Department of Nuclear Engineering & Radiation Health Physics
Department of Nuclear Engineering &
Radiation Health Physics
Flow Stagnation and Thermal Stratification in
Single and Two-Phase Natural Circulation Loops
(Lecture T17)
José N. Reyes, Jr.
June 25 – June 29, 2007
International Centre for
Theoretical Physics (ICTP)
Trieste, Italy
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
Flow Stagnation & Thermal Stratification in NC Loops (T17) Reyes
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Department of Nuclear Engineering & Radiation Health Physics
Course Roadmap
Opening Session
· INTRODUCTIONS
· ADMINISTRATION
· COURSE ROADMAP
Integral System Phenomena &
Models
· SYSTEMS MASS, MOMENTUM AND
ENERGY TRANSPORT PHENOMENA
· N/C STABILITY AND NUMERICAL
TECHNIQUES
· STABILITY ANALYSIS TOOLS
· PASSIVE SAFETY SYSTEM DESIGN
Introduction
Natural Circulation Experiemnts
· 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
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
· INTEGRAL SYSTEMS TESTS
· SEPARATE EFFECTS TESTS
· TEST FACILITY SCALING METHODS
Reliability & Advanced
Computational Methods
· PASSIVE SYSTEM RELIABILITY
· CFD FOR NATURAL CIRCULATION
FLOWS
Flow Stagnation & Thermal Stratification in NC Loops (T17) Reyes
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Department of Nuclear Engineering & Radiation Health Physics
Lecture Objectives
•
•
•
Describe the mechanisms by which
natural circulation flow is interrupted in
single-phase and two-phase loops
Identify the impact of loop stagnation on
thermal stratification within the loop
components.
Identify the methods that can be used to
calculate fluid mixing and plume
behavior in the system.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Outline
• Introduction
• Single-Phase Natural Circulation Stagnation
Mechanisms
– Loss of Heat Sink
– Negatively Buoyant Regions
• Two-Phase Natural Circulation Stagnation
Mechanisms
• Thermal Fluid Stratification and Plume Formation
–
–
–
–
Onset of Thermal Stratification
Axisymmetric Forced Plumes
Planar Plumes
Downcomer Plume Behaviour
• Conclusions
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Introduction
• Under certain accident conditions in a PWR,
natural circulation plays an important role in
maintaining a thermally well-mixed system.
• Pressurized Thermal Shock (PTS)
– If cold borated water is injected into cold legs while
cold leg flow rates are low, thermal stratification and
plume formation in the reactor vessel downcomer
can occur.
– Should a pre-existing flaw in the vessel wall or welds
exist at a location experiencing prolonged contact
with a cold plume, while at high pressure, there is a
potential for the flaw to grow into a “through-wall”
crack.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Thermal Stratification in a PWR Cold Leg and
Downcomer Plume Formation
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Department of Nuclear Engineering & Radiation Health Physics
Experimental Studies in APEX-CE
•
•
APEX-CE Integral System Test facility,
at Oregon State University.
Model of a 2x4 loop Combustion
Engineering PWR.
–
–
–
–
–
–
•
•
•
•
Reactor vessel with an electrically
heated rod bundle
Pressurizer
2 Inverted U-tube steam generators
4 Cold legs and reactor coolant pumps
2 Hot legs
Safety injection system
Length scale ratio 1:4
Volume ratio of 1:274.
Decay powers ranging down from 6%.
Tests conducted after reactor scram
with the reactor coolant pumps tripped
in a natural circulation mode of
operation.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Single-Phase Natural Circulation Stagnation
Mechanisms
Steam
Generator
Steam
Generator
Loss of Heat
Sink
Pressurizer
TH
TH
Negatively
Buoyant Loop
Seal Fluid
Coolant
Pump
Coolant
Pump
TC
Loop Seal
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
Reactor
TC
Loop Seal
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Department of Nuclear Engineering & Radiation Health Physics
Loss of Heat Sink
(Steam Generator Reverse Heat Transfer)
• Driving potential for natural circulation flow in a PWR:
– Density and elevation differences between the thermal centers of
the core (heat source) and the steam generators (heat sink).
– If the the heat sink is lost, the driving potential is also lost.
• Loss of heat sink can occur with a loss of main and auxiliary
feedwater supplies followed by steam generator dryout, or
• Main Steam Line Break (MSLB) in a single steam generator in a
multi-loop plant.
– Operators isolate the feedwater to the steam generators and close
the main steam isolation valves.
– “Broken” steam generator will continue to vent steam and
depressurize. This results in a rapid cooling of the entire primary
system fluid.
– Primary loop fluid temperatures may drop below the secondary
side temperatures of the isolated “unbroken” steam generator.
– Loop flow stops on “unbroken” side of plant.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
APEX-CE MSLB Test (OSU-CE-0012)
Comparison of Unaffected SG#1 and HL#1 Temperatures
SG#1 Temperature
Hot Leg #1 Temperature
Flows in Cold
Legs #1 and #3
Stop
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Flows in Cold
Legs #1 and #3
Resume
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Department of Nuclear Engineering & Radiation Health Physics
APEX-CE MSLB Test (OSU-CE-0012)
Cold Leg #1 and #3 Flow Rates
Co ld L eg 1 an d 3 F lo w
40
F M M -201
35
F M M -203
30
F lo w Ra te (g p m )
25
20
Flows in Cold
Legs #1 and #3
Resume
Flows in Cold
Legs #1 and #3
Stop
15
10
5
0
-150
850
1850
2850
3850
4850
-5
-10
Ti me (se c)
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Department of Nuclear Engineering & Radiation Health Physics
Negatively Buoyant Loop Seal Fluid
• During Safety Injection, the cold borated water
injected into cold legs spills into the loop seals.
• This creates a cold liquid plug with a gravity
head that resists loop flow-essentially adding an
additional resistance term.
• In multi-loop systems, flow is preferentially
diverted to the adjacent cold leg through the SG
lower channel head.
• This can occur under single-phase or two-phase
conditions.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Negatively Buoyant Loop Seal Fluid
• OSU Flow
Simulation of
Loop Seal
Cooling due
to HPI Flow
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Loop Seal
Dowcomer on
Vessel Side
Department of Nuclear Engineering & Radiation Health Physics
Asymmetric Loop Seal Cooling in Multi-Loop System
(OSU-CE-008)
Cold Leg Loop Seal 2 and 4 Temperatures
450
Loop Seal #4
Loop Seal #2
Temperature (F)
400
350
300
•Loop Seal #4 Cools Early
•Flow diverts to Cold Leg #2
250
200
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time (sec)
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Asymmetric Loop Stagnation
in Multi-Loop System (OSU-CE-008)
50
SG#2 Long Tubes
Begin to Drain
45
Cold Leg #2 GPM
Cold Leg #4 GPM
40
Flow Rate (gpm)
35
RCP Weir Wall Spillover
Begins in Cold Leg #4
30
25
20
Cold Leg #4 Stagnates Due
to Cold Loop Seal
15
10
Cold Leg #2 Stagnates Due
to SG #2 Draining
5
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Time (s)
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Two-Phase Natural Circulation
Stagnation Mechanisms
Steam
Generator
SG Tube
Voiding
Steam
Generator
Pressurizer
TH
TH
Negatively
Buoyant Loop
Seal Fluid
Coolant
Pump
Coolant
Pump
TC
Loop Seal
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
Reactor
TC
Loop Seal
Flow Stagnation & Thermal Stratification in NC Loops (T17) Reyes
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Department of Nuclear Engineering & Radiation Health Physics
Steam Generator Tube Voiding
• During a Small Break Loss of Coolant Accident
(SBLOCA) in a PWR, steam generator tube draining
will result in a gradual decrease in primary side natural
circulation flow until it transitions to a boilingcondensing mode of operation.
– As liquid mass is removed from the system, the loop void
fraction increases.
– Initial rise in loop flow rates due to increased density
difference.
– The loop flow reaches a maximum value when the two-phase
buoyancy driving head is at its maximum.
– Steam generator tubes begin to drain causing a decrease in
flow rate because the distance between the core and steam
generator thermal centers has decreased.
– Longest tubes drain first. Loop flow ceases when shortest
tubes begin to drain.
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Cold Leg Flow Rates Versus Primary Side Inventory
Stepped-Inventory Reduction Test (OSU-CE-0002)
8
Transient Data
Steady State Data
7
Core Flow Rate (kg/s)
6
Increasing Void Fraction
5
4
3
1-Phase N/C
2
1
0
40
50
60
70
80
90
100
RCS Inventory Percentage (Includes PZR Liquid Mass)
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Asymmetric Steam Generator Tube Draining
(Steam Generator #2 During SLOCA Test (OSU-CE-0008)
120
Long Tube
Long Tube
Short Tube
Short Tube
100
Level (in)
80
60
Shortest
Tubes
Longest
Tubes
40
20
0
0
500
1000
1500
2500
2000
3000
3500
4000
4500
5000
Time (s)
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Department of Nuclear Engineering & Radiation Health Physics
Criteria for Onset of Cold Leg
Thermal Stratification
Modified Froude Number: FrHPI / CL 
1. Theofanous, et al., (1984):
2. Reyes (2001):
FrHPI / CL
FrHPI / CL
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
QHPI

  CL 
aCL  gDCL HPI
 HPI 


Q 
 1  L 
 QHPI 
7
1
2
5
  L QHPI 
 1 


Q
HPI L 

1
2

QL 
1 

Q
HPI 

3
2
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Department of Nuclear Engineering & Radiation Health Physics
Onset of Cold Leg Thermal Stratification
1
L/H = 0.84
CREARE
1/5Scale
Stratified
Creare
1/5
CREARE 1/5 Well Mixed
Data
Ref 1
Equation (5.29)
Equation (5.50)
Fr(CL/HPI)
Ref 2
0.1
Well-Mixed
Stratified
0.01
1
10
100
(1 + QL/QHPI)
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Fundamentals of Forced Plumes
D
Z=0
Flow Establishment
Region
o uo
g
Momentum Dominated
0 > m
Intermediate
bg
Buoyancy
Dominated
bu
(r,z)
u(r,z)
Z
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
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Department of Nuclear Engineering & Radiation Health Physics
Fundamentals of Forced Plumes
(Entrainment Assumption)
•
G.I. Taylor’s Entrainment Assumption: Linear spread of
the plume radius with axial position implies that the mean
inflow velocity across the edge of the plume is
proportional to the local mean downward velocity of the
plume.
 vE   E u p
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Fundamentals of Forced Plumes
(Gaussian Velocity and Buoyancy Profiles)
•
Correlation of Velocity Distributions Measured in a Planar Jet (1934)
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Fundamentals of Forced Plumes
(Similarity of Velocity and Buoyancy Profiles)
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Department of Nuclear Engineering & Radiation Health Physics
Governing Equations for Axisymmetric
HPI Plumes
Gaussian Plume Profile Equations
Governing Equations
Velocity:
Plume Mass:
dQp
 r2 
ur , z   u p z exp   2 
 bu 
dz

dQE
dz
Momentum:
Buoyancy:
 r 
g r , z   g p z exp   2 
 bu 
2
Temperature:
 r2 
T  Tm   T  Tm p exp   2 
 bg 
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
2
d  Q p 
2
2

2

gb
g    L p
2 

dz  bu 
Energy:
d  Qp Tp 
dTm

  Qp
2 
dz  1   
dz
Flow Stagnation & Thermal Stratification in NC Loops (T17) Reyes
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Department of Nuclear Engineering & Radiation Health Physics
Dimensionless Equations for
Axisymmetric HPI Plumes
Dimensionless Balance Equations
 QE
Plume Mass:
dQ p
dz

Dimensionless Groups
  QE
dQE
dz 
FrHPI 
Momentum:

2 d  Q p 
FrHPI    2   2 bg2  p
dz  bu 

 QE 

 
 QHPI o


Energy:


d  Qp Tp 
 T   dTm 

 
Qp 

 
2 
dz  1   
2
 dz 
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
 T 
QHPI
1
 g p DHPI  2

aHPI 
  HPI o
DHPI
 dTm 


THPI  Tm o  dz o
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Department of Nuclear Engineering & Radiation Health Physics
Decay Correlations for Axisymmetric
HPI Plumes
Entrainment Correlation (Theofanous, et al.):
1.236
 z 

 QE  0.5176 
 DHPI 
FrHPI  0.414
Temperature Decay Correlation (Theofanous, et al.):

p
T 
Tp  Tm
THPI
 z 

 1  0.326 
 Tm
 DHPI 
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0.65
FrHPI  0.274
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Cold Leg
z=0
Downcomer
Planar Plumes
uDC
uDC
up
Wp
+x
+
z
g
Department of Nuclear Engineering & Radiation Health Physics
Governing Equations for
Downcomer Planar Plumes
Gaussian Plume Profile Equations
Governing Equations
Velocity:
Plume Mass:
dQp
 x2 
u x, z   u p z exp   2 
 bu 
Buoyancy:
 x2 
g  x, z   g p  z exp   2 
 b 
 g
Temperature:
 x2 
T  Tm   T  Tm p exp   2 
 bg 
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
dz

dQE
dz
Momentum:
2
d  Q p 
2 2

2

s g pbg
2 

dz  bu 
Energy:
d  Qp Tp  
dT

  Qp m
dz  1  2 
dz
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Department of Nuclear Engineering & Radiation Health Physics
Dimensionless Equations for
Planar Downcomer Plumes
Dimensionless Balance Equations
Plume Mass:

p

dQ
dz
  QE

E

dQ
dz
Momentum:
Dimensionless Groups
 QE
FrDC 

2 d  Q p 
FrDC    2     pbg
dz  bu 
2
Energy:


d  Qp Tp  
 T   dTm 

  
Qp 

 
2
dz  1   
2
 dz 
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
 QE 

 
 QHPI o
 T
Qp,o
1
 g p DCL  2

sDCL 

 p o

DCL  dTm 



Tp  Tm o  dz o
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Department of Nuclear Engineering & Radiation Health Physics
Correlations for Planar Plume
Velocity and Heat Transfer
Plume Velocity Correlation (Kotsovinos):
 Qp , o g  HPI   m  
u p  1.66 



s m
1
3
Dimensionless Plume Velocity Correlation:

p
u 
u p sDCL
Qp,o
 p 

 1.66 
 m 
1
3
FrDC 
2
3
Convective Heat Transfer Correlation:
Nu p  C  Re 0p.8 Pr 0.4
Where:
Nu p 
2sh p
kf
Re p 
IAEA-ICTP Natural Circulation Training Course, Trieste, Italy, 25-29 June 2007
2u p s
f
Pr 
cp f
kf
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Department of Nuclear Engineering & Radiation Health Physics
Heat Transfer Correlation for Planar Plumes
(Creare ½-Scale data)
1000
900
Creare 1/2 Data
Linear (Dittus Boelter Type)
800
700
Nu/Pr
0.4
600
500
400
300
200
100
0
0.0E+00
5.0E+04
2.0E+05
1.5E+05
1.0E+05
2.5E+05
3.0E+05
Plume Reynolds Number
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Photographs of the IVO Transparent Test Loop.
Cold Leg C flow rate = 66 gpm (4.2 liters/s)
HPI flow in Cold Leg B = 6.6 gpm (0.42 liters/s)
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Complexity of Downcomer Plume Behaviour
• Downcomer Plumes are quite complex in MultiLoop Systems.
– Plume position is not steady
– Plumes can merge
• Does not lend itself to simple models
– CFD Codes may be best method to predict
downcomer plume behavior.
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Complexity of Downcomer Plume Behaviour
(STAR-CD Calculation)
Department of Nuclear Engineering & Radiation Health Physics
Conclusions
• Natural Circulation Flow Interruption:
– SG Reverse Heat Transfer
– Loop Seal Cooling
– SG Tube Voiding
• Thermal Stratification can occur upon loss of
N/C flow
– Onset Criteria
• Simple Models for Axisymmetric and Planar
Plumes
• CFD needed to predict complex multiple
plume interactions.
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