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Development of Fuel Performance and Thermal Hydraulic Technology

KAERI/RR-2015/99

Development of Advanced LWR Fuel

Development of Fuel Performance and Thermal Hydraulic Technology

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S U M M A R Y

I. Project Title

Development of Fuel Performance and Thermal Hydraulic Technology

II. Objective and Importance of the Project

The spacer grid assembly is one of the major components of nuclear

fuel. It enables the fuel rods to be supported and located properly in

the fuel assembly throughout the fuel life. It also provides a flow

channel between the fuel rods, which affords the heat transfer from

the fuel pellet into the coolant in a reactor. Therefore, the spacer

grid is a highly ranked component when the improvement of hardware is

pursued for promoting fuel performance.

Up to now, the technology of fuel design and fabrication in Korea

has been established in the area of adopting and adapting proven

foreign technologies. However, foreign fuel vendors have been

developing new and improved features of fuel and trying to extend

their market into Korea with newly developed technologies. Under such

circumstances, it would be very difficult to achieve the

self-establishment of fuel technology here in Korea if we do not

endeavor to develop our own technology and just import foreign ones.

To come by our own technology, we think that it is very important

to derive some candidates for the spacer grid on which the inherent

right can be insisted. Besides, it is also highly necessary for us to

- xxv -

possess the fundamental technologies of developing the spacer grid,

for instance, mechanical and structural analyses and test

capabilities. We must have these technologies not only to achieve the

self-establishment of the fuel technology but also to compete with

foreign vendors in the international market under WTO circumstances.

Main objectives of current worldwide fuel development are the

improvement of fuel economy as well as reactor safety. As the fuel

discharge burnup increases and high performance features are

introduced into fuel design, development of fuel performance analysis

code has been focused more on its accuracy and predictability.

Technology of fuel performance analysis has been improved along with

the increase of burnup. Since the late 1990's when the high

burnup-specific characteristics were found, fuel performance analysis

technology for the burnup of 60 - 70 MWD/kgU has been extensively

developed worldwide.

As the burnup increases steadily, new phenomena were identified,

so that there has risen a need of new fuel performance analysis code

due to the limitation of the conventional analysis code. To develop

the new performance model and code to predict new phenomena,

systematic data base for fuel behavior are essential.

- xxvi -

III. Scope and Contents of the Project

1. To derive the candidates of the spacer grid for patent possession.

To conduct experiments comparing the mechanical/structural and

thermal-hydraulic performance with proven spacer grids after

fabrication of the candidates.

To modify the shape of the candidates and to apply for the patents

from the test results.

2. To research the following subjects to establish the mechanical and

structural technologies related with the spacer grid.

To implement the relevant test equipment.

A. Development of the Vibration Analysis Model and Performance of

the Vibration Test for the Single Fuel Rod

Free vibration analyses have been performed analytically and

experimentally for the fuel rod multiply supported by a spring system

and subjected to an axial force. For analytical approaches, an FEM

program was developed, which has been verified by ANSYS code and the

vibration test of a dummy rod.

B. Research on the FIV Mechanism for the Fuel Rod Assembly

The excitation of a sub-critical vibration due to axial flow was

studied for the FIV mechanism of the fuel rod, which was accepted by

many researchers. On this basis, an analytical study has been

performed to develop the FIV model of the fuel rod by utilizing the

experimental PSD for fluid pressure, the random vibration theory, and

the normal mode method.

- xxvii -

C. Spacer Strap Characteristic Test, Spacer Grid Buckling Strength

and Dynamic Impact Strength Test

The strap characteristic test was conducted using the universal

tensile testing machine in the air condition at room temperature. This

test was executed with several candidate models, which were made of

stainless steel and Zircaloy-4, The results of this will be applicable

as basic data for the predicting the fuel rod support condition under

core conditions and for a fuel fretting wear test between the fuel rod

and spacer grid support.

A static buckling test was conducted using the universal tensile

testing machine in the air condition at room temperature. This test

was executed with several candidate models, which were made of

stainless steel and Zircaloy-4. The results of this test are the basic

data for evaluating the structural integrity of the fuel assembly

under seismic and LOCA conditions.

The dynamic impact test was conducted using the free fall shock

machine in the air condition at room temperature. This test was

executed with several candidate models, which were made of stainless

steel and Zircaloy-4.

D. Analytical Evaluation Methodology of Spacer Grid Structural

Strength

A numerical analysis model was established using the static

buckling/impact test results and the theory of applied mechanics. The

structural integrity of the supposed model was examined. On this

basis, a numerical methodology was developed in order to examine the

nonlinear buckling phenomena. Nonlinear buckling analysis, which

incorporates material hardening, was established to generate the

- xxviii -

characteristic curve, load vs. displacement, of the specimen. The

analytical results were compared with the test results.

E. Shape Optimization Methodology of the Spacer Strap

A shape optimization procedure is necessary to obtain the

optimal and realizable shape of the strap, which can be performed by

the mechanical tests and remedy/supplementation of the candidate

specimen together with the optimization technique. In order to

optimize the shape of the strap, an optimal design program which

utilizes the design sensitivity, was linked with the finite element

method.

F. Identification and Analysis of the Fretting Wear Mechanism

The size of the contact patch between the fuel rod and the

spacer grid was evaluated by the finite element method. The shear load

path was suggested, which could simulate the feasible behaviour of the

contact during FIV. The contact shear stresses and their

characteristics were evaluated. Friction energy dissipation and the

surface cracking behavior were regarded as the wear mechanism.

G. Spacer Strap Characteristic Simulation, Spacer Grid Static and

Dynamic Analysis

The nonlinear characteristic of the spacer grid support is

simulated the FE analysis method and the results from the simulation

are compared with the test results. This analysis model considers the

elastic and plastic properties of the material. The analysis results

were verified with the test results. In addition, structural strength

- xxix -

analyses on the spacer grid candidates are carried out using ABAQUS.

The results from the analyses are compared with the test results.

H. Test Equipment Setup for Spacer Grid Development

(a) Dynamic Impact Test Equipment

The dynamic impact test results of a spacer grid are used to

develop the accident analysis model on the fuel assembly at a virtual

fault events. The dynamic impact coefficient, and the restitution

coefficient which are necessary for the analysis of virtual accidents

are obtained from the test. Two kinds of dynamic impact test methods

are currently used, i.e., the free-fall type test and the pendulum

type test. The former uses a dummy weight which drops from a certain

height and impacts on the grid, while the latter uses an impact hammer

which moves angularly and impacts on the grid. Both test equipments

have been established for our tests.

(b) Fuel Rod Vibration Test Equipment

For a vibration test of the fuel rod supported by spacer

grids, a controlled signal from a shaker can be utilized instead of an

impact input by a hammer. For this reason, additional equipment is

needed to monitor and control the input level of the shaker signal. In

addition, a pressurization chamber for the vibration test has been

built to study the pressure effects on the vibration characteristics

of the fuel rod. A sequential process for a performance test and

modifications for the chamber have been repeatedly carried out since

its basic shape was built.

(c) Fretting Wear Test Equipment

- xxx -

Fretting wear test equipment has been designed and fabricated

for analysing the parameters which are thought to affect the wear of

the fuel rod. A servomotor of variable speed was adopted for the drive

mechanism to change the rotation into reciprocating motion. Test

parameters such as contact normal and shear force, vibration amplitude

and frequency are monitored and stored continuously during the test. A

surface roughness tester was equipped to examine and measure the width

and the depth of the worn surface.

3. The contents and scope of the thermal-hydraulic area are described

hereafter.

A. Design of Flow Mixing Devices

The numerical analysis was performed by the CFD (computational

fluid dynamics) code CFX to investigate the flow characteristics of

the invented flow mixing devices. This analysis was also used to

optimize the design of the flow mixing devices. From the flow

characteristics results of the devices, the most probable candidates

might be recommended.

B. Preliminary Thermal-Hydraulic Performance Test

Two kinds of preliminary T-H performance tests were conducted: a

wind tunnel rod bundle test and a Refrigerant Tube CHF test. The wind

tunnel test was to investigate the flow structure of the turbulent

flow in the subchannel of a rod bundle downstream the spacer grid with

the swirl vane. On the other hand, the CHF test was to examine the CHF

enhancement due to an existence of a swirl vane in the grid.

Refrigerant R-134a is used as the working fluid for the test

- XXXI -

convenience, since this test is to understand the relative CHF

increase. In addition, the optimum design of the swirl vane was also

experimentally investigated with three kinds of vane angles such as

25, 30 and 35 °.

C. Establishment of Thermal-Hydraulic Technologies for Flow Mixing

Device

a) Establishment of Numerical Computation System for Fluid Flow

The evaluation of a commercial CFD code CFX was performed in

order to validate its analysis for the flow structure in rod bundle.

It was accomplished with the available experimental data of various

turbulent flows in the open literatures. However, even the limitation

of the CFX code is identified, actually it is difficult to modify the

commercial code. So, our own numerical code are tried to be developed

on the open numerical code for fluid flow by means of implementing

various turbulence models and numerical schemes.

b) Development of the Thermal-Hydraulic Models

A pressure drop model was proposed on the mechanistic

approach. It can predict the pressure drops of various spacer grids

with mixing devices. It was validated with the hydraulic data

available in the data base. On the other hand, a study on the

phenomena of two phase flow and the CHF mechanism could help to

develop a theoretical CHF model. In addition, the method to increase

the CHF was also investigated.

c) Thermal-Hydraulic Test Equipment Set-ups

The wind tunnel test equipment is used to figure out the flow

structure in rod bundle with mixing device. The turbulence is measured

- xxxii -

by the hot-wire anemometer, and the mean axial velocity by a Pi tot

tube. The turbulence data are extracted using a DAP provided by TS1.

The matched hot wire signals are monitored periodically on a HP 54602B

oscilloscope. This test data is to be utilized for the validation of

turbulent model.

Refrigerant CHF test facility is set-up to pre-estimate the CHF

performance before water CHF test. This test facility is also useful

to study the boiling and CHF phenomena because of easy treatment by

means of low boiling temperature. At present, the test section is a

single channel but it will be upgraded to accomodate the bundle size

CHF test.

4. Preparation of Fuel Characterization Tests and Procedures

For the general evaluation of the advanced LWR fuel being

developed, characterization tests and in and out of pile tests were

analyzed for the key parameters affecting fuel performance. And their

test procedures and methodology to produce the fuel performance data

base were studied.

5. Fuel Performance Data Base and Performance Analysis Model

Development

- Compilation of High Burnup Fuel Performance Data Base

Fuel performance data base obtained through the cooperation with

Siemens and ABB/CE, IFPE(International Fuel Performance Evaluation)

data base, test results obtained from the international research

program, Halden Reactor Project and the literature data found during

the model development were analyzed and compiled as a file.

- xxxiii -

- RAPID Program

Due to the radial variation of neutron energy spectrum and flux

inside UO2 pellet, there is variation in local fission density and

concentrations of the fissionable nuclides. To analyze the high burnup

phenomena such as Rim effects, accurate prediction of those variation

is necessary. Therefore, RAPID program to predict the radial

distribution of power, burnup and fissionable nuclide densities as

function of burnup and U-235 enrichment was developed.

- RAPID-GD Program

Since there is strong dependence of Gd content and subsequently

the local power upon the burnup in the gadolinia burnable poison rod,

separate models to predict the local power distribution were developed

depending upon the burnup such that at low burnup when Gd content is

high so that local variation of power is severe, and at high burnup

when majority of Gd nuclides have disappeared and local variation of

power is similar to UO2.

- Fission Gas Bubble Swelling Model

Fission gas bubble swelling model during steady state and

transient in UO2 fuel was developed. Since bubble swelling is

proportional to the bubble growth by the diffusion and bubble

interconnection, the model calculates the bubble growth as a function

of time and temperature. Based upon Greenwood-Speight bubble growth

model, empirical bubble growth model was developed as a function of

burnup, time and temperature,

- Cladding Creep-out Model

As the fuel burnup increases, the rod internal pressure may

become higher than the coolant system pressure due to the fission gas

- xxxiv -

release. Then the cladding becomes under tensile stress so that the

model to predict the cladding creep-out behavior was developed. After

analyzing the Halden in-pile creep-out test results, creep-out model

was developed based upon the conventional creep-down model of CARO-D

5. 5 code.

- Cladding Corrosion Model

By analyzing the corrosion mechanisms and key parameters

affecting the corrosion behavior, corrosion model was developed. Key

parameters affecting the corrosion behavior are material properties,

fast neutron fluence, hydride and lithium content. Effect of lithium

on the corrosion was considered as an factor in the activation energy

of oxygen diffusion in the corrosion protective layer.

- Evaluation of Nuclear Performance of Duplex Integral Burnable

Absorber Rod .

Duplex integral burnable absorber rod with Gd2C>2 inner core and

Er203 out layer was designed to optimize the reactivity control

capability, and its nuclear performance and characteristics viere

evaluated.

6. High Burnup Fuel Behavior Analysis

- Modelling of High Burnup Rim Effects

Formation mechanism of high burnup structure(HBS) or rim effects

in high burnup UO2 fuel was proposed in terms of fission gas behavior.

Fission gas bubble is nucleated and stabilized with the help of the

fission fragments at the critical concentration of gas atoms inside

the grain. Then, grain sub-division in HBS region is helped by the

over-pressure of the stabilized bubbles. Since local gas atom

- xxxv -

concentration inside the grain in the pellet depends upon temperature,

burnup and U-235 enrichment, variation in the measured widths of HBS

region in UO2 pellet could be explained by this mechanism.

- Thermal Conductivity Model of Irradiated UO2

Thermal conductivity model of irradiated UO2 fuel was developed

based upon the thermal diffusivity data measured during the multiple

thermal cycling. The model considers solid fission products, gaseous

fission product, radiation damage and porosity as separate factors.

Reliability of those factors was confirmed by comparison with the

measured thermal diffusivity data during thermal cycling and other

thermal conductivity models. Since developed model can consider the

effect of the fission products as a separate factor, it can be applied

to the thermal conductivity in the rim region of the high burnup UO2

fuel where fission gas atoms are precipitated into the fission gas

bubbles.

- In addition, fuel failure by secondary hydriding of zircaloy

cladding was studied in the areas of its causes, controlling

parameters and progress in cooperation with Hanyang University.

2-dimensional finite element analysis programs were developed in

cooperation with Kyungbook University in the area of steady state and

transient thermal and elastic and plastic mechanical analyses.

7. Fuel Rod Design for Integral PWR

Fuel rod for integral PWR was designed and its performance during

steady state and transient was analyzed. And fuel design basis and

criteria were determined considering the reactor operation

requirements.

- xxxvi -

IV. Results of the Project

1. Seven kinds of candidates have been invented and applied for

domestic and US patents. In addition, the demo spacer grids(3x3 array

and 5x5 array) were fabricated, for which the mechanical/structural

tests were carried out. Recently, a "Notice of Allowance" for the

doublet spacer was acquired from the US patent and trademark office.

2. The Results of the Research on the Fundamental Subjects for the

Spacer Grid and the Implementation of the Experimental Devices.

A. Development of the Vibration Analysis Model and Performance of

the Vibration Test for a Single Fuel Rod

An FEM program was developed to analyze the free vibration of a

fuel rod subjected to an axial force and multiply supported by grid

springs, which has been verified through the ANSYS code and the

vibration test. After verification the developed code was utilized for

the vibration analysis of a single fuel rod. For the vibration test, a

dummy rod stuffed with lead was made, and the equipment and technique

for a modal test were developed for the rod under water, as well as

for a rod in air. In addition, for the further research on the

specific field, a shield chamber where the vibration test can be

carried out under a pressurized environment has been designed and

built, and indispensible equipment for further tests are being

constructed.

B. State of the Art on the FIV Mechanism of the Fuel Rod Assembly

and the Development of the Prediction Model of Axial-flow-

induced Vibration

- XXXVII -

Based on the state of the art of the previous research, it has

been concluded that the bundle effect can be disregarded in developing

the applicable F1V model of the fuel rod considering the coolant

conditions, the geometry and the property of the fuel rod. It has also

been judged that hydrodynamic coupling is negligible because the

coolant velocity is sufficiently less than the critical velocity that

brings about instability, and the vibration amplitude(yrms/D) is

generally less than 10". Therefore, for this study, an analytical

model for the single span of a single rod has been developed to

predict the vibration amplitude of the fuel rod. The FIV model has

been developed with consideration of the fuel rod subjected to an

axial force that occurs due to the pressure difference between the

inside and the outside of the fuel rod cladding.

C. Structural Strength Analytical Evaluation Model Creation of the

Spacer Grid and Establishment of an Analytical Procedure

A 5 X 5 cell model was developed for the finite element analysis

of the candidates of the spacer grid. The reaction force at the

supported ends were evaluated using the nonlinear buckling strength

analysis. By comparing the FE results with the test ones, an adaptive

model was developed which incorporated the reliable boundary

conditions and reduced the calculation time. From the developed model,

it is possible to obtain reliable and economical results even though

the number of cells increases.

D. Strap Shape Optimization Methodology Development and Shape

Optimal Design of the H-type Spring

The shape optimization of three kinds of spacer grid candidates,

- XXXVIII -

i.e., H-type strap, doublet, and swirl-type strap, is executed by

varying the object function since it has not been known which object

function affects the supporting condition of the fuel rod. Therefore,

the object functions were optimized from the point of the equivalent

stress of the strap, the contact stress between a fuel rod and its

support, and the wear volume of the fuel rod. As a result, the

optimized shape of the H-type strap has been derived and applied for

the patent.

E. Development of the Analysis Method for Contact Shear Stress on

the Fuel Rod

It was found that the fuel cladding could be assumed to be a

semi-infinite body, and the normal stress profile was very similar to

the Hertzian from the FE analysis. From this, a numerical method was

developed to obtain the contact shear stresses using the classical

theory of elasticity. The shear stresses obtained in the case of a

rectangular and closed shear force were examined. The suggested path

of the shear force was intended to simulate the physical behaviour of

the contact during FIV. The characteristics of the shear stress such

as irresponsibility, compliance increase, etc. were also investigated.

F. Analysis of the Fretting Wear Mechanism

Fretting wear was regarded as a friction energy dissipation from

the contact surface or a surface cracking behavior, from which the

analysis methods of the energy and the crack were established. The

friction energy is the scalar product of the contact shear stress and

slip displacement, therefore, it will decrease as the width of the

contact locus due to vibration decreases. To design the contact

- xxxix -

condition such that the locus width is narrowed becomes beneficial for

restraining fretting wear. On the other hand, stress intensity factors

of the crack initiated from the contact edge were evaluated from the

internal stresses induced by the contact stress field. The mode II

stress intensity factor, Kn, was thought to be the major driving force

for the crack, which was thought to form the wear particle. It was

also found that a part of the shear cycle is attributed to the

effective period of crack growth. It was suggested to find the

parametric values of the contact which reduced the effective period to

restrain wear.

G. Spacer Strap Characteristic Test, Spacer Grid Buckling Strength

Test Equipment Setup

The strap characteristic test was conducted using the universal

tensile testing machine in the air condition at room temperature. The

test setup was composed of a loading bar for loading/unloading and a

fixture for a unit cell specimen. Data during both loading and

unloading were acquired from the test setup.

The static buckling strength test was accomplished using the same

test setup used for the spring characteristic test. Load-displacement

curves were collected until the load dropped to 80% of the initial

value. Two kinds of dynamic impact test equipment, i.e., the free-fall

type and the pendulum type, have been designed and setup. The pendulum

type impact equipment using an electronic driving mechanism has the

flexibility of a specimen size up to full scale. The test can also be

done at elevated temperatures by the installed chamber.

H. Design of the Fretting Wear Test Equipment

- xl -

The mechanical drive mechanism for the fretting wear test

equipment was developed and fabricated. The equipment affords the wet

test as well as the dry test. Up to the boiling point of water is

available for the wet test temperature. This was used primarily to

discriminate the wear resistance capability of the proposed grid

springs.

3. The Results of the Thermal-Hydraulic Research for the Flow Mixing

Device

A. Flow Characteristics of Flow Mixing Devices

The flow mixing characteristics analyzed with CFX code for the

invented flow mixing devices and the existing advanced mixing devices

of Westinghouse and ABB/CE as well. The results are compared for the

parameters such as swirl ratio, cross flow ratio and turbulent

intensity. It said that among the candidates the probable ones are

swirl vane, duct vane, and twisted vane. Since this CFX results comes

from the single phase flow, the similar comparison for two-phase flow

is further required to represent the CHF performance properly.

B. Preliminary Thermal-Hydraulic Performance Tests

- Wind Tunnel Turbulent Test

In a 3X3 bundle wind tunnel test, the time mean axial and

lateral velocity and turbulent intensity downstream of spacer grids

with two types of mixing vane angles were measured over a center

subchannel at Reynolds number of 1.2X105. The swirl flow with 30 vane

was stronger than that with 40 vane along the diagonal in subchannel.

The swirl flow at the end of test section was eccentric to the lower

- xli -

gap and the secondary flow was detected near the rod surface.

- Refrigerate CHF Test

The CHF enhancement is experimentally examined using with and

without the swirl vane grid units in a round tube. The simple grid (no

swirl vane grid) is utilized as a reference case. The test condition

simulates the PWR condition in water equivalence. For the results, the

swirl vane grids always showed better CHF performance than the simple

grid within the test conditions. Among the three vane angles, the 35

swirl vane revealed the highest CHF in most of the cases.

Particularly, for the condition of a 2.6 Mpa pressure and a mass flux

of 1500 kg/m2s (water equivalent to the normal operation condition of

PWR), the CHF enhancement is, at least, above 15% for the inlet

temperature range of 40 to 70 C.

C. Establishment of Thermal-Hydraulic Technologies for Flow Mixing

Device

- Establishment of Numerical Computation System for Fluid Flow

An orthogonal 2-dimensional numerical code TFC2D is made. The

present code contains nine kinds of turbulence models that are widely

used. They also include six kinds of numerical schemes including 5

kinds of low order schemes and 1 kind of high order scheme. To verify

this code, pipe flow, channel flow and expansion pipe flow are solved

with various options of turbulent models and numerical schemes and the

calculated outputs are compared against the experimental data.

- Thermal-Hydraulic models

i ) Pressure Drop Model

- xlii -

A pressure drop model for the PWR grids with and without

mixing device is proposed at single phase based on the fluid mechanic

approach. Total pressure loss is expressed in additive way for form

and frictional losses. As the results, the model shows better

predictions than the existing ones for the non-mixing grids, and

reasonable agreements within 11% error against the available

experimental data for mixing grids.

ii) CHF Model

A new theoretical CHF model was derived based on the

superheated liquid layer depletion process by evaporation, as an

integral equation from the developing bubbly layer to a certain

location where no liquid contacts the heated surface any longer called

CHF condition. In the derivation, the widely accepted two-phase

constitutive relationships are used without introducing the tuning

constant. The proposed model is validated for the bubble-detached to

the low quality range, mainly including the PWR conditions, through

the comparisons against the measured data from uniformly heated round

tubes: mean error of 0.002% and r.m. s. error of 10.4 % for 2249 data

points. The proposed model showed better predictions in accuracy

relative to the previous theoretical CHF models and correlation

assessed together.

4. Preparation of Fuel Characterization Tests and Procedures

For the new zircaloy cladding, characterization test procedures for

corrosion, creep, burst and in-pile test in research reactor were

prepared. For the new UO2 pellet and burnable absorber pellet,

procedures of characterization tests after manufacturing and in-pile

capsule test were prepared. For the fuel assembly structure components

- xliii -

such as spacer grid, procedures of flow induced vibrational test,

mechanical strength tests and spring force test as well as the

thermal-hydraulic tests such as pressure drop, flow mixing and CHF

tests were prepared.

5. Fuel Performance Analysis Model Development

- High Burnup Fuel Performance Data Base

High burnup fuel performance data base were analyzed and compiled

as a file from Siemens and ABB/CE data, IFPE data, Halden reactor test

data, data base compiled during FRAPCON-3 development and other

published data obtained during model development.

- RAPID Program

RAPID program can predict the radial distributions of power,

burnup and fissionable isotopes as a function of burnup, U-235

enrichment. It is based upon HELIOS neutronics code. RAPID considers

the specific variation of the different nuclides, prediction accuracy

of local power and burnup was improved compared with other programs

such as RADAR and TUBRNP which have more simple models. RAPID program

was validated up to 10 w/o U-235 enrichment and up to 150 MWD/kgU

pellet average burnup.

- RAPID-GD Program

Gadolinia rod is widely used as a burnable poison rod in high

burnup and longer cycle length fuel cycle. RAPID-GD predicts radial

power and burnup distribution as a function of Gd2O2 content, U-235

enrichment and burnup. It was developed and validated based upon

HELIOS neutronics code.

- xliv -

- Fission Gas Bubble Swelling

Fission gas atoms staying inside grain tends to move to the grain

boundary and forming the bubbles. Based upon the Greenwood-Speight

model, fission gas bubble swelling model was developed as a function

of burnup, time and temperature assuming constant bubble size with

variation of bubble number density.

- Cladding Creep-out Model

In-pile creep-out test results from Halden Reactor Project were

analyzed using CARO-D 5.5 and FRAPCON-3 codes. Then, new creep-out

model was developed based upon CARO-D 5.5 model by deriving new creep

constants and dependence of fast neutron flux and stress. It showed

good agreement with the test results.

- Cladding Corrosion Model

By analyzing the corrosion mechanisms as well as current

corrosion models, new corrosion model was developed. Key parameters

affecting the corrosion are material properties such as chemical

composition, cold work and microstructure, lithium content in the

coolant, hydride in the cladding and fast neutron fluence. Based upon

the derived model, ZIRCO program was developed to predict the

corrosion behavior along the axis of fuel rod.

- Evaluation of Nuclear Performance of Duplex Integral Burnable

Absorber Rod

By using the duplex integral burnable absorber rod, there is

flexibility in controlling the core reactivity, specially for longer

cycle length higher than 24 months. Even though its manufacturing cost

could be increased, there is still possibility and incentive to be

applied considering improvement in fuel economy.

- xlv -

6. High Burnup Fuel Behavior Analysis

- Modelling of High Burnup Rim Effects

Formation mechanism of HBS structure in high burnup UO2 fuel was

proposed in terms of fission gas atoms. Bubbles in HBS region were

nucleated and grown into the stabilized size near the displacement

spikes caused by the fission fragments at the critical concentration

of fission gas atoms inside the grain. Grain-subdivision results from

the bubble formation and over-pressurization. Variation of the HBS

width measured from the different irradiated fuels could be explained

by the proposed model considering the effects of temperature and U-235

enrichment. Detailed analysis of fission gas behavior showed that

fission gas release by bubble inter-connection at the grain boundary

occurs earlier for larger grain fuel than smaller grain fuel.

Therefore, fission gas release at low or intermediate burnup could be

higher for larger grain fuel, which was supported the in-pile on-line

measurement data of fission gas release in Halden Reactor Project.

- Thermal Conductivity Model of Irradiated UO2

Thermal conductivity model of irradiated UO2 fuel was developed

from the thermal diffusivity data measured during thermal cycling. The

model was validated by comparison with other models. Since the model

takes into account the effect of fission gas atoms as a separate

factor, it can be applied to the thermal conductivity of HBS region.

Evaluation of thermal conductivity of HBS region showed that thermal

conductivity degradation of HBS region by bubble porosity buildup

could be significantly compensated by positive effect of fission gas

depletion from the matrix.

- Fuel Failure by Secondary Hydriding(In cooperation with Hanyang

- xlvi -

University)

Experimental study was performed for kinetic of massive hydriding

of zircaloy cladding. It was found that critical ratio of H2/H2O for

hydriding is higher than 105. Effect of oxide layer upon massive

hydriding, and effect of pressure on steam corrosion and hydrogen

penetration were studied. Quantative kinetic model for hydriding was

derived through the identification of source of massive hydrogen.

- Finite Element Analysis Program(In cooperation with Kyungbook

University)

Finite element analysis programs were developed for steady state

elastic and plastic thermal and mechanical analysis, and transient

elastic and plastic thermal and mechanical analysis. Time dependent

deformation such as creep and swelling in the fuel rod were also

considered. In addition, finite element mesh generation module for

fuel rod was developed.

7. Fuel Rod Design for Integral PWR

Conceptual design of fuel rod for integral PWR was performed.

Design basis and criteria were determined and preliminary engineering

data were generated. In integral PWR, high purity pure water is used

as a coolant. Boron is not used as reactivity controlling element.

Ammonia is added to suppress the radiolysis of water. Fuel pellet

design is same as that of commercial PWR fuel, so that its performance

up to 60 MWD/kgU burnup was well confirmed already. However, due to

the severe power history of fuel rod, further study is needed in the

corrosion performance of the cladding. Fuel rod internal pressure and

centerline temperature met the design limit and mechanical integrity

was shown to be maintained.

- xlvii -

V. Proposal for Applications

1. All the patent-applied and patent-prepared candidates (each has

five different kinds) will be tested further in detail for examining

and analysing their mechanical/structural characteristics.

2. The fundamental technologies established will be utilized not only

for developing a spacer grid for ourselves but also for analysing the

characteristics of the proven spacer grids.

3. The test equipment procured for the spacer grid will be utilized

for data generation during the design and licensing of a new spacer

grid that might be developed by fuel vendors such as KNFC.

4. Developed performance models for high burnup fuel will become the

key part of the high burnup fuel performance analysis code to be

developed in the next stage.

5. Fuel performance data base will be used in the evaluation,

development and verification of the fuel performance analysis model

and code.

6. Procedures of characterization tests for fuel components such as

cladding, pellet and fuel structural parts will be used in the

verification tests and data base generation of those components in the

following stages.

- xlviii -

CONTENTS

Presentation

Summary (in Korean)

Summary (in English)

Contents (In English)

Contents (In Korean)

List of Tables (in Korean)

List of Figures (in Korean)

Chapter 1 Introduction 1

Chapter 2 Development Status 10

Section 1 Development Status Abroad 10

Section 2 Domestic Development Status 13

Chapter 3 Scope and Results of Project 16

Section 1 Development of Technology on Spacer Grid Structure 16

1. Development of Candidate Spacer Grid 16

2. Test for Performance Comparison of Candidate Spacer Grid 31

3. Research on the Basic Technologies Related to SG 49

4. Procurement of Test Equipnent for Structural Mechanics of SG 110

Section 2 Development of Thermal-Hydraulic Performance Enhancement

Technology 249

1. Introduction 249

2. Invention of Flow Mixing Devices 251

3. Flow Analysis of Flow Mixing Devices 256

4. Preliminary Thermal-Hydraulic Performance Test 272

5. Development of Thermal-Hydraulic Models 284

6. Establishment of CFD Codes 299

Section 3 Development of Fuel Performance Analysis Technology •••409

- xlix -

1. Preparation of Fuel Characterization Tests and Procedures • 409

2. Fuel Performance Data Base and Performance Analysis Model

Development 431

Chapter 4 Achievement of Objectives and External Contribution 559

Section 1 Achievement of Objectives 559

Section 2 External Contribution 569

Chapter 5 Application Plan of the Results 573

Chapter 6 References 574

_ I —

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- Ivi -

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3-1>1o6 ^ -^ l - a - y ^^ A] ^ J g . - ^ # ^ ^ - ^ S - ^ ^ ^ * } # 2093.1.107 ^- 9i^-ofl^ * I H ^ 7 | ^ t | ^ jgng 210

3.1.108 Hertz ^ ^ - ^ 4 ^ ^ ^ " ^ ^r^^^^ 210

3.1.109 S ^ ^ S t\^-o] z\^}^ ^-f^ 2 *R1 ^-g-^1 211

3.1.110 0 ] ^ . ^ A I - 4 ^ A I j . ^ _g.^ 211

3.1.111 Mindlin-Cattaneo ^^S\ sfl^ ^^ (C y / juJM). 5*1 ^ - f ) •-•212

3.1.112 ^ ^ - ^ ^51 iL> -g-^ (Qx < Qy 4 ) 212

3.1.113 ^ ^ - ^ ^$] ^^> -g-^ (Qx > Qy <£ itfl) 213

3.1.114 Qx7} ^--g-^- tcfl Compliances^]- 213

3.1.115 ^ ^ - ^ ^ B ^^d S^l (Qy/fiP= 0.33) 214

- Ix -

3.1.116 - M n l n ^ ^ | 6 ] H?}B]£ 214

3.1.117 ^ * } # ^ S ; (aM**l*ff*H 4&S1 #*fl £ * 1 ^ %$- :(b)

^-S.-fs l -7-sfl*] i ^ l ^ - i d * ^ 3 ^ M ^ ) 215

3.1.118 a^-3.1.11751 4 ^ H s ^ H ^ l ^ ^ 3 ^ ^ - s - ^ 217

3.1.119 S£-3:<g5l ^ ^ ] oj*> sejjEj 4 ^ 4 ^ AflA 217

3.1.120 dJ^^^]^j afl^S L M \ 3 ^^1%I A)-EH^ ^ ^ ^ < ^ 217

3.1.121 ^<i^] ^o]if 3 4 4 ^5f6]l ixf -g-^7o^7Jl^^ 7 ] ^ (Q /

jUP = 0 . 3 6 , Jl = 0 . 3 ) : ( a ) ^ ; ; ( b ) ^// 218

3.1.122 H^l 3.1.1175] 7flA>ofl Af^-s^ ^ ^ . ^ -§-^ 219

3.1.123 ZL l 3.1.1175] 5 : < i ^ ^ ^ . | ^of l4^ /^///T/ 219

3.1.124 (a) ^ ^ - ^^^f^ 4° l l " (aax / ^P = 0.36, y = 0.3; e f ^ ^

1,5,7,11,13<>fl4 JO! = G** / 3, * } # ^ 2 ,4 ,8 ,10^4 !fl! =

2Qmax / 3, G,/n = - Cffla, ): (b) ^^>*}# ^ ^ ^ 1 ^ 5 ] -§-^3-

Sl^Hr 7 ] ^ 220

3.1.125 £J*I-fHr ^ l^ l^^f ^ s ^ o 1 ^ ^- t l -S .^ s c l 221

3.1.126 4 * 1 3 4 4*1-fSj H l ^ ^ ^ s f l ^ l ^ - § - ^ TJl^^i 221

3.1.127 si^HH? 4 * 1 3 4 ^^BJ^1 a l ^ i^ sfl^^l ^t> ^-^^-^1 2223.1.128 H}*iig ^ 5 ] ) / ^ ) ^ « > ^ ^ ^ ^ ^ ^ B O I ^ ^ ^ ^ A J . 222

3.1.129 S]3HHf 4 4 3 4 ^ ^ ^ ^ 1 til^% *H^ 4^ 223

3.1.130 H^ ^>^34^ - ^ - l ^ i £ 1 224

3.1.131 134-Sl *}# ^ 3 ^ 2 2243.1.132 i£*l ^45] 2f^-S^ ^ ^ - 225

3.1.133 sfl^^l 4-§-^l <*M ^^ l^^^ l 7H^ 225

3.1.134 1>^ ^ 1>^.^ s f l ^ «>^-^/^t^| ^-^i H]ja. 226

3.1.135 47f4 - ^ - i ^ i S^-i-Sl ^ l ^ ^ / ^ ^ l ^ 226

3.1.136 3X3 34^1^1 *\^^ 9! 3 ^ 1 ^ ^ 227

3.1.137 3X3 34*ff£J -B-tl-S.^ S.'gsf ^ % ^ ^ - 227

3.1.138 5X5 34*11^1 -n-tl-S.^ 2.*£3} ^ 4.A 228

3.1.139 3 4 ^Ml i t ^ ^ ^ ^ / ^ l m* tilJ2. 2283.1.140 ^1^-5.^2} ^ | n _ t | ^ ^ ^ ^ 3 | . 229

- Ixi -

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3.1.142 %& 3.*i$] ^ ^ S 230

3.1.143 cV -1 ^ x } ^ ^ 4^s} SLxQ 230

3.1.144 37}*] JE^oU cR> ^ B<HW*j ^ ^ / ^ l ^ 231

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3.1.148 «]#% ^ ^ ^ ^ s f [ ^ ^ - ]*> ^711^^1 233

3.1.149 271 ^^^ -H^) nfa. ^ ^ ^ i j igSf 233

3.1.150 ^7] ^-^^S. 0.40 m/s«Hl>H I ^ ^ ^ 234

3.1.151 ^.7] ^ ^ ^ - £ 0.40 m/sofH*] von Mises -§-7f-g-^ ^3. ..-234

3.1.152 27] ^^fS. 0.40 m/s6flA| l ^ 7 } ^ ^ ^ ^ ! - ^ S 235

3.1.153 H^ 3X3 >i 4^]^1 # ^ S . ^ ^ ^ 236

3.1.154 5l H -§^1^*1^} P^S. 237

3.1.155 ^^t^u\$Ji 7H^H 238

3.1.156 ^ 1 ^ ZL^^l^?- 238

3.1.157 ^ ^ ^ 1 S ^ ^ ] # 3-]*> ^ A ^ 239

3.1.158 ii(ii) 239

3.1.159 ^ ^ . - g - ^ S ^ j ^ # ^|*> 6»^^-7l 240

3.1.160 ^^-8-71 wli^^l xlx|^x|-l- JL^*> S ^ 240

3.1.161 ^^^.-g- ^sfl^nl-ig X\^ %%]$) 7^S. 241

3.1.162 «?^S>g- ^^J^n}ig A ] ^ *)-*](Aj-tL) 242

3.1.163 «f«l-S.-g- ^ ^l^l^^f ^^Bo7 ^ 1 ^ 242

3.1.164 A ] ^ o]^Jf 243

3.1.165 * \ ^ %^^l(Load Cell) 243

3.1.166 LVDT 244

3.1.167 ## 244

3.1.168 ^ u | 4° i - r - (^^ ) 245

3.1.169 ^2ll^n}ig A ] ^ ^ * | cflo]^ JtAl s } ^ 245

3.1.170 S ^ 7]^7l 4 ^ ^w] 246

- Ixii -

3.1.171 Stylus ^ -7-i-f 246

3.1.172 Stylus^] Sjt> 4 ^ ^ 247

3.1.173 nftg^ ^ 42}$] ojefl 247

3.1.174 nJ-igiSS] ^ n j ^ #$(X 50) 247

3.2.1 sl^-fr-^ ^ |^7 f l7 f -f*}-^ 4 4 ^ 4 4 4 S. 338

3.2.2 S]*l-f}»§- «^^7fl 44IE. 338

3.2.3 ^ ^ 44 S 338

3.2.4 3]3-8-^ ^J^7||7} - f*v^ ^ ^ ^ «qo4S^^^ 4 4 ^ 4 ^

44S. 339

3.2.5 ^ tii^ ^ 4 <%M 4^ : 4 4 ^ 4 ^ 1 ^ ^ £ 339

3.2.6 si^i-fr-i- ai^y-7ll7l- ^ -^ f i ^ s ^ t f l<^5.^^| 4 4 ^ x } ^g £ 340

3.2.7 ^ ^ - ^ ^%^7fl 4 4 ^ 4 ^-4s. 341

3.2.8 e i^^ ^^y-711 4 4 ^ 4 *$^S- 341

3.2.9 ¥.4^ ^^^711 4 4 ^ 4 ^(strip) 4 ^ £ 342

3.2.10 ^ ^ " ^ ^% l^7| | S$45L 342

3.2.11 ^y-711 CFD JS.«g 343

3.2.12 ^ e j ^ y-7l)(split-vane) - f ^g . # ^ ^ i ^ o ^ ^ - £ ^ S •••344

3.2.13 ^ e ] ^ ^7|f(split-vane) - f ^ S . - § ^ ^ t i o ^ ^S .^S . . .345

3.2.14 ^ e l ^ ^7fl(split-vane) ^ - ^ S t>T^lM^] 346

3.2.15 ^ S ) ^ ^7fl(split-vane) JM\§. S l ^ - ^ ^ 3.71 346

3.2.16 ^ - ^ S ^-S.t*|B| M]3. (z/Dh=2) 347

3.2.17 -f^S. ^-S.«]Bi tijja (z/Dh=10) 348

3.2.18 ^SL ^*<m a l J l (z/Dh=20) 349

3.2.19 ^ - ^ 5 . ^ ^ i ^ % * ^ £ ^ ; £ 350

3.2.20 JM^S. ^ i ^ ^ ^ ^£^S 351

3.2.21 -f^S. 4°l(gap) ^ ^ - ^i^-S 352

3.2.22 -f-^S. 4-T- Sl^i-n-^ ^IJ- 3.71 353

3.2.23 -*M\S. 4°l ^ ^ - ^ ^ 371 353

3.2.24 -f-^S. ^ ° H ^ ^ - S 354

- Ixiii -

3.2.25 ^S- ^ VHHIM*] £ S 3543.2.26 $ 1 * 1 ^ £ ^ 7 f l ^ 4 ^ 1 ttf§ ^ r ^ - ^HH? ^ £ . £ 3 . -355

3.2.27 n&&£- ¥^7% ^45K>fl ttfg- Jf- jsL S]*i-8-§- 3.7} -356

3.2.28 3]*l-8-§- ^W7)J ^ -^4^^ ] ty^r -f^-g. Q^gS. 356

32.29 S]*Mf- ^ ^ A ^z\S.°\] ixf - - ^ 5 . # ^ t>#^m^l -357

3.2.30 $1$.$-^ ^ " i n ^ ^ 4 H ^ 1 I 4 € ^ S 5]^-^-^ 3.71 ^O

H ^ ^ ^Sj. 357

3.2.31 3J*i-fh£ ^^^7H ^ - ^ 4 ^ ^ ^ ^ 1 ttf€- ^-^r^ 5]^-^-^

3.71 358

3.2.32 SJ^-B-i- ^^^7fl -g-^^-S.^ ^ W | nfs. ^ . ^ ^ ^ ^ - ^ S .

^S(^-l) % 5]^-^^- 37l(o}Bfl) 358

3.2.33 ^-7) S.1 ^1^14^ 71*} tgJ£ 359

3.2.34 Al^-f 359

3.2.35 ^ ^ ^ 360

3.2.36 ^ - ^ ^ -S. :S 360

3.2.37 ^ ^ ^ ^ <*rS. ^"S 361

3.2.38 ^1^-f ^Hl^i ^ ^ ^ ^ - £ ^ : S 362

3.2.39 -*iS| <?]x} ^ 362

3.2.40 t f l zHIW V> - 4 £ ^ S 363

3.2.41 ^ ^ - ^ ^ VHf 4 S ^ 5 364

3.2.42 ^ o1-*©15 ^ ^ ^ ^ Hi3. 365

3.2.43 a } ^ ^ J£ ^ -S H]J2. 365

3.2.44 ^nfl# oj-g-tl ^711^-^-4 ^ l ^ ^ l ^ 7fl3>£ 366

3.2.45 ^ 1 ^ ^ ^ ^ ^ ^ - ^ - ^y :7 i ] ^ 367

3.2.46 # ^ 1.2 Mpa lA-1 o i ^ . ^ ^ ^ ^ ^ <y7}j .o_<fc- A ^ ^ 3 f ..-368

3.2.47 <>H 2.6 Mpaofl 6 ^ ^ 1 4 ^ - <g7fl<g-fl-4j- A I ^ ^ ^ ...369

3.2.48 «U^ 2.6 Mpa A-1 ^-^ .^^o]] tcj-S. c i^ l<i^-^ Aj^^^f ...370

3.2.49 4 SM-fr^ibll 4 S . 1 £ o | irfS. ^7ff<g-JH- &}% y l^- 371

3. 2. 50 ^ ^ 1 7 } -f^Sl^l & £ PWR 4^M1 tHtV o^^ l i f ^^^1^1 Hl i 372

3.2.51 ^HJ* l7 l - ^ Q PWR ^ 4 i 4 ^ : ^ l ^ l ^ f A J ^ ^ 1 ^ HI^L -373

- Ixiv -

HQ 3.2.52 FBR 2]*H] t}]*> o f l ^ i f > y ^ * l ^ H]iL 374

H ^ 3.2.53 <M<S-fMf S . ^ 7HM3 -7-^ 375

ZL ] 3.2.54 M ^ - f H ^ oJl^l^f ^ 8 * 1 ^ w]3. 376

ZL^ 3.2.55 ^%MH*r°fl c1l> o f l ^ m ^ 8 * 1 ^ * 1 ^ ^%* 377

ZLt] 3.2.56 6nT7fl<i-fMf 5 . ^ 7 J ) ^ - ^ 377

ZL^ 3.2.57 t ^ J ^ ] cH*> ofl^j i f 4 ^ ^ ^ u]*| ^ ^ 378

-L^ 3.2.58 ^ ^ ] ^ ^ ) cflsv ofl^jil- ^ ^ ^ 1 ^ M}$] 4*£ 378

HQ 3.2.59 L/Dofl cJJ^ of l^ l i f 4 ^ ^ ! ^ ul^l ^^o^ 379

ZL^ 3.2.60 i-JH A]^j^S.oJ| t:B*> <y>||^-fr4 ^ ] ^ ] i f ^-^^1^} «1 --379

ZLS] 3.2.61 Reynolds ^ ^ ^ 1 ^ } ^ ^ ^ 1 4 ^ - -fr^^Sf 380

ZL^ 3.2.62 #% -y^lx3| ^ ^ -^-^ ^-^ 381

ZL^ 3.2.63 VBfS-ioll ^\^r ^ ^ ^ Vi^^-i- ^-^ Hi a 382

ZL5] 3.2.64 ^ Bo ^ V>^-7o^ ^ S (P/D=1.25, Re=100000) 383

ZL^ 3.2.65 ^ S i } i-H-^^S. -^-^^-^ H]3. 384

ZL I 3.2.66 SA-^el^^i f ^ ^ ^ ^ - ^ ^ - ^ Hlja. 385

Zisi 3 2 . 67 ^ ^ ^ . ^ - f r ^ ^ ^ ^ S ^ r S M]i 386

ZL^ 3.2.68 ^ ^ S . ^ ] A - ] ^ ^ ^i^>-§-^ H]iL 387

n.^ 3.2.69 Sj-tH^ ^ ^ - ^ - ^ - ^ W ^ - S ^ : ^ 388

ZL^ 3.2.70 %c|l^- u>^-oim^l ^ : S 389

ZL*|] 3.2.71 ^ ^ S . ^ Matrix <^S. ^ ^ ^5. ^S. 390

H.^ 3.2.72 2r»£*2 ^£^S(Re=20000) 391

ZL5] 3.2.73 ^*&*£ ^-£^S(Re=40000) 392

ZL^ 3.2.74 -g-4°l # 6 o ^ ^ l ^ ^ ^ o ^ ^ i ^ S ( ^ l ) 91 t^^s.(o}efl)

(Re=40000) 393

ZL*!! 3.2.75 -g-^^MI^ ^ - ^ S ^>^ 394

ZLQ 3.2.76 TFC2D 3.H5] ^ i^ l^^ i J : ^ - £ 3g4

ZLs] 3.2.77 ^ % ^ * 1 2j*M-t^l(generated by wgridl routine) 395

ZL^T 3 .2 .78 ^ ^ ^ ^ A | ^ ^ ( g e n e r a t e d by wgrid2 r o u t i n e ) 395

Zisi 3.2.79 £ ^ ^ 7 ) 1 ^ ^ 5 ] ^«§- S.*H 395

ZL^ 3.2.80 ^ * } ^ ^}^1 A ] ^ ^ 396

- Ixv -

3.2.81 ^ ^ - f H f S l U <^S. ^S. (Re=17250) 397

3.2.82 ^ ^ H f ^ k ^ S (Re=17250) 397

3.2.83 ^ ^ - f r ^ - £ | U <SfS. ^-3£ <Re=40000) 398

3.2.84 31%3Mh§-S] k &£. (Re=40000) 398

3.2.85 *l% ^Ml^f 3*fX|£l til^- (Re-40000) 399

3.2.86 \S.-fH?£I U -S. -g-j& (Re=8200) 400

3.2.87 .S.-fHf2j c M f ^ - g ^ ^ a (Re-8200) 400

3.2.88 - %cB^^-^^ ^t*$*£ rS. S (Re=84000) 403

3.2.89 ^-^-cll^:^-^^ ^-W-^M^l S (Re=84000) 4063.2.90 ^-tTO-S-^JA-l ^|*^jjL2dfl rcf^ vb^oim^} £3*

(Re=84000) 408

3.3.1 Variation of radial fissile atomic density distribution

with the burnup(4 w/o 235U) 526

3.3.2 Radial variation of one group neutron flux(4 w/o 235U) 526

3.3.3 RAPID calculation flow 527

3.3.4 Variation of radial burnup distribution with the burnup

(4 w/o 235U) 528

3.3.5 Variation of radial burnup distribution with 5U enrichment

at the burnup of 30 MWD/kgU 528

3.3.6 Variation of atomic number density with the burnup at mid

radius(4 w/o 235U) 529

3.3.7 Comparison of radial distribution of total Pu concentration

with the measured STRO fuel data at the burnup of 29

MWD/kgU 529

3.3.8 Comparison of radial burnup distribution with the measured

STRO (2.9 w/o 235U) data and TUBRNP prediction at the burnup

of 29.571 MWD/kgU 530

3.3.9 Effect of 235U enrichment upon radial burnup distribution

in comparison with the measured BR-3 fuel(8.6 w/o Z35U) data 530

3.3.10 Comparison of total Pu concentration in the pellet with

- Ixvi -

0RIGEN(4 w/o 235U) 531

ZL^ 3.3.11 ^ J E ^ i ] 4 ^ . Gd-157 ^ £ ^Sf(0.71 w/o U-235) 531

H ^ 3.3.12 <a^So11 n}€ # 3 ^ 3 E ^S]-(9 w/o Gd2O3, 1.8 w/o U-235) -532

H^J 3.3.13 <£^S. 2 MWD/kgUoflA-js] # ^ £ S ( 1 . 8 w/o U-235) 532

ZL^ 3.3.14 <&£.S. 20 MWD/kgUoflA| # ^ ^ S ( 1 . 8 w/o U-235) 533

HQ 3.3.15 ^ S . ^ 1 4 € - Gd-157 £ S ^if(9w/o Gd203, 1.8w/o U-235) 533

nm 3.3.16 <&^S- 30 MWD/kgUofl*] U-235 -fe^Eofl 4 ^ # ^ ^ : S ^£f(12

w/o Gd203) 534

H ^ 3.3.17 ^ 4 i S 6 Ml»D/kgUofl>H^ S.^ <^)^} ^ ^ ( 4 w/o Gd203, 0.71

w/o U-235) 534

ZLQ 3.3.18 ^ [4 :£ 20 MWD/kgU^1^5] JS.^ ^ | ^ ] ^ ^ ( 6 w/o Gd2O3) 3 w/o

U-235) 535

H^ 3.3.19 #$-1 -fs}ofl^ 7 l S ^ %EH 7 f^s l 7]3E^^- ^ ^ 535

ZL^ 3.3.20 ^2}*]i|- I Zacharie ^ data point ti]J2. 536

~LS] 3.3.21 Aj^ofl nf^- ^3f-i|3f J. Burbach ^ ^ data point «lJ3. 536

3-Q 3.3.22 <^4iS6fl trf^- ^ ^ | ^ 4 Zimmermann ^ ^ data point H];2. . 537

ZL^ 3.3.23 ^rJ£o|| rcf - ^ 2 f ^ 2 f K. Une[10] ^ ^ data point ti]^L 537

O.& 3.3.24 FRAPCON-3 SH&fl 7}^] ^ ^ S . ' i ^-g-(BR-3^I ^ ^ w|3.) ...538

ZL^ 3.3.25 FRAPCON-3 3.^^1 7]*j| ^-grJE^ ^-§-(BR-3^| LHGR 10% ^7f u|

-2--^ ^ ^ ^ ) 538

D.% 3.3.26 IFA-585.1 ^ ^ # ^ ^ 1 ^ 7 l # 3 . H ^ 1 ^ ] 539

ZL } 3.3.27 IFA-585.4 ^ ^ ^-^^1 ^ 7 ) ^ 3 . ^ o f l ^ l 539

H ^ 3.3.28 Creep-out S « g ^ o f l ^ l i f ^^4^^1(IFA585.1) WJJ3. .-.540

H ^ 3.3.29 Creep-out S.^S] ^ 4 * 1 ^ - ^^^^^1( IFA585.4) W]i ---540

ZL I 3.3.30 FRAPCON-3 3 H ^ creep-out S 1! -§- 541

ZL^ 3.3.31 o ^ ^ ^ 1 ^ # ^ 1 , a)-4^ S ^ ^ £ ^ # ^ 541

ZLs] 3.3.32 Li %•£. ^S}o1| n:}^ A>J^f. ^ ^ ^ S f 542

ZL^J 3.3.33 Li ^ f£ . ^S } ^ ] ixf^- ^ - ^ ^ A>SJ-§. =-7)1 ^ 5 } 542

ZL^ 3.3.34 ^ ^ - ^ £ ^ % ^ 1 ^?> ^>5f# ^-^1 ^ 4 f 543

ZL5] 3.3.35 ^ 4 i ^ £ ^ S f ^ l ^ * > 4«J-*oi= ^>2f# ^-7)] ^ S f 543

- Ixvii -

f?fl ^ 4 f 544

3.3.37 ^ ^ ^ W - T - ^ I ] ^£1*1 VA ° f l^ l til^ 5443.3.38 Li <g*o*-§- JL5}t> ^*g*o* A>2].P1-=.^ 4 ^ * ] 545

3.3.39 Gd 7 } ^ ^ ^ ] # 4-§-*> *|<gfi^*||<il ^ ^ M ^ 545

3.3.40 °W 7}<£^^-g- T^S. 546

3.3.41 <>l

3.3.42 Variations of gas atom concentration 547

3.3.43 Gas atom concentrations in the bubbles in equilibrium •••547

3.3.44 HBS ini t ia t ion local burnup as a function of temperature,

grain size and fission density 548

3.3.45 Measured data of HBS width in the HBEP irradiation tests 548

3.3.46 : n * l l ^ < i ^ # < > 1 4 Hjja. (*M : ^ - ^ ^ 1 , *P : *K^1) 5493.3.47 7 l^ l^^ r< i^^ l -^ ] - a]jz 549

3.3.48 ao

v4^i^4^AoV<ll4 yl^- (*M : ^ ^ ^ 1 , *P : <^*1) 550

3.3.49 ^ S ^ l * } V]3. (*M : ^ ^ ^ ] , *P : ^1^1) 550

3.3.50 Hl^4Sj . U02 (95 % TD)£| < i ^ i £ £ 551

3.3.51 20 MWD/kgU U02^ < i ^ £ J £ 551

3.3.52 40 MWD/kgU U02£] < i ^ i £ £ 552

3. 3. 53 60 MWD/kgU U02£) <i^S.S. 552

3.3.54 Radial Power Distribution versus Pellet Radius for SMART

Fuel Rod 553

3.3.55 Rod Internal Gas Pressure versus EFPD for SMART Fuel 553

3.3.56 Cladding Oxide Layer Thickness versus EFPD for SMART Fuel • 554

3.3.57 SMART ^ < # 5 . -g-^n^H £.*£ 555

3.3.58 SMART «?<&§. i b ^ ^ I S-^ 556

3.3.59 SMART ^<&g. <g^^^ S.^. 557

3.3.60 SMART ^<^S.-g- S 1 ^ 558

- Ixviii -

1 & M

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- 67 -

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^ o.^ 3.1.1074

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(Semi-infinite Body) ^ ^ ^ ^ ^ l (Infinite Body)S 7}^f>}3_ $X^\

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(7f)

Hertz

^r Hertz ^ ^ ^ ^ «H^# #^f<^ ^ ^ 5 ] f e *H

Verion 5.

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ANSYSoflA-] 4 ^ - * f e ^ ^ - f i ^ t ^ , C0NTAC48 r Solid bodyi-f

, flexible-to-flexible body, rigid-to-flexible body-S] ^^~

L al4. C0NTAC48 A ^ ^ * > ^

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- 69 -

(ANSYS .3JS.61H "Target Surface"efjL ^ 5 ^ ) ^ -r" 4 nodeS

*} 3-node _S.-fc°M, 3*}^[ ^ M 4-§-*fe C0NTAC49

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# , Ao^^l Contact Bodyfe ^ ] - | - o ] 10 mm«>]n|, Inc-718^ # ^ ^ ] S ^ £1 =

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^ S . ^ 20

^ ^ ^ 4 1 ^ 10 N-i-

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3.1.22-b ANSYS S £ i oj*> S f l * ^ : ^ Hertz

Hertz

3.1.108^1 i ^ ^ i : } . ^ 4 ^ ^r^1 -§-3, ^ Hertz-§-^, p(y)^- ANSYS

- 70 -

3.1.108^ S 3.1.223]

o]i:V. ZL^ 3 . 1 . 1 0 8 ^

ll Node

ANSYS 3 . ^

(uf)

^ Hertz <>!-§-

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: 2

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d e J 3.1.109 %^) 4 £ ^^i (^^>) -§-^°)^, u 91 4 4 y

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3 i £ 2 *R1 ^ €"*!# *l«H*Rr 7 ^ 7 ] ^ o j «o^^o]uK A]

(3.1.13) ^ (3.1.14)5^ Sflfe ^ ^ - ^ ^ . 5 . ^^sfl(exact or closed form

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7)

^ . j a c o b i polynomial^

r ^ i*-^ 2

(3.1.13) JE

al-^-^ oil- ' S W T ^ (The Influence

Function Method)ole}

(4)

(7f) o-o

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- 74 -

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4

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ii ^ ^ o M axial direction, ZL^

- 75 -

y = nth Triangle)

qny{ £ ) = qny(\ -

I f an/5, rfl- a/SS. 4 4

J I+ constant.

(3.1.16)

(3.1.16)^1

(m— w— I)2 ln(m— n— I)2 —— w)2ln (m— n)2} + constant.

(3.1.17)

o)

(3.1.17)51

S im-n+I)2 In (m-n+I)2 +

(m— n— l)2ln(m— n— 1) —w)2ln (w— n)2} + constant.

(3.1.18)

- 76 -

-7- 1 M (3.1.16)^ ^ ^ s ^ ^ l ^ ^o^l ^ 3 SI

(transverse direct ion) £.£. $*\ *Ji£ *}^-o] 3]-§- - 4

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= - Qx (3.1.19)

(3.1.19)^-

(3.1.20)

/ rx /~» ' (3.1.21)

Modulus)#

. ^ ^ (3.1.20) Sl-^^M ^ur /e>x-= 0

- 0) ^1# i^^f^.^ r

(3.1.15) «HlA-| (3.1.18)

- 77 -

v(y) = g- In \y\ + constant . (3,1.23)

- L ^ 3.1.109)

y

^r *| (3.1.17) ^ (3.1

(3.1.20)51 rjK -b 4 # ^ } ^°1 ^ 4 .

d (d-\v\){y-v) (3 .1 .

\y\<Ldy

(3.1.25)

(3.1.26)

(3.1.21) , (3.1.22) gj (3.1.25) , (3.1

(3.1.27)

— 3 2 In 3;} + constant

(3.1.28)

— y2 In y] + constant

( \y\ > d ^nfl) . (3.1.29)

- 78 -

( 3 . 1 . 1 6 ) , ( 3 . 1 . 1 7 ) , ( 3 . 1 . 1 8 ) , ( 3 . 1 . 2 3 ) , ( 3 . 1 . 2 8 )

(3.1.29)ofl>H

*] (3 .1 .25) , (3 .1.26) 91 (3 .1 .28) , (3 .1.29)

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(y~ (y- 6) ] constant.

(3.1.30)

(3.1.30)7}

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7]7f

±f E= i ) \ l l ) g

M ( 3 . 1 . 3 0 ) # ^ 1 ^ H ^ ^ l <>l-§-*}7l

(discretization)^}1^ ^-5-2} ^

]

(3.1.18)2}

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( m - w-1) 2 In ( m - w - 1 ) 2 -2(M—w) 2 ln (m—w)2} + constant.

(3.1.31)

(3.1.16) ^ (3.1.18)2} ^ (3.1.30) 91 (3.1.31)

(Mindlin-Cattaneo

- 79 -

J2. OUir fe Hertzian

3.7] 7\ 21^[(Gross

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(Partial Slip)

Mindlin[3.1. Cattaneo[3.1.25]-b

]^. Mindlin-Cattaneo ^^z} ?>t:f. o|-§. 2

^ a ^ 3.1.1091- ccf^-uf).

(3.1.13)

(3-1-33)

^ composite compliances]!^, ^^- Dunders'

parameter[3.1.27]5.>M ^ ^ #^1 5l 4 ^ A ^ #

(3.1.34)

1 [ {(1-2V 1)/G 1}-{(1-2V 2)/G 2}

2

- 80 -

(3.1.

ntii tz, i CLII ^ ^ ^ ^ '-'1 X3 " n

) 2 (3.1.36)

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(3.1.37)^ q(^)fe p ( £ ) S ^ m ^ c } ) . o]4 AI (3.1.37)51

Q2 2 (3.1.38)a - yz

(singularity)^ ^ ^ ^ # <y- ^ ^uf. ZL^uf o ] ^ ^

n]7i^o] ^ .o . ^ S ^ ^ A I ^ . ^ ^ Hertzianperturbati

- 81

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q'iy)7\ (3.1.37)^1

(3.1.40)

c = ay 1 — (3.1.42)

2 ^}^J Mindlin-Cattaneo

(3.1.43)

(3-1-44)

(3.1.43)

(3.1.44)^]- ti|J2.^^cK Mindlin-Cattaneo

® ^ (3.1.18) 1

influence function)# . °M *\ (3.1.18) 4 "r#

- 82 -

collocation point iS. t\3L rr§r jS.

(i-y-D2 in (x-y-i)2-2(i—j)2\a(i—j)2} + constant.

(3.1.45)

collocation

rigid body displacement)^

^luf. o]irfl ^rf^ ^ ^ - ^ t

^^ r , A: = IS. * H ^«i^H i t e r a t ion^

collocation point(i =

collocation point^A| c f^-# *J*>r:f.

@ 4 collocation point7f JL*$ <

cy(i,j)SqyU, k—\

(3.1.46)

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- 83 -

iteration^

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(dqy(i,k) - 8

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(dqy(l,k) - 8qy{i,k-\)m ^ 4 * M ^ t ! ^

1 iterationo] ^^L^cf^ Jt = k +

£ =

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Application UtilityS.-^- Mathematica Version 3.0 -§

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(3.1.43) (3.1.44)51

(-D})

Mindlin-Cattaneo

- 84 -

*}%•*] 90°

Mindlin-Cattaneo

^r Mindlin-Cattaneo

^z;-Z/x - 0 ,

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u\

(3.1.47)

(3.1.48)

(3.1.49)

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(3.1.50)

(3.1.51)

(3.1.52)

(3.1.53)

Mindlin-Cattaneo

- 85

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(3.1.54)

(3.1.55)

, 8

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^ y th iteration ofl

^ l (3 .1 .54)4

8ux(i,k), 8uy{i,k) ^r i1 collocation point

8qx(i,k) JEi, 8qy{i,k)

dqx(i,k) S ^

29 [ A ^ Mathematica Version 3.0 o]-g-

0,7}

- 86 -

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£- &}*} *fi^ 3 # -§-3Sa K t>^ H ^ 3.1.1124}Mindlin-Cattaneo<g^|Sj Sfl ( q / 5

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^ ^ c f . ZL^ 3.1.114^)^ o|o|

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+ Qy2 =

O.^ 3. l.HSoflfe- nlzz.

- 87 -

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71STAR accelermeter

multi-channel analyzer*]

HP

IDEAS T-DAS

shakerl- -T-nfl*} !:]-. shaker^

^ Wf^- ^\^}^v\. Shaker5f

Power amplifier

- 114-

3-Q 3.1.159

3.1.1602}

3.1.161 oil

-; ofefl^

550 x 550 x 1400 rmHt*| n

§1-7]

. ^-^ 3.1.162-b

4

(1)

30 mm

¥-fe SS4151

*} 7fl

(2)

115-

(ZL% 3.1.163).

(3.1.66)

-^ 0 - 500

50Hz ^^-2}(Sinusoidal Wave)^.

: 300 rpm

# 4 : 50 W

y ^ ? l 6 j - : 24 V DC

220 V AC, 60 Hz, Single Phase

#4^1^: 0 ~ 24 V

(3)

^[Tfl^ O.^Ai 50

50 m

a ^ 3.1.164^)4 4Vol ^ 4 71

- 116-

Lash)

Dovetail^-

^ ^ . 4 ^ Dovetail^ 7>

(4)

Load Ce l l# ^•

^ - ^ 4 ^ Load Cell5] ^ ^ -g-^o^ 10 kg( <J> 100 N)

fe ~L^ 3.1.165^1-

(5)

- 117-

$) *1^§- £t%%k±3L^ ^%± ^ ai^h £ W f e LVDT(linear Variable

Differential Transducer ) # ol-g-*H ^ 1 ^ # ^ r ^ f e ^ S S 5j<H $l^.»l

fe 2.5 kHz - 20

^ S Dfl-f- 47]

(6) ^f-f$1*11

BI

^-U 3.1.1672f ^ ^

eater

(7)

Load

Al^ A}o]o]

Fourier Transform^f<^

^ - ^ 3.1.169^ ^

- 118-

1) ^ H ^ 7fl.fi.

7]?g7\ ^-^^tiKSurface Roughness Tester)#

SurfTest SV-624# -Pfl

7^711- ^-^K=r »^°_£-±= Stylus7f

Stylus^ ^©1

6.5. 3.7]}

- Vertical Travel: 300 mm

- Traverse Range: 100 mm

- Traverse Linearity: 0.2 Jim/100 mm

- Measuring Speed: 0.02 mm/s ~ 2 mm/s

- Measuring Range". 8 ]lm, 80 }im, 600 Jim

- Recording Magnification: 100X ~ 500,000X (Vert ical) ,

IX ~ 10,000X (Horizontal)

- Dimension: 710 X 450 X 890 mm

^ ^ # *}*H ^«l^l 4 -7-^^-1- -T-^^l^ 4 ^ ) ^ Joystick

Dj)o)B| ^Bl-§-^g. 4-g-^fe 5]>i^ ? ^ t - ol-g-^c}. ZL^ 3.

%} l 4 ^ Stylus

(2)

stylusl- n f ^ ^ ^ l 7]-7].o] ^ I ^ A I ^ Jf.

A J **l(Auto Start)-§• ^ ^ ^ K 4 ^ ^ ^ ° 1 3 ^ StylusA J * l

- 119-

Stylus-t

a, Rz, Rq, Ry

3.1.174^1

- 120-

1 3 . 1 . 1 M]

1

2

3

4

5

Swirl

34 ~

-

49 ~

-

105 ~

36

55

110

42 ~

-

52 ~

-

125 ~

>

45

56

133

Double^

34 '

49 '

115

- 35

u 50

"116

3.1.2 H

Swirl H 5O '

Dipper^ ^iS.^1

^r^1 *f-f (N)

19.8

20.5

20.0

20.0

19.8

20.89

20.3

20.5

*tH« ^ (N)

16.5

13.3

14.0

13.5

15.08

14.45

13.3

12.8

*K (P.)

14

15

16

14

14

14

16

17

y . [ $> ^ • *"

- 121-

3.1.3

Mode

1st

2nd

3rd

4th

5th

ke(Nm/rad)

100200300400100200300400100200300400100200300400100200300400

Swirl ^

k, =159.2 N/mm

34.46338.06140.55542.40839.75742.42144.18845. 45446.83347.88148. 52148.95566.61271.10474.21476.495106.12110.50112.35112.89

H %

kt =361.8 N/mm

34.65538.3040.83242.71540.61943.44445.33046.68649.03250.27451.03051.54270.25475.28878.86881.546108.82114.01117.96121.09

Double Strip %

k, =395.9 N/mm

28.645

35.833

46.628

62.932

101.64

3.1.4 R0DVIB2£f ANSYSS] JL^-)- k=395.9 N/mm)

Mode

1 (Hz)

2 (Hz)

3 (Hz)

4 (Hz)

5 (Hz)

R0DVIB2

28.645

35.833

46. 628

62.932

101.64

ANSYS

28.64

35.83

46.62

62.91

101.62

- 122-

13.1.5

Mode~~~~—-JJ£pe

1st Mode(Hz)

2nd Mode(Hz)

3rd Mode(Hz)

4th Mode(hz)

Max. Disp.(mm)

Swirl

35.2

46.4

49.2

88.6

0.050

H

44.4

50.5

52.3

-

0.016

Double S t r ip

42.7

48.4

51.0

94.7

0.027

1 3 . 1 . 6

Force Level

0. 5 N

1.0 N

2.0 N

Mode~~~-~-J^pe

1st Mode(Hz)

Max. Disp. (mm)

1st Mode(Hz)

Max. Disp. (mm)

1st Mode(Hz)

Max. Disp.(mm)

Swirl

35.2

0.050

33.6

0.098

30.7

0.196

H

44.4

0.016

42.1

0.040

39.5

0.106

Double S t r ip

42.7

0.027

40.6

0.044

37.4

0.072

i-fr^-cr-r;

Mode~~~~--~^JVpe

1st Mode(Hz)

2nd Mode(Hz)

3rd Mode(Hz)

4th Mode(hz)

Max. Disp.(mm)

Swirl

33.7

43.7

46.7

84.2

0.070

H

42.5

48.6

50.0

84.2

0.019

Double St r ip

40.8

46.7

49.0

89.7

0.034

- 123-

3.1.8

Force Level

0.5 N

1.0 N

2.0 N

^Eae-^yp^

1st Mode(Hz)

Max. Disp. (mm)

1st Mode(Hz)

Max. Disp. (mm)

1st Mode(Hz)

Max. Disp. (mm)

Swirl

33.7

0.070

31.5

0.113

28.8

0.229

H

42.5

0.019

40.2

0.053

37.5

0.134

Double Strip

40.8

0.034

39.6

0.045

37.0

0.075

3.1.9

Mode~~T~--~-Xype

1st Mode(Hz)

2nd Mode(Hz)

3rd Mode(Hz)

4th Mode(hz)

Max. Disp. (mm)

Swirl

33.9

44.2

48.4

84.2

-

H

44.7

49.2

50.2

-

-

Double Strip

41.4

46.4

50.8

90.4

-

3.1.10 M]7]o\] n f ^

Force

0.5

1.0

2.0

Level

N

N

N

Mod*

1st

Max.

1st

Max.

1st

Max.

ET~ lype

Mode(Hz)

Disp.(mm)

Mode(Hz)

Disp.(mm)

Mode(Hz)

Disp.(mm)

Swirl

33.9

-

32.4

-

29.5

-

H

44.

-

42.

-

39.

-

7

5

8

Double

41

39

35.

Strip

.4

.2

8

- 124 -

3.1.11 (Swirl

No.

1

2

3

4

Type

FEA

1

2

3

4

)

Hz

43.88

48.28

53.82

86.78

EMA

1

2

3

4

Hz

35.19

46.36

49.17

88.64

Error{%)

24.69

4.14

9.45

-2.10

MAC (SB)

83.2

55.4

94.8

51.3

3.1.12

3.1.13

«T-2-(H %)

No.

1

2

3

FEA

1

2

3

Hz

42.92

47.58

53.54

EMA

1

2

3

Hz

44.36

50.52

52.31

Error(%)

-3.24

-5.82

2.35

MAC(%)

88.8

59.5

92.6

H1J2. (DoubleStrip %)

NO.

1

2

3

4

FEA

1

2

3

4

Hz

28.68

36.04

47.23

64.00

EMA

1

2

3

4

Hz

42.7

48.4

51.0

94.7

Error{%)

-30.16

-22.62

-3.57

-32.42

MAC(*)

82.6

55.4

80.5

86.4

- 125-

3.1.14 (Swirl Type)

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Type

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

KY

E/N/S

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

OriginalValue

1.53E+005

1.53E+005

1.53E+005

1.53E+005

1.53E+005

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

8.84E+006

1st TunedValue

1.53E+005

1.53E+005

1.53E+005

1.53E+005

1.53E+005

5.79E+006

5.08E+006

1.38E+006

6.41E+005

1.77E+006

2.58E+006

6.98E+006

7.91E+006

1.06E+007

1.02E+007

2nd TunedValue

1.53E+005

1.53E+005

1.53E+005

1.53E+005

1.53E+005

5.62E+006

4.85E+006

1.4E+006

5.78E+005

1.83E+006

2.84E+006

6.86E+006

8.09E+006

1.17E+007

1.1E+007

3rd TunedValue

1.53E+005

1.53E+005

1.53E+005

1.53E+005

1.53E+005

5.47E+006

4.64E+006

1.41E+006

5.24E+005

1.93E+006

3.14E+006

6.64E+006

8.09E+006

1.8E+006

1.05E+006

3.1.15

No.

1

2

3

4

FEA

1

2

3

4

Hz

35.50

44.64

52.83

88.93

EMA

1

2

3

4

Hz

35.19

46.36

49.17

88.64

Error(%)

0.89

-3.70

7.44

0.33

MAC(%)

76.5

44.1

95.9

55.2

- 126-

S. 3.1.16 Chen f Kanazawaofli^M

Name

Chencase 1case 2Kanazawacase 1case 2

Ma(Kg/m)

1.980.376

0.1060.172

d(mm)

12.712.7

12.712.7

L(m)

1.190.914

1.221.22

dh

(m)

0.03810.0381

0.03810.0381

El(N/m2)

139.155.06

39.64150.73

3.1.17 KOFA

Parameter

Density (kg/mJ)Inner diameter (mm)Outer diameter (mm)Span Length (m)Young's Modulus at 310 °C(N/m2)

Value

6.6X10"8.229.70.62

7.98X1010

3.1.18 ^i£«1] n}ef KOFA(typical output of CARO)

BurnupMWD/kg0

8.2616.5224.7833.0441.3049.56

Day020040060080010001200

Axial Force (N)

-477-502-482-444-389-305-203

- 127-

3.1.19

V (m/s)

Force(N)

1

7

15

-470

17.20

17.15

16.94

-500

16.

16.

16.

40

34

12

-440

17.

17.

17.

97

91

72

-300

21

21.

20.

14

09

93

-200

23.

23.

22.

11

07

92

3.1.20

V (m/s)

Force(N)

1

7

15

-470

68.63

68.59

68.42

-500

67.98

67.93

67.76

-440

69.

69.

69.

28

23

07

-300

72.

72.

71.

19

15

99

-200

74.

74.

73.

17

13

98

3.1.21

V(m/s)

Force(N)

1

7

15

-470

142.

142.

142.

68

64

50

-500

142.

142.

141.

14

11

97

-440

143.

143.

143.

21

18

04

-300

145.

145.

145.

66

62

49

-200

147.

147.

147.

40

33

20

128-

3.1.22 ANSYS codeif Hertzo]SA] ofl

a (mm)Accuracy

\ .

(*)0

Inc-718ANSYS. 042883

95

- Zry-4

0.04475.8

0

Zry-4 -ANSYS.051513

99

- Zry-4

0.051833.4

3.1.23mm)

Spring -x- j

Dimple -x-3*H

Inc-718Zry-4Inc-718Zry-4Zry-4

14X140.35/0.42

0.350.350.35

0.725 nom.

16X160.305/0.355

0.3050.305-

0. 640 nom.

17X170.305/0.355

0.3050.3050.48

0.640 nom.

3.1.24

in]4^ ^fi,mm)16X16

i£^17X17

(0.640 nom. )

14X14

(0.725 nom.)

o —1— i— ct ^

-r- l] (mm)

0.305(Inc-Zry^-f)

0.355(Inc-Zry^-f)

0.48(Zry-Zry^-f)0.35(Inc-Zry^-f)0.42(Inc-Zry^^-)0.55(Zry-Zry^-f)

^ - *H(a, mm)

( -§- , N)0.0375(18 N)

0.0375(18 N)

0.04375(18 N)0.05(24 N)0.05(24 N)

0.05625(24 N)

(a, mm)

(^-§-*>^, N)0.04375(24 N)

0.04375(24 N)

0.05625(24 N)0.053125(33 N)0.05625(33 N)0.06875(33 N)

- 129-

3.1.25

^1^2-1

TJl -2

3^3-3

Mode 1

0.124

0.124

0.423

Mode 2

0.420

0.422

0.430

Mode 3

0.427

0.429

0.461

Mode 4

0.461

0.461

0.464

3.1.26

Mesh-1(556)

Mesh-2(1688)

Mesh-3(5872)

Mode 1

0.124

0.124

0.124

Mode 2

0.420

0.419

0.418

Mode 3

0.427

0.427

0.425

Mode 4

0.461

0.461

0.460

l.

« •

27 47|*| T3 O l }— Ol»J ^ ^^ -^-j

Mesh-1

2613.7

Mesh-2

2607.9

Mesh-3

2415.2

Mesh-4

2608.4

- 130-

^ 3.1.1

3-Q 3.1.2 ( 5X5

- 131-

(a)

(b)

^ T 3.1.3

- 132-

^ 3.1.4

^ 3.1.5

- 133-

f

Oh;*a si

IT

r..J

s

i ?

ss

H -

o:i

ZL& 3.1.6

- 1 3 4 -

(a)

(b)

ZL% 3.1.7

- 135-

3.1.8 (3X3

3.1.9

- 136-

(a) Slot

(b) »

3.1.10

h

Slot

- 137-

116

118

107

ZLQ 3.1.11 S

19

15 17

H^I 3.1.12

-138-

(a)

19

18-

IN

20

il

,18

,19

(b)

3-m 3.1.13

- 139-

(a)

115

-121

•122

(b)

H ^ 3.1.14

- 140-

,122

121

(a) H*g ^

-^ 3.1.15

119

1 /

(b) g #

(a)

121

(b)

122

3.1.16

- 1 4 1 -

H ^ 3.1.17

ZL^ 3.1.18

-142-

a ^ 3.1.19

ZIZZ

H ^ 3.1.20 7}^

143-

~L^ 3.1.21

- 144-

(a)

H^ 3.1.22

(b)

- 145-

IS)CO

11.80

ZL J 3.1.23

\

ZL J 3.1.24

- 146-

(Universal Tensile Testing

!

Machine)

I3ic^E>l|£(Cross Head)

i }\

1. AIH3(g¥(Loading Bar)2. AiaCSpecimen)3. XI (Fixture)

HQ 3.1.25

(P6.0

-L^ 3.1.26 A] ^

-147

250

o

200-

150-

100-

50-

Maf 1: 0.6 mm, STS304Double Grid, Kd=395.9

- Swirl Grid, K,=152.9

-H-type Grid, Kh=361.8

0.2 0.4 0.6 0.8

Displacement (mm)1.0 1.2

(a) ^

£

200

160

120

80

40

Mat'l: 0.457 mm, Zry-4

M

••t+-

-Upper Dip., Kud=111.6•Lower Dip., K^=116.2• H-type, Kb=171.2-Multi-1ype, Km=826.3• Swirl-type, K =254.0

0.0 0.2 0.4 0.6 0.8 1.0

Displacement(mm)

1.2

(b) * ]S =

H^ 3.1.27

- 148-

-38.4-12.8 1

38.40

12.80

a D

a D

(a) KOFA g (b)

ZLH 3.1.28

- 149-

38.40

12.80

11

I

"Ulr

I 12.80

38.40

38.40

12.80 .

DD

DD

VI UU U

DD

(c) 3} (d)

H ^ 3.1.28 3X3

150-

12.47 . , 12.8C 12.8-e.

\ I

64.0

=3-

A A

(a) (b)

H ^ 3.1.29 5X5 7j

- 151-

,,12.47 12.80 .

V W f

0 {) i(P

Q

(L_(L_ 4

® 0 P f

)0 0

(?

(c) (d) C f ^ ^ ^

a ^ 3.1.29 5X5 7)*}^

- 152-

ZL^ 3.1.30

6000SST 0.6mm

H spring kH=20.5 KN/mm• - - - KOFA 17x17 k..=35.6 KN/mm

Swirl vane

0.2 0.3 0.4

Displacement(mm)

ZMH 3.1.31 3X3

- 1 5 3 -

3000Zircaloy-4, 0.457mm

Dippertype k =13.6 KN/mtn

• Multi spring kM=14.9 KN/mmSwirl vane ks=20.8 KN/mm

0.2 0.3 0.4

Displacement(mm)

3.1.32 5X5

(a) (b)

ZL I 3.1.33 3X3

- 154-

(a) (b)

(c) (d) 4#>iS

ZL^ 3.1.34 5X5 4

- 155-

Spring Dannper

Accelerometer(ENDEVCO 2225)

Carriage

Force Transducer(RION PF-31)

Guide Rod

Fixture

Specimen

Base

D.Q 3.1.35

- 156-

I-STAR(ver. 4.0)

LABshock machine

FEMtOOls(ver. 1.4.3)

ar- S -

PC

3.1.36

- 157-

(a) zero load (b) energyequilibrium state (c) initial state (d) impact state

D.^ 3.1.37

- 158-

o

1.2

1.0 -

0.8 -

Free fall shock test

"?> 0.6

| 0.4

0.2

0.0

• co =1.27n

__/

/

i

1

_ _ _ i

•

1

•

0.0 0.2 0.4 0.6 0.8

Drop height (m)

1.0

3.^ 3.1.38

- 159-

6000

5000

2 4000

£ 3000

KOFA Grid(3x3 cell)

2000

—ry-

- c -. -A-

- v

- N o- No• No

123

• - Average

40 50 60 70

Drop Height (mm)

80

25

20

3.2 15tsto

<; 10

(a)

KOFA Grid(3x3 cell)

-a— No.1C- No.2

• A- • N o . 3

-V-- Average

40 50 60 70

Drop Height (mm)80

(b)

H ^ 3.1.39 KOFAf

160-

£Q.

4000

3000

2000

mnn

• A- •

_ --v-

^/

Double

-No.1No.2No.3

- Average

/

/

*

1

h .>

_ / ' •

Grid(3x3

V

i ,

cell)

• -

\ " " " * * — •

i i

40 50 60 70

Drop Height (mm)

(a)

80

20

15

038 10

Double Grid(3x3 cell)1 1

—o-No.1- o - No.2•A- No.3

- -v - Average

• / ^ ~

^ _ LJ

• 1 . 1 •

40 50 60 70

Drop Height (mm)

80

(b)

H ^ 3.1.40

- 161-

Q_

7000

6000

5000

4000

3000

2000

1000

Swirl Grid(3x3i

—z~ No.1" - C - No.2

-A—No.3-•<?---Average

1 1 1

/ '

cell)

a//

\

-

40 50 60 70 80

Drop Height (mm)

90

(a)

30

25

3 20o

Swirl Grid(3x3 cell)

to15 -

10 -

40

— o - No.1- c - No2—V- -No.3--V-- Average

1

i i i I • i . i •

50 60 70 80

Drop Height (mm)90

(b)

O.^ 3.1.41

- 162-

7000

6000

gs 5000

2 4000 -

1& 3000

~~ 2000

H Grid(3x3 cell)

1000

1 • 1

— i h - No.1- - c - No.2. • • A- - No.3

—v--Average

>•

' • / '

X~ X - 1 \

1 \ \1 \\\ "Ai -\

• i i i i i i

40 50 60 70 80 90 100

Drop Height (mm)

(a)

H Grid(3x3 cell)

z— No.1- c - No.2

A- • No.3--V--Average

40 50 60 70 80 90Drop Height (mm)

(b)

H ^ 3.1.42

- 1 6 3 -

Q .

7000

6000

5000

4000

3000

2000

inoo

3x3 cell grid

—a— KOFA Type- - o - Double Type

• -A - Swirl Type- V - • H Type

-

\\

\

40 60 80

Drop Height (mm)100

(a)

253x3 cell grid

20 -

15 -

i

- o-• -A-

- V

_

i"

I ' i

-KOFA TypeDouble Type

• Swirl TypeHType

/ ;

/ ^

i ' 1 ' 1 '

\

X •., \X " \ •

40 50 60 70 80

Drop Height (mm)90 100

(b)

3J% 3.1.43 3X3

- 164-

8

AC\r\n

3000

2000

1000

n

Swirl

-

Grid(5x5cell)

i ,

—c— No.1- o - No.2. . A- • No.3— -No.4- O-- Average

i i .

40 50 60 70

Drop Height (mm)

80

(a)

20

15 -

Swirl Grid(5x5 cell)

3cQ 10t3

5 -

40

1 1 • 1 I

fe^"^ „ . - • • • - " - • - -

— o —- - A- -

- O

-

No.1No.2No.3No.4Average

50 60 70

Drop Height (mm)

(b)

80

3.1.44 5X5

- 165-

5000

4000 -

3000 -

oz: 2000Ha.

— 1000

40

H Grid(5x5 cell)' f • 1 '

-S^yS

• l i t !

—z— No.1- - : - No.2- A- - No.3

No.4- 0 - - Average

50 60 70

Drop Height (mm)

80

(a)

H Grid(5x5 cell)

40 50 60 70

Drop Height (mm)

3.1.45

(b) *

5X5

- 1 6 6 -

5000

1000

Dipper grid(5x5 cell)

- e - No.2- - No.3

- V No.4--O-- Average

50 60 70 80

Drop height (mm)

90

(a)

Dipper grid(5x5 cell)

50 60 70 80

Drop height (mm)

(b)

90

n ^ 3.1.46 5X5

- 167-

5000

4000

g 3000

I£ 2000

Multi grid(5x5 cell)

1000

- - £ -. . A-

- o-

-No.1No.2No.3

-No.4Average

/?.'•/'

i | i | i

_ * * " * * • .

• I . I .

40 50 60 70

Drop height (mm)80

(a )

Multi grid(5x5 cell)

40 45 50 55 60 65 70

Drop height (mm)80

3.1.47

(b)

^ s s j 5X5 A*\H$\

- 168-

5000

4000 -

3000 •

I" 2000

5x5 cell grid

1000

/ / ' \/ Ji

f ••

= /

. i

-

—c—Swirl Type- c - H Type• -A- Dipper Type- V - MultiType

i

40 60 80

Drop Height (mm)

100

(a)

18

16

3o

14

12

<: 10

~ I

5x5 cell grid

f-r ,

\X \

- c -. -A- -

- v-

Swirl TypeHTypeDipper TypeMultiType

40 50 60 70 80

Drop Height (mm)

90 100

(b)

3.^ 3.1.48 5X5

-169-

(a) No. 1 (b) No. 2

(c) No. 3

H ^ 3.1.49 KOFA j 3X3

~ 170

(a) No. 1 (b) No. 2

(c) No. 3

H1J 3.1.50 3x3

- 171 -

(a) No. 1 (b) No. 2

(c) No. 3

3.1.51 3X3

- 172-

(a ) No. 1 (b) No. 2

(c) No. 3

H^ 3.1.52 3x3 -g

- 173-

* : T :»• **;

(a) No. 1 (b) No. 2

(c) No. 3

n.% 3.1.53 5x5

- 1 7 4 -

(a) No. 1 (b) No. 2

(c) No. 3

H^I 3.1.54 5X5

- 175-

(a) No. 1 (b) No. 2

(c) No. 3 (d) No. 4

a*U 3.1.55 5X5

- 176-

(a) No. 1 (b) No. 2

(c) No. 3 (d) No. 4

n ^ 3.1.56 ^ 5X5

- 177-

11.5 166

(100 x 20 = 2000)

100

Free Height = 200 Pb Pellet

2189

H ^ 3.1.57

accelermeter signal

1force signal

modal analysis(analysis SYS)

trigger input

data acqusition(acqusition SYS)

patchpanel

accelermeterconditioner

itanti-aliasing

filter(acqusition SYS)

H*& 3.1.58

- 178-

H ^ 3.1.59

I ,

1

n^ 3.1.60

- 179-

• • • • v•"•V-1.;

•• • • • ? . ' • ' • • • , • . > • •

. • - .'i

..jjT .••

.• > - • " '•

*

J l ^ 3.1.61 accelerometer

D.^ 3.1.62 ^

180-

4-Q6 drill throughl4-o]0 dcplh30 counlerbort

4-M5. depth 10

°i i+

Detail \ Bird Eve View Magnel Holder VIEW A

Ar---

J ! !\T Fuel Bod fixtta

I 13x^04 = 3121 I IQZ i 3x102=306• SO* I ' • » 3XJ08.US1

A'L

—1

l i

-HU 3.1.63 I E

- 181-

g/K|A ; 3/10 3/10 - 3/10A:H

( I r 1 I r

0.2 mm0.6 mm1.4 mm

80 30 ICO Hz

3.1.64 3.7]

Fretting Wear Test Result (2nd, Apr 07, 2000)

Axial DepthTransverse DepthAxial Width

I | Transverse Width

H Swirl Dip(U) Dip(L) Mul(U) Mul(L)

Spring Type

HQ 3.1.65 X\i&

- 182-

Dimple

Spring Fuel Rod

a) Rod Supported by Grid Spring

b) Rod Vibration Model by Tranrational and Rotational Spring

ZL^ 3.1.66

- 183-

cw6CDOrd

a,

Q

>•rH

mr-H

mode 1

mode 2

mode 3

mode 4

mode 5

i • r

I I

38.06 Hz

42.42 Hz

47.88 Hz

71.10 Hz

110.5 Hz

0.0 0.2 0.4 0.6

Relative Length

0.8 1.0

H ^ 3.1.67 Swirl

- 184-

1 i i i i i | -

mode 1

g(DO03,—I

aCO

a

01

mode 3

mode 4

mode 5

I . I0.0 0.2

I I ,

0.4 0.6

Relative Length

42.72 Hz

46.69 Hz

51.54 Hz

81.55 Hz

121.1 Hz

0.8 1.0

H ^ 3.1.68

- 185-

mode 1

mode 2

cg<x>u

CO•H

Q

0)

•H

4JtO

<-\

mode 3

mode 4

I

28.65 Hz

35.83 Hz

46.63 Hz

62.93 Hz

101.6 Hz

0.0 0.2 0.4 0.6

Relative Length

0.8 1.0

3.1.69 Double pla ted

-186-

I

oo

i

uCO

II—I

CD

CD

5

ojnc

CO

Hin

Relative DisplacementpCO

I—I

o

o

cT13

r+CD

Relative Displacement

Inot

(Dh-•0)rtH-

(D

tr1

CD

rttr

0000

uCO

CO

aotraT

(t>

Relative Displacement

o[n:

Hin

(D

r+

U

CO

roaocr0)

r

Relative Displacement

o|n;i£CO

faIn

°±a.

0.4 0.6 0.8

Relative Length

1.0

ZL^ 3.1.74 Double p l a t e d

- 189-

Test Environment: Water-Low

Force Level: 0.5N

I5" 2<nT3OCOCD

T 1

§ 1fto'

20 40 60

Frequency(Hz)

(a) FRF vs . Frequency

! i : jI : . ;

i n

• I Ii iO I

- hiiW\

\^ ~ Swirl Type° H Type" Double-Strip Type

!i |

i

• |

Test Environment: Water-Low

Force Level: O.SN

.08

•a

3 .04CD

l .02

0.00

—L_

_ Swirl Type* H Type" Double-Strip Type

i 1i

1 i

! ; IT i1 1

ao20 40 SO

Frequency(Hz)

(b) Displacement vs. Frequency

100

ZL^ 3.1.75

- 190-

Test Environment: Water-Low

Force Level : 0.5N

Tl

Tl-n 4-

|

Ienno

i

1 i !

1 i Tr rlt:* Swirl Type. H Type

Double-Strip Type

i

20 40 60

Frequency(Hz)

(a) FRF vs. Frequency

80 100

Test Environment: Water-Low

Force Level : 0.5N

.08

n 0 6

"a

83 .04(D

3• = • .02

o.oo

j I

AI

1

!Swirl Type

~ p ~ H Type" Double-Strip Type

1u 1 i

;

| i :

; i

;

! 120 40 60 80

Frequency(Hz)

(b) Displacement vs. Frequency

3.1.76

191-

Test Environment: Water-High

Force Level: 0.5N

Swirl TypeHTypeDouble-Slrip Type

40 60 80

Frequency(Hz)

100

3.1.77

SensiMyNonnafeed

Response

1E-2

1E-25

4

3

2

1

0

r5

.4

.3

.2

.1

.0

Parametef

a?J 3.1.78 A ^ H]ji(Swirl

-192-

SensitivityN a

1E-2

3.5

3

•2.5

• 2

1.5

1

0.5

0

Parameter

ZLQ 3.1.79 ^ S aj

Sensitivity

Response

1E-3

.6

Parameter

H^ 3.1.80 ^ S

- 1 9 3 -

Iteration No.

a^} 3.1.81

- 194-

o•H

G

o•H

U

0.01 -

0.003

• Test dat.O— Chen ' s mode!

—•— Present model

4 5 6 7 8 9 10

Velocity (m/s)

20

ZL% 3.1.82

o•H

05

c•H

aQ

o

uu

0.1 -

H 0.01 -

0.004

• Test data[20]-n— Kanazawa's model[20]-O— Present model

4 5 6 7 8 9 10Velocity (m/s)

20

H ^ 3.1.83 Kanazawas^

- 195-

10-

1 -

cCDgCDOU

roaCO•H

Q 0.1 - — • — Chen's model(case I)— A — Present model(case I)

Chen's model (case II)present model(case II)

5 6 7 8 910 20

Velocity (ft/s)

30 40 50 60

ZL^ 3.1.84 Chen

- 196-

-H

- P

CDea;o(0

to•H

Q

10-—a

•—A-

I

Test data (case I)

Present model(case

Test data (case II]

Present model(case I I '

1 -

0.16 7 8 910 20

Velocity (ft/s)

30 40 50

ZLQ 3.1.85 Kanazawa H|J2.

- 197-

Dimple

Spring Fuel Rod

a) Rod supported by grid spring

rfrb) Rod vibration model simplified by rotary and bent

spring

H ^ 3.1.86 i ^ ^ l

- 198-

Cn

Q

PQ

5 0 -

4 0 -

3 0 -

2 0 -

1 0 -

0 -

0 200 400 600 800

Burnup (day)

1000 1200

-100

-200

-300

-400

Ax

ial

on0)

-500

-600

-L^ 3.1.87

- 199-

A x i a l F o r c e (N)

-470 -500i . i

200 400 600 800Burnup (day)

1000 1200

3.Q 3.1.88

Axial Force (N)-440

200 400 600 800Burnup (day)

1000 1200

-L^ 3.1.89

- 2 0 0 -

F r e q u e n c y (Hz)

urfH,00

*

O

• •

Fn

rJ£°bi

r|iu

MCO

too

F r e q u e n c y (Hz)

Ol-i0CD

ofn-ft-Ja

r|iu

COOto

uCO

CO

r£

m

Relative Displacement

ob

?0fD

01rt

f1

fD

r t

©

CD

O

bo

inIX

oCD1

v «

o

|

p o, 1 t

y

] i

II

i

mooz

Oboi

\

)

IIII

i

rooo

21

uCO

CO

I Ti r

ojn;

tub

Jl

mi

inrt

Relative Displacement

pb'

oho

50fDt-1

0)rt

r t

pcn '

pbo '

0

b1 1

0ho1

II

enOO

Z

• • •

O

, 1

11

Tl11

II

1

(-O0O

Z

O p ->•O) 00 OI . I . I

COV-

1J//'J

rooi

uCO

CO

o(n;

r-fr

nib

pb

pho

QJ

rt

tr1

r+

pen

pbo

Relative Displacement

I*In

uOJ

CD

o(c;

r-D-_>^

nib

Hin

&j

rt

tr1

r t

Relative Displacement

pb

pho

p

obo

0.7-

1 •'} / / x ' " " - ^ ^ r ••••-..

\\

\

N.

X

V=l m/s- V=3 m/s

- - - - V=5 m/sV=7 m/sV=10 m/sV=12 m/sV=15 m/s

200 400 600 800 1000 1200 1400 1600

Frequency (Hz)

H*y 3.1.96

•

0.1 -

0.01 -.'•

•

•

•

1E-3-

•

.... v=l

V=3V-5V=7

V=10

V-12

m/sm/sm/sm/sm/s

m/sm/s

v \ \ \ \

\ w •.\ • " • • • ^

\ • • • . \

\

\

•

\ \

\ *

\

\

• . . '

1

F r e q u e n c y (Hz)

10

He] 3 - 1 .97 ix}^-

acceptance Jl

Joint

- 2 0 4 -

.

0.1 -

-

-

n m -U.VJ I ~

-

-

1E-3-_-

• i i i i

""*,\

\

V=l

V=3

V=5

V=7

v-ioV=12\T. ~\ c:

1 " " I I T )

, , , i

I

i

/m/sm/sm/sm/s

m/sm/sm/s

-r-r-TT

1

/ N • / / \ ' '

' \ / v'

\ 1 •' X:

\

\\

\

' I

\*

\ / \

sV)•V/ /

7\/ \\\\\

\

>.yr\ •

( \ \ :t \ -\ * \

\ \ * 'I \1 •1

\ \ *

\ \« \% \

\ ^ :

\ •

\ * t •

\

\

\ :

\ :

1

Frequency (Hz)

10

ZLQ 3.1.98acceptance J32

Joint

- 205-

1200 day

//I • I T .

7 IE-13g 1E-17§ 1E-9JS, IE-13S-1E-17

20 40 18020022024026

Frequency (Hz)

i • i • i • i18020022024026040

Frequency (Hz)

3.1.99

PSD

3.1.100 PSD

- 2 0 6 -

roo

uto

•£ -ft

rftrliu

ojn:

ooH-rr•<

Critical Damping Ratio

po

ooI

po

j

Freq.

II

23.

ccN

HFreq.

Freq.

» II

r ?pc mN N

T

Freq.

II

16..

N

M0 0

Critical Damping Ratio

it ±,it to

riiu

ojn;

P

a

0)O

I P.

p

poho

_j

pb

i

pb

pbCDi

Freq.

1!

17.

N

T

1T1

Freq.

II

i—1

<n

a:

I

Y-Axis: Displacement (mm)

CO

I—*

I—'

o

too00

ojn:

1*

p o o o oo o o o i—

CO

oCO

Critical Damping Ratio

to1-1

a

o[iE

00oo

ooo

N3O

o

p p

T X^SpacerP Grid

(a)

3.1.105(a) rubbing,

tapping or impacting; (b) whirling

VibratingFuel Rod

SpacerGrid

CoolantFlow

He] 3.1.106

-209-

D.Q 3.1.107

0.8

0.7

0.6 K

0.5

0.4

0.3

0.1

•—refined by 1/2•—refined by 1/4•-- Theory

o ooo 0.2 0.4 0.6X/a

0.8 1.0

25J 3.1.108 Hertz

- 2 1 0 -

3.1.109

0 th T

ZL^] 3.1.110

- 2 1 1 -

0.8

0.6

0.4

0.2

n n

SL

- 1P

- /

7f

Exact solution

\ /

sL1P

\

-1.0 -0.5 0.0

y/a

0.5 1.0

3.1.111 Mindlin-Cattaneo ^/ fiP= 0.5

Hm 3.1.112 (Or < Qy °i

- 2 1 2 -

1.0

-1.0

Q/AP=0.33

a ^ 3.1.113

1.U

0.8

0.6CL

a*0-4

0.2

no

~ 2-~ O + O

\ \

1 \\

1 , 1 p 1 1

= (fF)2

\ \

\ \

0.0 0.2 0.4 0.6 0.8 1.0

H^l 3.1.114 ^7]- Compliance

-213-

0)

a>ojoQ .CO

CD>

a:

Q//P =OfT^\

STICK X .

0.5

0.33

0.2

0.1

SLIP

.V0.0 0.2 0.4 0.6

y/a0.8 1.0

H ^ 3.1.115 ^ (Qy/vP= 0.33)

0.0 0.2 0.4 0.6y/a

0.8 1.0

ZL^ 3.1.116

- 214-

I

I

1 2

1

6

b

0.2

6:o"

Ay 0.0

4

6•-»

1

-0.5 0.0 0.5

3.1.117 ^ * f# 3 3 : (a)(b) * f l^

-0 .5 •

-1.0

(a) (b) 1-2

-1.0

(c) (d) 2-3

- 215-

1.0

0.5

a-Or" 0.0

-0.5 -

-1.0-1.0

sLIP

/

\

1

SL1P

\

-0.5 0.0

y/a

0.5 1.0

0.5 •

a-cf" o.o

a-

-1.0-1.0

sLIP

q,qy

sLIP

-0.5 0.0

y/a

0.5 1.0

(e) (f) 3-4

0.5

a-Or1 0.0

.1 n

sLIP

\ , — q.

siip

A

-1.0 -0.5 0.0

y/a0.5 1.0

-1.0

(g) (h) 4-5

1.0

0.5 -

•B-

0.0

-0.5 h

-1.0-1.0

.s

. L• ]

q,

sLI

-0.5 0.0

y/a

0.5 1.0

( i ) ( j ) 5-6

- 216-

1.0

0.5 -

Cr" 0.0

-1.0

sLIp

V21

Q,

. . . . i . . . .

sL1

-1.0 -0.5 0.0

y/a

(k)

ZL J 3.1.118 H^ 3.1.117^ 4

0.5 1.0

nf j 3.1.119

H ^ 3.1.120

- 2 1 7 -

(X10"2)0.5

0.0

o-0.5

-1.0 -

-1.5 -0

'. Crack*

-.

Closusuren°u

10°20°

30°

i i

•y * ^ ^

\ " \ ^ ^

N ^

N * \

\ N^

\

\

\

\

• t

2 32a/w

(a)

(X10'2)

(X102)1.0

0.8

o

^ 0.4

0.2

0.00

10°

20°

30°

(X10"2)

l ^ j 3.1.121

(b)

(Q / UP = 0.36, U = 0 .3 ) : (a) Kr, (b) Kn

218-

n.m 3.1.122 IHg 3.1.121^1

(X10~2)

3.1.123 3.1.121^

- 2 1 9 -

+ Q

Qmax

0

omm

1 2 3 4 5

(X10"2)

(a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13Load Point

(b)

time

U.*g 3.1.124 (a)

\Q\ = 2Qmax / 3 , Qmin =

= 0.36, fi = 0.3

fflax / 3, *}^-%- C^ ): (b) £

- 2 2 0 -

H ^ 3.1.125

H^ 3.1.126

-221-

Swirl Grid Spring

Mat'l: Zir-4, 0.457 mm Thick

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Displacement (mm)

ZL% 3.1.127

ZL^ 3.1.128

- 2 2 2 -

(a)

tl.48E+O2

- tl.73E+02

- +1.97E+01

- +2.21E+02

+2.46E+02

+1.71S+02

• t9.89E-01- ti.9BE-D3

- +2.97E-03

- + 3.95E-0.3

- +4.94E-03

tO.93E-03

(b)

ZL^ 3.1.129

- 223-

1a1

IT

H& 3.1.130

edges 1

point 2

edges 2

point 1

H1I 3.1.131

- 2 2 4 -

(Mode 1)(Mode 2)

(Mode 3) (Mode 4)

ZLB] 3.1.132

c^

(a) (b) (c)

ZL5j 3.1.133

-225-

6000

5000 -

2.5E-05 5E-05Displacement (m)

7.5E-05

3.1.134

3000

2500

Mesh-1

Mcsh-4

0 5E-05 0.0001 0.00015Displacement (m)

0.0002

H^ 3.1.135 47}^|

- 2 2 6 -

A c

r v

3.1.136 3X3 ^

3.1.137 3X3

- 2 2 7 -

n.^ 3.1.138 5X5

6000

0.0002 0.0004 0.0006Displacement (m)

0.0008

T.S] 3.1.139

- 228-

3.1.140

asymmetry

- 229-

3.1.142

3.1.143 /-fl^-Sf

- 2 3 0 -

0

Fine Mesh

Refined Mesh

5E-05 0.0001Displacement (m)

0.00015

n.^ 3.1.144

3.1.145

- 231 -

6000

5000 -

I£co"8a:

4000

3000

2000

1000 -

1 ' 1 ' t ' J

' - ' • • / • A--.\/ • • • • • . . •=

/ / ' * ^

— ^ - N o . 1- -:- - No. 2

No 3—r—No 4

No. 5No. 6

- » - 6-pdni welding model- • - 1-point welding modeJ

0.0 0.2 0.4 0.6 0.8 1.0

Displacement (mm)

a ^ 3.1.146

H ^ 3.1.147 3X3

- 232-

Initial Velocity

1

• y

ZLBl 3 .1 .H8 H

mass

\rigid surface

spacer grid

A () C) O

6000

5000 -

4000 -

3000 -

8f

2000 -

1000 -

H Grid (3x3 cell)

.

r

//

/

/

\

\

00.0 0.1 0.2 0.3 0.4 0.5 0.6

Initial Velocity (m/sec)

3.1.149

- 233-

o

o03

plate thick. 0.6 mm

30

Total Time(ms)40

ZL^ 3.1.150 S.7] 0.40

SECTIO1I POI11T 1

M3SES VALtE

- +2.57E+07

— +4 ,49E+07

~ t-€.7QE+07

t».92E+07-+ l . i iE tOf t

- +J .56E-K3S

,1— +1.73E+0S

\

cornerleg'

ZL& 3.1.151 0.40 von Mises ^7f-g-

- 2 3 4 -

- t».35E-03

- +4.69E-0i

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TFC2D 3 . ^ # 7 H ^ } ^ l ^ f l b i ^ ^ ^

^ ^ ^ > I ^ ^ ^ ^ ^ ^ f 4 SIMPLER

TFC2D 2 H

n

3.711

^3 " ^ ^ ^ ^ ^ *~'\ . •( 1 I VJLIL'

QUICK 9-^7} 4-g-5lJL al-^-1^ 7lEf ^Af5] - ^ - ^ S . ^ Central

^ 5 7 M -?^7f Af-g-SJJL &CJ-. QUICK

QUICK 9 ^ 5 ]

- 326-

- 3 2 7 -

.2.1

£%^7fl

^3l«g ^7fl(W)

^£*1*1 ^7fl(ABB-CE)SJ #-&-•§•

£^7fl

^ < g ^ 7 H

^ ^ U ^ 7 i |

^7H 7 | | ^

2

2

4

2

8(4)*

2

30°

90°

35°

45°

N/A

35°

#*1 ^7|{

^ ^ ^ ^ ( m n , 2 )

10.7

8.6

5.2

6.2

6.6

13.2

^ i ^ l ^7fl

^ ^ ^ ^ ( % )

23.8

19.1

23.1

13.8

28.3

29.4

44o]

- 328-

3.2.2

£^1*8 ^7fl(I)

(ABB-CE)

H } 7 M ^ y-7ii

3.7]

1.226

0.678

0.823

0.311

0.281

1.120

3.7]

1.258

0.735

0.0

0.454

0.760

1.380

letfr J- 371

0.0033

0.0033

0.0018

0.0023

0.0027

0.0055

&}(*)

36.5

22.3

8.4

14.3

69.1

34.4

(1)

(2)

(3)

(4)

3.7} = r38

^ i . i D h

3.7] = r

kchajV\uik

0.0)

0.0)

f 0.002)

- 329-

13.2.3

De Stordeur

(1961)

Rehme, K(1973)

Kim, N.H.

(1992)

s

S(\-s)2

K = C e2

V

( 2L} EA. — 1 C 4- C

(fe>105)Rehme (1973)

a = 6 ~ 7

(*e>M0<>

Cevolani, S (1995)

Cv=5+6133 i?e"0789

in(a)=7. 690-0.942in(i?e) +0.0379 in2 (/?e)

0/ - 0.9 ; oi*}4i 4 4 3g2>

- 330-

S. 3.2.4

is gridt^form

ry' mixing

form

Grid Elements

Strip

Spring

Dimple

Nugget

Mixing Device

Shape

Blunt

Stream shape

Horizontal

Vertical

Horizontal

Oval

Upstream

Downstream

frf-

0.9

0.45

0.45

1.2

0.45

0.76

1.17

0.42

1.17

- 3 3 1 -

13.2,5

\ i G r i d Type/X^Grid Shape

Parameters \ .

Rod Diameter, [mm]

P/D

Grid PluggingArea, £

Grid Height,[mm]

Strip Thickness,t [mm]

Mixing Device

PWR Type

Square(Wevy strap)

PI

9.7

1.314

0.333

35

0.58

P2

9.7

1.314

0.412

51

0.64

Square

(straight strap)

P3

10.75

1.330

0.289

48

0.575

P4

10.75

1.330

0.287

45

0.577

Non-splitVane

P5

9.5

1.337

0.251

40

0.453

SplitVane

FBR Type

Rhombus

Rl

12.

1.275

0.250

10

0.73

Honeycomb(T)

R2

6.

1.317

0.441

8

0.83

Honeycomb

(S)

R3

12.

1.213

0.254

12

0.86

T: Triangular Array

S: Square Array

3.2.6 P4 4

Re \

3x104

1x10"

Fraction of Individual Term

form

45 %

50 %

16 %

11 %

7/" rod

19 %

17 %

form

20 %

22 %

Grid LossCoefficient

K

1.60

1.43

- 3 3 2 -

13.2 .7

1. Region of interest(control volume)

2. Onset of CHFOccurrence

3. Influence of

upstream condition

on CHF

Liquid Sublayer Dryout Model

Thin liquid film between heating wall

and intermittent vapor blanket

Complete evaporation of the liquid

film during the passage time of vapor

Local condition type

(regardless of the upstream condition)

Bubble Crowding Model

Bubble boundary layer

Critical bubble packing in the bubble

boundary layer which can inhibit the

supply of cooling water from liquid

core to the heated wall

Semi-local condition type

(affected by integration of the

generated bubble from the bubble

detachment point)

3.2.8 4 2-^$] <^

Proposed model

Lee & Mudawar1*'

Celata1*'

Kattol*J

Weisman & Pei

Bowring

Look-up Table

N

2249

638

426

528

2261

2064

2261

A«(R)

1.00

1.06

0.85

1.02

1.09

0.99

1.01

r.m.s. e

0.104

0.157

0.183

0.129

0.133

0.094

0.059

aCR)

0.104

0.145

0.101

0.127

0.092

0.093

0.059

Subcooled data only (640)

- 3 3 3 -

1 3 , 2 . 9 cfl*}

R-l lLeung(1980)

R-12

Stevens(1980)

Merilo(1979)R-113

Coffield(1969)

TV

20

75

22

MR)

1.09

0.98

0.96

r.m.s. e

0.183

0.058

0.085

<T(R)

0.161

0.056

0.076

3.2.10

S.'i Identifier

IMO=1

IMO2

IM0=3

IM0=4

IM0=5

IM0=6

IM0=7

IM0=8

IM0=9

Turbulence model

Standard(1974)

Jones - Launder (1972)

Launder-Sharma(1974)

Lam-Bremhorst(1981)

Chien(1982)

Nagano-Hishida(1987)

Myong-Kasagi(1990)

Nagano-Tagawa(1990)

Chang-Hsieh-Chen(1995)

Model type

High Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

Low Reynolds number model

- 334-

3.2.11

Scheme identifier

ISCHEME=1

ISCHEME=2

ISCHEME=3

ISCHEME=4

ISCHEME=5

ISCHEME=6

Scheme type

Central difference

Upwind difference

Hybrid difference

Power law difference

Exponential difference

QUICK difference

Scheme order

Low order scheme

Low order scheme

Low order scheme

Low order scheme

Low order scheme

High order scheme

3.2.12

Continuity

Momentum

Kinetic energy

Dissipation

4>1

V

k

£

AMe

0

Ml

Me

s40

[v -(^v~^) + pl]pT• • v v — pe

CJxP T • • v~ve/k- C&f2pe2/k

0

0

D

E

3.2.13

Standard(1974)

Jones-Launder(1972)

Launder-Sharma(1974)

Lam-Bremhorst( 1981)

Chien(1982)

Nagano-Hishida(1987)

Myong-Kasagi(1990)

Nagano-Tagawa(1990)

Chang-Hsieh-Chen(1995)

c.0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

cA1.44

1.45

1.44

1.44

1.35

1.45

1.40

1.45

1.44

c&1.92

2.00

1.92

1.92

1.80

1.90

1.80

1.90

1.92

1.0

1.0

1.0

1.01.0

1.01.41.4

1.0

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.3

1.3

- 3 3 5 -

3.2.14 -g- / „

Standard(1974)

Jones-Launder (1972)

Launder- Sharma (1974)

Lam- Bremhorst( 1981)

Chien(1982)

Nagano-Hishida(1987)

Myong-Kasagi(1990)

Nagano-Tagawa(1990)

Chang -Hsieh -Chen (1995)

1.0-2.5/(1.0+i?,/50.0)

e- 3.4/(1.0+ #,/50.0)z

e( 1 . 0 - e~°-0165^)2(1.0 + 20.5/Rt)

LO_e-o.oii5>-

a.o-e-*'176-0)2

(l.0-e-y'noo)a.0 + 3A5/R°l-s)

(1.0- e- r / 2 6- 0) 2(1.0 + 4.1/i??-75)

(1 .0 - e"00215;?t)2(l.0 + 31.66//?P5)

3.2.15 /2

Standard(1974)

Jones-Launder(1972)

Launder-Sharma(1974)

Lam- Bremhorst( 1981)

Chien(1982)

Nagano-Hishida(1987)

Myong-Kasagi(1990)

Nagano-Tagawa(1990)

Chang-Hsieh-Chen(1995)

/ i

1.0

1.0

1.0

1.0 + (0.05//^)3

1.0

1.0

1.0

1.0

1.0

h1.0

1.0-0.3e"^

1.0-0.3e~*?

1.0-e"*1

1.0-0.22e~(/?l/6)2

1.0-0.3e"^!

a.o-2/9<r(*'/6)2)(i.o-e^+/5)2

(1.0-0.3e"W6"5)2)(1.0-e-^ / 6)2

(l.O-O.Ole'^Xl.O-e"0-0631^)

- 336-

JJ- O, t-r. 1 U 1

Standard(1974)

Jones - Launder (1972)

Launder-Sharma(1974)

Lam-Bremhorst(1981)

Chien(1982)

Nagano-Hishida(1987)

Myong-Kasagi(1990)

Nagano-Tagawa(1990)

Chang-Hsieh-Chen(1995)

D( fc-equation)

0

_IL( dk\2

2k\ dy)

.JLl dk\2

2k\ dy)

0

-2Mk/y2

_JJ_I 8k\2

2k\ dy)

0

0

0

E( e-equation)

0

0

-2ttetfe-0-5y~

(1.0 fM(\$)

0

0

0

- 3 3 7 -

23

•21

3.2.1

21

i U—"

H^I 3.2.2 15J 3.2.3 +^%

- 3 3 8 -

3-% 3.2.4

ZL^ 3 .2.5 ^ofl 4^-

- 339-

D.Q 3.2.6 £1

- 340-

14

D.m 3.2.7

"L^ 3.2.8

- 3 4 1 -

•12(14)

H.^ 3.2.9 ^l(strip)

28

12(14)

22

zi5i 3.2.10

- 342-

i

ij

Split-vane

(ABB-CE)

Split-vane

(Westinghouse)

Side-supported vane

(ABB-CE)

Swirl-vane Duct-vane Dipper-vane Twsited-vane

HQ 3.2.11 CFD

- 343-

1.4

1.2-

s 1.0-

0.8-MeasuredPredicted

0.0 0.5 1.0

X/P1.5 2.0

1.0-

0.8-

• • "

• •

- - •

•

— • - MeasuredPredicted

0.0 0.5 1.0

x/P1.5 2.0

1.2

0.8

— MeasuredPredicted

0 0 0.5 1.0

X/P

1.5 2.0

1.2

0.8

MeasuredPredicted

0.0 0.5 1.0

X/P1.5 2.0

1 0-

0 8 -

z/D=15.9

• • • • • • - • .

• •

• •• •

•

•

••••— Measured

Predicted

0.0 0.5 1.0

X/P

1.5 2.0

1.2-

1

LO-

OS-

Z/Oh=26.5

. . • " . . . . . • " • . -

- • MeasuredPredicted

0.0 0.5 1.0x/P

1.5 2.0

axi

al

bulk

1.2-

1.0!

0.8-

z/Dh=38.5 |

- • " • • - . . . . • • • • •

• - • • - Measured- Predicted

0.0 0.5 1.0

X/P1.5 2.0

0.0 1.0

X/P

2.0

O.5J 3.2.12 split-vane)

- 3 4 4 -

0.4-

0.2-

10.0-

0.2-

0.4-

OR-

z/Dt

I•

a

=1

a

ZJ -•B

/ a

aB

B

a

B

B

-• a

B

" • •MeasuredPredicted

0.0 0.5 1.0

x/P1.5 2.0

u.o -

0.4-

0.2-

0.0-1

-0.2-

-0.4-

-0.6-

z/Dh=2.1 j "

B

B

••

I > I

• ' • aB

a a

a MeasuredPredicted

' 1 •

0.0 0.5 1.0

X/P

1.5 2.0

0.2-

0.0,

-0.2-

-0 4-

1

a

• a a

BB

aB • " •

• ""•--. a a

a

- • - B - -

B

' B

" a

MeasuredPredicted

0.0 0.5 1.0

X/P

1.5 2.0

0.2-

0.0'I

-0.2-

0.0 0.5

MeasuredPredicted

1.0

X/P

1.5 2.0

0.2

^

-0.2

I =15.9

0.0 0.5

• BMeasured

- Predicted1.0

X/P

1.5 2.0

0.1

-0.1

Z/Dh=26.5

0.0 0.5 1.0

X/P

MeasuredPredicted

1.5 2.0

0.0-

-0.1-

z/On=38.5

—a — MeasuredPredicted

0.0 0.5 1.0

X/P

1.5 2.00.0 1.0 2.0

n.^ 3.2.13 it-vane)

- 3 4 5 -

0.05

0.04-

0.00

Center GapMeasured • •

-10 0 10 20 30 40

nm 3.2.14 ^7B(split-vane)^

0.25

0.20-

0.05-

0.00

D.Q 3.2.15

—•— Measured—•— Predicted

10

d7fl(spl

20

it-vane) 3.7}

- 346-

VTO, Split-vane(W)\**I^.*if Side-supported

vane (ABB-CE)

Swirl-vane

• r r f * > . \/r f !• r '

/ ? r .> ,-

>*•""•• < « i if

Y.W'iWl Duct-vane

Dipper-vane V Tw i s ted -vane

3.2.16

- 347-

A.V\

di:

T f n \

•'••'••'^^...^VV-.N-X

-. -^ ^ iTi"

» • • i

..,-•-•!

H ^ 3.2.17

- 348-

V-«-. »- "•

•*S>Sja

r ,' .» ;r »t •

«

i * •

, < < .

\

s

n

X

\\

f ,

g

I!

/

\

U

is.

f

• *

t:;;:;;;r : i;-;;?!;:;;

; ; . . - ^ ' n

.-•ft f • • ^ .c

r i T •'

' ' '!

O.^ 3.2.18

- 3 4 9 -

1.3-

1.2-

1.1-

1.0-

0.9

• • - z / D B = 1 . 1

» z/Dh=&5

*- z/DB=38.6

^ '"

•

* *

T T

•

Z«=2.1 * z/D=4.2

2^=15 .9 •*- z/D=2G.b

, . • • • • > - • , .

Split-vane (W) ^ ^

0.00 0.25 0.50x/P

0.75 1.00

1.4

1.3-

1.0-

0.9-

0.8

z/DB= 1.1

»••• z/D =38.6

!, , ! Side-supported'vane

0.00 0.25 0.50x/P

0.75 1.00

1.3

1.2-

^ 1-1"

0.9-

0.80.00 0.25

z/Dh=26.5

* * • » » •

Swirl-vane

0.50x/P

0.75 1.00

1.3

1.2-

1.1-

1.0

0.9-I

0.8

z/DA=1.1 --T

Z/D =2.1 » z O = 1 5 . 9

Z/D=26.5

its'

0.00

Duct-vane

0.25 0.50x/P

0.75 1.00

1.4

1.3-

1.2-

1.1-

1.0-

0.9-

0.8-

0.7

z/0^1.1 T z/Dh=8.5

z/D=2A o z/Dfc=15.9

0.00 0.25

Dipper-vane

0.50x/P

Z/D=26.5

0.75

1.3

1.2-1

^ 1.0-

0.9-

1.000.8

z/D=2A

- Z/D =4.2

z/D =8.5

• z/DB=15.9

< z/D =26.5

: * : • •

0.00 0.25 0.50x/P

Twisted-vane

0.75 1.00

H ^ 3.2.19

- 350

0.4-

0.2-

0.04

-0.2-

-0.4-

• z/D=\A • -o—z/Dft=15.9

•--• z/D =2.1 * - z/D =26.5 . . • • . .

A- z/Dh=4.2 ->-z/D ) )=38.s). ' ••••i*.

Split-vaneQV)

0.00 0.25 0.50 0.75 1.00

0.4-

0.2-

0.0-

-0.2-

-0.4-

- • -

• -

- T

o

z/Dn=1.1 •«

z/D,=2.1 *

z/DA=4.2z/D0=8.5Z/O6=15.9

•m m

* • • "

Z/DA=26.5

z/D =38.6

Side-supported

vane

0.00 0.25 0.50

x/P

0.75 1.00

0.00

ater

af

bu

0.4-

0.2-

0.0-

-0.2-

-0.4-

• z/D=2A

^-zA3 =4.2

- -<- z/Dft=26.5- »~ z/D =38.6

*• • • • •

Swirl-vane

0.25 0.50 0.75 1.00

0.4-

0.2-

-0.2-

-0.4-

» Z/Dh=1.1 • T • 2/

• - • z C , = 2 . 1 . • • .

1 1 1

0^=8.5 o

a

• •

2/0^15.9

Z^B=26.5

z^56=38.6• • •

•

••

a

Duct-vane

0.00 0.25 0.50

x/P

0.75 1.00

0.2

0.1-

1 0.0-

-0.1-

-0.2

• 7/D=\.\-

- Z/D=2A

- - 4 - z/D =4.2

a

• •. • a a a •

T

O

• • •

2^=8.5

z/Dft=15.9

• • •

J?

• a

Z/Dft=26.5

•-z© f t=38.6a • • a _a •

Dipper-vane

0.00 0.25 0.50

x/P

0.75 1.00

0.4-I

-0.2-

-0.4-

z©B=1.1

0.00 0.25

Twisted-vane

0.50x/P

0.75 1.00

DJ& 3.2.20 -4-:

- 351-

0

- Q

I0.0

0

Split-vane

Side-supp. vane

Duct-vane

Dipper-vane

0.00 0.25 0.50 0.75 1.00v/s Twisted-vane

3.2.21 4°l(gap)

- 352-

0.10Split-vane(W) :Side-supp. vane(ABB-CE)Swirl-vane [Duct-vaneDfpper-vape •Twisted-vane ;

z/D.

J^j 3.2.22 3.7]

0.20

0.15-

o 0.10-

Split-vane(W) ;Side-supp. vane(ABB-CE)Duct-van^

- Dipper-vanej - Twisted-vane

- 3 5 3 -

50000-Split-vane(W)Side-supp. vane(ABB-CE)Swirl-vaneDuct-vaneDipper-vane

— Twisted-vaneNo vane

-10

nm 3.2.24

z/D,40

0.020Peak at 0.03 ]

Split-vane(W) ;Side-supp. vane(ABB^-CE)Svyirl-yane • ..jDuct-vane ;Dipper-vane:Twisted-vane

S ^ No varie

0.00040

—LQ O. L. CD -\—T-

- 354-

3.2.26

0.30

•* 0.15-3

g 0.00

-0.15-

-0.30

Center of y

subchannel

z=l.\D,

-0.50 -0.25 0.00

x/P

•0=30°-0=35°•0=40°•5=45°

0.25 0.50

0.15

0.10-

=1 0.05-

^ 0.00

-0.10-

-0.15

z=8.5D,

-0.50 -0.25 0.00

x/P

•6=25°

0=30°

0=40°

0.25 0.50

- 355

D.^ 3.2.27

0.06-

0.04-

0.02-

0.0010 20

z/D,30 40

30000-

20000-

10000-

-10 0

3.2.28

- 356-

40

3.2.29

1.00

10 20 30 400.00

- 357-

nm 3.2.31

0.08-

0.06-

0.02-

0.000 10

• Swirl-vane (5=30°)—•— Swirl-vane (9=35°)—A— Swirl-vane (5=40°)

Swirl-vane (e=33°/42°)—<^~ Split-vane(W)

- Side-supported vane

20

3.7}

30 40

-f-

0.10

« 0.05-

I0.00

-0.050.00 1.00

0.20

3.2.32

0.15-

o 0.10-1

0.05-

0.00

Swirl-vane(19=330/420)Split-varied)Side-supported vane:

0 5 10 15 20 25

3.71 (ofefl)

- 358-

J

\

io

[QTV r

100

1U--

275

(a) (b) ^

ZL^ 3.2.33 ^-7) 7]*]-

PI

soacej

aoo

rmsu.

•30(T

ZL j 3.2.34 Al^^-

- 3 5 9 -

Rod

Test Grid

8=0-45° (d8=5°)r=39.5~50mm (dr=2.10mm).

3.2.35

_'L 30 40 50 60 70 80 90 100y(mm)

el ^ 9

- 360-

1/ i \i

°la} ;>

TO SD 90 100

(b) x/Dh = 4 . 4

(c) x/Dh = 13.2

(d) x/Dh = 22.4

30 Deg. Vane Angle

He] 3.2.37

"(ej' x

(f) x/Dh = 4 . 4

(g) x/Dh = 13.2

(h) x/Dh = 22.4

40 Deg. Vane Angle

- 361 -

1 1 I I I I I I 1 1 I I I ! I I I I I I I I I I 1 I I

0 10 20 30 40 50 60 70 80 90 100y(mm)

3.Q 3.2.38

H^ 3.2.39

- 3 6 2 -

(a) x/Dh = 1.8

(b) x/Dh = 4.4

2S.26.

2*22-20

£• 16-

, t

-» -u " (uv ) •

0.0 0.2 0 4 0 6 0.5 1.0

normalized distance

(c) x/Dh = 13.2

- . » - u-(uv)

- • - W(ira)

^ ^ - ^

0.2 0.-C 0.6 0B 1.0

oormalijeddistaDce

(d) x/Dh = 22.4

30° Vane

(e) x/Dh = 1.8

normalized distant

( f ) X/Dh = 4 . 4

0.0 02

(g) x/Z}, = 13.2

0.0 0.2

(h) x/Dh = 22.

40° Vane

3.2.40

-363-

- • - u-(uv) '

A - v|uv) '• w'(uw) -

:. u'(uw)-A- v'(uv)

(a) X/DH = 1.8

(b) x/Dt, = 4.4

rwnnalned <istarice

(c) X/DH = 13.2

2B-26-2*-22-20-

1 «~6

2

• • » u(uv) •: u'luw) "i-v'<uv) -

- • -W l im) •

•

00 02

(d) x/A = 22.4

30° Vane

(e ) x/Dh = 1.8

0 2 0* QG

normalized distance

(f) x/Dh = 4.4

2a-

26-24<22-20-

i- 16

1 "•

• • U"{UV) "

L; U'(UW) "

* - V(uv) "

(g) x/ft = 13.2

(h) x/Q, = 22.4

40° Vane

D.Q 3.2.41

- 3 6 4 -

a

1.4

1.2-

1.0-

0.8-

0.6-

T T • • • • T

o-o- o-g-Sc8^B=B='^^"—o—^—"

v~~v—v—v—v-z/D^ Measured Calculated1.8 • —a—

13.2 A —A—22.4 • — v -

0.0 0.1 0.2 0.3 0.4

Distance from center of subchannel, y/P

0.5

u s ] 3.2.42

z/Dh Measured Calculated

0.1 0.2 0.3 0.4

Distance from center of subchannel, y/P

0.5

3.2.43

- 3 6 5 -

3.2.44

- 366-

(7\)

ZL^ 3 .2 .45

- 367-

350

300

250

COCO

I

o

200

O 150

100

Inlet Pressure = 1200 kPaMass Flux = 1500 kg/m2s

18 20 22 24 26 28 30

Inlet Temperature [°C]

32

-0°-25°-30°-35°

34 36

(7f) G=750 kg/m2s

350

300

250

200

CDO

O 150

100

Inlet Pressure = 1200 kPaMass Flux = 750 kg./m2s

i . i i i i

18 20 22 24 26 28 30

Inlet Temperature [°C]

32

-0°-25°-30°-35°

34 36

(uf) G=1500 kg/m2s

H ^ 3.2.46 1.2

- 368-

350

300

250

x3

3 200

CDO

O 150

100

Inlet Pressure = 2600 kPaMass Flux = 750 kg/m2s

j i L

-O-25°

Inlet Temperature [°C]

(7\) G=750 kg/m2s

25 30 35 40 45 50 55 60 65 70 75

350

300

250

S 200

TOO

O 150

100

Inlet Pressure = 2600 kPaMass Flux = 1500 kg/m2s

I . I . I . I i , i

c—0°

-V-35 0

35 40 45 50 55 60 65 70 75

Inlet Temperature [°C]

3.2.47 <£^ 2.6

G=1500 kg/m2s

369-

350

300

2L 250

x_2LL

S 200

too

O 150

100

Inlet Pressure = 2600 kPa

Mass Flux = 750 kg/m2s

0.05 0.10 0.15 0.20

Outlet Quality [-]

0.25

-25°-30°-35°

0.30

(7}) G=750 kg/m2s

350

300

250

xlo-

200

eno

O 150

100

Inlet Pressure = 2600 kPa

Mass Flux = 1500 kg/m2s

i . i

-0°-25°-30°-35°

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

Outlet Quality [-]

G=1500 kg/m2s

ZL5] 3.2.48 # 3 2.6 Mpa<Hl*f

- 3 7 0 -

50

40 -

>oco 20itLU

10 -

20

Inlet Pressure = 1200 kPaMass Flux = 1500 kg/m2s

-

A• ~

& -^=_o-

-3-25°

-0-30°

^ ^ 3 5 °

—-Q

25 30

Inlet Temperature [°C]

35

(7\) P= 1.2 Mpa, G=1500 kg/m2s

50

40

C? 30

10

Inlet Pressure = 2600 kPaMass Flux = 1500 kg/m2s

40 45 50 55 60

Inlet Temperature [°C]

65

-25°30°

-35°

70

H ^ 3.2.49 4

P= 1.2 Mpa, G=1500 kg/m2s

- 3 7 1 -

K 1

• P1CevolaniKimProposed

(a) Square Grid - Wavy StrapRe

K

0.110000

P2• Cevolani-Kim- Proposed

(b) Square Grid - Wavy StrapRe

K

1 • • • •

• P3CevolaniKimProposed

1000O0

(c) Square Grid - Straight StrapRe

"L^J 3 .2 .50 PWR

- 3 7 2 -

100000

(a) Square Grid - Straight Strap

100000 Re

(b) Square Grid - Straight Strap

OL^ 3.2.51 £^H)"*l7} ^ - ^ PWR

^ * l ^ til a

- 373-

K

0.1

K

0.1

K

0.1

• R1

Cevolani

Kim

Proposed

• * • • • • • • * *

10000

(a) Rhombus Grid-Triangular Array

100000 Re

R2

Cevolani

-Kim

- Proposed

. . . i

10O0O

(b) Honeycomb Grid-Triangular Array

100000Re

R3

Cevolani

-Kim

- Proposed

:r*~~:.»::.it-m--j-

I \ < i

10000 100000 Re(c) Honeycomb Grid-Square Array

H.Q 3.2.52 FBR

- 3 7 4 -

CHFOccurrence

HeatingSurface //] m+ A m

A.'AmE

Superheated liquid layer

H ^ 3.2.53

- 3 7 5 -

9000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Measured CHF [kWm2]

ZL^ 3.2.54

- 376-

2.0

1.5

P/M 10

0.5D •

+20%

-20%

0.01000 2000 3000 4000 5000 6000 7000 8000

G [kg/m S]

=L% 3.2.55

P/M 10

20 100 120

P [bar]

a^J 3.2.56 7 **

- 377-

P/M 1-

-0.5

ZLB] 3 .2 .57

P/M i-

3.2.58

- 3 7 8 -

P/M 10

1000

LTD

D.^ 3.2.59

1000

XoT3

a;

£QL

100 -

o R-11A R-12n R-113

/

100 1000

Measured CHF [kW/m

ZLig 3.2.60

-379-

LQ 3.2.61 Reynolds ^ *J ^*1 ^ °fl -fMd*!*!-; (a) Re=200,

higher upwind (^Si^fl), (a) Re=450, higher upwind (^^^fl), (c)

Re=1000, higher upwind (4«i*H),(d) Re=1000, hybrid

-380-

"- 65

H.^ 3.2.62 CFX

- 3 8 1 -

1.0

0.8-

e3 0.4-

0.2-

(a)

k-z model(yw'=36)

° Low Re k-z model(yw*=0.6)

Low Re k-a model(yw*=0.6)

• Laufer0.0 <!>

0.0 0.2 0.4 0.6 0.8

Distance from wall, y/(D/2)

1.0

0.8-

<" „ 0.6-

? 0.4-

0.0-

: o

•

•

oo •

o

o

k-z model(yw*=36) °

Low Re k-z model(yw

Low Re k-a model(yv

Laufer

•o

* = 0 . 6 * o

>0.6)

(b)

O• .

o

0.0 0.2 0.4 0.6 0.8

Distance from wall, y/(D/2)

1.0

3-

2-

k-e model(yw'=36)

Low Re k-z model(yw*=0.6)

Low Re k-a model(yw*=0.6)

Laufer

(c)

0.0 0.2 0.4 0.6 0.8

Distance from wall, y/(D/2)

1.0

D.& 3.2.63

- 382-

r

3.^ 3.2.64 S. ( P / D = 1 . 2 5 , Re^lOOOOO); ( a ) Rowe

( b ) CFX

-383-

1.4

1.2 -

i" 1.0 -

.~ 0.8o

> 0.6 -

< 0.4

0.2 -

0.0

: (a)

: ys°^

: / •: •

-

A Pt-

r

/ *

B

Re

1 0E5

2.0E5

Measured Predicted

•

pt.C

1

0 5 10 15 20 25 30 35 40 45 50

Distance from wall, _y(mm)

0.12

0.00

Re Measured Predicted

] ,0E5 •

2.0E5 •

10 15 20 25 30 35 40 45 50

Distance from wal!,_y(mm)

O.^ 3.2.65 -, (b)

- 384-

1.4

0.4 -

0.2 -

0.0

3

0.12

0.10 -

0.08 -

0.06 -

0.04 -

0.02 -

o.oo

Re

I.0E5

2.0E5

Measured

•

•

Predicted

0 5 10 15 20 25 30 35 40 45 50

Distance from wall.^mm)

: (b)

1 >

Re Measured Predicted

1.0E5 •

2.0E5 •

• rN* • 1 •• 1 • • •

i

10 15 20 25 30 35 40 45 50

Distance from wall, y(mm)

O.S] 3.2.66 .; (a) (b)

-385-

0.700E 00 x 0.8<0E 00 ' 0.960E 00 « 0. I08E 01

0.7«E 00 • Q.870E 00 * 0.990E GO » 0. I IOE 01

0.760E 00 . 0.900E 00 o 0.10?E 01 x 0. I 12E 01

0.8I0E 00 x 0.930E 00 o.O.lOSt 01 • o: 1-HE 01

~L^ 3.2.67 (o

-386-

1.1

1.0

0.9

0.8

0.6

0.5

0.4

0.3

• ' • ' ' / '

Measured Predicted

Channel(Ar) — m—

Rod(e) - •»- •

. . . I • • • •

\

10 20 30 40 50 60 70 80 90

(9(deg) orx(mm)

ZL% 3.2.68

- 387-

1.0-1

0.8-

0.6-

0.4-

0.2-

0.0

z/D=0. 48

• Durret et al.o - Standard k-z model

A Non-linear k-z model

-0.2 0.0 0.2 0.4 0.6 0.8

U/U

1.0-

0.8-

0.6-

0.4-

0.2-

0.0

z/D=0.95

• Ourret et al.o Standard k-z modelA - Non-linear k-z model

-0.2 0.0 0.2 0.4 0.6

U/U0.8 1.0

1.0-,

0.6-

0.4-

0.2-

0.0

z/D=\. 90

• Durret et al.o Standard k-z model& Non-linear k-z model

-0.2 0.0 0.2 0.4 0.6

U/U0.8 1.0

1.0-I

0.8-

£}• 0.6-

"fc 0.4-

0.2-

0.0

z/D=2. 86

• Durret et al.o Standard k-z model

A Non-linear k-e model

ffl

-0.2 0.0 0.2 0.4 0.6 0.8 1.0U/U

z/D=A. 77

0.8-

0.6-

0.4-

0.2-

0.0-

•oA

Durret et al.Standard k-z model

- Non-linear k-z model

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

U/U

ZL3] 3.2.69

- 3 8 8 -

1.0-1

0.8-

0.6-

0.4-

0.2-

0.00.00

"A,o z/D=Q.48

"A. O

•P--.T--- a *

AOo " A ,

• Durretetal.o Standard k-z modelA Non-linear k-z model

0.03 0.06

1.0-,

0.8-

0.6-

0.4-

0.2-

A O-A ft...

z/ZfcO. 95

o o •

02.a o A

Q A

O Ai •

0.0 iS0.00

• Durret et al.o Standard k-z modelA Non-linear k-s model

0.03

k/U2

0.06

1.0-

0.8-

0.6-

0.4-

0.2-

0.0-IS

A. _O;...• Durret et al.o Standard k-z modelA - Non-linear k-z model

z/D=l. 90

A°-

OAO AO A

O AO A a

O AA

0.03

k/U2

1.0-

0.8-

0.6-

0.4-

0.2-

0.0

A O

0.00

AQ

• Durret et al.

o Standard k-z model

- A Non-linear k-t model

z/D=2.86 kA

„ AO A

O AO A

O AO A

OA0 03

k/U20.06

1 .U

0.8-

0.6-

0.4-

0.2-

0.0-

%m

% u%m

o •a3 •

•-o—

— A —

z/^4.77

Durretetal.Standard k-z modelNon-linear k-z model

0.00

ZL^J 3 .2 .70

- 389-

x»0Re* 10,000

I— +

R«« 20,000

Re-40,000

k-e

H^J 3.2.71 Matrix

390-

>

gUJ

co

LLJ

UJ

<UJ

1.6-r

1.4-

1.2-

1.0-

0.8-

0.6-

0.4-

0.2-

0.0

• Measured

— o — Standard k-z model

—A— Non-linear /f-e model

0.00 0.25 0.50 0.75 1.00 1.25

Y, DISTANCE FROM WALL / PITCH

1.50

1.6oo_JJJ

ULI

CO

_iJU>

o

a:JJ

1.4-

1.2-

1.0-

0.8-

0.6-

0.4-

0.2-

<LU

0.0

Measured

• Standard k-E model

Non-linear k-s model

0.00 0.25 0.50 0.75 1.00 1.25

Y, DISTANCE FROM WALL / PITCH

1.50

3.2.72

- 3 9 1 -

—•— Measured—o— Standard k-e model

—A— Non-linear k-e model

ogLU

X._ l

CD

1±J

<O

enHI

0.8

- - Y=1.5

___ Y=1.0

- - Y=0.5

.__ Y=0,29— Y~0 07

0.00 0.25 0.50 0.75 1.00

NON-DIMENSIONAL ROD GAP

3.2.73

- 392-

oOLLJ

m

LU

<

oa:LU

<LU

1.6-T

1.4-

1.2-

1.0-

0.8-

0.6-

0.4-

0.2-

0.0

• Measured—o— Standard /c-s model—A— Non-linear k-e model

0.00 0.25 0.50 0.75 1.00 1.25

Y, DISTANCE FROM WALL/ PITCH

1.50

oi 0.12

LU

LU

0.10

H 0.08 -

LU

o 0.06-

0.04-

0.02-

0.00

A

\

• Measured—o— Standard /c-s model— A — Non-linear k-t model

V\

0.00 0.25 0.50 0.75 1.00 1.25

Y, DISTANCE FROM WALL / PITCH

1.50

3.2.74

(Re=40000)

- 3 9 3 -

HQ 3.2.75 H

SUPPLY

| i

1 XMD2 \

, \KMU1 ^

; «™IK I

' WMIB '.

i SIIJM: j

; XH.IMIK !

; flusaiK i

WSDL"

h

H

-4

4

4

h

MainRtt

SETUP

.JEILH 2

lJD B^7 , . , r

SOLVE

H F I J O W

Oitnd Uiflurrce

1 iitnd

! >

i

USER

CMD1

c e ^LOLND

OOKT

4h

rJ

rJ-

—<

iart

TUISMODEL

, a).\?i\on3.

OHRINBrH.

f^fOBU-f";

! CBOLKQ; ;

ZL^ 3.2.76 TFC2D 3.^.

- 3 9 4 -

i

* —

•

•

•

—;—'

•

•

•

-•••••

*

*•

!. j

•

•

•

* i

ZL^ 3.2.77 ^^(generated by wgridl routine)

.i"

xutemo .

1-

•••••

•

•••••

•••••

•••••

•

•••••

•••••

•

•

1

ZLQ 3.2.78 ^^(generated by wgrid2 routine)

ZLQ 3.2.79 £

- 395-

w

w

P

«—

; E

>| 5x+ -—

3x •

ee

EE

3.2.80

- 396-

0.8 A

s 0.6 A

0.2 A

Measurement of Schildfcnecht etal(1979)S! and ard( 1974)

• Jones-Launder( 1972)•Launder-Sharma(1974)

Lam-Bremhofsl(1931)Ghien(l952)Nagano-Hishida(1987)Myong-Kasagi(1990)Magano-Tagawa[i99O)Chang-Hsieh.Chen{1995)

0.0 0.1 0.2 0.3 0.4 0.5

r/D

H ^ 3.2.81 (Re-17250)

5 -

4 -

3 -

2 -

1 -

0 -

i i ' i i i

• Measuemerts of Sehldknechtetal(i979)Standard{i974)

• Jones-Launder(1972)Launder-Sharma( 1974)Lam-Bferrtiorsl(1981)Chien(1982)Na9ano-l-ishida(1987)

• — Myorg-Kasag(1990)Nagano-Tag3wa(1990)Chang-Hsieh-Chen(1995)

1 1 ' i ' I

—' 1 '

•' «

.' J/rt-•'•#1

• • ' • # • !

••' •-•/ 1

—i 1 i i0.2 0.3 0.4 0.5

r/D

ZL^ 3.2.82 (Re=17250)

- 397-

1.2-

Measurements of Laufer(1954;-Siandard<1974)-Jones-Launder(1972>Launder-Sharma{1974)

- Lam-Bremhorsl(1981}-•Ctvei\(l982)• Nagano-Hishida(1937)-Myong-Kasagi(1990)-• Nagano-Tagawa(199O}- Chang-Hsieh-Chen( 1995}

0.5

r/D

O.^ 3.2.83 (Re=40000)

• Measurements of Laufer(19S4)Standard) 1974)Jones-Launder(1972)Launder-Sharma[i9?4)Lam-8remhofSt(198l)Chien(1982)Nagano-HishJda(1987J

- — - Myong-Kasagi{1990)Nagano-Tagawa(1990)Chang-Hsieh-Chen(i995)

0.0 0.1 0.2 0.3

1 2 ] 3.2.84 (Re=40000)

398-

• Measurements olLaufer(1954)Modihed treatmentUnmodified treatment

0 0 0 1 02 03 04 OS

r/D

(a) U profile (b) k profile

Modified treatmentUnmodified treatment

0 50 100 150 200 250 300

28-

25-

24-

22-

20-

- Modified treatment- Unmodified treatment• u'=2.39,iy"*5 15

Measuremerts of Lau(er(1954)

(c) c profile

3.2.85 ^

(d) Semi-log plot of U

wl L (Re=40000)

-399-

0.8-

» 0 6 -

1

0.0

-Standard(1974)-Jones-L3undef(1972)

- - Launder-Sharma( 1974)- LanvflrGfTHo/st(1981}-Chien(1982)- N3ffino+lisNd3(198r)- Myarg-Kasag(1990)-Nagano-Tagawa(1990)-Cfian5-HsJeh-Chen(1995)

Measurement of Ectelrrenn(197.l)

0.0 0.1 0.2 0.3

y/H0.4

3.2.86 V J=L sr (Re=8200)

Standard(i974)- - •Jones-Laundet[1972)

Launder-Sharma<1974)

3.2. 87 (Re=8200)

- 4 0 0 -

• Measurements of Durrel et al.(1988)Standards 974)Jones-Launder(1972)Launder-SharmaO 974)Lam-Bremhorst(19ai)Chien(1982)Nagano-Hishida(l9S7)Myong-Kasagi(1990)Nagano-Tagawa(1990)Chang-Hsieh-Chen(1995)

— I —0.2

10.4

u/u.

— I —0.6

— I —0.8-0.2 1.0

(a) x/D=0.48

-0.2 0.0 1.0

(b) x/D=0.95

-401 -

\J.\J —

0.4-

0 .3-

0.2-

0.1 -

0.0 -

1 1 1 i ' 1

-

' 1 • 1 * ' 1-0.2 0.0 0.2 0.4

u/u

0.6 0.8 1.0

(c) x/D=1.90

0.4-

0.3-

0 .2 -

0.1 -

0.0-

\

\

\

' 1 •"

— 1 • 1 ' 1 ' 1

-

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

u/u.,

(d) x/D=2.86

- 402-

-0.2 0.0

u/u.

(e) x/D=4.77

0.8 1.0

(Re=84000)

- 403-

0.5

0 .4 -

0 . 3 -

0 .2 -

0.1 -

0.0-

-0.02

• Measurements of Durret et al.(1963)Standard(1974)Janes-Launder{1972)Launder-Sharma(1974)Lam-8remhorst(1981)Chien(1982)Nagano-Hishida(1987)Myong-Xasagif 1990)Nagano-Tagawa{1990)Chang-Hsieh-Chen(1995)

0.00 0.02 0.04 0.06, 2

o.oa 0.10

(a) x/D=0.48

0.4-

0.3-

0 .2 -

0.1 -

0 .0 -

v ^ «^jj ' 1 ' 1 ' 1 >

*

l

J , 1 , , , , , 1 ,-0.02 0.00 0.02 0.04 0.06 0.08 0.10

(b) x/D=0.95

- 4 0 4 -

u.o -

0.4-

0 .3-

0.2-

0.1 -

0 .0 -

\^J^.;V.I ' 1 ' 1 ' 1 '

f .-0.02 0.00 0.02 0.04 0.06 0.08 0.10

Wu. , 2

(c) x/D=1.90

D

0.4-

0 .3-

0.2-

0.1 -

0.0-

Vf •,J! ' -

-0.02 0.00 0.02 0.04 0.06 0.08 0.10

k /u . 2

(d) x/D=2.86

- 405-

\J.-J —

0.4-

0.3-

0.2-

0.1 -

0.0-

. . . . _

11 •

r1

!

*

%—1 , 1 1 1 1 1 1

-0.02 0.00 0.02 0.04 0.06 0.08 0.10

3.2.89

(e) x/D=4.77

^ : S (Re=84000)

0.1 -

0.0

• Measurements of Durret et al.(1988)Upwind scheme

-Hybrid schemePower law schemeExponential schemeQUICK scheme

-0.02 0.00 0.02 0.04 0.06 0.08 0.10

(a) x/D=0.48

- 406-

-0.02 0.00 0.02 0.04 0.06 0.08 0.10

k/u,...2

(b) x/D=0.95

0.4-

0.3-

0.2-

0.1 -

0.0-

\ '

!—»-, 1 , 1 , , , , ,

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500ms

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^: 1FA-535.5 ^ IFA-535.6^14 4 4 ^i

27B ^S-g- 809 ^ 810^ 1985\1

811 ^ 812-b 1986\1 1

^ 1986^

1987^

\ IFA-535

IFA-535.

U02 ~ ^ ^ £ ^ 9.884% U-235, <>]&-$ ^SL^ 94.7 % o]

3 .7]^ 0.135mmoln}. «?lS.-g-^ 3^7] <£^-£: He 7 } ^ 1

bar °j£-°.u} A^A A^Q3?- ^ Q ^S-g- 809, 810, 811, 812 4 4 ^

•& 7.0, 7.6, 32.0, 32.1 °1&4. «J-g-^7]^lty-# ^}S-b <£^-g- 809

810 4 4 ^ 1 ^ 4 ^ 4 ^ 1 4 ^ -^s j 1.5 ccm ^ 1.7 ccm J ^S.-g-

IFA-535.5 ^ IFA-525.6^

- 442-

-g-

(3)

7]

(7f) 214^- creep-out ^ ^

creep-out^}

creep-out ^ ^

H»J SIERA 3.J£7|fwJ:6fl Af-g-^f^-^.^, Halden projec t^

IFA-585.1 [3.3.3]

2 7 ^ ^-§-5 .^1^ 2 : 4 ^ Zry-2S. ^3^. BWR-§-

3 . , PWR-g-

zero stress, creep-out A S ^ S f S l ^ K PWR

CWSR(Cold Worked Stress Relieved)^AS. *fl^S}&JL, PWR

300/an(Diametral Gap Width) ^ £ 5 . 3.7]} f>\&r.\.

- 4 4 3 -

370-380 °C &3L, PWR ^S-g-ofl * W #-g*Hr£ : LWR

5xlO13 n/cmJ-s(E>lMeV)

IFA-585.4 [3.3.4]

£ 4 ^ £ IFA-585.l3f

& ^ M^ £-§--§-£ KWO

^ 76*551

$1 PCI ^ ^ # as]4i4f*}7l *1*H 300/mi5. -Si-Sit:}.

^ 1.2xlO22 n/cnf(E>lMeV) o] £ a ,

^^1 26^-i- S ^ M 10.758

100 bar, 4 # ^ 4 ^ ^ : ^ ^ l ^ - g - ^ l 3.2xlO13 n/

cm3-s(E>lMeV) oj^JL *F-r-^l^^-°] 2.5xlO13 n/cm2-s(E>lMeV) ^ A ^ ,

^ 5 - ^ S ^ ^-T-^I^-g" 372-379°C, ^f^-AJ^-a 376-383 °C ^ A ^ ,

^ hoop s t r e s s ^ 4 4 85 MPa ^ 30 MPa ftt}.

900fph 7}4

Zircaloy-4

© Ringhals-3 ^^^;-^ Li

Ringhals-3

l-fi- Zircaloy -f^Ji

Zircaloy -f-^^-S.-^ ^7}^.] X\. °] 's^-S] ^ ^-^^c: Ringhals-3

Li - ri£.7f Zircaloy

444-

40.6 MWD/kgUoj^i 4

TT 39.7-43.4 MWD/kgU

4 <£:S.-^ ^7 l^ ]Ai 26.5 - 43

(2) PFCC(PWR Fuel Cladding Corrosion) 3.S.

Zircaloy ^ ^ ^ . s l^^o) ] 3. -r"^1 ^ hydridingo] tHJ^ofl tu>ef 3.<

PFCC (PWR Fuel Cladding Corrosion)# 7 f l ^ | - ^ c } . EPRKHl^^- PFCC

23737)1^

27H

20-102

® IFA-568.1[3.3.7]

IFA-568.1 A l ^ ^ ^ j ^ r Zircaloy-4^] -f-

Li ^ £ * ] ^%># ^7f*f7l £1*1] Halden #*K§.<q PWR f ^

1989hi 6 ^ ^ - ^ I99iid lO^^W ^ ^ S l S i c K ^ - g - £ KWU^A] ^ |

£l>ii) Goesgen ^Uf^oflA-j ^ ^ « > 47lj^ ^^--g-# S % V W . Halden #*}

$.o\]*\ e l i AJ2W <?1^£^ 28.5 MWD/kgU6| 5i^.ni, o|tUA| ^S}%- - ^ - ^ ^

10-40 /an o|^u>. ^ 4 ^ u f l Lii] - ^ £ ^ ^-§-^-^1 ^ 4 ^ ^ 7 f 2.2-2.5 ppm

°J ^3f tilJ2.SH 4 - 4 . 5 ppm# -S-x}*}^}. Halden

^ J 4 -g- ^ 4 i £ 7 f 45 MWD/kgU oj^cf. A>S | .^ - c ^ ] ^ 80, 245,

30-90/^

- 445-

(cf)

Rim

} ^ R A P I D ^ g . T .

Pu

(1)

L-235 ^ ^ £ 10 %<>]<>&,

Mechanical ^ % -

. 100,000 MWD/MTU O)AV

FEM(Finite Element Method)

- GUI

5 w/o

*i

- 446-

r 71^3} U02 «J£.g.S] ^ uj 2fS.^EH ^ * f | * j S H ^ I ESC0RE4}

FREY 3-B-M: -f-^^1 FALCON 3 . H # 7fliHrK2. $X£-tf, Siemens A } ^ 7 ] ^

CARO S B f tjf^W U02 <££.£] ^ ^ ^KE-^fl ^-^*1H ^ H ^ I SIERRA

a n t jflt^jL $14. on- 53.^ s.^- - f r*hs .^# 4-§-*K2. 014. a

B]J2. ^- ^f^Iofl^ 7H«i^ ^^M. ^ ^ ^ ^ 3 . ^ ^ Zj- ^ - ^ £ c | # Module .

^eltl 71 #

6J^ ^-ti] ^ 711^ ^2f5l JgB| ^ ^r^°l -g- ]«]-S.- - Graphic User

Interface!-

(2) U02 i ^ s f l ^ «V^^%> «g^S ^ :S - t 7fl-i>*fe RAPID

(7\) 7H J5.

uo2 ^4*\] *-M*\ # A ^f4^l 3.7]

7}

Ferti le

Empirical

^ 238U $) %.$*} ^-tri * . ^ ^ 6JsU 239Pu tfl^o] xfl

4* 2 - 3 wB ^ £

Kr Rim Effect7} ^ ^ ^ 1 4 . H}BM ojgf^ Rim

Effect^ ^ J # ^

- 447-

RAPID

S ^ L ^ RADAR[3.3.10]o]uK RADAR 5 1 2 ^ ^ 239Pu

] fl^ TUBRNP HS.-L^[3.3.11]^r 239Pu239Pu, 240Pu, 241Pu ^ 242Pu ^ Pu

238U «

238U

RAPID ^ S H

^. ^ 5 . ^ HELIOS 3.^7} A]-g-!E] uf. HELIOS ^^7fl3.S.[3.3.12]^ 2

. RAPID BSl^oI^fe ?> Hl- l ^ A ^ } ^ ^ 4

L-235 ^ fl

3 . 3 . 1 ^ 235U, 239Pu and 241Pu ^ ^ ^ ^ ^ H ^ l tcf^-

239Pu and 241Pu ^ ^ ) ^

Sll-^Df, ^ 4 x - £ 60 MWD/kgU ° 1 ^ H M T T ^ A ^ ^ 1 2 3 9PU^1 ^ ^ ^ ] ^ £ ^ 235U

cf 3.7]] £ ] D J , < ^ 4 i S 90 MWD/kgU ° l A c H M f e

RAPID ^ i = ^ | A f e 2 3 9pu , 240Pu, 241Pu , 242Pu ) (

235U ^ 238U

238U, 2 3 9Pu,

24OPu, 2 4 1Pu ^ 2 4 2Pu

^ iV235( f. r) = - iV235 ( t , r) o f (f, r ) «J (f, r )

- ^ iV238(/, r) = - iV238(*, r ) a f (/, r) (f, r)

- 4 4 8 -

jjNm(t, r) = -NZS3(t, r)( a f U r) * U r)+ /I 239) + A ^ U r)<r f U, r) 4 (t, r)

J-tN2io(t, r) = -Nm{t, r)( CT f (f, r) ^ (t, r)+ A 240) + Nw(t, r)cf9(t, r) <t> (t, r)

J-tNw(t, r) = -Nm{t, r)( ff f U , r) (f, r)+ A 241) + A^240(^ r) a ™ (t. r) <!> (t, r)

4:Nm(t, r) = -NmU, r){ a f {t, r) <!> (t, r)+ A 242) + N2il(t, r)af{t, r) 0 (t. r)

N,-(t,r) = atomic density of the nuclide-i (atoms/m )

a'a - neutron absorption cross section of the nuclide-i(m )

a 'c - neutron capture cross section of the nuclide-i (m )

Ai - decay constant of the nuclide-i (sec"1)

0{t,r)- neutron flux (n/cm.sec)

RAPID J E S H ^ ±.^^] i-ll-f-5] ^

*>!:}• J l 7 f ^ ^ ^ u f . trfsfA-] 4 t f l f i ^ <£^S_ ^ U-235

(^ r) = [ (Ci + Cl. EN+ Cl. EN2) + C\. BU+ Cl. BU]. POWDEN

-449-

, o){t,r)

a)(t) fe 4 4

^ 2 3 5 U

f;{ r)=Cax + Cl EN+ (Cl + Cl EN).r+( Cf + Ca

e. EN). r2 + (C? + ClEN)r3

2 3 5 u

6 j\t) — (, C j T 02. £Ll\ -r C3. ziiV ){ C-4 T \. C5 -r C6. l i iv j . tS U +^07 + Cg.

] epi-thermal235U

^ RADAR[3] a n d TUBRNP[3.3.

Cf + {Cl+ CiEN)exp(Cd4a - r)4)

- 4 5 0 -

o f (t) = (C? + C\. EN)( Cl + C\. BU+ C%. BU2 + C\. BU3)

240Pu2 3 5 u

235U

C{.BU3). [ C£+ Cf6.BU+ C^

C{0.

C?u= Cf+ CI.BU+ C^.

Clu= C\ + Cl BU+ Ct.BU2 + Cl BU3

Clu= C[ + Cl2. BU+ Cl

3. BU2 + C{. BU3

Cfu= CT + C2m. BU+ C™. BU2 + CT. BU3

C\ = constant

C{2. BU3). EN\

SBl7]

3 235r rcfe} 3.

Fertile 238U, 2 4 0Pu a n d 2 4 2Pu

235U

RAPID

"A 235ufe H J 3.3.33} ^uf.

.7} $1*1 Si 235u 4s} 44 ^

- 4 5 1 -

(Uf) RAPID ^SJ.^ ^ 7 } ^

RAPID 5 S 2 g ^ 235U, 238U, 239Pu, 240Pu, 241Pu * 242Pu « * # #

3 .3 .4^ 4 w/o 235U ^ ^ 5 . ^ <$.^S. ^ S # HELIOS % RAPID 4 4 Tj]

3 . 3 . 5 ^ 235U ^5L 3-10 w/o

a ^ I 3 .3 .6^ 4i^*f|<sflA-l^ Pu ^ - ^ 1 ^ ^ § ^ ^ 5 } # RAPID

HELIOSS 7ll^*> ^ 2 } # i ^ ^ ^ u f l , ^ S . ^ ^ ^ 1 ^ 1 - <t ^r S14. 235U239Pu ^ ^ F ^ H ^ ^711 <£i :£ 25 ~ 40

24i -2= 60 ~ 90

^ Pu

$>t}. STRO ^ < ^ S ^ BWR l Millstone-1 ^^ifcofl^ 4 4 23 MWD/kgU ^ 39

MWD/kgU o44i£7}^l ^ifc5|5it:K EPRI ^ ^ ^ . ^ PWR l BR3 ^ 4 5 . ^ 1 ^ 4 4

39.4 MWD/kgU ^ 64 MWD/kgU <£4iS-77}x\ <$.£.5\$X^}. D.Q 3.3.7^: 1*11 Pu

1 ^ ] ^ # RAPID HSZLefl « ^ ^ l i f ^ H * ] #

RAPID ^ s n ^ o l ^ ^ l ^ - ^ ^ <y-

Pu ^ ^ 1 ^ 4 ^ ^ ^ l i ] ^ r 5 *K£±r 4 ^ 5 . H

° } ^ # 6 i^r ai t}, a ^ 3.3.8^r STRO ^ ^ ^ . ( 2 . 9 w/o 235U)

29.571 MWD/kgUofl>M ^ M J S i ^ S l : RAPIDi} TUBRNP SS.ZL

9 f e 235U

c{[«> RAPID of l^ l i j - ^-^^17} Ul 3.5^0] ea^cfl, RAPID

- 452-

^ ^ l APPOLLO-2 3 . H [ 3 . 3 . o

Rim effects7}

3.3. lO^r RAPID^- ORIGEN ^ S Z L g [ 3 . 3 . 1 4 ] ^ Pu

^- tijj2.^1-jL 6iu>. < ^ ^ S 40^60

BJL.1- <£^S. 60 MWD/kgU

. ORIGEN 3-B.^ Pu

4 pu ^ ^ l ^ ^ ^ l ^ ^ F ^ - S - 1 ^ ^ ^ ^ £^51 il 235u*}J1 5^-b RAPID*] o j | ^ | 7 l - ORIGEN 3 . ^ 5 ] ^ ] ^ 1

(Bf) ^ ^

RAPID ELSJ.*&£: U02

2 3 5 U

=.^! HELIOS S J ^

. RAPID SSZLS^^- 4 $17] A^^ JB.cf ^>^-*l £ 1 ^ 1 4-g-Sl RADAR i i TUBRNP

. RAPID ^S-H^ 235U - ^ ^ £ 10 w/o

150 MWD/kgU7}x] U02

(3) 7}#elu jo}

(RAPID-GD)

(7 f ) 7)1 JSL

- 453-

[3.3.15-16]. Gd U02

uo2

Gd2O3 ^E±f- cfl7fl 4 ~ 8 w/o

. ZLSla Gd

^ 0.71 - 1.8 w/o

Gd

-fe Gd

U-235

Gd

. Gd2O3/UO2 U02

Gd £fJ§-8; ^ U02

Gd203/U02

( v f ) Gd

Gd Gd2O3

Cell

3 .3 .8£ Gd

H°J HELIOS

i f

^ Gd-155 ^ Gd-157 o]z\. H ^ 3 .3 .11^

3.7}o\] n

U-235

MWD/kgU

10 ~ 20 MWD/kgU ol

^ Stlcf. Z L ^ 3 . 3 . 1 2 ^ 9 w/o Gd2O3) 1.8 w/o

^ 4 . 10

20 MWD/kgU

a?J 3.3.13

^ - ^ ^ U02

3.3.14 - 4 4 2 MWD/kgU ^ 20

-454-

MWD/kgU<H 4 ^ - Gd7}

. He] 3 .3 .15^ Gd-157 ^4x^1 ^ - h £ ^ ] r

f. Gd-157^ # ^ 4 ^ ^ r ^ l Self-shielding 7}

3.3.16^ 30

6\] Gd7f

Gd fe S^l^ Gd

Gd , Gd

7F

7F

Gd

Gd

U02

Pu-2397F

fe oi

4 ^F%v-^ ^ Gd203

^ } . Gd f§

0.7, 1.8 91 3.0 w/o ^ 5 . 4 4 ^ 1 ^ ^ ] ^ , U-235^ xt\z}

20 MWD/kgU

- 455-

Gd203 ^JE-Ofc ^ r ^ F ^ l , U-235S]

g-^ Gd ^$] ^ ^ # ^ -g-S-fe U-235

l Gd ]

Gd

Gd ^ g 1 ^ ^ ^ ^ # ^ ^

] tii^i^ f i t t ing

20 MWD/kgU,

/>(r, Grf, -BfT) = d(Gd,BU) + C2(Gd, BU) • r+ C3(Grf, BU) • r2

r4

C6(Gd,BU)- e x p ( - A ( l - ^ ) ) + C7(Grf,5L0 • exp(-Z>2(l - r)2)

= c [ + c '2 • BU+ GD • ( c i + c \ • BU+ c !5- BU2+ c '5 • BU2)

> 20 MWD/kgU,

p(r,BU,EN)= E1(BU,EN) + E2(BU,EN) • r+Ez(BU,EN) • r1

+ E^BU, EN)- r3 + E5(BU, EN) • rA

+ Ee(BU,EN)- ex.p(-H1(l-r)) + E1(BU,EN)- exp(-H2(l- r)2)

, EN) = e [ + e \ • Gd+ e '3 • EN+ e \ • GD • EN

- 456-

=L^ 3.3.17 ^ 3 .3 .18^ al>d«g F i t t i n g ^ #Sfl - ^ Gd -Sj-g-S]

HELIOS ^ T f l

-& Gd

Pu-239ofl

RAPID(RAdial Power and Burnup

Prediction by following Fissile Isotope Distribution in the

Pel let) [3.3.18H ^7}${°] Gd

# ^ S # Gd2O3

^1-S-fe- Cell 7fl^ ^A^Tj] S ^ o | HELIOS*] 7}1 > )

20 MWD/kgU oj

^ Gd

(4) 3 . ^ 4 x S U02

(7\) U02 ^

U02 ^ ^ ^ 1 ^ J I ^ ^ # ^ * f SAfofl i|5|) cH^ 4 ~ 5 MWd/ kgU

- 457-

7)3,7} 5j*>

-, 7]

SEM

51

Zacharie. et. al. [3.3.19]5l

il-*f7ll s m SEM 4 ^ 1 5JS1-I3 25GWd/tU5l

60^: Annealingtl ^ - f 4.1 %,

71X151 71

^ D ( | 71

- 458

fe 7l5fe ^ t * ^ 3.7} S.

vlSL ^ atom

Rb o>6|| safe gas atom^ ^(m)fe 7 ] S

m=

^ i ^ £ pg fe -j-=B+(-^:)Rb olcK B r van der

^ Boltzmann

Rb 7} 0.1 ]imiu} H- ^-^- -#t:|)^_o_^. (kT/2T)Rb &°] ^Tj) 5 H ^1^1 71

Rb ^1^1 Safe gas atom5l ^ f e c } - ^ ^ ^cf. [3. 3.20]2

2r\ /o o 9 \

Y x en = C + M = mN ( 3 . 3 . 3 )

Yxefe #*l£-«£# <£$*} Xenons} Krypton^ .%• 4 ^ yield, Ffe

T^^I -f-2]Al^:^- ^ £ < i # , (fissions/cm3'sec), tfe ^ ^ W ^ ( s e c ) , Cfe

Matrix Volume* ^ ^ safe ^ 1 -f-sl^ gas atom ^ ( atoms/cm3), M^ 7 l 5

safe ^ 1 -T-21^ gas atom ^(atoms/cm3),

715^1 % ^ l n f . §i5l 7^ofl 4sf Solid

- 4 5 9 -

*> 3.7]$] 7]SL^S] %• *»|£<g 7M$] atom^ ^ - f ^ 7]

S] 7}^ atom

Greenwood and Speight S»g[3.3.21]«Hl ^s){ 7|

^g-f(Postirradiation Annealing)

gas atoml-^- ^ ^ s ^ ^ . J1^5]o] $1°] mN =

moNo = V|o|uK X[Dro] <$*-m Roo)) &$-*]• ^V^-fsl^- 7 l S ^ No l S fe 7f

[33.3.2US. ^ ^ ^ " ^ alAn^ 7 lS^ 3.7} R,o] z£^ 7 l S ^ £ # d ^ 7]3,

37} R27f ^ ^ 7lS-^S C27f ^ # ? « # n| # l"#^r K12dC27f 5]3.,

Kiz = 4JI(RI + R2) (Dbi + Db2) o]t[. <^7}M S.^ 7]3L$) 37}7} <£%

X&_H.£. Ci=C2=N, Ri=R2=Rb, Dbi=Db2=Db o|u>.

71S^ - -

fe 71S^ ^ ^

l V ] N ( 0 ) = No

(3.3.

- 460-

, _ r\ \ 0 .2

\RT) ( 3 - 3 ' 5 )

.0.2

o|l tr}5} ^^r}7l] ^ u } . postirradiation annealing^-

(AV/V)g = 3

AV\ AK ..o.2T?Vp/ - Q \ 0 - 2 / WkT\V )g~ 3 A i E X P l j I j

(3.3.6)

In-pile ^o>%^ Jg-f- ^ i £ o H ig%>^- tilTij 5 | S S (3.3.6)*]

^ 1 ^ ^41 ^-^l 1 ^ gas atom ^ , M(atoms/cm3)^

7] ^Isll Y x en = C + M = mN (C = 0)o|cf . 0^7 } ^ (3 .3 .2 ) * ]2 f (3 .3 .3 ) * ]

(3.3.3)*}ofl*] *£. = ^ # o]-g-*Hf 7]

= b^7}

N=a.tn %EH^1 Trial

N(0) -

(3.3.8)

- 461

( 3 . 3 . 7 ) ^ (3.3.8)*H*j In-pile ^%<>M a ^ M ^ t*\} tf^

(^|) ' (3.3.9)

1- (AV/V)g = (4JiRb3/3)Nofl

In-pile

(3.3.10)

] f l ^ i ^ F =Ft O|JL Fractional Burnup %FIMA(%B) = F/Nf° ojcf. o j 7 H N f

0^ ^L^l^-s]

^ ^ [ S ^ 2.7] atom^I ^©li:}. H}S}A-] (3.3.10)*]«sfl Fractional Burnup

Factor#

(3.3.11)

in-pile ^"%ofl-H 7}^o\] ^1*> ^ ^ b c : Fractional Burnup,

- ^r SI^K (3.3.6HSJ post irradiation anneal i

SEM £ * H ix}s.^ annealing

^ a lS lA^ o] *- *fl£o] saturation

rrfBf

Reynolds[3.3.22]7}

- 462-

(3.3.12)

:2.3j*> 78.5%ofl Trial solution^] ^ ^ n = 1/5

>, Fractional Burnup# Normal BurnupAS ^^1(1

%FIMA = 9.5 MWd/kgU)*H ^ ^ ^ H l

^^)lA^ Zacharie[6]i]

Empirical Data# ] ^

3.3.20^: 1. Zacharie[3.3.25M

image analysis ^.2}$} £ ^^$] z£2\*\3\ M}3.%} H^^-S.

^ ^ l ^ f e ^ # # ^ $lz}. °)7]A\ Af-g-Sl data poin ty

25Mwd/kgU# ^ ^ * > 4.5% ^ ^ ^ U02 4 i ^ l l § - 4 ^ r S ^ S . annealing*];^

l-. I. Zacharie Models] B]isj\

I. Zacharie Model^ ^ ^ ^ I ^ f e ^ # 6 i ^r $lty. 3.Q 3.3.21^-

36MWd/kgU <£^*i ^ ^ ^ 1 ^ 1 HOOTCofl out-pile technique^-

data pointif u U ^

^ H^ 3 .3 .22^

dataif

- 463-

H ^ 3 .3 .23^ K. Une[3.3.28]£| ^H<^] r c ^ *J,g- ^ data points}

t> 3J-2-.S. ^ ^ ^ ^ ^ : 44 MWd/kgUSj out-pile technique^ ©]-g-$};

(AP : 72~86 Mpa) ^ £ o J H -g^*} ^j-S^li:}. tfls* 10 *ofl>H

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NRC «?*lS-g- ^ - r o ^ 3^.<d FRAPCON-3 1 7^$. ^^ci 7]

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BR-3SJ Rod 24161- 7 ] § ^ S XI^I^^K ^ 4 -g-^^^fe 68 MWd/kgU lJI EFPD

^ ^ S l # S^^ - i - ttfl ^7liH>M 5.77

g ^ 0.138MPa

3.3.24

10%

^r ^ 25*^ igSj-t- i ^ - ^ . ^ ^ ^ s ^ o.43% # 7 } ^ ^ i

3.3.25 ^"^)U02 ^ ^ 5 . i | v}^ ^ ^ «?1^£# ^ -b BR-3 24i6

(4)

- 464-

} £ Greenwood & Speight 7l*M

data[3.3.19-22]5t

PCI51

NRC 3.B.91 FRAPC0N-3<Hl

. FRAPC0N-351JElo|l

U02

BR-3 2416

(5) creep-out

JL

lift-off 21

creep-outofl

lift-off ^

swelling

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- 4 6 5 -

creep-out!;,§-

3 ^ 7 ] ^ ] cU?> ^ ^ - ^ Halden Reactor Project^

creep-out >J- - I tfltl A J ^ # r*l^f^K [3.3.29-33]

Zircaloy-2 ^ Zircaloy-4 2]4^j]- ^ 4 ^ | 4 *>^ Zircaloy-4

l ai^K [3.3.34]

creep-out JE.^ 7fl^# ^ f l ^ ^ ^

CARO-D 5.5 3.Hif FRAPCON-3 3 . ^ #

creep-out ^}^B] ^ % ^ # ^ 7 ^ ] . ^ ^ ^ ) Halden

creep-out S«g# 7fl<t*f&c}-.

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^ 4#4 3.3.14 ^1

£ c r ^ £ l,ft+ £ 2,&+ £ l,!rr+ £ 2,irr (3.3.13)

O

- 466-

2,irr:= £ irr

, e2,ir

cr

Airr ^

O

th( 1 -

= e t h > t

eth

(3.3.14)

(3.3.15)

, eir

(3. 3.16)

0.821 MeV

(3.3.17)

(3.3.18)

4-§-

-26116/f /T c ) . 0)$-signer) (3.3.19)

- 467 -

£cr=D°C0 • ( e , , / r r + e2,I>y + £Uth+e2.th) (3. 3. 20)

D°ca ±.

ESCORE S ^ creep

ESCORE 3J^&1M ^]

PWR

ESCORE 3 . ^ . ^ 1 ^ A>^-Si creep S ^ ^

£ Toto/ = £ Thermal + £ Irradiati (3.3.21)

B A i A % { - A 1 I T ) (3. 3. 22)

4 J cos m a x ^ ] B ' (3. 3. 23)

(m/m)

(hrs)

. (E > 1 MeV, n/cm2-sec)

(7 hoop = hoop s t ress (MPa)

T = 2 1 4 ^ ^ ^ ^ r £ ( °K)

% V 4 ^ S (MPa) o]t\.

AJ-7] A) (3.3.21)^: Gorscakif- Pfenning worth [3.3.7]*fl ^sfl 7 } ^

- 468-

(3 .3 .23)^ Franklin[3.3.8]c5fl 5]*fl

T (3.321 - 23)

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FEMAXI-IV 3.S. Creep S.1!

FEMAXI-IV SHoflA^ Af-g-^ Zircaloy-4^1

= -1.07+ (-0.00343 +7.27xl0"5T)c7e?+1.05xl0"3T

^ (kgf/mm2) T fe ^

O

(3.3.24)

O <i

(3.3.25)

- 4 6 9 -

xiO-250L23aif (3.3.26)

(n/cmJs)o|cf.

FATES-3A 3.E, Creep

FATES 3 . ^ ^

71

(3.3.27)

(3.3.28)

, ] (3.3.29)

th= [B][ sinh(0.078<rfl)][ exp{ (277^-76000)/i?T,}] (3. 3. 30)

JL ^A$] A.B.C.K.R & £

7J t i . ^ 1 4 t i

tota/= I 'etotaidt (3.3.31)

- 4 7 0 -

Rc~R2^stotal (3.3.32)

/=0A i? c, (3.3.33)

rad ius )^

(T-1-)

down

if FRAPCON-3 a.S.o]cK FRAPCON-3 3 H f e

71 §• FRAPCON-2

creep-out ofl^-

£ ^ ^ ^ ^ - ^ ^ creep-

creep-out# <H

^ CARO-D 5.5

.HS, 37lf

Creep-out#

m±S>] 3.s]

^[3.3.3, 3.3.5]^)

^ 3.3.12} 3.3.2^ 7]

CAR0-D5. 5 3 . ^

Hal den Reactor Project

r ^ ^ ^ ^ ( ^ 3.3.1)1-

J£# 4-g-tl 4^^^SA-] 71 -5] 3.5]

creep-out^# Tij ^ f e # <y-

FRAPCON-3 SHJtr:]- -y^^ofl .cf ^

creep-outoj

creepdown gjc\ 20-30%

O.^ 3.3.2^

^-f 2^f 3.1] oj

FRAPCON-3

hoop stress7} 30MPa hoop stress7f

. CARO-D 5.5 3

CARO-D 5.5 3.^$]

L SI©.!-}, FRAPCON-3

- 471-

W <£ T $ L M . IE$> FRAPCON-3 3.JE.^

time s tep^ 3.7]6\] afs

Creep-out S . ^ 7 ^

FRAPCON-3 3 . - ^ ^ 3 . ^ ^ ^

CARO-D S ^ ^ C f 3.5] ^ ^ - # - § ^ 1 ^1^-^M ^-^rfS-S. CARO-D 5.5

4 4-§-^l H . ^ S . 1 ! ^ 7 1 ^ 5 . * ! ^ * } ^ creep-out S . ^ ^ - flyf

rK CARO-D 5. 5 S ^ ^ ] i f f ^ f

(3. 3.34

£ c r = £ l . t h + £ 2 , t h + £ l , i r r + £ 2 , i r r ( 3 . 3 . 3 4 )

= C • e • (1 - e~kA) (3.3.35)

£2 = e • t (3.3.36)

*] (3.3.35) ^ (3.3.36)5] £ ^ <

£ t h = K2 • A t h - e x p ( - 2 6 1 1 6 K/Tc) • ( 7 e f f 1 - 8 7 - s i g n ( ^ e q ) ( 3 . 3 . 3 7 )

£ i r r = % • A i r f • ^ ° ' 8 5 ' CTeff » s i g n ( CT eq) ( 3 . 3 . 3 8 )

strain-harden ing ^^r, t: A f 7 ] ^ , k: 5.5-

exp(-1460.2/Tc), Ath: <£$3.^91*}, Tc : s j ^ ^ § ^ ^ S (K), Airr: ^

(E>0.821MeV)

- 472-

ZL1I 3.3.26 ^ 3.3.27S-*f^ 1 4

irji, 24 3 ^ ^ M 4 - b ^

JE*> 24 31} ^ I H H ofHMlSl 7l#7]7f ^ § 4 ^ 3 ^ 7]-i-7]iul-

ttfl^ofl CARO 3H5 | H . H ] 5 . ^ 1 4 14 3.S]

strain-hardening ^ r C ^ j ; ^ 7fl"&l-JL secondary creep

1.7-1.75 x 10"20

K 24

14

3.3.951 4

hoop stress7f 7}% *}o]7\ ^>^-

^-47]- hoop stress7> D] ^ ^ ^ ^ - 1 1 ^1^4 -&*;} ^ A £ I 4 (3.3.37)

5 | (3.3.38)^1 stress ^ ^ 4 ^ ^ ^Tfl, # ^ 4 4 ^ ^ 4 ^ f e 37l] « H

^-^ 3.3.28 ^ 3.3.29ofl>HAf ^o] A^^

K °M stress ^ 4 ^ r ^ 1.87^^ 1.57

S i^g^fSi^., S.Q 143.U^^rfe 2800

h"1, 2 4 3 . ^ ^ ^ ^ 1.7xlO"20 (n/cnf-s)'0-85. (N/mrf)"1 • h"1 o]#u|.. a}ef4 ^

creep-out S . ^ ^ 1 ^ u}^- ^ 3.3.6 ^ 3.3.7S

e t h = ^ - A t h - e x p i - 2 6 1 1 6 K/Tc) • Jeff1 '57 » s i g n ( creq) ( 3 . 3 . 3 9 )

£ i r r = ^ 'A i r r • <P°M ' CTeff S lgn( ff e q ) ( 3 . 3 . 4 0 )

CARO creep 3.^2} 7^^. creep-out S

creep-out S ^ ^ ] # Frapcon-3 3.^<^) ^-g-^rf^uf. ~L^ 3.3.30^

Frapcon-3^] creep 3.^ tfl-il^l CARO-D a.H5] creep

- 473-

creep-out S.^o]

JL<g4i£. «?<££-^ I ] ^ - ^ lift-off

creep-out J5.*go] ^ ^ . ^ u ] - . HaldenS] creep-out

creepdown

creep-out

Haldeni)

3.^7} <$ 20-30%

creep-out ^ ^ s]

(6)

ASTM Zircaloy-4

/flS.^: Zirconium

^ Zircaloy

o| ^Df. -Le|*H Zircaloy

!4#<>1 43.°}Zircaloy-4

SJ .^

4Zircaloy-4

<*| 5] 51

1980 . 3 . 3 5 ] ^

COCHISE S ^ ^ r Li OH*] ^ ^ ^

. Billot #[3.3.36]

^l*fl Li

- 4 7 4 -

nfef

- <g*o* 4^-6] ^ A S ufEfi^uf. [3.3.37-38] n

Cheng[3.3.39]^ s l ^ - ^ ^ -?-*|o

Zircaloy matrix ^$] Zr(Cr,Fe)2

^ Zircaloy

(7\) Zircaloy

Zircaloy

2 [im77\*} SJ&%[ n | 7 f x | ^ - pre-transition 7}Z± - ^ 1 ^ 1 0.33

fi A-| ^7}^fr^, ZL ^ ^ f e - post-transition 7]Zt -

7]s] H|sjl*fo^ ^ 7 } ^ ] . ^ 7\3§~Br M.<(tr.}. Post-transition

100 yum ^ l ^ W S.^-^- ^r ^l^f. Post- transition

Zircaloy Matrix^

. [3.3.40]

Zircaloy

l Zircaloy matrix^}

Zircaloy 2 1 ^ - ^ ; ^ ufl^-AlAj^. * O ^ A | ^ 7 ] ^ * 1 | 71^5] Zircaloy-4

Specification uflolH Sf«]-^^, ^ ^ B ] ^

f. Zircaloyi) ^ ^ # tin

5)4ii|- Ajea^-^, Tin SHS. Carbon#

-475-

^h °l iMr Improved Zircaloy 4 £ - Low Tin Zircaloyefji

<H14 tf£J-# - M # 10-30% #^4?lfe ^^.S.Zircaloy-4 Specification^- 3Hi-H Tin^- 1.2

*}7f*> 4-§-£ W ^ S ] Zirconium ^g-oj

^ S . Zircaloyij- -g-A}^^],

] Annealing

Lot ofl rcfef ^ ^

Zircaloy s ] ^ - ^ ^ JJLA^J i g * ^ ^

^ ] ^ ) l f Li nj Boron

4?lfe ^ ^ ^

o) <^^o| <$$\}c\6\ 3114^-^ -f^o] ^7}

Zircaloy-4 2 ] 4 ^ ^ ±-q ^-A!^. 4 ^ ^ O ] ^ ^ - I | * > ^ - S^*}jL ^1-

^^Sf^u^lfe S^nfcf 4 S u}^- JL^g^-i- ^ i Slcf. [3.3.41] HBillot[3.3.42]£- JL^^ cfl-tl Li

Zircaloy-4

$uf.[3.3.35] 3.

Zircaloy Matrix^

(uf)

- 4 7 6 -

© KWU S-^i

ds/dt = A/s2 • exp(-Qi/RT)

ds/dt = B • exp(-Q2/RT)

B = C • F

Original EPRI S.1^

EPRI, CE ^ KWUofl^^- o | 4 i £ 50MWD/kgU°]^H Zircaloy^l

Li

EPRI S . ^ ^

ds/dt = A/s2 • exp(-Qi/RT)

- 477-

s t = D • exp(-Q3/RT - E • T)

ds/dt = B • exp(-Q2/RT)

B = C + U • (M • <p)?

Hillner

EPR1

t^r 6.4e9 18.9e9

B ^ ^

B = C + 5 -U • (M • <p)

© Original ESCORE

Original ESCORE

L" ?A^- 2.38e8//m/day o

, 5/an

£ original EPRI

1.91e-15

ESCORE S^l

ESCORE S'i^; original

35

- 478-

(6) CORPRO

CORPRO

£ original EPRI J5.«H]A] 4-§"3 S c | ^ 4 ^ 4 4 . EPRI

ESCORE

CORPRO £ 1 ^ .

ta = ka • exp(Qa/RT)

Al

ds/dt = C • E • exp(-Q2/RT)

E = 1 + u • <p • <s-sc>

<s-sc> -fe- Macauley

© COCHISE 3.^_

COCHISE 3.r^o_

7l>H-b 1991 Hi «J 1 9 9 4 ^ 1 U ^ 37fl^] SDi(C0CHISE-91B, C0CHISE-94P,

C0CHISE-94BH dJ*H

ds/dt = Kpre/s2 • exp(-Qpre/RT)

d s / d t = Kpost • exp(-Qpost/RT)

- 479-

|^ frequency factor - % A^ 3>HM *] # oxide/water ^

litium - -££} ^^rS ufE}u|^u}. COCHISE S . 1 ^ nucleate boiling^

^ L Frequency factorb

mul tiplcation factor7} ^ H ^ & ^ K H.Z\3L COCHISE-94B

frequency factors -b s ] ^ - ^ S ^ ^ -- 1 H^0]^}. Frequency factor

o C0CHISE-94P

K p r e = e a t b > [ L i ] . F B

o C0CHISE-94B

p r e = e • {l + (Q*pre/RT2) . (S0/X)} • FB

[ ! • ( S 0 / X ) } - F B - F i

Qpre/R = c + d • [ L i ]

R = 7 + 8 - [ L i ]

ln (Q p r e ) = f + g - l n [ L i ]

ln(Qpost) = £ + rj • l n [ L i ]

l e l l ^ o | ^ ^ - COCHISE-94P S . ' i ^ EPRI, ESCORE models}

C0CHISE-91B, -94B J S . 1 ^ t t = kt • exp(Qt/RT-at • T) o)uf.

NDC

- 480-

NDC £ 1 ^ t;}^ S ^ }

^ l ^ ° 1 35 mg/dm2 (2.4/um oxide)

dw/dt = C • F* • FH • exp(-Q2/RT)

^ pcikup ? >

FH = 1.0 CH < 200ppm

a + b • logCH CH > 200ppm

© ENIGMA

4 f ^ . al^-^. KWU 5ENIGMA S . ' g o f l ^ ^ 2,2/tan

Li

d s / d t = C • $>D + E • FHYD • FLITH • FRXA • exp(-QpoSt/RT)

FHYD = MAX{1.0, a + jS

FLITH = MAX(1.0, M I N { r ( C ! • [ L i ] j • t i ) , FL i , MAX})

FRXA = 1.0 - 0 . 3 4 1 «RXF

RXF : r e c r y s t a l l l z a t i o n f a c t o r

(nf) Zircaloy Jf

Zircaloy

- 481-

(3 .3 .41 )

ds = C2'FMat-FFlux- F H> e x p ( - Q'(CLi)/RT) ( 3 .3 .42 )dt

Pre-transit ion 7l # £ | -?-*]£ ^>S}#^t n^l7f 4* 2

£#^° f l ^r-b ^%H ^71 ttfl^ofl 7)^3] Garzarolli JS.«g-§-

. Post-transition l #

^-71 (3-3-2)if ^o

^ FFlux 614S ufEfvfl^cf. 3114^^ Hydride*} <g%K& FH

flgi^Dl}, EPRI*] PFCC S^iil- ^-o] 31^-^*1 ^ ^ 7 } 400 ppm

FH7]- oj-eU f ^o] ^7}e fe ^ 0.3

F H=\ for CH^mppm (3.3.43)

^ ^ 6 . 5 . Lio] 3x1^-^^ A>^#6fl -ff-*]

7} ^7f^6fl rcfef %

O*(CLl-)=28200-^- (CLl-0.5) (3.3.44)

Li5] ^ ^ ( p p m ) ^ ! ^ , A ^ 43.4 (cal/mol-ppm)

^ 1.2(W/m-K)

- 482-

(3.3.45)

Garzarolli7|- 4 ^ * ] ; 0. 24#,

1.4xlO"3 ((neutrons/cirf-s)"024!-

23 °C7f

3.3.32 51 3.3.33 ^ ^ 4

"A ^ ^ ^ S l - t ^ f \3^ f . Li*] ^ £ 7 } 0.5 ppmcHW 3.5 ppm^.

} l ^ | f } ^ ^ ^ 4 1 4 . ^-^ 3.3.343.3.35 ±r 2 1 ^ - ^ ^ ^ ^ i f ^ J - ^ . ^ ^%>o| 6T^- 4 ^ ^

400 p p l j f l ^

3.3 .36^

3.3.37^; EPRlcHlA-l t«64^ s j ^ ^ - f - ^ S ^ ^ l PFCC

3.3.38^ Ringhals-3

Zircaloy-4 ^ - ^ S . ^ ^ 1 ^ -?-^M < %> - ^ ^

Zircaloy

. Zircaloy

483-

Li

(7) o | ^ ^ ^ ] ^ 7}<£

Rod)*]

(Duplex Integral Burnable Absorber

(7\)

Gd2o3-b

^ <#*-:£..£.

-7f

-g-O) Ttfl

1.15 ttfi ZLU 3.3.39<HH

- 4 8 4 -

ZL

*}5L S^oflfe Er2O3 5]

Gd2037} S ^ qjjL «^,g.-g-Sj Jj^j-g. ^ S } ^ 1 ^ A ^ ^ Jit:}

7} al }. n i s ,

^gol 0.2825 cm ^ ^

0.4025 cm^ ^^^F^uf . vH^-7}<^^ ^ - ^ ^ - ^ ^ ^ ^ - f e f e ^ l 12 w/o<q

*l (4.95 w/o) ^<££.oi] 2 w/o^] Er203l-

^ - g - ^ ^ ^ 247HS -^-4*1 ^ ^ ^ 1 < a ^ ^ o j Gd203

167B

2 ^ 1 5 J 3.3.4131}

§ ^ ^ ^ 8 w/o Gd2O3

^-g- i67fl# 4-§-»> ^ ^ s ^ ^ i i f Hl.2.*H a 3.3.

MWD/MTU)

3.3.10.

- 485-

1.1783

0.9896

1.1588

0. 9928

Cf

H &

(1) U02 Rim Effect

(7\) 7H ^L

UO2 ^

Pu-2397f ^ - - f - ^ A ^ 3.7]}

~ o on ~o

^ ^ ^ 1 - 2 /zm 3.71*1 ^ " ^ 71S7V

- 0 . 5 ywin 3.7}5^ <

Rim effect ^^ High Burnup Structure(HBS)BfJL *}^ n]M]^-^7}

uf[3.3.43-7]. Rim ^^ -c r - -f- ^^-S- 60 - 80 MWD/kglWH

1*11

., U02 0.1

feel],

3 3.<$<i\ 7]

- 486-

3.3.42^ ^S. ^ ^ ^ ^ 3.7]6|| nf^- ^ ^ e j

c|, uf#5] Speight^ ^ ^ H>>;8*U3.3.48]-

C(r,t) = gas atom concentration as atoms and bubbles(atoms/m ),

D = diffusion coefficient of gas atoms(m2/s),

b = resolution rate of gas atoms from the in-grain bubbles(/s),

g = capture rate of gas atoms by the in-grain bubbles (/s),

YF(t) = gas atom production rate by fission(atoms/m3. s).

7l*lJ

. Booths

f^ ^ ^ ^ RAPID s

TUBRNP[3.3.50] ^ ^ cfg- S.^ ^.u} A 4 ^ O | 7 ^ ^ RAPID ^SJ.

[3 .3 .51]^ <^4i£ 5| U-235

^ r S l - 71 >^ ^ 51^}.

(cf) HBS

U02 ^ * ) 1 ^ yoUW ^ ^ f ^ ^ f e ^ ^ 5 J ^-Hl^ ~10"9 m

^ %*-$- ^ ^ ^ [ [ 3 . 3 . 5 2 ] . ZL% 3 .3 .43^

-487-

3.7],

. PWR §

i]-¥" 6J"^°1 9 MPao]jL 7}SL^\ 3 | ^ O ] 1.2

7]^] 4 * 1 i lS^r 1 x 1027 atoms/m3 £.#\ --f- ^ ^ i 7 f 70

rcfl 7M ^g^^[ 7 ) 4 ^ 4 ^ %^ 4j= 2 «H Ml l S]^l ^Mr^.

-2. ^ - ^ ^ M ^ ! # ^]Vl ^ f ^ « i ^ ^ # ^ : U02 4i^^f VH}A-| ^ 6.5 //m#

15 nm

10"9

^ Displacement Spike ^>tfo | y i ^*> t :} [3 .3 .53 ] .

Vacancy7} 7}^S. ^g-£]*l ^ ^ ^ ^ - ^ f e 7 l S ^ i-fl-f < ^ ^ ^ ^ 1 4 ^ 6J 7)

uflofl

U02

. o ] ^ - Rim effect ^ ^ High Burnup S t r u c t u r e s ] ^ *>i:f. rcf

U02 ^ ^ ^ 1 ^ ] Rim effect

- 4 8 8 -

cf. H^ 3 .3 .44^ HBS7f 7 l ^ ] ^ 4 ^ £ 5.1 x 1026 atoms/m3

JL 7pg«* 4 , ^rS., ^ ^ ^ 3 . 7 1 £ ? « ^ ; < i ^ £ ^ ^Sf^fl ttfej- HBS7>

5 | ^ ^ - ^ - ^ ^ £ ^ 1 3 .7 ]# i<H^^K 700 °C <>}}

80 MWD/kgU o l * H ^ ^^5]xln>F ^ £ 7 } 1000 °C

^ - # S i*H HBS7} o}^] ^ 5 ] * ] ^ ^ ^

3.71 ^ ^ ^ - « i ^ S 7 ] - #^H=- ^ ^ r ^--f ^^£<HlA-1 HBS7f

HBEP (High Burnup Experiment Program)

°fl-b ^ - ^ r ^ ] ^ ^ 4 ^ 1 BSH-06 ^IS-f-Jl- ^1^:^14 &*}& BK-365

a I 4 [ 3 . 3 . 4 7 ] . BK-365 ^ ^ - ^ - ^ r 220 w/cm o]*}*]

BSH-06 <dS-g-^r 400 <y <5]AO^ 7l^>^-^> 300 w/cm ^ ^ 1

[. BK-365 ^ S - g - ^ < ? 1 ^ £ ^ 69.4 MWD/kgU-rod avg. O ] J I 3.8 % J « ^

5 ] ^ ^ ^ , BSH-06 ^^.-g-^r < ^ ^ £ 7 f 59.8 MWD/kgU-rod avg.

8.4 96$) tfl

HBS -*M|# ^ ^fe^L ^ f ^ 1 ^ ^

^ 14 >44 H l 4 4 4 1 HBS

BK-365 ^ S - g - ^ 800 °C ° 1 ^ ] 4 ^ - f -g :^ 3S}7\ o ] ^ - o ] ^ A ^ , BSH-06

BSH-06 ^ S - g - ^ HBS - ^ f e 4^°114 2:4^1 BK-365 ^S-g- Jicf HBS

7} 4 ^ } . a}5^i o i l - HBEP

HBS

U02 ^ ^ ^ 1 1 ^ 1 HBS

fe 34 €45]

- 4 8 9 -

(Displacement SpikeH rc}5> ^ I ^ S M , ^*}£) n]Afl

HBS7}

-f-# ^ £%i& 3.7]*)

-fe Halden Reactor ^^.S. 2,*}X\^[3.3. 54] -§-

(2) 2A}sl U02

(7f) 7H ja.

U02 ^^^1^1 < i ^ £ H ^ ^ S . , 7l^g-S., Stoichiotnetry,

l uo2

^ < i ^ i £ £ ^ 1500 °C <>]*H-Hfe ^ ^ Phonon

1500 °C ° j ^

l U02

Phonon

ttj-e} ^ 7 ^ f 7 l ttfi^^l, < ^ ^ ^ Phonon

7f # 7 } ^ ^ 1 K}ef ^ ^ ^ ^

^ i ^ ^ £ £ 7 f ^ 7 f ^ ^ l trfef

Sfl Phonon 4-e-i] ol^ .^ . ^ f ^ # -*11 ^fl*}7l ttfl^l < i ? i£

K Phonon 2Xf - A>^> A ] ^ ) ^ £ ^ ^ ^ ^ , ^.4^ VA 7]

-490-

U02

71S ^^1 ^*H ^ ^ 4 . U02

Rim

U02

- Loeb J S . ^ ^ : fp = 1- a p

- Maxwell 3L%*\ • fP = (1-p) 1 '5

- Maxwell-Eucken i ^ ^ 1 : fp = ( l - p ) / ( l+

- Schulz i ^ ^ ] : fp = (1-1. 5p)

- Bakker JL%*\ : fp - (l-p)1 '7*0"7

Loeb % Maxwell-Eucken .S.^ ofl*) a^ 0 ^i^fe S.^ 7] g-o| ^-«go]

^ ^ : S £ l & # ^-f^ffe ° ] ^ A ^ z | 4 1 ^ 0.5 ojuK J 5 |

U02 d t ^ ^ l ^ -y^| ^ ^ s | <^^£H ^1-S# Fitting*! ^2} , or

^- 2.5 ± 1.5

Schulz ^ ^ ^

. Bakker 2i3l*l£ 25 MWD/kgU <^^S7M ^ 4 ^ 1 U02

- 4 9 1 -

£ uo2

: Sr, Zr, Nb, Y, La, Ce, Pr, Nd, Pm, Sm

.- : Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sb, Te

!§-•• Ba, Zr, Nb, Mo, (Rb, Cs, Te)

# ^ ^44i : Kr, Xe, Br, I, (Rb, Cs, Te)

SIMFUEL . 3. 59]

U02 3.71 4

6 d U02

^ BCC

Gd 2 O 3 l -

U0 2 /Gd 20 3

FCC ^-2LS>\ U02

£J£l- * J * M W

r°fl Phonon-Phonon

Stoichiometry

- 4 9 2 -

3JS.0] Stoichiometry#

^ - ^ t l ^2f, x7f ^ ^ ^(Hyper-stoichiometry)

-B-e ^-T-(Hypo-stoichiometry) < i ^ S £ f e <^# ^

U02 4i^*ll^ < i ^ £ S ^ I ^7HA"lfe Stoichiometry

Halden[3.3.61] ^ NFI ^ ^ ^ [ 3 . 3

^ Stoichiometryi)

U02 ^ ^ ^ H ] ^ ^ VA -Q^VL. Dislocation ^ Loop^ 4 _ o j^o . p h o n o n d| ^ » ^ fl

U02 ^%}$] «a^i£

^ ^ 4 1000 K

(2) 71-g- f U02 ^ ? i £ £ S c |

Lucuta S ^ [3. 3. 601

1996 \4ofl ^-S*> ^ 4 ? U02 4i^^l^l 4 t l Lucuta

= KldKtpK2pK3xKljrA0

1 4.715x10" , 16361,/L = — 1 exp( )

(0.0375 + 2.165 x l O ^ r ) T2 T

- 493-

A = thermal conductivity of irradiated UO2

Ao = thermal conductivity of unirradiated 100 % dense UO2

Kid = factor for fission products

Kip = factor for precipitated metal fission products

K2P = factor for porosity

K3X = factor for stoichiometry

K4r = factor for radiation damage

<$*££: Daniel ^ Cohen*] *Kg.#[3.3.64] 4-§-*f5i^K 7l3-.5E.-b

Maxwell-Eucken i L ^ T § - 4-§-^f^-^-^, 100 % ^S. U02

Harding ^ Martin^ 4 S # [ 3 . 3 . 6 5 ]

Halden S.^[3.3.61]

Halden S l ^ ] f Halden ^ ^ - ^ - ^ ^ ^ ^}<£^. ^ H 4 ^ ^ 1 ^ *}£-7} 4

.}. 1997 VN VfiesnackoH ^«fl ^ a ^ Halden $] £ 1

.00355t/ + 2.475xlO"4(l-0.00333Sf/)7

5 ^ 95

+ 0.0132exp(0.001887*)

U02

- 494-

NFi_SM.[3. 3. 62]

NFI J S . ^ 39.3 MWD/kgU^j

4 Laser Flash Method^ «]Sj|

U02

NFI

l

4.52x 10"2 + 2.46x 10"*r +1.87 x 10'"BU + 0.03SBU02' • h{T)

1

~ l + 396exp(-6380/r)

-5.47xlO"9r+2.29xlO"'4r4

^ 95 %

(^}) uo2 < i ^ i £ £ s^ i^ j 7j|^-

n]^- EPRI71- ^ ^ f e ^ -^1^ -^^^ r S S - H H t l NFIR(Nuclear

Fuel Industry Research )^ \— 2i*\Q U02 ^ ^ ^ . ^ 1 tfl*l| £ £ # ^5f^ |^ l

^ ^ U02 ^ <m^l Tjj^l- Laser Flash Method^] *|sfl 4^^r}^cf

[3.3.66-67]. ^ 4 ^ 1 U02 ^ & g . £ | X\^^. 24.9 MWD/kgU(U2), 36.23

MWD/kgU(U4) Q 59.93 MWD/kgU(U6) ^ 4 i £ ^ l 3 fM

3.3.11.

Cycle

1

2

3

4

Temperature(°C)

Initial

300

300

500

300

Peak

800

1100

1500

1600

Final

300

500

300

300

Duration of Cycle of Specimen(min)

U2

269

240

422

469

U4

330

375

412

542

U6

332

485

485

611

- 4 9 5 -

N r 300 TCofH 1600 100 °C

. Cycle

uo2 800

Cycle 1

Cycle 25]

1100 °C 6J Cycle 2

Cycle

uo2. Cycle 3 ^ 3)tfl i500 °C ~.7}X\%7] ttfl^^l Cycle 3

Cycle 4<H1-M

Cycle 1-

, U4 micron

U 6

micron 3.7}$] 7}^7

Cycle

uo2 AA

U02 ^

} ^ ^ Lucuta S ^ i [3.3.60]^ - -

if 7]^]S. ^ e ] * } ^ JL^-crfoJcf. 4 o]4fe NFIR^

<g*<>*•§•

- 4 9 6 -

- - fifpffgfrdfp^O

10.152 + 0.07627"

/- =

10.152 - 4 .80545U 0 3 + 1.5635(7 + (0.0762 + 4.724 x 10~'BU°5 - 8 . 624 x 10"4 BU) • T

10.152 - 4.&054BU" + 1.563BU + (0.0762 + 4.724 x 10 ' BU" - 8.624 x 10" BU) • T

10.152-1.4235(7" + ].6012BU + (0.0762 + 3.043 x 10''BU" -8.066 x!0'i5f7)- T

U 9

0.5608 + 0.5655 exp(l 79.38/7")

1 4.715xlO9 , 16361,/L = ; + exp( )

A = thermal conductivity of irradiated UO2

Ao = thermal conductivity of unirradiated 100 % dense UO2

fSfp = factor for solid fission products

ffg = factor for gaseous fission products

frd = factor for radiation damage

fp = factor for porosity

U02 4 i ^ H i tflsfl^^ Loeb ^-^r Bakker

4i^^l Rim ^ ^ ^ - j i j . ^-o] ^2-^

ofl^. o l ^ . ^ ^ . S -o.s.5^ Schulz*]

H5J 3.3.46-49^1^ J2XI *}£<

^ - ^ 3.3.47^

- 4 9 7 -

. 1100 °C °l

. H^l 3.3.49^ °1#

} ^ i ^ , 1300 °C

1 ^ 3.3.50-53^:

NFI ^ ^ ! 7l^-^| uo2

£ NFI l

7]}

cf[3.3.55]. Lucuta

el], 500 800 °C

Lucuta, Halden

fetl NFI

r:f. Halden ^ 800 °C o]

^ Halden

, ^714 uo2

U02 Rim ^

Rim

^ 15 17

Rim

•1 , Trim f srimAr\m — Jsfp JrdJ p

Rim

80

ffj^ofl Schulz

71 -£.7} 15 %

Rim ^ 600

- 498-

^ - ^ - ^ ^ . £ 7 1 - 80

U02 r t ^ l ^

15 % 7)S. 7}^rS.Cy\\ SjSfl < i ^ £ £ 7 f 23

18 K 7 K > 4 . tcl-sH Rim <§

7]S: 71^-5] ^ t t o ] <g*o*.g. ^ | 3.5(*1-^, ^-¥-<^^£7f 80 MWD/kgU

Rim ^ ^ * ] U02 * f l £ l 600 °C^1^^ < ^ ^ £ £ ^ ^ A o ^ ^ l n 2 - ^ U02

til3-^}^ ^ 9 % °> # ^ H r ^ ^ - ^ U^l-^V. ^-, i ^ H UO2

Rim <

U02

7]

4U02

71SS ^#^lfe JL^^S. U02 4i^^|5l Rim

2 ^

(7f)

*l ^ pre-exponential fac tor^

Zircaloy-2 : 1.1X 107exp(-20,800/RT)

Zircaloy-4 : 6. 9 Xl07exp(-23, 800/RT)

-499-

™ :ZIRLO™ : 1.5Xl06exp(-18,000/RT)

16,300 cal/mol J i i fe

20,800

:£©..§.

H2/H2O

io5,io3«y

+ ~

- 500-

5~15mg/dm2

*\ pre-transit ion ^^ofl Sfl^j-*}^ ^ S j - ^ fto] 4°i J^] 4 ^

} A ^ 50% 4 ^

150% ^ ^ i f ^

l f ^ ^ffe- pre-transition ^ ^ ^ f post-transition

j i oTuf. a 5 ] 3 . pos r t - t r ans i t ion^^

(700°C, 210^r)<^]A-|^ surface to edge ratio7f

100mm ^o]^j Aj^iiul- *>SJ-i£:z]- ^ r ^ ^ ^ ^ l ^ 1.5~2Hfl

# T-MT-fltl^f. ^ H 1 ^ surface to edge rat io£| ^ ^ 1 4

Hfe ¥ ^ t > edge ^ % ^ ^ t ^ ^r tt^}. 3L*} 370°C,

steam corros ion^l^^ - ^ p ^ ^ ^ ^ ^ l waterside corrosion<>|]^-l^.c|-

50%, 3&\5L <$ 200%4^ ^7}5]Sd-g-^ ^^f^-^-^ JL^<

] 17l<y-iuf ^ ^ 4 - ^ - ^ e ^ # ^ K f l j l oiu}. 700°C,

steam corrosion^l^l^l ^ T ^ ^ - T " ^ 0 ] waterside corrosionJS.t]-

^, steam corrosionoJH ^r^^^f-7} 7

f 700°C,

20~30^m 4 £ ^ 1 ^5}V\ ¥ ^ 1 # %^*>SSl^.^ post-transit ion

(nf)

o i]

-

Zr + 2H20 -> ZrO2 + 4H(ad)

- 501-

l^ 2-5 ppm

2H2O -»• 2H + 20H -> H2 + H20

o M

( continuous-source S.1^., instantaneous-source S-

two stage

single stage with grain boundary saturation S-^-Sr ojJEL J_o_jg_

FEMAXI-IV ^i^S-H^l two-stage S ^ #

^ *}^cf. n ^af 56,500 MWd/MTU

^ two stagea^oj 0.235(equal radial ring volume*] ^-y-), 0.192(equal

radial ring size*] ^-f) ZL51JI -^^^.i^o] ^-§-5|o] *\J~ single

stage S ^ o j 0.167S ^7}t}<^u\. ^^^j;«y 0.218^1 H|*H two stage S«I

- 502-

°1 ^ 5 : 4 ^ 1 %7}*}&.3- single stage 3 . ^ u f i ^^7}^f^uf . 0}

T:]-H.7|1 J2.^*|-7] 4^<»]Df. Single stage 5.^1 £ Turnbull*]

. $13- two stage B.*i£: 2 ^ M ^ C-1]O|B]

, power ramping -§••§• J l ^ * ] ; NRC it^g <^^fl- ^ 40,000

MWd/MTU ^ 4 i £ °]Ao1-^^ 2 M 20,000Bl|7H ^ 7 } # JL^^fJl $17] nfl-g^

^ 7 } ov 50,000MWd/MTU ^ H 4 ^ fl f

two stage JS.»go| single stage S-^

(4)

finite element analysis module ) #

1 oil- 71^^]

commercial finite element analysis program

NISA 11/DISPLAY

7fl

0}

- 503-

-g- -8-*Lfi.4i*lH S . # # 7]^$] -#-§- -ff-*h£L^JH-g- ^SZLiS^l n]^- EMRC

^Q NISA II/DISPLAY III ^ n]-5*- MARC45J MARC/MENTAT

total Lagrange^ofl ^*>

SS-ZLsfl^l NISA H ^j MARCif

Cf.

L 4 4 ^ -^-tl-S.^ ^ - ^ S # ( finite element analysis

module )-§• 7H

4-S] -8-*>-S.4i ^ r ^ S # ( finite element analysis

module

finite element analysis module

*]£ ^ 1 ^ ^ creepfinite element analysis module )-§-

tl ^ } , ^r^r ^ ^ § ^ ^ 1 4 4 ^ ^ l ^ ^ ^ NISA II

^ ^ creep sfl -g- -^-*>^.4i ^ - ^ S # ( finite element analysis module )

- 504-

(1) 7l|

} [ ^ g - £ 950 MWe

17x17 KOFA (Korea Fuel Assembly) ^^^.-g-^1 ^ 7 f l | | 7 ) ^ ^ . 5

3658 mm^M 2000 mmS #<>] 31°]t}.

^ 4.95 w/o°M, ^ 35 7J)^ ^ 7 ] 5 . ii-gSj ^ ^ 5 . # ^

^ ^ # ^ ^ 120 w/cmS.*i, ^^i-g- PWRSJ ^ 5 ^ 1 - ^ , 178

31 % 4^F. U 54^ r^ ii^J ^ ^ # ^ ^ £ ^ 4 4 270 °C

310 0C^.<^ PWR£] 291.6 °C ^ 326.8 °C i n f ig-g- 19.2 °C 7}

PWR i c f 3.uf. ^ z | ^ ^ ^ J L ^ i ^ ]

-8-Sfl ^ ^ S l - b Borons

fe U02 ^^^15.^1 ^ ^ S ^ ] A - | <£^S. 60,000 MWd/MTU-rod avg.

(2) SMART

> *fe ^ s.o] al^}[3.3.70]. SMART

. ^ 950 MWe PWR ^ ^ ^ . ^ 17x17 KOFA «|^S[3.3.71]5]

# 71^-^.5. 4-§-t>4. ^ ^ S ^ ^ l S.& *A ^ 1 ^ # 3 . ^ 3.3.57-60^

3.3.19^1 7]<£Z}&T:1 U02 ^4H$\ Zircaloy-4U02 4:

- 505-

$%•& 9.5 mm°]3L 4 ^ * f l ^ i ^ ^ r 8.05

fe 0.64 mmo]u}. **} £.&-§- ujj «J£.g. ^ * f l £ l ^

•%-S. ^ ° ] ) f e 2,000 mm^.^ 17x17 KOFA ^<£^.-g-£l zjo] 3,658 mm^ 55 %

S M A R T - g - ^ ^ g l m l | ^ ^ } ^

] ^ ^ ^ ^ ^ ^ j * | | ^ o ] ^ - 2,189

2,000 mmo]uK SMART tfl«^^.^-^ ^ ^ S . # 5 wt.%

60,000 MWD/ MTUojd]-^ ^ ^ 5 . ^ ^ 5 1 7 ] 4 ^ : ^ ] , ^:g:(£ 7]^}$] «]•

oflA-l SMART «?<&g.-g-£| ^I4i « l ^ o ] PWR^ KOFA

7.0 x 1021 n/cm2(E > 0. 8

(uf)

330MWt^- < y ^ | ^ ^ 4 5 . ^ 1 SMART

^ 0 4 ^ . - ^ ^ ^ 5wt*o]vJJ t "-g-"^) ^ ^ f l £ 5 1 7 ^ ,

l%Ap, ^ H ^ ^ l Keff 0.95ol*>

CASM0-3/MASTER ^i^>3.S^Ml# o]-g-*f<^ SMART-L

-fe 17x17 K0FA# 7 | ^ A 5 . -g-jLic^ ^ o ] ^ - 200cml- 7]

SMART

U02+Gd203

- 506-

4.95 w/o U-235

1.8 w/o U-

12 w/o Gd2O3

^ fi 3.3.13-15^1

fe Siemens/KWU

71] 37}*] ^ - f S . ^P-^r^f'H Long Term, Hot Channel ^ Stress

Long Term ^ ^ ^ ^

Hot Channel ^H4£- PC-1 2f PC-2 ^ ^ i ^ l tcfB>

- Cladding Stress ^ ^ ^ PC-1 3} PC-2

KOFA ^<££.^ ^7fl7l^(JE 3.3.12)^1

- Long Term Analysisif

equivalent plastic strain(eeq)

CH

- Hot Channel Analysis^}

- 507-

total tangential strain(

Cladding Stress Analysis^

« f < ^ ( PD )

T,flJjL ^ .g^tLa^^o} equivalent stresses

Alternating Bending Stresses

SMART-L-g- *9£.&-§• | ^ o | ^ Long Term ^ Hot Channel

H-b CARO-Df-

^ S-^- CARO-D T^l^l^l^ Engineering Factor(FT = 1.03)1- J

^°H^1 - f # ^ °l^^r Engineering Factor^] ^sfl 1.03

RIP, GEeq, Tcl,

• Long term 1 (LT1) - rod internal pressure (RIP)

• Long term 2 (LT2) - equivalent plastic strain of

the cladding (eeq)

• Long term 3 (LT3) - best estimate calculation of

fuel rod behavior

• Hot channel 1 (HC1) - fuel centerline temperature

(Tci )

• Hot channel 2 (HC2) - total tangential strain of the

cladding (^t)

Long Term H 4-§-3*f CARO

Emplrical Irradiation Fitting Factor)^

C0M0-C 3-^$] 4.3^^ Best estimated CARO

- 508-

TT 2.6 F i t t i ng

Fatcort- A f - g ^ ^ h

stress £ * j £ <£^<>ls|# J L ^ ^ ^^.7} &uh s j ^ stress*]

^l^-^-i] stress7} <g^

4 j ^ ^ g 4 ! ^ % # ^ f f l ^ H SPAN-C 3.H

Long Term ^ 2 - f Hot Channel ^ : ^ # *l*f| ^^7|1 H-i-^A-] Z]-Z{- J

. SMART ^

S^lA-1 Long Term ^ ^ 4 #

cj ^711 ufE^L-M, Hot Channel

Engineering Factor(FT = 1.03)7f

CARO- D5.5 3^. *\%^ [3.3.74]ofl

7}l^]^A-l[3.

3.3.13-15^1

Hot Channel ^ ^

SMART ^4^.-§- ^^^.-g-*] Hot Channel 7fl^^2]-i- S 3.3.18

- 509-

tangential strainJE

Long Term :^

SMART #*}-.§.-§- ^ 5 , - g - ^ Long term T f l ^ ^ - t S 3-6

Best Estimation 7fl>iHH 103.2um

500ppm#

KOFA

o o

CAR0-D5.5^1 oj-g-tf ^ ^ ^I*>^1«^ ^ ^ > * | ^ - 4 7 }

7f 4.

(3) SMART ^

(7}) SMART

i )

- 510-

ii) *

iii)

-g-:iv)

A

iii)

iv) °JS)I

Vi)

vn)

vifi)

- 511-

-( Coll apse )

ix)

*>u>.

Coll apse H

o SRP Section 4.2Fuel System Design

o 10CFR50 App. K GDC 10o ANSI/ANS 57.5

LWR' s FA Mechan i ca 1Design and Evaluation

SMART - i ^ ^ ^

(4)

^ r 950 MWe PWR-g-*] KOFA (Korea^4-S-(SMART)-§-

Fuel Assembly) «?£.g.-g-£| ^ 7

KOFA I 3658 mm<>M 2000 mmS

Engineering x}3.7\ ^5]$.^} S.^ ^ HQ-& S. 3.3.13^1

fe 4.95 w/oS. 1 ^ 35 7H

^ ^ i # ^ 122.2

^ # ^ , 178.3 w/cm^t:} ^ 3 1 % 4 ^ ^ 4 ^

4 4 270 °C ^ 310 °CS^1 PWRSJ 291.6 °C 5J 326.8 °C

7} \*u>. Hfiiv} ^ o 4 S ^ . ^ i | 4 ^ o . ^ o ] 47] trfl cHl

PWR

19.2 °C

l ^ U02 60,000

- 5 1 2 -

MWd/MTU-rod avg.

^ ^ 5 . 2 ) 4 ^ ^ . ^ 4-g-Sj-b Zircaloy-4^1

60,000 MWd/MTU-rod avg. °]<$7}x] ^£{$1°-^}, °]-

. Zircaloy-4

SMART ^<^^.^1 ^ ^ r # ^ ^ PWR &t[ <$ 31 % 4 - ^ h ^ ^ # ^ # T

^ ^-Jf # ^ ^ & PWR

z}o\7} ^ # ^ ^ . S ^ ) ^ 5 | ^ , SMART

Boron cfl>il^ ^ ^ 6 o ^ Gd

^ ^ 4 , 1 1 ^ ^ ^ } SMART # ^ j ^ l i j f ^ ^

46 MWd/kgU <>l*l-ofl>H s ] 4 ^ * ] «

f. He] jL SMARTS 6J^f7i)^f- ^ 5 } ^ PWR f cfs.uf

Borons] t| |-§-*M u<§4^r^l pH# - f S f ^ l ^ ^ f e - Lithium

SMARTS ^ S ^ ] o } # 10 ppm

SMARTS PW

50 ppmAS.^1 PWR5] 0.15 ppm

^ £ M SMART

o] 3i

- 513-

3.3.54-56

514-

fi 3.3.1 Frapcon-3 3.^

Reactor

Halden HBWR

Halden HBWR

Halden HBWR

Halden HBWR

BR-3 PWRBR-3 PWRBR-3 PWRBR-3 PWR

BR-3 PWR

NRX PWR

NRX PWR

EL-3 PWR

EL-3 PWR

ANO-2 PWR

Oconee PWR

Monticello BWR

TVO-1 BWR

Assembly andRod Number

HUHB

IFA-432Rl, R2, R3

1FA-513 R1.R6

IFA-429 Rod DH

36-1-8111-1-524-1-638-1-6

BNFL-DE

LFF

CBF

411O-AE2

4110-BE2

TSQ002

15309

Al

H8/36-6

Rod-AverageBurnup,GWD/MTU

80

30 to 40

12

74

61.548.660.153.3

41.5

2.2

2.6

6.2

6.6

53

50

45

51.4

Fuel ThermalVersus Burnup

oo

(Rod 3)

BOLThermal

O

O

FGR

O

OOOO

ooooooooo

Fue1 Swe11i ng andRod Void Volume

O

oooo

oo

13 ,3 .2 Frapcon-3 3.H

Reactor

0conee-l PWR

ANO-2 PWR

Monticelo BWR

TVO-1 BWR

Assembly andRod Number

15309

TSQ002

Al

H8/36-6

Rod-AverageBurnup,GWD/MTU

50

53

45

51.4

CladdingAxial Growth

O

O

o

o

CladdingCreepdown

o

o

o

Cladding Oxidation andHydrogen Uptake

o

o

o

o

- 515-

3.3.3

Reactorfor Base

Irradiation/for Ramp Test

Obrigheim/Pet ten

Obrigheim/Pet ten

Studsvik/Studsvik

Hal den DR-2

Assembly andRod Number

D200D226

PK6-2PK6-3PK-6-S

Rod 16Rod 18

F7-3F14-6F9-3

Rod-AverageBurnup,GTO/MTf

2544

353535

2118

352733

Fuel-CladdingDialmetral

Gap Size, mils(microns)

8 (203)6.7 (170)

5.7 (145)5.7 (145)5.7 (145)

5 (127)5 (127)

7.1 (180)7.1 (180)7.1 (180)

Fil l GasType andPressure,psi(MPa)

He, 305(2.10)He,305(2.10)

He,326(2. 25)He, 326(2. 25)He, 326(2.25)

He,1.47(.10)He,1.47(.10)

He,1.47(.10)He,1.47(,10)He,1.47(,10)

MaximumRod-AverageLHGR,k«/ft

(MV/m)

8.26 (27.09)8.26 (27.29)

8.2 (26.90)8.2 (26.90)8.2 (26.90)

13.1 (42.97)10.97 (35.98)

13.33 (43.72)10.43 (34.21)13.3 (43.7)

RampTermainal

Level,kW/ft(hrs)

13.8 (48)13.1 (48)

12.2 (12)13.1 (12)12.5 (12)

14.6 (24)12.5 (24)

13.0 (24)13.44 (24)13.3 (43.7)

FGR Pre-Ramp(Post-Ramp),

% of produced

6.6 (38)4.2 (44.1)

N'A (3.5)NA (6.7)NA (6.1)

NA (16)NA (4)

5.7 (11.5)5.8 (22.1)7.3 (17.5)

3.3.4 IFA-429

Rod

BC

BH

DD

EE

CD

CH

Freevo1ume

(ccm)

2.90

1.93

2.30

2.20

2.35

2.68

Gasvolume

NTP(ccm)

4.70

88.25

67.54

64.18

92.59

167.0

Pressureator

(bar)

1.62

45.77

28.99

29.16

39.40

62.30

Gas composition

He(Vol %)

0.0

73.93

81.64

94.59

58.59

45.25

Kr(Vol *)

8.47

2.16

1.47

0.51

5.00

6.75

Xe(Vol %)

91.43

23.24

16.89

4.90

36.31

48.00

Other(Vol %)

0.0

0.67

0.0

0.0

0.0

0.0

E0LFGR

{%)

2.15

8.65

9.06

2.66

13.3

32.0

- 516-

3.3.5 RISO-II

Test

Riso-a

Riso-b

Riso-e

Riso-h

Riso-i

Riso-k

Riso-1

GE-a

GE-b

GE-g

GE-h

GE-i

GE-1

GE-k

GE-m

GE-n

GE-o

FuelSegment

M78-1-39

M23-1-6

M23-1-9

M23-1-17R

M23-1-21R

M38-8R

M73-2-8R

STR017-3R

STR017-5R

STR025-3

STR018

STR026

STR016-4R

STR019-8

STR013-8R

STR027-7R

STR025-5R

Burn-up

%FIMA

4.66

4.36

4.62

3.36

5.29

3.35

3.33

3.4

3.5

3.1

3.1

3.1

3.1

2.3

1.7

-

3.2

MWd/kgUO2

37.27

34.87

36.95

26.81

42.31

26.79

26.63

28.54

29.38

26.02

26.02

26.02

26.02

19.31

14.27

-

26.86

BTLkW/m

39.8

40.0

41.6

40.4

40.1

40.7

39.8

42.4

38.7

42.3

42.7

43.6

42.0

42.5

41.7

-

44.5

FillGasbar

1 Xe

1 Xe

5 He

1 Xe

1 Xe

1 Xe

5 He

5 He

1 Xe

16 He

17 He

17 He

5 He

5 He

5 He

-

5 He

FGR %

14.0

15.3

24.9

16.7

13.3

24.6

15.7

18.8

19.7

18.2

5.1

7.3

19.3

30.0

11.1

-

33.8

Comment

Clad failure

-

Long hold time

-

-

Large gap

Large gap

-

-

-

Long hold

unopened

Long hold

unopened

With power dips

With peaks to 50

kW/m

With power dips

Failed

-

- 517-

3,3.6 FA-198

Rod No.

1714223141525869758696105113120126

Max. X-section

Burnup

MWd/kgU

58.3

57.8

53.0

58.0

49.0

48.0

49.0

56.1

57.3

48.6

>47.6

47.9

48.8

51.2

55.1

55.9

Average Rod

Burnup

MWd/kgU

50.8

50.6

45.9

4442.6

41.9

42.4

48.8

50.1

42.4

>41.3

41.7

42.6

44.6

48.7

49.8

Clad

creep-down

microns

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

50-60

Rod

Internal

Pressure

MPa

-1.33

0.93

0.95

0.87

0.93

0.91--

0.93

0.93

0.91

0.92

0.95

1.07

-

FGR

%

-1.22

0.84

0.61

0.58

0.52

0.65--

0.60

0.49

0.51

0.49

0.76

1.29-

3.3.7 FA-222

Rod No.

1714223141525869758696105113120126

Max. X-section

Burnup

MWd/kgU

64.0

63.8

59.4

>56.5

56.5

55.6

56.0

60.5

62.2

54.6

53.2

52.8

53.1

53.6

57.8

60.0

Average Rod

Burnup

MWd/kgU

55.4

55.3

50.9

>48.4----55.2

>45.8-

>44>45>4750.4

52.5

Clad

creep-down

microns

40-60

40-60

50-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

40-60

Rod

Internal

Pressure1 A ^S *mj ±J **H. ^^

MPa-1.401.131.401.400.981.01-1.381.011.010.991.001.011.10-

FGR

-3.712.081.631.630.820.99-3.511.001.000.811.122.182.26-

- 518

3.3.8 Gd

Isotope

Gd-152Gd-154Gd-155Gd-156Gd-157Gd-158Gd-159

Abundunce(a/o)

0.

2.1

14.8

20.6

15.7

24.8

21.8

Thermal neutronabsorption crosssection(barn)

10

80

61000

2

255000

2.4

0.8

1 3 . 3 , 9

oCladding

- Outer Diameter (mm)

- Thickness (mm)

- Oxide Layer Thickness(/an)

- cold work {%)

oPel let

- Outer Diameter (mm)

- Inner Diameter (mm)

- Enrichment (wt. %)

oFuel-Clad Diametral

Gap Width (/m)

oNeutron Flux (10"n/irf-s)

(E>lMeV)

oCladding AverageTemperature (°C)

oHoop stress (Mpa)

oRod Internal Pressure

at RT(bar)

oCoolant Pressure(bar)

oIrradiation Time (fph)

oPressure Difference(MPa)

IFR-585.1

10.75

0.73

-

76

8.9

-

8.0

300

5

370-380

50

-

162

4000

10

IFR-585.4

Upper Rod

10.75

0.725

26

76

9.0

3

9.0

300

3.2

375

85

100

157

3100

15.5

Lower Rod

10.75

0.725

26

76

9.0

-

8.0

300

2.5

380

30

100

157

3100

9

Remarks

pre-irradiated

hollow pellet

- 519-

3.3.12 Fuel Rod Design Criteria and Limits

No.

1

2

3

4

5

6

7

8

9

10

Design Criteria

The maximum fuel centerline temperature shall be lowerthan the fuel melting point

The maximum end-of-life internal pressure in the fuel rodshall not enlarge the fuel-to- cladding gap(i.e., the increasein the cladding tube diameter caused by the internalpressure shall be less than the increase in the pelletdiameter due to fuel swelling). The maximum permissibleincrease in the cladding tube diameter is limited bycriterion 4.

The total tangential strain (obtained through superpositionof elastic and plastic strains) which occurs as result of fastpower increase shall be less than or equal to 1 %

The equivalent plastic strain in the tensile range(composed of axial and tangential strain) shall be less thanor equal to 2.5 %

The corrosion layer thickness due to uniform corrosion onthe cladding tube outside surface shall be less than orequal to 100 um

The hydrogen concentration averaged over the wallthickness of the cladding tube shall be less than or equalto 500 ppm

The fuel rod design pressure shall be less than thecritical elastic buckling pressure

The fuel rod design pressure shall be less than thecritical pressure for plastic deformation

For the equivalent stresses in the cladding tube and inthe welding range the following design limits are appliedfor the individual stress categories

The alternating bending stresses due to dynamic loadsshall be less than 50 N/mm2

Limits

Tel < Tmelt

e t =si %

^ plastic,equiv. —

2.5 %

6zrO2

< 100 pm

CH2 ^500ppm

P D < Pcri.,el

P D < Pcrit.pl

Stress

Category*

o b < 50

N/mm2

Remarks

Stress CategoryPrimaryPrimaryPrimary

Membrane StressesMembrane and Bending Stressesand Secondary Stresses

MM+BM+B+S

Design Limit0.9 Rpo.2

1.35RPo22.7 RPO.2

= Minimum Value from; 0.5; 0.7; 1.0

Rm

Rm

Rm

RPO.2 = 0.2 % Yield Strength as Fabricated Value

Rm = Ultimate Tensile Strength as Fabricated Value

- 520-

3.3.13 Summary of Reactor Thermal Hydraulic Data in SMART

Parameter

o System pressure

o Coolant inlet temperature

o Mass flow rate

o Heat transfer coefficient

between coolant and fuel

rod

o Core average LHGR

o Heat production outside the

fuel rod

o Maximum possible LHGR

o Peaking factor due to fuel

rod tolerances

Unit

bar

°C

kg/s

W/K/m2

W/cm

%

W/cm

SMART

150

270

0.09446

14,300

120.05

2.6

420

1.03

Remarks

- 521-

3.3.14 Summary of Fuel Rod Data in SMART

Parameter

o Active length

o Upper plenum length- UO2 rod- U02/Gd203 rod

0 Cladding tube condition

0 Cladding tube0. D.I. D.

0 Plenum volume- U02 rod- UO2/Gd2O3 rod

0 Pre-pressure

0 Fill gas

Unit

mm

mm

mm

cm

bar

%

SMART

2000

166166

Highly cold-worked*

9.58.22

6.46.4

21.5

He > 96Ar < 4

Remarks

(*) : Primary Candidate Alloy

3.3.15 Summary of Fuel Pellet Data in SMART

Parameter

0 Density- UO2

- U02/Gd203

0 Enrichment- UO2

- U02/Gd203

0 Fuel pellet diameter

0 Fuel pellet height

Unit

g/cmJ

w/o

mm

mm

SMART

10.409.92

4.951.8/12

8.05

10

Remarks

- 522-

.3. 3.3.16 List of Computer Codes used in Design Calculations and

the Corresponding Design Limits

Design Calculation

Hot Channel

Longterm

Stress

Analysis

Fuel centerlinetemperature

Total tangential strain

Internal gas pressure

Equivalent plastic strain

Corrosion layer thickness

Hydrogen content

Equivalent stress

Cyclic bending stress

Elastic buckling

Plastic deformation

ComputerCode(*)

CARO-D

CARO-D

CARO-D

CARO-D

COMO-C

**

SPAN-C

SPAN-C

**#

***

Design Limit

Tel < Tmeli

e , < l %

No enlargement of Gap

*— plastic.equiv. — 2..J / o

6zrO2 ^ 100 lira

C H 2 ^ 5 0 0 p p m

O e < 0 adm.

ob < 50 N/nW

P D < Pcrii,el

P D < Pcril.pl

(>:<) CAR0-D5. 5 (PC Version)

(***) Stress Analysis-b o•a. •

- 523-

3.3.17. Results of Longterm Calculations in SMART

PowerHistory

UOLT

Fuel RodBurnup*

(MWd/kg)

46.21

OxideT (a)

LayerThickness

Oim)

103.2

RodInternal^Pressure

(bar)

120.8

Equiv.w

CladdingStrain(%)

0.89

Hydro.Cont.(ppm)

500.96

(a) The limit of the design criterion is 100 jUm.

(b) The non-lift off design criterion is satisfied, because the

internal gas pressure is below the coolant pressure (150 bar).

(c) The limit of the design criterion is 2.5 %.

S 3.3.18. Results of Hot Channel Calculations in SMART Fuel Rod

PowerHistory

UOHC

Fuel RodBurnup(a)

(MWd/kg)

10(591)

20(591)

HC-1

LocalBurnup(b)

(MWd/kg)

10.65

21.93

* melt

m2803

2767

m2585

2559

HC-2

e, w

(%)

0.45

0.91

(a) rod average burnup where the engineering factor(Fr = 1.03) is

included.

(b) local rod burnup where maximum centerline temperature occurs

(c) melting temperature of the fuel rod which depends upon the local

rod burnup :

Tmeit(U02) = 2837 - 3.2 «B

where, T in °C and B in MWd/kgU.

(d) maximum fuel centerline temperature whose design limit is fuel

melting temperature.

(e) maximum cladding tangential strain whose design limit is 1%.

- 524-

S. 3.3.19 SMART Data Summary

Cladding Tube- Outer Diameter- Inner Diameter

Minimum Clad

Thickness

Active Length

Fuel Rod Length

Active Length Position

Plenum Length

Pellet Diameter

Diametral Gap

Pellet Density

U-235 Enrichment

Plenum Volume

Min. Plenum Volumeafter Repair

Parameter

Cladding Tube

Fuel

End Cap

UO2

UO2+Gd2O3

Upper

Lower

Plenum Spring

Disk

Fuel Rod(Total)

mmmm

mm

mm

mm

mm

mm

mm

ft m

g/cm'*

w/o

cmJ

cmJ

KOFA

9.5 ± 0.058.22 ± 0.04

0.57

3,658 ± 6

3,847 - 2

11.5 - 0.8

166 ±(+7.6, -8)

8.05 ± 0.01

170 ± 50

10.4 ± 0.15

3.7

6.4 ± 0.6

5.7

Material

Zircaloy-4

Zircaloy-4

Zircaloy-4

1.4568(DIN)

1.4541(DIN)

SAMRT

9.5 ± 0.058.22 ± 0.04

0.57

2,000 ± 6

2189 - 2

11.5 - 0.8

166 ±(+7.6, -8)

8.05 ± 0.01

170 ± 50

10.4 ± 0.15

4.95

6.4 ± 0.6

5.7

Volumefcm3)

38.59

99.33

99.33

0.42

0.42

2.33

0.04

153.53(displacement volume)

Mass(kg)

0.2531

1.033

0.989

0.0028

0.0028

0.018

0.0003

1.3118(uo2)1.2678(uo2+Gd2o3)

ti\ H

Remarks

12w/o Gd.Oj

- 525-

""U (0 MWD/XgU)•""polOMWD-kgU):t>u(O MWD/kgU)

0.2 0 4 0.6 0.8 1,0

Normalized Radius

o

x_ 8.0x10* "

E

| e.oxio"*-

J;| 4.0.10--

Ato

mic

Nu

mb

er

b

"SU (30 MWD/XgU)-"'Pu(30 MWD'kgU)

:"Pu(30 MWD/kgU) |

//

0 0 0.2 0.4 0.6 0.8 1.0

Normalized Radius

:J )U (60 MWD'kgU)- : l*Pu{60 MWD/kgU)

. . . . ;"Pu|60 MWD/kgU)

0.0 0.2 0 4 0.6 t

Normalized Radius

8 0x10"*-

6.0x10'*-

4.0x10''-

2.0x10'-

I1SU (90 MWD/kgU)-:>BPu(90 MWO/kgU)

. . . . !"Pu(90 MWD/kgU)

0 0 0.2 0,6 0,8 1.0

Normalized Radius

3.3.1 Variation of radial fissile atomic density distribution

with the burnup(4 w/o 5U)

o.o 0.2

1 0

X3 0.8 -

1

ron

1

•5 0.6 -

2:

Q) 0.4 -

aliz

E0 0 . 2 -

z

0.0 -1

. . . . . .

n M\A^n/knl 1

30 MWD/kgU

60 MWD/kgU

90 MWD/kgU

- - 120 MWD/kgU

150 MWD/kgU

0.4 0.6 0.8

Normalized Radius

1.0

235,n.^1 3.3.2 Radial variation of one group neutron flux(4 w/o U)

- 526-

Time independent input data : pelletradius, U02 density and 235U enrichment

Radial nodalization : set radial positionof the node

r

Time-dependent input data : time andpower density

Calculate the pellet burnup

r

Calculate neutron flux and radialdistribution of cross sections of the

nuclides

Calculate radial atomic densities of thenuclides

Calculate radial power distribution

- Calculate radial burnup distribution

3.3.3 RAPID calculation flow

- 527-

2.5

oroLJ_

Q.C

CQ

"D<DN

EO

1.5 -

1.0 -

0.0

Normalized Radius

3.3.4 Variation of radial burnup distribution with the burnup

(4 w/o 235U)

o(0Q.3C

Eo

0.8 0.9

Normalized Radius1.0

235,H ^ 3.3.5 Variation of radial burnup distribution with U

enrichment at the burnup of 30 MWD/kgU

- 528-

1.4x10

E. 0CO

(ato

rris

ity

<DQ

0)

£

Z0

E0

1.2x10

1.0x10""

8.0x10"5

6.0x1 0"5

4.0X10"5

.c-£ 2.0x10 "

0.0

30 60 90 120

Burnup(MWD/kgU)

— —. . .

D

0

A

"8Pu(HELI0S)""PufHELIOS)!"Pu(HELI0S)!<!Pu(HELIOS)"'Pu(RAPID)!<°Pu(RAPID)!J'Pu(RAPID)'"Pu(RAPID)

150

3.3.6 Variation of atomic number density with the burnup at mid

radius (4 w/o 235U)

5.0

O

CD

C(1)

ooO13CL

CDN

E

4.5-

4.0-

3.5-

3.0-

2.5-

2.0-

1.5-

1.0-

o

V

•

31

29

27

479

571

663

MWD/kgU

MWD/kgU

MWD/kgU

-RAPID(29 MWD/kgll)

0.2 0.4 0.6 O.i

Normalized Radius

1.0

3.3.7 Comparison of radial distribution of total Pu

concentration with the measured STRO fuel data at the

burnup of 29 MWD/kgU[5]

-529-

o

(0

Q.

cCO"O

Ni

"toEo

2 -

0 -

D 29.571 MWD/kgU

V TUBRNP

RAPID

i

J

f

0.0 0.2 0.4 0.6 0.8

Normalized Radius

1.0

3.3.8 Comparison of radial burnup distribution with the measured

STR0 (2.9 w/o 235U) data and TUBRNP prediction at the

burnup of 29.571 MWD/kgU[5]

180

O BR-3 fuel(8.6%"'U, Nd-profile by EPMA)- - - -APOLLO-2 (B.6%235U)

RAPID (3.2%235U)RAPID (8.6%23SU)

0.0 0.4 0.6

Normalized Radius

^1^3 3.3.9 Effect of 235U enrichment upon radial burnup distribution235,in comparison with the measured BR-3 fuel(8.6 w/o U)

data[3.3.14]

- 530-

0.010

•£ 0.008-

Eo

0.006-

"S3E>

03

— 0.004-

D D

o.ooo M ' T ' T i

' ——

^ - i —. — -*

A '

v - • - - . . .

a 2MPu(ORIGEN)O 240Pu(ORIGEN)C, 24'Pu(ORIGEN)V 242Pu(ORIGEN)

23sPu(RAPID)24°Pu(RAPlD)

- - - -^'PutRAPID)242Pu(RAPID)

20 40 60 80 100 120

Burnup(MWD/kgU)140

O-Q 3.3.10 Comparison of total Pu concentration in the pellet with

0RIGEN(4 w/o 235,, >

4 w/o Gd 2 O,

6 w/o Gd 2O 3

9 w/o Gd2O3

12 w/o Gd 2 O,

6 8 10 12 14

burnup(MWD/kgU)

16 18 20

O.^ 3.3.11 } ^ Gd-157 w/o U-235)

- 531-

3.0

2 MWD/kgU6 MWD/kgU10 MWD/kgU20 MWD/kgU30 MWD/kgU50 MWD/kgU

0.0 0.2 0.4 0.6

normalized radius0.8 1.0

ZL^ 3.3.12.

(9 w/o Gd2O3, 1.8 w/o U-235)

3.0

2.8 -

2.6 -

2.4 -

2 2 -

o 2 . 0 -

» 1 8 ~

S 1-6 -

o 1.4 -

1.2 -

1.0

0.8 -

0.6 -

4 w/o Gd2O3

6 w/o Gd2O3

9 w/o Gd2O3

12 w/o Gd2O3

0.0 0.2 0.4 0.6

normalized radius0.8 1.0

ILiQ 3.3.13

(1.8 vv/o U-235)

- 532-

3.0

2.8 -

2.6 -

2.4 -

2.2 -

3 2 - ° ~Jj 1.8 -

S 16 -O 1.4 -Q.

1.2 -

1.0 -

0.8 -

0 . 6 -

4 w/o Gd2O3

6 w/o Gd2O3

9 w/o Gd2O3

12 w/o Gd2O3

0.0 0.2 0.4 0.6

normalized radius0.8 1.0

T.5] 3.3.14 20

(1.8 w/o U-235)

10

c.22coo

1 -

.E oi -o

<D~ 0.01 -=raEor - 1E-3-

CD1E-4

• 0 MWD/kgU2 MWD/kgU10 MWD/kgU20 MWD/kgU

0.0 0.2 0.4 0.6

normalized radius0.8 1.0

3.3.15 ^ S . o f l tcf^ Gd-157 ^ S

(9 w/o Gd2O3, 1.8 w/o U-235)

- 533-

0.71 w/o U-235•o- 1.8 w/o U-235A 3.0 w/o U-235

0.5

o.o 0.4 0.6

normalized radius0.8 1.0

3.3.16 30 U-235

w/o Gd2O3)

oCD

oQ.

3.4 -

3 . 2 -

3.0 -

O Q2..O -

2.6 -2.4 -

2.2 -

2.0 -

1.8 -

1.6 -

1.4 -

1 .2 -

1 .0-

).8 -0.6 -

• - • - -

HFI IOS—-#—• Model

t

•

•

/

0.0 0.2 0.4 0.6 0.8

normalized radius1.0

H ^ 3.3.17 6

(4 w/o Gd2O3, 0.71 w/o U-235)

- 534-

tact

orpo

wer

2 . 8 -

2.6 -

2.4 -

2.2 -

2.0 -

1.8 -

1.6 -

1.4-

1.2-

1.0-

0 . 8 -

0 . 6 -

0. 0

upi m^

-••••--Model

•

i • i • i • i

0.2 0.4 0.6 0.8

normalized radius

<

[

\

}1 0

3.3.18 <*[^£ 20

(6 w/o Gd203> 3 w/o U-235)

o

i0

o

/

ly

InLergran

0 •/ O,

fc3 /

<

oi O

o

/jlar bubbles

o

o

o

o

o

o

o

o

o

o

o

o

o

o

o

Hydrostatic Sresses

Surface Tension T

Intxagranular bubbles

H5J 3.3.19

- 535-

ZL5] 3.3.20

200 330

Tlnre (nin)

I Zacharie[7] data point

"CD

COCO

8CDCO

CD

a)40

30

20

00

A 36 MWd/kgU 14001

• • "

• — '

/ - - • - • • • " " " " "

•

t

— •—•

Zim 3.3.21

2 3 4

Tirre(txE3isec)

r}^3} J. Burbach[8] data point

- 5 3 6 -

30.0

25.0

ZLQ 3.3.22

13*) K DP

•1600-—1900K-DP

/ / A

0 10 20 30 40 50 60 70 80 90 100 110 120

Burnup(MWd/kgU)

Zimmermann[9] data point H}J2.

\0

cz

"Q3

COCO

oCDCO

CO(3

16.0

14.0

12.0

10.0

8.0

6.0

4.0

2.0

0.0

BJ lhr

A P

•

annealing

: 72 ~ 86timeMPa X

/ • - - —

1200 1300 1400 1500 1600 1700 1800

Temperature(C)

H.Q 3.3.23 K. Une[10] data point

- 537-

CD

6 -

5 -

4 -

3 -

2 -

1 -

—•— Original Swetling(Solid Swelling)

—#— Bubble Swelling Model in FRAPCON-3

10 20 30 40 50

Burnup(MWd/kgU)

60 70

3.3.24 FRAPCON-3

7-,

5-

5? 4 -

O)

= 3 -

W 2 -

1 -

OH

- 1 - Original Swelling(Solid Swelling)

- • - Bubble Swelling Model in FRAPCON-3

/

MI * = - , , , , , , r—

•

•

10 20 30 40 50

Burnup(MWd/kgU)

60 70

H^J 3.3.25 FRAPCON-3 3_E.<H

(BR-3^ LHGR 10% # 7 } «

- 538-

enCOD

uCO

CO

enooen

fl3t

4*

xa

tin

Inelastic Diameter Change (um) '

ro ro co

uCO

CO

tsiO5

Ion00cn

rah

in

Inelastic Diameter Chanae (ur

50

"g 40ZJ

£,35

g30

S 2 0

o

_roCD

£ 10

5

0

IFA 585.1

CARO New Model

20 40 60 80 100 120 140 160 180

Time (Days)

ZlQ 3.3.28 Creep-out 1 (IFA585.1)

Z)

octa

rCf

"SECO

bau>

45

40

35

30

25

20

15

10

__

_

*-•• IFA 585.4 (U)

• • - • I F A 585.4 (L)CARO New Model (L) ^

»•••*•••• Z**-

K

.-=r-.r.T «

20 40 60 80

Time (Days)

100 120 140

ZL^ 3.3.29 Creep-out IFA585.4)

- 540-

c<DE<uo

_rao.

55

50-

45 -

40-

35-

30-

25-

20-

15-

10-

5 -

0

U B ? S *l

- FRAPCON-3 Original

CARO-D Original

CARO Model in FRAPCON-3

Creepoul Model in FRAPCON-3

20 40 60 80 100

Time(Day)120 140 160

ZL5] 3.3.30 FRAPCON-3 3.^°]] creep-out

1.2

^ 0.8CO

I 0.6(0

EI 0.4

0.2

Surface Temp.(348C)LHGR(219W/cm)

Oxide Thickness(97.9um)

1 2 3 4 5 6 7

Axial Position10

IL^ 3.3.31

- 541 -

0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 700 800900 1000 1100

Time (Days)

ZL& 3.3.32 Li

16

14

12

;§ 10

CD

^ 8CO

I 64

2

0

Li : 0.5ppmLi : 2.2ppmLi : 3.5ppm

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

A<ial Position

D-^ 3.3.33 Li

- 542-

140

120

mes

s

o!cf—CD

X

O

80

60

40

20

with H effectw/o H effect

100 200 300 400 500 600 700 800 900 1000 11001200

Time (Day)

16

14

12

«10

1 8CD

I 6

—«— with H effect...A... w/o Heffect

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95Axial Position

n i l 3.3.35

- 543-

120

100

CD

I0)•IO

60

20

-Flux : 5.0E12-Flux : 5.0E13•Flux : 5.0E14

0 100 200 300 400 500 600 700 800 900 1000 1100

Time (Days)

3.3.36

120

100

•? 80

co|

£ 60

4 0

20

Predicted• measured

406 813 1219 1626 2032 2438 2845 3251

Axial Position (mm from BTM)

H ^ 3.3.37

- 544-

50

45

_. 4 0

o 35o

J 30CO

S 2 5

xO

15

10

5

0

Predicted(With Li Effect)

Predicted (w/o Li Effect)

• Measured

584 1097 1610 2159 2670 3145

Acial Position (rrm from BTM)

3548

ZL^ 3.3.38 Li *<>*•§•

1.20

wo

1.15

•» 1SGd{8%)— 16Gd(12%)•*• 20Gd(8%)

20

(MWO/KgU)

40

3.3.39 Gd A}-§-*>

- 545-

rl

n : 0.4025 cm

r2 : 0.2825 cm

=L^ 3.3.40

1.20

1.15 -

«JOh

1.10

1.05

1.00

10 20

2 i E (MWD/KgU)

30 40

H ^ 3.3.41

- 546-

E75Eo•2-

2

1

1

5

.0x1 0

.5x10

.0x1 0

.0x10

0

2 0

2 0 _

:

2 0 _

1 9 _

Q

—Z — D

_ .; _ . D— >—• D. . -_-- . D

; D...-. 0

D

• • ! .

- • - • £ " '

= 1 0= 40= 1 0= 40= 1 0= 40= 1 0

ji m\i mt> rn

ii mt i m

P m= 4 0 jim= g r a i n s

/ ' . •

y"

/

> ' s?

. , /

. T = 5 0 0 C

. T = 5 0 0 C

. T = 8 00 C

. T = 8 0 0 CT = 10 00 CT = 10 00 CT = 1 2 00 CT = 12 00 C

ize

•

/ -••' ; . r '

/./ sz ^ -// / / ^' ^"

- - ' • • \ 'r

f .-• /.---<- —;

10 15 20

B u rn u p ( M W D / k g U )25 30

ZL^J 3.3.42 Variations of gas atom concentration

at the grain boundary

.

ms/

m"

o

o

1Ec0oco

O

2.5x10"-

2.0x10""

1.5x10" "

1.0x10""

5.0x10" "

0.0 -

T=500CT=600 C

.. + .. T=800 C- O - T = 5 0 0 C

^. . . T=500 CT=500 C

RBu6=0.6 mmReub=0.6 mmRoub=0.6 mmRc b=0.1 mm

R =1.0 mmRb]]=bubble radius

o-

_..-A-. ^

.-o-—°'""'

- a - - - * " " ' * " " "

- • * - - " ^ ^ ^ ^ ^ ^

— ^ ^ • " • • ' " 1 • • - • • + • • "

-^Z-'W—•*•

A 6 8 10 12

External Pressure(MPa)14

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3.1.4 ^ ^ 5 : ^ 1 4<&, a5Lft2S.i§ ^ ^ ^ ^ ^Q*mn$) '98 ^tv^cf[5] ^«.^ f 1998.

3.1.5 A, Premount, "On the Vibrational Behavior of Pressurized Water

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1982.

3.1.6 F. S. Tse, "Mechanical Vibrations-Theory and Applications,"

Allyn and Bacon Inc., pp. 268-270, 1978.

3.1.7 ^^$] 4*1, "Sl*i ^ ^ i^soi 71^5. <^^. xlx]^ ^^.-a

^ ^£-7-," tl^-^-g-^l^^-n^ 1998 ^ ^ l n ^ ^ ^ t ^ ^ , PP.

454-460,1988.

3.1.8 J. W. Miles, "Vibration of Beams on Many Supports," J. of

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3.1.9 Y. K. Lin, "Free vibration of Continuous Beam on Elastic

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3.1.10 H. Chung, "Analysis Method for Calculating Vibration

Characteristics of Beams with Intermediate Supports," Nuclear

Engineering and Design, Vol. 63, pp. 55-80, 1981.

3.1.11 ^ A l i ] 36], "^^S. ^<$.g.J§^ icvfl *]*] £ ^ sfl*

^ l ^ W 1998 M l ^ t f l ^ l t ^ ] , PP. 177-183,1997.3.1.12 %%-*\$] 3*1, "

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98 ^ W ^ f i S ] , Vol.2,

pp. 297-302, 1998.

3.1.13 G. M. Corcos, "The Structure of the Turbulent Pressure Field in

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3.1.15 M. W. Wambsganss and P. L. Zaleski, "Measurement,

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3.1.17 R. M. Kanazawa, "Hydroelastic Vibration of Rods in Parallel

Flow, Ph. D. Dissertation, University of Illinois, 1969.

3.1.18 ° 1 ^ £ ] 40*1, 3.el 23171 | 7/8^7] g- H><g.S. Q°A

^ 92 £VL *&*! ^H^, KAERI/TR-387/93, tl^-^^f^^^^i, 1993.

3.1.19 D. Nowell and D.A. Hills, Contact Problems incorporating

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Fatigue, Ph.D. Thesis, KAIST, 1997.

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3.1.32 ^«g-M 3<y, SUl^ofl 21 *> £B|^n}£6flAlfil n l^o^*] *#«§•

7\%, W 7 1 W 3 1 '99 ^A^^m, fe-g^A, pp. 821-826,

1999.

3.1.33 N.P. Suh et al., Trans. ASME, J. Lubrication Technology, 96,

pp. 631-637, 1974.

3.1.34 N.P. Suh, Wear, 44. pp. 1-16, 1977.

3.1.35 J.R. Fleming and N.P. Suh, Wear, 44, pp. 39-56, 1977.

- 576-

3.1.36 G.C. Sih et al., Methods of Analysis and Solutions of Crack

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International Publishing, Leiden, 1973.

3.1.37 D. Nowell and D. A. Hills, J. Strain Analysis, 22(3), pp.

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3353-3354, 1965.

3.1.40 S. Krenk, Quarterly Applied Mathematics, 32, pp. 479-484, 1975.

3.1.41 £%^-£] 491, *9&§.-§-/*!*13*l-afl ^ # ^ -8-US-^ *1H,

KAERI/TR-1193/98, th^*}^<£^-^, 1999.

3.1.42 W. Elber, Engineering Fracture Mechanics, 2, pp. 37-45 1970.

3.1.43 G.R. Irwin et al., Proceeding of ASTM, 58, pp. 640-657, 1958.

3.1.44 ASME Code Section III, Appendix A, 1986.

3.1.45 ^ J L £) 2*1, "3*1- # ^ 1 H l ^ ^^s-ofl cfftl -8-S>J3L4i

*1M", tfl*>7l^I4]-^ '99 ^Tfl^tflSl^g:^, Paper No. 99F077,

1999.

3.1.46 K. H. Yoon et al., "FE Analysis of Nonlinear Buckling Behavior

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3.2.3 *m^ # ^ *fl 98-313331, m <t) 7*1, S

7M *%<&3.$%I;H 1^]^^}, Feb. 4, 1998.

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^Vi #^1# lt> ^ ^ ^^o^y-^B, March 31, 2000.

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Bundle Crossflow Mixing based on Measurements of Turbulent Flow

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^ ^ s . vHf-fr^ CFD q, '^^nn3.2.12 In W.K. , Oh D.S. , Chun T. H. and Jung Y. H. , 1998, CFD

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Title / Subtitle Development of Fuel Performance and Thermal HydraulicTechnology

Project Managerand Department

Youn Ho Jung (Advanced Reactor Technology)

Song, K. N.; Kim, H. K.; Kang, H. S.; Yoon, K. H.; Chun, T.H.; In, W. K.; Oh, D. S.; Lee, C. B.; Bang, J.G.; Kim, D. H.Bae, S. O.; Koo, Y. H.; Song, J. S.; Lee, K.B.; Hwang, D.H.;Park, J. H (Advanced Reactor Technology)

Kim, D. W.; Woo, Y. M.; Ryu, W. S. (HANARO Applications Research)

Researcher andDepartment

PublicationPlace

Taejeon Publisher KAERI PublicationDate

2000

Page 670 p. 111. & Tab. Yes( O ), No ( ) Size 29 Cm.

Note

Classified Open( OClass

, Restricted(Document

Report Type Research Report

Sponsoring Org. Contract No.

Abstract (15-20 Lines)

Spacer grid in LWR fuel assembly is a key structural component to supportfuel rods and to enhance heat transfer from fuel rod to the coolant. Therefore, theoriginal spacer grid has been developed. In addition, new phenomena in fuelbehavior occurs at the high burnup, so that models to analyze those newphenomena were developed. Results of this project can be summarized as follows.

- Seven different spacer grid candidates have been invented and submitted fordomestic and US patents. Spacer grid test specimen(3x3 array and 5x5 array)were fabricated for each candidate and the mechanical tests were performed.

- Basic technologies in the mechanical and thermal hydraulic behavior in thespacergrid development are studied and relevant test facilities were established.

- Fuel performance analysis models and programs were developed for thehigh burnup pellet and cladding, and fuel performance data base were compiled.

- Procedures of fuel characterization and in-/out of-pile tests were prepared.- Conceptual design of fuel rod for integral PWR was carried out.

Subject Keywords(About 10 words)

Spacer Grid, Fuel Rod Vibration, Buckling Strength of SG,Fretting Wear, Flow Induced Vibration, Fuel PerformanceAnalysis Model, Rim Effect, Corosion, Swelling