integral system experiment scaling methodology (lecture t14)

41
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes 1 Department of Nuclear Engineering & Radiation Health Physics INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14) José N. Reyes, Jr. June 25 – June 29, 2007 International Centre for Theoretical Physics (ICTP) Trieste, Italy Department of Nuclear Engineering & Radiation Health Physics

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Department of Nuclear Engineering & Radiation Health Physics. INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14). José N. Reyes, Jr. June 25 – June 29, 2007 International Centre for Theoretical Physics (ICTP) Trieste, Italy. Course Roadmap. Lecture Objectives. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes1

Department of Nuclear Engineering & Radiation Health Physics

INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY

(Lecture T14)

José N. Reyes, Jr.

June 25 – June 29, 2007

International Centre for Theoretical Physics (ICTP)

Trieste, Italy

Department of Nuclear Engineering & Radiation Health Physics

Page 2: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes2

Department of Nuclear Engineering & Radiation Health Physics

Course Roadmap

Opening Session

· INTRODUCTIONS

· ADMINISTRATION

· COURSE ROADMAP

Introduction

· GLOBAL NUCLEAR POWER

· ROLE OF N/C ADVANCED DESIGNS

· ADVANTAGES AND CHALLENGES

Local Transport Phenomena & Models

· LOCAL MASS, MOMENTUM AND ENERGY TRANSPORT PHENOMENA

· PREDICTIVE MODELS & CORRELATIONS

Integral System Phenomena & Models

· SYSTEMS MASS, MOMENTUM AND ENERGY TRANSPORT PHENOMENA

· N/C STABILITY AND NUMERICAL TECHNIQUES

· STABILITY ANALYSIS TOOLS

· PASSIVE SAFETY SYSTEM DESIGN

Natural Circulation Experiemnts

· INTEGRAL SYSTEMS TESTS

· SEPARATE EFFECTS TESTS

· TEST FACILITY SCALING METHODS

Reliability & Advanced Computational Methods

· PASSIVE SYSTEM RELIABILITY

· CFD FOR NATURAL CIRCULATION FLOWS

Page 3: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes3

Department of Nuclear Engineering & Radiation Health Physics

Lecture Objectives

• Describe the methodology needed to design a single-phase or two-phase natural circulation Integral System Test Facility.

– Understand the structure of a Phenomena Identification Ranking Table (PIRT) for a Natural Circulation Based System

– Understand the method used to conduct a detailed scaling analysis to obtain the geometric dimensions and operating conditions for an integral system test facility.

Page 4: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes4

Department of Nuclear Engineering & Radiation Health Physics

Outline

• Introduction– Scaling Analysis Objectives

• General Scaling Methodology– Description of the MASLWR Design– PIRT– H2TS Methodology

• Single-Phase Natural Circulation Scaling Analysis– Dimensionless Governing Equations– Steady-State Analytical Solution

• Two-Phase Natural Circulation Scaling Analysis– Dimensionless Governing Equations

• Conclusions

Page 5: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes5

Department of Nuclear Engineering & Radiation Health Physics

Introduction

• Integral system test (IST) facilities play a key role in the design, assessment and certification of innovative reactor designs.– Data used to benchmark the best-estimate safety analysis

computer codes used to evaluate nuclear plant safety.– Tests to assess the effectiveness of safety system functions

under simulated accident conditions.

• Requires detailed scaling analysis.– Scaling analyses have been successfully used to design APEX

and MASLWR at OSU.– AP600 and AP1000 design certification involved 3 scaled test

facilities.

Page 6: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes6

Department of Nuclear Engineering & Radiation Health Physics

Scaling Analysis Objectives

• To develop a properly scaled test facility, the following specific objectives must be met for each operational mode of interest.– Identify the thermal hydraulic processes that should be modeled.– Obtain the similarity criteria that should be preserved between

the test facility and the full-scale prototype.– Establish priorities for preserving the similarity criteria.– Provide specifications for the test facility design– Quantify biases due to scaling distortions.– Identify the critical attributes of the test facility that must be

preserved to meet Quality Assurance requirements.

Page 7: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

General Scaling Methodology

Document Test Facility Final Design and Operation Specifications and QA Critical Attributes (4)

Hierarchical System Scaling and Design (3)

Scaling Analysis forOperational Mode #1

Develop Similarity Criteria and Derive Scale Ratios

Calculate Scale Ratios·Obtain Physical Dimensions and Operating Conditions for Test Facility Components

Assess Scaling Distortions

Prioritize System Design Specifications

Design SpecificationsOperational Mode #1

Integral System Scaling Choices

·Identify Dominant Phenomena·Significant Scaling Distortion?

Design SpecificationsOperational Modes

#2 through N

If yes

Specify Experimental Objectives (1)

·Identify Range of Scenarios to be Examined in Test Facility

Phenomena Identification and Ranking Table (PIRT) (2)

·Review Related PIRTs·Define the Phases of each Scenario·Identify Important Thermal Hydraulic Phenomena for each Scenario

Full-Scale Plant (Prototype) Information

·Plant Operating Conditions·Physical Dimensions·Isometric Drawings·P&IDs·Safety Logic and Setpoints·Transient Code Analyses

Page 8: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes8

Department of Nuclear Engineering & Radiation Health Physics

Description of the MASLWR Design

• The Multi-Application Small Light Water Reactor (MASLWR)– 150 MW(t) modular nuclear reactor that uses natural

circulation for primary loop cooling.– MASLWR implements an integrated reactor vessel

with an internal helical coil steam generator.– Enclosed in a high-pressure steel containment

vessel that is partially filled with water to serve as a suppression pool.

– Containment vessel in turn resides in a large exterior cooling pool that acts as the ultimate heat sink.

• INEL, OSU and NEXANT-Bechtel Design team

Page 9: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

MASLWR Design

Concept

Page 10: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes10

Department of Nuclear Engineering & Radiation Health Physics

MASLWR Simple Schematic

Page 11: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes11

Department of Nuclear Engineering & Radiation Health Physics

MASLWR Normal Operating Parameters

Reactor Power (MW) 150.00Primary Pressure (MPa) 7.60Primary Mass Flow Rate (kg/s) 597.00Reactor Inlet Temperature (K) 491.80Reactor Outlet Temperature (K) 544.30Saturation Temperature (K) 565.00Reactor Outlet Void Fraction 0.00%

Steam Pressure (MPa) 1.50Steam Outlet Quality 1.00Steam Temperature (K) 481.40Saturation Temperature (K) 471.60Feedwater Temperature (K) 310.00Feedwater Flowrate (kg/s) 56.10

Primary Side

Secondary Side

Page 12: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes12

Department of Nuclear Engineering & Radiation Health Physics

MASLWR Passive Safety Systems

• Two, independent, small diameter, steam vent valves (SVV)

• Two, independent, small diameter, Automatic Depressurization System (ADS) valves

• Two, independent, small diameter, Sump Recirculation Valves (SV)

• A high-pressure containment vessel with an internal pressure suppression pool, and

• An external cooling pool that serves as the ultimate heat sink for the high-pressure containment and reactor decay heat.

Page 13: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes13

Department of Nuclear Engineering & Radiation Health Physics

MASLWR SBLOCA Behaviour

• BLOWDOWN PHASE:– Begins with the opening of the break and ends

with the ADS initiation.– Subcooled blowdown into the containment

suppression pool.

• ADS BLOWDOWN PHASE:– Begins with the opening of the ADS valve and

ends when the containment and reactor system pressures are equalized

– Saturated blowdown into containment suppression pool.

• LONG TERM COOLING PHASE:– Begins with the equalization of the containment

and reactor system pressures and ends when stable cooling is established.

– Stable Cooling: Natural circulation cooling established within containment and natural circulation cooling established in exterior pool.

PO

TIME

Primary Side

Containment

BL

OW

DO

WN

ADS LONG TERMCOOLING

PSAT

PEQ

Page 14: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

Scaling Analysis Flow Chart for

MASLWR

Specify ExperimentObjectives

SBLOCA PIRT

Perform Scaling Analysis(3)

(2)

(1)

Evaluate Key T/H PIRTProcesses to Prioritize System

Design Specification

OSU Test Facility DesignSpecifications and Q/A Critical

Attributes

(4)

NaturalCirculation

ScalingAnalysis

Sump RecirculationScaling Analysis

Reactor CoolantSystem

DepressurizationScaling Analysis

Develop Groups andSimilarityCriteria

Develop Groups andSimilarityCriteria

Significant ScalingDistortions inImportant

Groups?

Significant ScalingDistortions inImportant

Groups?

System DesignSpecifications

System DesignSpecifications

NoNo

YesYes

ContainmentPressurization

Scaling Analysis

Develop Groups andSimilarityCriteria

Significant ScalingDistortions inImportant

Groups?

System DesignSpecifications

No

Yes

Develop Groups andSimilarityCriteria

Significant ScalingDistortions inImportant

Groups?

System DesignSpecifications

No

Yes

• Scaling Analyses for Four Operational Modes:

– Natural Circulation– Sump Recirculation– RCS Depressurization– Containment

Pressurization

Page 15: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes15

Department of Nuclear Engineering & Radiation Health Physics

Phenomena Identification and Ranking Tables(PIRT Development Method)

Full-Scale Plant Data (Prototype)

Existing Related PIRTs

Define Evaluation Criteria and Ranking Method

·Impact on PCT?·Impact on Core Liquid Level?·Rank H, M, L

Establish PIRT Framework

·Partition Scenario into Time Phases·Partition Plant into Components·Identify Phenomena

Expert Ranking

·Rank Components and Phenomena·Document Rationale

Page 16: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes16

Department of Nuclear Engineering & Radiation Health Physics

• Evaluation Criterion– How does this particular phenomenon in this particular component impact

the fuel’s Peak Cladding Temperature (PCT) during this phase of the scenario?

• Ranking Scale– High (H): Phenomenon significantly impacts the PCT during a specific

phase of the scenario.– Medium (M): Phenomenon has a moderate impact on the PCT during a

specific phase of the scenario.– Low (L): Phenomenon has little impact on the PCT during a specific phase

of the scenario– Plausible (P): Phenomenon has not been previously assessed in other

designs or its impact on PCT is not well understood or modeled by computer codes. For purposes of test facility scaling, these phenomena were considered highly ranked.

– Inactive or Not Applicable (I): Phenomenon cannot physically impact the PCT during a specific phase of the scenario.

Phenomena Identification and Ranking Tables(Evaluation Criterion and Ranking Scale)

Page 17: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes17

Department of Nuclear Engineering & Radiation Health Physics

MASLWR SBLOCA PIRT (1 of 3)

System Component Process/Phenomenon1 2 3 1 2 3 1 2 3

Vent Valves H H H Valves H H H Mass Flow (Choked/Nonchoked) H H HPiping M M H Line Flow Resistance M M H

ADS I H H Valves I H H Mass Flow (Choked/Nonchoked) I H HPiping I M H Line Flow Resistance I M HSparger I H M Condensation I H M

Energy Release I H MMass Release I H M

Passive Cont. Cooling Sys. (PCCS) P P H External Cont. Cooling Pool I I H Natural Convection Heat Transfer I I H

Thermal Stratification I I LContainment Shell P P H Internal

Pressure L M H Buoyancy Driven Flow P P P Heat Transfer L L H Wall - condensation rate L L H Noncondensible Gas Mass Fraction L L HWall Thermal Capacitance L L H Thermal Conduction L L H

Passive Safety Recirculation System L L H Sump L L H ADS Heat-up of Sump I L M

Condensation (Surface of Pool) L I IThermal Stratification L L LRecirculation (Flow Resistance) I I HResupply from Containment L L H

Period 1 - Blowdown H - Significantly Impacts PCT I - Inactive during the transient PhasePeriod 2 - ADS Operation M - Moderately Impacts PCT P - PlausiblePeriod 3 - Long Term Cooling L - Little Impact on PCT

PeriodPeriod Period

Page 18: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes18

Department of Nuclear Engineering & Radiation Health Physics

MASLWR SBLOCA PIRT (2 of 3)System Component Process/Phenomenon

1 2 3 1 2 3 1 2 3Primary Coolant System H H H Hot Leg Riser H H H Flashing M H L

Flow Resistance (wall/control rod tubes) M M MRiser Inventory/Circulation/Level H H H

SG Tube Annulus H H H SG Tube Condensation H H HFlow Entrainment/De-entrainment L L I CCF I I I Flow Resistance H L L Multidimensional Flow L L LLevel L L HFlashing H H LStored Energy Release- Hot wall effect M M H

Reactor System H H H Vessel - Control Rods H L L Reactivity Change H L LVessel - Core Subchannels H H H Flow

Interfacial Drag L H L Mass Flow H H H Flow Resistance H H H Two_phase Mixture Level H H H Flashing M H L

Vessel - Downcomer H H H Flow Entrainment/De-entrainment L L I CCF L L L Flow Resistance H M H Multidimensional Flow L L LLevel L L HFlashing M H LStored Energy Release- Hot wall effect M M H

Period 1 - Blowdown H - Significantly Impacts PCT I - Inactive during the transient Phase

Period 2 - ADS Operation M - Moderately Impacts PCT P - Plausible

Period 3 - Long Term Cooling L - Little Impact on PCT

PeriodPeriod Period

Page 19: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes19

Department of Nuclear Engineering & Radiation Health Physics

MASLWR SBLOCA PIRT (3 of 3)System Component Process/Phenomenon

1 2 3 1 2 3 1 2 3Reactor System (continued) H H H Vessel - Fuel Rods H H H Fuel Heat Transfer

Conduction H H H Gap Conductance H H HStored Energy Release H H LCladding Convective Heat Transfer Subcooled Liquid H L L Subcooled Boiling H L L Nucleate Boiling L L H CHF by DNB L L H Film Boiling L L H Forced Convection to vapor L L HReactivity Void H I I Moderator temperature H I I Fuel temperature (Doppler) H I IDecay Heat H H H

Vessel - Guide Tubes L L L Film Draining L L IStored Energy Release L L L

Vessel - Lower Plenum H H H Flow transient Flow Resistance H L H Flashing M H LStored Energy Release M M H

Vessel - Structures L L L Stored Energy Release L L LVessel - Upper Head H H L Flow Transient

Entrainment/De-entrainment L L LStored Energy Release H H LFlashing M H L

Steam Generator/Heat Exchanger L L H Tubes L L H Heat Transfer with FW Available H H H

PeriodPeriod Period

Page 20: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

• The H2TS method developed by Zuber, USNRC (Appendix D of NUREG/CR-5809, 1991).

• Four Elements of H2TS– System breakdown– Scale Identification– Top-Down Scaling – Bottom-Up Scaling

Hierarchical Two-Tiered Scaling (H2TS) Methodology

TOP-DOWN/SYSTEM SCALINGANALYSIS

PROVIDE:

CONSERVATIONEQUATIONS

DERIVE: SCALING GROUPS AND

CHARACTERISTIC TIMERATIOS

ESTABLISH:

SCALING HIERARCHY

IDENTIFY:

IMPORTANT PROCESSESFOR BOTTOM-UP SCALINGANALYSIS

SYSTEMBREAKDOWN

PROVIDE:

SYSTEMHIERARCHY

IDENTIFY:

CHARACTERISTIC CONCENTRATIONS GEOMETRIES PROCESSES

SCALEIDENTIFICATION

PROVIDE HIERARCHYFOR:

VOLUMETRICCONCENTRATIONS

AREACONCENTRATIONS

PROCESS TIMESCALES

BOTTOM-UP/PROCESSSCALING ANALYSIS

PERFORM:

CONSERVATIONEQUATIONSDETAILEDSCALING ANALYSIS FORIMPORTAT LOCALPROCESSES

DERIVE AND VALIDATE: SCALING GROUPS

Page 21: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

HIERARCHICAL TWO-TIERED SCALING (H2TS) METHODOLOGY(MASLWR System Breakdown)

MASLWR

Integral Loop ContainmentHelical Coil Steam

Generator

Single andTwo-Phase

Fluid

Two-PhaseFluid

Single and Two-PhaseFluid, AIr, Metal Mass

TubesideSIngle-

Phase FluidInternals

TubesideSIngle-

Phase Fluid

RCSElevationLengths

RCSVolume

Containment Volume,Heat Transfer Surface,Vent and ADS Valves

SGTubesideVolume

Tube HeatTransferSurface

SGShellsideVolume

MassMomentum

Energy

MassEnergy

MassEnergy

TubesidePressure

Break Size

EnergyShellsidePressure

Single andTwo-Phase

NaturalCirculation

PrimarySystem

Blowdown

ContainmentPressurization

SG HeatTransfer

FW Temp& FlowControl

SecondarySide

Blowdown

SYSTEM

SUBSYSTEM

CONSTITUENTS

GEOMETRICALCONFIGURATIONS

FIELDS

PROCESS TO BESCALED

Page 22: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

Single-Phase Natural Circulation Scaling Analysis

Top-Down Scaling

Level: Primary Loop

Volumetric Flow Rate Core/SG Energy Exchange

Single-Phase Primary LoopNatural Circulation

Phenomena

Bottom-Up Scaling

Process

Primary Loop Resistance Core Decay Power SG Heat Transfer

Primary N/C SimilarityCriteria

Evaluate ScalingDistortions

Specify Loop Resistanceamd

Decay PowerRequirements

Page 23: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes23

Department of Nuclear Engineering & Radiation Health Physics

TH

TC TC

TH

TC

LTH

FEEDWATERSTEAM

PZR

TSAT

Single-Phase Natural Circulation Scaling Analysis(MASLWR Control Volume & Assumptions)

• Obtain Mass, Momentum and Energy Integral Balance

Equations • Simplifying Assumptions:

– 1-D flow along the loop axis, fluid properties were uniform at every cross-section.

– Boussinesq approximation was applicable.

– Incompressible fluid

– Tc is constant

– Form losses, primarily in the core and steam generator regions, dominate the loop resistance.

Page 24: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes24

Department of Nuclear Engineering & Radiation Health Physics

Loop Momentum Balance:

Loop Energy Balance:

N

i i

c

ihclthCH

N

i i

i

a

aK

d

fl

a

mLTTg

dt

md

a

l

1

2

2

2

1 2

1

lossSGCHplCM

sysvl qqTTCmdt

TTdMC

Single-Phase Natural Circulation Scaling Analysis(Governing Equations)

Page 25: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes25

Department of Nuclear Engineering & Radiation Health Physics

Single-Phase Natural Circulation Scaling Analysis(Dimensionless Initial and Boundary Conditions)

Characteristic Time Ratio:

Dimensionless Ratios:

loop

tt

om

mm

o

N

i i

c

ih

N

i i

c

ihN

i i

c

ih

a

aK

d

fl

a

aK

d

fl

a

aK

d

fl

1

2

1

2

1

2

2

1

2

1

2

1

oCM

CMCM TT

TTTT

oCH

CHCH TT

TTTT

oSG

SGSG q

qq

oloss

lossloss q

qq

Page 26: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes26

Department of Nuclear Engineering & Radiation Health Physics

Single-Phase Natural Circulation Scaling Analysis(Dimensionless Balance Equations)

N

i i

c

ihFlCHRiL a

aK

d

flmTT

dt

md

1

22

2

1

losslossSGSGCHT

CM qqTTmdt

TTd 1

ccol

sysN

i o

sysN

ii

i

iloop au

M

m

M

u

l

1 1

Loop Momentum Balance Equation:

Loop Energy Balance Equation:

Characteristic Time Constant:

Page 27: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes27

Department of Nuclear Engineering & Radiation Health Physics

Single-Phase Natural Circulation Scaling Analysis(Dimensionless Groups – Characteristic Time Ratios)

i

cN

i ref

iL a

a

l

l

1

cl

sysref a

Ml

2co

thoCHRi u

LTTg

3coplcl

thcoRi uCa

Lqg

N

i i

c

ihFl a

aK

d

fl

1

2

2

1

Loop Reference Length Number:

where:

Loop Richardson Number:

or

vl

pl

C

C

oCM

oCHT TT

TT

oCMplccol

SGoSG TTCau

q

oCMplccol

olossLoss TTCau

q

,

Ratio of Specific Heats:

Loop Energy Ratio:

SG Heat Transport Number:

Loop Heat Loss Number:Loop Resistance Number:

Page 28: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes28

Department of Nuclear Engineering & Radiation Health Physics

Single-Phase Natural Circulation Scaling Analysis(Steady-State Solution)

FlRi

31

Flplcl

thcoco Ca

gLqu

1

1

22

10

2

1

N

i i

c

ihFlCHRiL a

aK

d

flmTT

dt

md

Dimensionless Loop Momentum Balance Equation:

Steady-State Loop Momentum Balance Equation:

Solving for Velocity at Core Inlet:

Steady-State

Page 29: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes29

Department of Nuclear Engineering & Radiation Health Physics

Single-Phase Natural Circulation Scaling Analysis(Scale Ratios)

Time Scale Ratio:

Fluid Velocity Scale Ratio:

Loop Length Scale Ratio:

Loop Energy Scale Ratio:

SG Power Scale Ratio:

Heat Loss Scale Ratio:

Flow Area Scale Ratio (Kinematic Similarity):

31

231

,

Rco

Flc

R

pllRloop q

laC

31

31

RFlc

co

RpllR a

lq

Cu

RthR Ll

1

Rc

i

a

a

1

RoCM

oCH

TT

TT

1

Rco

SGo

q

q

1,

Rco

oloss

q

q

Page 30: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

Two-Phase Natural Circulation Scaling

Analysis

Two-Phase Primary LoopNatural Circulation

Phenomena

Top-Down Scaling

Level: Primary Loop

Volumetric Flow Rate

Bottom-Up Scaling

Process

Primary Loop Resistance Flow Regime Transitions Subcooled Boiling Low Flow CHF

Primary N/C SimilarityCriteria

Evaluate ScalingDistortions

Specify Loop Resistance,Heat Flux Requirements, and

Assess Flow PatternTransitions

Page 31: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes31

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(MASLWR Control Volume & Assumptions)

• Obtain Mass, Momentum and Energy Integral Balance Equations

• Simplifying Assumptions:– Constant core inlet enthalpy

– Uniform fluid properties at every cross-section,

– Homogeneous flow in the two phase region,

– Chemical Equilibrium – no chemical reactions,

– Thermal Equilibrium – both phases at the same temperature,

– The sum of convective accelerations due to vaporization and condensation are negligible,

– Viscous effects included in determination of form losses only.

– Form losses, primarily in the core and steam generator regions, dominate the loop resistance.

gs

LTH

FEEDWATERSTEAM

ls

TP

CC

C

PZR

Page 32: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes32

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Governing Equations)

Loop Momentum Balance:

Loop Energy Balance:

TP i

c

ihTP

l

SP i

c

ihclthTPl

N

i i

i

a

aK

d

fl

a

aK

d

fl

a

mLg

dt

md

a

l22

2

2

1 2

1

2

1

lossSGlTPlM

sys qqhhmdt

eedM

fg

fTPe h

hhx

g

gfe

fTP

x

1

Equilibrium Vapour Quality at Core Exit:

Homogeneous Two-Phase Fluid Mixture Density:

Page 33: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes33

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Dimensionless Initial and Boundary Conditions)

loop

tt

om

mm

oSG

SGSG q

qq

oloss

lossloss q

qq

oTPl

TPlTPl

olM

lMlM ee

eeee

olTP

lTPlTP hh

hhhh

oTPl

TPl

TP

l

oSP i

c

ih

SP i

c

ih

SP i

c

ih

a

aK

d

fl

a

aK

d

fl

a

aK

d

fl

2

2

2

2

1

2

1

2

1

oTP i

c

ih

TP i

c

ih

TP i

c

ih

a

aK

d

fl

a

aK

d

fl

a

aK

d

fl

2

2

2

2

1

2

1

2

1

Page 34: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes34

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Dimensionless Balance Equations)

ccol

sysN

i o

sysN

ii

i

iloop au

M

m

M

u

l

1 1

Loop Momentum Balance Equation:

Loop Energy Balance Equation:

Characteristic Time Constant:

TP i

c

ihTP

lF

SP i

c

ihFTPlRiL a

aK

d

fl

a

aK

d

flm

dt

md2

2

2

1

2

, 2

1

2

1

losslossSGSGlTPelM qqhhm

dt

eed

Page 35: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes35

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis

(Dimensionless Groups – Characteristic Time Ratios)

i

cN

i ref

iL a

a

l

l

1

cl

sysref a

Ml

Loop Reference Length Number:

where:

Loop Richardson Number:

Loop Energy Ratio:

SG Heat Transport Number:

Loop Heat Loss Number:

Loop Liquid Phase Resistance Number:

2,col

thoTPlRi u

Lg

SPo

i

c

ihFl a

aK

d

fl2

2

1

Loop Two-Phase Resistance Number:

olMo

coe eem

q

olMo

SGoSG eem

q

olMo

olossLoss eem

q

,

TP i

c

ihF a

aK

d

fl2

2 2

1

TP

l

Density Ratio:

Page 36: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes36

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Steady-State Solution)

Dimensionless Loop Momentum Balance Equation:

Steady-State Loop Momentum Balance Equation:

Steady-State

1

2

2

1

2

1

1

2

1

, 2

1

2

1

TP i

c

ihTP

lF

SP i

c

ihFTPlRiL a

aK

d

fl

a

aK

d

flm

dt

md

2, FFlRi

Page 37: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes37

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Steady-State Velocity at Core Inlet)

Velocity at Core Inlet:

where:

023 ccobcoaco uuu

2222

22

22

subFfggFFfggF

subFfggFF

cf

coa

hhh

hh

a

q

2222

22

222

2subFfggFFfggF

fggsubcfthcoF

cf

bhhh

hhagLq

a

2222

22

1

subFfggFFfggF

fggcoth

cfc

hhh

hqgL

a

21 FFF

lfsub

gf

hhh

and

Page 38: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes38

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Steady-State Velocity with Saturated Liquid at Core Inlet)

Dimensionless Cubic Equation:

where:

023 czbzaz

cof

fgog

Zuberz q

hm

N

1

F

FF

fa

2

F

F

fb

2

2

Fco

cfggth

fc q

ahgL 12

222

Page 39: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes39

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling AnalysisScaling Catastrophe Functions -Reyes (1994)

Criterion:

where:

cmzmbmzmamzmcpzpbpzpapzp 23233

Rz

Ra

Rb 2

Rc 3

Page 40: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes40

Department of Nuclear Engineering & Radiation Health Physics

Two-Phase Natural Circulation Scaling Analysis(Scale Ratios for Saturated Two-Phase Conditions)

Time Scale Ratio:

Fluid Velocity Scale Ratio:

Power Scale Ratio:

Loop Resistance Scale Ratios:

SG Power Scale Ratio:

Heat Loss Scale Ratio:

Flow Area Scale Ratio (Kinematic Similarity):

1

Rc

i

a

a

1

Rco

SGo

q

q

1,

Rco

oloss

q

q

21,

Rth

RRloop

L

l

21

RthR Lu

fggfRthRcRco

hLaq 2

1

,

1

1

2

1

RF

RF

Page 41: INTEGRAL SYSTEM EXPERIMENT SCALING METHODOLOGY (Lecture T14)

IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007 Integral System Scaling Analysis (T14) - Reyes41

Department of Nuclear Engineering & Radiation Health Physics

Conclusions

• A General Scaling Methodology for the design of a single-phase or two-phase Natural Circulation Integral System Test Facility has been described. – Discussed the structure of a Phenomena

Identification Ranking Table (PIRT)– Discussed the H2TS methodology to obtain

the geometric dimensions and operating conditions for a N/C integral system test facility.