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REMARKS
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DWG. No.
L5-04GA591 Rev.No.
Nuclear Plant Component Designing Department
Steam Generator Designing Section
1
Validity of Use of the FIT-III Results during Design
San Onofre Nuclear Generating Station, Unit 2 & 3 REPLACEMENT STEAM GENERATORS
PM(S
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CHECKED BY
DESIGNED BY
APPROVED BY
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ISSUE DATE
DRAWN BY ―――
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MITSUBISHI HEAVY INDUSTRIES, LTD.
Specification No. SO23-617-01R3
Purchase Order No. 4500024051
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Revision History
Document No.L5-04GA591
No. Revision Date Approved Checked Prepared
0 Initial issue See cover sheet
1 Revised in accordance with
SCE comments of
RSG-SCE/MHI-12-5741
2 Revised in accordance with
SCE comments of
RSG-SCE/MHI-12-5747
3 Revised in accordance with
SCE comments of
RSG-SCE/MHI-12-5779 and to
provide additional technical
discussion and clarification
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Table of Contents
Executive Summary ................................................................................................................... 4
1. Purpose .................................................................................................................................. 7
2. Background ............................................................................................................................ 7
3. Evaluation .............................................................................................................................. 8
3.1 Validation of FIT-III code .................................................................................................. 8
3.2 The reason for velocity prediction difference ................................................................. 12
3.3 Adequacy of tube stability ratio (SR) determination using FIT-III outputs ..................... 21
4. Relation between the use of modified FIT-III code outputs and tube wear of SONGS
RSGs ........................................................................................................................................ 29
5. Conclusion ........................................................................................................................... 32
6. References ........................................................................................................................... 34
Appendix-1 FIT-III Verification Test ......................................................................................... 35
Appendix-2 NUPEC Report (Comparison between FIT-III and ATHOS) ............................... 37
Appendix-3 Mass Balance and Heat Balance ......................................................................... 37
Appendix-4 Specification of Boundary Conditions .................................................................. 59
Appendix-5 Description of the solution process ...................................................................... 60
Appendix-6 Discussion to Prove the Uniqueness of Numerical Solution ............................... 61
Appendix-7 Modeling Error ...................................................................................................... 64
Appendix-8 Primary causes of the lower flow velocity produced by FIT-III ............................ 70
Appendix-9 FIT-III Gap Velocity Transformation ..................................................................... 75
Appendix-10 Modeled velocity variable in FIT-III .................................................................... 76
Appendix-11 Flow Peaking Effect............................................................................................ 78
Appendix-12 Stability Ratio Map ............................................................................................. 80
Appendix-13 Stability Ratios Calculations Using FIT-III and ATHOS Results ....................... 82
Appendix-14 Circulation ratio input from SSPC to FIT-III ....................................................... 86
Appendix-15 Assumption for uniform velocity in all tubes of the primary system in FIT-III .... 87
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Executive Summary
During the design phase of the SONGS Replacement Steam Generators (RSGs),
thermal-hydraulic modeling by the FIT-III code was used to predict flow conditions. These
conditions were used as inputs for a Fluid Elastic Instability (FEI) analysis and to establish a
margin for tube stability.
Following the discovery of tube-to-tube wear (TTW) in the SONGS RSGs a root cause
analysis was conducted and several investigations of the FIT-III code were performed.
Additional comparisons were made to flow conditions predicted using the ATHOS code. As a
result of the investigations and analysis the following three conclusions have been reached:
• The original FIT-III code for a square tube array SG was validated by experimental
verification tests and benchmarking analyses against a recognized industry code. The
modified FIT-III code for a triangular tube array SG (“modified FIT-III code”) was verified
by an experimental verification test.
• The flow velocities predicted by FIT-III are lower than those predicted by ATHOS. The
causes of the flow velocity difference are the different numerical correlations utilized by
the two codes (pressure loss coefficient for tube cross-bundle flow and two phase
mixture density) and the use of different gap velocity transformations to predict the flow
area. If MHI’s definition of the flow area had been obtained using a gap velocity in
conformance with the recommendations in ASME Appendix N-1331.1, MHI’s calculated
stability ratios against out-of-plane FEI would have approximately doubled and the design
margin would have been smaller than those calculated at the design stage, as described
in Section 3.3 (1).
• The stability ratios of the SONGS RSG based on the use of the ATHOS code outputs are
acceptable, however the design margin is lower than the stability ratios based on FIT-III
analysis. If MHI had determined the predicted thermal-hydraulic conditions needed to be
addressed based on the more conservative ATHOS analysis, the SONGS RSG design
may have been modified. The likely design modification would have been the insertion
of additional AVBs of flat bar type (which is the same type as the existing AVBs of
SONGS RSGs) to reduce the stability ratios.
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The tube wear of SONGS RSGs was caused by (i) insufficient in-plane tube support and (ii)
high localized thermal-hydraulic conditions1 in the SG secondary side. Based on analyses
following the discovery of the tube wear, MHI learned that the FIT-III outputs were not as
conservative as the ATHOS outputs. If MHI had used a more conservative thermal-hydraulic
code at the design stage, the predicted localized thermal-hydraulic conditions would have
been higher than those predicted by FIT-III code and the SONGS RSG design might have
been modified.
However, at the design stage, there was insufficient knowledge of the relationship between
tube vibration phenomena and effective tube support conditions at high localized thermal
hydraulic conditions. The practice in the nuclear industry at the time the SONGS RSGs were
designed was to provide measures to preclude out-of-plane FEI in the U-bend region.
Reflecting this industry practice, the Japan Society of Mechanical Engineers’ “Guideline for
Fluid-elastic Vibration Evaluation of U-bend Tubes in Steam Generators” states that in-plane
FEI does not need to be considered if out-of-plane FEI is controlled. The design of the
SONGS RSGs was consistent with the contemporary industry practice and guidance.
Additionally, any potential modifications of the SONGS SG design to improve the
thermal-hydraulic conditions were limited due to the requirements of the Certified Design
Specifications.
In retrospect, under these circumstances it is likely that the design modification, if any, to
accommodate a reduction in design margin would have been the insertion of additional
AVBs of flat bar type (which is the same type as the existing AVBs of SONGS RSGs) to
ensure control of out-of-plane FEI. However, most of the tube wear indications are due to the
in-plane FEI and random vibration at AVB support points. MHI has determined that neither
form of tube wear could have been prevented by the insertion of additional flat bar type
AVBs because this type of AVB did not and would not provide effective support in the
in-plane direction under high localized thermal hydraulic conditions.
Therefore, although the use of the FIT-III code may be regarded as a contributing cause2 of
the tube wear because its predicted thermal hydraulic conditions were not as conservative
1 As used in this White Paper, the term “high localized thermal-hydraulic conditions” refers to high
localized steam quality (void fraction), flow velocity, and hydro-dynamic pressure. 2 As used herein a “contributing cause” is defined as a cause that by itself would not create the
problem but is important enough to be recognized as needing corrective action. A contributing cause
is sometimes referred to as a causal factor. A causal factor is an action, condition, or event that
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as those predicted by ATHOS, the use of the FIT-III code is not a root cause because the
tube wear would not have been prevented if ATHOS had been used at the design stage. The
in-plane FEI had not been previously experienced in U-bend nuclear steam generators, and
industry practice and guidance required designs that avoided out-of-plane FEI as a bounding
design principle.
directly or indirectly influences the outcome of a situation or problem.
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1. Purpose
During the design stage of the San Onofre Nuclear Generating Station (SONGS) Units 2
and 3 Replacement Steam Generators (RSGs), the Flow in Bundle – Three-Dimensional
Analysis (FIT-III) computer code, a three-dimensional thermal-hydraulic analysis code for
the steam generator secondary side developed by MHI, was used to predict the
secondary side flow characteristics. These flow characteristics (flow velocity, flow density
and void fraction) were used as inputs for tube fluid elastic instability (FEI) analysis to
establish a margin for tube stability. The calculation methods of stability ratio are
provided in Ref.[17].
This document provides an evaluation of the use of the FIT-III computer code and seeks
to address certain issues raised by Southern California Edison’s root cause evaluation of
the tube wear in the SONGS RSGs (Ref.[1][2]) and the relation between the use of
FIT-III outputs and tube wear of SONGS RSGs.
2. Background
Southern California Edison’s root cause evaluation of the tube wear in the SONGS
RSGs has raised the following issues related to the use of the FIT-III computer code:
(1) The validation process of the FIT-III code.
(2) The reason why the fluid velocities predicted by the FIT-III code are significantly
lower than those predicted by the ATHOS code.
(3) The adequacy of the tube stability ratio (SR) determination based on the FIT-III
code outputs.
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3. Evaluation
3.1 Validation of FIT-III code
The original FIT-III code developed for square tube array SGs was modified for triangular
tube pitch SGs as shown in Fig.3.1-1.
MHI has determined that the original FIT-III code was properly validated as follows and
can predict the thermal-hydraulic conditions of the square tube array SGs:
FIT-III analyses results for a square array were verified by comparison with
several experimental test results (10MW Freon tests, etc.) and documented in
MHI internal document KAS-20050201 (Ref.[3]). (Appendix-1 contains an
excerpt of this validation report). Use of FIT-III up to a maximum void fraction
of is justified because the maximum void fraction encompassed by the
test results was and the Smith equation used as the slip model for the
FIT-III void faction calculation is a theoretical equation that is applicable
beyond the range. The applicability of the Smith equation was
subsequently confirmed by published test data up to of the maximum void
fraction.
The verification of the FIT-III code through benchmarking against an industry
recognized thermal-hydraulic computer code was provided in the “NUPEC”
report, which compares ATHOS and FIT-III results for a model steam
generator (See Appendix-2 which contains the relevant sections translated to
English from the original Japanese version of the NUPEC report (Ref.[4])). No
significant difference was found between the results obtained using the two
codes.
ATHOS was developed by EPRI and was verified with vertical straight flow model tests in
a higher void fraction region (See Ref. [18]) than the FIT-III tests.
The FIT-III was subsequently modified for use with a triangular array. MHI validated the
modified FIT-III code by an air-test (Ref.[3])(Appendix-1 contains an excerpt of this
validation report). The velocity profile of two phase flow is dominated by two phase flow
resistance that is composed of a pressure loss coefficient for the single phase flow and a
two phase multiplier. Since the two phase multiplier of triangular tube array is the same
as that of square tube array, MHI determined the single phase flow (air flow) test was
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sufficient to validate the pressure loss coefficient the triangular tube array SGs in the
single phase flow. No benchmark analysis was performed for the modified FIT III code
for the triangular tube array.
Prior to developing the SONGS RSGs MHI successfully designed and fabricated a
triangular tube array SG whose thermal hydraulic conditions were calculated using the
modified FIT-III code with a maximum void fraction. This triangular tube array SG
features a similar AVB design to the SONGS RSG design and has been in operation for
more than 10 years with no tube wear reported. The operating history of this array
provides additional justification of the modified FIT-III code.
The analysis inputs and calculation conditions for SONGS RSGs were determined as
follows.
(1) Input parameters -- The input parameters were correctly
determined based on design drawings.
(2) Mass balance and heat balance -- Any errors of mass balance
and enthalpy balance were negligibly small for 3000 iterations
as shown in Appendix-3.
(3) Boundary conditions -- As described in Appendix-4, the
boundary conditions of both of primary and secondary side were
appropriately determined.
(4) Solution process (Converge of model by number of iterations) --
3000 of iterations were performed for SONGS RSGs analysis,
which is large enough to obtain a converged solution as shown
in Appendix-5.
(5) Different mesh sizes -- Fine mesh modeling was applied for
SONGS RSG design and there is no significant impact of
changing mesh size as shown in Appendix-6
(6) Two-phase modeling -- Slip model is used for FIT-III. The
validity of this model is confirmed as shown in Appendix-7.
The localized thermal-hydraulic conditions predicted by ATHOS are higher than those
calculated using the modified FIT-III code as described in Section 3.2, so the use of
ATHOS would have provided a more conservative design basis than that provided by
FIT-III. The localized thermal-hydraulic conditions of SONGS RSGs predicted by another
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TH code (AREVA CAFCA) are reported to be similar to those predicted by ATHOS
(Ref.[19]).
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Fig.3.3-1 Validation process of the FIT-III code
Original FIT-III for square tube pitch SGs
- 10 MW Freon test of full scale SG mockup, etc.
(See Ref.[3] for details)
- Bench marking analyses (See Ref.[4] for details)
Modified FIT-III code for triangular tube pitch SGs
- Air flow test of U-bend tube bundle mock-up
(See Ref.[4] for details)
Modified pressure loss coefficients for triangular
pitch tube array
(See Attachment 3 of Ref. [20] for details)
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3.2 Reason for velocity prediction differences
The thermal hydraulic calculation models used in the FIT-III and ATHOS codes are
compared in Table 3.2-1.
The lower flow velocities predicted by the modified FIT-III code for the triangular tube
array SGs are due to the following three factors (See Appendix-8 for details):
(1) Pressure loss coefficient for tube bundle (affects cell velocity)
In the U-bend region, the friction factor correlation for cross-bundle flow results in a
higher resistance in the FIT-III model than in the ATHOS model. Consequently, the
velocity vectors tend to be more parallel to the tubes in FIT-III than in ATHOS. Because
the fluid induced vibration (FIV) analysis uses the velocity component normal to the tube,
the velocities reported using FIT-III are lower than those reported using ATHOS.
(2) Two phase mixture density (affects cell velocity)
ATHOS predicts less mixing between the hot leg side and the cold leg side of the tube
bundle than FIT-III because the cross flow resistance in the straight tube bundle is
greater in ATHOS than in FIT-III.3 This leads to higher steam quality and void fraction in
the hot leg side as computed by ATHOS. Additionally, the void fraction predicted by
ATHOS is larger than that predicted by FIT-III under same steam quality conditions
because of the difference between the slip model used in FIT-III and the drift-flux model
used in ATHOS. Consequently, FIT-III gives relatively smaller void fraction than ATHOS.
Because FIT-III predicts a lower void fraction and consequently a higher density, the
predicted velocity is lower in order to maintain global mass balance.
(3) Flow area definition (affects gap velocity)
The modified FIT-III code uses a surface permeability factor for output that is different
from the one used by ATHOS (and different from the factor provided by the ASME Code
in Appendix N-1331.1 (Ref.[5]) (See Appendix-9)) to transform the interstitial velocity into
gap velocity of the triangle tube array. FIT- III was originally developed as square array
code in which the surface permeability is consistent with gap velocity required for a
3 In contrast, the cross flow resistance in the U bend region is greater in FIT-III than in ATHOS.
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square tube array vibration analysis4. The surface permeability of the modified FIT-III
code is not consistent with the factor to calculate gap velocity recommended by the
ASME Code for a triangular array vibration analysis. Therefore, when using the modified
FIT-III code for a triangular array for vibration analysis, a gap velocity conversion is
needed.
This conversion is done outside of the modified FIT-III code and involves taking the
velocity calculated by FIT-III and converting it to gap velocity recommended by the
ASME Code for a triangular array vibration analysis. This conversion was not made for
the SONGS RSGs because the FIT-III manual and the vibration analysis procedure did
not specify such a requirement. Therefore, the velocities used in the vibration analysis
for the SONGs RSGs design is lower by a factor of about than those that would result
by using the proper conversion consistent with the ASME Code recommended gap
velocity.
If the proper conversion consistent with the ASME Code recommended gap velocity had
been used, the calculated stability ratios against out-of-plane FEI would have been
approximately double of and the design margin would have been smaller than those
calculated at the design stage, as described in Section 3.3(1).
4 The surface permeability factor for the original FIT-III for the square pitch SGs is defined in
accordance with ASME Appendix N-1331.1.
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Table 3.2-1 Comparison between ATHOS and FIT-III (1/7)
Category ATHOS FIT-III
Grid type
Mesh size
Time marching
Round off methodology
Outlet boundary condition
Inlet boundary condition
Iterative convergence
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Table 3.2-1 Comparison between ATHOS and FIT-III (2/7)
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Table 3.2-1 Comparison between ATHOS and FIT-III (3/7)
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Table 3.2-1 Comparison between ATHOS and FIT-III (4/7)
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Table 3.2-1 Comparison between ATHOS and FIT-III (5/7)
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Table 3.2-1 Comparison between ATHOS and FIT-III (6/7)
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Table 3.2-1 Comparison between ATHOS and FIT-III (7/7)
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3.3 Adequacy of tube stability ratio (SR) determination using modified FIT-III code
outputs
(1) SR evaluation performed at the design stage
The AVB assembly was designed to ensure that the effective cross-flow velocity under
design conditions for any span would be such that a sufficient margin exists to prevent
excessive tube wear by fluid elastic instability (FEI) or random vibration. MHI’s AVB
design methodology for preventing FEI is shown in Fig.3.3-1. The AVB design was
based on a stability vibration analysis performed pursuant to industry practice and
guidance in order to prevent tube out-of-plane FEI.
The standard procedure of stability ratio evaluation is based on ASME Section III
non-mandatory Appendix N-1330, where the recommended values for Connor’s constant
is 2.4 (which is a minimum value from the experimental data) and the recommended
damping factor is 1.5%. MHI evaluated the out-of-plane stability ratio in accordance with
this standard procedure to confirm the adequacy of AVB design (Base Case).
Additionally, MHI performed several case studies to evaluate the design margin of the
SONGS RSGs to out-of-plane FEI at the time of design stage. These studies were done
under different conditions (Base Case, Actual Case -1, Actual Case -2 and Extreme
Conservative Case). For each of these conditions, analysis was done assuming all
supports were active and assuming one support was inactive for a total of eight case
studies. The case studies looked at tubes with longer AVB support spans which have
higher out-of-plane stability ratios because of their lower natural frequencies. It was
confirmed that the stability ratios of these tubes are higher than others as shown in the
stability ratio map in Appendix-12.
For the purpose of this report, MHI focuses on two Base Cases (all supports active and
one support inactive) and two Extreme Conservative Cases (all supports active and one
support inactive). Conditions assumed for these four cases were as follows:
Base Case-1 – All supports are active and ASME recommended values (K=2.4, h=1.5%)
Base Case-2 – One support point is inactive (assume two spans) and ASME
recommended values are used. The assumption of an inactive support is not required by
the ASME Code, but it was used in this case and in the Extreme Conservative Case -2 to
provide an extra measure of conservatism in the analyses.
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Extreme Conservative Case-1 – All support are assumed active and reduced damping
values (K=2.4, h=0.2% (structural) + best estimate value for two phase damping) are
used.
Extreme Conservative Case-2 – One support point is assumed inactive (assume two
spans) and reduced damping values are used.
Results of the analysis for the Base Cases and Extreme Conservative Cases using
modified FIT-III code at the time of design are set out in Table-3.3-1 and Appendix 13
Table 2. The modified FIT-III code results for Base Case-1, Base Case-2 and Extreme
Conservative Case-1 resulted in stability ratios below 1.0 in all cases. With respect to
Extreme Conservative Case-2, one tube showed a stability factor greater than 1.05, but
as described in Section 8.2.2 of the Evaluation of Tube Vibration report (L5-04GA504),
MHI determined that Extreme Conservative Case-2 was too conservative and provided
unrealistic results, whereas sufficient conservatism was incorporated in the other case
studies evaluated
An evaluation of the flow velocity was performed assuming the peak velocity at the AVBs
to be times higher than the corresponding modified FIT-III code output value, as
shown in Fig.3.3-3. The purpose for this evaluation was to check the effect of higher flow
velocity in the region of AVBs. This multiplier was selected based on AVB flow peaking
experimental test results in a 35 row model. The difference between the peak flow
velocity and the modified FIT-III code output value did not increase with the addition of
more rows of tubes (such as the SONGS RSGs, which have 142 rows of tubes) as
shown in Appendix-11.
As a result of the stability ratio evaluation, a 12 support point design was developed for
use in the SONGS RSGs, which is greater than the number of support points compared
to similar RSGs for other CE PWR plants. The assumption of one missing support point
for the Base Case -2 and Extreme Conservative Case -2 stability analyses was an extra
measure of conservatism used by MHI.
5 This tube was not in the region of tube bundle where in-plane FEI was observed.
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(2) SR evaluation based on ATHOS
After the observation of tube to tube wear (TTW) in the SONGS RSGs, MHI conducted a
re-evaluation of the SONGS RSG design using the ATHOS code for the same four
stability analyses discussed above. These results using ATHOS are set forth fully in
Table 3.3-1 and in Appendix 13 Table 2.
As shown in Table 3.3-1, MHI determined that the maximum stability ratio based on
ATHOS outputs for the Base Case-1 when all supports are active, is which is less
than 0.75, which is the conservative industry practice for judging acceptability of stability
ratios (which in turn is less than the ASME Section III Appendix N-1330 recommended
criterion of 1.0). From this result, MHI concludes that the AVB design as evaluated by
using ATHOS, is adequate to prevent out-of-plane FEI.
MHI also confirmed that for Base Case -2, the stability ratios of tubes in the region of
tube bundle where in-plane FEI was observed (“in-plane FEI region”) are less than 1.0
based on ATHOS outputs even when one support is assumed to be inactive (Table
3.3-2).6 This table shows that the stability ratios for tubes in the in-plane FEI region are
less than 1.0 even assuming one inactive support.
In addition, as described above, MHI compared the ATHOS results to modified FIT-III
code results for the Extreme Conservative Case studies that had been performed as a
part of design of SONGS RSGs, as shown in Table 3.3-1 and Appendix-13 Table 2.
Assuming all supports are active, at the reduced damping for extreme conservative case,
the maximum stability ratio calculated using ATHOS is which is less than ASME
code requirement (i.e. 1.0)
For Extreme Conservative Case -2 (one support inactive and reduced damping), stability
ratio calculated using ATHOS exceeds 1.0 for four of the tubes but as discussed above,
these were determined at the time of design stage, too conservative and not realistic.
6 Although not reflected in the table, this evaluation also indicated out-of-plane stability ratios for two
tubes outside in – plane FEI region were greater than 1.0.
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Table 3.3-1 Out-of-plane Stability Ratios of Representative Tubes(1)(5)
Item Base Case-1 Base Case -2 Extreme
Conservative Case 1 Extreme
Conservative Case-2
Support condition All AVB supports
active One AVB support
inactive All AVB supports
active One AVB support
inactive
Critical factor K 2.4(1) 2.4(1) 2.4(1) 2.4(1)
Structural damping ratio
1.5%(2) 1.5%(2)
0.2%(3) 0.2%(3)
Two phase damping ratio Best estimate value
based on JSME database [Ref.14]
Best estimate value based on JSME database [Ref.14]
Tube address ATHOS FIT-III(4) ATHOS FIT-III(4) ATHOS FIT-III(4) ATHOS FIT-III(4)
R142 C88
R47 C89
R47 C7
R26 C88
R26 C4
R14 C88
R14 C2
R1 C89
R1 C1
(Note) (1) The suggested input of ASME Sec. III Appendix N-1330 is 2.4 (2) The suggested input of ASME Sec. III Appendix N-1330 is 1.5%.
(3) 0.2% is minimum value of the structural damping obtained from MHI test results. (4) All modified FIT-III code data is based on MHI’s original design calculations without consideration of flow peaking effect (5) A tube frequency correction factor of is applied to all stability ratio analyses for an additional measure of conservatism
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Table 3.3-2 Out-of-plane Stability Ratios of TTW Tubes with One Inactive Support Point
Based on ATHOS outputs(1)
Case ASME Sec.III Appendix
N-1330
Support condition One support point is inactive
Connor’s constant 2.4
Damping 1.5%
AVB peaking effect Not considered
R80 C88 (2)
R106 C78 (leak tube)
R120 C78 (2)
(Note) (1) A tube frequency correction factor of is applied to all stability ratio
analyses for an additional measure of conservatism.
(2) TTW was observed around Row 80~120 tubes in the center column region.
Row 80 Col.88 and Row 120 Col.78 are selected as representatives.
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Three Dimensional Thermal and Hydraulic Analysis by FIT-III
Stability Ratio Analysis by FIVATS
→Flow characteristics along tubes(Flow velocity, density and void fraction)
→Stability ratio of each tube
One-Dimensional Thermal and Hydraulic Analysis by SSPC
→Circulation ratio
Confirm all tubes are stable
AVB design (Decision of support point number)
Three Dimensional Thermal and Hydraulic Analysis by FIT-III
Stability Ratio Analysis by FIVATS
→Flow characteristics along tubes(Flow velocity, density and void fraction)
→Stability ratio of each tube
One-Dimensional Thermal and Hydraulic Analysis by SSPC
→Circulation ratio
Confirm all tubes are stable
AVB design (Decision of support point number)
(Note) The effects of high void fraction and velocities in the U-bend region were evaluated based on
the modified FIT-III code. Using the modified FIT-III code outputs, the possibility of dryout was
evaluated as shown in Fig.3.3-2.
Fig.3.3-1 MHI AVB Design Methodology
(See Appendix-14)
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Fig.3.3-2 Evaluation of Dryout at U-bend Region
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Fig.3.3-3 Flow distribution including flow peaking effect
(Note)
This chart shows the results of the AVB Peaking case study examining the
modified FIT-III code output for the tube in Row 142 Col 88 which was
selected because it has twelve (12) AVB contact points which is the maximum
number and therefore most affected by AVB peak velocity. The peak of flow
distribution at each AVB position is increased by a flow peaking multiplier of
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4. Relation between the use of modified FIT-III code outputs and tube wear of SONGS
RSGs
The mechanistic root cause evaluation of the tube wear of SONGS RSGs (see Ref. [21]
for details) concludes that the causes of the tube wear are (i) ineffective in-plane tube
support based on implementation of the “effective zero gap, without excessive preload
and gap uniformity and parallelism throughout the tube bundle” design concept and (ii)
high localized thermal-hydraulic conditions in the SG secondary side. The modified
FIT-III code was used to predict the thermal-hydraulic conditions at the design stage of
SONGS RSGs. The output of the modified FIT-III code was used in FIVATS to determine
the stability ratio.
At the time of the design, MHI and SCE recognized that the void fraction for the RSGs
would be high. MHI performed a design review with case studies taking into account the
higher void fraction and a feasibility analysis of different methods to decrease void
fraction (see Ref.[22]) The review and studies concluded that the SONGS RSG design
was valid and optimal based on the overall RSG design requirements.
After the tube wear indications in the SONGS RSGs were reported, MHI performed
benchmarking studies of the modified FIT-III code by comparison to ATHOS as
described in this White Paper. As a result, MHI found that the modified FIT-III code
outputs are not as conservative as ATHOS outputs. Therefore, if MHI had used ATHOS
as the thermal-hydraulic code, the predicted thermal-hydraulic conditions would have
been higher than those predicted by the modified FIT-III code. If MHI had determined
that the higher predicted thermal-hydraulic conditions needed to be addressed, the
SONGS RSG design might have been modified.
In considering the stability ratio, the practice in the nuclear industry at that time was to
provide measures to preclude out-of-plane FEI in the U-bend region. Reflecting this
industry practice, the Japan Society of Mechanical Engineers’ “Guideline for Fluid-elastic
Vibration Evaluation of U-bend Tubes in Steam Generators” states that in-plane FEI
does not need to be considered if out-of-plane FEI is controlled. The design of the
SONGS RSGs was consistent with the contemporary industry practice and guidance.
It is uncertain what changes, if any, MHI would have made to the design to address the
results predicted by ATHOS. The primary indicator of the potential need for a design
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change is the stability ratio. Even using the ATHOS outputs, with all AVBs assumed
active, the stability ratio was less than 1.0 for out-of-plane FEI, even for those case
studies assuming reduced damping that could occur under high void fraction conditions.
Some conservative case studies with one inactive AVB resulted in stability ratios greater
than 1.0 for some tubes.
Based on the knowledge available at the time of design, if MHI had determined that it
was appropriate to address such conditions by making design modifications, MHI
considers that the likely design modification would have been the insertion of additional
AVBs of flat bar type (which is the same type as the existing AVBs of the SONGS RSGs)
to reduce the stability ratio for out-of-plane FEI to less than 1.0. The fact that the number
of AVBs in the SONGS RSGs had been previously increased to 12 from the originally
proposed 10 as a result of the stability studies performed in the design process is
consistent with this conclusion.
However, MHI considers that the insertion of additional AVBs of flat bar design would not
have avoided in-plane FEI or random vibration in light of the “effective zero gap without
excessive preload and gap uniformity and parallelism throughout the tube bundle
design’ concept that was followed in the SONGS RSG design. This design was intended
to facilitate fabrication, minimize ding/dents, and maintain mechanical damping, but
resulted in ineffective in-plane support by minimizing the contact force between the AVBs
and the SG tubes. However, as shown in the Tube Wear of Unit 3 RSG - Technical
Evaluation Report (Ref.[21]), the lack of effective in-plane support resulted in the
occurrence of in-plane FEI, which was previously an unobserved phenomenon in U-bend
SGs such as the SONGS RSG. Most tube wear indications are due to in-plane FEI and
random vibration at AVB support points, which would not have been prevented by
additional AVBs, because flat bar type AVBs when used in the effective zero gap without
excessive preload with gap uniformity and parallelism throughout the tube bundle
design concept followed in the SONGS RSGs would not provide effective supports for
in-plane FEI and random vibration at high void fraction (steam quality) conditions.
However, if effective in-plane support had been provided, in-plane FEI would have been
avoided even with the higher localized thermal-hydraulic conditions predicted by ATHOS.
This is consistent with the fact that Unit 2, which has higher average contact force and a
longer period of operations than Unit 3, has experienced minimal TTW.
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Therefore, even assuming the modified FIT-III code underpredicted thermal-hydraulic
conditions (flow velocity and void fraction/steam quality) of SONGS RSGs, MHI
considers that the use of an alternative code, based on the information then available,
would not have prevented the tube wear. Therefore, although it may be regarded as a
as a contributing cause, MHI concludes that modified FIT-III code is not the root cause
because the tube wear would not have been prevented if a thermal-hydraulic code other
than the modified FIT-III code had been used at the design stage.
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5. Conclusion
The original FIT-III was developed for square tube array SGs and was validated by
experimental verification (10 MW Freon test, etc. up to void fraction) and
benchmarking studies. Further, the modified FIT-III code utilizes the Smith equation
which is applicable for void fractions beyond which has subsequently been
confirmed with experimental data up to a void fraction. The original FIT-III code
was modified for triangular tube pitch SGs and was validated by experimental verification
(an air test).
The flow velocity and void fraction predicted by ATHOS are greater than those predicted
by the modified FIT-III code. The causes of the lower flow velocity predicted by the
modified FIT-III code for triangular tube array SGs are due in part to the specific
numerical values/correlations selected as well as the gap velocity transformation
inconsistent with the ASME Section III Appendix-N 1331.1 recommendations. The latter
was an error.
After the observation of tube to tube wear (TTW) in the SONGS RSGs, MHI conducted
an evaluation of the SONGS RSG design using ATHOS. MHI confirmed that with all
supports assumed active the maximum stability ratio based ATHOS outputs does not
exceed which is less than 0.75, which is a conservative industry practice for
judging acceptability of stability ratios (which is in turn less than the ASME Section III
Appendix N-1330 criterion of 1.0). Even assuming reduced damping with all supports
active, the ATHOS-calculated stability ratio is less than 1.0. MHI concludes that the
AVB design is adequate to prevent the out-of-plane FEI. MHI also confirms that with
ASME recommended damping, the stability ratio for tubes in the in-plane FEI region (i.e.
the region of tube bundle that experienced in-plane FEI) is less than 1.0 even assuming
one inactive support.
If MHI had used a thermal-hydraulic code such as ATHOS, the predicted localized
thermal-hydraulic conditions would have been higher than those predicted by the
modified FIT-III code. If MHI had determined to address these higher predicted
thermal-hydraulic conditions based on the more conservative predictions, the SONGS
RSG design might have been modified. Based on the industry practice and guidance and
operational experience available at the time of the design, MHI considers that the likely
design modification would have been the insertion of additional AVBs of flat bar type to
control out-of-plane FEI. However, the tube wear indications due to the in-plane FEI and
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random vibration at AVB support points would not have been prevented, because flat bar
type AVBs, when used in the effective “zero” tube-to-AVB gap without excessive preload
design under operating (hot) conditions with gap uniformity and parallelism being
maintained throughout the tube bundle was used in the SONGS RSGs, would not
provide effective supports for in-plane FEI and random vibration at high void fraction
(steam quality) conditions.
Therefore, while the use of modified FIT-III code may be regarded as a contributing
cause of the tube wear experienced at the SONGS RSGs, it is not a root cause because
the tube wear would not have been prevented if a thermal-hydraulic code other than the
modified FIT-III code had been used at the design stage.
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6. References
[1] (Deleted)
[2] (Deleted)
[3] MHI, FIT-III Code Validation Report, KAS-20050201 Rev.2
[4] NUPEC ; Important structures safety evaluation report (Verification project of the flow
induced vibration evaluation method), HEISEI 14 year
[5] ASME Boiler and Pressure Vessel Code, 1998 edition with 2000 addenda, Section III
[6] Smith et. al “Void fractions in two phase flow; A correlation based upon equal an velocity
head model”
[7] Akagawa, 1974, ‘Gas-Liquid Two-Phase Flow” (in Japanese), P52
[8] Levy, S. , 1960, Trans. ASME, Ser. C, 86-2, 113.
[9] Zivi, S. M. 1964, Trans. ASME, Ser. C, 86-2, 247.
[10] S.Y. Ahmad, 1970, Trans. ASME, Ser. C, 595.
[11] P.J. Hamersma, J. Hart, A pressure drop correlation for gas/liquid pipe flow with a small
liquid holdup, Chemical Engineering Science 42 (1987) 1187–1196.
[12] R.H. Huq, J.L. Loth, Analytical two-phase flow void fraction prediction method, Journal
of Thermo Physics 6 (1992) 139–144.
[13] EPRI, 1016564, ATHOS/SGAP Ver.3.1 theory manual
[14] JSME S 016-2002, “Guideline for Fluid-elastic Vibration Evaluation of U-bend Tubes in
Steam Generators”
[15] MHI, KAS-20040233 Rev.3, SSPC Code Validation and Qualification Report
[16] MHI, L5-04GA510 Rev.5, Thermal and Hydraulic Parametric Calculations
[17] MHI, L5-04GA567 Rev.6, Evaluation of Stability Ratio for Return to Service
[18] EPRI, NP-2698-CCM,“ATHOS-A Computer Program for Thermal-Hydraulic Analysis of
Steam Generators Volume 4: Applications”
[19] MPR, DRN 0299-0029-MLC-01, Rev.1, Evaluation of Thermal Hydraulic Models for
SONGS Replacement Steam Generator Return to Service
[20] MHI, L5-04GA428 Rev.5, Design of AVB
[21] MHI, L5-04GA564 Rev.9 Tube Wear of Unit-3 Technical Evaluation Report
[22] SCE-MHI Design Review Meeting #6, October 17-21, 2005 and Attachment 17,
Technical Discussion of Performance, October 20, 2005
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Appendix-1 FIT-III Verification Test
1. Air test for Triangular tube array SGs
Flow peak of FIT-III at AVB is lower than that of experiment results (Approximately underprediction).
This effect of local flow peaking is included in the tube vibration evaluation by using multiplier of
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2. Full scale freon test for square tube array SGs
Oulet nozzle for Vapor
Vapor Separator
Anti-Vibration Bar
The 7th TubeSupport Plate(TSP)The 6th Tube
The 5th Tube
The 4th Tube
The 3rd Tube
The 2nd TubeThe 1st TubeInlet nozzle forsecondary side fluidFlow Distribution Buffle
Inlet nozzle forPrimary waterApprox. 4m
Approx.1m
Oulet nozzlefor the separatedliquid
Approx.16m
・U-bend tube bundle:
・Number of tubes: 46×5 (-)
・Outer diameter of tube: 22.23×10-3 (m)
・Thickness of tube: 1.27×10-3 (m)
・Tube pitch : 32.54×10-3 (m)
・Tube array : Square pitch
・Material of tube: Inconel 690
・Maximum bending radius: 1.52 (m)
Same as actual SG
Row7-8
Row17-18
Row30-31
Row45-46
θ
Row7-8
Row17-18
Row30-31
Row45-46
θ
Qualification Results of FIT-Ⅲ
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Appendix-2 NUPEC Report (Comparison between FIT-III and ATHOS)
3.1.3 Thermal Hydraulic Analysis by the ATHOS Code (1) Purpose
The result of SG reliability demonstration test will be evaluated using the “ATHOS” code, a
homogeneous flow code used in the U.S. comparable to the “FIT-III” code used in Japan, so
as to confirm applicability of homogeneous flow model code other than “FIT-III” as well as to
examine measures for accuracy improvement of such codes.
(2) Object of Analysis
U-bend heat transfer tube test result obtained from the SG reliability demonstration test
(10MW Freon test) will be analyzed. See Figure 3.1.3-1 for birds-eye view of the test
apparatus (model steam generator).
(3) U-bend Region Measuring Points
In the model SG test, sets of 3 V-shaped AVBs and 2 V-shaped replacement AVBs were
tested. Of these, only the set of 3 V-shaped AVBs will be analyzed here. Figure 3.1.3-2
shows the measuring points for void fraction and gas-liquid interface velocity in the U-bend
region.
(4) Test Case (object of analysis)
Table 3.1.3-1 shows the test case to be analyzed. The analysis model by ATHOS is shown
in Fig. 3.1.3-3. Figures 3.1.3-4~3.1.3-10 show the comparison between the analysis and
test data. 00~900 indicate HOT side and 900 ~1800 indicate COLD side in these figures.
(1) Case when β= 0.7, jg = 1.68m/s, jl = 0.72m/s
1. Void Fraction
FIT-III is more consistent with the test data than ATHOS in ROW 7; however, in
all other rows, both codes show consistency with the test data.
2. Gas-liquid Interface Velocity
According to the test data, the flow velocity in the area behind the AVB decreases
due to the AVB resistance. FIT-III is capable of showing such tendency
whereas ATHOS fails to do so. Therefore, with ATHOS, the AVB resistance
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model needs to be improved. Also, for the rows consisting of tubes with a small
bend radius such as ROW 7 & 17, the ATHOS flow velocity is higher than the test
data. This is attributed to the effect of the AVB resistance model by ATHOS, i.e.
smaller than actual AVB resistance calculation.
1) Other Cases
When the analyses of the other 6 cases are compared, results similar to those in
case (1) are obtained. Thus, with ATHOS, the void fraction for the tubes with a small
bend radius becomes somewhat larger compared to the test data. As for the
gas-liquid interface velocity, decrease in the flow velocity for the area behind AVB is
not captured with ATHOS; furthermore, the flow velocity is slightly higher than the
test data for the tubes with small bend radius.
With FIT-III, however, the void fraction and gas-liquid interface velocity are consistent
with the test data, both of which ATHOS failed to capture.
(5) Summary
The results of the evaluation as to the consistency with the test data for both FIT-III and
ATHOS are as follows:
1) Void Fraction
Both FIT-III and ATHOS had good consistency with the test data for the rows with
a large bend radius such as ROW 30 & 45. However, for the rows with a small
bend radius such as ROW 7 & 17, the void fraction calculated by ATHOS was
larger than the test data (particularly in ROW 7) which indicates less consistency
with the test data.
2) Gas-liquid Interface Velocity
The decreased flow velocity behind the AVB due to the AVB resistance is
captured by FIT-III whereas ATHOS seems unable to capture this phenomenon.
Also, according to ATHOS the flow velocity for the rows with small bend radius
such as ROW 7 & 17 is higher than the test data. One possible reason for this
is an inadequate modeling by ATHOS analysis for the large resistance that exists
in the small bend radius region where the AVB and heat transfer tubes are
parallel to each other.
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Based on these findings, it can be concluded that the ATHOS code needs further
improvement including its AVB modeling.
3) Summary
When using a homogeneous flow model code in the evaluation of thermal
hydraulics of two-phase flow in the secondary side of SG heat transfer tubes,
accurate modeling of AVB resistance model was found to be one of the
measures for enhancing accuracy of the analysis. Also, with the improvement in
its AVB resistance model, the applicability of ATHOS as analysis code for
cross-checking purpose was proven adequate.
Characteristics of the analysis codes as well as comparison of the analyses are
shown in Table 3.1.3-2.
Table 3.1.3-1 Analyzed Test Case
β: Gas Volume Flow Ratio (-)
jg : Gas Phase Superficial Velocity (m/s)
jl: Liquid Phase Superficial Velocity (m/s)
β jg jl
(-) m/s m/s
Set of 3 V-shaped ABVs
0.7 1.68 0.718 0.8 2.91 0.727
0.85 2.07 0.366 0.85 3.82 0.700 0.9 2.18 0.244 0.9 3.93 0.425 0.9 5.92 0.650
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Table 3.1.3-2 Comparison between the Analysis Codes T/H Analysis Code FIT-III ATHOS
Code C
haracteristics
Two-Phase Flow Model
Homogeneous Flow (slip model)
Homogeneous Flow (slip model)
AVB Resistance Model
Yes
Yes
Other Geometric Models
Plane Permeability Ratio and Porosity Approximation used
Plane Permeability Ratio and Porosity Approximation used
Analysis R
esults
Void Fraction
Large Bend Radius Region
Both Codes are consistent with the Test Data
Small Bend Radius Region
Consistent with the Test Data
Calculation is slightly larger than
the Test Data
Gas - Liquid Interface Velocity
Effect
of AVB
Decreased Flow Velocity behind
AVB is captured
Decreased Flow Velocity behind AVB is not adequately captured
Small Bend
Radius Region
Decreased Flow Velocity due to AVB Resistance is calculated
Calculated result is larger than the Test Data possibly due to smaller
than actual calculation of AVB Resistance
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Vapor outlet nozzle
Moisture Separator
AVB
Approx. 16m
Tube
Support
Plates
Outlet nozzle for
separated liquid
Inlet nozzle for secondary sidecirculating fluid
Flow distribution baffle Water
chamber
Inlet nozzle for primary side
circulating fluid
Approx. 4m
Figure 3.1.3-1 Bird’s eye view of the model
Approx.
1m
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○ Void Fraction: 24 Measuring Points
● Void Fraction, Gas-Liquid Interface Velocity: 50 Measuring Points
Fig. 3.1.3-2 Measuring Points (3 V-shaped AVBs)
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Secondary
Side Outlet
Heat Transfer Tubes
U-Bend Region
Secondary Side Inlet
Primary Side Inlet
Figure 3.1.3-3 ATHOS Analysis Model
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Figure 3.1.3-4 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.7, jg = 1.68 m/s, jl = 0.72m/s)
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
○Test Data
―― FIT-III
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-4 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.7, jg = 1.68 m/s, jl = 0.72m/s)
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○Test Data
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β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-5 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.8, jg = 2.91 m/s, jl = 0.73m/s)
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β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-5 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.8, jg = 2.91 m/s, jl = 0.73m/s)
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β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-6 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.85, jg = 2.07 m/s, jl = 0.37m/s)
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β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-6 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.85, jg = 2.07 m/s, jl = 0.37m/s)
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β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-7 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.85, jg = 3.82 m/s, jl = 0.7m/s)
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―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-7 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.85, jg = 3.82 m/s, jl = 0.7m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-8 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 2.18 m/s, jl = 0.24m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-8 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 2.18 m/s, jl = 0.24m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-9 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 3.93m/s, jl = 0.43m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-9 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 3.93m/s, jl = 0.43m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-10 (a) Comparison of Void Fraction between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 5.92m/s, jl = 0.65m/s)
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○Test Data
―― FIT-III
β: Gas Volume Flow Ratio (-)
Jg : Gas Phase Superficial Velocity (m/s)
Jl : Liquid Phase Superficial Velocity (m/s)
Figure 3.1.3-10 (b) Comparison of Gas-Liquid Interface Velocity between Analysis and Test Data (3V ABVs)
(β=0.9, jg = 5.92m/s, jl = 0.65m/s)
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Appendix-3 Mass Balance and Heat Balance
Figures show that iterations for SONGS type SG are sufficient to obtain converged
solutions to achieve both of the mass balance and the heat balance.
Fig.1 Change of error of mass balance
Fig.2 Change of error of enthalpy balance
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Appendix-4 Specification of Boundary Conditions
1. Secondary side
1.1 Inlet
Uniform mass velocity and enthalpy is set at the downcomer because the effect of small
profile at the inlet boundary of the actual plant to the thermal hydraulic in tube bundle is
negligible.
1.2 Outlet
Uniform pressure is set at the outlet of primary separators because the pressure is
almost uniform in a large space such as the dome.
2. Primary side
2.1 Inlet
Uniform velocity is assumed for each tube. The uniform velocity is used (see
Appendix-15).
2.2 Boundary between primary and secondary side
Heat transfer from primary to secondary side is calculated by using the heat transfer
model and the temperature difference between primary and secondary side.
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Appendix-5 Description of the solution process
Velocity profiles of U-bend region for each iteration are overlapped as shown in the
following figure. This figure shows that execution with iterations is sufficient to
obtain a converged solution. For SONGS RSG design, iterations were used.
Fig. Mesh convergence for normalized velocity of U-bend tube
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Appendix-6 Discussion to Prove the Uniqueness of Numerical Solution
1 Mesh conditions
Calculations with 3 kinds of mesh sizes for sample steam generator that are similar to
SONGS type are performed. Mesh conditions are shown in Table.
Table Number of mesh for each direction
Mesh size X direction* Y direction* Z direction*
Fine
Normal
Coarse
*; Number of mesh is only shown in the region of U-bend.
2 Calculation results
Mixture velocity (transformed by using surface permeability: See Appendix-8 for detail) in
U-bend for each mesh sizes are shown in Fig. 1. Flow pattern is similar in each mesh.
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Fig. 1(a) Velocity vector of fine mesh
Fig. 1(b) Velocity vector of normal mesh
Fig. 1(c) Velocity vector of coarse mesh
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Mixture velocity in U-bend for each mesh size is shown in Figure 2. This figure shows
there is no significant effect due to mesh sensitivity as long as normal or fine mesh
model is used.
Fig. 2 Mesh convergence
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Appendix-7 Modeling Error
Turbulence model is ignored in FIT-III. Important two phase model is slip model to
calculate void fraction. The following Smith model is used for FIT-III. This model is
validated by Freon test for square array shown in Appendix-1. The tuning factor in the
slip model should be correlated by the void fraction data. The reason why the Smith
correlation was selected is Zivi and Smith correlations have the tuning factors, and the
Smith correlation was the latest one.
α; void fraction x; quality e; entrainment coefficient
ρg; vapor density ρl; liquid density
Thus, FIT-III has been validated under the condition where the homogeneous void
fraction is smaller than for steam generator.
On the other hand, in general, Smith model is validated up to around of void fraction
as Fig.1. Note that the void fraction of RSG obtained by using FIT-III was within the
applicable range. If MHI had obtained the high void fraction over at the RSG design
stage at FIT-III, MHI may have investigated the FIT-III code validation range.
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(Reference; Smith et. al “Void fractions in two phase flow; A correlation based upon
equal an velocity head model”)(Ref.[6])
Entrainment
coefficient
Fig.1
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Entrainment coefficient e is tuning factor and normally 0.4 from original literature. Prof.
Akagawa summarized slip correlations in 1974. The result of summary is shown in Fig.2.
The figure shows that Zivi (e=0.2), Smith (e=0.4) matches experimental data. The red
line in the figure is calculation result of Smith (e= ) which is implemented in FIT-III also
matches experimental data (For detail, see note 1).
Fig.2 Relation between quality and void Fraction
(Reference; Akagawa, 1974, ‘Gas-Liquid Two-Phase Flow” (in Japanese), P52) (Ref.[7])
Smith (e= ) Ahmad
Void fraction
Quality
S; slip ratioG; mass flux q; heat flux tin; degree of subcooling
(e=0 on Zivi)
(e=0 on Smith)
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(NOTE 1)
By the investigation of recent slip ratio, although research on slip ratio is mainly carried
out in 1960’s and 1970’s, some papers on slip ratio are found after the late of 1970’s.
These slip ratio are compared with Smith. Prof. Akagawa summarized slip correlations in
1974. Zivi and Smith (e=0.4 and ) of slip correlation matches experimental data. Huq
and Loth (1992)” in recent slip ratios also matches above experimental data. The detail is
the followings.
(1) By the investigation of recent slip ratio, although research on slip ratio is mainly
carried out in 1960’s and 1970’s, some papers on slip ratio are found after the late of
1970’s. These slip ratio are compared with Smith (See (3)).
(2) Prof. Akagawa summarized slip correlations in 1974. The result of summary is shown
in following figure. The figure shows that Zivi (e=0.2), Smith (e=0.4) matches
experimental data. The added red line in the figure is calculation result of Smith
(e= ) which is implemented in FIT-III also matches experimental data.
(3) “Hamersma and Hart” correlation (1987) and “Huq and Loth” correlation (1992) is
more recent slip ratio than Smith(1969). “Hamersma and Hart”(added blue line) is
larger than experimantal data and “Huq and Loth”(added green line) matches
experimental data.
Voi
d fr
actio
n
Quality
Smith (e= )Ahmad Eq.(3.23), (3.52), (3.53), (3.55)
and relation ship between slipratio and void fraction areshown in appendix.
Reference; Akagawa, 1974, ‘Gas-Liquid Two-Phase Flow” (in Japanese), P52
(e=0 on Zivi)
(e=0 on Smith)
Hamersma and Hart
Huq and Loth
S; slip ratioG; mass fluxq; heat flux⊿tin; degree of subcooling
(68/90)
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Correlations shown in Figure
Relationship between slip ratio and void fraction
1
11
1
x
S
where,
g
Levy (3.23)
Zivi (3.52)
α; void fraction x; quality e; entrainment coefficient
ρg; vapor density ρl; liquid density S; slip ratio
References; Levy, S. , 1960, Trans. ASME, Ser. C, 86‐2, 113. (Ref.[8])
Zivi, S. M. 1964, Trans. ASME, Ser. C, 86‐2, 247. (Ref.[9])
Smith (3.53)
Ahmad (3.55)
α; void fraction x; quality e; entrainment coefficient
ρg; vapor density ρl; liquid density S; slip ratio
D; equivalent diameter G; mass flux μl; liquid viscosity
Reference; S.Y. Ahmad, 1970, Trans. ASME, Ser. C, 595. (Ref.[10])
)21()1(2
)21()1(2)21()21(
2
22
g
l
g
l
x
2.0
11
11
1111
1
31
32
e
xxe
xxe
x
ex
x
ex g
l
l
g
l
g
21
11
1
1111
1
x
xe
x
xe
x
ex
x
ex g
l
l
g
l
g
-0.016205.0
lg
l GDS
μ
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Hamersma and Hart
Huq and Loth
α; void fraction x; quality
ρg; vapor density ρl; liquid density S; slip ratio
Reference; P.J. Hamersma, J. Hart, A pressure drop correlation for gas/liquid pipe flow
with a small liquid holdup, Chemical Engineering Science 42 (1987)
1187–1196. (Ref.[11])
R.H. Huq, J.L. Loth, Analytical two-phase flow void fraction prediction method,
Journal of Thermo Physics 6 (1992) 139–144. (Ref.[12])
33.067.01
26.011
l
g
x
x
5.0
2
114121
121
g
lxxx
x
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Appendix-8 Primary causes of the lower flow velocity produced by FIT-III
MHI has reviewed the thermal hydraulic calculation models used in FIT-III and ATHOS.
Table-1 shows a comparison of the main characteristics of these two codes. The primary
causes of the lower flow velocity produced by FIT-III are considered to result from the
following three factors: (1) Pressure loss coefficient for tube bundle
(2) Two phase mixture density
(3) Flow area definition
Note) When considering velocity for use in fluid elastic stability analysis, only the velocity
normal to the tube in the in-plane direction is considered.
(1) Pressure loss coefficient for tube bundle
In the tube vibration analysis, only flow velocity in the normal direction to the U-bend
tubes is used.
In general, if the cross flow friction coefficient for the tube bundle is large, the magnitude
of the flow in the cross-bundle direction will decrease. Magnitude of flow velocity in other
directions will correspondingly increase.
The pressure loss coefficient used in FIT-III and ATHOS is shown as follows:
FIT‐III
(Based on JSME handbook)
ATHOS
where
f: Fanning Friction factor
G: Mixture mass velocity
d; Tube diameter
de; equivalent diameter
ρ: Mixture density ρ=αρg+(1‐α)ρl
(71/90)
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Re : Reynolds number
μm: Mixture viscosity 1/μm=χ/μg+(1‐χ)/μl
In condition of SONGS-2/3, the “f" of FIT-III is larger than ATHOS by more than times.
Since the flow direction has the tendency to align in parallel to the tubes and out-of-plane
direction due to larger friction, it is one of the causes of lower flow velocity in-plane
direction calculated by using FIT-III.
(2) Two phase mixture density
In general, low void fraction gives high two phase mixture density, which causes low flow
velocity because the two phase mixture density is calculated in by using the following
equation:
ρm= α×ρg+(1‐α)×ρl
When void fraction is calculated, the following equation, which is based on
homogeneous model, is used in the FIT-III codes:
FIT-III
α; void fraction x; quality e; entrainment coefficient
ρg; vapor densit ρl; liquid density
On the other hand, ATHOS code is based on drift flux model and void fraction is
calculated by key parameter of drift velocity wgj and distribution parameter Co:
ATHOS
Drift velocity, wgj
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rg; void fraction
σ; surface tension
g; gravity
Distribution parameter, Co
Pc; critical pressure
P; pressure
Re; Reynolds number
The maximum void fraction calculated by FIT-III for SONGS-2/3 is which is lower
than that the maximum void fraction calculated by ATHOS which is The lower void
fraction gives higher two phase mixture density, which causes lower flow velocity.
Therefore, the difference of calculation method of void fraction is one of the causes of
lower flow velocity by FIT-III.
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(3) Flow area definition
FIT-III
Flow area is modeled by surface permeability. In the U-bend region, the gap in each
direction is defined as follows.
X direction
Y direction
Z direction
ATHOS
The superficial velocities are transformed into gap velocity by factor αv as follows.
Please refer to ATHOS/SGAP Ver.3.1 theory manual (EPRI, 1016564) (Ref.[13]) for
more detail.
X and Z
Y
Pt
d
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Here, uS , vS & wS and u I , vI & wI are the interpolated superficial and interstitial
velocities at the point of interest and αV is the factor that transforms superficial velocities
into gap velocities.
Here, pV is the vertical tube pitch and dt is the tube outside diameter.
The gap in the normal direction to tube is defined as in ATHOS,
which is smaller than the definition of FIT-III in X and Z directions ( ). Therefore, the
gap velocity calculated by FIT-III would be smaller than a half ( ) of that
calculated ATHOS (The definition of the gap used in ATHOS is the same as ASME
Section III Division I Appendix N1331.1 definition.) if the approaching velocity were the
same and it is concluded that the difference of flow area definition is one of the causes of
lower flow velocity by FIT-III.
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Appendix-9 FIT-III Gap Velocity Transformation
The gap velocity output from FIT-III is the following.
U1 = Uap× P/( P-D)
Where
U1 : Gap velocity (based on large gap)
Uap : Approach flow velocity
P : Tube pitch, which as defined in Appendix-8 (3)
D : Tube outer diameter
The ASME B&PV Code Section III, Division 1, Appendix N-1331.1 specifies the following
gap velocity
U2 = Uap×P0/(P0-D)
Where
U2 : Gap velocity (based on small gap)
P0 : Tube pitch (nominal pitch as defined in ASME Fig. N-1331-3)
The U1 and U2 are both gap velocity, however, U1 is about half of U2.
Though the use of the “large gap” velocity transformation is inconsistent with ASME
Section III Appendix N-1330, SONGS AVB design still has a margin to the out-of-plane
FEI because the out-of-plane stability ratio is less than 0.75 (rather than 1.0) based on
ATHOS outputs as shown in Appendix-13.
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Appendix-10 Modeled velocity variable in FIT-III
Mass conservation equation is obtained by mass balance of control volume in Cartesian
coordinates using the superficial velocity for transport.
If both sides of the equation are divided by
The interstitial velocities, umX,umY,umZ are defined by the ratio of superficial velocity to
volume porosity. Thus, the mass conservation equation becomes:
Where, interstitial velocity is
Therefore, interstitial velocities are used in the governing equations of FIT-III.
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The gap velocities are defined by surface permeability; umP are shown as follows
where,
The velocities umP are used in the pressure loss calculation and vector plots.
For example, surface permeability of U-bend is shown as follows.
X direction
Y direction
Z direction
The velocity component normal to the U‐tube is defined by the large gap which is
consistent with the surface permeability of
αV; surface permeability dependent on direction
Z
X Y
Z
X Y
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Appendix-11 Flow Peaking Effect
The velocity prediction error becomes smaller with an increasing number of rows due to
the phenomenological approach for flow of U-bend and AVB modeling of FIT-III.
This evaluation is validated by the small ( rows) and medium ( rows) U-bend tests
as shown in Attachment-1. The AVB flow peaking factors (PF) for the outermost row of
U-bend for both small ( rows) and medium ( rows) U-bend tests are less than as
shown in Figure-1.
The flow resistance of the tube bundle has effects on the flow distribution profile over the
U-bend tube bundle. This flow resistance of the two-phase flow consists of that in single
phase flow and the two-phase flow multiplier due to gas-liquid interfacial drag. When
calculating two-phase flow resistance in the tube bundle, the two-phase flow multiplier is
multiplied to the single phase flow resistance. The two-phase flow multiplier is the
function of the gas and liquid mass flow rate, and physical properties. There is little effect
of structures in flow paths, such as the AVB and tube-bundle, on the two-phase flow
multiplier. Therefore, the velocity peaking factor was correlated by the single phase flow
test results.
Fig.1 Relationship between PF and outermost row no. of U-bend
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Attachment -1 Summary of Medium U-bend test
U-bend configuration
Number of rows; (2 dimensional test)
Triangular pitch; 25.4mm (1 inch)
Tube diameter; 19.05mm (3/4 inch)
AVB type; 2V+2V+2V
Test conditions
Fluid; water
Pressure; atmospheric pressure
Temperature; room temperature
Measured item; water velocity at the outside of outermost tube etc.
Test results
The difference of velocity between the FIT-III analysis results and the measurement data is
shown in Fig.2.
Fig.2 Comparison between Medium U-bend Test and FIT-III
Fig.1 Test Equipment
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Appendix-12 Stability Ratio Map
The highest stability ratio among all tubes in the bundle as calculated using the ATHOS
results and the ASME methodology (K=2.4 Connor’s constant, and h=1.5% damping)
when all supports are active is Note that the highest stability ratio
is obtained from the stability ratio calculations for over all tube bundle region as below.
The stability ratios of the representative tubes are evaluated by using ATHOS
outputs. The representative tubes are selected every rows and columns for the outer
row region and every rows and columns for other region as shown in Fig.1. The
stability ratios of other tubes are assumed by interpolating method. The distribution of the
stability ratio against FEV out-plane is shown in Fig.2.
Fig. 1 Evaluated Tubes
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Fig. 2 Distribution of stability ratio obtained by using ATHOS outputs when all AVB support points are active (K=2.4, h=1.5%)
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Appendix-13 Stability Ratios Calculations Using FIT-III and ATHOS Results
This attachment provides SR calculations using FIT-III and ATHOS. At the design stage,
the original SR calculations using FIT-III results were performed. These evaluations were
done under different conditions (Base Case, Actual Case -1, Actual Case -2 and Extreme
Conservative Case), assuming all supports were active and one support was inactive. For
the purpose of this report, MHI focuses on two Base Cases (all supports active and one
support inactive) and two Extreme Conservative Cases (all supports active and one support
inactive). The conditions for these 4 cases are shown in Table 1.
Table 1 Evaluation cases
Critical Factor K Support Condition Damping
Base Case 1 2.4 All supports active 1.5% (Total)
Base Case 2 2.4 One support inactive 1.5% (Total)
Extreme
Conservative
Case 1
2.4 All supports active 0.2% (Structural)
Extreme
Conservative
Case 2
2.4 One support inactive 0.2% (Structural)
The stability ratio calculations using ATHOS and FIT-III results for the nine
representative tubes, which stability ratios are higher than others as shown in
Appendix-12, are provided in Table 2. The stability ratios using FIT-III are less than 1.0
except for the tube R142 C88 under Extreme Conservative Case 2.
As shown in Table 2, at all AVB supports active conditions of Base Case 1 and Extreme
Conservative Case 1, the stability ratios using ATHOS are less than 1.0.
When MHI adopts ATHOS outputs for Stability Ratio evaluation, it confirmed that the
maximum SR is when all the supports are active. As shown in Table 3, MHI has also
confirmed that the Stability Ratios of the tubes that experienced tube to tube wear are
less than 1.0 if ATHOS outputs are used even if one support is assumed to be inactive.
3
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Table 2 Stability ratio calculations with assumptions (representative 9 tubes) (5)
Item Base Case-1 Base Case -2 Extreme Conservative
Case 1 Extreme Conservative
Case-2
Support condition All AVB supports activeOne AVB support
inactive All AVB supports active
One AVB support inactive
Critical factor K 2.4(1) 2.4(1) 2.4(1) 2.4(1)
Structural damping ratio
1.5%(2) 1.5%(2)
0.2%(3) 0.2%(3)
Two phase damping ratio Best estimate value
based on JSME database [Ref.14]
Best estimate value based on JSME database [Ref.14]
Tube address ATHOS FIT-III(4) ATHOS FIT-III(4) ATHOS FIT-III(4) ATHOS FIT-III(4)
R142 C88
R47 C89
R47 C7
R26 C88
R26 C4
R14 C88
R14 C2
R1 C89
R1 C1
(Note) (1) The suggested input of ASME Sec. III Appendix N-1330 is 2.4 (2) The suggested input of ASME Sec. III Appendix N-1330 is 1.5%. (3) 0.2% is minimum value of the structural damping obtained from MHI test results. (4) All FIT- III data is based on the following conditions. FIT-III calculation is based on MHI’s original design calculations The flow peaking effect of FIT-III is not considered. (5) A tube frequency correction factor of is applied for all stability ratio analyses to provide an additional measure
of conservatism (See Fig.1).
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(Note) Since there is a slight difference of the tube frequencies between the mock-up test and analysis, of the tube frequency correction factor
is assumed for the conservative evaluation.
Fig.1 Tube frequency correction factor
(a) U-bends mock-up(b) Tapping test result
Amplitude (mm)
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Table 3 Stability ratio calculations of the representative tube that experienced tube-to-tube wear (6)
Item Base Case 2 Extreme Conservative Case 2
Support condition One AVB support inactive One AVB support inactive
Critical factor K 2.4(1) 2.4(1)
Structural damping ratio
1.5%(2)
0.2%(3)
Two phase damping ratio Best estimate value
based on JSME database [Ref.14]
Tube address ATHOS FIT-III(5) ATHOS FIT-III(5) R106 C78
(leak tube)
(Note) (1) The suggested input of ASME Sec. III Appendix N-1330 is 2.4
(2) The suggested input of ASME Sec. III Appendix N-1330 is 1.5%.
(3) 0.2% is minimum value of the structural damping obtained from MHI test results.
(4) The TTWs are observed around Row 80~120 tubes in the center column region. Row 80 Col.88 and Row 120 Col.78
tube have SR of and respectively.
(5) All FIT- III data is based on the following conditions. - FIT-III calculation is based on MHI’s original design calculations - The flow peaking effect of FIT-III is not considered.
(6) A tube frequency correction factor of is applied for all stability ratio analyses to provide an additional measure of
conservatism (See Fig.1)
3
3
3
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Appendix-14 Circulation ratio input from SSPC to FIT-III
In the FIT-III model, the circulation ratio is the boundary condition that is forced on the
3-D model. Specifically, the mass flow rate of CR×W is forced on the flow rate in the tube
bundle (CR : Circulation ratio, W : Steam flow rate).
Since the circulation ratio calculation of SSPC is verified by the comparison between
SSPC output and the measured value at the actual plant (Ref.[15]), it is considered that
the circulation ratio input from SSPC (Ref.[16]) to FIT-III is adequate.
By the way, the circulation ratio is determined based on the balance of the pressure drop
in the circulation loop and circulation head. We can estimate the circulation ratio based
on FIT-III output. For reference, the predicted circulation ratios based on the FIT-III(*) and
SSPC are similar (CRSSPC= CRFIT-III= ). Since the difference is small, it is evaluated
that the use of the SSPC is adequate.
(*) FIT-III can calculate the pressure drop and head in the tube bundle. The downcomer
pressure drop and head are estimated by the hand calculation.
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Appendix-15 Assumption for uniform velocity in all tubes of the primary system
in FIT-III
In the FIT-III analysis, the assumption for uniform velocity in all tubes of the primary system
is used. Error due to assumed uniform velocity is estimated by the calculation of heat transfer
resistance. The error is between row 1 and 142. Details are shown in the followings.
Methodology
In order to calculate the heat source terms in the heat balance equation, it is necessary to
calculate the heat transfer resistance of
(a) The primary-side flow
(b) The tube metal wall
(c) The secondary-side flow.
The heat transfer resistance for the above sections is calculated using the SONGS
thermal-hydraulic design conditions, and the overall resistance error associated with
assuming an equal primary fluid velocity for all tubes is estimated by evaluating the relative
change in heat transfer coefficient on the primary-side film due to changes in the tube inner
velocity.
Calculation conditions for heat transfer resistance
Calculation is performed by using design conditions as in Table 1.
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Table 1 Calculation conditions
Calculation of heat transfer coefficient
The heat transfer correlations based on the MHI test and literature-based correlations are used as shown in below. The calculation results are provided in Table 2. ・Tube Wall (Based on MHI test):
(Btu/ft2‐hr‐oF)
(ft2‐hr‐oF/Btu)
(Btu/ft‐hr‐oF)
(oF) at U bend
・Outside (Jens‐Lottes):
(W/m2K)
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where, PS (MPa abs), qAS (W/m2)
(Btu/ft2‐hr‐oF)
・Inside (Dittus‐Boelter):
(Btu/ft2‐hr‐oF)
(ft2‐hr‐oF/Btu)
・All heat transfer resistances are based on tube outer diameter Do.
・Effect of tube fouling factor is ignored in this calculation to obtain conservative result.
Table 2 Calculation results
Heat Transfer
Resistance
(ft2hrF/Btu)
Ratio
Tube
Outside
Inside
Calculation of heat transfer sensitivity
The sensitivity to the primary-side flow heat transfer resistance between uniform and
non-uniformly distributed velocity is estimated by the consideration of the effect of tube
length (table 3).
Table 3 Summary of sensitivity
Row 1 Row 142
Length m
rL Length ratio (loss coefficient ratio)
rV Velocity ratio* (Vr142 / Vr1)
rh Heat transfer coefficient ratio of inside of tube**
*; Same differential pressure is assumed between hot and cold channel head
**; Calculated by Dittus-Boelter Equation.
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Conclusion
• The largest resistance to heat transfer from the primary to secondary side is in the tube
metal wall. The smallest resistance is in the primary-side film.
• The error due to equal velocity in all tubes is defined based on the relative change in
overall resistance considering the change in primary-side resistance between the
shortest radius tube (RI) and longest radius tube (RI):
Therefore, error due to assumed uniform velocity is .