube of the annulus as shown in detail in
Figure (3-3).
To ensure a uniform gap around the annulus, three set screws were tapped through
the outer pipe 120 °apart from one another at one-third and two-thirds the length of
the annulus as shown in Figure (3-4).
Bubble length was also determined against a length scale placed outside the outer
tube and the total rise time was measured by a stop watch.
46
3.2.2
Calibration of The Pressure Transducer
The transducer was calibrated by setting it equal to the difference of the two pressures
on its apertures. At the high pressure aperture, the pressure would be equal to water
height in the tube connecting the transducer to the upper NPT fixture in the annulus.
At the low pressure aperture of the transducer the pressure would be equal to the
water height in the annulus. The cross-sectional middle of the lower tube connecting
the transducer to the annulus was taken as the datum.
The water level in the annulus was changed by using the drainage valve. Different
values for low pressure and subsequently differential pressure were obtained and checked
against the pressure transducer readings. During the calibration process, the tubes
linking the annulus to the pressure transducer were always kept clear of bubbles and
the bleed valves on these tubes were used to release trapped bubbles.
3.2.3
Experimental Procedure
The followingsteps were taken in carrying out the experimental runs:
1. The first step in running the experiment was to make sure that the measuring
equipment was running properly and calibrated correctly. This includes testing
the thermocouples, the pressure transducer, the dial gauges, and the rotameters.
2. Water flowwas then started, with both bleed valvesin the pressure measurement
system open to evacuate any air bubbles from the Polyflo tubing.
3. After all air had been evacuated from the pressure measurement system, the
bleed valves were closed off and water flow was adjusted to the desired superficial
velocity. A period of time needed to pass before the measurement readings of the
system would stabilize and reach a steady state.
4. Due to frictional forces in the annulus, there might be a nonzero reading on the
pressure transducer. This value was noted and taken into account in the final
data, or the digital display zeroed at this value.
5. Air injection was started. The air flow rate was adjusted to the desired rate
corresponding to the desired superficial velocity. Again, a period of time had to
pass before the measurement readings stabilize.
6. At this point, the measurement data was recorded along with videotaping or still
photographing of the flow in the annulus. When all data has been taken, the air
flow rate was increased following the procedure in step 5.
47
7. After the experiment had been run through all desired values of air flow rate,
the annulus was drained and the experiment was started again from step 2, at a
different superficial water velocity,through all desired values of air flowrate.
3.2.4
Data Analysis
Determination of the flow regime in the visualization experiment presented here requires both quantitative and observational experimental data. Controlled variables,
such as air and water flow rate, are manipulated so that a wide range of data may be
observed and recorded. These data consist of:
* Water and air superficial velocities J,. and Ja in the annulus
* Bubble shapes and sizes in the annulus
* Bubble rise velocity
* Void fraction within the annulus.
Of these data, the void fraction a is the most important to determine. It requires
a separate system for measuring a differential pressure along the annulus, which is
explained in the next section. The general expression for the friction pressure loss
dependence upon the void fraction a along a length h is:
APa,, = p,(l - a)gh + paagh.
(3.1)
However, in this case there is an additional term due to the pressure from the
column of water in the upper link to the annulus. Thus, the expression in relation to
the pressure transducer is:
APta, = a(p, - Pa)gh
(3.2)
This expression is correct as long as the superficial velocity is kept so low that the
acceleration and friction pressure drop is negligible compared to the gravity pressure
drop. This is true with the range of velocities carried out in this investigation. The
error in determining the void fraction has been estimated to be 10% as shown in
Appendix B.
48
The other data are mostly observational, and the model is constructed of PVC
clear pipe to accommodate videotaping of the flow as well as visual observation. To
facilitate observation, a white plastic insert was placed within the model to provide a
background against which the bubbles can be seen more easily.
3.3
Experimental Results and Discussions
Table 3.1 consists of the parameter settings used in the run of the visualization experiment. The air and water flow fluxes (superfical velocities) are defined as:
Q
J =
-
=Q
-(D Q-- Dr
D2)
(3.3)
(3.4)
where Q. and Q, are the volumetric flowratres for air and water respectively. Do and
Di are the outer and inner diameter of the annulus.
The air volumetric flow ratio (V) is defined as:
Qa
Qn +Q -(3.5)
Q
+ Q.
First the volumetric flowrate of the water was varied, then the volumetric flowrate
of the air was varied. This was convenient since changing the air flow tubes was time
consuming, whereas necessary rotameters were permanently in place for measuring the
water flow.
3.3.1
Flow Description
The generally observed trends of the flow were the following:
* Low volumetric water flow and low volumetric air flow rates resulted in smooth
bullet shape bubbles, stable flow with low breakage of bubbles, and concentration
of bubbles along the inlet/outlet side of annulus.
49
* Lowvolumetric water flowand high volumetric air flowresulted in mixed slug and
bubbly flow(only large and small bubbles), being mostly turbulent with constant
rate of bubble breakage and coalescence,and with a uniform distribution around
the annulus.
* High volumetric water flow and low volumetric air flowresulted in roughly bullet
shaped bubbles, being mildly turbulent with breakage of bubbles near the top
of the annulus and coalescence near the bottom of the annulus, and partially
distributed around the annulus.
* High volumetric water flow and high volumetric air flow resulted in mixed slug
and bubbly flow, being very turbulent with constant breakage and coalescence
and with visible eddy regions, and with the bubbles being evenly distributed
around the annulus.
* Regardless of volumetric water flow, the height and width of the bubbles increased
with increasing volumetric air flow.
3.3.2
Data Correlation
Figure (3-5) shows the measured air void fraction a against volumetric air flowratio V
for different water Reynolds numbers Re,. The relationship between the void fraction
a and the volumetric air flow ratio V seems to approach a straight line as the water
Reynolds number increases. This behaviour can be more understood when the air
void fraction is plotted against water Reynolds number for different volumetric air flow
ratios as shown in Figure (3-6). Figure (3-6) shows that the air void fraction seems to
be insensitive to the increase in water Reynolds number for values higher than 2300,
while for Re, values less than 2300 the void fraction increases as the water Reynolds
number increases. This behaviour suggests correlating the data in the followingForm;
a = KVzRey
(3.6)
a = K'+ mV
(3.7)
for Rew < 2300, and
50
for water Reynolds numbers Re, greater than 2300. K, K', z, y, and m are
constants to be evaluated.
This has been performed and the results are given by;
057Reo,62 6
a% = 0.0022(V%)1.
(3.8)
for 187 < Re,, < 2300 and 5 < (V%) < 40, and by
a% = 0.454+ 0.263(V%)
(3.9)
for 2300 < Re,. < 5605 and 5 < (V%) < 40.
Figure (3-7) shows good agreement between the experimentally obtained void frac-
tions against those predicted using the above correlation.
3.4 Drift Flux Correlation
The drift flux model was first developed by Wallis [12]. The model considers the relative
motion of the two phases and relates the global to the local relative velocities and void
fraction effects. By definition the local air superficial velocity ja is related to the local
air actual velocity through the followingequation;
ja = aua
(3.10)
j = cj + (u - j)
(3.11)
which can be rewritten as;
where j is the two phase local volumetric velocity velocity given by;
i = ja + jw
51
(3.12)
where j, is the water local superficialvelocity. Taking the area average of Equation
(3.12), it becomes;
J = fai) + a ( - M)
(3.13)
where the upper case is used here for area-averaged values. Equation (3.13) can be
written as;
Ja = Co {,}{j} + {a}{vgj}
(3.14)
where Co is the concentration parameter given by;
{aj)
(3.15)
{a){j)
and {vgj} is the effective drift velocity given by;
{Vj = o{a
(Ua j)}
(3.16)
If we dropped the average sign over a for convenience, an explicit expression for
the void fraction a in terms of the above parameters can be written as;
Ja
(3.17)
C0 J + g
3.4.1
Distribution Parameter Co
The distibution parameter Co accounts for the difference in the cross sectional area
averaged velocities of air and water due to the radial distribution of the void and
velocity. According to Ishii[13], Co for a round tube is given as
C,=
1.2-
52
0.2
Pf
(3.18)
and for a rectangular channel is given by the relationship
C, = 1.35 - 0.35
(3.19)
Pf
where pg and pf are gas and liquid densities respectively.
Since Co seems to be a system geometrical parameter and in the absence of an
experimental correlation for Co for annuli, Co has been determined in the present
study by a slope of J vs
relations by assuming that COis constant in equation
(3.17). The result is shown in Figure (3-8) with CO value equal to 2.598.
3.4.2
Average Local Drift Velocity < Vgj >
The average local drift velocity accounts for the local velocity difference between gas
and liquid. Kataoka, et al [14] suggested constitutive relations for the local drift velocity
in various two phase flow regimes; for churn turbulent bubbly flow,
( V
,)2
)(3.20)
>
(= /2-
and for slug flow or cap bubble regime
1
O'g
<< Vj >= 0.0019
i D
D*0-809 P9
-0.157
N-
0562
for DH < 30
< Vgj>= 003 (g2 P
N-;052
(3.22)
for D > 30
The above correlations agreed with many experimental data over a wide range of
parameters such as vessel diameter, system pressure, gas flux and physical properties.
However, it should be noted that equations (3.21) and (3.22) are valid for low viscous
fluids satisfying the condition
53
N,, < 2.25 * 10- 3
(3.23)
where
(3.24)
N,,f =
and
D = DH
(3.25)
where DH is the vessel diameter or the characteristic length of the channel.
The use of Equation (3.20) or Equations (3.21) and (3.12) depends on a dimensionless gas flux defined as
J+ =
Jg
(3.26)
where J+ = 0.5, which corresponds to J. = 0.1 m/s in the present study, has been
suggested by Ishii to be used as the boundary between the above two flow regimes.
However, since this choice is rather arbitrary and since cap bubbles and slug flow have
been identified visually in the present study at much lower gas fluxes, we used a value
of J+ = 0.1 instead as the boundary between the two regimes.
3.4.3
Annulus Characteristic Flow Dimension
Griffith [13]found that the shround dimensionDo (the inner diameter of the outer tube
of an annulus) is the most important dimension in characterizing the two phase flow in
an annulus. Later, E. F. Ceatano, et al [7] recommended the use of an equi-periphery
diameter, Doi as the characteristic dimension,
54
Doi = D + Di
(3.27)
For annului the hydraulic diameter is defined as
DH = Do- Di
(3.28)
In the present analysis, the three dimensions have been employed in the above
equations in determining the void fractions. The results are plotted against the experimentally obtained void fractions as shown in Figures (3-9), (3-10) and (3-11). The
correlation seems to considerably overpredict the void fraction when the characteristic
length is used as DH = D,- Di as shown in Figure(3-9). Figure (3-10) shows that the
correlation reasonably predicts the void fraction when the characteristic length is used
as Do + Di. Figure (3-11) shows also a good agreement between the predicted and
the experiemntally obtained values of the void fraction when the characteristic length
employed in the correlation is Do.
3.5
Concluding Remarks
Within the range of the data taking from the visualization experiment as shown in
Table 3.1, the following are concluding remarks:
1. Cap or slug type bubbles existed at very low air fluxes over the entire range of
the investigation.
2. Efficient radial mixing over the entire length of the channel were attained within
a volumetric air flow ratio range between 20-30% for cooling water flow range
between 4-17 kg/min.
3. A drift flux-based correlation successfully predicted the appearance of cap or slug
flow and reasonably agreed with experimental findings.
4. The equiperiphery diameter, which is the sum of the inner and outer diameter
of the annulus, or the outer diameter of the annulus has been found to be more
appropriate than the hydraulic diameter for characterizing the two phase flow
within the annulus.
55
5. No secondary flow was observed within the unheated cooling water during the
course of this investigation.
56
Table 3.1: Test Matrix for Visualization Experiment
Q
(t/min)
0
1
2
4
8
16
30
Qa
(ml/min)
J
(m/sec)
J
%v
(m/sec)
222
0.0029
100
444
0.0059
100
1570
0.0209
100
3333
0.0441
100
7000
0.0926
100
53
111
0.0007
0.0015
5
10
250
0.0033
20
0.0088
0.0198
40
60
4000
0.0529
80
106
222
500
0.0014
0.0029
0.0066
5
10
20
667
1500
1334
0
0.0132
0.0177
40
3000
8000
0.0397
0.1058
60
80
212
0.0028
5
444
0.0059
10
1000
0.0132
20
0.0353
0.0794
0.1323
0.0056
40
60
70
5
0.0117
0.0265
10
20
5336
10,000
0.0706
0.1323
40
55
848
0.0112
5
1776
4000
6857
1579
0.0235
0.0529
0.0907
0.0209
10
20
30
5
0.0441
0.0992
10
20
2668
6000
10,000
424
888
2000
3333
7500
0.0265
0.0529
0.1058
0.2117
0.3969
57
t
-
-
-
t
:
-
-
-6"
I -
--
1
12"
Ito
phere
To pressure
transducer
I
-ess
PVCclear pipe
(ID: 1.610",Wall:.145")
50
1 1/2"
-8 1/4 ft.
(2.5 m)
PVCclearpipe
(ID:2.469",Wall:.203")
2 1/2"
PVC clearpipe
(ID: 2.067",Wall:.154")
2"
Pressuregauge
PVC whitepipe
(ID: 1.049", Wall: .133")
1"
Drainvalve
PVC whiteT
Flowvalve
uusingl
1256""
12"
(Diagramnotto scale)
Figure 3.1: Visualization Experiment
58
L
i
A
.
Figure 3.2: Transducer Setup
59
__
PVCclear pipe
(ID: 2.469",Wall: .203")
2 1/2"
PVC gray
t tanoineblock
62")
_·
Figure 3.3: NPT Connection to Annulus for Transducer Systen
r
I
1/8" set
2station
and2/3
annular
lear pipe
610, Wall: .145")
Annulus
I
I
Figure 3.4: Annulus Alignment
60
i.
I
Ik
uf
u
CA
UL~
un
kn
Q
E.-
1f
50F
IA
MI
tI
e
in
CO
61
m
0
o
o
o
-.
C)
Xn
0 a
o
Co I
.. _
orl
o
o
0
62
I
o
-Ez.
so
tez n
0~
OC
u--
rl~~~~~~a
el
X
oa
{~o
cT
e
3-
cJ2f
{:kl
O
o
i=
o
3eU
O
3-
o
Qesia
u
*Y
Om:
£
ToPr
;C)
g
h~~
iuoauuodxo
63
b
or
an
U,
'U ·
0
0.1
0.2
0.3
0.4
jw+ja (m/s)
Figure (3-8) The air velocity against the
total superficial velocity
64
0.5
30
25
20
15
10
5
a (correlation)
Figure (3-9) The experimental against the correlation
predicted void fraction when the characteristic
diameter is taken as [D - D]
65
1
E
a,
.E
.-
a,
la
0
X>
0
2.5
5
7.5
10
12.5
15
oc (correlation)
Figure (3-10) The experimental against the correlation
predicted void fraction when the characteristic
diameter is taken as [D of! + D.]
66
1
1
1
-
I=
d
0
2
4
6
8
10
12
14
16
a (correlation)
Figure (3-11) The experimental against the correlation
predicted void fraction when the characteristic
diameter is taken as [DO]
67
Chapter 4
Effects of Buoyancy in the Coolant
Side on In-Tube Steam Condensation
in the Presence of Noncondensables
4.1
Introduction
In University of California, Berkeley experiments [4], the condensing tube exhibited a
step increase of its wall temperature profile near the upper part, while in the present
investigation the step increase was near the middle of the tube. The phenomenon
was termed by the former as "Temperature Inversion" and it was dealt with briefly in
Chapter 2 with the conclusionthat it is most likely to be a coolant side phenomenon. In
Chapter 3, a visualization test section which is identical to the actual one was reported.
The cooling water inside the annulus was closely observed. No heat fluxes were applied
to the inner wall of the annulus in the visualization experiment. Secondaryflows,which
may exist because of the annular geometry, were not observed. However, in vertical
annuli, where the inner wall is heated and the outer surface is cooled or insulated, the
potential for buoyancy-induced recirculation or cellular flows and/or buoyancy-induced
early transition to turbulent flows exists and increases as the heat fluxes on the inner
wall increase and/or as Reynolds numbers of the cooling water decrease.
Scheele,et al [17]investigated the effect of natural convectionon the transition to
turbulent flow in a heat transfer section of a vertical pipe. These experiments showed
that the velocity profile must be distorted at least to a condition of flatness in order
for a transition to sinuous flow to occur. This condition corresponds to a value of
Grq/ReR > 23 for fully- developed flow, and this value increases as ReR increases for
developing flows.
Lawrence, [18]developed a transition curve using the experimental transition data
68
for heated upflow water in a vertical tube. Lawrence, et al [19] showed that experi-
mental measurements demonstrated that transition to turbulent flow process depends
on the developing velocity profiles and for the constant heat flux case, transition will
occur at some axial positionalong the channel. For a given entrance condition, the
distance to the transition point is fixed by flowrate and the wall heat flux.
Sherwin, and Wallis, [20] studied laminar flow systems in which buoyancy aids
the forced flow, causing the fluid velocities to increase near the heated surface and to
decrease elsewhere. In their experiment, flow visualization by dye injection was used
to determine the onset of flow instability. They concluded that unstable flow occurs
when the parameter Grq/ReR reduces as flow develops with an eventual value being
appropriate to fully developed flow of 209, in an annulus of radius ratio equal to three.
They also developed a transition regime map similar to that of Lawrence [18].
Barozzi, et al [21] also studied the transition effects for laminar flow combined
convection of water in vertical tubes. They compared their fresh experimental and
predictive transition data to that of Lawrence, et al [19] and found a new transition
map.
The objective of the analysis reported here is to investigate the possibility of having
buoyancy-driven secondary flows, early transitions to turbulence or both within the
coolant annulus. This is done in attempt to explain the wall temperature step increase
near the middle of the condenser tube, and corresponding effects on the local values of
condensation heat transfer coefficients.
4.2 Experimental Equipment:
4.2.1
Description:
The experimental loop used and its operation are described in details in chapter 2.
Figure (4-1) shows the details of the annulus and locations of thermocouples. The
inner tube of the coolant flow annulus is a stainless steel tube within which the
steam/noncondensable
gas mixture flows downward. The dimension of the tube are
50.8 mm (OD), 46.0 mm (ID) and 2.44 m effective length. The outer jacket of the
annulus is a 62.7 mm (ID) SS pipe. The cooling water supplied to the test section was
not recycled, i.e, once through constant flow was used. A flow control valve coupled
with a calibrated rotometer were used to control and measure the coolant flow. All
cooling water exited the annulus at the top of the test section directly to the drain.
69
4.2.2
Experimental Procedure:
The effect of cooling water flow rate upon local values of Grashoff and Reynolds'
numbers was observed by varying the cooling water flow rate (2-20 kg/min). The
effect of heat fluxes (range 0.01 -150 kW/m 2 ) was also observed by varying the inlet
steam flow rate (10 - 40 kg/hr) and the inlet noncondensable mass fraction (0.025 0.25). The steam/noncondensable mixture inlet temperatures were 100 and 130°C.
4.3
4.3.1
Data Analysis:
Coolant Annulus Side:
The local values of the heat fluxes were calculated from the following equation obtained
from a steady state energy balance on the coolant side:
mc Cc dTc
gal
= mhC, d 1 (z),
(4.1)
where th, is the cooling water flow rate and Di is the annulus inner diameter. The
local axial gradients of the cooling water temperature profile d (Z) were determined
using a least squares polynomial fit of the cooling water temperature profile. The
adjusted R2 value of the fit of the data to the polynomial was greater than 0.98 so that
the error adjusted with curve fitting is small.
The local values of Gr/Re 1l 8 were calculated, where Gr is the Grashoff's number
based on the temperature differenceand the annulus hydraulic diameter and is defined
as:
Gr =
where AT = T
h
(4.2)
- To, where Tai is the annulus inner wall temperature and T is
the coolant bulk temperature, and where Dh = Do - Di, where Di is the annulus inner
diameter, and Do is the annulus outer diameter, and where v is the bulk kinematic
viscosity, while Re is the Reynold's number based on the annulus hydraulic diameter
and is defined as:
Re = pUDh,
(4.3)
where Uc is the bulk cooling water velocity and Hctis the bulk dynamic viscosity.
The local values of Grq/ReR and the nondimensionalaxial coordinate (z/Rh)/(ReRPr)
were also calculated. Grq the local value of the Grashoff's number based on the local
70
heat flux and the annulus hydraulic radius is defined as:
Gr =
Grq
2
/3q'R
cRV
(4.4)
while ReR is the local Reynold's number based on the annulus hydraulic radius:
ReR = PUR,
,
(4.5)
PC
and Pr is the Prandtle number defined as Celle where Kcis the cooling water thermal
conductivity.
All properties are evaluated at a reference temperature T, = 2 (Tai + Tc), where
Tc is the coolant bulk temperature and T,i is the wall temperature at a given axial
location along the annulus length.
4.3.2
Coolant Properties' evaluation:
In order to assess the bouyancy effects in the coolant side of the test section, deter-
minations of the Grashoff, Reynolds and Prandtle numbers mentioned in the previous
section are required. These nondimensional numbers include the coolant physical and
thermal properties. However, in order to promote mixing in the coolant annulus for
better local heat flux determination, a small amount of air was bubbled into the annulus. Therefore, the coolant was basically a water-air system. Evaluation of two-phase
system properties requires the prior knowledge of the air void fraction. The following are the basic assumptions used in determining the air-water system physical and
thermal properties:
1. water and air are well mixed.
2. water and air are at thermal equilibrium with one another.
3. the void fraction is not a function of temperature.
It should be emphasized here that the first assumption does not mean that water
and air move with the same velocity as is traditionally assumed in homogenuous flow
modeling. Therefore, the void fraction expression obtained from homogenuous flow
model is not used here. Instead, straightforward, experimentally obtained void fraction
values are used.
Local void fraction a determination:
71
A seperate visualization experimental facility has been constructed in order to
obtain the void fraction. Details of this experimental setup are to be found in the
previous chapter. Figure (3-5) shows the measured air void fractions as a function
of volumetric air flow ratios in air-water systems flowing upward in the annulus for
different water Reynolds numbers. Figure (3-6) shows the measured air void fractions
as a function of water Reynolds numbers in air-water systems flowing upward in the
annulus for different volumetric air flow ratios. The measured air void fractions have
been correlated in terms of the water Reynolds number and volumetric air flowratio.
Measured air void fractions were plotted against the correlation predicted air void
fraction as shown in figure (3-7). The following are the steps taken in order to determine
the local air void fraction along the coolant annulus:
1. At a given axial position along the annulus, we calculate the water Reynolds
number from the relationship,
D
Re=,
(4.6)
where , is the water mass flow rate, and 1w is the water dynamic viscosity
corresponding to the coolant temperature at this axial location. Do and Di are
the outer and inner annulus diameter, respectively.
2. At the same axial position, we calculate the volumeteric air flow ratio V from
the relationship,
ma/Pa+
Qa=+ Q
/p(4.7)
where ha is the air mass flow rate. Paand p, are the air and water densities
corresponding to the coolant temperature at this axial location.
3. Substitute the obtained value from stepl and step2 into the correlation in Chapter
3 in order to obtain the corresponding air void fraction at this axial position.
Having the above steps followed, the void fraction range was found to be 0.04-0.05.
Corresponding to a maximum coolant temperature differential of about 50 C in the
present analysis, the void fraction increases slightly as the coolant moves up the heated
annulus. It should be emphasized here that boiling was not allowed in the annulus.
Density p:
72
Once the value of the void fraction, a, is known, the density of the water-air
mixture, p, can be expressed as,
(4.8)
p = ap + (- a) pw
Volumetric Thermal Expansion Coefficient f:
By definition the volumetric thermal expansion coefficient, Pj is given by,
_
(4.9)
()1 a)
With the assumption that the void fraction is not a function of temperature within
the range oftemperature differential employed in the present analysis, Equation (4.8)
can then be differentiated and substituted into Equation (4.9). Then an expression for
the air-water mixture volumetric thermal expansion coefficientcan be obtained as,
= Pal3a + P- (1 - a)3w
P
(4.10)
P
where l, and ,,, are the respective values of air and water volumetric thermal
expansion coefficients at a given temperature and are defined as,
a=
op
and
,,
_
aT,
(4.11)
Figure (4-2) shows the air-water system density and volumetric thermal expansion
coefficientas a function of the system air void fraction for different system temperatures
at atmospheric pressure using the expressions of Equations (4.8) and (4.10). At a given
temperature, while the water-air system density appreciably decreases as the air void
fraction increases from zer to unity, the water-air system volumetric thermal expansion
coefficientremains equal to that of the water as the air void fraction increases from
zero to 0.95. Above void fraction value of 0.95, an appreciable increase in the water-
air system volumetric thermal expansion starts as the void fraction further increases.
Eventually the water-air system volumetric expansion coefficient assumes the value of
air volumetric expansion coefficient when the air void fraction is equal to unity. To
understand this behaviour, the followingargument is made. For void fraction values
of about 0.8 and higher, annular two-phase flow exists and the assumptions of good
mixing of the two phases and thermal equilibrium between the two phases do not hold
the above expression obtained here for the mixture thermal expansion coefficient is
73
not valid. However, for bubbly (froth, cap slug, slug,..) two phase flow, where the
void fraction value is much less than 0.8, the above assumptions are justified and the
expression for the mixture volumetric thermal expansion coefficient gives the right
answer. This is because the bubbly flow is mainly discrete bubbles of different sizes
and shapes in a continuous fluid. Though the air volumetric expansion coefficientis
much higher than that of the water at a given temperature at atmospheric pressure,
the continuous water would put a limit to the expansion of the air bubbles within it.
Therefore, the water-air bubbly system volumetric expansion coefficient would assume
the value of the water volumetric expansion coefficient, i.e.,
p '- p
(4.12)
Specific Heat Capacity Cp:
An expression for the air-water mixture specific heat capacity Cp can be obtained
assuming that the sensibleheat per unit time absorbed by the air-water system is equal
to the sum of the sensible heat per unit time absorbed by both water and air, i.e.,
rhtCpdT = thCp,adT + iDCp,,,
(4.13)
where Cp,a and Cp,,, are the specific heat capacity for air and water respectively.
mt, r5 ,a and ,,, are the total mass flow rate, air mass flow rate, and water flow rate,
respectively. From the definitions;
ma = xmt,
and
h = (1 - z) ht
(4.14)
By invoking the assumption of thermal equilibrium between the two phases, i.e.,
dT = dTa = dT
(4.15)
and substituting Equation (4.14) and (4.15) into Equation (4.13), an expression for
the air-water mixture specific heat capacity can be obtained as;
Cp= XCp,a+ (1- z) Cp,
(4.16)
In the present analysis, z ~ 2.5 x 10 - 4. Therefore,
Cp M Cp,,
74
(4.17)
Thermal Conductivity :
Assuming good mixing of air bubbles and water, the total heat flux can be expressed
as the sum of the heat flux through the water and the heat flux through the air, i.e.,
dT
Kd
=a
dTa
d + (1- a) Kw dTw
d
(4.18)
where na and iw are the thermal conductivity for air and water, respectively, and
r is the radial direction. Sinceair and water are assumed to be at thermal equilibrium,
i.e.,
T =T =T
(4.19)
an approximate expression for the air-water system thermal conductivity, K, can
be weitten as;
= aK + (1 -a)
(4.20)
A practical approach to getting an appropriate value for the air-water system thermal conductivity would be to think of the problem as follows; Since the water is the
continuous fluid between the two walls of the annulus and since . < ;w, the air
bubbles (a x 0.04) may be viewed at worst as isolated thermal insulators within the
water body. The conductive heat will take the water path between the two walls of
the annulus almost unaffected by the presence of air bubbles. Therefore,
(4.21)
K K,
Dynamic Viscosity t:
Assuming good mixing of air bubbles and water, the total shear stress may be
written as the sum of the shear stress due to the air and the shear stress due to the
water, i.e.,
du
Adr =
du.
a
+
(1 -
a)
duw
d
(4.22)
where u, Ua and u are the mixture velocity, air velocity and water velocity, respectively. , a,9 and i, are the mixture viscosity, air viscosity,and water viscosity,
respectively. The velocities u, ua, and u
can be related together in terms of the void
75
fraction and the volumetric air flow ratio. The volumetric air flow ratio is defined as;
V=
Q.
Q + Q.
(4.23)
where Qa and Q, are the volumetric flow rates of air and water respectively. By
definition;
Q = Q. + Q,
or
uA = uaAa + uAw
(4.24)
A, = (1 - a) A
(4.25)
where,
Aa = aA,
and
With some algebra, once can get,
U = uV
a
and
ad(1
w=
- V)
a)
(4.26)
Substituting Equation (4.26) into (4.22), an expression for the air-water system
dynamic viscosity can be written as,
p = Va + (1 - V)p w
(4.27)
In literature, there exists few expressions for the two phase viscocity as cited in
Ref.[22] and Ref. [23]. However, they are only guesses and they do not carry much of
a physical sense. Again the fact that the water is the continuous fluid wetting the two
walls of the annulus makes it more appropriate the use of the water dynamic viscosity
as the air-water mixture dynamic viscosity, i.e.,
P~ ILW
1-1
(4.28)
One case analysis:
One experimental run has been analyzed in which the air-water system properties
have been treated in three different ways according to the following scheme;
Case I: in this case, all air-water system properties have been taken to be equal
to that of the water only.
Case II: In this case, the dynamic viscosity and the thermal conductivity are
assumed to be that of water only. The rest of the system properties are calculated
76
from Equation (4.8), (4.10), and (4.16).
Case III: In this case, the air-water system properties are determined from Equations (4.8), (4.10), (4.16), (4.20), and (4.27).
The three cases have been simulated and the results are shown in Figure (4-3). The
figure shows the local values of Grq/ReR versus that of (z/R)/(ReRPr) for three runs
whose heat flux profiles are shown in figure 2. The stability curve of Lawrence, W.T.
[8] is reproduced and plotted on the same figure. If we take case I as a reference case,
the figure shows that the ReR
Grg values in case II are slightly lower than those in case
I, while the ReR
Ger values in case III are slightly higher than those in case I. To know
the reason for this behaviour, the definitions of Grq and ReR are reproduced here for
convenience,
Grq=
gqR
(4.29)
r(Do + D)
(4.30)
and
ReR
Cases I and II differ only in air-water system density p evaluation. Since in case
II, the density is lower than that of case I, the kinematic viscosity v is higher and
consequently Grq/ReR value is lower than that in case I. Cases I and III differ not
only in density evaluation but also in the thermal conductivity and dynamic viscosity
evaluations as well. The reduction in the thermal conductivity and dynamic viscosity
values by the virtue of utilizing the expressions from Equations (4.20) and (4.27) results
in an increase in the Grq/ReR values. This increase is more than offset the decrease
due to the density reduction. It is worth-mentioning here to say that the expression for
the two-phase dynamic viscosity in Equation (4.27) yields the lowest value compared
to those values obtained from expressions cited in Ref.[22] and [23]. This means that
case III should be considered as the high bound. However, the differences between the
three treatments are slight in the present analysis. The reason is that the amount of
air injected is small (a z 0.05). These differences are expected to become higher as the
void fraction increases and different means of attacking the stability problem should
be sought. In the present analysis, the air-water mixture properties are evaluated
according to case I.
77
4.3.3
Steam/Noncondensable
Gas Mixture Side of the Apparatus:
In a steady state, the local values of heat fluxes on the inner wall of the condensing
tube is given by the relashioship:
q = q"Dt,
(4.31)
where Dti is the inner diameter of the condensing tube.
The local condensation heat transfer coefficient is defined as:
h
q' - ,
Tti - T'
(4.32)
where Tti is the condensing tube inner wall temperature and Tb is the centerline
bulk temperature of the steam/gas mixture.
Local values of Nusselt's number are defined as:
Nu= hDt,
hD
(4.33)
where kmi, is the steam/gas mixture's thermal conductivity.
Local values of Jakob's number are defined as:
Ja = Cp,miz(Tti
- Tat)
h =
(4.34)
19
hfg
where Cp,,,i is the condensate film specific heat capacity.
4.4
Results and Discussions:
4.4.1
Buoyancy Effects:
Figure (4-4) shows the heat flux profiles of three different experimental runs at the
same cooling water flow rates. The local values of Gr/Rel
8
were also plotted against
a nondimensional axial position z/Dh. The cooling water flow rate was 5 kg/min and
the inlet cooling water Reynold's number was - 880.
Byrne, et al [24] showed that the buoyancy will affect the flow when
Gr/Rel'
8
> 0.05
(4.35)
Therefore, the equality was also plotted as a horizontal line in Figure (4-4).
As can be seen in Figure (4-4), for the first run buoyancy starts to have an effect
near the middle of the annulus and it increases as one moves up the annulus. As
78
for the other two runs buoyancy has an effect over the entire length and that effect
increases as the flow moves upward. It is also noted that there is a marked increase
of the buoyancy effect near the middle of the condenser tube corresponding to the
temperature inversion.
Figure (4-5) shows the heat flux profiles for three cases with different cooling water
flow rates. The local Gr/Re l 8 values were plotted against the nondimensional axial
position z/Dh for the three runs. The cooling water flow rates were 5, 8, and 17
kg/min corresponding to inlet Reynold's numbers of 880, 1373 and 2780 respectively.
Increasing cooling water flow rate is to diminish the effect of buoyancy on the flow as
expected. However,for the three runs buoyancy is having an effect from the middle of
the channel upward.
4.4.2
Early Transition to Turbulence and Flow Recirculation:
Figure (4-6) shows the local values of Grq/ReR versus that of (z/R)/(ReRPr) for three
runs whose heat flux profiles are shown in figure (4-4). The stability curve of Lawrence
[18] is reproduced and plotted on the same figure.
Sherwin and Wallis [20] also studied the combined natural and forced laminar
convectionfor upflow through heated vertical annuli. They produced a stability curve
from their transition data similar to that of Lawrence. Unfortunately, their maximum
Reynolds' number based on the hydraulic radius was 300, whilethe minimum Reynolds
number of the present study is 420. This fact rendered their stability curve useless for
the present analysis.
Barozzi, et al [21] compared their experimental and minimum Nu-based data to
that of Lawrence. For Grq/ReR values between 75 and 200, the two agree. For values
above 200, the local values of the nondimensional position (z/R)/(ReRPr) of Barozzi
were shorter than that of Lawrence. Also, Lawrence's curve becomes very flat, with a
cut-off value of (Grq/ReR) of about 50 below which transition was not detected, while
the cut-off value of Barozzi was about 30.
In the present analysis, we take the conservative side in predicting the onset of
instability and compare our data to that of Lawrence.
As shown in Figure (4-6), the flowstars in the stable region, approaches the stability
line as it is heated up, crosses the stability line near the middle of the channel and
then ends up in the unstable region.
Figure (4-7), which corresponds to the three runs in Figure (4-5), shows the same
trend. It also shows that as the coolant flow rate goes up, the nondimensional distances
get shorter. It should be noted that the case of inlet Reynolds' number of 2780, while
79
the lower half of the annulus is wellin the stable region, the upper half jumps up and
clusters around the stable-unstable border. This behavior reflects the shape of the heat
flux profile of this particular case shown in Figure (4-5).
The foregoing discussion suggests that buoyancy-induced instabilities are present.
The step fall in wall temperature (as viewed from the coolant annulus), or the step
rise in wall temperature (as viewed from the steam/gas mixture side) is due to onset
of such instabilities. These instabilities may lead to early transition to turbulence in
case of laminar flows.
Yang, et al [25] developed a model to predict the local heat fluxes, local heat transfer
coefficients and local inner tube wall temperatures for forced convective condensation
of steam in the presence of noncondensable gas. The model allowed for flow pattern
transition form laminar to turbulent flow in the region of the coolant flow Reynolds'
number from 2400 to 2600. Their prediction reasonably agrees with experimental data
as shown in Figure (4-8). This gives support to the argument that instabilities may
lead to an early transition to turbulence in laminar flows.
Fewster, [26]recorded buoyancy-induced transition to turbulent flow in water at
atmospheric pressure at a Reynolds number of 1500. Transition to turbulent flownear
the end of the heated section was observed for Reynolds numbers of less than 1000
by Barozzi, et al [21]. However, the case of inlet Reynolds' number of 2780 shown in
Figure (4-7) requires special consideration. Since the flow is not laminar, the laminar to
turbulent flows argument does not strongly hold. This case suggests that instabilities
may have caused recirculation or cells within the annulus which are the cause of the
"Temperature Inversion". In the final analysis, it can be both mechanisms which are
responsible for this inversion.
4.4.3 Effects on Condensation Nusselt Numbers
Figure (4-9) shows the local values of Jakob number and condensation Nusselt number
along the condensing tube length for three runs of different heat flux profiles and
different cooling water flow rates. The figure shows the step rise in the middle of the
test section caused a step fall of the mixture Jakob number. The step fall in mixture
Jackob number is reflected as a step rise in the condensation Nusselt number near the
middle of the condensing tube. The strength of this step rise depends on the local
values and the shape of the wall heat flux. This behavior suggests that the interaction
between the coolant annulus side and the condensing tube side can be well represented
by including mixture Jakob number in correlations determining the condensation local
heat transfer coefficients.
80
4.5
Conclusions:
Within the range of data taken, here are the basic conclusions:
1. Buoyancy has an effect on the flow at least over the upper half of the condenser
and this effect increases as the heat flux increases and decreases as the flow rate
increases.
2. Buoyancy driven cellular flows and/or buoyancy induced early transition to tur-
bulence occurs near the middle of the channel upward. They are suspected to be
the reason for the "Temperature Inversion".
3. The effect of condenser tube wall temperature should be included in correlations
predicting the condensation heat transfer coefficientsin order to accommodate
the coolant conditions. Such effect can be well represented by employing Jakob
number in correlating the experimental data.
81
First
thermocouple
station
m
Nine similar
thermocouple
stations along
condendenser
tube.
50.8 mmnOD SS'
46.0 mm ID
62.7 mm ID SS Pip
2.44 m
Insulation
Last
thermocouple
station
tion
-
-
Figure 4.1: Schematic of the Coolant Annulus
82
- - - - - -
3
1000
800
f^
2
600
400
200
2
0
1
0
0.1 0.2
0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1.1
a (void fraction)
Figure(4-2) Air-water system density and volumetric
thermal expansion coefficient against the system air
void fraction for different system temperatures
83
E
104
,
10 3
-
Gr/Re]cr
*
caseI
O
case II
a
case III
L*
0-U.
04
I02
[18]
1 02
:-
I
j*'93~
~stable
I
. . . . II ....
Al
0
0.1
,.
I
0.2
0.3
0.4
.III..
..
0.5
0.6
(z/R)/(ReRPr)
Figure(4-3)
Grq/Re R variations along the coolant annulus
for the three treatments of the air/water system properties
for the same cooling water flow rate and same
heat flux profile
84
70
16
---
e
(O-°*,,
x0.10
0
o
0
'0
o
0.1
l- + r--, G0
.......
I
I
I
50
100
150
z/D h
200
250
Figure(4-4) The heat flux profiles and Gr/Re .8 variations
along the coolant annulus for three cases of different
heat flux profiles but with the same cooling
water flow rate[Re(inlet)-880]
85
ij
150
.
Mc=8
kg/min
-
100
:
Mc=5 kg/min
Mc= 17 kg/min
A
Mc = cooling wter
a
low rate.
_
50
0
X
A '
·
a
1
*
Gr/Re*
A
jI
0
50
C
CR
0.
.O.85
0.01
I
I
I
100
150
200
250
z/D h
Figure(4-5)
The heat flux profiles and Gr/Re '
8
variations along
the coolant annulus for three cases with different cooling
water flow rates[Re(inlet)-880,1373, & 2780]
86
lo4
--->n
Mc=5 kg/min
O
[
10 3
[Gr/Relcr
Mc=S kg/min
Mc=5 kg/min
-
kiakpr
·Lialah
An_
h..#
ke.
Lum
1 .fu
uw
-
-C-M..
04
02
[18]
o0
10
:e
stable
. .. i. I .. . I ... I
.1U-J
0
0.1
0.2
0.3
(z/R)/(ReRPr)
Me - cooling water flow rate
I . I .I I .. I.
0.4
0.5
Figure(4-6) The Gr/ReR variations along the
coolant annulus for the three cases with the same
cooling water flow rate[Re(inlet)~880]
87
0.6
104
[Gr/Re]cr
.
SA
1 03
A
-\·\h~~o
0
ea
Bn
0
&
Mc=5
kg/min
Mc=8
kg/min
A
Mc=17 kg/min
I1. C
unstable
Q3
102
instability line[18]
:AX
_
10
I
stable
Mc = cooling water
, . , , I , , , , I ,
10'
0
0.1
I I I
. ..
0.3
0.2
I , I
0.4
I
flow rate
.I . I
0.5
0.6
(z/R)/(ReRPr)
Figure(4-7) The Gr/ReR variations along the coolant
annulus for three cases with different cooling water
flow rates [Re(inlet)~880,1373, & 2780]
88
an/
7'U
80
-, L
,I---
F-
,
,I
,- ,-
-,I
h
'·
· I
-
.
-
.
.
.
*
.
.
CO Ti(experiment)
--Ti(prediction) [25]
I:
· '··n.
70
60
L
50
E
40
RUN 42-R3
30
steam/air inlet temp.=120.7 C
(
0
Steam inlet flow rate=27 kg/hr
air flow rate=4.8 kg/hr
cooling water flow rate=16.7 kg/min
20
In
AU
_-
0
0.5
1
1.5
2
2.5
length(m)
Figure (4-8) The condenser inner wall temperature
Profile against theoritical prediction [25]
89
0.08
Ja
g8
0.04
A
A
oo
0 Ja-(has42)
AB~
a Ja-(has76)
0
A
Ja-(PS1)
o
Nu-(has42)
A
Nu-(has76)
A
A
Nu-(PS1)
0
A
A
A
a
O
0
a
A
O
o
o 0l
0
0.5
l
A
10 4
Nu
10 3
A
I
1.5
condenser length (m)
1
2
2.5
102
Figure(4-9) The local values of Jakob number and condensation
Nusselt number along the condensing tube length for three
different experimental runs
90
Chapter 5
Experimental Results for In-Tube
Steam Condensation in the presence
of Helium and Helium & Air
5.1
Introduction:
Once the amount of air which is sufficient to achieve good radial mixing along the
length of the coolant annulus had been determined (see Chapter 3), it was possible to
turn our attention to measurements of steam condensation in the presence of helium
and in the presence of both helium and air. The existing facility was described in
details in Chapter 2. In addition, nine helium cylinders connected together through a
manifold, were added to the system in order to supply helium over a long period of time.
For the experiments involving steam with air and helium mixture, a gas proportioning
rotameter unit was added to the system. This unit consisted of two rotameters and
one tube; one rotameter was connected to the air source, the second rotameter was
connected to the helium source, and the tube served as the air/helium mixture outlet.
The unit had two built-in 16 turn precision valves, each connected to one rotameter,
for fine control of the flow. This arrangement served two purposes; first, it allowed
for measuring the helium and air flow rates and second, it helped in blending the two
gases into a homogeneousmixture with variable concentrations before they entered the
steam generator.
Table 5.1 provides the test matrix of the present steam/helium condensation experiments. The experiments covered steam/helium mixture inlet Reynolds numbers from
about 6,000to about 24,500,inlet helium mass fractions from 0.022up to 0.20, and mixture inlet temperatures of 100 and 1300 C. Reduced data are givenin Appendix F from
Table hsl to hs44. Table 5.2 provides the test matrix of the present steam/air/helium
91
condensation experiments. The experiments covered steam/air/helium
mixture Reynolds
numbers from about 6,500to 26,500,inlet helium mass fractions from 0.023 up to 0.20,
inlet air mass fractions from 0.045 up to 0.20 and mixture inlet temperatures of 100
and 130°C. Reduced data are given in Appendix G from Table has1 to Table has76.
Data reduction procedure and uncertainty analysis are given in Appendix A and B,
respectively.
The objectives of this chapter are to present the experimental results, compare with
pure steam correlations, explore the parametric dependencies of the condensation heat
transfer coefficients in the presence of helium alone and in the simultanuous presence
of both air and helium, and then correlate the data in terms of nondimensional groups
representing these parameters.
5.2
Steam condensation in the presence of Helium:
5.2.1 Comparison with Pure Steam Theory and Correlations:
Local values for Nusselt numbers of pure steam condensation, for the experimental
conditions, were calculated and compared with the experimentally obtained Nusselt
numbers of steam/helium mixtures. Expected Nusselt numbers of pure steam can be
based on Nusselt's assumptions [47] of negligible drag by the vapor, negligible effect
of condensate film waviness and negligible effect of condensate film acceleration and
heat convection were obtained. Employing these assumptions should yield conservative
(i.e. underestimated) valuesof pure steam Nusselt numbers. This Nusselt-assumptions
based approach is given in Appendix A. Also, a general film condensation correlation
developed by Chen, [27] has been used for realistic evaluation of pure steam Nusselt
numbers for the experimental conditions. This correlation is claimed to incorporate the
effects of interfacial shear stress, interfacial waviness, and turbulent transport in the
condensate film for annular-film condensation inside vertical tubes. The correlation is
given in Chapter 6.
Figure (5.1) shows the calculated condensation heat transfer coefficientsof pure
steam and the experimental heat transfer coefficientsof steam in the presence of helium against steam/helium mixture Reynolds numbers. The figure shows the gradual
increase of the experimental heat transfer coefficientsas the mixture Reynolds number
increases. As expected, the calculated pure steam (or film) heat transfer coefficients
are higher than those of steam/helium mixtures. The heat transfer coefficientsof pure
steam evaluated using Nusselt's assumptions are lower than those evaluated using the
correlation of Chen, et al [27]; a result which is expected as well.
92
Figure (5.2) shows the condensation heat transfer coefficientsagainst the helium
mass fraction. The experimental values of the heat transfer coefficientsin the presence
of helium decrease as the helium mass fraction increases. The corresponding calculated
values of pure steam also decrease with the helium but at a lower rate. The reason
for this is that the decrease in the pure steam case is only due to the increase in the
film thermal resistance while the decrease in steam/helium case is due to the combined
effect of the increase of the film thermal resistance and the helium mass fraction in the
mixture.
Figure (5.3) shows the plot of the heat transfer coefficientsagainst the helium mole
fraction. While the trend is essentially the same as in Figure (5.2), the steam/helium
heat transfer coefficients are higher on the basis of mole fraction in Figure (5.3) when
compared to that of Figure (5.2) for the same value on the basis of mass fraction. This
can be easily understood, since for the same fraction, helium will carry less mass on
the basis of mole fraction than that obtained on the basis of mass. Alternatively, for
the same fraction, helium will carry more molecules on the basis of mass than those
obtained on the basis of mole.
Figure (5.4) shows the steam/helium and pure steam heat transfer coefficients
against the Jakob number. The general trend of the steam/helium mixture heat transfer coefficient is to decrease as the Jackob number increases. The calculated values
of the condensate film heat transfer coefficientsbases on the Nusselt's assumptions
slightly share this trend while those of Chen, et al [27] do not. This may suggest that
the reduction in steam/helium heat transfer coefficientsas the mixture Jakob number
increases comes mainly from the steam/helium boundary layer. Increasing the Jakob
number implies increasing the wall subcooling. This would serve as a driving force
for higher helium concentration near the condensing tube wall which will block the
steam form reaching the wall, with eventual decrease in the condensation heat transfer
coefficients.
Figure (5.5) shows the steam/helium heat transfer coefficients and those of pure
steam against the mixture Schmidt number. The steam/helium heat transfer coefficients decrease rapidly as the Schmidt number increases. Increasing the Schmidt number, as will be discussed later, implies increasing momentum to mass diffusion transfer
ratio. Since the main source of heat transfer in the condensation process comes from
diffusion of steam toward the wall, increasing the mixture Schmidt number implies less
steam is getting condensed. Increasing the mixture Schmidt number also means that
the helium content increases, as the mixture goes down the channel. Both mechanisms
lead to decreasing the condensation heat transfer coefficients.
93
5.2.2 Condensate Film Thermal Resistance
In his modeling of forced convection condensation in the presence of air on a flat plate
using the heat and mass transfer analogy, Corradini [28]corrected for high transfer rates
for the air/steam layer and used the simple Nusselt analysis for the condensate film.
the Nusselt analysis is believed to give conservative (underestimated) values of condensate film heat transfer coefficients, i.e., conservative (overestimated) film thermal
resistance. Corradini [28] concluded that the condensate film heat transfer resistance
is insignificant compared with the overall thermal resistance. Later, Siddique, et al
[5] employed the assumption of negligible film thermal resistance in modeling steam
condensation in the presence of noncondensable in vertical tubes. To test the validity
of the above assumption, the ratios of steam/helium heat transfer coefficientsto those
of pure steam based on the Nusselt analysis and to those of pure steam based on a more
realistic correlation of Chen, et al [27], have been plotted against different parameters.
These ratios are also the ratios of the condensate film thermal resistance to the overall
thermal resistance.
Figure (5.6) shows the ratios of steam/helium heat transfer coefficientsto pure
steam heat transfer coefficientsagainst the mixture Reynolds number. The general
trend of the data is that the film thermal resistance is significant and tend to increase
as the Reynolds number increases. Even at low Reynolds number, a large number
of the data points shows the importance of the film thermal resistance. As expected
the Nusselt analysis is conservative (overestimating) as to the significance of the film
thermal resistance.
Figure (5.7) shows the ratios of steam/helium heat transfer coefficientsto pure
steam heat transfer coefficientsagainst the helium mass fraction. The figure showsthe
general trend of the ratio decrease as the helium mass fraction increases. It is obvious
that increasing helium mass content will increase the barrier for the steam from reaching the wall and get condensed. Thus, increasing the helium concentration will increase
the steam/helium boundary layer thermal resistance and diminish the significanceof
the film thermal resistance provided all other parameters remain the same. It should
be noted that even for 35% helium mass fraction, film thermal resistance represent
25% or more of the total thermal resistance.
Figure (5.8) shows the ratios of steam/helium heat transfer coefficients to pure
steam heat transfer coefficientsagainst the helium mole fraction. The same observations on Figure (5.7) hold true for this one except that for the same value of helium
fraction, the condensate film thermal resistance will be higher for a molar fraction than
it is for a mass fraction.
94
5.2.3 Comparison with Siddique-Golay-Kazimis Steam/Helium Correlation:
Siddique, et al [5] performed steam/helium
mended the following correlation:
condensation experiments and recom-
Nu = 0.537Re0 43 3 .
2 4 9 Ja-o. 24
(5.1)
within the range;
0.02 < WH, < 0.52,
300 < Re < 11,400,
0.004 < Ja < 0.07,
where Nu is the condensation Nusselt number given by:
Nu = Dti
kmia '
(5.2)
where h is the condensation heat transfer coefficient, Dti is the condensing tube inside
diameter and kmi, is the steam/helium mixture thermal conductivity. Re in Equation
(5.1) is the steam/helium mixture Reynolds number, WHe is helium bulk mass fraction
and Ja is Jakob number defined as:
Ja = Cp,mi(Tat- Tw)
hfg
(5.3)
where Tat is the saturation temperature, T, is the wall temperature, Cp,,,i is the
steam/helium mixture specificheat capacity and hfg is the latent heat of condensation.
The standard deviation of the above correlation in predicting Nusselt numbers were
reported to be 69% [5].
Within the range of validity of the above correlation, Equation (5.1), the experimental steam/helium heat transfer coefficientsare plotted against those obtained from
Equation (5.1) and are shown in Figure (5.9). An error band of i ± 100% was also
shown in the plot. The plot shows a good agreement between the heat transfer coef-
ficients predicted the Siddique-Golay-Kazimi'scorrelation and the experimental heat
transfer coefficients.
5.2.4 Steam/Helium Correlations of the Present Study:
From the previous sections, the dependence of condensation heat transfer coefficients
on various parameters, namely Reynolds number, helium mass fraction, helium mole
95
fraction, Jakob number and Schmidt number, have been established. However, in order
to comeup with a correlation which includes these parameters, the dependence of these
parameters on one another should be examined. For example, the mass fraction and
the mole fraction are related to one another through molecular weight. Therefore,
to include them in one correlation is to duplicate the effect. The same argument
holds true for the dependence between Schmidt number and the mass or mole fraction.
It should be mentioned here that in some experimental runs the steam was almost
depleted near the end of the test section and the coolant temperature rise per unit
length of the condensing tube was small. The uncertainty associated with these data
points was high. These data points were not included in developing the correlations
since including them would have unrealistically biased to higher value the total error
associated with determining the experimental heat transfer coefficients.
Steam/Helium Correlation # 1:
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.Re'WHeJaz
(5.4)
Equation 5.4 was linearized using logarithmic transformation, and then a multiple
regression analysis was performed in order to obtain the coefficientsvalues. The result
was the following correlation:
Nu = 1.279Re0 2 5 6
0 741Ja-0. 95 2
(55)
which is valid within:
852 < Re < 24460
0.022 < WH, < 0.654
0.007 < Ja < 0.119
with an adjusted R2-value for the fit of the data to the correlation of 0.938 which means
that the correlation explains 93.8% of the data variability. The standard deviation of
the Nusselt numbers obtained from the correlation from the experimentally obtained
ones was found to be 40% as shown in Appendix B. Figure (5.10) shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
96
Steam/Helium Correlation # 2:
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.Re=YeJaz
(5.6)
Equation (5.6) was linearized using logarithmic transformation, and then a multiple
regression analysis was performed in order to obtain the coefficientsvalues. The result
was the following correlation:
Nu = 1.253Re 0 32
S Yf0° 9- 7 Jaa09 5 7
(5.7)
which is valid within:
825 < Re < 24460
0.094 < YH, < 0.895
0.007 < Ja < 0.119
with an adjusted R2 -value for the fit of the data to the correlation of 0.921. The
standard deviation of the Nusselt numbers obtained from the correlation from the
experimentally obtained ones was found to be 40.8%. Figure (5.11) shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
Significance of Schmidt number:
Run hso-44 has been analyzed here as a typical example in order to assess the
significance of the Schmidt number. Figure (5.12) shows the helium dynamic viscosity,
steam dynamic viscosity and steam/helium mixture dynamic viscosity variations along
the length of the condensing tube. The figure shows that the helium dynamic viscosity
is more than twice that of steam, and that the dynamic viscosity of both steam and
helium decrease, but the steam/helium mixture dynamic viscosity increases along the
condensing tube. The reason for this behavior is that the mixture dynamic viscosity is
based on the molecular content of steam and helium in the steam/helium mixture. As
the steam/helium mixture flowsdown the condensing tube, steam condenses and the
helium content in the steam/helium mixture increases causing the mixture dynamic
viscosity to approach that of helium near the end of the condensingtube.
97
Figure (5.13) shows the helium mass density, steam mass density and steam/helium
mixture mass density profilesalong the length of the condensingtube. The figure shows
that helium mass density increases as bulk temperature decreases, while steam mass
density and steam/helium mixture density decrease along the length of the condensing
tube. The reason is that steam is depleted and its mass content decreases whilehelium
mass flowrate remains intact and since steam is much heavier than helium, the mixture
density will decrease.
Sincethe mixture dynamic viscosityincreases and its density decreases, the mixture
kinematic viscosity will sharply increase as the mixture flows down the condensing tube.
The relationship between the three variables is:
vmiz = Ilmi
Pmi:
(5.8)
where vmi, is the kinematic mixture viscosity, mia, is the dynamic mixture viscosity
and Pmiz is the mixture density. Fig. 5.14 shows the variation of the mixture kine-
matic viscosity along the length of the condensingtube. Since the kinematic viscosity
signifies the momentum transfer, this means that the momentum transfer increases
as the mixture flows down the tube. Figure (5.14) also shows the variation of the
mixture diffusion coefficient which decreases as steam condenses. Thus mass diffusion
decreases as the mixture flows down the tube due to both decreasing steam content
and decreasing coefficient for diffusion.
The mixture Schmidt number is defined as the ratio of the momentum to mass
transfer and is given by:
Sc
Vmi
Dmix
(5.9)
where Dmi= is the mixture mass diffusion coefficient. Figure (5.15) shows the Schmidt
number, helium mass fraction and condensation heat transfer coefficient profiles along
the length of the condensingtube. The heat transfer coefficientdecreases as the schmidt
number increases or the helium mass fraction increases. The schmidt number is higher
the higher is the helium mass fraction. Actually the Schmidt number represents the
static and the dynamic effects of helium content on the condensation heat transfer
coefficients. Therefore, a correlation which includes the Schmidt number as an independent variable should not include the gas fraction in order not to duplicate the
effect.
Steam/Helium Correlation # 3:
98
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.Re=Sc'Ja'
(5.10)
Equation 5.10 was linearized using logarithmic transformation, and then a multiple
regression analysis was performed in order to obtain the coefficients values. The result
was the following correlation:
Nu = 2.244Re0.161 Sc-
1 652 Ja -'l 03 8
(5.11)
which is valid within:
825 < Re < 24460
0.238 < Sc < 1.187
0.007 < Ja < 0.119
with an adjusted R2 -value for the fit of the data to the correlation of 0.951. The
standard deviation of the Nusselt nu mbers obtained from the correlation from the
experimentally obtained ones was found to be 38.9%. Figure (5.16) shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
5.3
Steam condensation in the presence Air/Helium mix-
tures:
5.3.1
Comparison with Pure Steam Theory and Correlations:
Figure (5.17) shows the calculated condensation heat transfer coefficients of pure steam
and the experimental steam/air/helium heat transfer coefficientsagainst steam/air/helium
mixture Reynolds numbers. The figure shows the gradual increase of the experimental heat transfer coefficients as mixture Reynolds number increases. As expected
the calculated pure steam or film heat transfer coefficientsare higher than those of
steam/air/helium mixtures. The heat transfer coefficientsof pure steam evaluated using the Nusselt assumptions are lower than those evaluated using the correlation of
Chen, et al [27]; a result which is expected as well.
Figure (5.18) shows the condensation heat transfer coefficientsagainst the air mass
fraction. The experimental values of the steam/air/helium heat transfer coefficients
decrease as the air mass fraction increases. The corresponding calculated values of
99
pure steam also decrease with the air but at lower rate. The reason for this is that
the decrease in the pure steam case is only due to the increase in the film thermal
resistance while the decrease in steam/air/helium
case is due to the combined effect of
the increase of the film thermal resistance and the steam/air/helium boundary layer
thermal resistance.
Figure (5.19) shows the condensation heat transfer coefficientsagainst the helium
mass fraction. The experimental values of the steam/air/helium heat transfer coefficients decrease as the air mass fraction increases. The corresponding calculated values
of pure steam also decrease with the air but at lower rate. The behavior is essentially
the same as with air mass fraction. However,from comparing Fig. 5.19 with Fig. 5.18
it should be noted that steam/air/helium heat transfer coefficientsare lower at a given
helium mass fraction than those at the same air mass fraction.
Figure (5.20) shows the plot of the steam/air/helium heat transfer coefficients
against the air mole fraction. While the trend is essentially the same as in Figure
(5.18), the steam/air/helium
heat transfer coefficients are lower on the basis of mole
fraction in Figure (5.20) when compared to that of Figure (5.18) for the same value on
the basis of mass fraction. This can be easily understood, since for the same fraction,
air will carry more mass on the basis of mole fraction than that obtained on the basis
of mass. Alternatively, for the same fraction, air will carry less molecules on the basis
of mass than those obtained on the basis of mole.
Figure (5.21) shows the plot of the steam/air/helium heat transfer coefficients
against the helium mole fraction. While the trend is essentially the same as in Figure
(5.19), the steam/air/helium heat transfer coefficients are higher on the basis of mole
fraction in Figure (5.21) when compared to that of Figure (5.18) for the same values
on the basis of mass fraction. This can be easily understood, since for the same frac-
tion, helium will carry less mass on the basis of mole fraction than that obtained on
the basis of mass fraction. Alternatively, for the same fraction, helium will carry more
molecules on the basis of mass than those obtained on the basis of mole. However, from
comparing Figure (5.21) with Figure (5.20) it should be noted that steam/air/helium
heat transfer coefficientsare higher at a given helium mole fraction than those at the
same air mole fraction.
Figure (5.22) shows the steam/air/helium and pure steam heat transfer coefficient
against the Jakob number. The general trend of steam/air/helium mixture heat transfer coefficient is to decrease as the Jakob number increases. The calculated values of
condensate film heat transfer coefficients based on the Nusselt's assumption slightly
share this trend while those of Chen, et al [27] do not seem to share this trend. This
suggests that the reduction in steam/air/helium heat transfer coefficients(as the Jakob
100
number increases) is due mainly to the steam/air/helium boundary layer. Increasing
the Jakob number means wall subcooling increase. This would serve as a driving force
for higher air and helium concentrations near the condensingtube wall which will block
the steam from reaching the wall with eventual decrease in condensation heat transfer
coefficients.
Figure (5.23) shows the steam/air/helium heat transfer coefficientsand those of
pure steam against the mixture Schmidt number. The steam/air/helium heat transfer
coefficients decrease rapidly as the Schmidt number increases. Increasing the Schmidt
number, as discussed in section 5.2, means increasing the ratio of momentum to mass
diffusion transfer. Since the main source of heat transfer in the condensation process
comes from diffusion of steam toward the wall, increasing the Schmidt number means
less steam is getting condensed. Increasing the Schmidt number also means that the air
and helium content increase down the channel. Both mechanisms lead to the reduction
of the condensation heat transfer coefficients.
5.3.2
Condensate Film Thermal Resistance:
As done in Section 5.2.2 with the steam condensation in the presence of helium only,
the ratio of the condensate film thermal resistance to the total themal resistance of
steam/air/helim
mixtures as a function of relevent parameters will be presented here.
Figure (5.24) shows the steam/air/helium heat transfer coefficientsto pure steam
heat transfer coefficientsratios against steam/air/helium mixture Reynolds number.
The general trend of the data is that the film thermal resistance increases as Reynolds
number increases. Even at low Reynolds number, a large fraction of the data shows
the significance of the film thermal resistance. As expected, the Nusselt analysis is
conservative (overestimating) as to the significance of the film thermal resistance.
Figure (5.25) shows the steam/air/helium heat transfer coefficientsto pure steam
heat transfer ratios against air/helium mixture mass fraction. The figure shows the general trend of ratio decrease as the air mass fraction increases. It is obvious that increasing air mass content will increase the barrier for the steam to reach the wall and to get
condensed. Thus, increasing the air concentration will increase the steam/air/helium
boundary layer thermal resistance and diminish the significance of the film thermal
resistance provided all other parameters remain the same. It should be noted that
even for 30% air mass fraction, the film thermal resistance represents about 20% of the
total thermal resistance.
101
5.3.3 Steam/Air/Helium
Correlations:
From the previous sections, the dependence of steam/air/helium heat transfer coefficients on various parameters, namely; steam/air/helium
mixture Reynolds number,
air mass fraction, helium mass fraction, air mole fraction, helium mole fraction, Jakob
number and Schmidt number, has been explained. However,in order to come up with
a correlation which include these parameters, the dependence of these parameters on
one another should be explained. For example, the mass fraction and the mole fraction
are related to one another through molecular weight. Therefore, to include them in one
correlation is to duplicate the effect. The same argument holds true between Schmidt
number and the mass or mole fraction.
Steam/Air/Helium Correlation # 1:
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.ReCWAi W eJaJ
(5.12)
Equation (5.12) was linearized using logarithmic transformation, and then a multiple regression analysis was performed in order to obtain the coefficientsvalues. The
result was the following correlation:
5 54 W.Nu = 0.12Re0 .368WA--0;
676 Ja-0. 9 3 1
(5.13)
which is valid within:
846 < Re < 26537
0.045 < WAir < 0.574
0.023 < WHe < 0.405
0.007 < Ja < 0.102
with an adjusted R2-value for the fit of the data to the correlation of 0.938. The
standard deviation of the Nusselt numbers obtained from the correlation from the
experimentally obtained ones was found to be 40%. Figure (5.26) shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
Steam/Air/Helium Correlation # 2:
102
Page 103 - Equation 5.17 should read:
Nu = 0.199Re0
3 2 7 Sc-2- 17 1 5Ja
.0 5 8
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.Re'Yi,rYeJaw
(5.14)
Equation 5.14 was linearized using logarithmic transformation, and then a multiple
regression analysis was performed in order to obtain the coefficients'values. The result
was the following correlation:
Nu = 0.095Re0 427 YAi414 Ye
Ja 0
1
(5.15)
which is valid within:
846 < Re < 26537
0.02 < YAir < 0.345
0.096 < YHe < 0.77
0.007 < Ja < 0.102
with an adjusted R2 -value for the fit of the data to the correlation of 0.925. The
standard deviation of the Nusselt numbers obtained from the correlation from the
experimentally obtained ones was found to be 41%. Figure (5.27) shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
Steam/Air/Helium Correlation # 3:
The data of the present study was correlated by a relationship which takes the
following form:
Nu = const.Re=ScvJaz
(5.16)
Equation 5.16 was linearized using logarithmic transformation, and then a multiple
regression analysis was performed in order to obtain the coefficientsvalues. The result
was the following correlation:
Nu = 0.0348Re0°
60 25-2-8 5 9 Ja- 0. 9 7 6
which is valid within:
846 < Re < 26537
103
(5.17)
0.314 < Sc < 0.864
0.007 < Ja < 0.102
with an adjusted R2 -value for the fit of the data to the correlation of 0.94.9. The
standard deviation of the Nusselt numbers obtained from the correlation from the
experimentally obtained ones was found to be 39%. Figure 5.28 shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
5.3.4 Steam/Air/Helium + Steam/Helium Data-Based Correlation:
To produce this correlation, the steam/air/helium experimental data was substituted
into the steam/helium correlation 1 and the resultant Nusselt numbers were designated
by Nuh °. The steam/air/helium experimentally obtained Nusselt numbers were later
divided by Nuha and the resultant ratios were correlated as;
Nu
(5.18)
Nuha = (1- mWai)
where m is a constant to be determied. The ratios were plotted against Wi, and
m was determined to be 1.681. This correlation can be written explicitly as;
Nu = 1.279Re
25 6
(1 - 1.681WAi,) Wia° 7 4-1 Ja0
9 52
(5.19)
which is valid within:
846 < Re < 26537
0.000 < WAit < 0.574
0.023 < WHe < 0.405
0.007 < Ja < 0.102
with an adjusted R2 -value for the fit of the data to the correlation of 0.915. The
standard deviation of the Nusselt numbers obtained from the correlation from the
experimentally obtained ones was found to be 41%. Figure 5.29 shows a comparison
between the correlation predicted Nusselt numbers and the experimentally obtained
Nusselt numbers.
104
5.4
Conclusions:
5.4.1
Conclusions regarding steam condensation in the presence of
helium
Within the range of the experimental data, the following are the main concluding
remarks regarding steam/helium forced convection condensation in a vertical tube:
First, regarding steam/helium condensation heat transfer coefficients:
1. Steam/helium condensation heat transfer coefficients are mainly dependent on
the followingparameters:
(a) steam/helium mixture Reynolds number
(b) helium mass fraction,mole fraction, or steam/helium mixture Schmidt number
(c) Jakob number (wall subcooling)
2. Steam/helium condensation heat transfer coefficients increase with the steam
mixture Reynolds number, keeping the other parameters constant.
3. Steam/helium condensation heat transfer coefficients decrease as helium mass
(mole) fraction in the mixture increases keeping the mixture Reynolds number
and Jackob number constant.
4. Steam/helium condensation heat transfer coefficients decrease as steam/helium
mixture Schmidt number increases keeping the mixture Reynolds number and
Jackob number constant.
5. Steam/helium condensation heat transfer coefficients decrease as Jakob number
increases keeping the other parameters constant.
Second, regarding condensate film thermal resistance:
6. In general, the condensate film thermal resistance is significant in forced convec-
tion in-tube condensation in the presence of helium and it should be included in
future steam/noncondensable gas modeling.
7. The ratio of the condensate film thermal resistance to the total thermal resistance
is mainly dependent on the following parameters:
105
(a) steam/helium mixture Reynolds number
(b) helium mass, mole, fraction, or steam/helium Schmidt number
8. The ratio of the condensate film thermal resistance to the total thermal resistance
increases as steam/helium mixture decreases as the mixture Reynolds number
increase for a fixed helium fraction or fixed mixture Schmidt number.
9. The ratio of the condensate film thermal resistance to the total thermal resistance
decreases as helium mass (mole) fraction in the mixture increases for the same
mixture keeping Reynolds number.
Third, regarding comparison with existing correlation:
10. Siddique-Golay-Kazimi's steam/helium correlation prediction of the condensation heat transfer coefficientsis in good agreement with the experimental data.
Fourth, regarding new steam/helium correlations:
11. Three steam/helium correlations have been produced from the existing data.
12. Correlation # 1 can explain 93.8% of the data variability. The standard deviation
of the correlation predicted Nusselt numbers from the experimentally obtained
ones is 40%.
13. Correlation # 2 can explain 92.1% of the data variability. The standard deviation
of the correlation predicted Nusselt numbers from the experimentally obtained
ones is 40.8%.
14. Correlation # 3 can explain 95.1.7% of the data variability. The standard de-
viation of the correlation predicted Nusselt numbers from the experimentally
obtained ones is 38.9%.
15. Correlation #2 is just an alternate form of correlation #1 since the mass fraction
and the mole fraction are related together through the molecular weight. Correlation #3 is different and it captures more of the physics of the problem because the
Schmidt number is more representative of the steam/noncondensables boundary
layer dynamics.
106
5.4.2
Conclusions regarding steam condensation in the presence of
air and helium mixture
Within the range of the experimental data, the following are the main concluding
remarks regarding steam/air/helium forced convectioncondensation in a vertical tube:
First, regarding steam/helium condensation heat transfer coefficients:
1. Steam/helium condensation heat transfer coefficients are mainly dependent on
the followingparameters:
(a) steam/air/helium mixture Reynolds number
(b) air mass fraction (mole fraction),and helium mass fraction (mole fraction),
or alternatively, mixture Schmidt number
(c) Jakob number (wall subcooling)
2. Steam/air/helium condensation heat transfer coefficientsincrease with steam/air/helium
mixture Reynolds number, keeping the other three parameters constant.
3. Steam/air/helium condensation heat transfer coefficients decrease as air mass
(mole) fraction in the mixture increases keeping the mixture Reynolds number,
Jackob number and helium mass (mole) fraction constant.
4. Steam/air/helium
condensation heat transfer coefficients decrease as helium mass
(mole) fraction in the mixture increases keeping the mixture Reynolds number,
Jackob number and helium mass (mole) fraction constant.
5. Steam/air/helium
condensation heat transfer coefficients decrease as steam/air/helium
mixture Schmidt number increases keeping the mixture Reynolds number and
Jackob number constant.
6. Steam/air/helium condensation heat transfer coefficientsdecrease as Jakob number increases keeping the three parameters constant.
Second, regarding condensate film thermal resistance:
7. In general, The condensate film thermal resistance is significant in forced con-
vection in-tube steam condensation in the presence of air/helium mixtures and
it should be included in future steam/noncondensable
107
gas modeling.
8. The ratio of the condensate film thermal resistance to the total thermal resistance
is mainly dependent of the followingparameters:
(a) steam/air/helium mixture Reynolds number
(b) air and helium mass (mole) fraction.
9. The ratio of the condensate film thermal resistance to the total thermal resistance
increases as steam/air/helium
mixture Reynolds number increases for fixed air
and helium fractions.
10. The ratio of the condensate film thermal resistance to the total thermal resistance
decreases as air mass (mole) fraction in the mixture increases keeping the mixture
Reynolds number, and helium mass (mole) fraction constant.
11. The ratio of the condensate film thermal resistance to the total thermal resistance
decreases as helium mass (mole) fraction in the mixture increases keeping the
mixture Reynolds number, and air mass (mole) fraction constant.
bf Third, regarding new steam/air/helium correlations:
12. Three new steam/air/helium
correlations have been produced from the existing
data.
13. Correlation # 1 can explain 93.8% of the data variability. The standard deviation
of the correlation predicted Nusselt numbers from the experimentally obtained
ones is 40%.
14. Correlation # 2 can explain 92.5% of the data variability. The standard deviation
of the correlation predicted Nusselt numbers from the experimentally obtained
ones is 41%.
15. Correlation # 3 can explain 94.9% of the data variability. The standard deviation
of the correlation predicted Nusselt numbers from the experimentally obtained
ones is 39%.
16. As is said regarding the steam/helium correlations, steam/air/helium
correlation
#2 is just an alternate form of correlation #1 since the mass fraction and the
mole fraction are related together through the molecular weight. Correlation
#3 is different and it captures more of the physics of the problem because the
Schmidt number is more representative of the steam/noncondensables boundary
layer dynamics. The correlation also fits better with the experimental data.
108
17. Steam/air/helium correlation #4 as given in Equation (5.19) is an extension to
steam/air/helium correlation #1 to include air mass fractions lower than 0.05.
The correlation, as given in Equation (5.19) can explain 91.5% of the data vari-
ability. The standard deviation of the correlation predicted Nusselt numbers
from the experimentally obtained ones is 41%.
109
Run
set
#
Steam/Helium Helium
Mixture Inlet Inlet
temp. (C)
Mass (%w)
1
100
2
100
3
100
2.5, 5, 7.5, 10
12.5, 15, & 20
2.5, 5, 7.5, 10
12.5, 15, & 20
2.5, 5, 7.5, 10
4
100
& 12.5
2.5, 5, 7.5
Steam Inlet
Flow rate
fraction (kg/hr)
10
20
30
40
& 10
5
130
6
130
7
130
8
130
2.5, 5, 7.5, 10
12.5, 15, & 20
2.5, 5, 7.5, 10
12.5, & 15
2.5, 5, 7.5
& 10
2.5, 5, & 7.5
10
20
30
40
* Cooling water flow rate = 4 - 8 kg/min
* Volumetric air to cooling water ratio = 20%
Table 5.1: Test Matrix for Steam/Helium Mixtures
110
Run
Set
Steams/Air
Mixture
Air Inlet
Mass
Helium
Inlet Mass
Inlet
Fraction
Fraction
Temp. (C)
(%w)
1
100
2A
100
2B
3
4
130
100
100
Steam
Inlet Flow
Rate
(%w)
(kg/hr)
5
10
15
20
2.5,
2.5,
2.5,
2.5,
5,
5,
5,
5,
7.5,
7.5,
7.5,
7.5,
10,
10,
10,
10,
5
10
15
20
2.5,
2.5,
2.5,
2.5,
5,
5,
5,
5,
7.5,
7.5,
7.5,
7.5,
10, 12.5, & 15
10, 12.5, & 15
10, & 12.5
& 10
5
2.5, 5, 7.5, & 10
12.5,
12.5,
12.5,
12.5,
&
&
&
&
10
2.5, 5, 7.5, & 10
15
2.5, 5, & 7.5
20
2.5, &55
5
10
2.5, 5, 7.5, 10, & 12.5
2.5, 5, 7.5, & 10
15
2.5, & 5
20
2.5
5
2.5, 5, & 7.5
10
2.5, & 5
15
2.5
15
15
15
15
30
40
* Volumetric air to cooling water flow ratio = 20%
111
20
20
* Cooling water flow rate = 4-8 kg/min
Table 5.2: Test Matrix for Steam/Air/Helium
10
Mixture
0
Ir)
~ ~
P
PU
kn~~~Q
;;i~Cp
co
C Z u: f
o~
0n
0n
o
m Q
o
X3·Ius
E
m~
N
To
_1
112
co
a
sh
ANT
~
To~
(3 Ztu/MA) q
co cof
~
~
a
~~
C_
CM
o
J
CN
0
o
*
c
*o
-
O CM3s
C Q
a co
U)
Ca COb
;LE
eq
0C
Ca^
0~~~SO·w
_fi=
S:E
U~~~)
qD
L; c
bD Li
._
o~v
.
(3 zru/MA)
113
_
O
-"f
6t=
oi o
E C) E) ,KE
= =o
o
Q)
ou
r o
Cu
,
~o
d
d~U
m
0~~
_ X
XOe
E
Ce
O
60 V
C ;
u~~.
a;
(3 Zu/MI) q
114
L
le
.. W
0
ok
-~~~:s
oOuO
|o
0
oo
o
Ioa
OF O
CU
= ° u0
K
o.
O o~
o
115
E
os a
d
OD v
0
v
0o
(D Zu/AA,)) q
E
0~~~~~c
e:
I4~
O
o6o
ac=
*8
i
rl
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Figure (5-9) Comparison between the experimental condensation heat
transfer coefficients and those obtained using a correlation
produced by Siddique, et al [5]
120
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Figure (5-12) The bulk
viscosity profiles
helium, and mixture dynamic
length
along the condensing tube
123
140
100
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length(m)
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Figure (5.13)
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8
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helium mass fraction and condensation heat
transfer coefficient profiles along the
condensing tube length
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Chapter 6
Modeling In-Tube Steam
Condensation in the Presence of Air,
Helium, and Air/Helium Mixtures
6.1
Introduction:
In general, there exists two main methods for analyzing the forced convective condensation of steam in the presence of noncondensables. The first is the Boundary Layer (BL)
based models which employ similarity solutions, integral methods and finite difference
techniques [29-37].
The second one is the Heat and Mass Transfer (HMT) analogy based models.
Colburn and Hougen [38]were the first to develop a stepwise iterative solution method
for predicting the condensation heat transfer rate from a vapor-noncondensablemixture
based on the heat and mass transfer analogy. Since then, a number of researchers [28,
39-45] have proposed approximate numerical analyses to simplify and improve the
Colburn and Hougen methodology which is practically cumbersome. However, all the
experimental studies so far investigated the effect of only one noncondensable gas in
the vapor/gas mixture on the local values of condensation heat transfer coefficient.
In the present study, the effect of air and helium as noncondensables in steam-airhelium mixtures on local condensation heat transfer coefficientsisbeing investigated.
Hydrogen was replaced by helium because hydrogen is harder to handle. However, both
hydrogen and helium are light elements and their thermal and diffusivecharacteristics
are very similar. On the analytical side, a diffusion boubary layer based model has
been developed. The model includes the effect of more than one noncondensable gas
on steam consensation.
141
6.2
Modeling:
The condensate film will be dealt with first. An appropriate correlation for consensate
film heat transfer coefficient is to be selected. Given the local wall temperatures Tw, the
local values of the interface temperature Ti can then be calculated along the condensing
tube length. Next, the steam/noncondesable gases mixture will be modeled. The heat
transfer coefficientsof steam/noncondensable gases mixture, obtained using the model,
will then be compared to those obtained from the experimental measurement.
6.2.1
Condensate film:
The condensate film will be modeled as an annular layer on the inside of the vertical
condensing tube. Chen, et al [27] developed a general in-tube condensation correla-
tion which incorporates the effects of interfacial shear stress, interfacial waviness, and
turbulent transport in the condensate film. This correlation is established on the basis
of analytical and empirical results from the literature and is found to be in excellent
agreement with all existing data [27]. For local condensation Nusselt numbers for
cocurrent annular-film flow inside vertical tube, the correlation is expressed as;
2.4
Nufilm
03Re-32+
NU?'~=
O'31Re~I-X'
1/3
3.9
113
+ 771r6 (ReT - Re,)1 Re 0 4
771.6
Rel pr04)
2.37x 1014
. 1/2
(6.1)
where A is given by;
n 252s~1.1 77 0.1 56
3 p. 78
-Ad 2 g2/3p.55
(6.2)
In equations (6.1) and (6.2), Rel is the local condensate film Reynolds number,
ReT represents the film Reynolds number of the condensate if total condensation of
the steam takes place, A is a system parameter which accounts for the gravitational and
viscous forces, and d is the condensing tube inside diameter. Once the local condensate film Nusselt number is known, the local condensate film heat transfer coefficient
hf ilm and the local condensate film thickness 56 can be obtained from the following
expressions;
hfm
ki
142
Nufim
(6.3)
(6.4)
= (Nul/g
The condensate film Reynolds number at location I of the condensing tube length
in equation (6.1) is given by:
Refilm
4h,
Re
1
(6.5)
ir (d - 261) I
(6.5)
and in situations where (26/d) < 1, which is the case in the present analysis, Rel
can be written as:
eilm _ 4l
2b
rdpl
d
In equations (6.1)-(6.6) Pr is the condensate film Prandtle number, kl is the condensate film thermal conductivity, #l is the condensate film dynamic viscosity, and vl is
the condensate film kinematic viscosity. The condensate film properties are evaluated
at a reference temperature T, = T, + 0.33 (Ti - Tm). Ti is the interface temperature
and To is the condensing tube inner wall tempearture.
The local condensate film flow rate nc¢can be calculated from the experimental
measurement as described in Appendix A. An initial guess for the interface temperature
is assumed and equations (6.6), (6.1), (6.2), and (6.3) can be used in this order to
obtain the local condensate film heat transfer coefficient hfilm. Once hf il m is known,
the interface temperature Ti is calculated from:
I,
Ti = Tw + hq-
--
(6.7)
where q" is the local heat flux obtained from the experimental measurements. The
new interface temperature is then used together with the system of equations (6.6),
(6.1), (6.2), and (6.3) to improve this initial guess. This is repeated till a consistent
solution is reached.
6.2.2
Steam-Noncondensables Boundary Layer:
The steady state diffusion equation in the radial direction y of each component in the
mixture can be written as;
m, =
+ Wpmt
143
(6.8)
.,
m--
P+
mh = -Dha
and
WaMt,X
OWh
,
+ Whme,
m t = m + ma + ma
II
. II
, II
(6.9)
(6.10)
(6.11)
II
where m m,a , mh, and 7m are the steam diffusive mass flux, air diffusive mass flux,
helium diffusive mass flux, and total diffusive mass flux respectively. Wv, Wa, and Wh
are the steam mass fraction, air mass fraction and helium mass fraction respectively.p
is the mixture density. Dv, Da, and Dh are the effectivemass diffusivities for steam,
air and helium respectively.
In the problem at hand, while the steam condenses at the inner wall of the condensing tube, the air and helium do not. In other words, the condensate interface is
impermiable to both air and helium. Therefore, the net diffusiveair and helium fluxes
should be zeros. This is expressed mathematically as;
II
II
II
ma = m" = 0
II
(6.12)
+ WmV,
(6.13)
m = m = Const.
and equations (6.8)-(6.10) are reduced to;
m =-pD
0 = -pD
0 = -pD
+ Wa'i/n
Wh + Whm
(6.14)
(6.15)
Therefore, the transport phenomenon within the gaseous boundary layer can then
be viewed as unimolal unidirectional diffusion, only one molecular species -that of
vapor- diffuses through helium and air which are motionless in the radial direction
relative to stationary coordinates. D, in the above equations is equal to Dv[46]which
is given by:
(De(+
D=h)
(6.16)
where Yv refers to the mole fraction compositions on a vapor-free basis. D,,, and
144
Dvh, are the binary diffusion coefficientsbetween vapor and air, and vapor and helium
respectively and are obtained from the followingequation [34];
D12
6.6 x 10- 4 T' 8 s3
()
3
+
(T
(6.17)
6.17)
where 1 refers to one component in the binary mixture, while 2 refers to the other
component. T (K) refers to the critical temperature and Pc (kPa) refers to its
corresponding critical pressure.
Steam/noncondensables boundary layer thermal equilibrium condition
The basic assumption in the present analysis of the steam/noncondensables boundary layer is that the components of the steam/air/helium mixture are in thermal equilibrium with one another. Another assumption is that the steam within the mixture
is, and remains, saturated over the entire length of the condensing tube. The mixture temperature at any location within the steam/noncondensables boundary layer is
therefore equal to the saturation temperature corresponding to the vapor pressure at
this location, i.e.,
Ta= Th = T = T
T = Tat (P)
(6.18)
Alternatively;
p. = psat(T)
(6.19)
The third assumption is that each of the gases in the mixture obeys the perfect gas
law and consequently Gibbs-Dalton perfect gases mixture equation, i.e.,
W, = M PV
(6.20)
where M, is the vapor molecular weight, Pt is the system total pressure, and M is
the mixture molecular weight given by:
1 =1 W, + W,
Wa+ W
W
From
theconservation
of mass;Mh
From the conservation of mass;
145
(6.21)
w, + w, + Wh = 1
(6.22)
Also, over the entire length of the condenser, the air flow rate and the helium flow
rate remains the same and are equal to their values at the condenser inlet. This leads
to their ratio at any location be the same and given by;
Wh
_
= Const.
(6.23)
where Wi' and Whn are the inlet air mass fraction and the inlet helium mass
fraction respectively.
Steam mass flux m' at the interface
With the assumption that the mixture density p and the effectivemass diffusivityD
are not function of the radial position r (they will be evaluted at a reference temperature
and a reference composition as shown in Appendix C), equations (6.14) and (6.15) can
be added, rearranged and then intergrated as follows;
(1- W,)
,
pD
1- W
Jo
dy
)
(6.24)
(6.25)
By definition;
Wnci = 1 - W,,i
(6.26)
Wnc,b = 1 - Wv,b
(6.27)
Wnc,i - Wnc, = Wv,b - Wv,i
(6.28)
and therfore;
Using equations (6.26), (6.27), and (6.28), equation (6.25) can be written as;
.,
pD W,b - Wv, l (W
Wnc,i
-
Wnc,b
146
(6.29)
,
(6.29)
Now define W.m such that;
Wc
(6.30)
Wni
,b
In Wm,1 ~,\
is the logarithmic mean difference between the noncondensable gas concentrations
in the bulk and at the interface. Equation (6.29) can then be rewritten as;
-r
MV
pD
Wzm (W,b
,)-
(6.31)
The noncondensable gases do not diffuse. However, their concentration gradients
are established by friction with vapor molecules as they move towards the condensate/gaseous boundary layer interface. This intermolecular friction is the source of
the noncondensables inhibiting effect on the condensation process. This inhibiting effect can be well represented by the average noncondensables concentration Wn
which
appears in equation (6.31).
Effect of axial flow; effective mixture boundary layer thickness 6ff
So far, the effect of axial flow has not been considered in the above analysis. The
distance y from the interface is the parameter which carries this effect and is going to
be replaced by the symbol 6eff from now on. This effective thickness is very similar
in concept to the boundary layer thickness. The higher the axial flow, the thinner
this effective thickness is, and consequently the mass transfer mha. This is also what
has been observed in practice; the higher the mixture Reynolds number, the higher
the condensation rate. As the mixture flows down in the condensing tube, vapor
is continuously sucked toward the wall. In the absence of this suction, the mixture
boundary layer would develop as the mixture flows down till it becomes fully developed
at a certain axial location depending on the mixture Reynolds number at the entrance.
However, within the condensation region, the mixture boundary layer will not have
the chance to fully develop and the mixture boundary layer thickness is expected to be
much thinner than that without condensation. Therefore, we will assume relationships
between the mixture boundary layer eff and the mixture Reynolds number Remi,
which are similar to those without condensation, but they do not explicitly carry the
axial dependence, i.e.,
147
d
Rfef=C m
Rel. Scmi
(6.32)
where C, n, and m are constants to be determined. In the present analysis we use
,for laminar flows, C = 5, n = , and m = 3, whilefor turbulent flows, C = 0.17,
n = -, and m = 0, with the dependence on mixture Schmidt number dropped.
Local interfacial heat flux qmizi and the mixture Nusselt number Numiz
Within the condensation length, the local heat fluxes are practically due to the
latent heat given up by the steam at the wall. The sensible heat from the mixture
due to the temperature differential in the radial direction can be practically neglected.
Therefore, the local heat flux q.izican be simply obtained by multiplying both sides
of equation (6.31) by hfg with y replaced by &ff , i.e.
qmiz,i= mvhf- =
W.T (W,b - Wv,i )
(6.33)
Define the mixture heat transfer coefficienthmi and the mixture Nusselt number
Numi, as;
I.
hmi = qi,.
(6.34)
(6.34)
Tb - Ti
NUmi = hmi x d
(6.35)
K
where K is the mixture thermal conductivity. The mixture Nusselt number is therefore;
Prmz
d
1m
Numix = Jami$Scmi, dJf W
(W.,b - W.,i)
(6.36)
Substituting for 6ff from equation (6.32) into equation (6.36) a final expression
for the mixture Nusselt number Numiz is obtained. It is given by;
Prmi Re Scm-l
Numiz = Jmi z
C
"' (Wv,, - Wvi)
(6.37)
where Prmi, Jami,, and Scmi, are mixture Prandtle, Jackob, and Schmidt numbers respectively. They are defined by;
148
Prmi , =
(6.38)
Jami = Cp (Tb - Ti )
(6.39)
Scmiz = pD
(6.40)
hfg
An explicit expression for the mixture heat transfer coefficient can be obtained from
the definition;
hmiz =-x
Nu.mi
(6.41)
d
with the expression for Nmiz, in the above equation is obtained from equation (635). All mixture properties in the above equations are evaluated using the procedure
outlined in Appendix D, and hfg is evaluated at the interface temperature Ti.
6.3 Results and Discussion:
Figures (6-1) and (6-2) show the measured bulk, measured wall, and the calculated
interface temperature profiles for two experimental runs. The first run, shown in
figure (6-1) is for condensation of steam in the presence of helium only, while the
second run, shown in figure (6-2) is for condensation of steam in the presence of both
helium and air. The mixture Reynolds numbers in both runs are relatively low and
cover the range from about 1,000 to 4,000. The flow is believed to be laminar for
mixture Reynolds numbers less than 2300 and turbulent for mixture Reynolds number
greater than 2300. The mixture Reynolds number profiles are also shown in the two
figures. The interface temperatures are calculated following the procedure outlined
in section 6.2.1. In both cases, the calculated interface temperature profile is very
close to the wall temperature profile and eventually converges into it near the end
of the condensing tube as the mixture Reynolds numbers get well into the laminar
flow region. This shows that, at these relatively low mixture Reynolds numbers the
thermal resistance due to the condensate film is a small fraction of the total thermal
resistance and almost negligibleas the mixture flowbecomes laminar. In other words,
at relatively low mixture Reynolds numbers, the main thermal resistance comes from
the steam/noncondensable gases mixture and in practice the interface temperature may
be assumed to be equal to the wall tepmperature without introducing any significant
error.
149
Figures (6-3) and (6-4) show the measured bulk, measured wall, and the calculated
interface temperature profiles for two other experimental runs. The first run, shown
in figure (6-3) is for condensation of seam in the presence of helium only, while the
second run , shown in figure (6-4) is for condensation of steam in the presence of
both helium and air. The mixture Reynolds numbers in both runs are high and cover
the range from about 5,500 to 20,000. The mixture flow is definitely turbulent.
The
mixture Reynolds number profiles are also shown in the two figures. In both cases,
the calculated interface temperature profile starts almost halfway in between the bulk
temperature profile and the wall temperature profile. As the mixture flows down, the
interface temperature profile parrallels the wall temperature profile while it diverges
from the bulk temperature profile. This behaviour is due to two reasons. First, as
the mixture flowsdown the condensing tube, the mixture becomes less turbulent, and
second it gets richer in noncondensable gas content. Both mechanisms contribute to
the mixture thermal resistance increase. This shows that, in forced convection flows,
at high mixture Reynolds numbers the thermal resistance due to the condensate film
is comparable to the mixture thermal resistance at relatively low noncondensable mass
fraction and it gets smaller as the noncondensable mass fraction increases. In general,
at high mixture Reynolds numbers, the thermal resistance due to the condensate film is
important, and the assumption of equal interface temperature and wall tepmperature
would introduce significant error.
Now, let us turn to the comparison between the mixture heat transfer coefficientsas
obtained from experimental measurement and those obtained from the model presented
in section 6.2.2, namely equations (6-35) and (6-39).
coefficient and Nusselt number are obtained from:
The measured heat transfer
It
qe,
hmi,ep
T- - T
NUmiz,ezp = hmix,empX d
(6.42)
(6.43)
where Ti is the interface temperature calculated using the procedure outlined in
section 6.2.1 and q'
is the measured wall heat flux at the inner wall of the condensing
tube and is obtained using the gradient of the coolant temperature profile as explained
in Appendix A. This measured value of q,p is practically equal to the heat flux at the
interface since the condensate film thickness 6 is much less than the condensing tube
inner diameter d so that dl (d - 26)
1.
150
Figures (6-5)- (6-16) show the measured and the calculated mixture heat transfer
coefficient profiles for different experimental runs. The experimental runs include ex-
periments on steam condensation in the presence of helium and in the presence of both
air and helium. The selected runs span a wide range of all parameters affecting steam
condensation in the presence of noncondensables, namely; mixture Reynolds number,
mixture Jackob number, mixture Schmidt number, mixture Prandtle number, and noncondensable gasses' mass fraction. The mixture Reynolds number and the condensate
film heat transfer coefficient profiles are also shown in these figures. In general, the
mixture heat transfer coefficients obtained using the model are in good agreement with
the measured mixture heat transfer coefficients.
Figure (6-17) shows a comparison between the model-predicted steam/noncondensables
mixture Nusselt numbers as calculated from equation (6-37) and the experimentally
obtained Nusselt numbers. Again, the figure shows good agreement between the model
and the experiment with the values of n, m, and C in equation (6.32) are taken equal
to 0.2, 0.0, and 0.185, respectively for turbulent flows, while for laminar flows the n,
m, and C values taken equal to 0.5, 1/3, and 5, respectively. Figure (6-17) shows that
below Nusselt number of 100 ( corresponding mainly to laminar flows) the scattering is
high between the model-predicted values and the experimentally obtained ones. Figure
(6-18) shows good agreement between the model and the experiment for turbulent flows
only. However, Figure (6-18) suggests that a better agreement can still be reached. In
fact with proper choice of C and n in equation (6-32), a better agreement is obtained
as shown in Figure (6-19). For that agreement the values of n, m, and C in equation
(6.32) were taken equal to 0.29, 0.0, and 0.46, respectively for turbulent flows
6.4
Conclusions:
The main conclusions of this chapter regarding in-tube forced convection steam condensation in the presence of noncondensables are the following:
1. For mixture Reynolds numbers of about 5000 or less and for noncondensable mass
fractions in the mixture of about 0.20 or higher, the condensate film thermal
resistance can be neglected and the interface temperature can be assumed equal
to the wall temperature without introducing any significant error.
2. For mixture Reynolds numbers greater than 5000, the condensate film thermal
resistance cannot be neglected and the assumption that the interface temperature
is equal to the wall temperature is not a good one.
151
3. Within the condensinglength of the condensing tube, the mixture flow does not
fully develop due to the continous suction of steam from the mixture boundary
layer.
4. With proper correlations for the effective mixture boundary layer thichness 6 eff,
equation (6.37) is capable of predicting the condensation process with noncon-
densables. The importance of this equation lies in the fact that it captures most
of the physics of the problem at hand.
152
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171
Chapter 7
Conclusions and Recommendations
7.1
Conclusions:
Condensation in steam/helium systems and steam/air/helium systems has been experimentally investigated over a wide range of system parameters. A simple diffusion
boubary layer based model has been introduced as well. For better assessment and
control of data quality, theoretical and experimental investigations on the coolant side
of the condensation test facility have been conducted. The results obtained from this
study can be used in chemical and power generation industry where the presence of
noncondensables is considered an important factor in the design of the condensing
equipments.
7.1.1
Experimental findings regarding steam condensation in the presence of noncondensable gases
Within the range of the experimental data, the followingare the main conclusions
regarding steam/noncondensable (steam/helium and steam/air/helium) forced convection condensation in a vertical tube:
1. Steam/noncondensable gases condensation heat transfer coefficientsare mainly
dependent on the following parameters:
(a) steam/noncondensable gases mixture Reynolds number
(b) the mass (mole) fraction of any noncondensable component in the steamnoncondensable gases mixture, or steam/noncondensable gases mixture Schmidt
number
172
(c) steam/noncondensable gases mixture Jakob number (subcooling)
2. Steam/noncondensable
gases condensation heat transfer coefficients increase with
the steam mixture Reynolds number, keeping the other parameters constant.
3. Steam/noncondensable gases mixture condensation heat transfer coefficients decrease as the mass (mole) fraction of any noncondensable component in the mix-
ture increases keeping the mixture keeping the other parameter constant.
4. Steam/noncondensable gases mixture condensation heat transfer coefficients decrease as steam/noncondensable gases mixture Schmidt number increases keeping
the other parameters constant.
5. Steam/noncondensable
gases mixture condensation heat transfer coefficients de-
crease as mixture Jakob number increases keeping the other parameters constant.
6. The experimentally obtained local condensation heat transfer coefficientswere
correlated in terms of the above parameters. The developed correlation predict
the experimental data very well and can be used in order to predict the local
condensation heat transfer coefficientsinside vertical tubes for the range of conditions utilized in the experiments reported in this study. A performance model
is outlined in Appendix D for using these correlations in practical applications.
7. Correlations including the mixture Schmidt number did better in representing
the condensation process in the presence of noncondensable gases.
Second, regarding condensate film thermal resistance:
8. In general, the condensate film thermal resistance is significant in forced convection in-tube condensation in the presence of noncondensable gases and it should
be included in modeling the steam condensation in the presence of noncondensable gases.
9. At the same bulk temperature, the ratio of the condensate film thermal resistance
to the total thermal resistance is mainly dependent on the followingparameters:
(a) steam/helium mixture Reynolds number
(b) the noncondensable mass (mole) fractions of noncondensable gases present
in the mixture, or the steam/noncondensable gases mixture Schmidt number.
173
10. At the same bulk temperature, the ratio of the condensate film thermal resistance to the total thermal resistance increases as the mixture Reynolds number
increases for fixed mass (mole) fractions in the mixture or fixed mixture Schmidt
number.
11. At the same bulk temperature, the ratio of the condensate film thermal resistance to the total thermal resistance decreases as the mass (mole) fraction of the
noncondensable gases in the mixture increases for the same mixture Reynolds
number.
Third, regarding comparison with existing correlation:
12. Siddique-Golay-Kazimi's steam/helium correlation prediction of the condensation heat transfer coefficientswas found to be in good agreement with the steam/helium
experimental condensation heat transfer coefficientsreported here.
7.1.2
Conclusions regarding modeling in-tube steam condensation in
the presense of noncondensables:
The main conclusions of regarding modeling in-tube forced convection steam conden-
sation in the presence of noncondensables are the following:
1. For mixture Reynolds numbers of about 5000 or less and for noncondensable mass
fractions in the mixture of about 0.20 or higher, the condensate film thermal
resistance can be neglected and the interface temperature can be assumed equal
to the wall temperature without introducing any significant error.
2. For mixture Reynolds numbers greater than 5000, the condensate film thermal
resistance cannot be neglected and the assumption that the interface temperature
is equal to the wall temperature is not a good one.
3. Within the condensing length of the condensingtube, the mixture flow does not
fully develop due to the continous suction of steam from the mixture boundary
layer.
4. With proper correlations for the effectivemixture boundary layer thichness ,eff,
equation (6.37) is capable of predicting the condensation process with noncon-
densables. The importance of this equation lies in the fact that it captures most
of the physics of the problem at hand.
174
7.1.3
Effects of Cooling Water Conditions:
Within the range of the data taken, the followingare the conclusionsregarding the
effects of cooling water conditions on in-tube forced convection steam condensation in
the presence of air:
1. If the cooling water flow rate is kept so low that the coolant flow is laminar, local
values of condensation heat transfer coefficientsare overpredicted near the upper
part of the condensing tube.
2. If the cooling water flow rate is increased so that the flow is turbulent, the uncer-
tainties associated with the local values of condensation heat transfer coefficients
might become high except at high power levels (high inlet steam flow rates) where
the coolant temperature change per unit length of the condensingtube is large.
3. In situation where the coolant flow is laminar, bubbling air into the coolingwater
can provide the desired amount of mixing. However, pre-analysis must be made
to determine the amount of air to be introduced with the cooling water. The
adequate amount of air would depend upon the cooling water flow rate and the
power level (inlet steam flow rate).
4. Siddique [5] did not seem to have injected the amount of air which is sufficient
for good mixing. There fore, the local heat transfer coefficients near the top of
the condenser so obtained by him were overpredicted.
5. injecting air with the cooling water in the annulus seems to be effective in re-
moving the "Temperature Inversion".
6. the "Temperature Inversion" seems to be a coolant side phenomenon. The cause
is unclear with the possible explanation ranging from a geometrical artifact to
thermally-induced secondary flow within the annulus.
7.1.4
The Visualization Experiment Findings:
Within the range of the data taking from the visualization experiment, the following
are the concluding remarks:
1. Efficientradial mixing over the entire length of the annulus were attained within
a volumetric air flow ratio range between 20-30% (corresponding to air void
fraction range from 4-5%) .
2. No secondary flows were observed within the unheated water during the course
of this investigation.
175
7.1.5
Buoyancy Effects in the Coolant Side Analysis:
Within the range of the experimental data taken, the followingare the basic conclusions
regarding the effects of buoyancy on an upward flow of water in a vertical annulus with
a heated inner tube and insulated outer tube:
1. Buoyancy has an effect on the flow at least over the upper half of the condenser
and this effect increases as the heat flux increases and decreases as the cooling
water flow rate increases.
2. Buoyancy-driven cellular flows and/or buoyancy induced early transition to turbulence occurs near the middle of the channel upward. They are suspected to be
the reason for the "Temperature Inversion".
3. The effect of condenser tube wall temperature should be included in correlations
predicting the heat transfer coefficients in order to accommodate the coolant
conditions. Such effect can be well represented by employing Jakob number in
correlating the experimental data.
7.2
Recommendations for Future Work:
1. The new test facility described in details in Appendix E is an improvement in
many aspects over the existing facility particularly noteworthy are the localization of the measurements near the top of the test section and the redundancy in
heat flux measurements. It should be used for further work which may include
the following:
(a) Studying the stability of steam/noncondensable systems natural circulations
in closed loops.
(b) Augmentation of steam/noncondensable systems heat transfer by using static
mixers.
2. The model presented here can be improved and extended to include flows under
natural circulations by solving rigorously for the mixture boundary layer effective
thickness.
3. The model can be tested using University of California, Berkeley (UCB) experi-
mental data and others if available.
4. The application of the condensation heat transfer coefficientsin two-fluidmixture
currently used by the nuclear industry will require a different model formulation.
176
References
1. Jensen, K.M., "Condensation with Noncondensables and in Multicomponent
Mixtures," Kadac, et al, Two Phase Flow Heat Exchangers, pp. 293-324,1988.
2. Vierow, M.K., "Behavior of Steam-Air Systems Condensing in Concurrent Vertical Down Flow," MS Thesis, Nuclear Engineering, UCB, 1990.
3. Dehbi, A. A., Golay, M. W., Kazimi, M. S., "The Effects of Noncondensable
Gases on Steam Condensation under Turbulent Natural Conditions," Report
No. MIT-ANP-TR-004, 1991.
4. Ogg, G.D., "Vertical down Flow Condensation Heat Transfer in Gas-Steam Mixtures," MS Thesis, Nuclear Engineering, UCB, 1991.
5. Siddique, M., Golay, M. W., Kazimi, M. S., "The Effect of Noncondensable
Gases on Steam Condensation under Forced Convection conditions," Report No.
MIT-TR-010, 1992.
6. Kellessidis, V.C., and Dukler, A. E., "Modeling Flow Pattern Transitions for
Upward Gas-Liquid Flow in Vertical Concentric and Eccentric Annuli," Int. J.
Multiphase Flow, Vol. 15, No 2, pp. 173-191, 1989.
7. Taitel, Y., Barnea, D., and Duler, A. E., "Modeling Flow Pattern Transitions
for Steady Upward Gas-Liquid Flow in Vertical Tubes," AIChE J. 26:345, 1980.
8. Griffith, P., and Synder, G. A., "The Bubble-Slug Transition in a High Velocity
Two Phase Flow," MIT Report 5003-29 (TID-20947), 1964.
9. Knudsen, J. G., and Katz, D. L., "Fluid Mechanics and Heat Transfer," University of Michigan, Engineering Research Institute, Bulletin No 37, 1954.
10. Streeter, V. L., Handbookof Fluid Dynamics, First Edition, McGraw-Hill Book
Company, Inc. 10-36, 1961.
177
11. Hall, W. B., and Jackson, J. D., "Laminarization of a Turbulent Pipe Flow by
Buoyancy Forces," ASME, 69-HT-55, 1969.
12. Wallis, G. B., "One-dimensional Two-Phase Flow," McGraw-Hill New York,
1969.
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the institution of Mechanical Engineers,
1 5 th
September, 1971.
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Int. J. Heat Mass Transfer, Vol. 12, pp. 223-237, 1969.
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181
999-1018,
Appendix A
Data Reduction Procedure
A.1
Steam/Noncondensables
Mixture Side
1. Fit the coolant bulk temperature Te and then obtain the gradient dT(L) where
L is the axial position starting from the top height of the condensing tube.
2. Calculate the local heat flux at the inner wall of the condensing tube from the
following equation:
q'(L)=
MC dT.(L)
'Dti
dL
(A.1)
where:
nc¢
= cooling water flow rate,
CP
Dti
= water specificheat capacity,
= condensing tube inner diameter.
3. Calculate the local condensation heat transfer coefficient from the following equa-
tion:
h(L) = T
(L)
(A.2)
where:
Tat
Tz;-
= the saturation temperature corresponding to the vapor pressure at position L,
= condensing tube inner wall temperature at postion L.
182
4. Determine the local condensate film flow rate from the followingequation:
on(L) = 7rDtifoj q(L)dL
hf (L)
(A.3)
where h7 is the modified latent heat given by:
hpfg(L)= hfg(L) + 3 Cp(L)[Tot(L) - Ti(L)]
(A.4)
where hfg is evaluated at the saturation temperature Tsat and Cpl is the condensate film specific heat capacity evaluated at T, which is given by:
T,(L) = Tti(L) + 0.33[Tat(L)- Ti(L)]
(A.5)
5. Calculate the local condensate film Reynolds number from the followingequation:
Ref
~4V~on(L)
(L)
-(A.6)
7rDtipl(L)
where Al is the condensate film dyamic viscosity evaluated at T,.
6. The local condensation heat transfer coefficientsof the condensate film, according
to Nusselt theory can be calculated from [47]:
Nu
(L)
j(diJ)
y (L)
Nufilm(L)
= h ,Ki(L)
3
= (3Refilm(L))*
(A.7)
where:
NuNilm
hfilm
VJI
KCI
= condensate film Nusselt number based on Nusselt theory,
= condensate film heat transfer coefficientbased on Nusselt theory,
= condensate film kinematic viscosity evaluated at T,,
= condensation film thermal conductivity evaluated at T,.
7. Calculate the local experimental heat transfer coefficientsh to condensate film
heat transfer coefficienthNim ratio:
ENhR=
183
h(L)
him(L)
(A.8)
8. Calculate the local steam mass flow rate from:
m.tcam(L) = miatLa (L)where
7.c.on(L)
(A.9)
isnlcetis the inlet steam mass flow rate.
9. Calculate the local steam/noncondensables mixture flow rate from:
n
mmi,(L)= rhJteam(L)
+ Z nc
i
(A.10)
where 7hin is the ith component of noncondensable gas in the mixture from:
Wini(L)
nL)
(A.11)
and the local bulk steam mass fraction in the mixture can be determined from:
n
Wteam(L)
mE =
Wi(L)
(A.12)
i
10. Calculate the local bulk miole fraction of the i th component of noncondensable
gas in the mixture from:
ne
Yi (L) =
(A.13)
e
Mni,(L
where Mmi,(L) is the local steam/noncondensables
is given by:
1
_ Wsteam(L) +
Mmi(L)
Mtem
Msteam
mixture molecular weight and
Win(L)
Mi
(A.14)
where Mteam is the steam molecular weight and MC is the ith noncondensable
gas molecular weight. The local steam mole fraction can be determined from:
Yteam(L) = 1-
Yn(L)
(A.15)
11. Calculate the local steam/noncondensables mixture Reynolds number from:
Remi(L) =-4
,
7rDtiismi(
184
(A.16)
where ,mi= is the steam/noncondensables
mixture dynamic viscosity and is de-
termined from [48]:
/m4iz
=
E
i.
Ad
(A.17)
where ~tij and 4ji are calculated from:
tjii =
(A.18)
and,
ii = HLiM bij
(A.19)
The steam, air and helium dynamic viscosities are evaluated according to [49].
12. Calculate local steam/noncondensables mixture experimental Nusselt number
form the followingequation:
Numi_= h(z)Dti
(A.20)
nKmiz
where rcmi=is the steam/noncondensables mixture thermal conductivity and is
determined from [48]:
r-mi =
Ei;
i=1
(A.21)
1=Y
where qij and bji are calculated from:
=bij
[=
[8 (1+ Mi)]
(A.22)
and,
=
~ji
Mi ij
Ic;Mj
(A.23)
The steam, air and helium thermal conductivities are evaluated according to [49].
13. Calculate the steam/noncondensables mixture Schmidt number from:
SCmiz =
185
mi
PmizDv
(A.24)
where pi,
is the mixture density and is given by:
n
Pmi. = A pi
(A.25)
i=l
and Pi is evaluated according to [49].
D, is the multicomponent mass diffusion coefficient and can be given as [46]:
y-free
n
=
where rY-f'*e
i-1
'
ri
Dti
(A.26)
is the molar fraction of the it h noncondensable gas on a vapor-
free basis and D,i is the binary vapor ith gas mass diffusion coefficient and is
determined according to [34].
A.2
The Coolant Side
1. Fit the cooling water bulk temperature T¢ and get teh local gradient
z is the axial position starting at teh inlet of the annulus.
d-
where
2. Calculate the local heat flux at the inner wall of the annulus (i.e. at the outer
wall of the condensing tube) as follows:
q'(z) =
C,:dT,(Z)
rDa dz
(A.27)
where:
C,
Dj
= the cooling water specific heat capacity,
= the annulus inner diameter.
3. Calculate the annulus inner wall temperatures (i.e. the condensing tube outer
wall temperatures) as follows:
T.i(z) = Two(Z) = Ti(Z)where,
186
oq(z) n
Dt
(A.28)
Dto
=
=
=
=
It
Ti
Tai
condensing tube outer diameter (i.e. annulus inner diameter, Dai),
condensing tube thermal conductivity,
condensing tube inner wall temperature,
annulus inner wall temperature.
4. Calculate local Grashoff's number based on the temperature difference and the
annulus hydraulic diameter from:
Gr(z)
g()(z)Dh
(A.29)
where,
g
= acceleration of gravity,
AT
= Tai - T,
l3
= cooling water volumetric thermal expansion coefficient,
Dh
= annulus hydraulic diameter and is equal to D,, - Di,
'Ce
= cooling water kinematic viscosity.
5. Calculate the local Grashoff's number based on annulus inner wall heat flux and
hydraulic radius from teh followingequation:
Grq(z)= gt(z)q(z)
(A.30)
where,
Rh
, =
Dh/2,
cooling water thermal conductivity.
6. Calculate local cooling water Reynolds number from:
Re(z) = pVDh =
P,,
4rhm
rz ¢e(D +
ReR(Z) = Re(z)
2
187
V,,)
(A.31)
(A.32)
Appendix B
Uncertainty Analysis
B.1
Experimental Heat Transfer Coefficient Error Analysis
The overall maximum unceratinty uf of function f resulting from the individual uncertainties xi, ...x, can be written as [50]:
U
=
zl + Uzz
+f U|-.
+-.....+
6
(B.1)
(B.
Since it is unlikely that the maximum value will be attained, a value corresponding
to the Pythagorean summation of the discrete uncertainties would be more reasonable
estimate of the uncertainty, i.e.,
f
\|(
)
+ (2
)
+
+ (on
)
The local condensation heat transfer coefficientis given by the relationship:
h(L) = -D
C(T
-
d(L
(B.3)
where Cp, Dti will be treated as error free variables. Differentiating equation (B2) with
respect to me, (Tat - T,), and
dT(L)
6h =_
6m,
respectively, one can get:
C
dT.(L)
7rDti(T.t -T.)
dL
188
'
6h
6(Tat - T)
_
mcCp
7rDti(T.t-T)
6h
2
dTc(L)
dL
(
_,mC,
6 (dL)
(B.6)
7rDt(T.-T)
(B.6).)
Rewriting equations (B1) and (B2) in terms of h, me, (Toat - Tw), and -(dL) one
can get:
Uh mia =
a
|un
|
+
U(TJ
T (Tat-T.)
6
dL
dTc(L)
and,
Uh=
6h
6f
2
f
c6-(
m ) + u(T.T-.)
)(T..t-
2
T.)
2+
dTc(L)
dL
6f
f
d
)
.
(B.8)
Substituting Equations (B4), (B5), and (B6) in equations (B?) and (B8), then
dividing both sides by the right hand side of equations (B3) one can get:
JUm,,,
Uhmea
= |mUc|
+ |(T,,U
(That-Tae)
+ |d-+
Ua,ma,~
_
2|(B.9)
h
(°t- T-
mc
.)
dL
and,
Uh
B.1.1
(T1 t-T.)
(TJ- T)
c/T
Coolant Flow Rate Experimental
+
/ UdT
d2
7
\ dL)
(B.10)
Error
The absolute error obtained in measuring the cooling water flow rate was +0.01 of the
full scale reading of the flow meter.
The minimum flow rate used in steam/helium
and steam/helium/air experiments was 5 kg/min. Therefore, the maximum error in
measuring the cooling water flow rate was,
u
mc
=-0.011.
189
(B.11)
B.1.2 Wall Subcooling Experimental Error
The maximum observed standard deviation of th ethermocouples was 0.30 C. The minimum wall subcooling was 6.9 °C. Therefore, the maximum error associated with wall
subcooling is:
UTot = UT,, = UTc =
0.30 C
(B.12)
U(Tt-T.) =
+
(B.13)
= 0.061
U(T.t-T)
(B.14)
(Tat - T)
B.1.3
Coolant Temperature Gradient Experimental Error:
The local gradients of the coolant axial temperatures
dTe
was determined from a least
squares, third degree polynomial fit of the coolant temperature as a function of con-
densing tube length with an adjusted R2 -value for the fit of the data to the polynomial
of about 0.98. Therefore, the error due to curve fitting of the coolant axial temper-
ature profiles was negligible. However, the uncertainty associated with the coolant
temperature gradients can be written as:
UdT =
(B.15)
UT + UT
dL
= =,ma
UdTc
UdL or17
steamdL
flow
ratewaslowAconservaivev
ddT[
dL oor, tenatey
aternaey err(B.16)
U dTr
2
=
__
dL
I,.3
(B.17)
The minimum temperature difference between two successive measuring stations
was 2.0 C. This occured near the end of the condensing tube in runs where the inlet
steam flow rate was low. A conservativevalue of the absolute error in measuring the
distance between two successive measuring stations of 12" was taken to be ±0.25"/
Therefore, the maximum error associated with cooling water temperature gradient is:
U dTm
dT,
=
±0.233
(B.18)
dL
or, from Equation (B.17) one obtains the result
-0.213.
dL
190
(B.19)
Though the errors associated with cooling water temperature gradients should be
much less than the above values as water flows up away from teh condensing tube lower
end, these values will be used in the overall evaluation of the error in the experimental
heat transfer coefficientsas they lead to a conservatinve overall error estimate.
B.1.4
Overall Experimental Error
Substituting values from equations (B.11), (B.14), (B.18), and (B.19) into Equation
(B.9) and (B.10) and simplifying we obtain:
Uh,maz = 0.305
(B.20)
-h = 0.222.
(B.21)
h
and,
h
Therefore the maximum uncertainty associated with the experimental condensation
heat transfer coefficientsin ±30.5%, while the uncertainty value corresponding to the
Pythagorean summation of teh discrete uncertainties is ±22.2.
B.2
Correlation Predicted Nusselt Numbers' Uncertainty
The standard deviation of the correlation predicted Nusselt numbers from the experimentally obtained Nusselt numbers was assessed as follows:
1
2
(B.22)
UNu =
Using the above equations the standard deviation of the correlation predicted Nusselt number
(UNu)
of new correlations in Chapters 5 were calculated.
B.3 Void Fraction Experimental Error:
Equation (3.2) can be rewritten as
a=
Apt,
ptPtpnh-
(P. - p.)gh
(B.23)
where h is the distance between the two fixtures connectingthe annulus to the differential pressure transducer, APt,an, is the pressure difference across the transducer, and
191
g, p,, and p are treated as error-free variables. The differential pressure transducer
gives its readings in terms of inches of water, i.e.:
APtrans = Pwgz
(B.24)
Therefore, equation (B.23) can be written as:
a=
Put
,
(B.25)
(P - pa)h'
Differentiating equation (B.25) with respect to z, and h, one obtains:
6a
Pw
_
Sz
(B.26)
(Pw - pa)h
ah
2
(Pw-ZP)h
6h
(pw - p)h2
(B.27)
Rewriting equations (B.1) nad (B.2) in terms of z, and h, one obtains:
and
U a|+
=
Ua,mtac
Uh
a=(iz +(uh)
(B.28)
(B.29)
Substituting (B.26) and (B.27) in (B.28) and (B.29), then dividing both sides by
the right hand side of (B.25) we get:
aUmax= Uz | + | Uh
Ua =
+
(B.30)
(B.31)
The uncertainty in measuring the distance h, uh was 0.25". The distance h was
99". The resolution of teh digital display connected to the transducer was very high,
the uncertainty being of 0.01". However,the reading of z used to fluctuate maximum
of ±10% of the recorded value. Therefore:
Un,mao= 0.103
a
u = 0.10
a
192
(B.32)
(B.33)
Appendix C
Reference Composition and
Reference Temperature
C.1
Introduction
In order to calculate the condensate mass flux mre given by equation (6-31), proper
evaluation of the steam/noncondensables mixture properties is necessary. Knowledge
of a reference temperature value is needed in order to evaluate the individual densities
of the mixture components and the binary mass diffusivitiesof each pair in the mixture.
Also, a reference composition is needed in order to calculate the mixture density and
diffusivity once the individual properties of each component in the mixture are known.
Knuth, E., L. [51,52] obtained an expression for the reference composition for binary
mixtures. In the present analysis, their approach is adopted and extended to ternary
mixtures. The reference temperature value will be then taken as that of the saturation
temerature corresponding to the vapor pressure at this reference composition.
C.2
Reference Composition, W*, W, and W:
The steady state diffusion equation in the radial direction y of each component in the
mixture are reproduced here from Chapter 6:
" = -pD OWv+ Wvm
0 = -pD 'da- + Wm
a ,
193
(C.1)
(C.2)
0 =-pD
+ WhM,.
(C.3)
Equation (C2) can be intergrated over the gaseous boundary layer to take the form:
r
(d - 26) =
j
pD dW
(C.4)
Wa
Wa,b
where d is the condensing tube inner diameter, and 6 is the condensate film thickness.
For a mixture of ideal gases in thermal equilibrium at temperature T and system
pressure P, the mixture density is written as:
P
p= -M,
RT
(C.5)
where R is the universal gas constant and M is the mixture molecular wieght.
Now, if the mixture temperature is fixedin the above equation, the mixture density
will be a function of the composition only and therefore equation (C4) takes the form:
.(C.6)
RT Jwb M W,
mh"(d - 26) = PD
The mixture molecular weight in equation (C5) is given by:
1
w,
M
Mu
w,
Wh
Ma
Mh
1+ W W.
+. Wh.
(C.7)
The conservation of mass requires that
Wv + Wa + Wh = 1
(C.8)
and
Wh = W
= C1
(C.9)
where W 'n and Wan are the helium inlet mass fraction and air inlet mass fraction
respectively. C1 is an arbitrary constant.
With some algebraic manipulations, the mixture molecular weightM can be written
in terms of the air mass fraction only as
M,
M=1 + C2 Wa'
where C 2 is another constant given by:
194
(C.10)
C.,
I=
M _ 1+C1 Mv
1).
(C.l1)
Substituting for M from equation (10) into equation (9) and carrying out the
intergration, Equation (Cll) yields the result:
'" (d - 26)= PDMln
RT
M~
Wa,bMb'
(C.12)
where Mb and Mi are the mixture molecular weight at the bulk and the interface
between the condensate film and the gaseous boundary layer respectively.
Now, if M is chosen to be a constant equal to a reference mixture molecular weight
M*, equation (6) can then be intergrated to yield the result:
h. (d- 26)= PD
M*lnn W,b
RTM
(C.13)
(C.13)
By inspecting equations (12) and (13), an expression for the reference mixture
molecular weight in terms of the bulk and interface compositions can be written as:
= , 1 In
(W/W,b
(Mi/Mb)
]
(C.14)
Once the bulk and interfacial compositions Mb, Wa,b, Mi, and Wa,,i are known, a
reference molecular weight M* can be obtained from equation (14). Equations (C8Cll) can then be used to calculate Wa*,Wh*,and W*.
C.3
Reference Temperature, T*
Once the reference composition is known, the vapor pressure P* corresponding to it
can be calculated from:
P = W*-
P.
(C.15)
The reference temperature T* is equal to the saturation temperature T °at corresponding to this vapor pressure P,*, i.e.,
= T ' at (P*).
195
(C.16)
Appendix D
Performance Model
The following steps outline a procedure by which the correlations developed in Chapter
5 are to be used in practice in sizing a vertical condensing tube in which a mixture
of steam and noncondensable gases flows downward. In this model the temperature
profile of the condenser wall as well as the conditions at its inlet are assumed to be
known. The inlet conditions are the system total pressure, mixture bulk tempererature,
mass fractions of the noncondensable gases, steam flow rate, and the flowrates of the
noncondensable gases:
1. At one step ATb down the the condensertube length 1,the new bulk temperature
bT(k+)
is given by
T(k+) = T(k)-
ATb.
(D.1)
Assming the mixture components are in thermodynamic equilibrium with one
another, the vapor pressure p(k+l) corresponding to this new bulk temperature
is calculated from
p(k+l)= psat [Tb(+)].
(D.2)
Since the total system pressure P is almost constant along the condening tube,
W(k+l)) W(k+l) and W(k+l)) can be obtained by solving the system of equations
v,b
ab
h,b
(6.20)-(6.23) at T(k+l).
2. Since the noncondensabe gases mass flow rate is constant and equal to its value
at the inlet of the condensing tube, the local steam flow rate Tmte~a, and the
196
condensate flow rate d(k+l)
given by
between the node (k) and the node (k + 1) are
1
(ike+l)
=nete
-_(ksteam--inlet
-
uf(k+i)
(D.3)
rWck
nc,b
nc,b
and
dih(k+l) = 7n(k) -(g
l
sm
s=mteam
-- teml
(D.4)
Wnc = Wa + Wh
(D.5)
(D.4)
where:
3. Assume a value to the wall temperature T (,k+l ). The mixture properties can be
evaluted at the correspondingbulk temperature. Once the mixture properties are
known, the mixture Reynolds, Schmidt, and Jakob numbers can be calculated.
The local wall heat flux is then obtained from,
qw = h (Tb- To),
(D.6)
where h is the local condensation heat transfer coefficient and is obtained using
one of the correlations developed in Chapter 5.
4. Assuming linear profile of the wall heat flux along Al of the condensing tube
length, for steady state conditions the total heat transfer for the k - node Aq (k)
can be related to the local heat fluxes at the condenser wall qw(k)and qw(k+l)as
follows
Aq(k) = rd[
(q(k) + q',(k+l))] Al(k);
for
<
(D.7)
where Aq (k) is given by
Aq(k) = dhm(k+l)h( +
iZl)Cpmi
and the mixture mass flow rate Fn~+ l) is given by
197
ATb
(D.8)
nmi-ni
(k+1)=-- msteam
i(k+l)+
+ Miet
·
(D.9)
Step 4 yeilds a value for Al(k). The tube length l(k+l) at the end of the k - node
can be expressed as
l(k+l ) = E Al( k ).
(D.10)
k=1
5. From the givenwall temperature profile, the tube length l(k+l) is used to calculate
T(k+l). If this is deferent than the guessed value in step 3, a new value is assumed
and the steps from 3-5 are repeated till a consistent solution is reached.
6. A new bulk temperature step ATb down the condenser tube length is taken and
the calculations from step 1 to step 5 is repeated. The calculation is terminated
when the steam in the mixture is depleted or when the end of the condensing
tube is reached, i.e., when (k+l) > lo, where lo is the effective length of the
condensing tube.
198
Appendix E
Design of New Test Facility
E.1
Introduction:
Although the existing facility has been used efficientlyin providing good quality data,
it suffers many shortcomings.
For example, the condensing tube inner wall second
thermocouple from the top was not functional. The condensing tube outer wall five
thermocouples were also, for some reason, malfunctioning; three of them at the top
of the condensing tube and the other two were near the bottom. Replacing these
thermocouples was not possible because of the nature of the current design. This
situation and in the absence of back-up thermocouples, rendered the service of the
outer wall thermocouples useless. The outer wall thermocouples were supposed to be
used to provide an independent means of determining the local heat fluxes.
There has been also the question of the uniformity of the annulus gap and, con-
sequently the unanswered question of the uniformity of the heat flux around the circumference of a given axial cross section. Also, the coolant annulus of the existing test
section extends up about 2-3 inches past the first measurement station. This small
extension creates a region where the coolant behavior is uncertain.
Because of these questions and similar ones and the failure to answer them through
the current test section, a new design for the test section was necessary. The design
was made but the construction was stopped because of a funding problem.
Since the new design is definitely an improvement in several respects, a brief de-
scription of it is given in this chapter. A brief comparison between the current design
and the new design is listed in table E.1.
199
E.2 Description of Apparatus:
The new apparatus consists of an open once-through coolingwater circuit and an open
once-through steam/gas circuit. The main components of the steam/gas circuit are the
steam generator (SG), and the condensing tube which is the newelyfabricated peice of
the apparatus. Steam is generated in a 4.5 m high, 0.45 m inside diameter, cylindrical
stainless steel vessel, by boiling water using four immersion type sheathed electrical
heaters. The heaters can be individually controlled (on or off) and are nominally rated
at 7.0 kW each. A Variac is wired to one of the heaters for finer control of the power
level. Compressed air or helium or both are supplied to the base of the steam generator
via pressure regulators, calibrated rotameter, a gas proportioning rotormeter, and a
flow control valve. The steam generator serves also as a mixing chamber, where the
noncondensable gases attain thermal equilibrium with the steam as well as form a
homogeneousmixture with it.
Figure (E.1) shows the new test section as a whole. The steam/noncondensable
gas mixtures leave the steam generator from the top through an isolation valve fitted to the side of the SG, and through 2" inner diameter stainless steel pipe to a
cylindrical block. The pipe diameter is four times that of the existing facility. This
would make it much easier for the system to be used for studying natural circulation of
the steam/noncondensable gas system. The cylindrical block serves multiple purposes
as shown in Figure (E.2). It forms a connection to the test section entrance. The
centerline thermocouple assembly extends down the entire length of the condensing
tube through this cylindrical block. Static mixers can be inserted from the top of the
cylindrical block into the condensingtube if needed.
Downstream from the boiler the steam/noncondensable mixture flow rate is measured with an accurately calibrated vortex flowmeter. Before it enters the test section
and after it passes the cylindrical block, the mixture temperature and pressure are
measured. The test section consists of a single vertical 304 stainless steel tube inside
which condensation would occur. Unlike the current test section, this new one has a
thermal entrance of about 18" in length just before the first temperature measuring
station of the test section. The outside diameter of the condenser is 2.25", with a
wall thickness of 0.25". This thickness is almost three times that of the current condenser. The greater thickness would result in larger temperature differences across the
condenser wall which would, in turn result in smaller errors associated with heat flux
calculations.
A 316 S.S. concentric jacket tube surrounds the condenser tube, The jacket tube
is 3.5" OD and 0.438" thick. The steam/gas mixture flows down through the tube
200
while cooling water flows counter-currently up through the annular gap. The decision
to use Stainless Steel (SS) tube instead of SS pipe as used in the current test section
was made to ensure the uniformity of the annular gap since tubes have much better
commercial straightness than pipes.
In the forced convectionmode of operation, the condensate and uncondensed passing the test section will be separated in a collector drum and the respective parts vented
to the atmosphere. In the natural circulation mode of operation, the uncondensed
steam/noncondensable gas mixture will recirculate to the steam generator. Depending
on the mode of operation, a valve is used to shut off manually the other line from the
test section, either completing the natural circulation or venting to the atmosphere via
the collector drum.
The building main water supply is used to supply the test section via a calibrated
rotameter flow control valve. To ensure a uniform cooling water flow around the con-
denser, the water enters/exits the annular gap from four inlets/outlets equally spaced
around the annulus as shown in Figure (E.3). Detailed design of these inlet/outlets is
shown in Figure (E.13). This is an improvement over the current test section which
has only one inlet/outlet, which may cause nonuniform coolant flow and consequently
nonuniformheat flux at a given axial cross section. The cooling water exits the annular
gap through the four outlets and is then sent directly to the drain.
Another major improvement of the new design is the elimination of the uncertain
flow region near, but extending away from the annular gap outlets as shown in Figures
(E.18) and (E.19). This has been accomplished by designing the upper part (Figure
(E.4)) and the lower part (Figure (E.5)) so that such regions do not exist.
E.3
Description of the Thermocouple System:
Since determination of local heat fluxes and consequently local heat transfer coefficients
is implemented through temperature measurements, reliability of thermocouple system
becomes a major concern of the designer. Out of the time, money and efforts spent
on the new design, almost 90% were spent on designing, machining, soldering for
the placement of the thermocouples. Later calibrations of these thermocouples will
be a major task by itself before performing any shake-down experiments. Therefore,
detailed description of thermocouple machining and placements are given in this section
or shown in figures at the end of the chapter.
201
E.3.1 Thermocouple System Placement
The new design has more than twice the number of thermocouples than the existing
design. As shown in Figure (E.6), the temperatures of steam/gas centerlines, the cool-
ing water, and the condensing tube inner and outer surfaces are measured at nineteen
stations along the length of the condensing tube. The distance between each station
are 6". Because most of steam condensation takes place near the upper region of the
condensingtube and more detailed information is needed there, the measuring stations
for the top 12" of the tube are spaced 3" apart. This is as opposed to only nine mea-
suring stations in the current test section. These nine stations are spaced 12" apart.
Four inlet and four outlet thermocouples were also installed to ensure the uniformity
of coolant temperature
All temperature measurements are made by 1/32" OD 304 S.S. J-type (IronConstantan) thermocouples. Figure (E.7) shows the thermocouple assembly by which
the centerline bulk temperatures are measured. The assembly consists of a 3/16" OD
316 S.S. tube connected to a 1" NPT. In this tube, there are 17 thermocouples, spaced
6" from the bottom. This is in contrast to only nine stations, spaced 1" apart in the
existing test section. In order to reach the centerline in the current design, centerline
temperature thermocouples were inserted through both the jacket and the condensing
tube. This situation is avoided in the new design since the condensing tube will be
kept self-contained. All coolant thermocouple probe leads are taken out of the annular
gap through stainless steel lead sealing fixtures as shown in figures (E.16) and (E.17).
E.3.2
Surface Thermocouple's Machining
The inner wall 1/32" OD 304 S.S. thermocouples are to be inserted in holes (1/32"
+ tolerance) in diameter and 1.689" deep at and angle of 832 ' , leaving 0.01-0.015"
between the end of the hole and the inner wall of the condensingtube. The slanted slots
for the inner surface thermocouples were machined using Electric Discharge Machining
(EDM). These slots were first machined with a copper-tungsten electrode of identical
thickness of the thermocouple for initial machining, and then with a tungsten electrode
for deeper machining. The slots were then widened to have a clearance of 0.005-0.006"
between the slot wall and the thermocouple to meet the soldering (brazing) requirement
for good bonding.
The outer wall 1/32" OD 304 thermocouples are to be embedded in longitudinal
grooves 1.23" long, (1/32" + tolerance) wide and 1/32" deep, and brazed (or soldered).
These outer grooves were machined with EDM-L200 Poco electrode graphite cut and
ground to have a thickness and a curvature identical to the 1/32" OD 304 S.S. ther202
mocouples plus 0.005-0.006" clearance. Figures (E.8) to (E.12) show schematics of the
machining methods and surface thermocouple placement. However, the top station
was machined differently as shown in Figure (E.10) in order to get their leads out.
The inner slots were machined the same way as the rest except that the electrode
was directed so that it moves along the tangent to the inner circle of the top cross sec-
tion. Thermocouples will be inserted so that their tips be located on the circumference
of the inner circle of the top cross section within 0.01-0.015".
The outer slots were machined the same way as the rest of the outer slots except
that the electrode was shot circumferentially.
E.3.3
Surface Thermocouple's Soldering (Brazing):
The maximum operation temperature of the system is about 150°C ( 302°F). In
order to ensure strong attachment of thermocouples to the body of the condensing
tube, the flowing temperature of the bonding material should be higher than 300°C
(~ 600°F), which provide the assembly with a safety factor of 2. Because of this
requirement, soldering was ruled out since a 94%+lead alloy, the only known soldering
alloy with a high enough running temperature, does not wet well to stainless steel
surfaces. Therefore brazing was adopted.
Brazing is done for every thermocouple at a time with a continuous cooling down
of the neighboring joints which have already been brazed to avoid undoing them. An
acid flux is used first in order to dissolve oxides on the surface for a strong joint. Then
a torch is used to heat the local region to the flowing temperature of the silver alloy
used for brazing (
11250 F, 607°C). The inner thermocouples are brazed along the
entire 1.689" length of the slanted hole length and the outer thermocouples are brazed
along the entire 1.25" length of the outer slot. All exposed joints are then cleaned and
neutralized.
All inner and outer condensing tube wall thermocouple probe leads are taken out
of the annular gap through stainless steel multiple probe sealings in the outer jacket
as shown in Figures (E.14) and (E.15).
203
Table E.1: Comparison between Current Test Section and New Design
Parameter
Condensing tube
Outer jacket
Current Facility
New Design
304 S.S. tube
2" OD,
0.09"wall
304 S.S. tube
2.25" OD, 0.25" wall
304 S.S. pipe
316 S.S. tube
2.469" ID, 0.203" wall
3.5" OD, 0.437" wall
#9 and arrangement
(see Fig. 2.2)
#17 and arrangement
(see Fig. E.7)
9 stations
(Details see Fig. 2.2)
none
19 stations
(Details see Fig. E.6)
4 stations
see Fig. E.18
(Details see Figs. E.11, E.12)
see Fig. E.4
see Fig. E.19
see Fig. E.5
Thermocouple
see Fig. 2.2
see Fig. E.6
location
Details of thermocouple
see Fig. 2.3
see Fig. E.7,
none
E.9, E.11, E.12
18
Steam/gas centerline
temp. stations
Axial temp.
measuring stations
Azimuthal temp.
measuring stations
Upper end
Lower end
installation
Entrance length
* Top parts designed so that static mixers can be installed as well.
* Piping of the new test facility is arranged so that natural circulation may take
place.
* New Data Acquisition System
204
CenterlineTC
setup fixture
- vortexflowmeter
fixture
/ fix
Top section
(Diagramnot to scale)
Bottom section
Figure E.1: New Test Section Design
205
Centerline Thermocouple
1/2" NTP fixture
Assembly 1" NPT socket
for vortex flowmeter
_ 304 S.S. pipe
(ID: 2" wall: 1/8")
I
I
/
7I
steam
3"
1/8
e
4 S.S.
ylindrical block
onj
diameter x
length
(OD: 2.25" wall: 1/4")
Figure E.2: Gas/Steam Link to Test Section Entrance
206
4 water inlets/outlets
Figure E.3: Cooling Water Inlets/Outlets
207
1/4" NPT hole
for pressure
transducer
(tube extends
approximately
1' above flange)
gasket
0.025" clearance
between flange
and inner tube
Ik flanges
seal welds
pples
idewelded
IPT)
teroutlet
0.438")
1:0.25")
Figure E.4: Top End of Condenser
208
wall:0.25")
ill: 0.438")
r sockets
eaterinlet
0.025" clearance
between flange
and inner tube
kflanges
i.
O-ring for sealing
ty gasket
1/4" NPT hole for pressure
tran sducer
l
Figure E.5: Bottom End of Condenser
209
O
.....
O
...........
3"
3 in
.............
3 ot
ng
6"
stat
coo
43
steam/gas
mixture
............
15
6
78
)....
le
16
,.
.......
12.....
....
Figure E.6: Thermocouple System
210
~
1" NPT 316 S.S.
iT
316 S.S. tube
1'6"
OD 3/16"
I
C2
l*
ocations of
centerline thermocouples
equi-spaced 6" apart
c3
c4
05
C6
c7
08
10
C9
c10
C11
C 12
C 13
C 14
C 15
C 16
C 17
6
!
(Diagram not to scale)
Figure E.7: Centerline Thermocouple Setup
211
-
-
-
Federal
micrometer
304 S.S. tube
(OD: 2.25" wall: 1/4")
32'
Tungsten\
Copper-Tungsten
EDM electrode
TC slot machined
1.689" long
Figure E.8: Inner Wall Thermocouple Machining for All Stations (Except Top Station)
212
I
304 S.S tube
(OD: 2.25" wall: 1/4")
1.689"
1.25"
_
* Thermocouples
Figure E.9: Thermocouple Placement of All Stations Except 1, 2, 11, 19
213
_·
·
Tungsten\
Copper-Tungsten
EDM electrode
F
I..
.. .... ...
.... ....
304 S.S tube
\XJ.
...
J
Wo i. ).
j
Figure E.10: Inner Wall Thermocouple Machining for Top Station
214
0.25"
0.25"
TC embeddec
halfway alonl
the tangent
(OD: 2.25" wall: 1/4")
embedded
in tube surface
_
Figure E.11: Top Station Thermocouple Placement
215
\--
304 S.S tube
(OD: 2.25" wall: 1/4")
* Thenrmocouples
Figure E.12: Thermocouple Placement for Stations 2, 11, 19
216
(topof outerjacket)
1"
1/16"
I
I
T I
1.305"
.61 _ .878"
.I. -
-L,
.828'
109"
for coolingwateroutlet
-7
.61"
1.305"
I
.878"
I I
2, I -41 P
I
1116"
109"
I T
1.
four304SSnipples
(3"long,one sidewelded
oneside 1/2"NPTthread)
forcoolingwaterinlet
rI
(bottomof outerjacket)
Figure E.13: Details of Cooling Water Inlet/Outlet
217
1.305"
4 1/2"
4 coo
outle
(not t
(see
in Fig
16 1/2"
18"
I_
j
1/4"N
for TC
sealing
12"
I.
18"
18"
4 coo
inlets
(not t
..............................................................
( s ee
ill rig
I
-F-
Y)
Figure E.14: Fixtures on Outer Jacket for Surface TC Leads
218
9"
1.305"
4 probes (Dia. 0.032")
- ceranr
Figure E.15: Probe Sealing Fixture in Outer Jacket
219
-a-I
I
1.3"
3"
1.3"
I
6"
4 coolant outlets 0.61"
(not threaded)
(see details
in Fig 8)
9" l
6"
12"
A
12"
12"
12"
12"
1/16"NTP holes
for TC probe
sealings
6"
6"
12"
12"
12"
12"
12"
12"
I
12"
-
I
1.3"
t
4 coolant
inlets 0.61"
(not threaded)
(see details
in Fig 9)
l
6"
1.3"
9
Figure E.16: Coolant TC Fixture Locations on Outer Jacket Tube
220
-
-
annulus
Outer Jacket
304 S.S. tube
/ ln
" .- lI nAQ!"
-sealant
.94"
1
5/16"
'f
1/16" TC probe lead
flushing block
(if needed)
304 S.S. tube
(OD: 2.25" wall: 0.25")
Figure E.17: Lead Sealing Fixture in Outer Jacket
221
-
141
_I
6-1/8"
-i
2-7/8"
2.05"
I
.1.
!
!
V
3/4"
i
fI
III
it
T
i
l/It 6"
l
L iL
I
I
I
I
- Dia. of hub at
base: 2-7/16"
Dia. of boltcircle 4.5"
Dia. of boltholes 3/4"
Dia. of bolts5/8"
No. of bolts 4
3"
Eight, 1.16"NPT,
compression
fittingsarrangedat
equalspacingalong
the circumference
First temperature
measuringstation
- 304 S.S. tube
2" OD BWG #13
2-1/2", Sch 40S
SS 304 pipe
ID 2.469"
OD 2.875"
Figure E.18: Details of the Upper Part of the Current Design
222
- 2-1/2", Sch 40S
SS 304 pipe
ID 2.469"
OD 2.875"
t for
rinlet
t
NMMUVMlr
Eight, 1.16"N
compression
fittingsarrange
equal spacing
the circumfere
..
1/4" collar to jacket
pipe, mates with
tubeflange
--
304 S.S. tube
2" OD BWG #13
circle4.5"
holes 1/2"
s3/8"
6
1/4" thick flange
3" long 1/8" sleev
ths slidesover the
tube with a clears
' Rubber 0 ring sits
in the groovein
the sleeve
Figure E.19: Details of the Lower Part of the Current Design
223
Appendix F
Steam/Helium Reduced Data
224
Nomenclature for Steam/Helium Mixture Reduced Data
Tinet
Moi
Ptotal
=
=
=
=
=
=
=
=
Tb
= bulk temperature (C)
T,.
Tf
Tc
Tf
dTc/dL
q
h
dQ
Tsat
n
Mco,,
MJ
Wa
Wh
Ya
Yh
Densm
Velm
Vism
Re,
Km
Nu(mix)
=
=
=
=
=
=
=
=
=
Mai
Mhi
Mc
Wai
Whi
inlet temperature (C)
inlet steam mass flow rate (kg/s)
inlet air mass flow rate (kg/s)
inlet helium mass flow rate (kg/s)
cooling water mass flowrate (kg/s)
inlet air mass fraction
inlet helium mass fraction
total pressure (MPa)
wall temperature (C)
fitted wall temperature (C)
cooling water bulk temperature (C)
fitted cooling water bulk temperature (C)
coolant temperature gradient (°C/m)
heat flux (kW/m2 )
heat transfer coefficient(kW/m2 °C)
incremental heat rate (kW)
saturation temperature (°C)
= condensate mass flow rate (kg/s)
=
=
=
=
=
=
=
=
=
=
=
steam flow rate (kg/s)
air mass fraction
helium mass fraction
air mole fraction
helium mole fraction
density of steam/helium mixture (kg/m3 )
velocity of steam/helium mixture (m/s)
viscocity of steam/helium mixture (Pa.s)
Reynolds number of steam/helium mixture
thermal conductivity of steam/helium mixture (W/m°C)
Nusselt number of steam/helium mixture
Re(film) = Reynolds number of condensate film
Dn,
= condensate film thickness (m)
hf
ENhR
= condensate film theoretical heat transfer coefficient (kW/m2 ° C)
= experimental to condensate film Nusselt heat transfer coefficientsratios
225
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Appendix G
Steam/Air/Helium Reduced
Data
270
Nomenclature for Steam/Air/Helium Mixture Reduced Data
Tindet
Mi
Mai
Mhi
Mc
Wai
Whi
=
=
=
=
=
=
=
inlet temperature (C)
inlet steam mass flow rate (kg/s)
inlet air mass flow rate (kg/s)
inlet helium mass flowrate (kg/s)
cooling water mass flow rate (kg/s)
inlet air mass fraction
inlet helium mass fraction
Ptotal
Tb
= total pressure (MPa)
= bulk temperature (C)
Tw
= wall temperature (C)
Tf
= fitted wall temperature (C)
= cooling water bulk temperature (C)
Tc
TCf
= fitted cooling water bulk temperature (C)
dTc/dL = coolant temperature gradient (C/m)
q
= heat flux (kW/m2 )
h
= heat transfer coefficient(kW/m2 C)
dQ
= incremental heat rate (kW)
Tat
= saturation temperature (C)
Mon
= condensate mass flow rate (kg/s)
MJ
Wa
= steam flow rate (kg/s)
= air mass fraction
Wh
= helium mass fraction
Y.
Yh
Dens,
Velm
Vis,
Re,
K,
Nu(mix)
=
=
=
=
=
=
=
=
air mole fraction
helium mole fraction
density of steam/air/helium mixture (kg/m3 )
velocity of steam/air/helium mixture (m/s)
viscocity of steam/air/helium mixture (Pa-s)
Reynolds number of steam/air/helium mixture
thermal conductivity of steam/air/helium mixture (W/m°C)
Nusselt number of steam/air/helium mixture
Re(film) = Reynolds number of condensate film
D,
= condensate film thickness (m)
hf
ENhR
= condensate film theoretical heat transfer coefficient(kW/m2 ° C)
= experimental to condensate film Nusselt heat transfer coefficientsratios
271
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