Validity of Use of the FIT-III Results during Design of... · 2018-12-19 · SCE comments of...

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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

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DRAWN BY ―――

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MITSUBISHI HEAVY INDUSTRIES, LTD.

Specification No. SO23-617-01R3

Purchase Order No. 4500024051

Edison

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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


SCE comments of

RSG-SCE/MHI-12-5747


SCE comments of

RSG-SCE/MHI-12-5779 and to

provide additional technical

discussion and clarification

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Document No.L5-04GA591(3)



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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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

(38/90)




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)


Jg : Gas Phase Superficial Velocity (m/s)

Jl : Liquid Phase Superficial Velocity (m/s)

○Test Data

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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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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.

(60/90)




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.

(62/90)




Fig. 1(a) Velocity vector of fine mesh

Fig. 1(b) Velocity vector of normal mesh

Fig. 1(c) Velocity vector of coarse mesh

(63/90)




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

(64/90)




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.

(65/90)




(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

(66/90)




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)

(67/90)




(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)




Correlations shown in Figure

Relationship between slip ratio and void fraction

1

11

1

x

S

where,

g

Levy (3.23)

Zivi (3.52)


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)



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

(69/90)




Hamersma and Hart

Huq and Loth

α; void fraction x; quality


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

(70/90)




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)




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


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

(72/90)




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.

(73/90)




(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

(74/90)




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.

(75/90)




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.

(76/90)




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.

(77/90)




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

(78/90)




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

(79/90)




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

(80/90)




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%)

(82/90)




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)


1.5%(2) 1.5%(2)

0.2%(3) 0.2%(3)



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).

3

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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)


1.5%(2)

0.2%(3)



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

(86/90)




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.

(87/90)




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.

(88/90)




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)

(89/90)




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.

(90/90)




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 .

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