ML16221A275

ANP-3274NP, Revision 2, Analytical Methods for Monticello ATWS-I.

ML16221A275
Person / Time
Site:	Monticello
Issue date:	07/31/2016
From:	Northern States Power Company, Minnesota, Xcel Energy
To:	Office of Nuclear Reactor Regulation
References
L-MT-16-037, TAC MF5002 ANP-3274NP, Rev 2
Download: ML16221A275 (186)

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L-MT-16-037 Enclosure 4 Enclosure 4 AREVA Report ANP-3274NP Non-Proprietary Analytical Methods for Monticello ATWS-1 Revision 2 July 2016 185 pages follow Controlled Document AREVA Inc. ANP-3274NP Revision 2 Analytical Methods for Monticello ATWS-1 July 2016 A AREVA AREVA Inc. Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 AREVA Inc. AREVA Inc. Controlled Document Analytical Methods for Monticello A TWS-1 Copyright© 2016 AREVA Inc. All Rights Reserved ANP-3274NP Revision 2 Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page i Nature of Changes Item Page Description and Justification

1. A-55, 8-3, Updated coefficients and results to correct for the issue described in CR 8-11, 8-12, 2016-4193 D-2, and Sections D.2, D.3 and D.4 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page ii Contents 1.0 Introduction

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1-1 2.0 Physical Phenomena Pertinent to ATWS-1 ....................................................................

2-1 2.1 Unstable Oscillations in General ........................................................................

2-1 2.2 Density Waves in a Boiling Channel. ..................................................................

2-2 2.2.1 Density Waves in Parallel Channel between Two Plena ......................

2-3 2.2.2 Density Wave with Power Oscillations due to Density-Reactivity Coupling ...............................................................................

2-4 2.3 Oscillation Modes -The Global Mode ................................................................

2-5 2.4 Oscillation Modes -The Regional Mode .............................................................

2-6 2.5 Oscillation Modes -The Rotational Mode ...........................................................

2-7 2.6 Oscillation Modes -Axial Power Shape ..............................................................

2-8 2.7 Large Amplitude and Limit Cycles of Global Mode Oscillations with Linearized Hydraulics ......................................................................................... 2-8

2.8 Large

Amplitude Regional Mode Oscillations with Linearized Hydraulics

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2-9 2.9 Large Amplitude Pure Thermal-Hydraulic Density Waves ...............................

2-10 2.1 O Very Large Nonlinear Oscillations of Global and Regional Types ....................

2-11 2.11 Prompt-Criticality

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2-13 2.12 Effect of Bypass Flow with Possible Boiling .....................................................

2-13 2.13 Cyclical Dryout and Rewetting

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2-14 2.13.1 Impact of Cyclical Dryout and Rewetting on Very Large Oscillations

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2-15 3.0 Phenomena Ranking ......................................................................................................

3-1 4.0 The ATWS-1 Transient Scenarios

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.4-1 4.1 ATWS-1 Analysis Methods .................................................................................

.4-1 5.0 References

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5-1 Appendix A AISHA Theory Manual for BWR Transient Analysis Including Large Oscillations

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A-1 A.1 Introduction

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A-2 A.1.1 Objective

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A-2 A.1.2 Summary of AISHA Model ................................................................................

A-2 A.2 Theory Description

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A-5 A.2.1 Major Assumptions

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A-5 A.2.2 Neutron Kinetics Model .....................................................................................

A-8 A.2.2.1 Adaptive Kinetics Theory .....................................................................

A-8 A.2.2.1.1 Derivation of Adaptive Two-Group 3-D Neutron Kinetics ...............................................................................

A-8 A.2.2.2 Numerical Solution ............................................................................

A-13 A.2.2.2.1 lnterfacial Diffusion Coefficient Approximation

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A-14 A.2.2.2.2 Steady State and Initialization

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A-17 A.2.2.2.3 Time Integration Procedure

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A-18 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page iii A.2.2.3 Cross Sections Representation

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A-21 A.2.3 Thermal-hydraulic Model .................................................................................

A-21

• A.2.3.1 [ ] ..................................... , ......................................

A-22 A.2.3.2 Vapor generation rate ........................................................*...............

A-26 A.2.3.3 Mass conservation

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A-29 A.2.3.4 Energy conservation

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A-30 A.2.3.5 [ ] .............................................................................

A-33 A.2.3.6 [ ] Momentum Conservation

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A-35 A.2.3.7 Friction Pressure Drop ......................................................................

A-40 A.2.3.8 Recirculation Loop Model. .................................................................

A-42 A.2.4 Pin Heat Conduction

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A-45 A.2.4.1 Power distribution in the pellet ..........................................................

A-53 A.2.4.2 Heat transfer coefficient

[ ] *................................

A-54 A.2.4.3 Pellet-Clad Gap Conductance

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A-56 A.2.5 Material Properties

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A-57 A.3 References

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A-58 Appendix 8 SI NANO Theory Manual for 1 D Single Channel Transient Code for Two Phase Flow with Dry out and Rewetting

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8-1 8.1 Introduction

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8-2 8.1.1 Objective

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8-2 8.1.2 Summary of SINANO Model. .............................................................................

8-2 8.2 Theory Description

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8-4 8.2.1 Major Assumptions and Model Attributes

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8-4 8.2.2 Dryout and rewetting reduced order model .......................................................

8-6 8.2.3 Thermal-Hydraulic Model Equations

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8-14 8.2.3.1 [ ] ............................................................................

8-14 8.2.3.2 Vapor generation rate ........................................................................

8-18 8.2.3.3 Mass conservation

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8-21 8.2.3.4 Energy conservation

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8-22 8.2.3.5 [ ] ............................

• • • • • • • .................................

8-25 . 8.2.4 Pin Heat Conduction

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8-27 8.2.4.1 Heater Rod Conduction Model ..........................................................

8-27 8.2.4.2 Fuel Rod Conduction Model. .............................................................

8-30 8.2.4.3 Heat transfer coefficient

[ ] .................................

8-40 8.2.4.4 [ ] ........................................................

8-41 8.2.5 Anchoring

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8-46 8.3 References

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8-48 Appendix C Steady State Dryout Correlation CPROM ........*..............................................

C-1 C.1 Description of CPROM Correlation

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C-2 C.2 Anchoring to a licensing correlation

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C-5 C.3 CPROM Correlation for ATRIUM 10XM ............................................................

C-5 C.4 CPROM Correlation for GE14 .........................................................................

C-17 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page iv Appendix D Heat Transfer Data from KATHY Loop Stability Testing of ATRIUM 10XM ................................................................................................

D-1 D.1 Summary of Heat Transfer Coefficient Data and Observations

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D-1 D.2 Heat Transfer Coefficient under Wetted Conditions

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D-2 D.3 ] .....................................

D-3 D.4 ] ...................................

D-5 AREVA Inc.

Controlled Document r Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Pagev Tables Table C-1 : Statistics

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C-9 Table C-2: Statistics

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C-10 Table C-3: Table C-4: Table C-5: Table C-6: Table C-7: Table C-8: Statistics

[ Statistics

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[ Statistics

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[ Table C-9: Statistics

[ Table C-1 O: Statistics

[ Table C-11: Statistics

[ Table C-12: Statistics

[ Table C-13: Statistics

[ Table C-14: Statistics

[ Table C-15: Statistics

[ Table C-16: Statistics

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C-26 Controlled Document Analytical Methods for Monticello ATWS-1 ANP-3274NP Revision 2 Page vi Figures Figure A-1: Fuel rod discretization

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A-48 Figure B-1: Fuel rod discretization

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B-34 Figure C-1: Calculated versus measured critical power, [ ] .......................................................................................................

C-6 Figure C-2: ] .................................

C-7 Figure C-3: ] ................................

C-7 Figure C-4: ] .....................

C-8 Figure C-5: ] ..................

C-8 Figure C-6: ] ........................................

C-9 Figure C-7: Calculated versus measured critical power, [ ] .....................................................................................................

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C-12 Figure C-9: ] ............................

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C-13 Figure C-11: ] .............

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C-14 Figure C-13: Calculated versus measured critical power, [ ] ....................

C-16 Figure C-14: ] ............................. C-18 Figure C-15: ] ...........................................

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C-24 Figure C-24: Calculated versus measured critical power, [ ] ..................

C-26 Figure D-1: Measured versus calculated heat transfer coefficients

[ ] ............................................

D-3 Figure D-2: ] ..............................

D-4 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-3: Figure D-4: [ Figure D-5: Figure D-6: Figure D-7: Figure D-8: Figure D-9: Figure D-10: Figure D-11: Figure D-12: Figure D-13: Figure D-14: [ AREVA Inc. ANP-3274NP Revision 2 Page vii ] ....................

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D-16 Controlled Document Analytical Methods for Monticello A TWS-1 Abstract ANP-3274NP Revision 2 Page viii This report presents the methodology for licensing the Extended Flow Window (EFW) operation of Monticello BWR plant with regard to Anticipated Transient without Scram with Instability (ATWS-1).

The methods aim at analyzing the fuel specific differences needed to license Monticello with AREVA fuel type ATRIUM 10XM. By the time ATRIUM 10XM is loaded in Monticello, the plant would be already licensed for extended flow window operation under GE MELLLA+ with GE14 fuel type. The comparative analysis applying the methodology described in this report covers a full core loaded with GE14, an equilibrium cycle fully loaded with ATRIUM 10XM, as well as a transition cycle of mixed GE14 and ATRIUM 10XM fuel types. The methodology presented in this report utilizes two computer codes: AISHA and SI NANO. AISHA is a detailed core model capable of simulating severe power and flow oscillations that are associated with core instabilities unsuppressed with scram. [ ] Selected bundles for which the operating conditions are the most severe under unstable oscillations will be analyzed further using the single channel code SINANO. SINANO [ ] The code applies advanced models for post-dryout heat transfer for the calculation of the cladding temperature excursion in the [ ] rod. SINANO models are based on, and benchmarked against, data obtained from Karlstein hydraulic loop where full scale electrically heated ATRIUM 10XM bundle has been tested under realistic ATWS-1 conditions of severe unstable density waves with simulated reactivity and feedback.

A full description of the codes AISHA and SI NANO is given in Appendices A and B, respectively.

AREVA Inc.

Controlled Document Analytical Methods for Monticello ATWS-1 ANP-3274NP Revision 2 Page 1-1 1.0 Introduction This document presents a description of the BWR instability transients that are not terminated by scram, and thus power and flow oscillations are allowed to grow to large amplitudes (see References 1 and 2). This class of transients is the Anticipated Transients Without Scram with Instability (ATWS-1).

This report aims at identifying and ranking the importance of the physical phenomena and operating parameters that influence the inception of such instabilities and determine their magnitude.

Of special importance is the resulting possible degradation of heat transfer that may combine with high power generation in fuel rods to induce clad temperature excursions with the potential to challenge the limits of fuel coolability.

The presentation of the phenomena is divided in two parts: (1) the phenomena affecting the inception and growth and ultimate amplitude of density wave oscillations, and (2) the phenomena responsible for the possible degradation of heat transfer and influence the clad temperature excursion and its peak temperature.

For a coherent presentation of the instability phenomena, a gradual approach has been adopted. The presentation starts with density wave stability in a vertical boiling channel, inception of instability with small amplitude oscillations, then introduce the effect of power modulation due to reactivity feedback.

The density wave oscillations with reactivity feedback will be divided according to the neutron flux harmonic that is excited, and accordingly the global mode and regional mode oscillations are discussed.

The role of the [ ] is also discussed.

After the presentation of the phenomena associated with the reactivity-coupled density wave oscillation of small magnitude, the range of parameters will be expanded into the nonlinear regimes where the oscillation magnitude of the various state variables describing the dynamics of the thermal-hydraulic oscillations is allowed to grow without suppression by scram. [ AREVA Inc. l

Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 1-2 The phenomena responsible for the degradation of the heat transfer will be presented to cover the flow conditions associated with the [ ] density wave oscillations.

The presentation of the degradation of heat transfer will be coupled to unique experimental data where the phenomena of cyclical dryout and rewetting and possible failure to rewet were measured in a full-scale electrically heated BWR mockup. Following the presentation of the phenomena, a tabulated ranking is provided.

AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 2.0 Physical Phenomena Pertinent to A TWS-1 ANP-3274NP Revision 2 Page 2-1 In this section, a review of the basic physical phenomena is presented.

These can be divided into the phenomena leading to power and flow oscillations, and the dryout phenomena under these oscillatory conditions.

[ ] 2.1 Unstable Oscillations in General A feedback system is unconditionally unstable in the case of positive feedback, i.e., a perturbation in a system parameter results in enforcing the perturbation.

This kind of divergence is not oscillatory.

In systems with negative feedback, i.e., a perturbation in a system parameter results in reducing the perturbation may or may not be stable depending on other system characteristics.

Immediate negative feedback makes the system unconditionally stable. On the other hand, delayed negative feedback may render the system unstable if the magnitude of the feedback is sufficiently large. In the case of strong delayed negative feedback, the corrective effect of the feedback overshoots the original perturbation and the system undergoes oscillations of exponentially increasing magnitude.

This type of oscillation is possible in BWRs. The simple description of the feedback effects outlined above applies to linear systems, or nonlinear systems that behave as a linear system when the oscillation magnitude is sufficiently small. As the oscillation magnitude grows, the magnitude of the feedback is no longer proportional to the original perturbation due to the nonlinear effects. The nonlinear effects can be stabilizing, and in this case an initially exponentially growing oscillation will grow at a slower rate as the oscillation magnitude increases, and finally reach a stable limit cycle. Nonlinear effects may also act in the opposite direction, and an initially exponentially growing oscillation will accelerate its growth rate further as the oscillation magnitude increases.

Normally in a complex nonlinear system, like a BWR, there are regions of different nonlinear effects. [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 2.2 Density Waves in a Boiling Channel ANP-3274NP Revision 2 Page 2-2 The mechanism capable of inducing a strong and delayed negative feedback in a boiling channel is the propagation of density waves (See Reference 3 for a comprehensive review). The kinematic description of density waves can be best described in the idealized boiling channel where the rate and axial distribution of the heat source remain invariant, and the pressure drop between the inlet and exit of the channel is kept constant.

A perturbation of the inlet mass flow rate travels up the channel and its magnitude changes and phase lag increases.

The mass flow rate wave generates a corresponding change in the steam quality and void fraction and equivalently the mixture density. The single-phase and two-phase friction components will also respond to the perturbation in the mass flow rate and the resulting steam quality response.

In a slow (quasi-steady state) perturbation, the net resulting feedback is negative, that is for a positive inlet mass flow perturbation, the average void fraction decreases lowering the density head that drives the flow and the frictional pressure drop will increase forcing the restoration of the original inlet mass flow. The inlet flow perturbation can take any functional form, which can be linearly decomposed into sinusoidal waves of different magnitudes and frequencies.

The variation in density results in gravitational head change, while the mass flux variation results in friction variations.

The net pressure drop variation across the channel due to the gravitational and frictional components must be compensated for by flow acceleration in order to satisfy the constant channel pressure drop boundary condition.

The feedback strength is maximal for an inlet flow perturbation with a frequency comparable to the inverse of the delay time, and if the magnitude of the feedback is sufficiently strong, the channel hydraulic parameters will oscillate at that preferred frequency with an increasing magnitude.

The hydraulic stability of the density waves depends on the strength of the feedback processes.

The quantitative parameter for measuring the degree of stability is the decay ratio defined as the oscillation magnitude at a given cycle relative to the previous cycle's magnitude.

Under typical BWR conditions, the decay ratio is increased (less stable) with the following system variables:

• High power to flow ratio: This increases the density contrast along the channel (and hence the gravity head) which drives the instability.

• Low flow: In addition to being the denominator in the power-to-flow ratio, low flow is destabilizing because it decreases the preferred frequency (because lower flow speed reduces bubble transit time) and thus reduces the axial attenuation of the mass flux and void fraction.

AREVA Inc.

Controlled Document Analytical Methods for Monticello ATWS-1 ANP-3274NP Revision 2 Page 2-3

• Bottom-skewed power peaking: This power shape results in creating the bubbles at lower elevations which remain for a longer time, thus increasing the average density contrast and thus is destabilizing.

• Low system pressure:

Low system pressure is destabilizing as the difference in saturated liquid and vapor densities increases which drives the gravitational component, hence a destabilizing effect. . [ 1

• High inlet subcooling:

The inlet subcooling does not have a monotonic effect on stability, as very high and very low inlet subcooling are both stabilizing.

Sufficiently very high inlet subcooling prevents boiling and suppresses density response by preventing phase change. Reducing inlet subcooling to allow boiling, while remaining sufficiently high such that the boiling boundary is high, the two-phase-to-single-phase pressure drop ratio is low and the system remains stable. [ 1 The discussion of the hydraulic density waves, idealized under constant pressure drop and constant rate of heating, remained in the linear small amplitude regime. The large oscillation amplitude effects will be discussed separately.

2.2.1 Density

Waves in Parallel Channel between Two Plena In describing the idealized density wave instability a constant channel pressure drop was imposed as a boundary condition, which can be assured using a recirculation loop much larger than the boiling channel. In the case the recirculation loop is not so large the oscillating flow will result in pressure drop boundary changes which are stabilizing.

Two identical boiling channels AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 2-4 connected in parallel to the same recirculation plena will be coupled only if the recirculation loop is finite and the common pressure drop responds to the net flow change in the two boiling channels.

The coupling results in the two channels oscillating out-of-phase (180 degrees phase shift) such that the pressure drop boundary fluctuation is minimized.

For three identical boiling channels connected in parallel to the same plena, the coupling forced by the recirculation loop will result in the channels oscillating 120 degrees apart. However, for four channels, there are two possibilities, either the four channels will oscillate 90 degrees apart, or two channels will oscillate in-phase with each other and out-of-phase with the other two channels.

The situation can become very complicated when hundreds of channels are connected to the same plena. In real situations, the channels are not identical and therefore have natural frequencies that are not identical, and their respective degrees of stability are also different.

Coherent oscillations where many channels share the frequency and phase depend on the coupling mechanism of the neutron flux in addition to the recirculation loop. Yet, hydraulically unstable channels if sufficiently destabilized may break away and oscillate independently from other channels and experience a superposition of multiple oscillation modes. 2.2.2 Density Wave with Power Oscillations due to Density-Reactivity Coupling The propagation of the density wave along the boiling channel results in an oscillation of the bundle average coolant density (equivalently void fraction).

The change in void fraction changes the neutron absorption and fission cross sections and produces a neutron reactivity response.

The reactivity oscillation in turn produces a fission power response.

There are two components of the power response, the first is the fission power deposited in the U0 2 pellets, and the second is the power deposited directly in the coolant as gamma radiation and neutron moderation.

The direct energy response is practically immediate, i.e. in-phase, with the original density change and results in an opposing effect on coolant density, i.e. negative feedback.

The phase negative feedback of the direct energy deposition in response to density change has a stabilizing effect on the density wave. The fission energy deposition is eventually transported to the coolant via heat conduction through the fuel rod. The dynamics of the transport of heat through the fuel rod to the coolant are governed by the heat capacity and the various thermal resistance components between the pellet interior and the coolant. These thermal resistances include the U02 pellet, the Zircaloy AREVA Inc.

ControUed Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 2-5 clad wall, the gap between pellets and clad, and the coolant contact with the outer clad wail. The result of the thermal resistance and heat capacity inertia is a delay of the heat transport to the coolant, i.e. phase lag, of slightly less than 90 degrees. It also accounts for considerable attenuation of the heat source to the coolant. The attenuation of the heat flux amplitude relative to the fission power oscillation amplitude is of the order of 10-1 and increases with increasing the conduction time constant, which in turn increases with increasing the fuel rod diameter and increasing pellet-gap resistance.

Unlike the direct energy deposition in the coolant, the time lag of the coolant heating response through clad wall heat flux relative to the perturbation of the fission power deposition in the pellet results in destabilizing the density wave. The void reactivity-to-power feedback not only provides the coupling needed for the different channels to oscillate coherently, but also has a destabilizing effect that makes it possible for the system to be unstable even when every channel in it is individually stable hydraulically.

The coherence is broken if a single channel becomes hydraulically unstable and the flow in that channel will reflect a superposition of its intrinsic instability and the driven component via the oscillating power. Unstable single channel oscillations have been observed in unusual situations, for instance when a BWR bundle is not properly seated and deprived of flow (as occurred in Forsmark-I and Brunsbuttel Reference 9). Single channel instability also occurred in Garigliano during a special test (Reference 3). Aside from these unusual situations, single channel instabilities have been predicted and special effort has been made to exclude the possibility of their occurrence in the approved AREVA methodology for DIVOM calculations (Reference 6). 2.3 Oscillation Modes -The Global Mode As mentioned earlier, several boiling channels connected in parallel to two plena may not oscillate coherently absent a mechanism for coupling the density waves among the individual channels.

In the case of a BWR core, the density-reactivity feedback provides the required coupling.

The neutron flux in the core responds to reactivity changes anywhere in the core due to neutron diffusion.

Thus the reactivity change in one channel results in a corresponding power change not only in that channel but to all other channels -with varying strength.

The oscillation mode where the power in every channel oscillates coherently, and in-phase with the power in all other channels, is called the global mode. The inlet mass flow in all the channels oscillate similarly, in-phase, and with the same frequency.

As the inlet mass flow rate AREVA Inc.

Controlled Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 2-6 in all channels is in-phase, the total core inlet mass flow rate must also oscillate, and similarly for the core exit mass flow rate. The core pressure drop (between the upper and lower plena) must also oscillate.

Accordingly, the recirculation loop flow must interact with the core flow, and its dynamics must be considered in the analysis of the global mode osciilations.

Generally, the friction and inertia of the recirculation loop exert a stabilizing influence on the global mode, and the extent of this stabilizing effect depends mostly on the dynamics of the steam separator assembly.

In a BWR core oscillating in-phase the fundamental mode of the neutron flux distribution function is excited. The excitation of all the other planar harmonics is not needed for the global

• mode. The axial flux harmonics must be driven as a result of the density waves causing the observed phase lag between neutron detector responses of the upper core elevation relative to lower elevation.

[ ] 2.4 Oscillation Modes -The Regional Mode The regional mode is characterized with half the core bundles oscillating out-of-phase with the other half. The two core halves are separated by a vertical plane, which is also called the neutral line when a planar projection is considered.

The net core flow remains unchanged during the regional oscillation provided its magnitude is not so large as to introduce nonlinear effects that do not cancel out. The main reason the hydraulic channels prefer to oscillate out-of-phase is the cancellation of the recirculation loop damping. The regional mode oscillation in a BWR is forced to be coherent with half the core bundles oscillating in-phase and the other half oscillating with a 180 degree shift due to neutronics coupling.

The half-core oscillation is preferred because it excites the first azimuthal neutron flux mode and thus receives the highest possible amplification.

The other AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 2-7 flux harmonics that can be excited by other channel groupings are characterized by large subcritical reactivities, and therefore are significantly damped. It is important to notice that the decay ratios of the regional and global modes are comparable.

The regional mode is preferred for

• Large cores, which result in small eigenvalue separation for the first azimuthal flux mode.

• Low center power peaking (ring of fire), which also decreases the eigenvalue separation.

• Loose inlet orifice, which destabilize the hydraulic channels.

This effect favors the regional mode in the absence of recirculation loop damping. It must be emphasized that the regional oscillations are isolated, and thus independent from the recirculation loop. 2.5 Oscillation Modes -The Rotational Mode In the regional oscillations described above, the neutral symmetry line is stationary.

The rotational mode is similar to the regional mode where the neutral line is oscillating or rotating (See Reference 15). The rotational mode essentially results from the simultaneous excitation of two orthogonal azimuthal modes. Assuming the core loading and control rod patterns are symmetric, the first two azimuthal modes are degenerate (approximately equal eigenvalues), and are thus indistinguishable.

In the case the stability threshold is crossed with a decay ratio slightly greater than unity, and the core symmetry is not exact, it is expected that only one first azimuthal flux harmonic is excited leading to a regional mode oscillation with fixed neutral line. In the case the core is destabilized further, the orthogonal azimuthal mode is excited next, and interference patterns emerge depending on the relative amplitude and frequency differences between the two modes. The neutral line may oscillate or rotate slowly in response to unequal magnitude and frequency of the two excited azimuthal modes. The most interesting case is when the two azimuthal modes are degenerate and oscillate with the same frequency and amplitude, which leads to the neutral line rotating at the same frequency.

[ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 2.6 Oscillation Modes -Axial Power Shape ANP-3274NP Revision 2 Page2-8 As the density wave propagates upward, not only the total reactivity oscillates, but also the axial reactivity distribution is altered where oscillating reactivity difference between the upper and the lower parts of the core is created. As a result, the axial neutron flux harmonic is driven by density waves. The effect of the axial power shape oscillation on the decay ratio is rather minimal but it is noticeable as the cause of the phase lag of the upper LPRM power signal relative to the power signal from the lower LPRM on the same string. The axial mode excitation is significant when the global or regional/rotational oscillation

' amplitude is large and large axial power shape changes are expected during the oscillations.

[ ] 2.7 Large Amplitude and Limit Cycles of Global Mode Oscillations with Linearized Hydraulics As the oscillation magnitude increases, the nonlinear effects are introduced (Reference 4). The neutron kinetics nonlinear effects become significant before the hydraulic nonlinear effects. This is the case because the reactivity oscillations required to induce large neutron flux response can be produced by relatively small coolant mass flow oscillation magnitude.

In the idealized case of assumed linear thermal-hydraulics, with only the nonlinear effects of reactivity on the power response being allowed, a stabilizing effect has been observed which eventually leads to saturating the growth of the oscillation until a stable limit cycle is reached. The nonlinear stabilizing effect originates in the negative reactivity shift that is produced in response to the average power increases, the latter is due to the oscillating reactivity where the increase in reactivity during half a cycle increases power more than compensated for by an equal reactivity decrease in the subsequent half cycle. This asymmetric power response to reactivity oscillation is also responsible for generating high and sharp power peaks compared with the flat power minima. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 2-9 The power drift under oscillatory reactivity results in an average power increase that is balanced by the negative reactivity due to the increased average void fraction.

[ l 2.8 Large Amplitude Regional Mode Oscillations with Linearized Hydraulics The power oscillation magnitude considered here is sufficiently large for the nonlinear neutron kinetics effects to manifest, but not high enough for the nonlinear effects of the hydraulics to become important.

The regional oscillation of large amplitude differs in basic ways from a global oscillation (Reference 5). Most importantly, is no reactivity bias associated with the first azimuthal harmonic excitation and growth, unlike the fundamental flux excitation and growth in the global mode oscillation.

The only negative reactivity that reduces the first azimuthal mode growth is the subcriticality associated with its steady state eigenvalue being less than unity, and this subcriticality is not affected by the oscillation magnitude and therefore not a nonlinear effect. The main nonlinear effect of the growth of the first azimuthal mode is the emergence of a driven fundamental mode oscillation component with relative magnitude proportional to the square of the first harmonic magnitude and at double its frequency (see References 10 and 11). The double frequency fundamental mode will grow until it becomes equal to the first harmonic in magnitude.

A negative reactivity shift is generated, [ For growing regional oscillations, unlike the global mode, the nonlinear effects accelerate the rate of growth, and the oscillation magnitude is not self-limited (Reference 5). The eventual arrest of the regional mode oscillation growth is due to [ l ] This is one reason why large amplitude regional oscillations are of special interest and can be considered limiting compared with the nonlinearly self-limiting global oscillations.

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Control!ed Document Analytical Methods for Monticello A TWS-1 2.9 Large Amplitude Pure Thermal-Hydraulic Density Waves ANP-3274NP Revision 2 Page 2-10 Flow in a boiling channel includes highly nonlinear processes.

For example, the frictional pressure drop is approximately proportional to the square of the flow rate, and the void fraction dependence on the steam quality is also nonlinear.

When unstable density waves in a boiling channel, without neutron kinetic feedback, are allowed to grow the oscillation magnitude may reach a limit cycle [ ] Detailed numerical models are needed to simulate the behavior of a boiling channel as an integral system whereas purely analytical models are of limited use for understanding the effects of various phenomena particularly for large amplitude oscillations.

However, it is still possible to discern the role of these phenomena by observing the behavior of oscillating channels in test loops, and in simulations, and guided by knowledge of the fundamentals of flow dynamics.

Using these tools, a qualitative description of the nonlinear effects and their influence on density wave oscillations growth is offered here. [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 [ ] The main nonlinearly destabilizing effect originates from the [ ] [ ANP-3274NP Revision 2 Page 2-11 ] The maximum oscillation amplitude at the channel inlet is negative, where the reverse flow magnitude

[ ] The inlet flow oscillation has broad peaks and sharp minima signifying the nonlinear processes involved in the generation of these high amplitude oscillations.

2.10 Very Large Nonlinear Oscillations of Global and Regional Types For small amplitude oscillations, the system behavior is linear and the principle of superposition is applicable.

Accordingly, all the possible unstable modes will be manifested without coupling to each other, for example in the case the decay ratios of the global and regional modes are comparable and greater than unity, both types of instabilities will be excited and the. resultant oscillations will reflect a superposition mix. This is not the case for large oscillations where nonlinear effects are significant.

[ ] AREVA Inc.

Controiied Document Analytical Methods for Monticello A TWS-1 [ ANP-3274NP Revision 2 Page 2-12 ] An exception for this behavior is the case of two regional modes representing the excitation of a first azimuthal flux harmonic and a nearly degenerate mode where the corresponding neutral lines are orthogonal.

The nonlinear effects of the growth of one of these modes will impact both modes, and simultaneous growth of the two modes would lead to oscillating or rotating neutral line, i.e. the mixed mode oscillation of the rotational type is not discouraged by nonlinear effects. [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 2.11 Prompt-Criticality ANP-3274NP Revision 2 Page 2-13 The very large power oscillations result from very large reactivity oscillations due to the severe flow oscillations.

It is important to consider that reactivities in excess of the delayed neutron contribution may occur, i.e. prompt-super-criticality.

The possibility of prompt-super-criticality requires the neutron kinetics models to be able to handle it properly with finite neutron velocity and Doppler reactivity feedback.

However, from theoretical analysis (see References 4 and 5) and experience with numerical calculations (Reference 2), it has, been found that criticality may be expected only under unrealistically rapid rate of oscillation growth, before the system has time to respond by increasing the average power and shift the average reactivity to a large negative value. Even in this case, the prompt criticality is exceeded by only a few cents, not dollars like the reactivity insertion accidents.

No qualitatively distinct power pulses result from small super-prompt-critical reactivity.

[ ] 2.12 Effect of Bypass Flow with Possible Boiling Boiling is possible in the upper part of the core bypass at natural circulation under relatively high power (Reference 12). This effect is modeled in steady state simulators which provide the initial conditions and neutron cross sections to the transient codes used in this application.

The main effect of the bypass boiling is a shift of the axial power shape to more bottom-peaking.

The important question here is the transient response of the bypass, with or without boiling, in the presence of large regional mode oscillations.

Under regional oscillations, the core pressure drop remains nearly invariant as the effects of flow in the two halves of the core oscillating out-of-phase tend to cancel out. [ ] AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 [ ] 2.13 Cyclical Dryout and Rewetting ANP-3274NP Revision 2 Page 2-14 Large oscillations of flow and power in a BWR bundle can result in conditions of degraded heat transfer and clad temperature excursions beyond the safe limits designated to maintain fuel coolability.

In the steady state operation, the conditions of heat transfer degradation are associated with the inception of dryout. Dryout correlations based on critical heat flux or critical quality concepts are used to obtain the critical power ratio, which provide quantitative measure of allowable bundle power and define the safety margins to protect that limit. Quasi-steady state application of the dryout correlations has been the basis for protecting the fuel against dryout. Steady state dryout correlations were extended for applications to DIVOM oscillatory transients (Reference 6), which are rather mild, compared with power and flow oscillations accompanying anticipated transient without scram. [ ] With the detailed accounting of the phenomena governing the cyclical dryout and rewetting, the limiting consideration for fuel safety is shifted from dryout inception to failure to rewet. Accordingly, cyclical dryout and rewetting is not considered a threat to fuel integrity as long as clad high temperature excursion does not occur. [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 [ ] ANP-3274NP Revision 2 Page 2-15 A detailed [ ] model for cyclical dryout and rewetting with possible failure to rewet [ ] 2.13.1 Impact of Cyclical Drvout and Rewetting on Very Large Oscillations The phenomena of large density wave oscillations and cyclical dryout are interlinked.

The previous section addresses the cyclical dryout and rewetting, with possible failure to rewet, [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 [ AREVA Inc. ANP-3274NP Revision 2 Page 2-16 ]

Controlled Document Analytical Methods for Monticello A TWS-1 3.0 Phenomena Ranking ANP-3274NP Revision 2 Page 3-1 The development of very large power and flow oscillations follows a progressive path from the initial inception of instability, exponential oscillation growth from noise level to mild amplitudes, and further growth to large amplitudes that can be prevented from further growth by nonlinear effects. Intuitively, the phenomena and parameters participating in all the stages of the evolution of the transient from inception to maximum oscillation amplitude are ranked such that any important phenomenon at any stage remains important for the ultimate maximum oscillation event under consideration.

[ ] The phenomena considered in this section pertain to the core and fuel behavior.

[ ] The following tabulation and ranking of parameters and phenomena related to large unstable oscillations draws on considerable experience in all aspects of BWR stability.

These include frequency-and time-domain simulation and hydraulic loop testing and events and tests in power plants. No phenomena were identified as both important and not adequately understood.

All relevant phenomena are included in the applicable models for large oscillations.

The ranking of a parameter or phenomenon is entered for three independent categories.

The first category is ranking a parameter's importance for stability (and inception of oscillations).

The seconq category is for determining the possibility and magnitude of very large oscillations.

The third category is the parameter's impact on characterizing post-dryout behavior and the severity of fuel rod temperature excursions in response to large oscillations.

The knowledge and importance levels are entered on a scale from 1 to 4 where 4 is the highest. Importance of zero is entered when a parameter is inactive or does not apply. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 3-2 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 3-3 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 3-4 Controlled Document Analytical Methods for Monticello A TWS-1 4.0 The A TWS-1 Transient Scenarios ANP-3274NP Revision 2 Page 4-1 Several scenarios have been identified where both recirculation pumps trip and the core state transitions to natural circulation at relatively high power. Unstable power and flow oscillations ensue and grow without possibility of scram. In the case the first instigating event is a turbine trip, then both recirculation pumps would also automatically trip (due to an ATWS high reactor pressure signal), the turbine is isolated and the turbine bypass valve opens. With the turbine isolated, the extraction steam feeding the feedwater heaters stops. With the loss of feedwater heating, the core inlet subcooling gradually increases and significantly destabilizes the core. [ l 4.1 A TWS-1 Analysis Methods [ ] The thermal-hydraulic representation applies the maximum detail of one fuel bundle per flow channel. The neutron kinetics is modeled in 3-D with the same number of nodes as the steady state simulator MICROBURN-82.

The dryout and post-dryout response [ ] the code SINANO. SINANO calculates a single bundle thermal-hydraulic response using [ ] The clad temperature excursion of the hot rod is the basis for evaluating the ATWS-1 transient consequences.

AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page4-2 It should be noted that the bundle selection for SI NANO analysis is made conservatively.

Bundles with the highest power, highest power oscillation amplitude, and highest flow oscillation amplitude, are selected.

Conservative adjustments are be applied to [ ] Detailed description of the AISHA code is given in Appendix A. Detailed description of the SI NANO code is given in Appendix B. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 5.0 References ANP-3274NP Revision 2 Page 5-1 1. "ATWS Rule Issues Relative to BWR Core Thermal-Hydraulic Stability," NED0-32047-A, Class I June 1995. 2. W. Wulff et al., "BWR Stability Analysis with the BNL Engineering Plant Analyzer," NUREG/CR-5816, BNL/NUREG-52312, October 1992. 3. J. March-Leuba, "Density-Wave Instabilities in Boiling Water Reactors," NUREG/CR-6003, ORNL/TM-12130, September 1992. 4. Y. M. Farawila and D. W. Pruitt, "A Study of Nonlinear Oscillation and Limit Cycles in Boiling Water Reactors -1: The Global Mode," Nuclear Science and Engineering:

154, 302-315 (2006). 5. Y. M. Farawila and D. W. Pruitt, "A Study of Nonlinear Oscillation and Limit Cycles in Boiling Water Reactors -II: The Regional Mode," Nuclear Science and Engineering:

154, 316-327 (2006). . 6. BAW-10255(P)(A)

Rev. 2, "Cycle-Specific DIVOM Methodology Using the RAMONA5-FA Code," AREVA NP Inc., May 2008. 7. Hiroyasu MOCHIZUKI, "Density Wave Oscillations Beyond Dryout under Forced Circulation," Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 38, No. 1, p. 76-84 (January 2001). 8. W. Wulff, "Simulation of Two-Phase Flow in Complex Systems," Nuclear Technology Vol. 159, September 2007. 9. Carsten Lange et al., "Comments on local power oscillation phenomenon at BWRs," Progress in Nuclear Energy 60 (2012) 73-88. 10. Y. M. Fa*rawila, "Application of Modal Neutron Kinetics to Boiling Water Reactor Oscillation Problems," Nuclear Science and Engineering:

129, 261 (1998). 11. Hideaki IKEDA et al., "Nonlinear Behavior under Regional Neutron Flux Oscillations in BWR Cores," J. Nuclear Science and Technology, Vol. 38, No. 5, p. 312-323 (May 2001). 12. D. W. Pruitt, D. R. Tinkler, and Y. M. Farawila, "Considerations for Bypass Boiling during BWR Power Oscillations," Trans. Am. Nucl. Soc., Vol. 99, pp. 739-740 (Nov. 2008). 13. D. W. Pruitt, K. R. Greene, F. Wehle, R. Velten, J. Kronenberg, A. Beisiegel, and Y. M. Farawila, "Stability and Void Fraction Measurements for the ATRIUM 10XM BWR Fuel Bundle," Proceedings of 2010 LWR Fuel Performance Top Fuel WRFPM, Orlando, Florida, Sept. 26-29, 2010. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page 5-2 14. F. Wehle, R. Velten, J. Kronenberg, A. Beisiegel, D. Pruitt, K. Greene, and Y. Farawila, "Full Scale Stability and Void Fraction Measurements for the ATRIUM 10XM BWR Fuel Bundle," 2011 Jahrestagung Kerntechnik, Berlin, Germany, May 17-19 2011. 15. A. Wysocki, J. March-Leuba, T. Downar, and A. Manera, "TRACE/PARCS Analysis of of-Phase Power Oscillations With a Rotating Line of Symmetry," The 15th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, NURETH-15, paper 457, Pisa, Italy, May 12-17, 2013. AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 Appendix A AISHA Theory Manual for BWR Transient Analysis Including Large Oscillations Abstract ANP-3274NP Revision 2 PageA-1 AISHA is a computer program for calculating BWR transients which is especially optimized for simulating large power and flow oscillations associated with anticipated transients without scram with instabilities (ATWS-1).

The optimized order model of AISHA is a selective mix of the full BWR system code RAMONA5-FA, the reduced order model in the original AISHA-10 code (a two-channel single use code), and the [ ] code SINANO. Additional features not present in the parent codes, RAMONA5-FA, AISHA-10, and SINANO, are included in the present model. [ ] Details of the model and comments on its order optimization are presented.

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Document Analytical Methods for Monticello A TWS-1 A.1 Introduction A.1.1 Objective ANP-3274NP Revision 2 PageA-2 The objective of this work is to develop an optimized order BWR transient code capable of simulating the large amplitude power and flow oscillations associated with anticipated transients without scram with instabilities (ATWS-1) (Reference A.1 ). The model is required to have the ability to account for the phenomena relevant to large oscillations which result in extreme conditions such as large inlet flow reversal and complete dryout with steam superheating and the possibility of large reactivity insertion resulting in large power shape transients with large amplitude power peaks. [ 1 A.1.2 Summary of AISHA Model The optimized order model AISHA is constructed from a selective mix of models from three parent codes. These parent codes are RAMONAS-FA (Reference A.2), AISHA-10 (Reference A.7), and SINANO. [ ] The optimized model aims at achieving the best possible fidelity and efficiency in modeling BWR anticipated transients without scram accompanied with very large unstable power and flow oscillations.

The main features of AISHA are described below.

• The fluid flow thermal-hydraulics is [ 1 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 3. [ 1 ANP-3274NP Revision 2 PageA-3

• The geometry and pressure drop components in each channel follow the same model as in RAMONA5-FA.

Axial variations of flow area and hydraulic diameter are accounted for to accurately simulate bundles with part-length fuel rods. Nodalization into [ 1 . [ ] fuel pin conduction is [ ] in equal-area shells in the fuel pellet and one or more shells in the cladding wall with azimuthal symmetry.

The thermal resistance of the pellet-clad gap is represented

[ 1

• The neutron kinetics model is a [ which is taken from RAMONA5-FA.

[ ] The cross section coupling to MICROBURN-82 is the same as in RAMONA5-FA.

[ 1 ] model,

• The closing relations and correlations are taken from RAMONA5-FA unless otherwise stated. 1. [ 1 AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 3. [ ANP-3274NP Revision 2 PageA-4 1

• Water thermodynamic and transport properties are taken from the most up-to-date AREVA package based on the IF97 formulations.

[ 1

• The core channels are coupled through 1. Common pressure drop 2. Neutron kinetics

• The recirculation loop is represented by

[ 1

• The model components are tightly coupled as time integration is performed

[ 1

• The input to AISHA is mostly automatic via coupling to MICROBURN-B2.

• The main output of AISHA [ 1 AREVA Inc.

Controlled Document Analytical Methods for Monticello ATWS-1 [ ] A.2 Theory Description ANP-3274NP Revision 2 PageA-5 Detailed description of the theory is given in this section. First, the major assumptions are listed and discussed.

Description of the various components of the model, the neutron kinetics, the fluid flow, pin heat conduction and heat transfer to the fluid, is given in separate subsections.

Notice that the nomenclature is defined in each subsection as the model description is presented and the meaning of symbols may differ within each model. For example, prefers to reactivity in the description of the neutron kinetics, while the same symbol is used for density in the fluid flow model. Model description is brought to the level of discretized formulation, with the aid of governing differential equations

[ ] A.2.1 Major Assumptions Assumptions are necessary measures and approximations needed to create any practical analytical or numerical tool such as done in this work. The listing of the key or major assumptions is desirable, at least in part, to put the accuracy and expectations of the model performance in the right perspective, enlighten the user as to the application limitations, and point to areas of future improvements.

The identification and justification of assumptions is often an exercise of engineering common sense more than a quantitative analysis with objective metrics. Fortunately in this particular case, the AISHA model and code are based on a solid foundation of practice and experience with codes of similar nature, [ ] The assumptions which represent simplifications or AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 improvements or any deviation of significance from the experience base [ will be listed and discussed.

Complementing assumptions in models [ ANP-3274NP Revision 2 PageA-6 l ] will be also discussed depending on their particular significance to the correspondence between the particular model/assumption and the important A TWS-1 phenomena which is the key application of the code. The key assumptions are listed below along with the consequences and justification thereof. 1. The neutron kinetics representation using [ l AREVA Inc.

Controlled Document Analytical Methods for Monticello ATWS-1 [ AREVA Inc. ] ANP-3274NP Revision 2 Page A-7 Controlled Document Analytical Methods for Monticello A TWS-1 A.2.2 Neutron Kinetics Model [ ] A.2.2.1 Adaptive Kinetics Theory A.2.2.1.1 Derivation of Adaptive Two-Group 3-D Neutron Kinetics ANP-3274NP Revision 2 PageA-8 The two-group neutron diffusion equations in the steady state simulator MICROBURN-82 are: where 1 -V * ( D 1 (r )Vl¥1 (r )) + L 1 (r)ll'1 (r) =-(vL 11 (r )l¥1 (r) + VL 12 (r)l¥2 (r)) ko -V * (D 2 (r )Vl¥2 (r )) + L 02 (r )l¥2 (r) = L 12 (r )l¥1 (r) D 1 Fast group diffusion coefficient AREVA Inc. (A-1) (A-2)

Contro!ied Document Analytical Methods for Monticello A TWS-1 D 2 Thermal group diffusion coefficient k 0 Effective multiplication factor (eigenvalue) r Space vector L 1 Fast neutron removal cross section (by absorption and slowing down) Laz Thermal neutron absorption cross section L 12 Slowing down cross section VL 11 Fast fission neutron production cross section VL 12

• Thermal fission neutron production cross section \f 1 Fast flux steady state distribution

\f 2 Thermal flux steady state distribution The transient form is given by 1 N k ( VL 11 ( r,t)<I\ ( r,t) + VL 12 ( r,t)2 ( r,t)) + L An ( r,t) en ( r,t) 0 ANP-3274NP Revision 2 PageA-9 (A-3) (A-4) ae n ( r' t) /Jn ( r' t) ( ( ) ( ) ( ) ( ) ) ( ) ( )

dt = k VL11 r,t r r,t +VL12 r,t 2 r,t -An r,t en r,t ' n=l,-**,N (A-5) where t N AREVA Inc. 0 Time Fast neutron velocity Thermal neutron velocity Total number of delayed neutron energy groups

Document Analytical Methods for Monticello A TWS-1 Delayed neutron fraction in the group n Decay constant for the delayed neutron precursor of the group n Concentration of the delayed neutron precursor of the group n <l>l Time-and space-dependent fast flux distribution Time-and space-dependent thermal flux distribution The total delayed neutron fraction is the sum of the group-wise fractions, thus N /J(r,t)= LfJn(r,t) n=I ANP-3274NP Revision 2 PageA-10 (A-6) The fast removal cross section is the sum of absorption and slowing down components, thus L 1 (r,t) = L 01 ( r,t) + L 12 (r,t) (A-7) where Fast absorption cross section Notice that the eigenvalue k 0 is retained to maintain consistency with the steady state cross sections and force the initial condition to exact criticality.

[ ] AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page A-11 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-12 Controiied Document Analytical Methods for Monticello A TWS-1 and A.2.2.2 Numerical Solution ANP-3274NP Revision 2 Page A-13 The cross sections and fluxes are defined on the same 3-D mesh as MICROBURN-82.

The x-coordinate is associated with the index i, the y-coordinate with j , and the vertical z-coordinate with k. For example '¥ ( r) = '¥ ( x,y,z) = '¥;,;,k AREVA Inc.

Controiied Document Analytical Methods for Monticello A TWS-1 A.2.2.2.1 lnterfacial Diffusion Coefficient Approximation AREVA Inc. ANP-3274NP Revision 2 Page A-14 Controlled Document Analytical Methods for Monticello A TWS-1 which leads to AREVA Inc. ANP-3274NP Revision 2 PageA-15

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-16

Document Analytical Methods for Monticello A TWS-1 and: A.2.2.2.2 Steady State and Initialization AREVA Inc. ANP-3274NP Revision 2 PageA-17 Controlled Document Analytical Methods for Monticello ATWS-1 [ A.2.2.2.3 Time Integration Procedure AREVA Inc. ANP-3274NP Revision 2 Page A-18 J Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-19

Document Analytical Methods for Monticello A TWS-1 Using to simplify Equation (A-59), we get AREVA Inc. ANP-3274NP Revision 2 PageA-20 Controlled Document Analytical Methods for Monticello ATWS-1 ANP-3274NP Revision 2 Page A-21 Equations (A-63), (A-64), and (A-65) constitute a complete set which is programmed in the [ ] module. A.2.2.3Cross Sections Representation The cross section input is automated through coupling to MICROBURN-82.

[ ] A.2.3 Thermal-hydraulic Model The thermal-hydraulic balance equations are written for two-phase one-dimensional flow. The channel is divided into N nodes, which are control volumes [ ] The flow area and hydraulic diameter for each node is allowed to vary in order to account for specific bundle design features such as part-length fuel rods. [ ] AREVA Inc.

Controlied Document Analytical Methods for Monticello A TWS-1 [ ] In the following sections, the transient

[ ANP-3274NP Revision 2 PageA-22 ] These equations are written directly for control volumes which directly correspond to the as programmed model. The control volume formulation is straightforward, and there is no need to follow the customary style of first writing the partial differential equation set and applying finite differencing over the control volume as approximations.

[ ] A.2.3.1 [ ] AREVA Inc.

Controi!ed Document Analytical Methods for Monticello A TWS-1 Similarly for the vapor mass conservation, where AREVA Inc. ANP-3274NP Revision 2 PageA-23 Controiied Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 PageA-24 Controlled Document Analytical Methods for Monticello ATWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-25 Controlled Document Analytical Methods for Monticello A TWS-1 A.2.3.2 Vapor generation rate The vapor generation rate is modeled [ ] [ AREVA Inc. ANP-3274NP Revision 2 PageA-26 J Controi!ed Document Analytical Methods for Monticello A TWS-1 where where AREVA Inc. ANP-3274NP Revision 2 PageA-27 Controiied Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 PageA-28 Controlled Document Analytical Methods for Monticello A TWS-1 A.2.3.3 Mass conservation The mass conservation equation is solved for the liquid and vapor phases. [ ] [ where where AREVA Inc. ANP-3274NP Revision 2 PageA-29 J

Document*

Analytical Methods for Monticello A TWS-1 Where ANP-3274NP Revision 2 Page A-30 It is important to notice that the mass balance solution of Equation (A-90) is valid regardless of the flow direction and is thus applicable whether vapor and or liquid flow is in the normal upward direction or in the negative (reverse) direction.

This distinction is important when integrating the energy equations as presented next. A.2.3.4 Energy conservation Energy conservation in AISHA, which is adopted from SINANO, requires solving [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-31*

Controlled Document Analytical Methods for Monticello ATWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page A-32 Controlled Document Analytical Methods for Monticello ATWS-1 and A.2.3.5 l l where and AREVA Inc. ANP-3274NP Revision 2 PageA-33 Controlled Document Analytical Methods for Monticello A TWS-1 [ for the vapor and liquid respectively, where and [ ANP-3274NP Revision 2 PageA-34 The heater wall surface temperature is obtained by solving the heat conduction equation for the heater rod, which is presented in the next section. [ ] AREVA Inc. J J Controlled Document Analytical Methods for Monticello A TWS-1 A.2.3.6 [ ] Momentum Conservation The momentum balance equation [ [ where AREVA Inc. ANP-3274NP Revision 2 Page A-35 ] is written as J Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-36 Controlled Document Analytical Methods for Monticello ATWS-1 Define, AREVA Inc. ANP-3274NP Revision 2 PageA-37 Controlled Document Analytical Methods for Monticello A TWS-1 and AREVA Inc. ANP-3274NP Revision 2 Page A-38 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page A-39 Controlled Document Analytical Methods for Monticello A TWS-1 A.2.3.7 Friction Pressure Drop ANP-3274NP Revision 2 Page A-40 The pressure drop components contributing to the momentum balance are the acceleration, gravitation (density), and friction.

The first two components have been given in the previous section. The friction components are the bare rod friction and the local pressure drop components at the inlet and exit and the grid spacers. The same treatment of friction pressure drop of RAMONA5-FA is adopted for AISHA. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 where where The two-phase friction multiplier is calculated from [ AREVA Inc. ANP-3274NP Revision 2 PageA-41 ] as

Document Analytical Methods for Monticello A TWS-1 A.2.3.8 Recirculation Loop Model AREVA Inc. ANP-3274NP Revision 2 PageA-42 Contro!!ed Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-43 Controlled Document Analytical Methods for Monticello A TWS-1 where / AREVA Inc. ANP-3274NP Revision 2 PageA-44

Document Analytical Methods for Monticello A TWS-1 A.2.4 Pin Heat Conduction ANP-3274NP Revision 2 PageA-45 Heat conduction in the fuel pin is assumed to be azimuthally symmetric with no axial component.

The transient heat conduction equation is thus pear =-1 l.-(kr ar)+qH' CJt r CJr CJr (A-141) where r radial coordinate from the fuel pin center t time T(r,t) temperature q 0' ( r, t) volumetric heat generation rate P density C specific heat at constant pressure k thermal conductivity The fuel rod is made of 3 components, fuel pellet, clad and pellet-clad gap. Heat generation is assumed in the fuel pellet only, where gamma heating of the cladding material is neglected.

Non-uniform heating in the pellet is allowed where the radial distribution is a function of pellet burnup. The boundary condition at the pellet center is ar -=0 at r=O CJr The boundary condition at the outer clad surface is obtained as heat flux continuity, thus ar[ -kc -d = h ( T;vall -) r r=R where heat sink (coolant) temperature R outer clad radius T;vall outer clad surface temperature h heat transfer coefficient AREVA Inc. (A-142) (A-143)

Controlled Document Analytical Methods for Monticello A TWS-1 k clad thermal conductivity c ANP-3274NP Revision 2 PageA-46 The pellet-clad gap is modeled as a thin layer with no thermal inertia but finite thermal resistance.

Thus the inner clad radius is approximated as equal to the outer pellet radius, Rf . The heat flux across the gap is obtained from where hgap gap heat conductance T 1 temperature at fuel pellet outer radius i:; temperature at clad inner radius kc clad thermal conductivity k 1 pellet thermal conductivity Rf pellet outer radius (Rf-and Rf+ refer to the pellet and clad sides of the gap respectively)

AREVA Inc. (A-144)

Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-47 Controiied Document Analytical Methods for Monticello A TWS-1 Figure A-1: Fuel rod discretization AREVA Inc. ANP-3274NP Revision 2 PageA-48

Document Analytical Methods for Monticello ATWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-49 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-50

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page A-51 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 PageA-52 Controlled Document Analytical Methods for Monticello A TWS-1 A.2.4.1 Power distribution in the pellet with [ AREVA Inc. ANP-3274NP Revision 2 Page A-53 J Controlled Document Analytical Methods for Monticello A TWS-1 and [ where A.2.4.2 Heat transfer coefficient

[ ] AREVA Inc. ANP-3274NP Revision 2 PageA-54 J Controlled Document Analytical Methods for Monticello A TWS-1 where [ AREVA Inc. ANP-3274NP Revision 2 PageA-55 J Controlled Document Analytical Methods for Monticello A TWS-1 A.2.4.3 Pellet-Clad Gap Conductance AREVA Inc. ANP-3274NP Revision 2 PageA-56 Contro!!ed Document Analytical Methods for Monticello ATWS-1 A.2.5 Material Properties ANP-3274NP Revision 2 PageA-57 Pellet and clad material properties are taken from RAMONA5-FA.

Water properties utilize the new IF97 formulation (Reference A.6). AREVA Inc.

Controlied Document Analytical Methods for Monticello A TWS-1 A.3 References ANP-3274NP Revision 2 Page A-58 A.1 "ATWS Rule Issues Relative to BWR Core Thermal-Hydraulic Stability," NED0-32047-A, Class I June 1995. A.2 . EMF-3028(P)

Vol. 2 Revision 4, RAMONA5-FA:

A Computer Program for BWR Transient Analysis in the Time Domain --Theory Manual, January 2011. A.3 EMF-2279(P)

Revision 0, STAIF: A Computer Program for BWR Stability in the Frequency Domain --Theory Manual, September 2001. A.4 EMF-2158(P)(A)

Revision 0, Siemens Power Corporation Methodology for Boiling Water Reactors:

Evaluation and Validation of CASM0-4/MICROBUR.N-B2, Siemens Power Corporation, October 1999. A.5 F. P. lncropera and D. P. De Witt, Introduction to Heat Transfer, John Wiley & Sons, Inc., Second Edition 1990. A.6 W. Wagner and H.-J. Kretzschmar, "International Steam Tables -Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97/'

second edition 2008 Springer-Verlag Berlin Heidelberg.

A.7 51-9090455-000, "Responses to NRC RAI -Round 18 and Round 20 for Browns Ferry EPU," September 2008. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page B-1 Appendix B SINANO Theory Manual for 1 D Single Channel Transient Code for Two Phase Flow with Dryout and Rewetting Abstract A model for dryout and rewetting under density wave oscillations in BWR bundles is presented.

New analytical/numerical methods are presented for the transient calculation of the heat transfer transitions between wet and dry states as a dynamical system capable of predicting failure to rewet. [ ] The outer pin wall temperature is obtained by solving the heat conduction equations for a heater rod or for a fuel rod. The model and numerical methods used in SINANO are described in this Appendix.

AREVA Irie.

Controlled Document Analytical Methods for Monticello A TWS-1 8.1 Introduction B.1.1 Objective ANP-3274NP 2 Page 8-2 The objective of this work is to develop a 1 D single channel thermal-hydraulics transient code for two phase flow including a model for dryout and rewetting capable of predicting failure to rewet. [ ] B.1.2 Summary of Sf NANO Model The SI NANO code is a single channel two phase flow thermal hydraulic code [ ] The code is capable of modeling oscillatory behavior including reversal of the inlet flow, and associated rod dryout and rewetting.

The dryout and rewetting model is described below: where AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-3

Document Analytical Methods for Monticello A TWS-1 Fuel pin heat conduction model has the following attributes:

• The axial conduction is neglected. . [

• The thermal resistance of the pellet-clad gap is represented

[ ] B.2 Theory Description B.2.1 Major Assumptions and Model Attributes ANP-3274NP Revision 2 Page B-4 ] 1. A single 1-D boiling channel representing the KA THY loop test section or a fuel bundle is modeled. 2. One-dimensional two-phase flow [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 9. Post-dryout heat transfer [ 1 AREVA Inc. ANP-3274NP Revision 2 Page B-5

Document Analytical Methods for Monticello A TWS-1 B.2.2 Dryout and rewetting reduced order model ANP-3274NP Revision 2 Page B-6 The dryout and rewetting model is based on a transient mass balance for the liquid film wetting the heated surface. Dryout occurs when the liquid film vanishes.

[ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 where and AREVA Inc. ANP-3274NP Revision 2 Page Controiied Document Analytical Methods for Monticello A TWS-1 where where AREVA Inc. ANP-3274NP Revision 2 Page B-8 Controlied Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-9 Controlled Document Analytical Methods for Monticello A TWS-1 where where AREVA Inc. ANP-3274NP Revision 2 Page B-10 Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-11 Controi!ed Document Analytical Methods for Monticello ATWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 8-12 Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-13 Controlled Document Analytical Methods for Monticello A TWS-1 B.2.3 Thermal-Hydraulic Model Equations ANP-3274NP Revision 2 Page B-14 The thermal-hydraulic system of equations is described here. It is comprised of the field equations for [ ] These equations are defined and solved for a discretized channel [ ] Model variables are defined as average values for each node with the exception of vapor and liquid velocities which are defined at the node boundaries.

[ ] Forward, reverse or counter-current flow are supported by the model equations.

B.2.3.1 [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-15 Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-16

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-17 Controlled Document Analytical Methods for Monticello A TWS-1 where B.2.3.2 Vapor generation rate The vapor generation rate is modeled [ AREVA Inc. ANP-3274NP Revision 2 Page B-18 ]

Controlled Document Analytical Methods for Monticello A TWS-1 where where AREVA Inc. ANP-3274NP Revision 2 Page B-19 Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-20 Controlled Document Analytical Methods for Monticello A TWS-1 [ ] B.2.3.3 Mass conservation The mass conservation equation is solved for the liquid and vapor phases. [ ] [ where where AREVA Inc. ANP-3274NP Revision 2 Page 8-21 J Controlled Document Analytical Methods for Monticello A TWS-1 where ANP-3274NP Revision 2 Page 8-22 It is important to notice that the mass balance solution of Equation (B-45) is valid regardless of the flow direction and is thus applicable whether vapor and or liquid flow is in the normal upward direction or in the negative (reverse) direction.

[ ] B.2.3.4 Energy conservation Energy conservation in SINANO requires solving [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-23

Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-24 Controlled Document Analytical Methods for Monticello ATWS-1 and [ B.2.3.5 L l where AREVA Inc. ANP-3274NP Revision 2 Page B-25 J

Document Analytical Methods for Monticello A TWS-1 and [ for the vapor and liquid respectively, where ANP-3274NP Revision 2 Page B-26 The heater wall surface temperature is obtained by solving the heat conduction equation for the heater rod, which is presented in the next section. [ ] AREVA Inc. J Controlled Document Analytical Methods for Monticello A TWS-1 B.2.4 Pin Heat Conduction B.2.4.1 Heater Rod Conduction Model AREVA Inc. ANP-3274NP Revision 2 Page 8-27 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-28

Document Analytical Methods for Monticello A TWS-1 [ where [ ANP-3274NP Revision 2 Page B-29 The steady state solution is obtained by setting the time derivative on the left hand side of *Equation (B-63) to zero. [ ] [ where where [ AREVA Inc. J J J J Controlled Document Analytical Methods for Monticello A TWS-1 8.2.4.2 Fuel Rod Conduction Model Heat conduction in the fuel pin is assumed to be azimuthally symmetric with no axial component.

The transient heat conduction equation is thus AREVA Inc. ANP-3274NP Revision 2 Page B-30 Controiled Document Analytical Methods for Monticello A TWS-1 where ar 1 a ( ar) ,,, pC-=---kr-+q dt r dr dr r radial coordinate from the fuel pin center (m) t time (s) T(r,t) Temperature (K) q"'(r,t) volumetric heat generation rate (W/m 3) P density (kg/m 3) C specific heat at constant pressure (J/kg.K) k thermal conductivity (W/m. K) ANP-3274NP Revision 2 Page B-31 (B-72) The fuel rod is made of 3 components, fuel pellet, clad and pellet-clad gap. Heat generation is assumed in the fuel pellet only, where gamma heating of the cladding material is neglected.

Non-uniform heating in the pellet is allowed where the radial distribution is a function of pellet burnup. The boundary condition at the pellet center is ar =O dr at r =0 The boundary condition at the outer clad surface is obtained as heat flux continuity, thus arl -kc-= h(T:val/

dr r=R where heat sink (coolant) temperature (K) R outer clad radius (m) T:vall outer clad surface temperature (K) AREVA Inc. (B-73) (B-74)

Controlied Document Analytical Methods for Monticello A TWS-1 h heat transfer coefficient (W/m 2.k) ANP-3274NP Revision 2 Page B-32 The pellet-clad gap is modeled as a thin layer with no thermal inertia but finite thermal resistance.

Thus the inner clad radius is approximated as equal to the outer pellet radius, Rf . The heat flux across the gap is obtained from where hgap gap heat conductance (W/m 2.K) T 1 temperature at fuel pellet outer radius (K) I',,; temperature at clad inner radius (K) kc clad thermal conductivity (W/m.K) k 1 pellet thermal conductivity(W/m.K)

Rf pellet outer radius (Rf_ and Rf+ refer to the pellet and clad sides of the gap respectively) (m) AREVA Inc. (8-75)

Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-33 Controlled Document Analytical Methods for Monticello A TWS-1 Figure 8-1: Fuel rod discretization AREVA Inc. ANP-3274NP Revision 2 Page B-34 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-35 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 8-36 Controiied Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-37

Document Analytical Methods for Monticello ATWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-38

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-39 Controlled Analytical Methods for Monticello A TWS-1 B.2.4.3 Heat transfer coefficient

[ ] AREVA Inc. ANP-3274NP Revision 2 Page B-40 Controlled Document Analytical Methods for Monticello A TWS-1 which leads to B.2.4.4 l ] AREVA Inc. ANP-3274NP Revision 2 Page B-41 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-42 Controlled Document Analytical Methods for Monticello A TWS-1 where AREVA Inc. ANP-3274NP Revision 2 Page B-43 Controlled Document Analytical Methods for Monticello A TWS-1 which leads to The transient solution is obtained as follows. AREVA Inc. ANP-3274NP Revision 2 Page B-44 Controlled Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page 8-45 Controiied Document Analytical Methods for Monticello ATWS-1 B.2.5 Anchoring

[ ] The critical power computed with CPROM is given by: where AREVA Inc. ANP-3274NP Revision 2 Page B-46

Document Analytical Methods for Monticello A TWS-1 AREVA Inc. ANP-3274NP Revision 2 Page B-47

Document Analytical Methods for Monticello ATWS-1 8.3 References ANP-3274NP Revision 2 Page 8-48 B.1 EMF-3028(P)

Vol. 2 Revision 4, RAMONA5-FA:

A Computer Program for BWR Transient Analysis in the Time Domain --Theory Manual, January 2011. B.2 F. P. lncropera and D. P. De Witt, Introduction to Heat Transfer, John Wiley & Sons, Inc., Second Edition 1990. B.3 TRACE V5.0 THEORY MANUAL --Field Equations, Solution Methods, and Physical Models (chapter 12 Structural Material Properties), US Nuclear Regulatory Commission.

B.4 G. F. Hewitt, J.M. Delhaye, N. Zuber, Multiphase science and technology, Volume 2. B.5 J. M. Delhaye, M. Gior, and M. L. Riethmuller, Thermohydraulics of Two Phase Systems for Industrial Design and Nuclear Engineering, Mc Graw-Hill Book Company, 1981. B.6 Chexal, B. and Lellouche, G., A Full-Range Drift-Flux Correlation for Vertical Flows, EPRI NP-3989-SR, Electric Power Research Institute, June 1985. B.7 ANP-3138(P)

Revision 0, Monticello Improved K-factor Model for ACE/ATRIUM 10XM Critical Power Correlation, August 2012. B.8 EMF-2209(P)(A)

Revision 3, SPCB Critical Power Correlation, AREVA NP, Inc., September 2009. AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 Appendix C Steady State Dryout Correlation CPROM Abstract ANP-3274NP Revision 2 Page C-1 A new dryout correlation is presented.

This correlation, named Critical Power Reduced Order Model (CPROM), has been developed based on AREVA correlation development guidelines similar to dryout licensing correlations such as ACE. The CPROM correlation range of applicability is wide [ ] making it well-suited to fitting into transient models of post-dryout that include cyclical dryout and rewetting with possible failure to rewet. CPROM is an integral part of the SI NANO transient model described in Appendix B. The correlation coefficients for a given BWR fuel type are obtained by fitting to the dryout testing database for that fuel type. For application in SI NANO, [ ] The following sections provide more details. The form of the CPROM correlation is presented, the values of the correlation coefficient set are given for ATRIUM 1 OXM, the range of applicability defined, and the quality of the fitting is presented by figures comparing calculated versus measured data. Similar information is provided for GE14 fuel type. I AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 C, 1 Description of CPROM Correlation A dryout correlation of the critical heat flux type is developed.

[ ] AREVA Inc. ANP-3274NP Revision 2 Page C-2 Controlled Document Analytical Methods for Monticello A TWS-1 where: AREVA Inc. ANP-3274NP Revision 2 Page C-3 Controiied Analytical Methods for Monticello A TWS-1 where ANP-3274NP Revision 2 Page C-4 Equation (C-10) satisfies all known properties and trends of the critical power measurements.

AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 C.2 Anchoring to a licensing correlation C.3 CPR OM Correlation for ATRIUM 1 OXM The correlation coefficients for ATRIUM 10XM are given below. AREVA Inc. ANP-3274NP Revision 2 Page C-5 ControUed Document Analytical Methods for Monticello A TWS-1 [ ] Figure C-1: Calculated versus measured critical power, [ ] AREVA Inc. ANP-3274NP Revision 2 Page C-6 Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-2: [ Figure C-3: [ AREVA Inc. ANP-3274NP Revision 2 Page C-7 ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-4: [ Figure C-5: [ AREVA Inc. ANP-3274NP Revision 2 Page C-8 ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-6: [ Table C-1: Statistics

[ AREVA Inc. ] ANP-3274NP Revision 2 Page C-9 ]

Controiied Document Analytical Methods for Monticello A TWS-1 Table C-2: Statistics

[ Table C-3: Statistics

[ Table C-4: Statistics

[ AREVA Inc. ANP-3274NP Revision 2 Page C-10 ] ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 [ 1 Figure C-7: Calculated versus measured critical power, [ 1 AREVA Inc. ANP-3274NP Revision 2 Page C-11 Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-8: [ Figure C-9: [ AREVA Inc. ANP-3274NP Revision 2 Page C-12 ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-10: [ Figure C-11: [ AREVA Inc. ANP-3274NP Revision 2 Page C-13 ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-12: [ Table C-5: Statistics

[ AREVA Inc. ANP-3274NP Revision 2 Page C-14 ] ]

Controlled Document Analytical Methods for Monticello A TWS-1 Table C-6: Statistics

[ Table C-7: Statistics

[ Table C-8: Statistics

[ AREVA Inc. ANP-3274NP Revision 2 Page C-15 ] ] ]

Document Analytical Methods for Monticello ATWS-1 ANP-3274NP Revision 2 Page C-16 The figure below shows comparison of the calculated and measured critical power. The mean critical power ratio is [ ] and the standard deviation of the calculated versus measured critical power for the entire database is [ ] and the number of data points is [ ]. Figure C-13: Calculated versus measured critical power, [ ] AREVA Inc.

Document Analytical Methods for Monticello A TWS-1 C.4 CPROM Correlation for GE14 The correlation coefficients for GE14 are given below. AREVA Inc. ANP-3274NP Revision 2 Page C-17

Document Analytical Methods for Monticello A TWS-1 Figure C-14: [ AREVA Inc. ANP-3274NP Revision 2 Page C-18 ]

Document Analytical Methods for Montice.llo A TWS-1 Figure C-15: [ Figure C-16: [ AREVA Inc. ] ] ANP-3274NP Revision 2 Page C-19 Controlled Document Analytical Methods for Monticello A TWS-1 Figure C-17: [ Figure C-18: [ AREVA Inc. ] ] ANP-3274NP Revision 2 Page C-20 Controiled Document Analytical Methods for Monticello A TWS-1 Table C-9: Statistics

[ Table C-10: Statistics

[ Table C-11: Statistics

[ AREVA Inc. ] ] ] ANP-3274NP Revision 2 Page C-21

Document Analytical Methods for Monticello ATWS-1 Table C-12: Statistics

[ Figure C-19: [

• AREVA Inc. ] ANP-3274NP Revision 2 Page C-22 ]

Contro!ied Document Analytical Methods for Monticello A TWS-1 Figµre C-20: [ Figure C-21: [ AREVA Inc. ] ] ANP-3274NP Revision 2 Page C-23

Document Analytical Methods for Monticello A TWS-1 Figure C-22: [ Figure C-23: [ AREVA Inc. ] ] ANP-3274NP Revision 2 Page C-24 Controlled Document Analytical Methods for Monticello A TWS-1 Table C-13: Statistics

[ Table C-14: Statistics

[ Table C-15: Statistics

[ AREVA Inc. ] ] ] ANP-3274NP Revision 2 Page C-25 Controlled Docun1ent Analytical Methods for Monticello A TWS-1 Table C-16: Statistics

[ ] ANP-3274NP Revision 2 Page C-26 The figure below shows comparison of the calculated and measured critical power. The mean critical power ratio is [ ] and the standard deviation of the calculated versus measured critical power for the entire database is [ ], and the number of data points is [ ]. Figure C-24: Calculated versus measured critical power, [ ] AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 ANP-3274NP Revision 2 Page D-1 Appendix D Heat Transfer Data from KATHY Loop Stability Testing of ATRIUM 10XM Abstract The SI NANO code models used for evaluating the transient temperature response of heated rods in a BWR bundle under oscillatory conditions with cyclical dryout and rewetting including the possibility of failure to rewet are presented in Appendix B. Essential elements of the SI NANO model pertaining to the heat transfer coefficient behavior under wetted and dry conditions.are extracted from measured data. The data set used for this purpose is the stability testing of the ATRIUM 10XM BWR bundle represented in full scale electrically heated module in the KA THY test facility.*

The testing conditions include steady state where the flow rate fluctuates only at the noise level. They also include very large unstable oscillations where significant inlet flow reversal occurs. The power leve.1 was kept constant under manual control for some tests. For other test points, a feedback loop determined the power input to the bundle and the resulting coherent power and flow oscillations of large amplitude provided a close simulation of the realistic conditions under A TWS-1 transient.

The following sections provide the heat transfer parameters determining the wet and dry conditions and [ ] . These parameters extracted from the testing results provide necessary elements for the SI NANO models. D.1 Summary of Heat Transfer Coefficient Data and Observations The needed measured data include the test section power, pressure, inlet flow rate, inlet subcooling and the temperature of the heater rods. [ ] The following provide a summary of the data and observations regarding the behavior of the extracted heat transfer coefficients.

AREVA Inc.

Controlled Document Analytical Methods for Monticello A TWS-1 D.2 Heat Transfer Coefficient under Wetted Conditions ANP-3274NP Revision 2 Page D-2 The heat transfer extracted at the initial testing time, where wet conditions are guaranteed, are compared with [ ]. The figure shows the data separately at [ ] to verify the consistency of the data. AREVA Inc.

Controned Document Analytical Methods for Monticello A TWS-1 Figure D-1: Measured versus calculated heat transfer coefficients

[ ] D.3 ( ] AREVA Inc. ANP-3274NP Revision 2 Page D-3 Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-2: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-4 Controlled Document Analytical Methods for Monticello A TWS-1 D.4 [ Figure D-3: [ ] AREVA Inc. ] ANP-3274NP Revision 2 Page D-5 Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-4: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-6 Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-5: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-7 Controlied Document Analytical Methods for Monticello A TWS-1 Figure D-6: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-8 Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-7: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-9

Document Analytical Methods for Monticello ATWS-1 Figure D-8: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-10 Controlled Document Analytical Methods for Monticello A TWS-1 Figure D-9: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-11 Contro!ied Document Analytical Methods for Monticello A TWS-1 Figure D-10: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-12 Controiled Document Analytical Methods for Monticello A TWS-1 Figure D-11: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-13 Contro!ied Document Analytical Methods for Monticello A TWS-1 Figure D-12: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-14 Controiied Document Analytical Methods for Monticello A TWS-1 Figure D-13: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-15

Document Analytical Methods for Monticello A TWS-1 Figure D-14: [ ] AREVA Inc. ANP-3274NP Revision 2 Page D-16