COBRA-FLX: A Core Thermal-Hydraulic ~~~~;~n361 Analysis …

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A .AREVA

COBRA-FLX: A Core Thermal-Hydraulic ~~~~;~n361

Analysis Code Errata 1NP-ooo

May 2017

AREVA Inc.

(c) 2017 AREVA Inc.

Copyright© 2017

AREVA Inc. All Rights Reserved

ANP-10311 Revision 0

Errata 1 NP-000

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COBRA-FLX: A Core Thermal-Hydraulic Analysis Code

Item 1

Section(s) or Page(s) All

Nature of Changes

Description and Justification Initial Issue


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Pa e i

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1.0 SUMMARY

ANP-1031 1 Revision 0

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Pa e 1-1

AREVA Inc. (AREVA) is seeking clarification on the use of the standard friction factor

correlation within ANP-10311 PA, Revision 0 "COBRA-FLX: A Core Thermal-Hydraulic

Analysis Code". While the NRC's Safety Evaluation (SE) is clear on the approval of the

Lehmann correlation , approval of the standard friction factor is not apparent. AREVA

believes that the original intent of the reviewer was to approve the standard friction

factor for the following reasons. First, the discussion on the friction factor provided in

Section 3.4 .2 of the SE points out that the standard friction factor correlations "are for

the most part venerable and well validated models in widespread general use in

subchannel codes" and that Lehmann attempts to correct the standard correlation to

account for surface roughness and "entrance effects". The SE argues that, while the

usefulness of the corrections is arguable , they do attempt to capture physical effects

generally ignored in subchannel modeling and results in very small corrections when

applied in the range typical of reactor operations. Additionally, this subject has been

discussed with the NRC in several teleconferences where the NRC verbally confirmed

that the reviewer's original intent was to approve the standard friction factor. Finally,

this is consistent with the wording in Section A.3 .1 of ANP-10311 PA which presents the

Lehmann correlation "as an alternative" to the standard model. AREVA is requesting

written concurrence that the standard friction factor correlation is approved for use in

COBRA-FLX. A markup of Table 1-2 of ANP-10311 PA, Revision 0 has been provided

in Section 1 .1 .

AREVA has also identified several corrections in the COBRA-FLX to L YNXT transient

benchmarking . Section 5.7.2.1 and 5.7.2.2 of ANP-10311 PA, Revision 0 contains an

error in the diversion cross flow resistance factor (Kij). Kii is derived from test results

and is dependent on the code use to analyze the results. Hence, the Kii factor for one

code is not compatible with other codes. In the original benchmarking the COBRA-FLX

based Kii was used in L YNXT. This error has been corrected by using the L YNXT

based Kii and errata have been provided below in Section 1.2. This resulted in changes

to the numbers provided in summary tables; however these changes do not alter the

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COBRA-FLX: A Core Thermal-Hydraul ic Analysis Code


Errata 1 NP-000

Pa e 1-2 conclusions presented in the topical because the benchmarking remains within the

acceptable range. Note that several typos in Section 5.7.2.1 and 5.7.2.2 have also

been corrected .

Additionally, several errata have been provided in Section 1.3. These errata correct

typos and provide clarification of wording . These errata do not impact the code or the

conclusions of the topical report. These errata do not require concurrence. They have

been provided for information and to provide a complete list of corrections to the Topical

Report.

1.1 Friction Factor

The following corrections have been made to ANP-10311 P-A, Revision 0.

Item 1

Table 1-2 currently reads as:

Table 1-2: Empirical Correlation Application for Requested Review and Approval

Empirical Correlation Used for Safety-Related Analyses Water Properties

• IAPWS 97 Friction Factor Correlation Constants

• Lehman friction factor (with or without Szablewski correction) • Wall viscosity correlation option for the wall friction factor

Two-Phase Friction Multiplier

• HomoQeneous model Bulk Void Correlation

• Chexal-Lellouche void correlation using the full curve fit routine or tables with interpolation

Subcooled Void Option • Saha-Zuber subcooled void correlation

Subcooled Boiling Profile Fit

• Zuber-Staub profile fit

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Table 1-2 should read as:


Errata 1 NP-000

Pa e 1-3

Table 1-2: Empirical Correlation Application for Requested Review and Approval

Empirical Correlation Used for Safety-Related Analyses Water Properties

• IAPWS 97 Friction Factor Correlation Constants

• Standard • Lehman friction factor (with or without Szablewski correction)

• Wall viscosity correlation option for the wall friction factor

Two-Phase Friction Multiplier • Homoqeneous model

Bulk Void Correlation

• Chexal-Lellouche void correlation using the full curve fit routine or tables with interpolation

-Subcooled Void Option • Saha-Zuber subcooled void correlation

Subcooled Boiling Profile Fit

• Zuber-Staub profile fit

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1.2 COBRA-FLX to L YNXT Transient Benchmarking

The following corrections have been made to AN P-10311 P-A, Revision 0.

Item 1

The beginning of section 5. 7 .2.1 currently reads as:


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Pa e 1-4

The COBRA-FLX and L YNXT DNBR predictions for a 4 pump coastdown transient case are shown in Figure 5-39 and Table 5-8 when using the typical code options (e.g., the P solution method for COBRA-FLX and PV solution method for L YNXT and the licensing empirical models) . The observed difference in DNBR between the two codes is 0.065.

The beginning of section 5.7.2.1 should read as:

The COBRA-FLX and L YNXT DNBR predictions for a 4 pump coastdown transient case are shown in Figure 5-39 and Table 5-8 when using the typical code options (e.g., the P solution method for COBRA-FLX and PV solution method for L YNXT and the licensing empirical models) . The observed difference in DNBR between the two codes is 0.068 as shown in Table 5-8.

Item 2

The wording in the first paragraph on p. 5-45 currently reads as:

The observed differences between COBRA-FLX and L YNXT were investigated and are attributed to various modeling differences, such as the void fraction models, turbulent momentum factors , and crossflow resistance factor (Kij) . A series of COBRA-FLX and L YNXT cases were analyzed ...

The wording in the first paragraph on p. 5-45 should read as:

The observed differences between COBRA-FLX and L YNXT were investigated and are attributed to various modeling differences, such as the void fraction models and turbulent momentum factors , and crossflow resistance factor (Kijj. A series of COBRAFLX and L YNXT cases were analyzed ...

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Errata 1 NP-000 COBRA-FLX: A Core Thermal-Hydraulic Analysis Code

Item 3

Table 5-9 and 5-10 currently read as :

Table ~9: COBRA-FLX and: L YNXT Minimum DNBR Sensitivity t o Modeling Parameters for the 4 Pump Coastd.own

MDNBR (BWCMV-A)

Parameter Parameter COBRA-FLX l YNXT Change

Individually Production Case Using the 1.899 1.84'6 PV Solution Method

Individually Homogenous Vojd Model for 1 .. 920 1.'922 both Cooes

Individually Common Kii for both Codes 1.923 1.846

Individually common Turbulent 1.878 1.84'6

Momentum Factor (FTM)

Combined Combined Effect of AH 1.9385 1.923 Parameters Above

Table 5-10: Summary of DNBR Compariso:n for the 12-Chan e·1 Model for the Locked Rotor

Parameter COBRA-Fil X LYNXT

MDNBR (BWCMV-A) 0.915 0.801

Time at MDNBR (sec} 2 .78. 2.80

Pa e 1-5

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Table 5-9 and 5-10 should read as:


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Pa e 1-6

Table 5-9: COBRA-FLX and L YNXT Minimum DNBR Sensitivity to Modeling Parameters for the 4 Pump Coastdown

Parameter Parameter

MDNBR (BWCMV-A) Change COBRA-FLX LYNXT

Individually Production Case Using the 1.899 1.846

PV Solution Method Individually Homogeneous Void Model and

homogeneous 2-phase friction 1.919 1.922

multiplier for both Cases Individually Common Turbulent Momentum

1.878 1.846 Factor (FTM)

Combined Combined Effect of All 1.895 1.922

Parameters Above

Table 5-10: Summary of DNBR Comparison for the 12-Channel Model for the Locked Rotor

Parameter COBRA-FLX LYNXT

MDNBR (BWCMV-A) 0.915 0.801

Time at MDNBR (sec) 2.80 2.80

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Item 4

Figures 5-42, 5-43 and 5-44 currently read as:

f;igure 5-42: DNB:R Comparison for the Combined Effect of All 1Modeling Parameters in Tab 'e 5-9 for th.e 4 Pump Coastdown

2.80 ------.....-----------.......------

<"° 2.60 +------+---- --LYNXT ). - COBRA-FLX

:a ~· 2.40

al

0:: 2.20 -l-------= ......... +------1---------"'r---#----~ al z c :i 2.rno -1-----+-----""~1::----~¥-ir--------1

1.ao --------------------1 2 3 4 5

Transient T 1irre. Seconds

Pa e 1-7

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Pa e 1-8

!Figure 5-43: Mass Velocity C,omparison for the Combined Effect of All Modeling Parameters in Table 5·9· tor the 4 Pump Coastdown at

the Time of !Minimum DNBR

0.150

~· 0.125 Cl)'

...;,.;.. tn·

.lli:!. 0.100

~· .Q 0.075 G,)·

> U} 0.050 ti). lO ::! 0.025

0.000

..

0

I I - LYNXT

- COBRA-FLX

' ~

100 200 300 400

Axial Height, cm

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Pa e 1-9

Fiigure 5-44: Thermodynam:ic 1QuaHty Comparison for the C1ombined; Effect of AH Modeling Parameters 1in Table 5-9 for the 4 Pump·

Coastdown at the Time of M1nimum DNBR

0.15 ~---~----~---~----~

-~ 0.05 (t'I

-LYNXT - C-OBRA-fLX

~ -0.05 +-----+-----+---..,,,,._~,__ ___ --I 0 ~ -0.15 +-----+------t-.,,..__--~f-------1

·c ...0 ·s -0..25 -------+----------------,__ ___ __, i::r Lil

-0.35 +---=r"i=+----+----~f-------I

-0.45 +-----+-----+--------1~-----1

0 100 200 300 400

Axial Height, cm

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Pa e 1-10 Figures 5-42, 5-43 and 5-44 should read as:

Figure 5-42: DNBR Comparison for the Combined Effect of All Modeling Parameters in Table 5-9 for the 4 Pump Coastdown

2.80 ------------....... ----....... -----

~ 2.60

> ~

--LYNXT

- - - COBRA-FLX

u 2.40 -+--------1------+------+----R-----I

~ .......... 0::: 2.20 4-------'"""'----4-------+-----+--.H------I

Cil z 0 ~ 2.00 -1--------+--------......,__f-----~....+-------I

...._ __ .--1.80 ......,_ ____ ..... _____ .,_ ____ ..... ____ ___.,

1 2 3 4 5

Transient Time, Seconds

L

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Pa e 1-11 Figure 5-43: Mass Velocity Comparison for the Combined Effect of All Modeling Parameters in Table 5-9 for the 4 Pump Coastdown at Time of Minimum DNBR

0.150

(.) 0.125 Q) Cf) -C) 0.100 ~

~ (.) 0.075 0

~ Cf) 0.050 Cf) ca ~ 0.025

0.000

....

0 100

I I --LYNXT

- - - COBRA-FLX

- ~ -

200 300 400

Axial Height, cm

'-

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Errata 1 NP-000

Pa e 1-12 Figure 5-44: Thermodynamic Quality Comparison for the Combined Effect of All Modeling Parameters in Table 5-9 for the 4 Pump Coastdown at Time of Minimum

DNBR

0.15

0.05 --LYNXT

>-- - - COBRA-FLX

:!::: ro -0.05 ::s a E -0.15 ::s

"i:: ..c

-0.25 ::s C"' w

-0.35

-0.45 0 100 200 300 400

Axial Height, cm

Item 5

The beginning of section 5.7.2.2 currently reads as:

A locked rotor transient comparison of COBRA-FLX and L YNXT predictions was performed by substituting the earlier 4 pump coastdown forcing function with a locked rotor forcing function. This substitution results in a more abrupt reduction in DNBR as can be seen in Figure 5-45 with a minimum DNBR difference of 0.093 as shown in Table 5-10.

The beginning of section 5.7.2.2 should read as:

A locked rotor transient comparison of COBRA-FLX and L YNXT predictions was performed by substituting the earlier 4 pump coastdown forcing function with a locked rotor forcing function . This substitution results in a more abrupt reduction in DNBR as can be seen in Figure 5-45 with a minimum DNBR difference of 0.114 as shown in Table 5-10.

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Item 6

Table 5-11 currently reads as:


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Pa e 1-13

Table 5-11.: COBRA-FLX and LYNXT !Minimum DNB'R Sensitivtty t o Modeling Parameters for the Locked Rotor

MONBR (IBWCMV-A)

Parameter Parameter COBRA-FLX tYNXT Change

Combined Combined Effect of All 0.944 0.'918 Parameters as in Table 5-9

Table 5-11 should read as:

Table 5-11: COBRA-FLX and L YNXT Minimum DNBR Sensitivity to Modeling Parameters for the Locked Rotor

Parameter Parameter

MDNBR (BWCMV-A) Change COBRA-FLX LYNXT

Combined Combined Effect of All 0.861 0.894

Parameters as in Table 5-9

Item 7

The bulleted items on p. C-36 currently read as:

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The bulleted items on p. C-36 should read as:

Item 8

The first paragraph on p. C-37 currently reads as:

COBRA-FLX's response to this particular test geometry with its [


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Pa e 1-14

] results in higher M/P values yielding an average M/P notably higher than the average M/P obtained from using L YNX2 local conditions as seen when comparing results between Table C-11 and Table C-12 . The standard deviations of the M/P values using COBRA-FLX local conditions were comparable to those obtained using L YNX2 local conditions .

The first paragraph on p. C-37 should read as:

COBRA-FLX's response to this particular test geometry with its [

] results in higher M/P values yielding an average M/P notably higher than the average M/P obtained from using L YNX2 local conditions as seen when comparing results between Table C-11 and Table C-12. The standard deviations of the M/P values using COBRA-FLX local conditions were comparable to those obtained using L YNX2 local conditions.

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1.3 Additional Errata

The following errata apply to ANP-10311 P-A Revision 0.

Item 1

The paragraph directly below equation 2-10 currently reads as:


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Pa e 1-15

The density of each phase in Equation 2-10 is a function of two independent thermodynamic properties, the pressure and temperature , for example. The equation of state and the transport properties used in COBRA-FLX are discussed later in this report.

The paragraph directly below equation 2-10 should read as:

The saturated density of each phase in Equation 2-10 is a function of the system pressure. The channel cross-sectional density is a function of temperature and pressure when the liquid is subcooled or superheated . The equation of state and the transport properties used in COBRA-FLX are discussed later in this report.

Item 2

The first paragraph of Section 2.2.5.4 currently reads as:

Finally, the equation of state will complete the system of basic equations. All thermodynamic state and transport properties in COBRA-FLX are the saturation properties corresponding to the system pressure. Subcooled liquid properties are calculated at pressure that corresponds to the saturated condition for the given fluid inlet temperature . Superheated vapor properties are available and used for some special applications.

The first paragraph of Section 2.2.5.4 should read as:

Finally, the equation of state will complete the system of basic equations. All thermodynamic state and transport properties in COBRA-FLX are the saturation properties corresponding to the system pressure. Subcooled liquid properties are calculated at pressure that corresponds to the saturated condition for the given local fluid ff:Het temperature. Superheated vapor properties are available and used for some special applications.

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Item 3

- ----------------~


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Pa e 1-16

In Section 2.3.1.1.1 , the paragraph directly after Figure 2-8 currently reads as:

The spatial derivatives, all only in the axial direction for the subchannel equations, are approximated with the donor-cell approach. Generally, a backward difference from level J is used for the spatial gradients in the continuous equations. Additionally, the quantity being transported is computed as that of the donor cell: the cell , or node , from which the fluid is flowing. For example, the finite-difference form of the mass flux derivative in the mass conservation equation is approximated by

In Section 2.3.1.1 .1, the paragraph directly after Figure 2-8 should read as:

The spatial derivatives, all only in the axial direction for the subchannel equations, are approximated with the donor-cell approach. Generally, a backward difference from level J is used for the spatial gradients in the conservation equations. Additionally , the quantity being transported is computed as that of the donor cell: the cell , or node, from which the fluid is flowing . For example, the finite-difference form of the mass flux derivative in the mass conservation equation is approximated by

Item 4

The statement at the top of page 2-52 currently reads as:

Furthermore, Equation 2-140 is written in the following vector form needed by the SCHEME solution methods:

The statement at the top of page 2-52 should read as:

Furthermore, Equation 2-140 is written in the following matrix form (where [S]T is defined after equation 2-127) needed by the SCHEME solution methods:

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Item 5

Section 2.3.2.2.1, the paragraph after equation 2-206 currently reads as:


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Pa e 1-17

Thus, -Dk.Pi is analogous to a lateral pressure gradient where a sum is taken on i . The transpose Dk,; performs an operation that is the divergence in the lateral direction . The sign of Dk.Pi accounts for lateral flow into, or out of, the control volume. The array D is very useful to compact and simplify the notation used in the control volume equations. The operations of D are performed in the coding by logic using i(k) and j(k) rather than by actual matrix multiplication. The COBRA-FLX code uses arrays IK(K) and JK(K).

Section 2.3.2.2.1, the paragraph after equation 2-206 should read as:

Thus, -Dk.Pi is analogous to a lateral pressure gradient where a sum is taken on i . The transpose Dk,i performs an operation that is the divergence term in the lateral direction. The sign of Dk,ipi accounts for lateral flow into, or out of, the control volume. The array D is very useful to compact and simplify the notation used in the control volume equations. The operations of D are performed in the coding by logic using i(k) and j(k) rather than by actual matrix multiplication . The COBRA-FLX code uses arrays IK(K) and JK(K).

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Item 6

The first paragraph in Section 2.3.2.4 currently reads as:


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Pa e 1-1 8

The COBRA-FLX PV numerical solution strategy uses a combination of iterative and direct solution . The thermal-hydraulic numerical solution is conceptually split into two parts . The first part solves the momentum and mass equations for the flows and pressure. The second part solves the energy equation and calculates the mixture density from the state equation. Both the flow and energy solutions use the Newton method . The use of the Newton method is of value because it permits a program structure where it is easier to : 1) check the equations being solved ; 2) compact the coding ; 3) make changes ; and 4) monitor convergence.

The first paragraph in Section 2.3.2.4 should read as:

The COBRA-FLX PV numerical solution strategy uses a combination of iterative and direct solution . The thermal-hydraulic numerical solution is conceptually split into two parts. The first part solves the momentum and mass equations for the flows and pressure. The second part solves the energy equation and calculates the mixture density from the state equation . Both the flow and energy solutions use the Newton method . The use of the Newton method is of value because it permits a program structure where it is easier to : 1) check the equations being solved ; 2) compact the coding ; 3) make changes; and 4) monitor convergence .

Item 7

Equation A-7 on Page A-5 currently reads as:

q" Twall = T bul k + p h

h bulk

Equation A-7 on Page A-5 should read as:

Twall = Tbulk + p h h bulk

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Item 8


Errata 1 NP-000

Pa e 1-19

The paragraph directly above equation A-85 through equation A-87 currently reads as:

When the cladding surface is in transition boiling one of two different transition boiling heat transfer models is used. One model is based on the methodology outlined in References A-16 and A-17. The other method is based on Stosic's rewet model as defined in Reference A-18. For both the original method and the method based on Stosic the film boiling heat transfer coefficients , wh ich are defined later, are generated . For the original method from References A-2 and A-3 the transition boiling heat flux is defined as follows :

where

" - .x- 2 " (1 .x- 2) " qTB - u qTB + - u q MSFB

0 = (TMSFB - Twall) TMsFB - TcHF

A-85

A-86

where the MSFB heat flux is based on the appropriate film boiling heat transfer coefficient, the MSFB temperature from Equation A-81 and the vapor temperature . For Stosic's method the appropriate film boiling heat transfer coefficient (h FB ) is used to calculate the heat flux as follows :

A-87

The paragraph directly above equation A-85 through equation A-87 should read as:

When the cladding surface is in transition boiling one of two different transition boiling heat transfer models is used. One model is based on the methodology outlined in References A-16 and A-17. The other method is based on Stosic's rewet model as defined in Reference A-18. For both the original method and the method based on Stosic the film boiling heat transfer coefficients , which are defined later, are generated. For the original method from References A 2 and A 3 A-16 and A-17 the transition boiling heat flux is defined as follows :

" - .x-2 " (1 .x-2) " qTB - u qCB E + - u qMSFB A-85

where

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(j = (TMSFB - Twall) TMsFB -TcHF


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Pa e 1-20

A-86

where the MSFB heat flux (q~SFB) is based on calculated using the appropriate film

boiling heat transfer coefficient evaluated at the MSFB temperature T SEBJ from Equation A-81, the MSFB temperature (T MSFB) and the vapor temperature. For Stosic's method the appropriate film boiling heat transfer coefficient (hFB ) is used to calculate the heat flux as follows:

A-87

Item 9

Section C.6.3 currently reads as:

The ranges and limitations of the BWCMV-A CHF correlation from the L YNXT based SER in Reference C-18 will be maintained with the exceptions where the use of COBRA-FLX local conditions warrant a change for local conditions and the DNBRL value

Local Conditions: Pressure: 1475 to 2465 psia Mass Velocity: 0.900 to 3.535 Mlb/hr-ft2 Thermodynamic Quality at CHF: <27%

Fuel Design: Spacer Grid Type: Mark-BW17 Hydraulic Diameter: 0.3747 to 0.4637 inches Effective Spacing

Main Grids [ ]

Mid-Span Mixing Grids ( ]

Application : Code: COBRA-FLX DNBRL: 1.21

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Section C.6.3 should read as:


Errata 1 NP-000

Pa e 1-21

The ranges and limitations of the BWCMV-A CHF correlation from the L YNXT based SER in Reference C-18 will be maintained with the exceptions where the use of COBRA-FLX local conditions warrant a change for local conditions and the DNBRL value

Local Conditions: Pressure: 1475 to 2465 psia Mass Velocity: 0.900 to 3.535 Mlb/hr-ft2 Thermodynamic Quality at CHF: <26%

Fuel Design: Spacer Grid Type: Mark-BW17 Hydraulic Diameter: 0.3747 to 0.4637 inches Effective Spacing

Main Grids [

Mid-Span Mixing Grids [ Application:

Item 10

Code: COBRA-FLX DNBRL: 1.21

Table C-11 currently reads as:

] ]

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Table C-11 should read as:

Item 11

Table C-17 the BWCMV-A correlation limits are currently:

CHF Parameter British Units Correlation

Pressure 1475 - 2465 psia

BWCMV-A Mass Velocity 0.900 - 3.535 Mlb/hr-ft2

Thermodynamic Quality <27% Design Limit 1.21

Table C-17 the BWCMV-A correlation limits should be:

CHF Parameter British Units Correlation

Pressure 1475 - 2465 psia

BWCMV-A Mass Velocity 0.900 - 3.535 Mlb/hr-ft2

Thermodynamic Quality <26% Design Limit 1.21


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Pa e 1-22

SI Units

101 .7 - 170.0 bar 1220.6 - 4794.4 kg/m2-s <27% 1.21

SI Units

101 .7 -170.0 bar 1220.6 -4794.4 kg/m2-s <26% 1.21

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Item 12

Table E-1 card group 2 currently reads as:

Card Input Description Group Identifier

Flow correlations

• N 1 = 2 (Saha-Zuber subcooled void correlation)

• N2 = 8, 9 (Chexal-Lellouche void correlation)

• N3 = 0 (homogeneous two-

2 GCC2 phase friction multiplier)

• N4 = 0 (wall viscosity correlction not included)

• N5 = 0 (Lehmann friction factor with the Szablewski correlation)

• N6 = 1 (Zuber-Staub profile fit)

Table E-1 card group 2 should read as:

Card Input Description Group Identifier Flow correlations

• N1 = 2 (Saha-Zuber subcooled void correlation)

• N2 = 8, 9 (Chexal-Lellouche void correlation)

• N3 = 0 (homogeneous two-2 GCC2 phase friction multiplier)

• N4 = 1 (wall viscosit correction included)

• N5 = 0 (Standard* friction factor model)

• N6 = 1 (Zuber-Staub profile fit)

I _ ____ _


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Pa e 1-23

Comments

Note that N2 = 9 uses Chexal-Lellouche void correlation using tables with interpolation. This option is advantageous with respect to runtime for large cases, e.g. full core subchannel-by-subchannel calculations.

Comments

Note that N2 = 9 uses Chexal-Lellouche void correlation using tables with interpolation. This option is advantageous with respect to runtime for large cases, e.g. full core subchannel-by-subchannel calculations.

*Note that N5=0, however, since AA>O in card group G2-1, the standard friction facto model is used by default.

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