WO
· S
JU
-WOSUBA SUBCHANNEL CODE FOR STEADY-STATE AND
TRANSIENT THERMAL-HYDRAULIC ANALYSIS OF
BWR FUEL PIN BUNDLES
VOLUME III
ASSESSMENT AND COMPARISON
by
L. Wolf, A. Faya, A. Levine,
W. Boyd, L. Guillebaud
Energy Laboratory Report No. MIT-EL 78-025
October 1977
__I
_
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·
_I_
t
-WOSUBA SUBCHANNEL CODE FOR STEADY-STATE AND
TRANSIENT THERMAL-HYDRAULIC ANALYSIS OF
BWR FUEL PIN BUNDLES
VOLUME III
ASSESSMENT AND COMPARISON
by
L. Wolf, A. Faya, A. Levine,
W. Boyd, L. Guillebaud
Energy Laboratory Report No. MIT-EL-78-025
October 1977
Topical Report for Task 3 of the
Nuclear Power Reactor Safety Research Program
Sponsored by
New England Electric System
Northeast Utilities Service Co.
under the
M.I.T. Energy Laboratory Electric Power Program
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__
ii
ABSTRACT
The WOSUB-codes are spin-offs and extensions of the
MATTEO-code [1]. The series of three reports describe WOSUB-I
and WOSUB-II in their respective status as of July 31, 1977.
This report is the third in a series of three, the
first of which [2] contains all the information about the
models, solution methods and constitutive equations and the
second
[3] being the user's manual of the code.
This report summarizes the assessment of the WOSUBcode against experiments and compares its results with the
results of other subchannel codes.
The following experiments
are used for the purpose of the assessment
of the code under
steady-state conditions:
1) 9-rod GE-tests with radially uniform and nonuniform peaking factor patterns.
2)
16-rod Columbia
tests with slight power tilts.
3) Planned 9-rod Swedish tests with very strong
power tilts.
4)
Actually performed 9-rod Swedish tests with
power tilt.
5)
9-rod GE-CHF experiments.
The comparison with these data shows that WOSUB is capable of
predicting the lower-than-average behavior of the corner subchannel and the higher-than-average behavior of the center
subchannel for both quality and mass flux. None of the other
well-known subchannel codes is indeed capable of specifically
predicting the correct corner subchannel behavior.
These codes
seem to inherently suffer from major deficiencies associated
with their incorporated mixing models. Therefore, it is concluded that only improved models for the description
of two-
phase flow phenomena are capable of handling these situations
and that the vapor drift flux model together with the vador
diffusion model as incorporated into WOSUB is doing a good job.
The fact that WOSUB does not perfectly match the experimental
results over the whole spectrum of experimental evidence can
be attributed to the vapor diffusion model which was originally
fitted to air-water test results in a geometry consisting of
two subchannels only.
Obviously, this geometry leads to overemphasizing the importance of the vapor diffusion as compared
to what actually happens in a multi-rod geometry.
WOSUB gives the user the option of calculating
the
critical power as a function of the boiling length - a concept
which is especially useful to easily account for axially
___
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1_
1
iii
nonuniform power profiles and which closely resembles the
procedure now used by GE. Furthermore, the code determines
four heat transfer coefficients around the circumference of the
fuel pin, thus giving the user the possibility of selecting
the minimal one for the purpose of hot spot calculations.
Overall, the assessment and comparison presented in
this volume show that the WOSUB-code
has to be considered
a
valuable tool for BWR bundle and PWR test bundle analysis with
a potential for further improvements.
The commonly used concept of power-to-flow ratio
fails to explain most of the test data used for comparison
this report.
in
The WOSUB-code is still in the stage of evolutionary
development.
In this context, the results presented in this
present report have to be considered preliminary.
reflect the development
as of July 1977.
They
iv
ACKNOWLEDGEMENTS
The assessment
and comparison of the WOSUB-subchannel
code results was started in the Fall of 1976, when Louis
Guillebaud worked on his N.E. Thesis.
His preliminary results
were updated by Alan Levin who provided the additional subroutines for calculating the heat transfer coefficient and
the critical heat flux.
By his efforts the spectrum of the
assessment and the comparison was greatly enlarged.
He was succeeded by William Boyd in January 1977, who
largely concentrated his work on a parametric sensitivity study
of the drift flux parameters and their effects upon the overall
results.
When he left M.I.T., Artur Faya started working on
His first achievement,
his Ph.D. Thesis.
was to fully inte-
grate the fuel pin model into WOSUB thus making it possible
calculate pointwise
the first time.
assessment
temperatures
in fuel and clad regions for
Again, this step enlarged
of the code.
to
Furthermore,
the spectrum of the
he provided
all the
left
necessary help to collect all the pieces of information
from the others to put this report together.
To all these gentlemen I owe a great deal of gratitude for their devotion
as well as their tireless efforts in
accomplishing all these achievements.
would like to acknowledge the financial
Finally,
support as well as the fruitful discussions
by the New England
Electric System and Northeast Utilities Service Company as part
of the Nuclear
·--- ·---- I----_
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Eactor Safety Research
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Pro-ram under the M.I.T.
_
v
Energy Laboratory's Electric Power Program.
Lothar Wolf
Principal Investigator
Associate Professor of
Nuclear Engineering
--111111··-···-LI
_1
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vi
TABLE OF CONTENTS
Page
Chapter 1
1.
Comparison of WOSUBResults with Steady-State Experiments
1.1
9-Rod GE Test Bundle Experiments
1.1.1
1.1.2
Introduction
Bundle and Test Description
1.1.3 Results for Isothermal Test Data
1.1.3.1 Comparison with Experiments
1.1.3.2 Comparison with Analytical Results and
Other Subchannel Codes
1.1.3.3 Conclusions
1.1.4 Results for Radially Uniform Peaking Factor Patterns
1.1.4.1 Overall Comparison
1.1.4.2 Detailed Subchannel Behavior and Comparison
1.1.4.2.1 Corner Subehannel
1.1.4.2.2 Side Subchannel
1.1.4.2.3
1.1.4.3
Center Subchar.nel
1
1
2
10
10
10
17
18
18
23
23
26
26
Comparison with Results of Other Subchannel
Codes
1.1.4.4 Conclusions
1.1.5 Results for Radially
30
35
Nonuniform Peaking Factor
Patterns
1.1.5.1
1.1.5.2
1
Comparison of WOSUB Results with the Experiment
Comparison with Other Subchannel Codes
1.2 16-Rod Columbia Test Bundle Experiment
1.2.1 Introduction
1.2.2 Description of the Bundle and Test Conditions
41
44
50
57
57
57
1.2.3
1.2.4
Results of the Experiment
Comparison of Columbia Tests with GE Tests
59
61
1.2.5
1.2.6
Comparison of COBRA-II with the Experiments
Comparison of WOSUB withthe Columbia Eeiments
and COBRA-IIIC/MIT
61
1.2.7
Conclusions
72
65
1.3
*
Planned 9-Rod Studsvik Test Bundle Experiments with
Strong Power Tilt
1.3.1 Introduction
73
73
1.3.2
1.3.3
1.3.4
76
76
88
Description of the Geometry and the Test Conditions
Comparison of WOSUB with Other Subchannel Codes
Conclusion
vii
Table of Contents continued
Page
1.4
Performed 9-Rod Studsvik Test Bundle Experiments with
Power Tilt
96
1.4.1
Introduction
1.4.2
Description
96
of the Geometry
and the Test Conditions
Comparison of WOSUB with the Experiment and the
Other Subchannel Codes
1.4.3.1 Comparison of the Quality Predictions
1.4.3.2 Comparison of Mass Flux Predictions
1.4.3.3 Comparison of Predicted Individual Subchannel
97
1.4.3
Qualities
1.4.3.4
1.4.4
1.5
113
Comparison with Predicted Individual Subchannel
Mass Fluxes
120
Conclusion
123
Hitachi 7 x 7 BWR Fuel Pin Bundle with 3-D Power
Profile
1.5.1 Introduction
1.5.2 Description of the Bundle and Physical
1.5.3 Results and Comparison
1.5.4 Conclusions
1.6
Input Data
GE-CHF Tests
1.6.1
1.6.2
1.6.3
1.6.4
1.7
103
103
110
125
125
126
129
136
139
Introduction
Bundle and Test Descriptions
Results and Comparison
Conclusions
Sample Cases for the Prediction
139
139
140
150
of the Heat Transfer
Coefficient and the Pin Temperature Distribution
1.7.1 Introduction
153
153
1.7.2
155
Results and Discussion
1.8
Sensitivity Study of the Void Concentration Parameters
and Relaxation Length
1.8.1 Introduction
1.8.2 Results and Discussion
162
162
162
1.8.3
166
1.9
Conclusions
Other Supporting Evidence
for the GE Findings
and the
Drift-Flux, Vapor-Diffusion Model
1.9.1 Introduction
1.9.2 Results and Discussion
168
168
168
1.9.3
174
Conclusions
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·
viii
Table of Contents continued
Pag,
Chapter
178
2
Tests of WOSUB-I in Transient
2.
Situations
178
2.1
Introduction
2.2
Mass Flow Reduction Transients
2.3
2.4
Depressurization
Power Transient
2.5
Discussion and Conclusions
Transient
Chapter 3
3.
Steady-State Calculations
Transient Calculations
187
191
194
196
Recommendations
196
Calculations
4.1
Steady-State
4.2
Transient Calculations
Refeernces
184
184
191
Chapter 4
4.
178
191
Conclusions
3.1
3.2
178
196
198
200
ix
LIST OF FIGURES
Page
Figure
1
9-Rod GE Bundle Geometry
Figure
2
Radial Power Peaking Pattern for the 9-Rod
3
GE Bundle
Figure
Figure
Figure
3
4
5
8
THINCII',THINC-IV [9], and WOSUB Results for
Nine Rod Bundle Isothermal Flow Tests
15
Comparison of Measured Versus Calculated
Subchannel Exit Mass Velocities for the SinglePhase Isothermal Data (COBRA-IV-I, WOSUB)
16
Comparison of WOSUB with GE Experiments 2D
for Subchannel
Figure
6
Figure 7
Exit Qualities
as a Function
of
Bundle Averaged Exit Quality
20
Comparison of WOSUB with GE Experiments 2E for
Subchannel Exit Qualities as a Function of
Bundle Averaged Exit Qualities
21
Comparison
of WOSUB with GE Test 2D for the
Subchannel Mass Flux in the Corner Subchannel
as a Function of Subchannel Exit Quality
Figure
8
Comparison of WOSUB with GE Test 2D for the
Subchannel Mass Flux in the Side Subchannel
as a Function
Figure 9
25
Comparison
of Subchannel
Exit Quality
27
of WOSUB with GE Test 2D for the
Subchannel Mass Flux in the Center Subchannel
as a Function
of Subchannel
Exit Quality
Figure 10 Comparison Between Experimental Data and
Predictions by Various Subchannel Codes for
the Individual Subchannel Mass Flux Deviations
from Bundle Average Behavior
28
36
Figure 11 Nine Rod Bundle Uniform Radial Power Distribution
Tests, Mass Velocity Comparion
THINC-IV, and WOSUB
Figure
THINC-II,
37
12 Nine Rod Bundle Uniform Radial Power Distribution
Tests, Quality Comparison THINC-II, THINC-IV, and
WOSUB
38
x
List of Figures continued
Page
Figure
13
Figure 14
Figure 15
Figure 16
Comparison of Measured Versus Calculated
Subchannel Exit Mass Velocities for the
Two-Phase Data (COBRA - IV - I, WOSUB)
39
Radial Power Peaking Pattern and Subchannel
Numbering Scheme
42
Nine Rod Bundle Non-Uniform Radial Power
Distribution Tests, Quality, Comparison
THINC-II, THINC-IV and WOSUB
55
Nine Rod Bundle Non-Uniform Radial Power
Distribution Tests, Mass Velocity Comparison
THINC-II, THINC-IV and WOSUB
56
58
Figure
17
Columbia University 16-Rod Test Geometry
Figure
18
Mass Flux Deviation from Bundle Average for
the Hot Center Subchannel
Figure
19
Figure 20
of
66
Mass Flux Deviation from Bundle Average for
the Cold Center Subchannel as a Function of
Bundle Average Exit Quality
67
Mass Flux Deviation from Bundle Average for
the Hot Center Subchannel
the Exit Quality
Figure 21
as a Function
the Bundle Average Quality
as a Function
of
68
Mass Flux Deviation from Bundle Average for
the Cold Center Subchannel
its Exit Quality
as a Function
of
Figure 22
Layout of Planned 9-Rod Studsvik Text Bundle
Figure
Numbering
23
Figure 24
Figure
25
69
74
Scheme for the Subchannel of the
Studsvik Test Bundle
77
Comparison of Various Subchannel Codes for
the Deviation of Exit Subchannel Qualities
from Bundle Average as a Function of Subchannel
Number and Bundle Power a Parameter
91
Comparison
Deviations
of Various Subchannel Codes for the
of Exit Subchannel 2 and 8 Mass
Fluxes from Bundle Average as a Function of
Bundle Power
92
xi
List of Figures continued
Page
Figure
26
Comparison of Various Subchannel Codes for the
Deviation of Subchannel Exit Qualities Versus
Subchannel Exit Mass Fluxes from Bundle Average
for Subchannels
2 and 8
93
Figure 27a Geometry of the 9-Rod Studsvik Test Bundle
98
Figure 27b Spaces Locations in the 9-Rod Studsvik Test
Bundle
99
Figure 28
Flow Split Device in the 9-Rod Studsvik Test
Bundle for Sampling Two Neighboring Subchannels
102
Figure 29
Layout of the 7x7 Hitachi Pin Bundle
127
Figure 30
Axial Heat Flux Profiles at the Corners a and
b of Bundle 3 and Control Rod Positions of
Rods A and B
128
Heat Flux Distribution Across the Bundle
Diagonal at Four Axial Elevations
130
Comparison of Void Fraction Distributions Across
the Bundle Diagonal at Three Axial Elevations as
Determined by COBRA-IIIC/MIT, FASMO and WOSUB
132
Schematic View of Test Channels, Showing Axial
Positions of Heated Length and Grid-Type Spacers
141
Comparison of Three CHF Correlations with
Measurements
144
Figure 31
Figure 32
Figure
Figure
Figure
33
34
35
Critical Heat Flux Versus Quality, Test
Channel No. 1
Figure
Figure
Figure
36
37
38
Comparison
of Measured
145
and Calculated
CHF as a
Function of Bundle Average Quality
147
Comparison of Measured and Calculated CHF Versus
Bundle Average Quality for the 9-Rod GE Bundle
at High Mass Flux
148
Comparison of Measured and Calculated CHF Versus
Bundle Average Quality for the 9-Rod E Bundle
at Low Mass Flux
149
xii
List of Figures continued
Page
Figure
39
Figure 40
Comparison Between Measured and Calculated
Critical Bundle Power Versus Subcooling
Logic for the Evaluation
fo the Heat Tansfer
Coefficient
Figure 41
42
154
Heat Transfer Coefficients and Clad Surface
Temperatures
Figure
151
Around a Corner Pin in a 3x3
Pin Bundle
156
Temperature Distribution in a Fuel Rod During
a Power Transient - Comparison Between the
Finite Difference Method and the Collocation
Method
160
43
Steady-State Temperature Profiles in the Fuel
as Obtained by the Collocation Method Using
Hermite Cubic Spline Functions
Figure 44
Effect of the Variation in Ze Upon Subchannel
Quality and Mass Flux
164
Effect of the Variation in Ze Upon Subchannel
Quality and Mass Flux
165
Subchannel Mass Flux Deviations from Bundle
Average Versus Bundle Average Quality [191
169
Subchannel Mass Flux Deviations from Bundle
Average Versus Bundle Average Quality [19]
170
Subchannel Exit Quality Deviation from Bundle
Average Versus Bundle Average Quality [19]
172
Subchannel Exit Quality Deviation from Bundle
Average Versus Bundle Average Qualtiy [19]
173
Figure
Figure
Figure
45
46
Figure 47
Figure 48
Figure 49
Figure 50
Cross Flow Enthalpy Between Side and Corner
Channels
Figure 51
Figure 53
175
Cross Flow Enthalpy Between Center and Side
Channels
Figure 52
[19]
[19]
176
Center and Corner Subchannel Exit Qualities
Versus Time for a Mass Flux Reduction Transient
Transient Subchannel Mass Fluxes for a Severe
Mass Flux Reduction
of 50% in ls
179
xiii
List of Figures continued
Page
Figure
54
Deviation of Subchannel Exit Quality from Bundle
Average Exit Quality as Function
Figure 55
Figure 56
Figure 57
Figure 58
of Time for the
Mass Flux Reduction Transient Shown in Figure 53
183
Subchannel Mass Fluxes Versus Time for a
Depressurization Transient
185
Subchannel Exit Qualities versus Time for a
Power Transient
i86
Boiling Length and Clad Surface Temperature
Versus Time for the Power Transient
188
Calculated
CHF as Function
Power Transient
--
-1
of Time for the
189
xiv
LIST OF TABLES
Page
Table 1
Table 2
Table 3
Geometric
and Hydraulic
Parameters
of the
9-Rod GE Bundle
4
Experimental Test Conditions for the 9-Rod
GE Isothermal Tests
6
Test Conditions for Uniform Radial Peaking
7
Runs
Table 4
Test Conditions for Non-Uniform Radial Peaking
Runs
Table 5
Table 6
Table 7
9
Comparison of Experiments and Calculations for
Single-Phase Subchannel FlowSplits
11
Comparison of WOSUB with Vapor Diffusion Model
and GE-Test Data for Radially Uniform Peaking
Factor Pattern in a 9-Rod Bundle
19
Comparison of the Results of Different Subchannel
Codes with the Experimental Results for Test
33
Run 2E2
Table 8
Comparison of the Results of Different Subchannel
Codes with the Experimental Results for Test
34
Run 2E3
Table 9
Comparison Between GE Data and WOSUB Results
for
Table 10
Channels
1, 16,
2, 15 and
45
6
WOSUB Predictions for the Individual Subchannels
for Test 3E1 with X = 0.0304 and G = 1.097 x 106
2
lb/ft-hr
Table 11
48
WOSUB Predictions for the Individual Subchannels
for Test 3E2 with
= 0.096 and
= 1.077 x 106
lb/ft2-hr
49
Table 12a Comparison Between Test Results and Subchannel
Code Results
51
for 3D!
Table 12b Comparison Between Test Results and Subchannel
52
Code Results for 3E1
ii
I
xv
List'of Tables continued
Page
Table 13
Comparison Between Test Results and Subchannel
Code Results
Table 14
Table 15
Table 16
for 3E2
53
Test Conditions for the Columbia 16-Rod Bundle
Tests
60
Test Conditions for the 9-Rod Bundle with
Tilted Power Distribution
78
Comparison
of Results for Subchannel
1 and 2
Qualities from Various Subchannel Codes with
WOSUB (Vapor Diffusion) and (No Vapor Diffusion)
Table 17
Comparison
of Results
for Subchannel
1 and 2
Mass Fluxes from Various Subchannel Codes with
WOSUB (Vapor Diffusion and (No Vapor Diffusion)
Table 18
Comparison
of Results for Subchannel
Comparison
of Results
for Subchannel
Comparison
of Results
for Subchannel
Comparison
of Results
for Subchannel
Trends in Quality for the WOSUB Options When the
Total Bundle Power is Raised from 346KW to 870KW
for the Studsvik BWR Bundle
Table 23
Test Conditions
Table 24
Steam Quality (%) in Each Split Channel Comparison Between Experiment and Various
Subchannel
Table 25
83
7 and 8
Mass Fluxes from Various Subchannel Codes with
WOSUB (Vapor Diffusion) and (No Vapor Diffusion)
Table 22
82
7 and 8
Qualities from Various Subchannel Codes with
WOSUB (Vapor Diffusion) and (No Vapor Diffusion)
Table 21
81
5 and 6
Mass Fluxes from Various Subchannel Codes with
WOSUB (Vapor Diffusion) and (No Vapor Diffusion)
Table 20
80
5 and 6
Qualities from Various Subchannel Codes with
WOSUB (Vapor Diffusion) and (No Vapor Diffusion)
Table 19
79
Codes (Case 1)
[91
84
94 95
101
104
Mass Flux in Each Split Channel - Comparison
Between Experiment and Various Subchannel
Codes
(Case 1 continued)
105
xvi
List of Tables continued
Page
Table
26
Steam Quality in Each Split Channel - Comparison
Between Experiment and Various Subchannel Codes
(Case 4)
Table
27
106
Mass Flux in Each Split Channel - Comparison
Between Experiment and Various Subchannel
Codes
Table
Table
Table
28
29
30
Table 31
(Case 4 continued)
107
Steam Quality in Each Subchannel - Comparison
Between Various Subchannel Codes (Case 1)
114
Mass Flux in Each Subchannel - Comparison
Between Various Subchannel Codes (Case 1
continued)
115
Steam Quality in Each Subchannel - Comparison
Between Various Subchannel Codes (Case 4)
116
Mass Flux in Each Subchannel - Comparison
Between Various
Subchannel
Codes (Case 4
continued)
Table 32
117
Comparison of CHF Results Between Experiments
and Predictions
Table 33
for Test Channel No. 2
142
Comparison of a Finite-Difference Method with
the Collocation
158 -
Method at Time = 2 seconds
and 4 seconds
I
-
-
I
--
159
-
-- ---
-- ---
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----.-- -- -
--
CHAPTER
I
COMPARISON OF WOSUB RESULTS WITH STEADY-STATE EXPERIMENTS
In this chapter a comparison between the WOSUB results
and a number of experimental
discussed.
test data will be performed
and
These efforts are mainly focused on the following
test data which are available in the open literature:
1)
9-Rod
2)
10-Rod Columbia Test Bundle
3)
9-Rod Swedish Test Bundle
4)
GE-CHF Data [5]
GE
Experiment
4,
5,
6,
7]
[8]
[9, 10, 11. 12]
It should be noticed at this point that although
larger bundles were tested, no detailed information concerning
subchannel
quantities
are available
for those.
Thus, this
study has to be limited to bundles of comparatively
size,
Fortunately,
a lot of computer
small
codes have been tested
against the aforementioned experimental evidence.
Therefore,
it is possible not only to show how WOSUB compares
to the ex-
periment but at the same time to indicate
commonly
used codes for the analysis
its superiority
over
of encapsulated bundles.
All
of these comparisons are performed for steady-state conditions
because no information is available for subchannel quantities
in transient situations.
1. Comparison of WOSUB Results with Steady-State
Experiments
1.1
1.1.1
9-Rod GE Test Bundle Experiments
Introduction
Test conditions typical of operating BWR situations
2
have been investigated at GE with electrically heated (3 x 3)
rod bundles for both uniform and nonuniform radial power distributions.
The experimental
have been widely published
findings of the various tests
[3, 4, 5, 6] but the reports
GEAP-13049 and GEAP-10347 have to be considered the main documents.
It should be noticed that the GE-data were the first
published for square-array arrangements.
ticularly
important
for the development
It is therefore par-
of the WOSUB code to
assess its analytical predictions against these findings.
The
data were the first to indicate deficiencies inherent to
commonly used subchannel models.
Although this was already
explicitly stated in 1971 [6, 7] by comparing the data with
COBRA--i nothing was really done about it.
Therefore,
deficiencies
including the most
were carried through up to and
recently developed codes as will be shown
the same
n Section l..4.3.by
comparison.
The assessment of WOSUB consists in comparing the
data against results obtained for both vapor and no-vapor
diffusion options.
ocal qualities and mass fluxes are the
relevant physical quantities for the following series of comparisons.
1.1.2 Bundle and Test Description
The 9-rod bundle test section is shown in Figure 1
and its geometrical and hydraulic data relevant for the comparison are summarized
in Table 1.
Reference
[4] describes
in
great detail the set-up of this experiment as well as the
3
I 1l
An
CORNER SUBCHASNNEL
0
_"
0.40
ADIUS(TYPICAL)3'
O o~i
0.7 38
(TYPICAL)
FIGURE 1:
9-Rod GE Bundle
0. 420
(TYPICAL)
eometry
-
-- --------
-L-*-
Number of Rods
9
Rod Diameter
.570 inch
Radius of Corner Subchannel
.400 inch
Rod Rod Clearance
.168 inch
Rod Wall Clearance
.135 inch
Hydraulic Diameter
.474 inch
Heated Length
-
-----
..
Table 1:
72 inches
___
__
__
________
Geometric and Hydraulic
Parameters of the 9-Rod GE-Bundle
measurement techniques.
this reference
The interested reader should consult
for a complete review.
Three types of experiments were performed:
1)
Unheated, isothermal tests in order to determine
the flow split between
subchannels.
The corresponding
test conditions are summarized in Table 2.
2)
Tests where all rods were uniformly heated in
the radial direction as well as in the axial direction.
The corresponding test conditions used for the
purpose of comparison are reported in Table 3.
3)
Tests where the rods were non-uniformly
radially but uniform in axial direction.
heated
The radial
peaking pattern is shown in Figure 2 whereas the
corresponding
test conditions
used for the purpose
of comparison
in this study are reported
in Table 4.
6
Test Point
Bundle
Average
Corner
Subchannel
Side
Subchannel
Center
Subchannel
G x 10 - 6
G 1 x 10 6
G2 x 10 6
G3 x 10
lb/hr-ft
i
lb/
lbft
/hr-ft2
lb/hr-ft 2
1B
0.480
0.311
0.462
0.526
1C
0.990
0.701
0.939
1.150
1D
1.510
1.095
1.441
1.690
1E
1.97
1.62
1.91
2.190
_
i
Table 2:
Experimental
._
6
i
Test Cond'itions for the 9-Rod
GE Isothermal Tests
_i
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CM
CM
x
H
C
_
8
FIGURE
RADIAL
POWER PEAKING
PATTERI
2
FOR THE 9-ROD
GE BUNDLE
9
E-e
H
x
H
[
iii
I
ICO
I
C
i
i
i
oO
i
i
rU
r.
.r
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=..
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,o
C',O
G
oC
o
b
rn
a,
0
Q
H
EcK
0
Ov
r
-i
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X
COH
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H
o
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4Q,
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i
0
zHC
10
1.1.3
1.1.3.1
Results for Isothermal Test Data
Comparison with Experiments
GE performed several unheated tests with the bundle
described in the foregoing section.
results are given in Table
and 1E.
5
The test conditions and
for the test points
The purpose of these single-phase
B, 1C, 1D
flow tests was to
establish the flow splits between the subchannels and at the
same time to check the validity of the turbulent mixing models.
The comparison
of the WOSUB-results
mental test data shows excellent agreement;
being not larger than ±5%.
with the experi-
the differences
The only data point which falls out
of this range is that of the center subchannel at the highest
lbm/ft 2-hr.
flow rate of G = 1.97 x 106
Unfortunately,
error bands are given by GE for these measurements
no
but it can
be safely assumed that it is finite and may even increase with
an increase in flow rate.
The agreement between experiment and
WOSUB results is best for the side subchannels.
for test point
measurements.
D show the overall best agreement with the
It can be safely concluded that the single-phase
mixing model built into the WOSUB-code
1.1.3.2
The results
[31 is working just fine.
Comparison with Analytical Results and Other Subchannel Codes
A first estimate
for the flow split between
sub-
channels
can be obtained by assuming that no mixing takes place
at all.
With this assumption
from [
4
].
ui
=
2/3
hi
u3
Gi(i = 1,2,3) can be determined
11
1B
1E
2
G3 x10- 6
lbm/
0.311
0.322
0.352
0.462
0.447
0.456
0.526
0.562
0.565
COBRA-IB = 0.01
0.352
0.451
0.551
COBRA-IB = 0.005
0.336
0.447
0.560
Data
0.701
0.939
1.150
0.664
0.922
1.159
WOSUB
0.730
0.942
1.160
COBRA-IB = 0.01
0.740
0.934
1.128
COBRA-IB = 0.005
0.704
0.925
1.149
Data
1.095
1.441
1.690
1.013
1.406
1.768
WOSUB
1.120
1.440
1.767
COBRA-IB= 0.01
1.143
1.427
1. 713
COBRA-IB = 0.005
1.085
1.414
1.746
Data
1.62
1.91
2.19
Dh2 /3 -Prediction
1.321
1.834
2.306
WOSUB
1.54
1.937
2.37
COBRA-IB= 0.01
1.502
1.865
2.229
COBRA-IB = 0.005
1.424
1.847
2.273
3-Prediction
[
II
I
I
Table 5:
III
I
I
I I I I
Gx1O6
lm/
hr ft-hr
Data
Dh2 / 3 -Prediction
WOSUB
h2 / 3 -Prediction
1D
lbm/
ft
Dh
1C
6
Gxx10-6
ibm/
TEST
POINT
I~~~~~~~~~~~~~
Comparisonof Experirents
and Calculations
for Single-Phase SubchamnelFlow Splits
0.48
0.99
1.51
1.97
12
Results according to this formula are listed in Table 5.
The
comparison with the experimental data indicates that this simple
model gives fairly good results especially for side and center
subchannels
at low average mass fluxes.
This suggests
that un-
der these conditions the flow split is indeed fully developed.
In order to cope with the other data the concepts
of
mixing and crossflows have been introduced into subchannel
codes.
Various processes are known to generate crossflows
among them pressure gradients and turbulence effects.
Under
the assumption of a totally ventilated bundle cross section the
contribution
due to diversion
crossflow is zero and only tur-
bulent mixing remains to be considered. This approach has
been taken by all the subchannel codes of the first generation
and is accepted
to be valid for the encapsuled
Therefore,
Lahey et al
subchannel
mass fluxes.
specified
4,7] used COBRA-I [131 to compute the
One of the variables
as input to the commonly
the mixing parameter
W'
=
BWR bundles.
that has to be
used subchannel
codes is
which is indirectly defined by
sG
where W' = mass flux per unit length
s
= rod-rod or rod-wall
gap spacing
= dimensionless mixing parameter
G
= average mass flux of adjacent
The mixing parameter may be redefined
subchannels.
in terms of an eddy
diffusivity of momentum as:
G1
where
1 is the mixing
length or the effective mixing
13
distance between subchannels.
The latter approach
is used in WOSUB as described
in
as a result the supply of a appropriate
necessitates
tutive equation
2] and
consti-
For COBRA-I, Rowe [ 7 ] recommends
for E.
for
B the following equation:
Dh
=
(0.0062)
-h
0
(Re) -
.1
which for the geometry under consideration gives a value for
B of the order of 0.005.
Lahey et al [4 ] used this value and
= 0.01 to obtain the results as listed in Table 5.
The
comparison with the experimental data indicates that the best
overall agreement is achieved by taking 3 = 0.005.
for the highest
flow rate it seems that B >0.01
However,
would result
in better agreement with the data.
By comparing the WOSUB results with those obtained
from COBRA-I it can be concluded that the former present a
trend which resembles data obtained for
>0.01.
Therefore,
the high flow rate results are indeed in better agreement with
the test data than the COBRA-results
In the underlying
are.
concept of turbulent mixing
in
single-phase flow nothing has changed until now since the
generation of COBRA-I with the exception that due to more
experimental data slightly different coefficients and exponents
for
are recommended now.
However, the functional dependancy
remained essentially unchanged.
Due to the fact that most publicly
available
sub-
channel codes today are applied for both PWR and BWR core design
modern versions
of COBRA, such as COBRA-II,
COBRA-III-C
and
14
COBRA-IV-I [14] contain a diversion crossflow model which is
essential to deal with semi-open cores.
Therefore, the whole
solution procedures of these codes are even oriented towards
this phenomenon.
In order to examine the question of whether
diversion crossflow and/or improved correlations for
changes
the computational results it seems prudent to compare WOSUB
with more recent versions of subchannel codes.
Fortunately,
two sources of information are available for this purpose.
Figure 3 shows the comparison of THINC-II and THINC-IV results
[15
with the GE test data.
are added into this graph.
The most deviating WOSUB-results
Overall, the indications
are that
WOSUB generates more reliable data than either of these codes.
In most cases the WOSUB results fall just in between those
obtained by THTNC-II and THINC-IV.
Figure 4 shows the same comparison
tained by COBRA-IV-I [l14.
with results ob-
WOSUB results are added for test
lE because there the largest deviations were observed.
Again, overall WOSUB shows closer agreement.
No outlier,
i.e. where differences are larger than ±10% are produced by
WOSUB, rather all data are within ±5% as shown in Figure 4
with one exception.
Finally, it can be concluded that obviously diversion
crossflow does not play a role for the tests considered here.
The assumption of zero pressure gradient between subchannels
seems therefore justified
at least for the single-phase
tests.
I
__
flow
15
i
6035-17
t
[
(
2.6
W
.... D:
LEGEND:
TH I C-l
2.2
i
I
IsIjITH
5h
h/WOSUTH
I C-'
L"
X
,..
A
SUBCHASNEL
CORNER
S1DE
El
CENTER
-
to
x
1.8
0
0
I-I
cZ3
I.4
-
.i=
-;
ui
1 .0
0.6
0.2
0.2
I
I
0.6
1.0
GPREDIOTED
FIGURE 3:
(L
l
!
1'. 4
"I
I.
IIF
THINC-II; THIINC-IV [9];
Results for Nine Rod Bundle
Isothermal Flow Tests
I
(
i
!o. ~),
and WOSUB
2.2
2.G
2.6
, 2.4
22
= 2.0
=LS
xL2
b-
Z LO
I
Q 0.8
C 0.6
, 0.4
U
0.2
0
0
02
0.4
06
8
LO u1
L4
L6
L8
2.0 2.2
2.4
2)
- (106Iblhr - ft
EXITMASSVELOCITY
SUBCHANNEL
MEASURED
FIGURE
__
4:
-Comparison of Measured Versus Calculated Subchannel Exit Mass Velocities for the SinglePhase Isothermal Data (COBRA-IV-I,WOSUB)
17
1.1.3.3
Conclusions
The comparisons of WOSUB results with single-phase
flow test data and results obtained by various subchannel
codes indicate the code generates results which are equal if
not even superior in accuracy.
The fully ventilated-bundle
assumption is valid for single-phase flow conditions.
.____
18
1.1.4
Results for Radially Uniform Peaking Factor Patterns
1.1.4.1
Overall Comparison
The comparison with the experimental data from GE
concentrates
upon the 2D and 2E series as summarized
Table 6. Figures 5 and 6 illustrate
in
the trends in the subchannel
qualities with respect to the bundle average quality.
are taken at the exit of the bundle.
quantities
All
The subchannel
qualities increase with the average quality, the center subchannel
(#3) being the "hottest" and the corner subchannel
the "coolest".
The side subchannel
(#1)
(#2) behaves about the same
The center subchannel quality is seen
as the bundle average.
to be consistently higher than the average whereas the quality
of the corner subchannel is lower than the average.
There
appears to be a trend such that subchannel qualities
tend to
converge to the average at approximately 5-15% bundle average
quality.
This can be attributed to enhanced mixing in the
slug-annular
transition
flow-transition
regime.
Due to the fact that this
occurs in different subchannels at different values
this effect may not occur simultaneously
of the average quality,
in all subchannels.
As Figures 5
and 6 depict, WOSUB overpredicts
the
quality in the corner channel at low values of x but underpredicts
it at high values of x.
For the 2D series the qualities
of side and center subchannels are predicted well within the
experimental
error band.
For the 2E series the center sub-
channel quality is slightly overpredicted
for x > 5%.
The
deficiency in calculating the corner subchannel quality becomes
T ___
__
___
19
H
C-1
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O
0
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2NVHDGnflS
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21
I
I
I
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/
THI
0.24
-
SUBCHANEL
3
0.20
0.16
x
Es
" 0.12
03
al
a
-~~~~---
ct
0.04
0
J
-0.04
I
0.05
0
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0.10
0.15
0.20
AVERAGE
,IrTJIT
65:
Comparison
Qualities as a
ofe
QUALITY,
WTOSUB wiith GE
unction
0.25
X
Exneriments
2E
of Bundle Averaged Exit
for Subchannel Exit
ualities
.
.
22
more apparent for this series especially for high bundle average
quality
(x =20%).
However,
this deficiency
has to be seen in
the light of the results obtained from THINC-IV
corner subchannel
[ 15 ] for the
as shown in Figure 6 for 2E2 and 2E3 as
taken from Tables 7 and
8 . As the dotted line indicates,
THINC-IV predicts the corner subchannel always "hotter" than
the bundle average,
i.e., it gives a completely wrong picture.
As the tables show, the failure of predicting
the correct corner
behavior is representative for all the other known subchannel
codes, too.
It should be kept in mind that although
the WOSUB
results are not perfect as compared to the experiments. it
still has the potential
for corrective actions.
it is hoped to increase
the gradient of the line xl
at the same time decrease
qualitatively
In this context,
=
f(x) and
that of the line x 3 = f(x) as shown
by the directions
of the arrows in the figure
below.
XCh
Xx
No
equivalent
correction
seems to work for the other subchannel
codes, because even with high mixing factors they cannot predict the substantially
lower-than-average
qualities
in the
corner subchannel, and higher-than-average qualities
23
in the center subchannel.
In fact, if mixing were made even
infinitely
large the three subchannels
would all be at average
conditions
and thus the data cannot be explained
in terms of
mixing.
The most reasonable explanations for the trends of
the data are the tendancy of the steam to move preferentially
to the center of the rod bundle and/or the presence of thick
liquid "cold" film on the unheated channel wall.
1.1.4.2
1.1.4.2.1
Detailed Subchannel Behavior and Comparison
Corner Subchannel
For the 2D seriesWOSUB with vapor diffusion model
included overpredicts the quality at low bundle average qualities,
x, and underpredicts
The same behavior
Figure 6.
it for x > 20% as can be seen from Figure 5.
shows up for the 2E-series as depicted
in
If WOSUB is run without the vapor diffusion option
it generates qualities comparable to those of the other subchannel codes such as COBRA-IV and THINC-IV.
qualities are determined
This means that
far too high in the corner subchannel.
There is no way to correct this wrong trend by changing
coefficients in the mixing models of these subchannel codes.
However, the vapor diffusion model in WOSUB can be changed such
that the corner subchannel does not lose too much vapor at
high x and gives up more at lower x.
The reason that the
built-in vapor diffusion model overemphasizes the vapor transport at higher bundle average qualitites has to be attributed
to the fact that this model as described
in [2] was fitted to
results of air-water
consisting
tests in a geometry
_II____I___·I1_IIII_1_111^1111111-sl-1
--IYDII·---
-Il_--_t--ll
I
-
of two
-
_
·
24
sized subchannels.
differently
As Lahey et al [ 7] pointed out,
mixing data stemming from these types of test sections tend to
the transport
overpredict
Thus, it must be concluded
effects.
that multi-rod bundles show a damping effect as compared
to
the data obtained from simplified test section set-ups.
Corrective actions will be made during the next round of model
improvements
in the future.
In terms of the mass flux behavior,
Figure
7 shows
for the 2D-series that WOSUB predicts overall the characteristic
behavior
lower-than-average
gradient
over the range of x.
of the computational
However,
the
It is hoped
results is too high.
though that the aforementioned corrective actions with respect
to the vapor diffusion model will cure this problem,
same behavior
as for the 2D-series is experienced
too.
The
for the 2E-
series where for x > 15% WOSUB is giving a slightly higher-
than-average result.
Again, it is thought that the correction
in the vapor diffusion model will help to move the curve back
into the lower-than-average region.
It should be noticed that both test series were
calculated
model.
taking the same parameters
in the vapor drift flux
As explained in Section 11.8.
something can be gained
by individually fitting these parameters according to test
conditions.
However,
this margin
is not very large and it
must be concluded that WOSUB's deficiencies are with the
vapor diffusion model as outlined above.
fusion WOSUB predicts
subchannel
_
__
far too low mass fluxes in the corner
as do THINC-IV
___
____
11____
Without vapor dif-
and COBRA-IV as shown in Figure
___I_·
25
_
I
__
I
I
-1
0
'A
uI
O
wl
er
-
>1
-C
s
'L
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-a
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kO- z
0
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Q11
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r=
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6
6
i
e4
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0
1e
=
oC)
26
Finally,
it must be pointed out that the well known
concept of power-to-flow
ratio which is mostly used to get a
first estimate for the thermal-hydraulic subchannel behavior
totally fails in predicting
the GE test results.
be kept in mind in interpreting
This should
the other test results in the
following sections.
1.1.4.2.2
Side Subchannel
In general,
which
the side subchannel shows a behavior
closely follows that of the bundle average.
series the side subchannel
shows a very slightly higher-than-
average quality at high x whereas in the 2E-series
the lower-than-average
In the 2D-
region for all x.
it stays in
WOSUB with vapor
diffusion model included does an excellent job in predicting
the qualitites
for both series as can be seen from Figures
5
and 6 by comparison.
In terms of the behavior
underpredicts
of the mass flux, WOSUB
the mass flux for both test series at lower x
(O - 10%), whereas it predicts
tained by the experiment
fr
It is interesting
very closely the data as ob-
x > 10%.
(Compare with Fig.
8.)
to notice that the option without
vapor diffusion gives reasonable results for the side subchannel.
1.1.4.2.3
Center Subchannel
The GE test data show that the center subchannel runs at a
higher-than-average quality and mass flux. The WOSUB results (see
Fig. 9 ) are in excellent
quantities
__
agreement with the test data for both
in the case of the 2D-series.
However,
the code
27
rt
a)
_I
v~
.I
6
I
az
s(U ri
C
,.
4:
C
;n
od
a
-J
w
Cd
t.
c
H
4
U PCd)
a:
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ILl
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o
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rr
Cd
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w~3
28
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6
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C
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Co
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41
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x
29
30
slightly overpredicts
predicts
especially
the quality of the 2E-series and under-
the mass flux for x > 5%.
It is hoped that
this trend can be reversed, once the vapor diffusion model has
been corrected.
distribution
This correction should indeed lead to a re-
of flows.
It is interesting
to note that WOSUB without the
vapor diffusion model gives closer results
the center subchannel
or the quality in
for higher values of x than does the
vapor diffusion option as compared with the experiment. This
finding supports the aforementioned reasoning, namely that too
much vapor is transferred from the corner into the center subchannel thus making it too "hot".
1.1.4.3
Comparison with Results of Other Subchannel Codes
Due to the complete documentation
of the GE-test
series, these data have been widely used by various researchers
and institutions
in order to check the validity
of their sub-
channel codes against local exit subchannel quantities.
This
is very fortunate indeed because it makes it possible to compare the results obtained by WOSUB with those generated by a
whole variety of well-known
codes.
Although
the results of the
latter show widespread differences between them, no explanations
are given for these phenomena in what follows.
considered
behind
as one group as compared to WOSUB.
this approach
ticated two-phase
Rather they are
The reasoning
is that whereas WOSUB uses a more sophis-
flow model as well as a vapor generation and
transport model, the other subchannel codes are mainly characterized by the fact that they all use the homogeneous
__
flow
31
model as the basic underlying flow model.
As a result, dif-
ferences between these codes are mainly attributable to
differences in the mixing model and their associated input
data.
What is of interest here, instead,
answer to the question
is to find an
of whether or not the introduction
of
a more sophisticated flow model results in improvements in
the interpretation
is worth mentioning
of experimental
data.
Inthis context, it
that inherent deficiencies
in the sub-
channel codes were discovered and pinpointed as early as
1971 [ 6 ].
However, until then nothing had been actually
done in the area of subchannel code development
this situation,
was introduced.
to improve
up to the point where the MATTEO-code
Despite of its appearance
new code developments.
[1]
it did not spark
Instead, as most recent developments
such as THINC-IV and COBRA-IV show, most institutions stayed
within the concepts and models already being used about a
decade ago.
This has to be considered very unfortunate
be-
cause on the other hand side trends in the thermal-hydraulic
reactor safety analysis clearly indicate the need for improved
two-phase flow models.
Indeed, these developments are well
underway and first results
ustify the efforts.
As a result,
the gap in the model sophistication between design and safety
codes widens, although
it is not clear where and how to draw
the line between these two classes,
felt that the application
yet.
Therefore,
it is
of the drift flux model is indeed
needed to bridge this gap and thereby to enlarge the range of
applicability of design codes.
.______
32
By inspection
of Tables 7 and
that the common subchannel
8
it becomes obvious
codes using the homogeneous
flow
model together with common state-of-the-art mixing models
strongly overpredict the quality of the corner subchannel. At
the same time they underpredict
by a substantial margin.
difference.
the mass flux in this subchannel
Especially COBRA-IV shows a large
In the context of the applied mixing models there
seems to be no way to reverse the trend in quality by pushing
it into the lower-than-average
region by an appropriate
choice
of input parameters to the mixing model because even infinitely
large mixing coefficients would only result in a corner subchannel quality which equals just the bundle average one.
a result,
if one accepts the experimental
As
findings - and there
is more evidence to support them today (see Section 1.9)- it
must be concluded that the flow model together with the transverse transport mechanisms employed by those codes show inherent dificiencies which are obviously unrepairable in the
context of the theory used by the codes.
This is to say,
that as long as these subchannel codes are used to analyze
encapsuled bundles where diversion crossflows are less likely,
their results are of limited value.
With respect to the side and center subchannels
the
following conclusions can be drawn from the calculational
results by these codes.
They all cverpredict the side sub-
channel quality and underpredict that of the center subchannel
to some extent.
are equally wrong
With respect to the mass fluxes the trends
especially
for the side subchannel as shown
33
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35
in Figure 10 for THINC-IV.
If at that point in time one
worries about the wrong trend given by WOSUB for the mass flux
in the center subchannel as a function
Section
of x as discussed
in
one should realize that all the other subchannel
codes are not doing better basically in all the subchannels.
This fact has been obviously overlooked
if error bands of ±10% are assigned
trends of side and center
thus far.
the details of values and
subchannel quantities
good example for this approach
Indeed,
get lost. A
is given in Figures
for the mass flux and quality results,
11 and 12
respectively,
as obtained
by THINC-II and THINC-IV, as well as in Figure 13 for the mass
flux calculated by COBRA-IV-I.
For the purpose of comparison
There is
the WOSUB results have been added into these graphs.
no doubt that they compare more favorably
to the measurements.
1.1.4.4. Conclusions
From the foregoing comparison of the results with
experiments and other widely used subchannel codes the
following
conclusions
1)
can be drawn:
The drift flux model together with the vapor
diffusion model produces data which are in good
agreement with the experimental data.
2)
The drift flux model without the vapor diffusion
model generates results which are close to those
obtained by the common subchannel codes.
3)
The widely used subchannel codes such as COBRA
and the like are unable to predict the lower-thanaverage behavior of the corner subchannel quality
_..__·__I____·
__
36
__
0.1Z
0.0
0. 4
I
I
I
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I
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1
I
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0.25
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x
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:3
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2E SERICS trSTS
i
CORNERSUSCANNEt.
.
SDE
. .....
--
1I
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1Q
i J El
i V·
W
SCAHANNNEL
fR SU8CHA N(L
C,
GE-EXP.
-. -. -_ WOSUB
O.24
m
O
-
THING IV
COBRA IV
,
0.O
0.0o
SUBCHANNEL QUALITY,
I7JURE 10:
Compariscn. Between
X
xperimental Data and
Predictions by Various Subchannel Codes for the
Individual Subchannel M-'assDeviations
Average
..-. c.
---
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1.._
from Bundle
ehavior
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39
'-
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=C
w
c
0.1 02
0.3 04
0.5 0.6 07
0.
0.9
1
L1
1.2
MEASURED
SUBCHANNEL
EXITMASSVELOCITY106Iblhr - ft2 )
FIGURE 13: Comparison of Measured Versus Calculated Subchannel Exit Mass Velocities for the Two-Phase
Data (COBRA-IV-I, WOSUB)
111111111
-
40
and mass flux as well as the higher-than-average
behavior
of the two quantities
in the center sub-
channel.
4)
There is no hope of effectively
inherent deficiency
correcting the
of these codes in the framework
of the mixing models used thus far.
5)
A model like the vapor diffusion model seems to
be necessary
to predict the trends observed
in the
data.
6)
Still existing
differences
which show up in the
comparison between the data and the WOSUB results
are consistent
in themselves,
that is to say, they
follow a logical pattern which can be attributable
to a too strong vapor diffusion transport coming
mainly out of the corner channel.
7)
The vapor diffusion model is simple in its
structure and without changing the underlying theory
can be improved very easily in order to fit the
multi-rod test data more closely.
8)
Empirical transport correlations stemming from
simplified
geometries
should be carefully
such as two-subchannel
tests
checked for their applicability
to
multi-rod geometries. The latter introduce a damping
effect upon the transverse transport.
9)
The widely used power-to-flow
to interpret
_
the experimental
_I
_·
ratio concept fails
data.
41
1.1.5
Results for Radially Nonuniform Peaking Factor Patterns
For this test series, GE ran subchannel
sampling tests
with different power on the nine rods in order to obtain a
radial peaking factor distribution, whereas the heat flux was
kept uniform in the axial direction.
The radial peaking factor
pattern is shown in Figure 14 together with the numbering
scheme of the subchannels.
As can be seen the pattern is nearly
diagonally symmetrical with the hot corner rod power being approximately
twice the cold rod power.
The test conditions
for
the three out of four runs performed by GE which are considered
in this report are summarized in Table 4.
The experimental
findings by GE [5-7] can be summarized
as follows:
1)
The hot center subchannel runs at the highest
quality in all cases.
2)
The cold side subchannel
is the lowest in quality
and generally has the highest mass flux.
For tests
3D1 and 3E1 this channel is even substantially
sub-
cooled at the exit.
3)
The hot corner subchannel runs at higher-than-
average quality and has generally the lowest mass
flux.
4)
The quality of the hot corner subchannel runs
much higher than that of the corner subchannel for
uniform local peaking conditions discussed in the
preceeding section.
It also runs higher than the
bundle average.
.___. _·__11_______1_111_Y___···LII·^.·_
I__
_
_
_
_
42
FIGURE 14
RADIAL
POWER PEAKING
PATTERN
I
AND SUBCHANNEL
NUT4BER SCHEME
_
5)
The quality of the cold corner subchannel is not
very much affected and behaves close to the corner
subchannel under radially uniform heating conditions.
Some data indicate even that the quality is slightly
higher than that in the uniform case.
6)
The quality of the hot side subchannel
than in the uniform
is higher
case and higher than the bundle
average quality.
7)
The hot center subchannel quality is higher than
that obtained without local peaking which as was
shown in the preceeding section was already the hottest
subchannel for uniform heating.
8)
The trends in mass flux are not as clearly defined
as those for the quality.
9)
With one exception the hot corner subchannel has
the least flow when compared to the uniform case and
cold corner subchannel flows.
10) The cold side subchannel has a greater mass flux
than the uniform case except at low flow and quality.
11) The hot side subchannel flow is lower than the
side subchannel
flow in the uniform case.
12) The hot center subchannel has a lower flow rate
than the center subchannel in the uniform case except
at low average flow rate and quality.
Altogether,
these findings
give a fairly complex picture of
what happens in this more realistic case.
Unfortunately, the
results obtained by GE suffer from the fact that no mass and
__1__1_1_
_
44
and energy balances were performed because not all subchannels
were sampled.
1L1.5.1. Comparison of WOSUB Results with the'Experiment
Table 9
summarizes the comparison for the three test
cases 3D1, 3E1, 3E2 for the hot and cold corner subchannels,
hot and cold side subchannels
It should be recalled
the
and the hot center subchannel.
that with the exception of the local
peaking factor pattern the test conditions for 3D1 are identical
to those of 2D1, 3E1 is identical to 2E1 and 3E2 is identical
to 2E2.
This makes it easy to refer back to the radially
uniform heated tests discussed in the preceeding section.
The following conclusions can be drawn from Table
with respect to the WOSUB results (if not
therwise stated
"WOSUB results" means with vapor diffusion):
1)
The hot center subchannel has the highest quality
only for 3E2 whereas for 3D1 and 3E! the hot side
channel shows the highest quality.
2)
The cold side subchannel is the lowest in quality
and has the highest mass flux.
The exit qualities
for tests 3D1 and 3E1 are subcooled.
3)
The hot corner subchannel runs with the exception
of that in test 3E2 at higher-than-average
quality.
In general it has the lowest mass flux.
4)
The quality of the hot corner subchannel is pre-
dicted higher for local peaking than for uniform
heating condition.
It is higher than the bundle
average with the exception
· ____
_
I_ _·_1_ 1__1__1___
_
_
of test 3E2 where it is
______ _ __ _ L___
45
-0
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46
slightly lower than predicted.
5)
The quality of the cold corner subchannel is
underpredicted
compared
to the experiment and to the
uniform case.
6)
The quality of the hot side subchannel
higher than that for the uniform case.
is predicted
Furthermore
it is higher than the bundle average.
7)
The quality in the hot center subchannel
dicted to be higher
is pre-
for the local peaking factor
pattern than without it.
8)
(Intentionally left blank for easier reference
with uniform peaking pattern.)
9)
The mass flux in the hot corner subchannel is
smaller than that obtained by the code for the uniit is smaller than that of
Furthermore,
form case.
the cold corner subchannel.
10) The cold side subchannel has a greater mass flux
for the nonuniform
case than for the uniform one.
11) The hot side subchannel flow is determined
lower than the subchannel
to be
flow in the uniform case.
12) The hot center subchannel flow is determined
to
be lower than for the uniform case.
13) Bundle average.mass fluxes and qualities are
determined by both options in WOSUB equally well and
are in excellent agreement with the data.
deviation
I_·__I__
II___
________
I
_
_
in quality shows up for 3E1.
_ I_
_______
__1_1
A small
47
By comparing
this list point by point with the list given in
the preceeding section it becomes obvious that WOSUB predicts
the same trends as obtained
experimentally.
Epecially,
it
should be noticed that it is consistent with the experimental
findings in the transition
uniform case.
from the uniform case to the non-
The deviations
observed in points 1, 3 and 4
are minor and are believed to be well within the limits of
experimental uncertainty.
Furthermore, closer agreement should
be achieved once the vapor diffusion model has been updated to
produce better agreement in magnitude for the uniform case.
In terms of the absolute
value of the individual
quantities excellent agreement has been achieved with WOSUB
expecially for the qualities, the only exception being probably
the hot corner subchannel quality for test 3E2.
it is observed that too much vapor is removed
Here again,
from the hot
corner subchannel.
For the individual mass fluxes a data-to-data comparison with the experiment reveals that WOSUB slightly overpredicts
the mass fluxes in the hot and cold corner subchannels,
in the hot side subchannel as well as in the hot center sub-
channel. The mass flux is underpredicted however for the cold side
subchannel.
Tables 10 and 11 show the results for all 16 subchannels
for 3Eland 3E2. The results shown in these tables are somewhat
different from the foregoing ones because it was tried to reach
a closer agreement with the experiment by changing the parameters.
The results obtained by WOSUB without including the vapor
diffusion model look quite reasonable with the exception of the
qualities
for the hot corner and the hot center subchannels.
The
former are determined far too high whereas the latter are too low.
______
__
48
Table
10:
WOSUB Predictions for the Individual Subchannels for
Test 3E1 with X = 0.0304 and G = 1.097 x 106 lb/ft2-hr
Subchannel #
Xch
Gch
Xch
-X
G
- G
G
1
2
3
4
5
6
7
8
9
10
11
12
I
0.096
0.113
0.066
0.045
0.113
0.084
0.029
0.014
0.065
0.028
-0.016
13
14
-0.026
0.044
0.010
15
-0.031
16
-0.027
0.773
0.846
0.949
0.900
0.854
1.016
1.213
1.115
2.16
2.72
1.17
0.48
2.72
1.76
-0.05
-0.30
-0.23
-0.13
-0.18
-0.22
-0.07
-0.54
0 .11
0.02
0.952
1.14
-0.13
1.214
-0.08
1.413
1.253
-1.86
0.886
0.45
1.122
-0.67
-2.02
0.11
0.29
+0.14
-0.19
0.02
0.16
-1.89
-0.02
1.271
1.075
-1.53
I
49
Table 11:
WOSUB Predictions for the Individual Subchannels for
Test 3E2 with
Xch
Subchannel #
= 0.096 and G = 1.077 x 106 lb/ft 2-hr
Gch
G h
ch
X ch
G
X
1
2
0.107
0.877
0.11
0.o76
o .83
-0.18
3
4
0.127
0.32
-0.11
5
6
0.177
0.211
0.882
0.957
0.979
0.888
7
0.105
8
0.073
9
0.124
0o.,069
10
11
0.103
12
0.030
o .068
0.042
13
14
0.071
0.025
15
16
----·--
-
· P
-
0.022
-
-
I---
-0.28
0.84
1.20
0.917
1.113
1.094
0.964
1.119
1.367
1.268
0.967
1.095
1.288
1.145
-0.19
o .09
-0.18
-0.15
0.03
-0.24
0.02
0.29
-0 . 10
0.07
-0.56
-0 .69
-0.29
-0.26
-0.74
-0.77
-I-
0.04
0.27
0.18
-0 .10
0.02
0.20
0.06
50
Finally,
that the experiments
it should be emphasized
clearly revealed that even for locally nonuniform heating the
hot center subchannel
corner subchannel.
this trend.
qualities
has the highest quality and not the hot
The WOSJUBdata are in total agreement with
of the
This is what counts although the magnitude
as determined
by the code are not yet in perfect
agreement when compared to the experimental findings.
However,
there is no doubt that this can be fixed by corrective measures
in the vapor diffusion
power-to-flow
model.
Again, the data indicate that the
ratio concept fails to estimate
the correct trend.
11.5.2 Comparison with Other Subchannel Codes
Only two sources of information
could be found to
compare the test series "3" and the WOSUB results.
Fortunately,
both deal with highly regarded subehannel codes, namely
COBRA-IV-I and THINC-IV.
numbers are available
Whereas for the former the individual
only graphs can be given for the latter.
Tables 12a,b and 13 summarize and compare the COBRA-IV-I
results with both experiments and WOSUB results.
A point-to
point comparison with the list of experimental findings given
in Section
reveals that COBRA-IV-I determines the hot corner
subchannel having the highest quality which totally contradicts
the experiments.
code determines
(Point
in Section
1.a)
the
he cold corner subchannel as having the lowest
quality which contradicts
point 2 in Section 11.5. As a result
it fails to predict exit subcooling
in test case 3D1 and naturally
for the cold side channel
does not agree with point 5.
All other points are seemingly satisfied.
·_
Furthermore,
____
By recognizing these
51
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54
deviations from the experimental findings it must be concluded
that COBRA-IV-I
fails to predict the main feature originating
from the tests, namely that despite local peaking
center subchannel still remains the hottest.
the hot
As was observed
in the uniform heated case no remedy exists in the framework
of the applied mixing model theory to reverse the trend as
predicted by COBRA-IV-I.
As a result it must be concluded that
WOSUB is superior, because not only are the trends predicted
correctly but there are corrective measures
effect that the magnitude
available
to the
of the results come into closer
agreement with the data.
Figures15 and 16 show the comparison between THINC-IV
results and the test data for quality and mass flux, respectively.
For convenience,
WOSUB results are added into these
figures to more easily comprehend differences
in the codes'
predictions.
__________I______II____
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57
16-Rod Columbia Test Bundle Experiment
1.2
1.2.1
[ 8 ]
Introduction
Simultaneous measurements of flow and enthalpy were
made at the exits of two subchannels
in a sixteen rod electri-
cally heated full-scale bundle of a typical LWR fuel rod geoThe tests were carried out for both subcooled and bulk
metry.
boiling conditions.
findings
The authors compared their experimental
with predictions
by the COBRA-II subchannel
in order to assess the code's applicability
possible
and to determine
Therefore,
the turbulent mixing at the same time.
code [ 16 ]
it is now
to not only compare WOSUB with the test data but also
to another subchannel
used for comparing
code.
the same test data were
Fortunately,
the COBRA-IIIC/MIT
code
Liu [ 18]
17].
reported this comparison which allows a comparison of WOSUB with
a more recent version of the COBRA-code family with regard to the
Columbia tests.
1.2.2
Description
Figure
of the Bundle and Test Conditions
17 shows the layout and the dimensions
rod bundle cross section.
The power profile
of the
is uniform in the
axial direction but varies radially as indicated
in the figure,
i.e., two rows of rods have a peaking factor of 1 whereas the
other two rod rows have a peaking factor of 0.8.
Obviously,
the unequal heating results in a slight power tilt.
are centered by three short longitudinal
The rods
fins inside each
cylinder and are designed to give minimum flow disruption.
Spacer grids are located at 10 inch intervals
from the end of the heated lengths.
PII.I
I
_ I
IIP-I-·^--I
--
starting
7 inches
Flows and enthalpies
-- I ·.
11
were
58
m
A
I
II
..
u^_@.
-
..
'tIIIAi4c.L
^^..^..^._.
CERAMJIC
LINER
li
M
93
In
C%
I
lB
i
2.333 in.
R03 OUTSIE CIAMETER
0.422 n.
0.555 in.
0.:;3 in.
0.;33 in.
RC3TO '¢;ALLt
RODTO tRCO,
SAC,;;G
TOTA Fr.o , ARZA
W!ISMIAN;4 AREA
G.C0.!3 ft2
YOT ;DS Hi
EAT[
CC In.
LE4GCTH
FIGURE 17:
CJ"Irik!aa
niPvetzy IC-Rcd T,'st S-cm;-rr/
"-
59
measured in the cross-hatched center subchannels, denoted as hot
and cold subchannels
in Figure
17 , respectively.
The test
conditions covered by the experiments are summarized in Table 14.
1.2.3
Results of the Experiments
The results of the experiments can be summarized as
follows:
1)
In subcooled and bulk boiling a significant flow
redistribution is observed.
2)
The hot center subchannel
experiences
the change
before the cold center subchannel.
3)
Both hot and cold center subchannels
show a higher
than bundle average enthalpy behavior with the former
having the largest deviation.
4)
In all cases, the initiation of bulk boiling
curred in the center subchannels
accompanied
oc-
by a
relatively sharp decrease in the flow, due to the
increase in local pressure drop and void volume.
In-
dications are that this reduction finally slows down
and that even a change in direction
occurs once the
outer channels start bulk boiling (compare findings
by Bayoumi et al [ 19 ]1in Section 1.9).
5)
Subcooled boiling is an important phenomenon
during redistribution.
The data indicate that as
much as 30% flow reduction occurs before zero quality
is even reached.
6)
The subcooled flow redistribution is more signifi-
cant the higher the heat flux and the lower the
60
Pressure
500 and 1200 psia
Average Bundle Mass Flux
1 x 106;
Inlet Temperature
172F
Average Heat Flux
0.384 x
2 x l0 ;
Table
14 :
lbm/hr-ft
to 484°F
O6;
0.56 x 106;
0.967 x 106
Tranverse Heating Ratio
3 x 10
Colder/Hotter
Btu/hr-ft
:
0.86
Colder/Average:
1.02
Hotter/Average:
1.08
Test Conditions
2
for
the Columbia 16-Rod Bundle Tests
- --- I--------
- -
---~- --"----
------- ------- ----- -
- ---------- --- ---
--
61
pressure because of the strong increase in void formation and two-phase frictional pressure loss with
increasing heat flux and decreasing pressure.
In conclusion the experimental results indicate that the inner
subchannels are hotter than average, that strong redistributions
occur and that subcooled boiling is an important contributor
to this phenomenon.
1.2.4
Comparison of Columbia Tests with GE Tests
In the context of this research
it is of general
interest to find out whether the Columbia tests support and how
they compare with the experimental
findings by GE.
In general,
the trends in the data as observed by the Columbia team agree
with what has been found by GE, the only exception being that
the GE test data show little effect of heat flux on the center-
subchannel flow rate or of the bundle average flow rate on the
subchannel quality.
On the other hand, the center-subchannel
quality was found to increase when the heat flux was increased.
In order to comprehend
these differences
it must be recalled
that the Columbia tests were primarily performed with subcooled
exit conditions.
1.2.5
Comparison of COBRA-II with the Experiments
As already indicated in Section 1.2.1, Castellana and
Casterline
8 ] compared their test data with predictions by
COBRA-II with the objective of assessing the accuracy of subchannel codes.
It is interesting
to see what these authors
found in 1972 in order to compare it with what exists to date.
At this point it should be recalled
that COBRA-II already
62
contained the Levy subcooled boiling model [ 20].
In addition,
it should be remembered that energy and momentum transport in
the non-boiling regime is mainly due to turbulent transport
whereas in the subcooled and bulk boiling regimes the additional
transport phenomenon of gross diversion of flow comes into the
picture either modeled as a mass-to-mass (COBRA-approach) or
volume-to-volume exchange (WOSUB-approach). It becomes obvious
then that a clear cut between turbulent and gross diversion
(diffusion) phenomena is dependent upon the appropriate selection of two-phase correlations. The results of the comparison
performed by Castellana
and Casterline can be summarized as
follows:
1)
A mixing coefficient
of zero, i.e., no turbulent
interchange, results in flow reductions and positive
enthalpy deviations which are greater than experimentally found.
2)
A value of
somewhere between 0.01 and 0.02 gives
reasonable predictions for the hot center subchannel
up to the point of bulk boiling quality at the
channel exit.
3)
The recommended
value of
in point 2 fails to
predict the behavior of the cold center subchannel.
Instead for this channel a value of
somewhere be-
tween 0.0 and 0.01 should be selected.
4)
Subcooled boiling initiates earlier than predicted.
This may indicate an inadequate void model or the
failure of the donor cell approach for enthalpy exchange in the subchannel codes, because
_
___
__
in reality the
63
fluid in the gap region between two subchannels should
be relatively hotter.
5)
The selection of an appropriate and accurate two-
phase flow pressure drop multiplier seems to be
important.
6)
The COBRA-II results are unable to consistently
match the test data for one selected
qualities above -5%.
B for average
The overall agreement is indeed
fairly unsatisfactory.
7)
Some data suggest even a negative
As a result of the aforementioned
were able to really Justify the validity
8.
findings
of COBRA-II
the authors
only for
the non-boiling regions whereas for subcooled and low bulk quality
boiling the subchannel code results have to be taken with care,
especially
due to the inadequacy of using a constant turbulent
mixing coefficient despite of wide variation of coolant conditions into the subchannel
a.
codes.
8 should be allowed to vary both axially and trans-
versely, to account for mixing rate differences in the
single-phase, subcooled boiling and bulk boiling
regions.
b.
At higher qualities,
the possibility
of prefer-
ential transverse phase transport, namely different
turbulent transport rates of the liquid and gas phases
should be considered.
These recommendations
are certainly good advice in light of the
comparison with COBRA-II.
The question then is whether this
advice has been taken seriously enough by industry and
institutions which developed and refined subchannel codes until
then.
The general answer to this question
exception being
the MATTEO
[
is no, with the
1 ] and thus the WOSUB codes.
Especially, the COBRA-code family has been improved in the
meantime without consideration of the aforementiond recommendations
and indications
are that the same is true for the
proprietary codes of the vendors.
COBRA-IV code
Only the recently published
gives the user the opportunity
now to provide
as function of quality.
a table input to the code with
The
reluctance of industry and institutions to meet the two requirements
may be partly explained as follows:
1)
Most well-known
PWR analysis
subchannel
codes were designed
with the implication
for
that for these
analyses only the non-boiling and subcooled boiling
regions need to be covered.
2)
The experimental
data base is not broad enough to
allow the specification
of
as function of the flow
regimes.
However, in view of what is done and what is available to date
both arguments
do not hold any longer.
First of all, the same
subchannel codes which have been thoroughly checked and approved
in the subcooled boiling regime are applied for analyzing severe
transients which undoubtedly lead to qualities far beyond those
even covered by the Columbia tests although it was noticed that
the methods already fail to predict those where the bundle average
exit quality approaches zero.
Secondly, there has been generated
enough experimental evidence in the past which supports the GE
and Columbia findings.
Even if these are considered to be not
__
65
sufficient
in general they would have justified at least the
implementation of more flexible mixing models as indicated above,
with the understanding
to improve the input parameters
as more experimental evidence becomes available.
has not been done thus far indications
as soon
Because this
are that even to date
people are busy matching data with the wrong models and concepts
al-
trying to squeeze out and argue about the third digit in
though this is totally fruitless in view of the evidence shown
above and in what follows.
In contrast, when the recommendations
a) and b) are
compared with what has been incorporated into the MATTEO [ 1
and the WOSUB-codes
[ 2 ] the following
conclusions
can be
drawn:
1)
By virtue of the drift flux and vapor diffusion
both recommendations are accounted for.
2)
of the code only
Although the present version
contains the basic formulation
of the drift flux model
as it was known in 1973, it has the potential
for
improvements by incorporating recent correlations for
annular and mist flow developed
This flexibility
In conclusion,
by Ishii et al [21,22].
is not available
it can be expected
in the other codes.
that WOSUB should at
least follow the trend better than the other subchannnel codes.
1.2.6
Comparison of WOSUB with the Columbia Experiments and
COBRA-IIIC/MIT
Figures 18 and 19 show the mass flux deviations
from
bundle average as functions of the bundle average exit qualities
for the hot and cold center subchannels,
respectively.
___
A
r
I
I
1
HOT CHANNEL
o.1
-~-·-Z%
Is
0.
\\
%
C
0
3' 0.02
0
- 0.1
= 0.01
0
-
o.2.
WO c
-a3
-. -
CO]
0
EX]
I
0
I
I
-0.2.
-0.3
I
I
0
-0.1
8 uw 4 le
A verage
QuGi;ty
ITCIJ.E 18: Mass Flux
Hot Center
Deviation
Subchannel
as a Function
Avere
s--
----------------------
_
-----^---·l··r·-----
from Bundle
.
4vera;e
of
he Bundle
Qualitv
.
_~~~~
-
II---------
for the
-
67
II
I
I-
I
COLD CHANNEL
0.1
p~~~~~~~~~
0.05
W
0O
0
P 0.01
-0.1
-O.2
0
WOSUB
COBRA-3C [18]
--.0
EXPERIMENT
I
I
I
_ 1v.' A
-
_ n
-
n
j
s"C
-_
I
I
-l
O.
-"
-
BUNDLE A VERA GE
QLJAL Ir
Flux Deviation from Bundle Averaze for the
Cold Center Subchannel as a Function of Bundle
FIGURE
19:
'lass
Average Exit
uality
68
«
O
_
I
I
I
i
I
G-G
.'\
0.
\
®
*_
(
O.
I
- 0.
(
- 0.2
POT -CIANNEL
e
-a
COLUMBIA DATA
I
WOSUB RESULTS
-- -
COBRA-3C RESULTS
I
-0o.
I
- o.2
-0.3
!
-0o.
I
I
O.
0.1
I
0.2
SUBCHANNEL QUALITY
i7GURE 20A: MlassFlux Deviation from Bundle Averare for
Hot Center
---~-
--
Subchannel
-----------
as a Function
the
of its Exit quality
69
_
_
_ __
I
I
'
I
I
I
G-G
o.l
----
fB
O~~
O.
-
.
-0o.1
-02.
COL
COLUMBIA
®
DATA
WIOSUB RESULTS
-0.3
COBRA-3C RESULTS [183
-.--
I
-0.+
- .3
-!
.
I
-O.1
. I..
0
0.1
.
0.2.
SUBCHAUNEL QUALITY
FIGURE 21B:
Mass Flux Deviation from Bundle Average for the
Cold Center Subchannel as a Function of its Exit Quality
70
comparison with the data points reveals that the results obtained
by WOSUB follow closely the trends given by the data in both
subchannels over the whole band width of quality variations.
The predictions
by WOSUB even indicate the reversal
flux deviation at
higher qualities
of the mass
in the hot center subchannel.
However, whereas the WOSUB predictions are in magnitude fairly
close to the test data in the highly subcooled boiling regions
the curves
show a systematic nearly constant and parallel
to the left of the data points.
The off-set is smaller for the
cold channel than fcr the hot channel.
The reason for this disare pre-
is that the mass fluxes in both subchannels
placement
dicted too low for a given bundle average exit quality.
fact this systematic
compariscn
shift
trend has been already observed
In
in the
with the GE test data for uniform radial peaking
that hot and cold center subchannels
are surrounded by four
equally heated rods, respectively).
As already mentioned in
Section 1.1.5 the
(note
apor inflowinto this channel has to be reduced
by modifying the vapor diffusion model.
This change should
lead to an even closer agreement with the data points in the
future.
A more stringent
the mass flux deviation
criterion
for comparison is to plot
versus the subchannel exit
uality.
Figures 20 and 21 summarize and compare these results.
Again,
the inability of COBRA-IIIC/yjIT to predict reliable results
for x > 0 becomes apparent, whereas WOSUB follows fairly
closely
the experimental
data
oints.
By comparing the predictions obtained from COBRAIIIC/MIT
1
C-
[ 1S ] with the data points and the WOSUB results as
------rr·1-o--L-------·----·--
·-- rr-----
I
--___-·i___l___l_.I_
__
71
well as with the earlier published
COBRA-II results
[ 8 ] the
following conclusions must be drawn
1)
The predictions by COBRA-IIIC/MIT are seemingly
more off than those by COBRA-II although it contains
an improved transverse momentum equation compared to
the latter.
2)
as recommended
Varying the value of
by the
Columbia team does not help to match the data.
3)
The predictions
do not follow the trend for
x av > 0.
4)
Indications
are that by setting B = 0 even would
not help instead the trends of the data and the predictions
call for B's smaller than zero, i.e.,
negative values!
The aforementioned evidence is fairly discouraging
for COBRA-IIIC-users.
Indeed computational results for condi-
tions where xav > 0 should be accepted with very great caution.
In all fairness
it should be noticed that one of the
reasons for statement 1 above is that at the time when these
data were produced Levy's subcooled boiling model did not work
properly.
As was mentioned
in point 4 of Section 1.2.5. this is
however absolutely necessary to obtain the correct flow reduction at least in the subcooled boiling regime.
This point
will be checked out with the corrected version of the subroutine in the near future.
the accuracy
However,
of the COBRA-IIIC/MIT
beyond that of the COBRA-II
_ --1_-111111····111111
it is not believed
predictions
results.
that
will go far
72
1.2.7
Conclusions
The evidence produced in this chapter clearly indi-
cates again the superiority
of the WOSUB code in predicting
correct trends of the Columbia
tests.
the
It has been also shown
that the code is equally well performing
in the non-boiling
and
subcooled boiling regimes as compared to the accepted COBRA-II
and COBRA-IIIC codes.
dictions
Systematic differences between the pre-
and the data can be attributed to the yet not optimized
vapor diffusion model.
This fact was already discovered in the
comparisons described in the foregoing chapters.
code behaves in a consistent and pre-predictable
As such the
way which is
very important to know in order to guide future improvements.
More comparative runs are needed for completeness.
Especially,
it is suggested to go even higher with xav in order to follow
the reversed
trend in the mass flux deviation.
The reason
for
this suggestion becomes more obvious when Bayoumi's results are
discussed
I
in Chapter i.9.
_
__
___
I
73
1.3
Planned 9-Rod Studsvik Test Bundle Experiments with
Strong Power Tilt
1.3.1
Introduction
In 1971 a series of tests were described
and Kellen
9
by Gustafson
in a 9-rod, square array test section with a
very high radial power gradient.
As shown in Figure 22 it was
planned that the power generated in the first row of rods is
zero, 0.9 in the second and 2.1 in the third row.
results are given in [9
Although
from runs in different loops for
the development of the water film, and void needle
meters the experiments themselves were never really carried
out.
Rather a modified
set of tests as described
chapter were actually performed later on.
in the next
Still, what makes
the planned tests valuable in the context of this comparison
here is the fact that during the planning
stage of the experi-
ment a unique collection of results from subchannel codes was
put together by Flinta
[ 12 ] in order to perform a benchmark
test.
data are published
Some additional
in [ 9
together
with a complete list of results from the various participants.
According to the time when these predictions were handed in all
participating codes must be considered as subchannel codes of
the 1. generation.
The comparison which follows will include
results from the following codes and specific proprietary versions thereof by the various institutions:
1)
COBRA-AE (AB - Atomenergi Version of COBRA-I)
2)
COBRA/KTH (Royal Institute of Technology (Sweden)
version of COBRA-I)
3)
I
COLIBRI (Asea - Atom version of COBRA-I)
_I
_
_
____
74
5'i.?
or-
-
/ SlMME TRY
REL. 14EAr FLUX
Pla.h4o Pe.orme.l
I'
HEATED
16G.3
LENGTH
FLOW AREA
I---
-----··--------I--
22:
--
1j--12,2
:
1.5
o
(o)
0.9
(0o.3)
2.1
(0.7)
25s-
M
: 1625
x 10 -3
2
M
Layout of Pl-anned9-'od Studsvk Test Bundile
----
--
-----
---
-
---
-------
-------
75
4)
DYNAMIT (INTERATOM, Germany)
5)
FLICA/CENG (Centre d'Etude Nucleaire de Grenoble,
France)
6)
HAMBO/AE (AB - Atomenergi version of HAMBO,
Sweden)
7)
HAMBO/Ris8 (Belgo-Nucleaire version of HAMBO,
Belgium)
8)
THERMOHYDRAULIC (KWU, Germany)
9)
TRASAM (AB -Atomenergi, Sweden)
This list shows a broad cross section of participants
of different nations.
versions
The individual features of the various
of COBRA-I and HAMBO ar not known but it will be in-
teresting to see how they compare with each other and to WOSUB
in the final results.
At this point it should be remembered
that most of the codes listed above are still around and in use
presumably with various updated versions of the different
transport phenomena.
What has been certainly kept though is the
basic underlying model.
The objective of this chapter is to analyze and com-
pare the WOSUB predictions with those obtained by the various
codes as given in [ 9
.
Because of the severity of the planned
tests one can expect more pronounced
redistributions
transverse
effects and
as those observed by the Columbia tests.
It is
of special interest then to run WOSUB with both options in order
to more easily comprehend how especially the vapor diffusion
model will cope with the strong power gradient effects.
The attention will focus particularly upon the quality
and mass flux distribution
across the bundle at the exit in order
__
76
to establish a direct comparison with the previously collected
9
data in
.
that final con-
it must be fully understood
clusions can be only drawn if experimental evidence becomes
In this respect the conclusions
available.
drawn in the
following sections must be considered tentative and relative
to the computational
1.3.2
Description
predictions.
of the Geometry
and the Test Conditions
The layout of the bundle and the subchannel numbering
scheme are shown in Figure 23 whereas the test conditions
in Table
summarized
15.
are
The heated length is 1.5 m with an
axially uniform power distribution.
The test conditions were
planned to consist only of changes in total bundle power in
keeping all other parameters
such as mass flow rate, pressure
and subcooling constant.
1.3.3
Comparison of WOSUB with Other Subchannel Codes
Due to the symmetry of the bundle with respect to
the local peaking pattern only half of the bundle needs to
be analyzed
by the code and consequently
the analysis
reduces
to eight subchannels.
Tables 16 through 21
summarize all available infor-
mation about qualities and mass fluxes together with the WOSUB
results as function of total bundle power for subchannels 1
and 2, 5 and 6, and 7 and 8.
The form of the presentation,
namely in terms of deviations from the bundle average behavior
as
Deviation (
= ) k(I)
k
__ ________I _____
__1___1____
_ _ __ _I_
____
ak(Z)
A
k
k
77
0
0,90
2,10
5, 9
FIGURE 23
NUMBER SCHEME FOR THE SUBCHANNELS OF THE
PLANNED STUDSVIK TEST BUNDLE
--------
·
-- - --
- ---
78
TEST
POINT
AVERAGE
MASS-FLUX
(kg/sec-m2 )
PRESSURE
(Bars)
POWER
(KW)
DEGREE OF
INLET
SUBCOOLING
AVERAGE EXIT
QUALITY
X
e
(0C)
SW-346
70
1000
346
-10
.10618
70
1000
462
-10
.15347
70
1000
870
-10
.31980
(V)
sw-462
(V)
SW-870
(V)
Table 15:
Test Conditions
for the 9-Rod
Bundle with Tilted Power Distribution
-
---
--
----
- --·
--
--
- -----
---
79
Table 16
AX/X(%),
POWER(KW)
CODE
.
mm {
.I
CHANNEL
m.
l-
-66
-91
3466
COBRA/KTH
325
360
346
HAMBO/Ri s
THERMOHYDRAULIC
WOSUB(v.d.)
-115.
346
WOSUB( no v.d.)
-117.23
462
COBRA/AE
DYNAMIT
FLICA/CENG
HAMBO/AE
494
431
462
X/ ( %)
CHANNEL 2
1
-6 3
lo. 6
9.
-90
-87
4
,
-120
-120 11
10.6
-120.75
10.6
-60
15.6
-120
16.8
13
-83
15.4
-87
15.4
462
TRASAM
WOSUB(v.d.)
-o6
-106
-111
15.34
462
WOSUB(inio v.d.)
-110 .42
-113.0
15.3
686
COLIBRI
-84
-86
870
HAMBO/BN
-67
-67
870
WOSUB(v.d.)
-86
-100
31.9
870
WOSUB(rno v.d.)
-103
31.9
----
462
I
30
i-
-102
COMPARISON OF RESULTS FOR SUBCHANNEL 1 AND 2 QUALITIES
FROM VARIOUS SUBCHANNEL CODES WITH WOSUB (VAPOR DIFFUSION)
AND (NO VAPOR DIFFUSION)
----
--
L
80
Table 17
POWER(KW)
CODE
AQ/Q(%)
AQ/Q(%)
CHANNEL 1
CHANNEL 2
346
COBRA/KTH
+12
+18
325
HAMBO/Ris8
+29
+36
360
THERMOHYDRAULIK
+28
+39
346
WOSUB(v.d.)
- 4.9
+12
346
WOSUB(no
-
+12
462
COBRA/AE
+20
+26
494
DYNAMIT
- 7
+ 8
431
FLICA/CENG
--
--
462
HAMBO/AE
+44
+51
462
TRASAM
+ 7
+18
WOSUB(v.d.)
+ 9
+26
1462
WOSJUB(no v.d.)
+ 6.1
+24
686
COLIBRI
+53
+77
870
HAMBO/BN
+25
+36
870
WOSUB(v.d.)
-42
+79
870
WOSUB(no
+50
+72
OF RESULTS FOR SUBCHANNEL
1 AND 2 MASS
|
462
COMPARISON
v.d.)
v.d.)
5.9
FLUXES FROM VARIOUS SUBCHANNEL CODES WITH WOSUB
(VAPOR DIFFUSION ) AND (NO VAPOR DIFFUSION).
___
__._
__._
___
__
81
Table 18
aX/X(%)
POWER
___
CODE
AX/X(%)
CHANNEL
CHANNEL
5
346
COBRA/KTH
+33
+47
325
HAMBO/Ris8
+62
+77
360
THERMOHYDRAULIK
+i00
+143
346
WOSUB(v.d.)
+58
+151.25
346
WOSUB(no
+654
+120.85
462
COBRA/AE
431
DYNAMIT
+74
+136
462
FLICA/CENG
462
HAMBO/AE
462
TRASAM
462
WOSUB(v.d.)
+56
+175.62
462
WOSUB(no
+72
+132.61
686
COLIBRI
+94
+132
870
HAMBO/BN
+43
+53
870
WOSUB(v.d.)
+18
+297
870
WOSUB(no v.d.)
v.d.)
v.d.)
.
.
~
+197
+93
~
6
-
-
COMPARISON OF RESULTS FOR SUBCHANNEL 5 AND 6 QUALITIES
FROM VARIOUS SUBCHANNEL CODES WITH WOSUB (VAPOR DIFFUSION)
AND (NO VAPOR DIFFUSION)
_,~
.
.1
_
1~-·
82
Table 19
AQ/Q(%)
POWER(KW)
CODE
CHANNEL
AQ/Q(%)
CHANNEL
5
346
COBRA/KTH
-9
-7
325
HAMBO/Ris8
-17
-13
360
THERMOHYDRAULIK
16
-20
346
WOSUB(v.d.)
-8.9
346
WOSUB(no v.d.)
-10.9
462
COBRA/AE
-!1
-11
431
DYNAMIT
-15
-11
462
FLICA/CENG
--
--
462
HAMBO/AE
- 14
-10
462
TRASAM
-12
-5
462
WOSUB(v.d.)
-13
-20
462
WOSUB(no
-I6
-14
686
COLIBRI
-30
-27
870
HAMBO/BN
-18
-10
870
WOSTB/(v.d.)
-11
-47
870
WOSUB(no v.d.)
-27
-41
COMPARISON
v.d.)
OF RES-JLTS
FROM VARIOUS
FOR SUBCHANNEL
-9.9
-5.5
5 AND 6 MASS FLUXES
SUBOHANNEL CODES WITH WOSUB "VAPOCR DIFFUSIO
AND (NO VAPOR DIFFUSION)
"
-~II
I
--- s,*.--,----·p·
rp·-r·s---llslr^--------·
_aa
-_--
----
__
6
83
Table 20
AX/X(%)
CHANNEL 7
CODE
POWER (KW)
AX/X(%)
CHANNEL
+67
+83
HAMBO/Risb'
+115
+134
366
THERMOHYDRAULIK
+165
+206
346
WOSUB(v.d.)
346
WOSUB(n.
462
COBRA/AE
494
DYNAMIT
+150
+224
431
FLICA/CENG
+127
+154
462
HAMBO/AE
462
TRASAM
462
WOSUB(v.d.)
462
WOSUB(no v.d.)
+138.41
+190.45
686
COLIBRI
+179
+226
870
HAMBO/BN
+97
+108
870
WOSUB(v.d.)
870
WOSUB(no v.d.)
346
COBRA/KTH
325
v.d.)
+40.31
+147.05
+135.19
+183.04
--
8
+80
__
.
-+27.06
-4.5
+150
192
+141.7
+93
+245
COMPARISON OF RESULTS FOR SUBCHANNEL 7 AND 8 QUALITIES
FROM VARIOUS SUBCHANNEL CODES WITH WOSUB (VAPOR DIFFUSION)
AND (NO VAPOR DIFFUSION)
84
Table 21
POWER(KW)
AQ/Q(%)
CHANNEL 7
CODE
AQ/Q(%)
CHANNEL
346
COBRA/KTH
-19
-18
325
HAMBO/Risb'
-29
-26
360
THERMOHYDRAULIK
-30
-29
346
WOSUB(v.d.)
-15.9
-16.9
346
WOSUB(no
-26
-20.9
462
COBRA/AE
-23
-23
494
DYNAMIT
-33
-33
431
FLICA/CENG
-33
-34
462
HAMBO/AE
-28
-25
462
TRASAM
-28
-24
462
WOSUB(v.d.)
-19
-22
462
WOSUB(no v.d.)
-31
-27
686
COLIBRI
-48
-48
870
HAMBO/BN
-34
-30
870
WOSUB (v.d.)
-28.9
-18
870
WOSUB(no v.d.)
-33
-43
v.d.)
COMPARISON OF RESULTS FOR SUBCHANNEL 7 AND 8 MASS
8
MASS FLUXES FROM VARIOUS SUBCHANNEL CODES WITH WOSUB
(VAPOR DIFFUSION) AND (NO VAPOR DIFFUSION)
85
where k(I)
I
x or G
subchannel number
bundle average exit quantity, x or G,
was necessita .ted by the fact that the data of the other
ccides are given as such in
subchannel
9
.
All WOSUB
results have been generated by using the standard parameters
as supplied
Unfortunately,
.n th,e code.
some of the results
of the other subchannel codes were obtained for different
power levels.
unable
In addition, some participants were either
or not willing to provide the information
for all
subchannels. As a result, the comparison is not as complete as
it could be.
Nevertheless,
it can be considered
as being the
first of its kind and the data provide enough information for
getting some ideas about general trends.
By comparing the results for the bundle-average
qualities as listed in the third column of Table 16 it can be
concluded that all codes give equivalent answers.
are due to different
Differences
powers used in the individual predictions.
With respect to the local quality and mass flux
predictions it is noticed that tremendous differences exist not
only between different codes such as COBRA and HAMBO but
what looks especially
disappointing
the same code by different
larger discrepancies.
of
is that the application
institutions
leads to seemingly
even
Especially disappointing is that already
large differences between the codes' results exist for channels
1 and 2 which are essentially subcooled for all powers considered in these tests.
____··I____
The general trends which can be seen
___
86
from Table 16 are:
1)
The deviation in quality from bundle average is
slightly smaller for the cold corner subchannel than
for the cold side subchannel.
2)
Increasing the total bundle power leads to a
decrease in the deviation.
Both trends are predicted
by both options in the WOSUB code, too.
The actual
numbers show that WOSUB overall comes up with larger
deviations than the other codes.
By comparing the results from WOSUB with vapor
diffusion model with those without accounting for vapor diffusion it should be recognized that the former approaches
nicely the latter in the subcooled boiling regime where the
vapor diffusion is indeed negligible.
This is very interesting
because it shows that the code can be safely used with the
vapor diffusion model even in this region without forcing
the user to take special precautionary
measures.
By comparing the mass fluxes as given by Table 17
for subchannels i and 2 it becomes apparent that codes which
predicted
about
he same deviations
in quality show huge dif-
ferences in their mass flux predictions (see for instance
HAMBO/AE
and TRASAM for 462 KW).
In general,
the following
trends are observed in the data for the mass flux deviations
from bundle average:
1)
They are smaller for the cold corner subchannel
than for the cold side subchannel for all power levels.
2)
The deviations
in the subchannel mass fluxes from
bundle average increase with increasing power.
1
_ ___
·I
__
_
_
_
_
_
_·
87
Both WOSUB options do predict these trends.
The agreement
between WOSUB and some of the other codes seems to be better
for the mass flux predictions than for those of the quality.
Table 18 and 19 show quality and mass flux deviations
from bundle average for subchannels 5 and 6.
Both channels
are characterized by higher-than-average qualities where the
center subchannel shows the largest deviations increasing with
total bundle power.
The quality deviation of the side channel
decreases with increasing power as predicted by WOSUB with the
vapor diffusion model.
Without including the vapor diffusion
model the results show a similar behavior than those of the
other codes, namely an increase of quality.
It should be
noticed that the differences even between the other codes are
as high as 300%.
As with respect to the differences
in the
WOSUB result due to the different options it becomes clear
from Table 18 that the vapor diffusion model gives higher
deviations
for the center subchannel but lower ones for the
side subchannel than does the option without the vapor diffusion model.
Table
19
shows the mass flux data for the same
subchannels. Obviously, the mass fluxes are lower-than-average
for both subchannels.
All codes predict that.
Again, the
agreement in the mass fluxes seems to be closer in general
than that in the predicted qualities.
At lower power WOSUB
with vapor diffusion model predicts lower deviations than the
other codes.
At high power level this trend is reversed
the center subchannel.
_____
for
It should be noticed that the other
88
subchannel
codes predict
in general larger deviations
for the
side subchannel.
Table 20
summarizes the quality deviations for hot
corner and hot side subchannels. Both are naturally higherthan-average.
In fact, all subchannel codes including WOSUB
without vapor diffusion model, however with the exception of
the vapor diffusion model predict channel
and channel 7 being the next hottest.
being the hottest
The trends indicated by
the results of these codes seem to show an increase in quality
with total bundle power.
In contrast, WOSUB with vapor dif-
fusion does not predict channel 8 being the hottest.
Further-
more, the deviation from bundle average decrease with increasing
power.
In case of the hot corner subchannel this even leads to
a lower-than-average quality at the highest power considered
here.
On the other hand, WOSUB without vapor diffusion is in
substantial
agreement with the results of the other subchannel
codes.
Finally, Table 21 shows the mass flux deviations
bundle average for subchannel 7 and 8.
from
WOSUB with vapor
diffusion predicts that the mass flux deviation decreases with
increasing
quality.
total bundle power, i.e., increasing bundle exit
The reverse
is predicted
for channel 7 where the
deviation increases.
1.3 .4
Conclusion
As was the case in the foregoing comparisons
with
the experimental evidence, WOSUB with vapor diffusion model
included predicts again the center subchannel being the hottest
11111_
__
_
_
__
_
89
in contrast to the other subchannel
hot side channel being the hottest.
codes which determine
However,
the
it was clearly
shown that all these codes failed to correctly predict the
trends especially for positive bundle average exit quality.
Therefore,
there is no reason to believe that these codes are
correct under these circumstances.
Rather, the WOSUB results
should be trusted which proved to be reliable
comparisons.
emphasis
However,
in the foregoing
it is admitted that due to the over-
of the vapor transport
from the corner and the side
subchannels to the center subchannel the latter may be determined to be too hot.
This has been shown to happen
in the
foregoing chapter and should occur even more pronouncedly under
these circumstances with the large power gradient involved.
Furthermore,
it can be assumed that the hot channels
are in
annular flow for the higher of the power levels considered
here.
Due to the fact that the drift flux model incorporated
into WOSUB does not contain information
concerning
the two-
phase annular flow regime, this may result in another source
of uncertainty.
Despite these shortcomings it is believed
that WOSUB more correctly predicts the trends whereas with
respect to the magnitude
of the data it is suggested
first to
correct the vapor diffusion model such that it more closely
predicts
the GE and Columbia
tests and then to apply again to
the Swedish test conditions.
In order to more easily comprehend the various trends
observed by both WOSUB options for the individual subchannels
Table
22 summarizes
the finding of the computer runs described
-.
IIILIXII-
I
sil
__i
90
in this chapter.
In addition, Figures 24
through 26
display some of the trends which have been discussed in detail.
Especially helpful for understanding the general trends is
Figure 26
where
x/x is plotted as function
of
G/G.
In summary, it becomes obvious again that the concept of
power-to-flow ratio fails to predict the hottest subchannel.
This was already found in the previous
heating conditions
less severe tilted
and is also confirmed here.
Table 22 summarizes
the trends in quality in the
various subchannels as found by both options in WOSUB when the
bundle power is increased
4_1_1__ _____
____
__
___
____
from 346 KW to 870 KW.
_____
91
FIGURIE 24:
of Various Subchannel Codes for the
Comarison
from Bundle Average
Deviation of Exit Subchannel Qalities
as a Function of Subchannel Number and Bundle Power as
Parameter.
'd
x
),
NOMENCLATURE
Z40
.··''
!0
i.
.4 /
I
I
/
~.
.' / 1
llE
,'
I,.
II
K .//
\
(462
*
COBRA/KTH
(346 KW)
(636 KW)
+
(494 iCW)
/.
<b- .
HAMBO/BN
(870 K;W)
o
HAMBO/Riso
(325
A
THERMOHYDRAULIC( 360
V
TRASXA
*
WOSUB(VAP)
346 KiW
o
WOSUB (NO VAP)
346
i(-
4z
ir.i
(462
_n--,
,O.,'.FI
n\............,
/'....
%
.WU3U]
(VAY)
WOSUB(NO VAP) 462
OSUB(VAP)
A
'
V
0 -
WOSUB (JO
I
*6
z/
w
5
CHANN6
7
CHANNEL NUMBER
-ll----UIIIII~~I"U"U~UII-III(--^s
----.
I^-·I·IPLWL·C-·l--·--·-·Llill
VAP)
870
870
tJW)
IW)
KW)
;,W
;'W
K;'
-
/
40 0
(431 KWI)
. .
)
( 4 b ZIj
^
--
0
I
/
DYNAIT
w tM±KJ/AZ
l7
iCMW)
El· COLIBRI
-
140
120
COBRA/AE
< FLICA/CENG
1,
..
i°
O
---
I
92
%C
4
_
Q
%A:of
1.
q:"
.
U,
a
O
(' o
ujsN.
X
*f
la qa
Ge0
I
laC
-ALx
U
zt.,
a
."r x
-
VV z
'W-,
zc
Q' I-
\
j
C40
o
g
:C
Ist o0 r.
IC* <
Qt
UV
+m
x
__
__
- _
I
I
·
0
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a
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FIGURE 26:
C'omarison of Various Subchannel Codes for the
Deviation of Subchannel Exit
Exit
I
Mass
'
Qualities versus Subchannel
Fluxes from Bundle Average for Subchannels
2 and 8.
-
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96
1.4 Performed 9-Rod Studsvik Test Bundle Experiments with
Power Tilt
1.4.1 Introduction
The experimental
tests as described in Sect. (1.3)
were obviously never performed.
Instead as proposed in [10] a
less severe power tilt has been finally used in actually
carrying out this experiment.
In fact, for the first time
experimental results are now available for this kind of strong
radial power tilt.
of various
Moreover, a unique collection of results
subchannel
codes has been assembled
experiment as a benchmark test.
[11] using this
Nine institutions participated
in this exercise with the following codes, most of them being
of proprietary
character:
1)
HAMBO
2)
COBRA-IIIC
3)
SDS
-Belgonucleaire, Bruxelles,
J
Belgium
-AB Atomenergik,
Studsvik
Sweden
4)
COBRA-II
-Royal institute of Techno-
5)
MATTEO
-Consorzio Nuclital,
6)
THERMOHYDRAULIK
7)
VIPER old (COBRA-IIIC) -KWU, Erlangen, Germany
8)
VIPER new (TORC?)
9)
MIXER
logy, Stockholm, Sweden
Italy
2
10) COLA I
-Institut for Space-Aviation
and Nuclear Engineering
11) COLA IIS
Tu Braunschweig,
Germany
12) FLICA
-Centre d'Etude Nucleaire,
Grenoble, France
13) SDS
-Research Establishment
14) TORC
Denmark
-Combustion Engineering, USA
Rise
97
The comparison
of the results of these codes together
those from WOSUB and the experimental
cases will be presented
in Sect.
evidence for two test
1.4.3. The coverage
test cases would go beyond the scope of this report.
a critical
review and evaluation
with
of all
However,
of the whole set of data and
numerical results will be issued at a later time [12] together
with a reevaluation of WOSUB, once the vapor diffusion model
has been optimized.
1.4.2 Description
of the Geometry and the Test Conditions
The geometry of the test section is given in Fig. 27a
together with the power skew applied in the tests.
It should
be noticed that the diameters
of the pins for two rows differ
from those of the third row.
The bundle contains four spacers
typical for BWR-design.
Fig. 27b.
Their positions are depicted in
The subchannel spacer coefficients and flow areas
as given in [10] are:
Subchannel
Spacer
Coefficient
Flow Area
2 _
(velocity heads)
1
1.22
62.9
2
2.03
100.7
3
2.08
99.6
4
1.53
150.2
5
2.13
98.4
6
1.58
147.8
7
1.27
61.7
8
2.13
98.4
0 1
E
S 0
S
Rod no. 1,2,3,4,5
and 6.
98
12.25 mm.
Rod no 7,8 and 9 j 12.0 rr. n
Flow area :1639. 6.10
Heated
length
-6
m
2
1.5 m.
Ir.tet calming length: 0.29B m.
Flow split walls
in the
ower distribution
'1-
SPLI T-
CHANNEL
*-70 *I.
SPLIT . 1IANNEL
30
4
)t'Ll
1.
I
, HANNFL
0 %.
., PLI TCHANNE
L
Figure
27a:
Geometry
of the 9-Rod Studsvik Test Bundle
nf
I
I
I
l
011
oom
*LtTLtJ
4
Figure
27b:
Spaces Locations
9-Rod Studsvik Test Bundle
in the
100
These values are used as input into the subchannel codes.
in Table 23.
The test conditions are summarized
Only cases 1 and 4 will be used for the purpose of compariThe rest of the cases will be presented
son in this report.
in [23].
The outlet of the test section was equipped with
and pressure
taps.
flow split devices as shown in Fig.
28
The flow split devices were arranged
such that always two
subehannels were sampled together according to the following
scheme:
Split Channel
Subchannels
1
7 &8
2
5
3
3 & 4
4
1 & 2
As a result of this procedure,
channel data available.
&6
there are no individual sub-
Thus, final conclusions may not be
reached at this point in time.
However,
there is some hope
that individual subchannel data may become available in the
future.
The following quantities were measured
in the four
split channels:
a) mass flow
b) quality
c)
enthalpy
in subchannel
In addition, the pressure drop was measured
a location
.-_.
I..__-
--- -1---
-
- .
0.6 4 6 m downstream
_ I-
- -_
_
- _..__-1
3 at
from the inlet to the location of
_ L_
___.,,
_
_
_
___
______ _. __
101
P
bar
Case
Pcl
KW
G 2
kg/m s
1
70
900
380
10
2
70
900
380
20
3
70
900
380
30
4
70
1200
420
10
5
70
1200
380
30
6
70
2000
500
10
7
70
2000
500
20
Imll I I I
Table
I
23:
II
II
I
I I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
Test Conditions
for the Studsvik
BWR Bundle [9]
--------
e sub inlet
oC
1
F;/
i
I
iI
i
-,
- the 9-gRod
ion
rw
evie
oTestP
-~~~~ir 8
WS33t eiei
a
h ~0
cua_
cn
t '
103
the flow split device.
1.4.3 Comparison of WOSUB with the Experiment and the Other
Subchannel Codes
1.4.3.1 Comparison of the Quality Predictions
Tables
27 ,
24
and
25
as well as Tables
26
and
summarize the steam quality and the mass fluxes for
cases 1 and 4, respectively.
Comparing the experimental findings with the WOSUB
results as shown in Tables
24
and
26
the following
con-
clusions can be drawn with respect to quality predictions in
the various split channels:
1)
WOSUB predicts
the quality in split channel 1
very well for both cases.
2)
It overpredicts
the quality in split channel
2
in both cases.
3)
WOSUB underpredicts the quality in split channel
3 more so in case 1 than in case 4.
4)
WOSUB underpredicts
the quality in split channel
4, again more so in case 1 than case 4.
These conclusions do not come unexpectedly because as already
indicated in the foregoing sections too much vapor is diffused
into the hot center subchannel which leads on the other hand
to an overcooling
effect in the cooler split channels.
By
changing the vapor diffusion it is hoped to match the experimental results better in the future.
By comparing the results of the other subchannel
codes with the experiment,
the following
conclusions
can be
.I-·
III·LL- - _- Il···--_··_II
I------II·
___
104
Table
Case
24:
Steam Quality (%) in Each
Split Channel - Comparison Between Experiment
1
and Various Subchannel Codes
Split Experiment
Channel
SDS*
HAMBO
COBRA-IIIC
THERMO
HYDRAULIK
VIPER
(old)
1
26.7
27.6
29.7
29.3
31.7
32.3
2
22.7
20.8
22.6
22.3
23.9
24.3
3
10.2
11.1
8.9
8.3
7.7
9.3
4
1.8
3.4
2.2
1.9
1.6
2.2
VIPER
IMIXER-2 MATTEO
COBRA-II
COLA I
COLA 2S
(new)
1
34.0
28.0
37.2
30.4
34.6
24.9
2
25.7
21.9
29.1
23.4
25.3
19.1
3
9.3
9.9
6.1
9.1
6.6
10.5
4
0.8
3.2
-1.3
2.7
0.6
6.4
SDS**
TORC
WOSUB
FLICA
1
36.0
36.5
33.2
26.7
2
30.4
27.5
24.6
27.8
3
8.8
9.0
8.7
5.3
4
0.2
1.0
1.2
-1.6
IIJ~I-
* Studsvik
** Ris8
= 70.3 bar
D
G
av
= 907 kg/m 2s
ATsub = 9.3C
Power = 380 KW
I-
`
105
Table 25:
Mass Flux (kg/m x) in Each Split Channel
Comparison Between Experiment and Various
Subchannel Codes
Case 1 (continued)
Split Experiment
Channel
SDS*
HAMBO COBRA-IIIC
VIPER
(old)
1
678
631
661
689
624
562
2
812
800
794
837
724
736
3
951
1009
1024
1058
1036
1031
4
1204
1177
1140
996
1261
1313
VIPER
(new)
MIXER 2 MATTEO
COBRA-II
COLA I
COLA 2S
1
2
554
720
632
784
607
733
612
760
594
727
650
802
3
1015
1018
1074
1044
1074
1027
4
1369
1189
1217
1208
1210
1148
FLICA
SDS**
TORC
WOSUB
1
541
595
581
774
2
652
734
762
834
3
4
1045
1382
1033
1279
1078
1183
1056
924
-
-"
THERMOHYDRAULIK
..,
-
106
Table
Steam Quality in Each
26:
Split Channel - Comparison Between Experiment
And Various Subchannel Codes
Case
4
Experiment
Split
SDS*
THERMO-
HAMBO COBRA-IIIC,
HYDRAULIK
Channel
VIPER
(old)
1
23.1
23.5
24.4
26.1
26.8
26.8
2
20.5
13.1
18.2
19.6
19.4
19.8
3
7.6
8.2
6.2
5.4
5.1
6.7
0.6
-0.7
0.1
0.7
-0.
4
VIPER
(new)
MIXER
2 MATTEO
COBRA-I
i
COLA I
COLA 2S
1
27.5
22.4
30.3
24.8
30.9
20.0
2
20.5
18.0
23.6
18.8
22.0
15.5
3
6.8
7.3
4.3
6.5
4.4
8.0
o0.0
0.8
-2.1
1.2
-1.56
.
4
FLICA
SDS**
TORC
OSUB
1
29.2
29.9
26.5
21.5
2
2L.7
22.5
19.8
24.1
3
24.8
6.5
6.1
5.0
4
-0.9
0.4
i
-0.4
-1.6
l i ..1
- I-
*
Studsvik
D
**
Ris8
G
= 70.9 bar
av
= 1209 kg/m2s
m
= 11.1°C
-sub
Power = 422 KW
II
Ill--···-·rllllll·CIII----·U
107
Mass Flux (kg/m2x) in Each Split
Table 27:
Channel - Comparis.onBetween Experiment
and Various Subchannel Codes
Case .4 (continued)
Split Experiment
Channel
THERMOHYDRAULIK
VIPER
(old)
858
772
718
SDS*
HAMBO COBRA IIIC
781
852
1
800
2
1009
999
1027
1043
914
944
3
1303
1323
1375
1369
1419
1349
4
1767
1770
1579
1558
1760
1875
COLA I
COLA 2S
VIPER
(new)
MIXER 2 MATTEO
COBRA-II
1
712
831
779
965
733
653
2
929
1008
742
998
939
747
3
1319
1335
1422
1378
1427
978
4
1948
1686
1700
1697
1734
1296
SDS**
TORC
WOSUB
FLICA
1
736
771
768
934
2
876
943
998
959
3
1366
1389
1417
1366
4
1882
1764
1640
1608
-
-
108
drawn:
a)
The closest predictions
come from the institution
which performed the experiment (SDS, Studsvik).
b)
The majority
of the subchannel codes overpredicts
the quality in split channel
, some of them by a
substantial margin, however all of them predict split
channel 1 as the hottest.
c)
Some codes
qualities
(MATTEO, FLICA, SDS-Eis8) predict
in split channel 2 even higher or about the
same as WOSUB does.
d)
The majority
of the codes predict the quality in
the split channel 3 about correctly, although
is a group consisting
of THERMOHYDRAULIK,
COLA I which tends to underpredict
there
MATTEO,
the quality
in
that channel as WOSUB does.
e)
The codes which are doing about right in three
of the split channels at least from the point of
view of trends overpredict
the
uality in the coldest
split channel 4, -ith especially
good examples
this being COLA 2S, and even SDS-Studsvik
for
and
MIXER-2.
f)
Codes which are identical but are serviced by
different institutions produce substantially different
answers
(see SDS-Studsvik
differences
versus SDS-Ris8).
The
between the results of the codes are
about as large as the differences
of the WOSUB results
to the experiments.
--m·
109
g)
Codes which are designated
as new versus old or
III versus II etc., do not show overall consistent
improvement
s.
h) Institutions closest to the BWR design area produced results which came closest to the experimental
results.
i)
Judging from our experience with WOSUB, the
results shown for the MATTEO code must have been
obtained without the vapor diffusion option included.
In summary, the picture given above by the points a) thru i)
is in fact quite confuse.
In general,
it is found again that
most of the other subchannel codes as indicated in the foregoing
chapter overpredict the quality in split channel 1.
exceptions
are SDS-Studsvik
and MIXER 2-KWU.
Noticeable
On the other
hand both codes do overpredict the quality in the coldest split
channel.
Indications
are that the input data play the major
role in the final results.
SDS-Studsvik obviously benefited
most from the experimental evidence, whereas MIXER 2 relies
heavily upon the GE experience.
A comprehensive analysis of
these data together with a check of the trends suggested by
the various codes will be issued in [23].
A warning should be issued with respect to the codes
with the familiar names such as COBRA-IIIC, COBRA-II and the
like.
It is more than possible that these codes underwent sub-
stantial modifications in the mixing model, cold wall effects,
etc.
at the various institutions.
Therefore,
it is by no
means obvious that these codes are in fact equivalent to
_I___
_
1111
_
110
COBRA-IIIC/MIT or to those versions which are publicly available.
In any case, runs will be performed
with COBRA-IIIC/MIT
in the near future to check this point.
As with regard to WOSUB it can be concluded
code behaves as expected.
With the vapor diffusion model being
still not tuned, the transport
overemphasized.
into the center subchannel is
Once this is corrected the other split channels
should close in with the experimental
important
results
that the
results,
too.
How
tuning really is can be clearly seen by comparing the
of the two SDS-code versions
and the two COBRA-IIIC-
versions from Belgonucleaire and KWU although the differences
are not that apparent
Finally,
there.
it should be pointed out that the average
quality of each split channel has been obtained from the individually predicted subchannel quantitites according to
x G F
G F
eGeFe+ x mm
m
GeF
as prescribed
subchannel
this formula.
in quality
by Ulrych and Kemner
areas.
j......4
+ G F
m = 10
-
2j
e
-
2j
=
9
[11], where the F's are the
It is not clear why these areas enter into
As a matter
of fact, x
reduces by about 0.5%
(i.e. 34% instead of 34.5%) by disregarding
the
averaging process.
1.4.3.2 Comparison of Mass Flux Predictions
Tables
25
and
data and the predictions
27
summarize the experimental
of the subchannel codes for the mass
flow rates in the four split channels
9RIll_
for cases 1 and 4
I
111
respectively.
According to [11] the split channel averages
were obtained from the individual subchannel predictions by
using
G Fe + G F
G
=
Fe
;
Fe
j = 1 .....4
Fm
m = 10
Fm
e =
- 2j
9 - 2J
According to the experimental evidence the mass flow rates increase steadily going from split channel 1 to split channel 4.
In case all subchannel code results follow this trend with the
exception
of COBRA-IIIC by Belgonucleaire and WOSUB both of
which predict higher mass flow rates in split channel 3 than
in split channel 4.
However,
in case 4 both codes are in line
with the general trend.
By comparing the experimental findings with the WOSUB
results the following conclusions can be drawn
1)
WOSUB predicts slightly higher mass flow rates
for split channel 1.
2)
The code gets about the right for split channel 2.
3)
For case 1 the predicted mass flow rate is the
high but only slightly higher in case 4 for split
channel
4)
3.
WOSUB predicts much too low mass flow rates for
split channel
4 in case 1, however this difference
is much smaller in case 4.
Essentially, WOSUB shows again here the same general trends
as already observed in the GE-test with radially non-uniform
peaking factor pattern, namely overprediction in hot regions
and underprediction
in the cold regions.
It is hoped that these
112
deficiencies
can be fixed by virtue of changes in the vapor
diffusion model.
Comparing the results of the other subchannel codes
the following
a)
conclusions
can be drawn:
The best predictions come from institutions which
either performed the experiment or are closest to BWR
bundle design (SDS-Studsvik and MIXER 2-KWU).
b)
The group VIPER old and new, COLA I, FLICA, SDS-
Ris8 and TORC underpredict the mass flow rate in
split channel 1 by about the same amount that WOSUB
overpredicts
it in case
.
in case 4 these codes do
better but COLA 2S does substantially worse.
Further-
more, COBRA-II which give a reasonable answer for
case 1 predicts an even higher mass flow rate than
WOSUB for split channel in case 4.
c)
The behavior
of split channel 2 is predicted
quite well by most of the codes.
Noticeable excep-
tions are FLICA for both cases and COLA 2S in case 4
where both codes underpredict the experimental result
by quite a margin.
d)
All codes overpredict
the mass flow rates in
split channel 3 by more or less big margins.
COLA 2S
exceptionally underpredicts case 4 although its predicted quality is so close to the experiment.
e)
Whereas the mass flow rate in split channel 4 for
case 1 is calculated quite well by most of the codes
(exceptions being
OBRA-IIIC
and WIOSUB too low, but
-
----
· le
·TI·u
113
VIPER old and new, and FLICA, too high) larger
differences
and scatter show up in case 4.
COLA 2S,
being consistent in its trend, gets by far the lowest
G whereas VIPER new and FLICA predict too high
values for G.
COBRA-IIIC and HAMBO predict also too
low mass flow rates.
The resultant picture is again quite diffuse, with the exceptions being SDS-Studsvik
a surprise though.
and MIXER 2 which should not come as
On the other differences
of the codes especially
in the predictions
for split channel 4 are larger than the
difference in the measured quantities between split channels
3 and 4!
This is indeed a surprise because one would assume
that in the low and subcooled quality regime reliable results
could be predicted
by the codes now.
This is obviously
not
the case under the given circumstances.
1.4.3.3 Comparison of Predicted Individual Subchannel
Qualities
Some of the participants provided information about
the individual subchannel qualities.
and compared with the WOSUB
30 ,
These data are summarized
redictions
for cases 1 and 4, respectively.
in Tables
28
and
Due to the lack of
experimental evidence on the individual subchannel basis,
MIXER 2 is taken as a standard because it performed
the split channel averages
4, i.e., subchannels
disregarded
with the exception
1 and 2.
well in
of split channel
These two subchannels
will be
for the purpose of this comparison here.
By comparing the MIXER 2 with the WOSUB results,
_
the
__
114
Table 28:
Steam Quality (%)
in Each Subchannel - Comparison
Between Various Subchannel Codes
Case
1
--
Subchannel
Number
-
--------
THERMOHYDRAULIK
VIPER
(old)
VIPER
(new)
1.77
2.7
0.9
3.5
1.14 3
1.9
0.7
3.0
7.38
9.2
9.0
9.3
7.85
21.82
9.4
9.5
10.2
22.4
23.8
18.4
25.23
25.4
26.8
24.1
29.23
30.0
30.7
25.4
33.18
33.6
36.0
29.6
TORC
WOSUB
COLA
_
--
---
I
I
I
1.1
6.9
1.4
-1.3
0.8
6.1
1.0
-1.7
5.9
16.5
8.4
5.0
5.9
10.5
8.9
22.7
17.8
22.6
5.5
26.2
27.1
19.9
25.8
32.9
31.3
22.8
30.6
20.1
36.7
26.2
34.7
30.9
I I I
I
_
----
COLA 2S
MIXER
-
.
'll I
------
II
------
2
---
---
---
-----
--------
---
-------
--
115
Table
Mass
Flux
Rate
(kg/m2
Mass Flux Rate (kg/rn
s)
29:
in Each Subchannel - Comparison
Between Various Subchannel Codes
Case 1 (continued)
__I
Subchannel
THERMOHYDRAULIK
VIPER
I ,1
VIPER
(new)
(old)
MIXER
2
II I
1230
1205
1354
1148
1281
1381
1378
1214
991
950
939
978
1066
1084
1066
1044
716
696
677
767
729
763
748
796
629
545
547
636
621
573
558
630
TORC
WOSUB
COLA
IIII~-
--
-·-
COLA 2S
1046
1095
1126
842
1317
1181
1219
978
1014
1005
1014
992
1113
1042
1120
1101
728
806
724
846
727
800
787
826
590
655
563
782
596
648
593
769
I I
--
I
I
..
I -I
I
IIII
116
Table
Steam Quality
in Each Subehannel - Comparison
30:
Between Various Subchannel Codes
Case
4
Subchannel
THERMOHYDRAULIK
-
VIPER
(new)
MIXER
0.9
0.5
0.0
0.0
4.8
6.6
6.7
6.9
4
5.3
6.8
6.9
7.6
5
17.5
18.1
18.8
15.3
6
20.5
20.8
21.5
19.8
7
24.5
24.8
24.5
20.6
8
28.2
28.0
29.3
23.6
TORC
WOSUB
0.2
1.1
2
0.0
3
I
COLA
2S
-1 .1
3.7
-0.2
-1.4
2
-1.8
2.7
-0.5
-1.8
3
3.8
8.1
5.7
4.7
4
4.7
7.9
6.3
5.2
5
19.3
14.5
17.9
17.2
6
23.7
16.1
20.9
28.9
7
27.6
18.4
24.2
15.2
8
32.9
21.0
27.9
26.1
I
----
---
--
I
I I
I
---
-1.--
2
0.7
1
II.
--
(old)
1
COLA
----------------
VIPER
I I LI II I I
_
.__
___
117
Mass Flux (kg/m2s)
in Each Subchannel - Comparison
31:
Table
Between Various Subchannel Codes
Case 4 (continued)
---
Subchannel
Number
THERMOHYDRAULIK
VIPER
VIPER
(old)
(new)
MIXER
2
II
1730
1757
1924
1658
1778
1948
1963
1703
1366
1261
1220
1285
1454
1407
1385
1368
895
895
873
989
927
977
966
1021
7b1
699
711
834
767
730
713
829
COLA
I
-
COLA 2S
I
TORC
WOSUB
1641
1534
1560
1676
1792
1632
1690
1566
1345
1292
1353
1278
1481
1349
1460
1424
917
1045
955
984
955
1047
1027
942
730
896
748
1023
734
885
780
878
I
.
I
--
--
-
II
!_~~~~~
118
following
conclusions
1)
can be drawn:
WOSUB underpredicts the qualities in subchannels
3 and 4, the differences
being larger for case 1 than
for case 4.
2)
WOSUB is doing a decent job for subchannel
5, it
slightly overpredicts the qualities in both cases.
3)
As expected,
hefty margin
WOSUB overpredicts
the quality by a
in the hot center subchannel
6 in both
cases.
4)
It underpredicts
subchannel
5)
the quality in the hot corner
7 in both cases by the same amount.
WOSUB gives quite a reasonable
side subchannel
answer for the hot
3 as compared to MIXER 2.
For case
1 the result to MIXER 2 is closer than for case 4,
however both qualities are too high.
In summary of the above mentioned observations, it becomes
again very obvious that in WOSUB too much vapor is diverted
from the hot corner subchannel into both center and side sub-
channels.
Once this process has been damped the WOSUB data will
certainly close in to the MIXER 2 results which indicate about
the same quality for both how center and hot corner subchannels
under the given heating conditions.
it is of great
nterest to see how the other sub-
channel codes compare to MIXER 2.
a)
This comparison reveals that
All codes with the exceptions
of COLA I and
THERMCHYDRAUTLIK give close predictions
3
·4111
and
4.
for subchannels
119
b)
With the exception COLA 2S, all codes overpredict
the quality in subchannel
c)
5.
With the exceptions of COLA I which overpredicts
and COLA 2
which underpredicts
the quality in sub-
channel 6, the rest of the codes are doing pretty
well.
d)
Not unexpected major differences
show up in sub-
channels 7 and 8 for all codes with the exception
of
COLA 2S which comes closest to the MIXER 2 results
than all of the other codes, although
a tendancy to underpredict
channels
the qualities
6, 7 and 8 in both cases.
codes overpredict
the latter has
the qualities
in sub-
All the other
in subchannels
7 and
8.
e)
Given the fact that the same codes are in close
agreement especially for subchannel 6, and in general
also subchannel
5 and 4, there seems to be no logical
way to reduce easily the differences
subchannels
7 and 8.
showing up in
This in contrast to WOSUB where
imbalance between the qualities in the various
sub-
channels can be clearly seen and an explanation
and
remedy can be given.
f)
From the results given in these tables it seems
reasonable to infer that MIXER 2 and COLA 2S may work
also with a vapor diffusion model or have the
capability of accounting for individual subchannel
mixing parameters because both codes avoid the trap
--.--.-1111111_
1
q
__
---
·--ll/·--^··IWILII---·
II-·-
Il-·IY-
I·--YF-·--·---·--·I
__
__
120
of overemphasizing
the hot corner and side subchannels
as do the other common subchannel codes.
must have the same capability.
SDS-Studsvik
It seems that by
virtue of these undisclosed features COLA 25 obviously
distributes too much into the colder channels which
becomes especially apparent in subchannels 1 and 2.
On the other hand it is surprising that it matches
the MIXER
2 data for subchannels
turn is indicative
g)
3 and 4 which in
of some non-consistency.
With respect to the hot side subchannel WOSUB
comes closest to the MIXER results.
Again, the aforementioned observations indicate WOSUB's potential for real improvements.
This cannot be said about the
other subchannel codes which show already matching results for
the majority
side ones.
of subchannels
but fail for the hot corner and hot
There is no easy way out of this situation without
affecting also already matched results.
1.4.3.4 Comparison with Predicted Individual Subchannel Mass
Fluxes
Tables
29
and
31
summarize the predictions
of the participants for the individual subchannel flow rates
for cases 1 and 4, respectively,
and show at the same time
the WOSUB results.
Following
the same argument
as in the foregoing
section for the quality, MIXER 2 is taken as standard for the
mass flow rates, too, because
---- --
---
---- ---
--
--
I--
-
L-
its predictions
___
__
I
__I
matched
_
the
____
_
_
121
averaged split channel results very well.
By comparing MIXER 2 and WOSUB the following conclusions can be reached:
1)
In case 1 WOSUB underpredicts
the mass flow rates
in subchannels 1 and 2 by quite a large margin,
whereas in case 4 subchannel 1 agrees very well and
the difference
in the results for subchannel
2 is
smaller.
2)
The mass flow rates in subchannels
3 are cal-
culated very well by WOSUB for both cases.
3)
The mass flow rates in subchannel
4 are predicted
slightly too high by WOSUB in both cases.
4)
WOSUB gives a somewhat higher mass flow rate for
subchannel
case
5)
5 for case 1 but gives a perfect answer for
4.
For subchannel 6, WOSUB predicts a slightly
higher mass flow rate in case 1 but a too low one in
case
6)
4.
The mass flow rates in subchannels
7 and 8 are
predicted too high in case 1 as well as in case 4
although
the difference
for subchannel
latter case is not very large.
ence for subchannel
8 in the
However, the differ-
7 is large, mainly because the
quality has been predicted
so low, as denoted
in the
foregoing section.
The overall result of this comparison
flow predictions
C---
is that the WOSUB mass
are not that bad, especially
I
in view of the
___
122
fact that the differences
are explainable
and will be
certainly decreased by taking appropriate measures.
The fact
that WOSUB cannot handle pins with different diameters in a
bundle at this point in time might contribute also to the ob-
served differences.
By comparing
MIXER
the rest of the subchannel
2 results the following
1)
observations
Various codes overpredict
subchannel
flow rate.
codes to the
can be made:
the MIXER 2 result for
1 in case 1; others underpredict
the mass
Obviously VIPER (new) and (old) have a
strong tendancy to too high values in both cases.
2)
The same holds for subchannel
2.
3)
The mass flow rate in subchannel
3 is predicted
by all codes very well in both cases.
4)
The predictions are more widely scattered for
subchannel
4 where THERMOHYDRAULIK,
COLA I and TORC
tend to overpredict.
5)
The predictions
for subchannel
5 are quite close
to the MIXER-2 results in both cases for all codes
with the exception of VIPER (new) which underpredicts.
6)
All codes predict reasonable
values for the mass
flow rate in subchannel 6 in case 1 but the majority
of them tend to underpredict
7)
the result in case 4.
Most of the codes underpredict
rates in subchannels
the mass flow
7 and 8 in both cases with the
exception of COLA 2S which overpredicts.
_··I_C
_
__
__
______
__II_
__
123
1.4.4 Conclusion
The Studsvik experiment is certainly an important
step for the verification
process of subchannel codes.
order to supply final conclusive
evidence,
In
it is however
necessary to measure individual subchannel quantities.
It is
strongly hoped that Studsvik will undertake this badly needed
experiment. Unfortunately, Studsvik did not supply an error
analysis for the measured
quantities.
Thus, it is very
difficult to assess the true reliability
of the subchannel
predictions supplied by the various participants and to assess
the additional
efforts needed in the future to bridge the gap
between experiment and predictions.
The predicted data show a scatter between the results
of various subchannel codes which is larger than the differences
measured between the individual split channels.
codes do not show a consistent behavior.
are SDS-Studsvik
Most subchannel
Noticeable
exceptions
and MIXER 2, and to some extent COLA 25, al-
though even these are not totally perfect, especially at very
low qualities.
There is reason to believe that these three
codes use either advanced two-phase modeling schemes and/or
mixing models because all three avoid consistently the prediction of too high qualities
in the hot subchannels
-- a
disadvantage of all common subchannel codes as observed throughout this whole assessment.
parameters
How important
really is can be inferred by comparing
of the two SDS codes serviced
tively.
1
the tuning of input
Naturally,
I.--·---·III-·----··-·^DI.·1P-LI.
at Studsvik and Ris8, respec-
it does not come as a surprise
^I-----lp
the results
· III-
that the
124
Studsvik version performs better.
Similar observations can be
made with respect to the various COBRA-IIIC versions applied by
some participants.
channel codes
It seems that for the rest of the sub-
(with the exception
of the three above-mentioned
ones) there is no room for substantial improvement unless individual subchannel mixing models are introduced.
As with respect to WOSUB, all deficiencies already
observed in the foregoing benchmarks show up again here.
In
that regard the code's behavior is consistent from benchmark
to benchmark.
ts data indicate the possibilities
tial improvements.
of substan-
hus, the tuning of the model parameters
is absolutely necessary and will be performed in a next step.
The Studsvik experiment will serve as benchmark as well as the
IXER 2 subchannel data in lieu of experimental evidence.
the author's knowledge
were made available.
all seven experimental
the predictions
To
this is the first time that MIXER 2 data
A forthcoming report [12] will focus on
cases and try to illuminate trends in
of the various subchannel
codes by using a
unique set of information.
Finally,
it should be noticed that the presentation
of the comparison between experiments and predictions in
Ref. [11] leaves something to be desired because there the
deviations
number.
are graphed only as a function of the split channel
What is needed however are graphs which show the de-
viation in the mass flow rates versus the deviations
qualities.
11111111111111111188lls·1
Ref.
in the
23] will supply this kind of information.
_
1
11111--··-··-··lg··-···-·-·--·-
-.
125
1.5 Hitachi 7'x 7 BWR Fuel Pin Bundle with 3-D Power
Profile
1.5.1 Introduction
FASMO
[24] is a three-dimensional,
steady-state,
coupled neutronic-thermal-hydraulic computer code for the
analysis of BWR fuel pin bundles.
The neutronic part uses
three-group diffusion theory and accounts for local void and
control rod effects.
From the little information available about the
thermal-hydrualic
part, it can be reasoned
fied version of COBRA-II.
that it is a modi-
This version includes the Armand
model for the calculation of the two-phase friction multiplier,
Levy's subcooled void model and the modified Armand model for
the two-phase void fraction calculation, respectively.
Further-
more, it accounts for turbulent and diversion crossflow effects
between the subchannels
according to the following
formulas:
turbulent crossflow
mi + m.
Wi = i
ai
where B is a prescribed function of the quality,
i.e.,
8 = f(x).
transverse momentum equation
Cij Wij
= Pi-
with
fl
Sgcij
gc ijPi
P
126
Both models differ from the original COBRA-II.
interesting is that
has been made a function of the quality,
the source for this information
although
has not been disclosed
It is a well acknowledged
by the authors.
Especially
should
fact that
indeed vary from flow regime to flow regime in the two-phase
However, the only disadvantage
region.
of this concept is that
not enough information has been effectively available thus far.
FASMO iterates on the power and void distributions
solution.
to achieve a convergent
Thus, for the purpose of
the comparison which follows, a 3-D power profile was obtained
[25] and the check on WOSUB as well as the comparison with
FASMO and COBRA-IIIC/MIT
three-dimensional
was performed
only with respect to the
Due to the fact that the
void distribution.
number of subchannels in this case is higher than can be
handled by WOSUB-I,
it is necessary
to use WOSUB-II
for this
analysis.
1.5.2 Description of the Bundle and Physical Input Data
The subject of this study is a Hitachi 7 x 7 BR
Its geometrical layout is depicted in
fuel pin bundle.
Fig.
29.
This bundle has to be thought of as bundle number
3, shown in the insert of this figure.
Due to the fact that
control rod B is deeply inserted into the core whereas control
rod A is nearly withdrawn,
steep power gradient
as shown in Fig.
30 ,
exists across that bundle.
a fairly
On top of
this gradient an axially varying disturbance is superpositioned
due to control rod B, i.e., in the immediate neighborhood
I
_____
_
_
___
__ _
_ _________I_________·I__________I_
___·
127
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ao)
'
?,-Htvx)
__
________
c
o
~ xnqa ltaR
_
o
129
(point a) of this control rod, the power is fairly much
suppressed over the whole inserted length of the rod, but it
jumps nearly discontinuously
at the top of the rod.
Naturally,
the axial disturbance is smeared out with increasing distance
from that bundle: corner.
flux profiles
Figure
30
shows the axial heat
at the corner rods a and b as well as the bundle
average one.
Assuming symmetry in bundle 3, 36 subchannels with
28 fuel pins have to be analyzed.
flux profile was supplied
Q(i,k) = Qavg
where
avg
[25] in the following
x
=
Information
about the heat
form
q(i,k)
average bundle heat flow
i = rod number
k = axial position.
The heat flux distributions across four diagonal transverses
at different
interesting
axial locations are shown in Fig.
to see by comparing
31 .
It is
the trends of the heat fluxes
along the diagonal below and above the control rod tip that
the trend reverses drastically just above the control rod.
The question then is how does the void distribution respond to
this nearly discontinuous change.
1.5.3 Results and Comparison
WOSUB-II has been run for both options, namely the
vapor and the no vapor option.
uses a
0.06
The results of FASMO which
as a function of quality varying between 0.01 and
have been published
in [ 24 ].
In addition, COBRA-IIIC/MIT
___
130
02
ol
i
ca
-4)
C:
x(d
Cl
0Ce
in
a
Mc
tr
En~
a
CL
o
oo
o0
O
Sd
;h.
02
02
D
__c
0:
C
C)
0r
ua
a
m
Cc
;-
N
0
<
(1
z
0
rz
-
N
\
X
Im
:
·q
H
,
CW7~~~~~C
'-4
L
as
I. i
IL:
(D
ac
C
0
C:
0o
Q
<5
F--
(0z/PYXn
0I?1
_ ___I____
__
_
_ _
I__
___
I
_I
________I_
131
has been run with the same two-phase flow correlations as used
in FASMO
[24 ].- However,
due to the fact that COBRA-IIIC/MIT
to vary as a function of the quality,
does not allow
two runs
= 0.01 and the other with 8 = 0.06,
have been made, one with
as
in order to assess COBRA at the lower and upper bounds of
used by FASMO.
shows the comparison
32
Figure
channel codes at the four axial locations.
of the various sub-
The following
general observations can be made by first comparing the FASMO
with the WOSUB results:
1)
At location
5, FASMO starts to predict a higher
void fraction than both of WOSUB's options whose
results
fall on one and the same curve because
is no substantial
2)
vapor generated
there
to be distributed.
At location 11, FASMO and WOSUB start off at the
same value of a in the cold corner subchannel. After
that, a constant difference between the WOSUB results
and FASMO exists up to rod
15, the WOSUB results
staying always below those of FASMO.
Beyond rod #15,
both WOSUB versions go through a plateau where the
differences
to FASMO increase and then start to
rise sharply at rod #21.
WOSUB with vapor diffusion
reaches a peak in subchannel 28 which is essentially
the hot center subchannel and drops off in the hot
corner subchannel
the well-known
vapor
I
_
_
I
36.
This effect is again due to
effect of distributing
too much
from the corner into the center subchannel
_
as
132
FIGURF 32: Comarison o
the.Void
raction Distributions Across
the Bundle Diagonal at Three Axial Elevations as Determined
by COBRA-IIIC/MIT, FASMO and WOSUB
i
FASMO
COBRA III-CIMIT _/_ _
-o
o--
APOR
WOSUB WOSUB
\NO
VAPOR - )X-- ---x-
IV
0.7
it
0.6
0
0.5
OC
0.4
0.3
.
8
0.2
.1
O
1
3
6
10
15
ROD NUMBER
21
28
36
133
experienced in the foregoing comparions.
the drop should not be that sharp.
it is not believed
On the other hand,
that a36 is larger than c 2 8 simply
by inferring this from the observations
GE non-uniform
Certainly,
made in the
heating cases in Sect. (1.1).
FASMO,
for example, shows the void fractions to be equi-
valent in both subchannels.
At this point it should
be remembered that MIXER 2 showed only very small
differences
as discussed
in the qualities
in these two subchannels
in Sect. 1.4.3.3.
From these observations
it becomes obvious that the WOSUB model without
vapor diffusion included errs by overshooting the
FASMO results.
3)
At location 20 both WOSUB versions produce data
which fall closely around those of FASMO in the
central section of the bundle.
subchannels
In the hot corner
they show the known behavior
of a drop
for the vapor diffusion model and a steady increase
for the non-vapor
diffusion model.
to see that WOSUB's predictions
It is surprising
for the hot center
subchannel are in close agreement with FASMO.
the "cold" corner of the bundle,
At
the vapor diffusion
option predicts smaller void fractions than FASMO.
WOSUB without vapor diffusion starts off at about the
same value as FASMO in the cold corner subchannel but
then drops in the cold center subchannel
in order
to increase again at about the same rate as does
_
I__
134
WOSUB with vapor diffusion.
4)
It is of general interest to note, that although
the heat flux distribution changes its tilt between
locations 11 and 20, the void distribution lags
behind;
and although it increases and flattens, it
does not follow the heat flux distribution.
Comparing the two COBRA-IIIC/MIT runs with the FASMO
the following
and the WOSUB results,
a)
can be concluded:
At all locations both runs produced results which
are conservative throughout.
b)
The quality in the hot corner subchannel
predicted by a huge margin.
could not generate
is over-
For B = 0.06 the code
data for this subchannel
for the
locations 11 and beyond at all.
c)
By taking
= 0.06, results are obtained which
are closer to FASMO than those for
d)
= 0.01.
The COBRA data show a plateau similar to the
WOSUB data, which does not show up in the data by
FASMO.
e)
For B = 0.06, COBRA-IIIC/MIT
result in subchannel
f)
matches the FASMO
21.
Trendwise, COBRA-IIIC/MIT shows a similar be-
havior for
= 0.01 as does the WOSUB without vapor
diffusion model in the cold corner region.
g)
By inference
of the data it seems that in the
middle section of the bundle COBRA-IIIC/MIT closes
in with FASMO at higher elevations.
··lllllllrrrrr··llrllllrr·lrrr
135
g)
In the hot corner subchannel COBRA-IIIC/MIT
overpredicts
--·II"--
-··--··-·I-
-
-
-
--- r------rr-------u-r^-__
c by as much as 50%.
-r r
-
---- r---··-·-·--·---r---
rr--r------.
-r-
136
Conclusions
1.5.4
From the aforementioned observations it becomes
clear that subchannel codes with constant mixing factor overpredict the void fraction by a substantial margin.
As a
result the input data for the neutronic moderator feedback
analysis
are in error.
From a thermal-hydraulic
point of view
the overconservative results are not desirable either, because
wrong decisions may be made based on an erroneous calculation.
32
The behavior
of the curves in Fig.
matter how
is changed, COBRA-IIIC/MIT
matching
the FASMO data.
The more
the flatter the distribution
indicates
that no
will not be capable of
is increased beyond
0.06
becomes in the cooler section of
the bundle and the steeper its increase
in the hot part of the
bundle.
It is obvious that the simple changing
types of codes will never lead to a matching
of
in these
of the FASMO data.
Similar behavior was noticed in discussing the Columbia tests
in Sect.
1.2.
with respect to the mass flow rate distribution,
where it was shown that no matter how
was chosen the data
could not be matched.
On the other hand, incorporating
as a function of
the quality leads to results roughly similar to those predicted
by MIXER
2, namely a fairly flat behavior
in the hot region.
With respect to the WOSUB-II with vapor diffusion
model,
it can be concluded
that its results are close to the
FASMO predictions with the exception of its hot corner
--r---u
"I"llrrr*·l·rrCL-----·UIII·
lsl---··111(·1111·
CI
III1
137
which is too low as noticed in a number of previous
prediction,
situations. WOSUB-II without vapor diffusion shows trends
which are perfectly similar to the COBRA-IIIC/MIT prediction
with
= 0.01 -- the only difference
being that the overall
level is substantially lower.
It should be noticed that it is by no means obvious
that FASMO predicts the correct results although this has been
assumed for the purpose of this comparison.
However,
at least
with respect to the trends set by COBRA-IIIC/MIT findings from
the foregoing comparisons could be confirmed.
for WOSUB.
The same holds
Whether the details of the FASMO calculations are
correct cannot be judged from the information received.
the observations
From
made in the foregoing tests it may be argued
that the void fraction
in the cooler section of the bundle
is
slightly overpredicted.
Finally, the following remarks seem to be in order.
Comparing the bundle average void fraction with the void
fractions calculated for the hot and cold corner subchannels
shows quite a large difference.
For instance
at the elevation
of 120 cm a is about 40% at the hot corner and nearly
the cold.
In fact, the difference
zero at
of the boiling boundaries
is more than 80 cm between both corners.
Furthermore,
it
should be noticed that the void distribution follows quite
closely the heat flux distribution across the diagonal over
the inserted
length of the control rod.
It is surprising
to
recognize that the vapor does not distribute itself more
between the subchannels. As a result, the uniform void
--
I----·-IIlll-Llyl-Y·l·-·--srsl-31C·l*
--·-
1_11
·_
138
treatment
as used by COBRA-IIIC/MIT
in applying
the code in the
BWR mode denotes the possibility of highly overestimating the
CHF.
This should be kept in mind when whole bundles are lumped
for computational convenience.
·. -----·I . -
--1.
-
-----
I---
I
--- ..-. - -- ---
--
---- -. -- .----
--· --- -C-____
139
1.6
GE-CHF Tests
1.6.1
Introduction
The purpose of this section is to test the four
critical heat flux correlations built into WOSUB-I which are
1)
Israel correlation
2)
Janssen-Levy correlation
3)
Modified Barnett correlation
4)
CISE-correlation
These correlations
are discussed
it should be remembered
in detail in [ 2 ].
However,
that the first three are bundle-
average correlations whereas the fourth is a hot-channel correlation using the boiling length concept.
The experimental tests which are used for comparison
in what follows were all performed
by GE [ 26 ].
The comparison
focuses upon small bundle tests in order to perform the analysis
with WOSUB-I because WOSUB-II does not contain the heat transfer
and CHF package yet.
1.6.2
Bundle and Test Descriptions
Most of the CHF tests performed
the same bundle as described
in Sect.
compared against the GE-9-rod data.
in this section use
1.1. where WOSUB was
A full description of the
geometric details and the actual measurement procedure is
_
___·_
140
In all cases, the heat flux is uniform,
given in [ 26].
direction.
axially and in the transverse
both
A total of five test
Test channel No. 1, 2, 2A and 3 used
channels were used by GE.
a 6-foot heated rod which was located 3 1/2 feet before the end
in test channel No. 4 it
of the 10-foot test length, whereas
right at the end of the whole test length.
was positioned
33
Figure
the layout of all five channels.
summarizes
five of the channels
All
used the same grid-type spacers typical
of modern BWR (at that time) and essentially
the same rods.
The principal differences between the five test channels were,
besides the positions of the heated length, the axial positions
with respect
of the spacers particularly
heated length.
to the end of the
in Fig. 33.
The details are also disclosed
In view of the fact that for test channel 4 the end of the
heated
length is located 2 inches before the channel exit
which is typical for most out-of-core
it
test bundle.
has been taken as the reference
1.6.3
CHF test assemblies,
Results and Comparison
Table
32
and the predicted
summarizes the experimental test data
for Test Channel No. 2.
CHF-results
The
results of the CISE-correlation have not been listed because
Before this correlation can
they are by far too conservative.
it must be corrected to account for
be used in any analysis
enthalpy exchange out of the hot subchannel. More information
and its pitsfalls
about the CISE-correlation
WOSUB-I is given in Ref.
_
___
______
__
___I__
___
as used by
[2].
__
_
_
_
_
_
____
_
__I
_
___
___I
___
___
,vil
-i-'
-i- ViNlAwat A -W, *VW
141
,
?
cm
I-
I
)
(0
r
i
}
Q
i
e
.\
~
C
Ci
L
LL
ir
I;
t
'
ie
q
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i
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C
r5j
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iq:
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11
(a
i
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a
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a
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II
CA is
w
i
i
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q
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qd
C4
CZ
C,
U
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'.'3.
i
i
re
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13
0
ci
1Z
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Ca
z
:I.
CM
Lb
ci
0
-
c01.
E
sz
.!!
cn
I-CE
uj Q
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w
m:
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2i
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w
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en
-30---
I
142
TABLE 32
COMPARISON OF CHF RESULTS BETWEEN EXPERIMENTS AND PREDICTIONS
FOR TEST CHANNEL NO. 2
Test
Pressure
I Mass Flux
Inlet
'
CHF
CHF
cooling
1
1399
197
800
170
1000
HF
Btu/ft-h
'__________
Btu/lb
218
CHFS
ft -h
1.01
1203.4
1.005
I
35.1
I 0.635
1.25
'188.4
0.819
1.249
1136.8
1.242
I 97.4
0.660
10.7173 '0.729610.7445
,0.3515 10.5475 0.567
'0.8108 10.7584'0.8728
I
172
1000
167
l1000
CHFmeas:
---
'
Il~~~
1
Jannsen-Levy
CHFIS:
Israel critical
CHF B :
Barnett critical heat flux
--
I 0.710
Il~~I
~
0.6411
j0.457
~Il
:0.7137:0.7711
i0.669110.6918
~~~~~~~~I
~ ~ ~~
I
measured critical heat flux
CHFJL:
----- ---
~
I 0.748
----- - --------
critical
- -------
heat flux
heat flux
-- --- -----
t
Calculated
i
J
-
-...
._ __ _ _____ _
.____
____
~
143
Figure 34
compares the measured with the
predicted CHF-values. Error bands for ±5% and ±15% have been
included for convenience. The following conclusions can be
drawn from Fig.
1)
34:
The Janssen-Levy
correlation
gives far too
conservative results under certain conditions. This
may be the reason why it has been abolished
by GE and
replaced by the Hench-Levy correlation which in turn
has been recently replaced by GEXL.
2)
For the limited cases studied here, the modified
Barnett and Israel correlations produce results
which fall well within the
dictions are within the
3)
±15% band.
Other pre-
±5% bands.
In the context of present standards
the pre-
dictions have to be considered satisfactory especially
in view of the fact that the grid-spacer
loss coef-
ficients were not known for the predictions.
Figure
35
shows the measured
No. 1 as a function
test data for Test Channel
of the average bundle quality bounded by
the best fit curves of the results for Test Channel No. 4.
circles show the results of CHF-predictions
The
for the test point
3E2 discussed in Sect.l.l.5. with radially non-uniform
peaking factor pattern.
These results lead to the following
conclusions:
a)
The predictions
for this quite differently
heated case fall within the range given by the best
curve fits.
_
·_
I
144
FIGURE 34:
Comparison of Three CHF Correlations with Measurements
0.
0.
x-f
40.
.-
.
t1
A/,3
".
n.
..9i
V.
-v-.
(1ewr
· I-n-- -- ---·---
I
--I
-
----
----I---_
_
1.
-.
'Ia 1
-
A .
U.
6
V.
W.r
.
U./
(BU/LB-FT 2 )
_ ____
____
___
____
'1
145
2
S
I
0
o
F-
-
d
.
%0
%A
U
w
:Z
..
It
0 /
I
V
_3
a
I
-.
I
-
/0
4
-4D
0
O
'Si
Pao
i
0
a/
-
r~'I
i
i
i
N.0
I
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30
i
a6l
N
-
c50
0
-4i-
f
co·
UIC-----I------ _I_
C
q
.- ·._
_
_
_ _
146
The results according to Barnett's correlation
b)
fall in line with the Test Channel No. 1 data.
forms about the best fit
The Israel correlation
c)
The result of this comparison of widely differing cases shows that the 3E2
CHF data are also within the bounds given by Test
Channel 4, according
Figure
36
to the predictions.
compares the test data for Test Channel No. 4 in the
case of G being G = 0.5 x 106 lb/hr-ft 2 with the predictions
to the Barnett and Israel correlations.
for this case according
The average bundle exit quality varies between 0.35 and 0.5.
Two test cases were run and the results are shown in Fig. 36.
which
The conclusions
can be drawn from this figure are:
Both correlations predict conservative answers
I.
within the framework of WOSUB-I
The modified Barnett correlation give slightly
II.
more conservative results than the Israel correlation.
III.
For high average bundle quality the predictions
get closer to the test data.
Figures
37
summarize the comparison with another
38
and
271
set of 9-rod CHF-data
mass flow rates,
for two different
For the high mass flow rate, i.e., low exit
respectively.
quality up to 30%, Fig.
agrees very well wth
37
shows that the Israel correlation
the trend of the test data, whereas the
modified Barnett correlation depcits again a slightly conservative trend.
At the low mass flow rate, i.e. high exit qualities
as shown in Fig.
1__11
_1_
___
38
__ __ __I__
both correlations
_ _ _____
__
_
_
show a slightly
_
_ _
_1__________1_
__
_____
·____II___
147
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150
conservative trend which increases toward the lower end.
Favorable
agreement
exists at the high end of the test data.
Again the Barnett correlation is a little bit more conservative than the Israel correlation.
Finally, to show WOSUB's capability of predicting
the critical bundle power, Fig.
between
39
test [28 ] and predictions
cooling at the inlet.
power as determined
too conservative
shows a comparison
as a function of the sub-
The figure indicates
by the CISE-correlation
although
the gradient
that the critical
is far too low and
is simulated very well.
This should not come as a surprise because as was already
noticed before, the CISE-correlation gives very conservative
results
for the CHF.
determined
reason
In turn,the boiling
length is erroneously
and thus affects the critical power.
for the failure of the CISE-correlation
The primary
is that it has
been developed for a rod-centered subchannel concept which has
been modified for use in WOSUB.
Furthermore, the specific
version which has been built into the code does not account
for energy transfer across the subehannel boundaries.
Both
effects certainly sum up very conservative predictions as confirmed by the present comparison.
1.6.4
Conclusions
Within the framework of the limited test performed
it can be concluded
fairly reliable
that the CHF-predictions
by WOSUB-I are
for the small bundles considered
in this
comparison. The Israel and/or modified Barnett correlations
------- 1..
--
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151
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152
are recommended, although for low exit qualities both exhibit
conservative trends.
The Jannsen-Levy correlation will be
replaced by the Hench-Levy correlation in a future version of
the code.
Special attention must be put into the modification
of the CISE-correlation
in order to obtain reliable
values for
the boiling length which should be compared to GEXL results in
the future.
Future comparisons have to cover a broader range of
test conditions as well as larger bundles which necessitates
the incorporation
of the heat transfer and CHF package
into
WOSUB-II.
In summary,
it can be concluded
that this first
attempt of confirming WOSUB with respect to its CHF predictions
was successful by present standards.
Due to the fact that the
user of this code gets four CHF-values according
correlations
built
to the four
into the code, he can use engineering
judge-
ment to make his final decision.
·
_I
___
_
__
__
___
___
_
__
____
__
153
1.7
Sample Cases for the Prediction
of the Heat Transfer
Coefficient and the Pin Temperature Distribution
1.7.1
Introduction
WOSUB-I contains a fairly elaborate logic as
described
in [ 2 ] for the prediction
of the heat transfer
coefficients in the various single and two-phase flow regimes.
(See Fig. 40).
The kernel of thissubroutine
centers around the Chen
correlation which was thought to cover consistently the spectrum
of conditions
of special interest to BWRs.
Rather than
modeling each pin in the bundle it was decided to model the
hot subchannel and its immediate neighbors as precisely as
possible.
For this reason the code determines four heat trans-
fer coefficients
around each pin corresponding
to the four
subchannels. The user has the option to choose the minimum
or the average of the four heat transfer coefficients
calculation
of the pin temperature
distributions.
the code prints out all four values.
for the
In any case,
It is recommended
that
in a future version of the code all four values be used to
perform four one-dimensional temperature calculations at least
for the corner rod which experiences
the largest circumferen-
tial variations in the cooling conditions.
This would lead
to discontinuities at the subchannel interfaces. However, this
is unimportant
in view of the fact that the calculation
would
give a first estimate of how changes in the heat transfer
coefficient will effect the center line fuel temperature.
cases of PUO 2 /UO 2 fueled bundles an additional
power generation
4111-·-----
_ _
_
tilt in the
in the fuel could be superimposed.
_
-
--- _
_I
In
154
FIGURE
40: LOGIC FOR THE EVALUATION
OF THE
HEAT TRANSFER COEFFICIENT
Yes
No
Single Phase
HTC
s
Dittus-Boelter
Yes
No
No
Average Heat Transfer
Coefficient
-----
----------
----
-
-
--
----
----
-
--
-
-----.-
---------
155
For the determination
of the temperatures
in the
fuel and the clad a collocation method using Hermite cubic
splines is used which is described
in detail in [ 2
].
This
procedure has been extensively tested before it was incorporated into WOSUB-I.
the temperature
However, no other solution scheme for
calculations
has been built into the code for
comparison. Therefore, the whole numerical comparison relies
upon the tests made without the fluid-dynamic solution scheme.
Results and Discussion
1.7.2
Figure 41
summarizes the four heat transfer
coefficients and corresponding clad surface temperatures for the
corner pin in GE-test 3E2 at the axial position
from the inlet.
transfer
A surprisingly
large variation
exists at the circumference
conditions
of test 3E2 resulting
clad temperature
variation
of 50.4 inches
in the heat
of the corner pin for the
in a maximum
of about 140F.
circumferential
The lowest heat
transfer coefficient and thus the highest clad surface temperature is associated with the hot center subchannel. This may
be indicative
of the location where CHF starts.
Such detailed
maps of heat transfer coefficients and temperatures have not
They pro-
been produced previously by other subchannel codes.
vide useful input into structural codes.
Observations made under various cooling conditions
indicate that in fact a thorough
logic
(see Fig.
40
set-up of the heat transfer
) pays off because then even extreme
In
cases such as pool boiling can be handled with ease.
contrast, the heat transfer
logic in COBRA-IIIC/MIT
barely
covers the regions of interest.
IC---(--------··-r-·
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156
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I
= IrURE
Heat Transfer Coefficients and Clad Surface
41:
Temoeratures around a Corner Pin in a 3x3 Pin Bundle
_
-.---
,
__._ __
_
..
__
_
-_
_____
__-
_
_ _
157
With respect to the temperature calculations in fuel
and clad, Table
33
and Fig.
42
here for convenience from [ 2 ].
are again reproduced
This comparison suggests that
the solution method chosen for WOSUB-I is indeed very powerful.
Not only is it superior
in accuracy but in addition
it
provides reliable point values instead of nodal values for
the temperatures.
This is of special importance
in arriving
more reliable heat flux predictions.
Figure
profiles
43
shows two steady-state temperature
in the fuel as a result of a WOSUB-I run, showing
that the subroutine has been successfully integrated into the
subchannel code.
will be reported
Its transient capability is now tested and
in the future.
I
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4000
3500
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3000
2500
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Fig.
I
___.
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.8
1.2
1.6
2.0
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10
1
(in.)
Temperature Distributions in a Fuel Rod During a Power
Transient - Comparison Between the Finite Difference Method
and the Collocation Method
_---I
L
.___
__.__.
_I
_
_
----
_J__
__
__
_
..
__
2500
2000
1500
1000
500
0
0.1
0.2
INCHES
FIG T URE
43:
Steady State Temperature Profiles in the wuel as
Obtained by the Collocation
ethod Using Hermite Cubic
Spline Functions.
1111111--
1_----^·1111111··Ilslllf-·-
-·-SPIIIYIISIII--I
--
I
162
1.8
Sensitivity Study of the Void Concentration Parameter
and Relaxation Length
Introduction
1.8.1
A limited sensitivity
study has been performed
examine the effect of the void concentration
and the relaxation
length, Ze' upon the predictions
GE-test runs 2D1 and 2D3 (see Sect.
it should be recalled
parameter
parameter,
[ 2 ] that C
for adiabatic
1.1.4).
to
C,
of the
At this point,
is the void distribution
flow, whereas
Ze is a relaxation
length
to account for diabatic conditions.
WOSUB-I has built-in standard reference parameters
using C
= 2.5 and Z e = 0.
following
determined
grounds.
These values are chosen on the
For two-phase
to not exceed 1.4.
flow in tubes C
However,
has been
the sutchannel
geometry is a more complicated geometry. Therefore, a value
has been chosen which
square channels
suppresses
is close to the value of C
29 .
measured
On the other hand, setting Z
the vapor source under the assumption
conditions.
Naturally,
= 0
that the
diabatic void profile is the same as the asymptotic
adiabatic
in
one under
the code user has the option
to override the standard parameters by specifying them in the
input to whatever
1.8.2
he thinks best meets the physical
Results and Discussion
For the two test conditions o
in C
from 1 to 4 for Ze =
changes in the qualities
subchannels.
..---~II----
situation.
2D1 and 2D3, changes
do not result in any appreciable
or mass flow rates in the individual
No reason for this insensitivity
can be given at
P--
II
163
this time.
Positive values of Ze lead to increases
in the mass
flow rates especially in the corner and center subchannels
while decreasing their qualities, because in this case a
specific fraction depending upon Ze is subtracted from the
vapor flux.
This means essentially that recondensation takes
place in the bulk of the coolant.
For negative values of Ze
the vapor flux is increased and so are the qualities whereas
mass fluxes are decreased.
The aforementioned trends reflect only general
tendencies. The whole picture is in fact more complex for the
individual subchannels and largely depends upon the case under
study, i.e., average exit quality,
Figure
44
inlet subcooling,
shows a sample of this sensitivity
reveals the complexity
an "optimized"
study which
as well as the difficulty
set of input parameters.
of deriving
As can be seen from
this sample, improvements can certainly be made.
the same time it becomes apparent
etc.
However, at
that this type of change
does not lead to closing the gap with the experimentally
determined quality of the corner subchannel.
can be made however as depicted
in Fig.
45.
Some improvement
Changing
the
input parameters too drastically leads naturally to physical
nonsense.
During the course of benchmarking
all the experiments
described
the code against
in the foregoing
sections
it
has been-noticed how important the vapor diffusion model is.
Unfortunately,
this has not been examined
-·------·------
·L--·l"·----*l·-----ar-----·l·-·-rr
in the sensitivity
.__1..1
16 4
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____
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165
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4.
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166
study because
it was thought that the void distribution
parameter was of greater importance. Furthermore, the
vapor diffusion model has been fitted against experimental data
and for this reason it was believed at the time of this study
that the model was reliable.
experimental
Now that the comparisons
tests always show the same shortcoming,
with
i.e., too
low quality in the corner, and too high quality in the center
subchannel,
it is thought that only a change in the vapor
diffusion model can bring adjustments in the right direction.
1.8.3
Conclusions
The limited sensitivity study revealed the following
conclusions:
1)
C o has no effect as long as Ze is set equal to
zero.
2)
Z e affects the results in quality and mass flow
rates.
The changes depend upon the range of system
parameters under consideration.
3)
Changes in C
and Ze alone will not meet the
requirements set forth by experimental evidence.
4)
In order to more closely meet the experimental
trends in subchannel
quantities it is necessary
refit the vapor diffusion model.
to
Once this model
fits the bundle data better the sensitivity
study
should be repeated.
One of the reasons why changes in C o and Ze do not
affect drastically
.I---
-
--
-----.
_
--__
the overall trend is that they have about
__
__
_
_
_
__
_
_I_.._
I
.
__
____
167
In this situation
the same impact on all of the subchannels.
the only remedy for redistributing
the vapor diffusion model.
the phases is by the use of
The reason why this model does not
work to great satisfaction right now is that it has been fitted
a)
to air-water
data
b)
the data stem from test sections which simulated
only two subchannels.
Obviously, both effects lead to a far too large diffusional
redistribution.
The only way to refit this model is by per-
forming a parametric
study on the whole set of GE and Studsvik
At the same time the effect of changing C
data.
be studied again.
However,
and Ze should
it is suggested that the drift flux
model in WOSUB be completed by extending it into the other
two-phase flow regimes before this new sensitivity study is
initiated.
llr
-C
I^-·ll·lll···-lr.r.·1111111
11
_-
·1
1----------·--1-11
111
11
__
1
168
1.9
Other Supporting Evidence
for the GE Findings
and
the Drift-Flux, Vapor-Diffusion Model
1.9.1
Introduction
When GE published
its measurements
at the same time that the subchannel
giving correct answers,
codes were not capable of
most people questioned the measure-
ments and their accuracy.
surfaced.
[ 4 ] and showed
In the meantime, supporting evidence
There are the Swedish three-dimensional void
measurements in round bundles on the one hand [ 30 - 32
and on the other, the recently
published French data
,
19 ]
for a square-array, four-pin bundle tested in a Freon-loop.
Unfortunately,
in the assessment
the
both cases could not be integrated
of WOSUB for the purpose of comparison because
ode does not handle round bundles nor Freon properties.
Therefore, this evidence is only added for convenience here.
However,
in what follows, emphasis
will be put on the square-
channel arrangement only.
1.9.2
Results and Discussion
The following data are taken from Bayoumi et al
[ 19].
The purpose of these measurements
mixing model
was to provide
in the FLICA code with reliable
input data.
the
The
isokinetic sampling method has been used by the authors.
Figures
46
and
47
show the deviation
in the individual
subchannel mass flow rates as a function of average quality.
The following general conclusions can be drawn for both mass
flow rates considered.
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171
1)
The side subchannel follows the bundle average
behavior.
2)
The center subchannel is characterized by a
larger than bundle-average mass flow rate, whereas
the corner subohannel is characterized
by a smaller
than average bundle mass flow rate.
3)
In the subcooled regime both mass flow rates in
the subchannels diverge with increasing quality,
whereas beyond the inception of bulk boiling they
converge towards the bundle average behavior.
4)
The functional dependence as described under
point 3 essentially means that in subcooled boiling
the cross flow is from the corner to center sub-
channel whereas in bulk boiling an inversion of cross
flow takes place.
Figures
48
and
49
show the deviations
in the thermo-
dynamic quality distributions in the individual subchannels as
a function of the bundle average one, for the two mass flow
rates, repectively. The following conclusions can be drawn
from these data
a)
The side subchannel behaves
like the bundle
average.
b)
The center subchannel always shows a higher-than-
average quality.
c)
The corner subchannel always shows a lower-than-
average quality.
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----
174
d)
The differences in quality between the subchannels
decrease with increasing bundle average quality but
stay constant
Figures
enthalpies
for x i > 0.10.
50
and
51
in the gap as afunction
show the cross flow
of the center and corner
subchannel qualities respectively. These data were obtained
from non-isokinetic sampling.
I.
The donor
These figures reveal that:
cell concept for energy exchange
is
not valid to describe the transfer process between
center and side subchannel.
In fact, over most of
the quality range the enthalpy
in the gap region is
higher than both subchannel enthalpies. Dependent
on the two-phase
flow regime which exists, it drops
below both enthalpies in order to increase again.
This essentially
confirms
the data by Lahey et al
[4-7].
II.
Over a certain quality range the donor channel
concept can be used to describe the energy transfer
from the side to the corner subchannel.
for x
i corner >
However,
0.10, the enthalpy in the gap starts
to fall below both subchannel enthalpies.
1.9.3
Conclusions
The French data presented in the foregoing section
confirm the findings by GE as well as the other observations
made during this assessment. Because they were obtained under
diabatic and bundle conditions, they essentially constitute a
more sophisticated data base for fitting the vapor diffusion
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--
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1.
i
i
177
model than the two adiabatic subchannel data by Gonzales
33 ].
All these measurements confirm what has been basically
presented already by GE and, most of all, support the finding
that subchannel codes such as COBRA contain inherent defiThe French data make it again very clear that
ciencies.
single phase mixing models using constant coefficients are
totally insufficient and indicate furthermore that the donor
cell concept is also in error especially
for higher
qualities.
Essentially, the drift flux model with vapor diffusion eliminates the ambiguities inherent in common subchannel
codes with respect to the various models, and proved to be
successful
tests performed.
in all the benchmark
still exist are explainable
which
Deviations
in terms of not yet
perfectly fitted input parameters; however what is important
at this stage in the development
correct.
IPY-------rsl--·-.·---I
-Irrrl
-
-
is that the trends are
This has been confirmed by the French data.
·-- l·----y·l*----r-.PUI----
-
-
-
·Lsllllllli·lllll·l·llllli·l··P
C
.
_
178
2
2.1
Tests of WOSUB-i in Transient Situations
Introduction
In contrast
to the steady-state
condition
there are
no individually measured subchannel quantities available in
For this reason it is impossible
to
transient
situations.
benchmark
the code with respect to local quantities at this
Therefore, the results which follow in the
point in time.
next sections are only of scoping character in order to show
transient
some basic
run by the code resemble
2.2
as closely as possible
some of GE's
However, these transients were compu-
experimental tests.
for only a few seconds.
followed
tationally
The sample cases
features of WOSUB-I.
Mass Flow Reduction Transients
Figure
exit qualities
shows the corner and center subchannel
52
as a function of time for a 40% flow reduction
in 3 seconds in a 3 x 3 GE pin bundle with radial peaking
factor pattern
(3E2 series, see page 41).
that the qualities
still increase
The results indicate
further for about 1.5 s.
before they reach their new asymptotic values, although the
flow has already reached its new steady-state value.
tial differences
show up in the response
Substan-
of the subchannels.
Whereas the corner subchannel is rather sluggish, the center
subchannel responds much faster to the change in the mass
flow.
In addition,
the ratio of the final asymptotic
value
to the initial value in quality is larger for the center
subchannel, which naturally remains the hottest one during the
transient.
___________
_______
___
I
179
[MASS FLUX REDUCTIONI
C
CENTER SUBCHANNEL
FIGURE 52
L EXIT
MASS
.,
.4
u.l
A;
3I--
1001
CORNER SUBCHANNEL
o0
(
+o
U
~4
o
I
3
2
TI
E (S EC)
'3.S
5
180
Another, more severe mass flow reduction transient
was run with a 50% reduction
actually
in 1 second.
This transient
simulates run number 9-152 as reported
in Ref.
[27]
However, during the computation the time at minimal mass flux
which has been reported
to be approximately
was taken to be only 3 s.
25 s. for this run
Another discrepancy
may exist for
the time to reach the minimal mass flux which seems to be
shorter than
differences,
s. in the experiment. Despite these possible
CHF is predicted
at 0.7 s. after the minimum mass
flux has been reached which compares favorably with what is
reported
in [27 ] where
it is stated that CHF occurred at
about 0.5 to 1 s. for the various tests after reaching
lower flow.
the
The calculated boiling length increased from about
4.2 feet to 5.1 feet during the transient which roughly agrees
with values reported
in [34
mass fluxes in the individual
time.
.
Figure
53
subchannels
shows the exit
as a function
As can be seen from this figure, a substantial
of
redis-
tribution in the mass flux takes place during the transient.
The corner subchannel starting with the highest mass flux
initially reaches an asymptotic value which is slightly higher
than that of the corner subchannel. The side subchannel which
is close to the bundle average mass flux at the start of the
transient approaches a value somewhat higher than the bundle
average.
In general it can be noticed that the spread
initially
existing between the mass fluxes in the subchannels
substantially
is
reduced at the end of the transient which is an
indication of redistributions taking place during the transient
-
-
- -- ·-----
-··- -----------
--II
181
Ca
Ca
, n0C
rJ2
Up
C
a)
I-
-j
-11(1.
0
c,..
6Z
\0
6
6
_
___
0
_
182
process.
Figure
54
shows the deviation
of the exit sub-
channel quality from that of the bundle average at the exit as
a function of time.
It is interesting
to notice that the center
subchannel becomes even more hot relative to the bundle average
compared with its initial value.
The substantial increase
occurs at about the time when the transient is finished.
On
the other hand, the corner subchannel which starts out with a
quality below that of the bundle average responds immediately
and its quality lags more and more behind the bundle average
with increasing
time up to about 2.4 s. into the transients
where the difference establishes itself at a new asymptotic
value.
The side subchannel which has been observed to follow
about the bundle average in steady-state follows this trend
approximately also for the mass flux transient.
transient
this subchannel
the quality difference.
During the
stays at the steady-state
value for
Starting at the end of the transient
the quality difference slightly drops below its initial value.
Overall, the trends as observed in steady-state are also
confirmed in transient situations, where obviously the difference of the behavior
in the subahannel qualities
grows.
It
should be noticed that this calculated difference may be too
large because the vapor transport into the center subchannel
is overemphasized leaving the corner subchannel too cool as
discovered
in all of the steady-state
benchmark
tests.
From the point of view of the CHF calculational
procedure, the predictions suggest that the center subchannel
· _
_
______1
______I
183
O.l
4>)
..QUAIr
XC'
-H
X- X
b-4
al a
>
4- ri
4=)
0
a Q
04 or
44 ;4
03
4-)
00
au x
=
C
rdm
c)
m:
E-4
0e 0CJ
O
-0.
-H a,
Xc
4-)o
4.)
C k
r-4
cd
.E.
_H
_
O4
O
cd:;
-H r
- 0.2
>
iz
0.
1.
2.
T. r
(SEC)
z
bc
C F=
184
quality be taken for these calculations.
As expected, the
corner subchannel with its cold wall effects substantially
lags behind the bundle averaged quality behavior.
2.3
Depressurization Transient
Reference
transients
[27] reports some depressurization
from an initial pressure of 1000 psi to a nominal
value of 800 psi.
Run 206 has been modeled for the scoping
purpose of this report where a depressurization rate of
100 psi/second
was used over 2 seconds.
Figure
the mass fluxes at the exits of the individual
a function of time.
According
55
shows
subchannels
to these results,
as
the mass
fluxes increase rapidly at about the same rate in each subchannel,
reach a maximum at 0.4 s., and decay.
No C
calcu-
lations were performed for this transient.
Furthermore, no
time step sensitivity study was performed.
Therefore, these
results have to be considered preliminary in nature.
2.4 Power Transient
For the purpose of comparison an example for a
power transient
in a 3 x 3 GE rod bundle has been constructed,
where tne power is increased by 50% in 0.5 s. and then reduced
back to its initial value at 1 s.
for the validity
This example is a good check
of the code because the same qualities must
result finally as those at the start of the transient.
56
Figure
confirms that indeed the calculated exit subchannel
qualities approach their respective initial values more than
1 s. after the actual transient is over.
Again, as already
1113Llllllls.___lC--rr____l__l_
-·r-
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O
r4
C
z1
4-)
N
Cc
U)
U)
ja;
U)
U)
V7
asx
U:
_
e-
Q
0L4
o
Z
'V
0
C)
Ci
O
d
Q
·lllllllllllsllllllls391
~~~~~~~~C1)
l
a 1C
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7
--...--.III----.I----.
_
I
186
.Wosua-:
Il
$11~~~~~~~~~~~~~~~~~~~
PowER7ANSIrMT1
FIGURE
56
SUBCHANNEL EXIT QUALITIES VERSUES TIME
FOR A POWER TRANSIENT
I.S
/
P
/
.4
.
/
2
en
'I'
U
U
%J
I
/
/
4
*
L4 1
1.0
CENTE R
I
I..a
5lOE
CORNER
0
1
2
rUIC
-
---
I
(strc)
187
observed during the mass flux transient, the center subchannel
responds fastest and reaches the highest quality in the bundle
earliest
in the transient, but still about 0.3 s. after the
power peak.
subchannels
slowest of all the
The corner subchannel responds
and peaks latest nearly at the overall end of the
transient.
Figure
shows the increase
57
length
in the boiling
and its return to the initial value.
during the transients
summarizes the calculated CHF results
Figure 58
according to the Israel and Jannsen-Levy correlations.
As can
be seen from these results, the Jannsen-Levy correlation gives
larger values for CHF than the Israel correlation
initial and asymptotic period of the transient.
during the
Towards the
point of power peaking the Jannsen-Levy correlation approaches
the Israel correlation and even undershoots it.
2.5 Discussions and Conclusions
erformed with
Very few transient runs have been
WOSUB.
Their results have to be considered exploratory.
Certainly,
no real conclusions
can be drawn at that point in
time other than that the code operates
in the various modes of
transients considered.
lance, the predicted
At a first
results seem to be
reasonable although the calculated mismatch between center and
corner subchannels with respect to quality may be again too
large due to the well known reasons already discussed
for the
steady-state predictions.
Indications are that WOSUB is giving reasonable
------ --- --
-----
-
----
-------
I
--
188
4~L
I'
0
a0
C)
0C4
U,
n
C)
(d)
O~
QI
k£aU,
Cd
d-Cd
.
QE-'
Ed
Is
m3
To
oa) -
rl v
t-
1 S3
hO
C
I04o
bOO
- ._
.
L
0
hO
0
0
C
C')
(i4 H V
I77
----
3Nr47J8g
I-- --
-
189
Figure
Calculated CHF as Function of Time for
the Power Transient
58:
In
-.
O
Ii
V-
0
a
d
- -
N
I
190
answers with respect to integral parameters such as CHF, and
CP.
However,
most of these transients have to be run out for
longer periods of time in order to make final conclusions.
It should be pointed out that unfortunately
only the
integral parameters mentioned above and the time to CHF are
available for benchmark purposes.
To the author's knowledge,
no local subchannel quantities were ever measured and reported
in the open literature.
for these quantities
Therefore, the predictions
cannot be benchmarked,
of the code
other than by com-
paring them with results of other subchannel codes.
As regards
the predictions of CHF, it should be recalled that these heavily
depend upon the empiricism entering into the various correlations.
This is especially
agreement
important
in the engineering
for BWRs where there is no such
community as exists for the
PW9Ranalysis by using the W-3 and B&W2 correlations.
?·lllllllllr*rrlrrrul·ll·*rlrr·rmrr
I
191
3
3.1
Conclusions
S'teady'-StateCalculations
During the assessment phase of the research period,
WOSUB has been tested against the following experimental data:
1)
GE 3 x 3 pin bundles under isothermal
2)
GE 3 x 3 pin bundles with uniform radial peaking
3)
GE 3 x 3 pin bundles with non-uniform radial
conditions
peaking
4)
Columbia 4 x 4 pin bundle with different radial
peaking
5)
factors in two of the rod rows
Swedish 3 x 3 pin bundle test with power tilt
Overall, the following conclusions can be drawn with respect to
the performance
a.
of the code:
The predictions by WOSUB with vapor diffusion
model follow the trend of the data better than the
results of the common subchannel codes do.
in accordance
In fact,
with the GE data, WOSUB determines
the
center subchannel quality above bundle-average, the
side subchannel quality about bundle average, and the
corner subchannel below bundle average.
b.
The determination
of the magnitudes
of the sub-
channel quantities by WOSUB is not perfect yet for
the following two reasons.
flux correlation
First, the built-in drift
covers only the bubbly
and bubbly-
shape two-phase flow regimes and second, the parameters entering the vapor diffusion model have been
fitted against isothermal air-water data in two-subchannel geometry.
The latter fact especially leads
192
to overemphasize
the vapor transport
into the
center sutchannel, increasing its quality too much by
lowering that in the corner subchannel
same time.
This becomes especially
comparison
too much at the
apparent
in the
with the Swedish test data, where the
code predicts
the combination
of side and center sub-
channels
to be the hottest due to the aforementioned
reasons,
in contrast
to the data, which indicate that
in fact the combination
is the hottest.
mismatch
agreement
c.
of corner and side subchannels
With the exception
the rest of the predictions
of this explainable
are in good
with the data.
The predictions
substantial
for the Columbia tests indicate
agreement
for the calculated mass fluxes
of both the "hot" and the "cold" center subchannels
as
functions of either subchannel or bundle exit qualities.
Mcre details are given at the end of the indi-
vidual sections.
Besides primarily benchmarking the code against actual
test data, it was the intention
of this study to compare WOSUB
with the results of other commonly used subchannel codes.
Fortunately,
for all experiments
considered
in this study, a
whole variety of subchannel code results were available, thus
allowing
mental
a direct comparison between these codes and the experi-
results as well as between WOSTIB and the experiments,
and WOSUB as compared
five experiments
CP6r
to the other codes.
mentioned
at the beginning
In addition
to the
of this section,
I IC.
·
193
the following
two tests were found in the literature
for which
however no experimental results are available:
6)
Planned Swedish 3 x 3 pin bundle tests with very
strong power tilt,
7)
Hitachi 7 x 7 bundle with 3-D power distribution.
According to the evidence which has been accumulated throughout
this report, the following conclusions can be drawn:
d.
The comparison of various subchannel codes in
different situation presented in this report has to
be considered to represent a fairly concise picture
of the state-of-the-art.
e.
WOSUB with vapor diffusion model included is
superior overall to common subchannel codes which use
constant mixing factors.
f.
Subchannel codes which more closely predicted the
experimental results such as the proprietary MIXER 2
and SDS-codes do include presumably the same model as
WOSUB but had the additional advantage of being well
tuned in advance.
g.
Other subchannel codes using the common mixing
models have seemingly no potential to be readjusted
such that they would predict the trends as denoted
in conclusion
h.
Although
(a.).
all subchannel codes do predict the
bundle average quantities very well it must be acknowledged following conclusion (g.) that the majority
of them is in fact unable to predict the hottest
__
___
194
subchannel which must be considered a severe limitation in the applicability
of these codes.
even true for codes such as THINC-IV
This is
and COBRA-IV-I
and it is no surprise that recent developments
Batelle and elsewhere
concentrate
at
in fact upon the
drift flux model.
i.
The inclusion of the concepts
and critical
certainly
power although
of boiling
not yet perfected
a step in the right direction
length
is
to follow as
closely as possible the recently developed design
philosophy as employed by GE.
More details are given in the respective sections.
3.2 Transient Calculations
Very few coping runs have been made with WOSUB under
transient conditions. From these limited experiences the following preliminary
a.
conclusions
Benchmarking
can be drawn:
of WOSUB will be only possible
with
respect to measured integral parameters such as CHF,
boiling,
length, time to CHF and the like. 'With
respect to local subchannel quantities,
be only bencnmarked against
the code can
ther subchannel
cdes.
However, due to the findings summarizedin Section
3.1, this seems to be a questionable
cause the majority
of existing
rocedure be-
subchannel codes is not
giving reliable answers for BWR analysis even in the
steady-state situations. The only reliable data
could come from the proprietary
_.
_I_
I_--
1.
__.
__
I
___
codes.
I_
__
In this sense,
___
______
__
____
195
the situation for BWR analysis is much more complicated than that for the PWR analysis.
b.
The preliminary runs made with the code indicate
that it works for various types of transients
and that
its results are in agreement with the few indications
given in the literature. However, much more must be
done in this area.
c.
The results obtained by the code for the three
types of transients studied indicate that the center
subchannel remains the hottest one during the course
of all transients.
However,
it must be expected
that
the magnitude of its heat-up is again overemphasized
due to the vapor diffusion model which is not tuned
yet for diabatic multi-subchannel conditions.
196
4
4.1
Recommendations
Steady-State Calculations
According
stated in the foregoing
to the conclusions
chapter the following
recommendations
can be formulated for
future work.
1)
Available drift flux correlations for annular and
mist flow regimes should be added to the code in order
to cope with situations where either one of them occurs
in steady-state
or transient
situations.
This neces-
sitates the inclusion of a flow logic into the code.
2)
A sensitivity
study for the vapor diffusion model
should be performed.
For this purpose the GE test
data should be taken as a basis for the comparison.
When better agreement has been achieved, it is suggested that the Swedish test data be recalculated,
because individual subchannel data are available from
the code MIXER 2 which should be considered
the standard
3)
as being
in this context.
Having more closely fitted the vapor diffusion
model to reality it seems to be appropriate
a second look at the selection
parameter C
to have
of the distribution
in subchannel geometry and the relaxa-
tion parameter Ze
4)
For both parameters additional correlations if
necessary
should be added to the codae to account for
their dependencies
5)
~~ Xlllll~~r
on pressure and mass flux.
Cther models entering the code should be checked
ru~~r
r__ r~
-----
-- · r~~~sl-·____
197
for their applicabilities
in light
and capabilities
In this context, especially
of recent developments.
the single-phase mixing concept should be thoroughly
tested and probably more options provided for the
user of this code.
6)
The spectrum of available heat transfer correlato include a suitable post-
tions should be extended
CHF correlation.
This would enable the user to test
the calculations against clad temperature measurements
under severe conditions.
7)
Changes should be made in the available
correlations.
First, the Jannsen-Levy correlation
should be replaced
by the more suitable
Hench-Levy
must be
Second, the CISE-correlation
correlation.
CHF-
extended to include a quality correction term
(CISE-IV) accounting for enthalpy exchange across
subchannel boundaries.
improvements
This would certainly lead to
in the calculation
which is now too conservative
of the critical power
due to the adiabatic
hot
center subchannel approach employed by the CISE-III
correlation.
8)
the heat transfer package,
Once
the drift flux
package and the vapor diffusion model have been updated
in WOSUB-I,
the whole set should be implemented
into
WOSUB-II.
9)
Once
WOSUB-II
has
been
completed,
7 x
7 and
bundle designs can be calculated.
'
-"1----"11-·
" ^"·"·-LL"ls-n*--Y-·IILIIIU·I·III
-- r-
---
8 x
8
198
10) The effect of axial power distributions upon
boiling length and critical quality should be parametrically studied.
11) Non-uniform radial power peaking patterns which
also change axially (asymmetric control rod insertions)
should be studied systematically and their effect
upon local quantities and bundle average quantities
determined.
12)
It should be checked under what circumstances a
bundle lumped-parameter approach is equivalent to the
more elaborate subchannel approach and where it fails.
4.2 Transient Calculations
According
to the conclusions
stated in Chapter 3.2,
the following recommendations can be added to those already
listed above for steady-state calculations.
13)
A set of transient benchmark data should be
collected by screening the available information in
the literature for power, flow and pressure transients.
14)
The capability
different
of handling
types of transients
combinations
of
should be added to the
cede.
15)
Recently published transient CHF correlations
should be checked for their applicability and implemented
16)
into the code if necessary.
The effectiveness
of the temporal differencing
scheme employed by the fuel pin model should be
checked and if necessary replaced by a numerically
J*
199
more effective one.
17)
A variable fuel-clad gap model should be added.
18)
Temperature-dependent properties should be
included into the fuel pin model.
19)
Results for the various transients
recommendation
13 should be presented
selected
in
in terms of
axial penetration of the boiling transition versus
time.
20)
Freon properties should be eventually added to
the code in order to recalculate
experiments
void propagation
performed by Staub et al.
This list is by no means complete but these additional
features would help to broaden the range of applicability of the
code and could identify other sources of uncertainty which have
not surfaced yet.
As mentioned
already in the introduction
WOSUB is still in the stage of development
the code
and some of the afore-
mentioned recommendations may be included in the near future.
The list of recommendations
presents
a ranking of priorities
which will be followed in the future development.
200
REFERENCES
[1i
G. Forti, J.M. Gonzalez-Santalo, "A Model for Subchannel
Analysis of BTR Rod Bundles in Steady State and
Transient," Int. Conf. Reactor Heat Transfer, Karlsruhe,
Germany,
[2]
1973.
L. Wolf, A. Faya,
A Subchannel Code
Thermal-Hydraulic
Fuel Pin Bundles,"
A. Levin and L. Guillebaud, "WOSUB for Steady-State and Transient
Analysis of -Boiling Water Reactor
Vol. 1: Model Description, MIT
Energy Laboratory Report, October 19'7.
[3]
L. Guillebaud,
A. Levin, W. Boyd, A. Faya and L. Wolf,
"WOSUB - A Subchannel Code or Steady-State and Transient
Thermal-Hydraulic Analysis of Boiling Water Reactor
Fuel Pin Bundles," Vol. II: User's Manual, MIT Energy
Laboratory Report, July 1977.
[4]
R.T. Lahey, et a,
"Two-Phase Flow and Heat Transfer
Multirod Geometries:
Measurements
in
Sutchannel and Pressure Drop
in a Nine-Rod Bundle for Diabatic
and
Adiabatic Conditions," GEAP-13049, 1970.
[5]
E. Jannsen, "Two-Phase Flow and Heat Transfer in Mlultirod Geometries," Final Report, GEAP-10347, 1971.
U6]
R.T. Lahey, et al, "Out-of-Pile Subohannel Measurements
in a Nine-Rod Bundle for Water at 1000 sia,
rogress
in Heat and Mass Transfer, Vol. VI, Pergamcn Press, N.Y.,
1972.
L7]
R.T. Lahey, et al, "Mass Flux and Enthalpy Distribution
in a Rod Bundle for Single- and Two-Phase Flow Conditions,"
J. Heat Transfer, 93, 197, (1971).
]
F.S.
Pr2
astellana, J.E. Casceriine,
Enthalpy
Distributions
Subc~iannel
Flow and
at the Exit of a Typical Nuclear
(1972).
[9]
B. Gustafsson,
B. Kjellen,
"Two-Phase
low in a Nine-
Rod Bundle with Tilted Power Distribution," AE-RL-1301
(SDS-20), 1971.
[10]
B. Gustafsson, H. Gransell, "Boundary Conditions for the
Exercise at the Eurouean Twoc-Phase Flow Meeting 1976,"
AP-RL-7431, -0 3 -01, 1976.
[11]
G. Ulrych, H. Kemner, "Survey on the Experimental
and
Computed Results, Exercise of the European Two-Phase Flow
Group Meeting 197576" rlarngen, '7"ermany, 19i77.
-"
201
[12]
J. Flinta, "Steam/Water Distvsflion
with Nine Rods," AE-RL-1239
[13]
D.S. Rowe, "Crossflow Mixing Between Parallel Flow
Channels During Boiling,"
[14]
in a Boiling Channel
(SDS-2), 1970.
BNWL-371,
Pt. 1, 1967.
C.W. Stewart et al, "COBRA-IV: The Model and the Method,"
BNWL-2214, July 1977;
for detailed subchannel predic-
tions, see D.S. Rowe et al, "Core Thermal Model Develop-
ment and Experiment," BNWL-1924 -1, July 1975.
[15]
H. Chelemer et al, "THINC-IV - An Improved
Program for
Thermal-Hydraulic Analysis of Rod Bundle Cores,"
WCAP-7956, 1973.
[16]
D.S. Rowe, "COBRA-I: A Digital Computer Program for
Thermal-Hydraulic $ubchannel Analysis of Rod Bundle
Nuclear Fuel Elements," BNWL-1229, 1970.
[17]
R. Bowring, P. Moreno, "COBRA-IIIC/MIT Computer Code
Manual," to be issued as an EPRI report.
[18]
J. Liu, "Thermal-Hydraulic Analysis for PWR's by a
One Pass Method,"
N.E. Thesis, M.I.T., June, 1977.
[19]
M. Bayoumi et al, "Determination
of Mass Flow Rate and
Quality Distributions between the Subchannels of a
Heated Bundle," European Two-Phase Flow Meeting,
Erlangen, Germany, 1976.
[20]
S. Levy, "Forced Convection Subcooled Boiling-Prediction of Vapor Volumetric Fraction," Int. J. Heat Mass
Trans.
[21]
10 (1967), 951-965.
M. Ishii, T.C. Chawla, N. Zuber, "Constitutive
Equation
for Vapor Drift Velocity in Two-Phase Annular Flow,"
A1ChE J.. 22 (1976), 283-289.
[22]
M. Ishii, "One-Dimensional Drift-Flux Modeling: OneDimensional Drift Velocity of Bubbly, Droplet, Annular,
and Annular Mist Flows in Confined
Channel in Light-
Water Reactor Safety," Research Program: Quarterly
Progress Report, Oct. - Dec., 1976, ANL-77-10, March,
1977.
[23]
L. Wolf, A. Faya, "Review of the Studsvik BWR Test
Bundle Data and Subchannel Code Result," MIT-Report
to be published.
L
I
202
[24]
K. Doi et
_Tehree
Dimensional Nuclear Thermal-
Hydraulic AaT ysis of BWR Fuel Bundles,' J. Nucl.
Sci. Technol.,
976.
l
[25]
T. Kiguchi, private commtnication,
[26]
E. Jannsenr, "Two-Phase
August, 1976.
low and Heat Transfer
in
Multirod Geometries," Final Report, GEAP-10347, March,
1971.
[271
Anon., "eFIcient Cooling," Ninth Quarterly Progress
Report, July 1 - September 30, 1971, GEAP-10221-9,
October,
[28]
1971.
B.S. Shiralkar et al,
Critical Heat Flux -
Transient
Experimental Results," GEAF-13295, Seotember, 1972.
[29]
N. Zuber et al, "Steady State and Transient Void Fraction
in Two-Phas Flow System," GEAP-5417, 196,.
[30]
O. Nylund et al, "Hydrodynamnic and Heat Transfer
'P1ll! Scal.e -_Rod
Mrvikern
,1ue;
Measu.srements on
Element with Uniform Heat Flux Distribution," FRGG-2
R4-447/RTL-i007, 1968.
[31]
J.A. Skang et al, "Resuits of Void Measurements,
FRIGG-PM-15, 1968.
[32]
F.W. Cortzen, "T Jse of he Thermohydraulic Subcharnel
Programme HAMBO on the Test Elements FT36a and FT 36b
Pt. 1: The Local Void Distribution," RTGG-P-39,
February 1969.
[33]
J*M.
[34'
Gonzalez-Santalo, "Two-Phase Flow Mixing in Rod
Bundle Subchannels," Ph.D. Thesis, Deot. Mechanical
February, 1.972.
Engineering, M.I.T.,
Anon, "GETAB: Data, Correlation
and Design Application,"
NJEDO-10958,November, 173.
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