Framatome, Inc., ANP-10337, Rev. 0, Suppl 1NP, 'Deformable ... · Instead, a special deformable...

framatome

Deformable Spacer Grid Element ,

Topical Report

September 2018

(c) 2018 Framatome Inc.

ANP-10337 Revision 0 Supplement 1 NP Revision 0

Copyright© 2018

Framatome Inc. All Rights Reserved

ANP-10337 Revision O

Supplement 1 NP Revision O

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Deformable Spacer Grid Element Topical Report

Item 1

Section(s) or Page(s) All

Nature of Changes

Description and Justification Initial Issue



Page i

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ANP-10337 Revision 0

Supplement 1 NP Revision 0

Page ii

Contents

Page

1.0 INTRODUCTION ............................................................................................... 1-1

1.1 Purpose .................................................................................................. 1-1

1.2 Method Overview .................................................................................... 1-1

1.3 Summary of Sections .............................................................................. 1-1

2.0 APPLICABILITY ................................................................................................ 2-1

2.1 Spacer Grid Behavior. ............................................................................. 2-1

2.2 Applicability to Base Methodology .......................................................... 2-1

3.0 REGULATORY REQUIREMENTS .................................................................... 3-1

3.1 Regulatory Basis ..................................................................................... 3-1

3.2 Acceptance Criteria ................................................................................ 3'-1

4.0 DEFORMABLE GRID ELEMENT ...................................................................... 4-1

4. 1 Overview ................................................................................................. 4-1

4.2 Load-Deflection Behavior. ....................... , ............................................... 4-1

4.3 Loading and Unloading in the Large Deformation State ......................... 4-3

4.4 Viscous Damping ...... 1 ............................................................................. 4-5

4.4.1 Damping from Unloading Stiffness ............................................... 4-5 4.4.2 Piecewise Linear Damping ........................................................... 4-6

4.5 Sliding Friction ........................................................................................ 4-7

4.6 Deformable Grid Element Benchmarking to Experimental Data ........................................................................................................ 4-8 4.6.1 Reduction of Experimental Data ................................................... 4-8 4.6.2 Deformable Grid Element Benchmark .......................................... 4-9 4.6.3 Validation of the Deformable Grid Element

Benchmark ................................................................................. 4-11 4.6.4 Conversion to Operating Conditions for End of Life

Models ....................................................................................... 4-11

5.0 SEISMIC AND LOCA ANALYSIS ...................................................................... 5-1

5.1 Implementation in Row Model ................................................................. 5-1 5.1.1 Homogeneous Core Configuration ............................................... 5-1 5.1.2 Mixed Core Configurations ........................................................... 5-2

5.2 Processing Deformation Results ............................................................. 5-4

5.3 SSE+ LOCA Combination ...................................................................... 5-5

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Page iii

5.4 Experimental Uncertainty and 95% Confidence Limit ............................. 5-7

5.5 Seismic Sensitivity Analysis .................................................................... 5-8

6.0 NON-GRID.COMPONENT STRENGTH EVALUATION .................................... 6-1

7.0 REFERENCES .................................................................................................. 7-1

APPENDIX A: EXAMPLE SPACER GRID BEHAVIOR ............................................... A-1

APPENDIX B: DEFORMABLE GRID ELEMENT BENCHMARK ................................ 8-1

APPENDIX C : SAMPLE PROBLEM SUMMARY ....................................................... C-1

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List of Tables



Page iv

Table 2-1: Changes Relative to Reference 1 ............................................................... 2-2

Table 4-1: Deformable Grid Element Input Parameters ............................................. 4-12

Table B-1: Target Behavior for Deformable Grid Element Benchmark ......................... B-9

Table B-2: Deformable Grid Element Input Parameters ............................................. B-10

Table B-3: BOL Analysis of Covariance Results ........................................................ B-11 '

Table B-4: Coefficients of Determination .................................................................... B-11

Table B-5: Root Mean Squared Error. ........................................................................ B-11

Table C-1: GAIA Fuel Assembly Lateral Model Input Parameters .............................. C-8

Table C-2: Rotational Stiffness from Lateral Benchmark ........................................... C-10

Table C-3: Benchmark Comparison to Test Data ...................................................... C-10

Table C-4: Rotational Stiffness Values at Operating Conditions ............................... C-11

Table C-5: Grid External Stiffness, External Damping, and Strength ........................ C-11

Table C-6: Deformable Grid Element Input Parameters at Operating Conditions ..... C-12

Table C-7: Equivalent and Internal Spring Stiffness and Damping at Operating Conditions .............................................................................................. C-13

Table C-8: Mixed Core Deformable Grid Element Input Parameters at Operating Conditions .............................................................................................. C-14

Table C-9: Spacer Grid Deformations, Full Core ....................................................... C-15

Table C-10: IGM Impact Forces, Full Core .......................... , ..................................... C-15

Table C-11: Spacer Grid Deformations, Mixed Core ................................................. C-16

Table C-12: IGM Impact Forces, Mixed Core ............................................................ C-16

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List of Figures



Page v

Figure 4-1: Deformable Grid Element Configuration ............................................ , ..... 4-13

Figure 4-2: Deformable Grid Element Load-Deflection Behavior ............................... 4-14

Figure 4-3: Loading / Unloading Behavior .................................................................. 4-15

Figure 4-4: Restrictions on Elastic Energy Coefficients .............................................. 4-16

Figure 4-5: Illustration of Damping from Unloading Stiffness ..................................... 4-17

Figure 4-6: Illustration of Piecewise Linear Damping ................................................. 4-18

Figure 4-7: Effect of Sliding Friction on Load versus Deflection Response ................ 4-19

Figure A-1: Dynamic Compression Results, Impact Force Squared versus Impact Kinetic Energy, BOL Condition .................................................................. A-3

Figure A-2: Dynamic Compression Results, Residual Deformation versus Impact Kinetic Energy, BOL Condition .................................................................. A-4

Figure A-3: Dynamic Compression Results, Impact Force Squared versus Impact Kinetic Energy, EOL Condition .................................................................. A-5

Figure A-4: Dynamic Compression Results, Residual Deformation versus Impact Kinetic Energy, EOL Condition .................................................................. A-6

Figure A-5: Dynamic Compression Results, Reverse Protocol Test, BOL Condition ................................................................................................... A-7

Figure A-6: Dynamic Compression Results, Reverse Protocol Test, EOL Condition .............. : .................................................................................... A-8

Figure A-7: Measured Guide Tube Positions for Deformed Spacer Grid ...................... A-9

Figure A-8: Deformed Spacer Grid, Unloaded State .................................................. A-10

Figure B-1: Regression of [ ] BOL ... B-12

Figure B-2: Regression of [


] BOL .......... B-13

] BOL .... B-14

Figure B-4: Benchmark Comparison of Impact Force Squared as a Function of Kinetic Energy, BOL Hot. ......................................................................... B-15

Figure B-5: Benchmark Comparison of Total Deformation as a Function of Kinetic Energy, BOL Hot ..................................................................................... B-16

Figure B-6: Benchmark Comparison of Impact Force as a Function of Total Deformation, BOL Hot ............................................................................. B-17

Figure B-7: Benchmark Comparison of Residual Deformation as a Function of Kinetic Energy, BOL Hot.. ........................................................................ B-18

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Deformable Spacer Grid Element Topical Report ·



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Figure B-8: Benchmark Comparison of Restitution Coefficient as a Function of Kinetic Energy, BOL Hot.. ........................................................................ B-19

Figure C-1: Operational Basis Earthquake Motions, X-Direction ............................... C-17

Figure C-2: Operational Basis Earthquake Motions, Z-Direction ............................... C-18

Figure C-3: Safe Shutdown Earthquake Motions, X-Direction ................................... C-19

Figure C-4: Safe Shutdown Earthquake Motions, Z-Direction ................................... C-20

Figure C-5: Accumulator Line Break Motions, X-Direction ........................................ C-21

Figure C-6: Accumulator Line Break Motions, Z-Direction ........................................ C-22

Figure C-7: Mixed Core Row Configurations ............................................................. C-23

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Acronym

ACC

ANCOVA

BOL

OGE

EOL

IGM

LOCA

OBE

PWR

RCCA

SSE

Nomenclature

Definition

Accumulator Line Break

Analysis of Covariance

Beginning of Life

Deformable Grid Element

End of Life

Intermediate GAIA Mixer

Loss of Coolant Accident

Operating Basis Earthquake

Pressurized Water Reactor

Reaction Control Component Assembly

Safe Shutdown Earthquake



Page vii

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1.0 INTRODUCTION

1.1 Purpose



Page 1-1

The purpose of this report is to supplement the methodology to evaluate the structural

response of a fuel assembly design to external dynamic excitations from seismic and

Loss of Coolant Accident (LOCA) events as presented in the AREVA Topical Report

ANP-10337P-A (Reference 1). The report focuses on the implementation of a

nonlinear, deformable spacer grid model and the necessary changes to the generic·

methodology. The nonlinear spacer grid behavior cannot be adequately described by

the linear visco-elastic spring prescribed in the base methodology of Reference 1.

Instead, a special deformable grid element was developed to represent the spacer grid

behavior and to predict the spacer grid residual deformation in seismic and LOCA

events.

1.2 Method Overview

This topical report defines the methodology for introducing a nonlinear, deformable

spacer grid design into the base methodology detailed in Reference 1. The horizontal

analysis is updated to include the nonlinear response of the spacer grid through a

deformable spacer grid element rather than a linear visco-elastic spring. The procedure

to define the numerical models which represent the dynamic response of the fuel

assembly is altered only by the inclusion of the nonlinear grid element. The numerical

models capture the motion of the fuel assembly and the interaction between

neighboring fuel assemblies as well as between the fuel assembly and the core baffle.

The primary outputs from the horizontal analysis are the spacer grid deformations due

to spacer grid impacts, and the deflections experienced by the fuel assemblies. The

vertical analysis is not affected by the methodology presented in this topical report.

1.3 Summary of Sections

This report is presented in six sections:

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Page 1-2

Section 1 defines the purpose of the report and an overall description of the

methodology.

Section 2 discusses the applicability of this report and the how the methodology

presented in this report alters the methodology presented in Reference 1.

Section 3 describes the regulatory requirements and the associated acceptance criteria.

Section 4 describes the mathematical model that will be used to represent the spacer

grid in the horizontal seismic and LOCA analyses.

Section 5 presents the method for including the deformable grid element in the overall

horizontal seismic and LOCA analysis.

Section 6 describes the method to account for spacer grid deformation in the non-grid

component strength evaluation.

There are three appendices for this report:

Appendix A presents the dynamic impact test data for a spacer grid design that meets

the applicability requirements of this supplemental topical report.

Appendix B presents a demonstration of how to benchmark the deformable grid element

to experimental data.

Appendix C presents the application of this methodology to a sample problem.

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2.0 APPLICABILITY



Page 2-1

The methodology defined in this topical report is applicable to fuel assembly designs

with spacer grids that do not meet the definition of a [ ] as

defined in Reference 1 due to either a nonlinear impact response or the accumulation of

permanent, or residual, deformation.

2.1 Spacer Grid Behavior

This section identifies the spacer grid behavior that must be satisfied for this

methodology to be applicable. These behaviors must be satisfied over the anticipated

range of residual deformations.

2.2 Applicability to Base Methodology

The methodology presented in this report replaces certain aspects of the base

methodology presented in Reference 1 . The specific sections of Reference 1 that are

affected by this report are listed in Table 2-1 along with the general description of the

methodology change.

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Table 2-1: Changes Relative to Reference 1

Section in Ref.1

Section 2.2 The spacer grid model is changed from a [

] Section 3 The applicable regulatory requirements are unchanged

Section 4.1 The QBE acceptance criterion is changed from a load limit associated with a deformation limit to a deformation limit associa.ted with the spacer grid envelope tolerance.

Section The SSE+LOCA load limit [ 4.2.1

] is replaced with a deformation limit which ensures control rod insertion and coolability.

Section The SSE load limit [ ] 4.3.1 is replaced with a deformation limit which ensures control

rod insertion and coolability.

Section Completely replaced by this topical report 5.2.2.2

Section While the dynamic spacer grid crush test protocol is 6.1.2 unchanged, the test data post-processing and

characterization are defined in Section 4.6 of this topical report. The lateral impact test and the calculation of the equivalent stiffness and damping are unchanged. The calculation of the internal stiffness and internal damping are updated in this topical report.

Section 7.1 The comparison of impact loads to the load criteria, [

] is updated with a comparison of the predicted residual deformation to the allowed residual deformation.

Section 7.4 The method of combining the seismic and LOCA impact forces through square root sum of the squares (SRSS) is

updated in the topical report to define [

] Section 7.5 The sensitivity study description is clarified to specify [

]



Page 2-2

Section in this report

Section 2.0

Section 3.1

Section 3.2

Section 3.2

Section 3.2

Section 4.1 to 4.5

Section 4.6

Section 5.4

Section 5.3

Section 5.5

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3.0 REGULATORY REQUIREMENTS

3.1 Regulatory Basis



Page 3-1

The regulatory requirements listed and discussed in detail in Section 3.1 of Reference 1

are applicable to this topical report.

3.2 Acceptance Criteria

The acceptance criteria listed and discussed in Section 4 of Reference 1 are applicable

to this topical report with the following exceptions:

The limiting impact load is replaced with the limiting residual deformation. [

]

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4.0 DEFORMABLE GRID ELEMENT

4.1 Overview



Page 4-1

The Deformable Grid Element (OGE) is a gapped spring-damper element developed for

CASAC with geometric and structural nonlinearities. The presence of a gap means that

the element is only active in compression. [

]

The OGE is incorporated into the overall CASAC program as a user defined force

element. The element is defined by the primary node, the secondary node, and the

assigned degree of freedom. The degree of freedom is the same for the primary and

secondary nodes. During the solution phase, the CASAC program exchanges four

variables with the OGE:

An illustration of the OGE configuration is provided in Figure 4-1. The OGE model input

parameters define the [

] The

input parameters are listed in Table 4-1.

4.2 Load-Deflection Behavior

The load-deflection behavior of the OGE can be described by three distinct states:

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Page 4-2

As illustrated in Figure 4-2, the monotonic loading behavior of the element is defined by

the following parameters:

The residual deformation is the key state variable. During the CASAC solution, the

residual deformation defines the current position on the load-deflection curve. The

residual deformation is updated at each iteration step. Three specific values of the

residual deformation are used as input parameters:

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4.3 Loading and Unloading in the Large Deformation State

[



Page 4-3

] is chosen based on

observations from testing and mathematical simplicity. As seen in the inset of

Figure 4-7, the [

] as the residual deformation increases.

The coefficients [

] The threshold force is the force at which the element switches from

the loading/unloading curve to the monotonic loading curve. [

] Figure 4-3 illustrates this concept. The [

]

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Constraints are placed on [

the constraints require that both the [



Page 4-4

] As illustrated in Figure 4-4,

] to preclude any non-physical behavior. From the equations for k1 and k2

above, a simple inequality can be derived to ensure that both [

]

It is clear from the inequality that the [

]

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4.4 Viscous Damping



Page 4-5

Viscous damping is included in the model as a force that is the product of the damping

coefficient and the relative velocity of the two grid nodes. Two options are available for

the viscous damping formulation. For both options, a nominal value for the damping

coefficient, Co, must be defined.

4.4.1 Damping from Unloading Stiffness

The first damping option is based on the [

]

[

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The damping based on the [

relationship between the [



Page 4-6

J ] As stated in Section 4.2, the

]

This relationship is shown in Figure 4-5 where A% represent the percentage the [

]

4.4.2 Piecewise Linear Damping

The second damping option is a [ - ] This model provides

additional flexibility for the user to define the damping over each state of the element. A

reference damping coefficient is provided as an input parameter, then the damping in

the [

]

[

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Page 4-7

In the elastic range, the damping coefficient is constant. In the other states, the

damping is [

] is

illustrated in Figure 4-6.

4.5 Sliding Friction

The effect of sliding friction is included in the OGE model as a source of energy

dissipation. The physical phenomenon being modeled is the friction between the fuel

rods and the spring hulls as the spacer grid is deformed. The effect is observed as a

[ ] as

illustrated in Figure 4-7.

The force is modeled as a function of the [

]

J

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The sliding friction force can be reduced to a [



Page 4-8

]

Figure 4-7 illustrates the hysteretic effect of the sliding friction when it is combined with

the elastic force.

4.6 Deformable Grid Element Benchmarking to Experimental Data

The three following sections provide an overview of the method to benchmark the

deformable grid element to the experimental data. A detailed example of the

benchmarking process is presented in Appendix B.

4.6.1 Reduction of Experimental Data

The linear visco-elastic spring defined in Reference 1 is characterized by stiffness,

damping, and strength values. These values are calculated from experimental data by

linear regression (stiffness and damping) and statistical evaluation (strength). The

experimental data reduction process is similar for the deformable grid element, but

linear visco-elastic theory is not used to define any properties. Instead, the response of

the spacer grid over the range [

]

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Page 4-9

Given that the spacer grid response is nonlinear, a simple linear regression is not

appropriate and a multiple linear regression is needed. [

l

The values for Xi define the value of the independent variable where there is a clear

[

l

4.6.2 Deformable Grid Element Benchmark

The input parameters for the deformable grid element are defined by performing a

benchmark analysis. The benchmark analysis simulates a dynamic impact test in

CASAC with a single grid element and a prototypical lumped mass. [

l

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

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Supplement 1 NP Deformable Spacer Grid Element Revision 0 Topical Report Page 4-10

The regressions calculated per Section 4.6.1 are used to develop a target behavior to

be matched by the output of the deformable grid element. [

]

The values for the deformable grid element input parameters are determined

semiempirically. Some quantities can be estimated from first principles like the

conservation of energy. Other quantities are defined by experimentally observed data,

i.e. [ ] However,

the final values for the input parameters will be defined by an iterative process. The

simulation is performed, and parameters are adjusted to match the target behavior.

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4.6.3 Validation of the Deformable Grid Element Benchmark


Supplement 1 NP Revision 0 Page 4-11

The output of the deformable grid element is compared to the target behavior only to

guide the selection of the input parameters. The validation of the deformable grid

element benchmark is made through an Analysis of.Covariation (ANCOVA). The goal of

the ANCOVA is to state that the output of the deformable grid element is not statistically

different than the experimental data. The hypothesis in the analysis is that [

]

4.6.4 Conversion to Operating Conditions for End of Life Models

Since the dynamic impact test for the spacer grid at End of Life conditions is performed

at room temperature, the model benchmark is also performed at room temperature. The

deformable grid model must then be converted to operating temperature [

]

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Table 4-1: Deformable Grid Element Input Parameters



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Figure 4-1: Deformable Grid Element Configuration



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Figure 4-2: Deformable Grid Element Load-Deflection Behavior

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Figure 4-3: Loading / Unloading Behavior


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Figure 4-4: Restrictions on Elastic Energy Coefficients



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Supplement 1 NP Revision O Page 4-17

Figure 4-5: Illustration of Damping from Unloading Stiffness

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Figure 4-6: Illustration of Piecewise Linear Damping



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Figure 4-7: Effect of Sliding Friction on Load versus Deflection Response

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5.0 SEISMIC AND LOCA ANALYSIS

5.1 Implementation in Row Model

5.1.1 Homogeneous Core Configuration



Page 5-1

The horizontal row model defined in Section 5.2.2.2 of Reference 1 is unchanged by the

introduction of the deformable grid element. The spring between two adjacent fuel

assemblies is represented by the external, or through-grid, stiffness and damping

properties of the full spacer grid. The two remaining springs between the outer

assemblies and the baffle plates are represented by the stiffness and damping

properties of a half spacer grid. The half spacer grid stiffness and damping are two

times larger than the full spacer grid values. The same approach of the linear model is

applied to the deformable grid elements.

The deformable spacer grid model, as benchmarked according to Section 4.6.2,

represents the response of the full spacer grid and replaces the spring between two

adjacent fuel assemblies. Similar to Reference 1, the half deformable grid model is

derived from the full deformable grid model by altering the model input parameters in

the following way:

By altering the full deformable grid model in this manner, the stiffness and damping are

doubled consistent with the methodology described in Reference 1.

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5.1.2 Mixed Core Configurations



Page 5-2

In the case of mixed core configurations where the fuel assembly with deformable

spacer grids is adjacent to a dissimilar fuel assembly design with linear spacer grids, the

OGE must account for the stiffness and damping properties of the adjacent assembly.

The half deformable grid element and the adjacent linear impact spring are modeled as

springs in series.

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Page 5-3

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5.2 Processing Deformation Results



Page 5-4

The horizontal row model defined in Section 5.2.2.2 of Reference 1 is unchanged by the

introduction of the deformable grid element. Therefore, no single impact element is

associated with a single full spacer grid. Instead, the two springs representing a half

grid of neighboring assemblies are replaced with a single spring. The desired output of

the row model with the deformable grid element is the residual deformation of a spacer

grid for a given fuel assembly.

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5.3 SSE + LOCA Combination



Page 5-5

The spacer grid residual deformations from the worst-case LOCA break and the SSE

are combined to determine a residual deformation for the Design Basis Accident. This

combination is performed to demonstrate conservatism and satisfy the requirements of

GDC 2, but it does not reflect any inter-dependency between the two events.

Therefore, the SSE and LOCA events are analyzed separately.

The combination of the SSE and LOCA residual deformations is performed by [

]

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Page 5-6

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5.4 Experimental Uncertainty and 95% Confidence Limit



Page 5-7

Based on the discussion in Section 4.6, the deformable grid element is benchmarked to

[

] To comply with the

requirements of SRP 4.2, a 95% upper confidence limit must be calculated based on

the variability of the experimental data. The 95% upper confidence limit for a

multivariable regression is calculated from the following equation:

Where Ypred is the value predicted by the regression at X0,

tn-k-1, 95% is the critical value of the t-distribution for n-k-1 degrees of freedom and a

95% confidence interval,

Xo is the matrix of desired regressors,

X is the model matrix containing the experimental data,

MSres is the mean squared residual from the regression of the experimental data.

The matrix of desired regressors, Xo, can be found by [

] Then, the 95% upper confidence of the regression at that

particular Xo can be calculated.

If a sensitivity factor, as defined in SRP 4.2 Appendix A.11.3, is needed for the residual

deformation, then the Ypred in the calculation of the 95% upper confidence limit shall

include the necessary sensitivity factor.


Supplement 1 NP Deformable Spacer Grid Element Revision O Topical Report Page 5-8

The 95% UCL residual deformation is the quantity for comparison against the maximum

permissible residual deformation.

5.5 Seismic Sensitivity Analysis

The sensitivity of the horizontal model results to variations in seismic input motion is

studied per the recommendation in Section 4.2 Appendix A of NUREG-0800 (Reference

4) and Section 7.5 of Reference 1. In the case of the deformable grid element, the

quantity of interest is the spacer grid residual deformation rather than any impact force.

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6.0 NON-GRID COMPONENT STRENGTH EVALUATION



Page 6-1

This topical report does not change the methodology described in Reference 1 for the

non-grid component strength evaluation. [

]

J

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7 .0 REFERENCES



Page 7-1

1. ANP-10337P-A, Revision 0, PWR Fuel Assembly Structural Response to

Externally Applied Dynamic Excitations, April 2018

2. Nuclear Regulatory Commission, Title 10, Code of Federal Regulations,

Part 50, Appendix A

3. Nuclear Regulatory Commission, Title 10, Code of Federal Regulations,

Part 50, Appendix S

4. Nuclear Regulatory Commission, NUREG -0800: Standard Review Plan,

2007

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APPENDIX A: EXAMPLE SPACER GRID BEHAVIOR

A. 1 Dynamic Impact Testing


Supplement 1 NP Revision 0 Page A-1

The dynamic impact test protocol defined in Reference 1 is still applicable to a spacer

grid that is covered by this topical report. As described in Reference 1, the peak impact

force, impact velocity, rebound velocity, total deformation, and residual deformation are

measured for each impact. The experimental data is then used to define the

deformable grid element input parameters through a benchmarking analysis. The

benchmarking analysis is discussed in Section 4.6 and Appendix 8.

Representative experimental data for a GAIA spacer grid from Beginning of Life and

End of Life dynamic impact tests are shown in Figure A-1 through Figure A-4. The

impact test data confirms that the GAIA spacer grid meets the requirement defined in

Section 2.1 that [

]

As part of the dynamic test protocol, both loading directions should be tested to

confirm any directional dependence of the spacer grid design. The loading direction

which produces the more conservative result should be used for seismic and LOCA

analyses.

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A.2 Confirmation of [

A.3 Confirmation of [

1

1



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Supplement 1 NP Revision 0 PageA-3

Figure A-1: Dynamic Compression Results, Impact Force Squared versus Impact Kinetic Energy, BOL Condition

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Figure A-2: Dynamic Compression Results, Residual Deformation versus Impact Kinetic Energy, BOL Condition

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Supplement 1 NP Revision O Page A-5

Figure A-3: Dynamic Compression Results, Impact Force Squared versus Impact Kinetic Energy, EOL Condition

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Figure A-4: Dynamic Compression Results, Residual Deformation versus Impact Kinetic Energy, EOL Condition

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Figure A-5: Dynamic Compression Results, Reverse Protocol Test, BOL Condition

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Figure A-6: Dynamic Compression Results, Reverse Protocol Test, EOL Condition

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Figure A-7: Measured Guide Tube Positions for Deformed Spacer Grid

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Figure A-8: Deformed Spacer Grid, Unloaded State


Supplement 1 NP Revision O PaqeA-10

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Supplement 1 NP Revision 0 Page B-1

APPENDIX B: DEFORMABLE GRID ELEMENT BENCHMARK

B. 1 Introduction

The Deformable Grid Element response is required to be representative of the spacer

grid response measured during the dynamic impact test. A benchmark analysis is

performed to confirm and validate the element response. The benchmark analysis is

performed in three parts:

1. Process experimental results to define a target behavior for the element

response

2. Adjust the element input parameters to match target behavior

. 3. Confirm that no statistical difference exists between the element response and

the experimental data

Step 1 is discussed in Section 4.6.1, and Step 3 is discussed in Section 4.6.3. In this

appendix, an example benchmark analysis is performed to illustrate the benchmarking.

B.2 Processing of Experimental Data

[

]

The following equation is used to describe the overall model for the data.

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An examination of the experimental data in Figure 8-1 indicates that the [

]

The values for Zi are calculated for each experimental data point, and a linear

regression is performed to calculate the coefficients, ai. The same values of [

] are shown in Figure 8-1 through Figure 8-3.

B.3 Adjustment of the Deformable Grid Element Input Parameters

There is no single method for setting the values for the deformable grid element input

parameters. Instead, engineering judgement is used to decide how each input

parameter should be adjusted to match the target behavior.

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A simple CASAC model is used to simulate the dynamic impact test. The excitation for

the simulation is an applied acceleration time history that is calculated from the

prescribed impact velocity, the simulated rebound velocity, and the impacting mass.

The prescribed impact velocities are from the chosen representative test. Since the

simulated rebound velocity depends on the given input parameters, the acceleration file

must be built through an iterative process. The process is defined below:

The first step in the benchmark analysis is to model the [

] due to the small deformations, and will not

significantly affect the deformable grid element response.

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The range over which the spacer grid can be described as linear elastic, meaning a

linear response to [ l and negligible residual deformations,

is identified from the experimental data. The initial elastic and plastic force limits

(FEMAX and FPMAX) should be sufficiently large to ensure the element is operating

only in the elastic phase. The simulation is then run for [

] identified as having a linear elastic response.

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The restitution coefficient is a useful parameter for visualizing the energy dissipation for

the progression of impact kinetic energies. Energy is dissipated by the deformable

element [

]


Supplement 1 NP Deformable Spacer Grid Element Revision 0 Topical Report Page B-6

Through iteration, a set of input parameters are determined. These input parameters

are given in Table B-2. Comparisons of the element response, the predicted (target)

response, and the experimental data are given in Figure B-4 through Figure B-8. At this

point, the validation of the element response is based on a visual or qualitative

comparison. The next step in the benchmark process is to validate that the element

response is not statistically different than the experimental data.

B.4 Statistical Validation of the Deformable Grid Element Benchmark

The main goal of the deformable grid element benchmarking analysis is to define a set

of model input parameters which will describe the experimental behavior of the grid.

The deformable grid model output should reflect the same behavior as the experimental

data. If the CASAC grid model output is the same as the experimental data, then [

] An analysis of covariance (ANCOVA) is

performed to determine if there is any statistically significant difference between the

deformable grid element output and the experimental data.

Assume that the experimental data can be described by the following model:

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Supplement 1 NP Revision O Page B-8

With regards to the benchmarking of the CASAC deformable grid element, the analysis

of covariance is performed for the [

] A summary of the ANCOVA results for the example

benchmark is provided in Table B-3. The coefficients of determination for the full model

regressions are provided in Table B-4. The root mean squared errors of the full model

regressions are provided in Table B-5.

The conclusion of the analysis of covariance for the example benchmark is that the

difference between the CASAC model output and the experimental data is not

statistically significant.

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Table 8-1: Target Behavior for Deformable Grid Element Benchmark

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Table 8-2: Deformable Grid Element Input Parameters



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Table 8-3: 80L Analysis of Covariance Results

Table 8-4: Coefficients of Determination

Table 8-5: Root Mean Squared Error



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Figure 8-1: Regression of [

] BOL



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Figure 8-2: Regression of [

] BOL



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] BOL



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Supplement 1NP Revision 0 Page 8-15

Figure B-4: Benchmark Comparison of Impact Force Squared as a Function of Kinetic Energy, BOL Hot

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Figure 8-5: Benchmark Comparison of Total Deformation as a Function of Kinetic Energy, BOL Hot

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Figure 8-6: Benchmark Comparison of Impact Force as a Function of Total Deformation, BOL Hot

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Figure 8-7: Benchmark Comparison of Residual Deformation as a Function of Kinetic Energy, BOL Hot

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Figure B-8: Benchmark Comparison of Restitution Coefficient as a Function of Kinetic Energy, BOL Hot

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APPENDIX C: SAMPLE PROBLEM SUMMARY

C. 1 Summary and Introduction


Supplement 1 NP Revision 0 Page C-1

The purpose of the sample problem is to demonstrate the application and modeling

techniques described in the body of this topical report. The design considered for this

sample problem is a 17x17 GAIA design for use in Westinghouse reactors, but the

analysis methodology is applicable to other fuel designs which meet the applicability

requirements defined in Section 2.1.

The scope of this sample problem includes the deformable grid element benchmark, the

lateral assembly model benchmark, and the lateral row analysis. The vertical model

benchmark, vertical analysis, and faulted component stress analysis are not included

since the methodology for these calculations are unchanged from Reference 1. The

lateral analysis considers an Operational Basis Earthquake (OBE), a Safe Shutdown

Earthquake (SSE), and one LOCA event (Accumulator Line Break (ACC)). The non

irradiated (Beginning of Life) and irradiated (End of Life) condition for the fuel assembly

are included. The presence of a co-resident fuel design is also included in the sample

problem. The detailed model inputs, the seismic and LOCA input excitations, analysis

results, and acceptance criteria are presented in this appendix.

The fuel design analyzed in this sample problem is a GAIA 12ft assembly. The fuel

assembly has the following features:

• 24 Q12 MONOBLOC Guide Tubes

• 264 M5 Fuel Rods

• 1 Nickel Alloy 718 HMP Lower End Grid

• 1 Nickel Alloy 718 Relaxed HMP Upper End Grid

• 6 M5 GAIA V10 Intermediate Spacer Grids

• 3 M5 Intermediate GAIA Mixing (IGM) Grids

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• AGORA Top Nozzle

• GRIP Bottom Nozzle

• Welded Cage Structure


Supplement 1 NP Revision O Page C-2

The reactor type considered in this analysis is a 157-assembly, 3-loop reactor with 12 ft.

17x17 array fuel assemblies. The horizontal excitations of the full core will be

considered in this analysis through a series of 2-D row models with lengths of 3, 7, 9,

11, 13, and 15 fuel assemblies. Representative seismic and LOCA excitations in both

horizontal directions will be considered.

C.2 Lateral Model Input

The input parameters for the lateral model are provided in Table C-1. The input

parameters for the lateral model, with the exception of the deformable grid element

input parameters, use the same definition of model parameters from Section 6.1 of

Reference 1.

C.2.1 Grid Rotational Stiffness

The rotational spring stiffness values are adjusted until the lateral model produces the

same dynamic characteristics of the fuel assembly, which are determined through the

free vibration and forced vibration tests.

C.2.1.1 Fuel Assembly Free Vibration Test

The free vibration test provides the first natural frequency of the fuel assembly. The test

is performed for initial deflection values ranging from [ ] for the BOL

test and from [ ] for the EOL test. For the BOL test assembly, [

] For the EOL

test assembly, [

]

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C.2.1.2 Fuel Assembly Forced Vibration Test



The forced vibration test provides information regarding the relationship between higher

model frequencies and the fundamental frequency. In the lateral model benchmark,

[

]

C.2.1.3 Grid Rotational Stiffness Benchmark

[

] The rotational stiffness values for the intermediate spacer

grid and intermediate GAIA mixing grid are presented in Table C-2. A comparison of

the frequencies from the test and the frequencies from the lateral model are presented

in Table C-3.

[

] The final

values used in the model are presented in Table C-4.

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C.2.2 Spacer Grid Impact Characteristics



The spacer grid impact characteristics are defined by external and internal impact

elements. The external impact parameters are measured from dynamic grid crush

tests. After the external impact parameters have been determined, the internal impact

parameters are benchmarked to match the results of the fuel assembly lateral impact

test.

C.2.2.1 Dynamic Spacer Grid Crush Test

Dynamic crush testing was performed on three spacer grid types:

• Non-irradiated GAIA intermediate spacer grids

• Simulated-irradiated GAIA intermediate spacer grids

• Non-irradiated intermediate GAIA mixing spacer grids

[ ] spacer grids of each type were tested. For each test, the several

measurements are recorded, including:

• Impact velocity of the carriage

• Rebound velocity of the carriage

• Spacer grid impact force

• Carriage displacement

• Spacer grid residual deformation

For the IGM spacer grids, the grid impact response is characterized by a [

l were calculated in accordance with Reference 1. The stiffness, damping, and strength

values for the intermediate GAIA mixing spacer grid are given in Table C-5.

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Deformable Spacer Grid Element . Topical Report

C.2.3 Deformable Grid Element Benchmark



The measured data from the non-irradiated and simulated-irradiated GAIA intermediate

spacer grid tests were processed in the method described in Section 4.6.1 and

Appendix B. [

]

The quality of the benchmark analysis is validated by performing an Analysis of

Covariance between the experimental data and the deformable grid element response.

The response of the deformable grid element was validated as equivalent to the.

experimental data at a [

Appendix B.

[

] Additional details are provided in

]

The deformable grid element input parameters are given in Table C-6.

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C.2.4 Fuel Assembly Lateral Impact Tests

ANP-10337 R.evision O


.Fuel assembly lateral impact testing was performed for both the BOL and EOL

. assemblies. A model of the test configuration was built, using the benchmarked

parameters established in Section C.2.1. The equivalent stiffness and damping

parameters were benchmarked to match the impact forces measured during the test.

The benchmarked equivalent stiffness and damping values are adjusted to operating

temperature by the ratio of the elastic modulus. The internal stiffness and damping

values are calculated in the same manner as described in Section 6.2 of Reference 1.

For the GAIA intermediate spacer grid, the elastic stiffness and elastic damping are

used in the calculation of the internal stiffness and damping. The equivalent and

internal stiffness and damping values are presented in Table C-7.

C.3 Co-Resident Fuel Assembly

The lateral model inputs for the co-resident Advanced W17 HTP™ fuel assembly are

taken from Table B-1 of Reference 1 with the exception of the nodal elevations, which

are given in Table C-1. The difference in nodal elevations has a negligible effect on the

response of the Advanced W17 HTP ™ model. The properties of the linear impact

springs between two different adjacent fuel assembly designs are calculated according

to Section 5.2.2.1.1 and Section 5.2.2.2 of Reference 1. The properties of the

deformable grid element between the two difference adjacent fuel assembly designs are

calculated according to Section 5.1.2 and presented in Table C-8.

C.4 Seismic and LOCA Input Excitations

The seismic and LOCA time histories (Figure C-1 through Figure C-6) are applied to the

row models as forcing functions at the lower core plate, upper core plate, and baffle

wall. Each of the seismic and LOCA events is defined by time histories in the two

horizontal directions, X and Z.

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C.5 Analysis Results



Lateral row models were constructed using the inputs defined in Sections C.2 and C.3

to represent a core having row lengths of 3, 7, 9, 11, 13, and 15 fuel assemblies. Each

row type is modeled in this sample problem. The mixed core configurations are

illustrated in Figure C-7.

The GAIA intermediate spacer grid residual deformations and the IGM grid peak impact

loads, as well as the associated margins to the allowables, for the full core cases are

summarized in Table C-9 and Table C-10, respectively.

The GAIA intermediate spacer grid residual deformations and the IGM grid peak impact

loads, as well as the associated margins to the allowables, for the mixed core cases are

summarized in Table C-11 and Table C-12, respectively.

C. 6 Conclusions

This sample problem has demo.nstrated the practical ·application of the methodology

defined within thts topical report. The analysis has yielded positive margins for the

spacer grid criteria.

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Table C-1: GAIA Fuel Assembly Lateral Model Input Parameters


Supplement 1 NP Revision 0 Pa e C-9

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Table C-2: Rotational Stiffness from Lateral Benchmark

Table C-3: Benchmark Comparison to Test Data



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Table C-4: Rotational Stiffness Values at Operating Conditions

Table C-5: Grid External Stiffness, External Damping, and Strength

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Table C-6: Deformable Grid Element Input Parameters at Operating Conditions

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Table C-7: Equivalent and Internal Spring Stiffness and Damping at Operating Conditions

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Table C-8: Mixed Core Deformable Grid Element Input Parameters at Operating Conditions

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Table C-9: Spacer Grid Deformations, Full Core

Table C-10: IGM Impact Forces, Full Core



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Table C-11: Spacer Grid Deformations, Mixed Core

Table C-12: IGM Impact Forces, Mixed Core



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. Deformable Spacer Grid Element Topical Report



Figure C-1: Operational Basis Earthquake Motions, X-Direction

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Figure C-2: Operational Basis Earthquake Motions, Z-Direction

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Figure C-3: Safe Shutdown Earthquake Motions, X-Direction

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Figure C-4: Safe Shutdown Earthquake Motions, 2-Direction

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Figure C-5: Accumulator Line Break Motions, X-Direction

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ANP-103.37 Revision 0


Figure C-6: Accumulator Line Break Motions, Z-Direction

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Figure C-7: Mixed Core Row Configurations

I HTP I HTP I GAIA I HTP I HTP I HTP I GAIA I HTP I HTP I 9A

HTP HTP HTP HTP HTP HTP GAIA HTP HTP HTP HTP HTP

HTP GAIA HTP HTP HTP HTP HTP HTP HTP HTP HTP GAIA

HTP HTP HTP HTP GAIA HTP HTP HTP GAIA HTP HTP HTP

HTP HTP HTP HTP GAIA HTP HTP HTP HTP HTP GAIA HTP



HTP 13(

HTP 130

HTP 13E

HTP HTP HTP lSA

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