IAEA Training CourseWorkshop on Natural Circulation in Water Cooled Nuclear Power Plants, ICTP, Trie

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IAEA Training Course/Workshop on Natural
Circulation in Water Cooled Nuclear Power Plants,
ICTP, Trieste, June 25-29,2007
PHENOMENA ASSOCIATED WITH NATURAL
CIRCULATION by Dilip Saha
Reactor Engineering Division Bhabha Atomic
Research Centre Trombay, Mumbai 400085, INDIA
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COURSE ROADMAP


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INTRODUCTION

• Natural circulation in a closed loop
• heat sink at an elevation higher than the
• heat source
• The flow can be single phase or two phase
• Natural Circulation Flow Rate
• - balance between the driving and the resisting

forces

• parameters of interest
• (a) density(single two phase)
• (b) pressure loss components

Fig1. A Rectangular Closed Natural Circulation
loop
- the driving force in a natural circulation loop
is small
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INTRODUCTION

• Heat Transfer in Source
• Resistance to heat transfer is
• restricted to a thin layer
• q h ( Tw - Tb)
• This expression underscores the importance
  of the film heat transfer coefficient, h.
• The maximum heat flux achievable in fuel is
  mainly limited by
• Critical Heat Flux (CHF).
• - Departure from Nucleate Boiling
• (DNB)
• - Dryout

Fig.2. Radial Temperature Distribution in Fuel
and Coolant
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INTRODUCTION

• Heat Transfer In Sink
• In PWR and PHWR, primary coolant transports heat
  to steam generator. Secondary fluid starts
  boiling

• In BWR primary coolant itself boils
• In condenser condensation of steam takes
  place

Condenser
Steam Generator
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INTRODUCTION
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INTRODUCTION
In new generation of reactors, a large water
pool is being used as heat sink

• Thermal stratification in the pool is an
  important phenomenon

Isolation Condenser Immersed in Large
Water Pool
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INTRODUCTION
Important Phenomena/Parameters Relevant to
Natural Circulation

• A number of correlations given in the
  following sections are derived based on
  experimental data generated with forced
  circulation. Though in most of the cases these
  correlations can be used for natural circulation,
  applicability of these correlations for natural
  circulation should be judiciously checked when
  secondary flows are present like natural
  circulation through large diameter pipe at low
  Reynolds number.

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NATURAL CIRCULATION FLOW RATE

• Density
• Single phase flow - established relationships for
  thermophysical
• properties of
  fluid (IAEA, 1997) exist
• Two phase flow - it is necessary to predict
  void fraction accurately
• to determine
  density.

Void Fraction (?)
Void fraction correlations

• slip ratio models
• K? models and
• correlations based on the
• drift flux model

Two Phase Flow In a Vertical Heated
Channel
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VOID FRACTION

• Slip Ratio Models

where

• empirical equation for the slip ratio, S (uG/uL)

• For homogeneous flow, uG uL and S 1
• usually, the slip ratio is more than unity for
  both horizontal and vertical flows
• A commonly used slip ratio model is Modified
  Smith (Mochizuki and Ishii (1992))

where K 0.95 tanh(5.0x)0.05
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VOID FRACTION

• K? MODEL

• by multiplying the homogeneous void fraction, ?,
  by a constant K Armand (1947) K 0.833
  0.167x

Drift flux model

• largest number of correlations for void fraction
  are based on the drift flux model
• The general expression is

where
VGj is the drift velocity ( uG - j, where j is
the mixture velocity) and for homogeneous flow C0
1 and VGj 0

• The various models differ only in C0 and VGj
  which are empirical in nature.
• The Chexal and Lellouche (1996) correlation is
  applicable over a wide range of parameters
• Details of this and some other commonly used
  correlations can be obtained from IAEA-TECDOC
  (IAEA, 2001).

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PRESSURE DROP

• Components of Pressure Drop

Total pressure drop has three components -
?Pf, due to skin friction (also known as
friction pressure drop) - ?Pl , due to form
friction (also known as local pressure drop) -
?Pa , acceleration pressure drop
Configurations considered - friction
pressure loss (a) circular pipe (b) annulus
and (c ) rod cluster - local pressure
loss (a) spacer (b) bottom and top tie plates
and (c ) configurations causing flow area
changes like contraction, expansion, bends,
tees, valves etc.
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PRESSURE DROP COMPONENTS

• Friction Pressure Drop

• Irreversible component of pressure drop caused by
  shear stress at the wall

where Dh is equal to 4 times flow area / wetted
perimeter

• occurs all along the length and hence referred to
  as distributed pressure drop
• applicable for single-phase and homogeneous
  two-phase flows
• The following pressure drop correlations are
  applicable to steady state fully developed flow

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FRICTION PRESSURE DROP
Circular pipe Adiabatic single-phase flow
Fully developed laminar flow f 64 / Re
for Reynolds number less than 2000 Turbulent
flow
4 x 103 ? Re ? 1012
For switch over from laminar to turbulent if
ft fL then f ft
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FRICTION PRESSURE DROP CIRCULAR PIPE
Diabatic Single-phase Flow

• Generally isothermal friction factor correlations
  are used with properties evaluated at the film
  temperature, Tf
• Tf 0.4 (TW - Tb) Tb
• Multiplying the isothermal friction factor with a
  correction coefficient, F
• F (?b/?w)-0.28 Leung and Groeneveld

Adiabatic two-phase Flow

• Empirical correlations based on homogeneous model
  
• Empirical correlations based on two-phase
  friction multiplier concept
• Direct empirical models
• Flow pattern specific models

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FRICTION PRESSURE DROP CIRCULAR PIPE
Homogeneous flow model
The friction factor is calculated using
equations given for single phase using
two-phase viscosity in calculating the Reynolds
number Cicchitti (1960)
Multiplier concept
Two-phase pressure drop is calculated from
single-phase pressure drop by multiplying with
two-phase friction factor multiplier
Denominators refer to the single-phase pressure
gradient for flow in the same duct with mass flow
rates corresponding to the mixture flow rate in
case of ?LO2 and ?GO2 and individual phases in
case of ?L2 and ?G2
Lottes-Flinn (1956)
Martinelli Nelson (1948) is a commonly used
correlation in this category
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FRICTION PRESSURE DROP
Diabatic two-phase Flow

• Tarasova (1966) two phase friction pressure
  drop is higher in a heated channel
• Koehler and Kastner (1988) two phase pressure
  drops are same for heated and unheated channels
• Leung and Groeneveld two phase multiplier is
  larger for low heat flux than high heat flux
• There is no well established procedure to take
  the affect of heat flux into account and
  alternate approaches are suggested in IAEA-TECDOC
  (IAEA, 2001)

Annulus

• Correlations for circular pipe are normally used
  for the calculation of single phase pressure drop
  in annulus using the hydraulic diameter concept
• For two-phase pressure drop, the same concept is
  expected to be applicable

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FRICTION PRESSURE DROP ROD BUNDLE
Rod bundle

• PWRs and BWRs

• fuel bundles are long (approx. 1.8 to 4.5 m)
• grid spacers
• total pressure drop comprises pressure drop in
  bare rod bundle and the spacers

• PHWRs

• fuel bundles are of 0.5 m length having end
  plates
• split-wart spacers
• total pressure drop is sometimes expressed in
  terms of overall loss coefficient due to the
  closeness of the spacers and the complex geometry
  of the end plates

• FBRs

• Wire wrapped bundles are used

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BWR ROD BUNDLE
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PHWR ROD BUNDLE SPLIT WART SPACER
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PHWR ROD BUNDLE WIRE WRAP SPACER
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FUEL BUNDLE PRESSURE DROP
Wire wrapped rod bundles
UG US UD UK UB US UD
and uR u. ?F
Bare rod bundles
Single-phase
Correlations for circular pipes using hydraulic
diameter of the rod bundle
Two-phase
M is given by M xvG(1-x)vLG2
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LOCAL PRESSURE DROP
This is the localized irreversible pressure drop
component caused by change in flow geometry and
flow direction. Pressure drop across valves,
elbows, tee, spacer, etc. are examples. The local
pressure drop is given by
Grid spacers

• Extremely difficult to establish a pressure loss
  coefficient correlation of general validity for
  grid spacers. But methods of calculation
  reasonably accurate for design purpose can be
  achieved

Single-phase
?p K ? VB2/ 2 can get reasonable value
of K from Idelchik (1986)
Rehme (1973) K Cv ?2 where ? Ag/AB
For ReB ? 5x104, Cv 6 to 7
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LOCAL PRESSURE DROP
Grid spacers
-Two phase flow
?p K(Resat) v G2/2 v x vG (1-x) vL
Homogeneous model
Slip model
Grillo and Marinelli (1970) S 2 for grid
spacers
Tie plate

• Structurally joins all the fuel pins at the ends
• Flow areas at downstream and upstream are
  different unlike spacer
• Located in the unheated portion of the bundle
• Contraction and expansion model for local
  pressure losses,friction along thickness
• For two-phase

The homogeneous the slip model described earlier
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TIE PLATE
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LOCAL PRESSURE DROP
Area changes
Single phase Idelchik (1986) Two phase Romey
see Lottes (1961)
Bends and fittings
Single phase Idelchik (1986) Two phase
Chisholm Sutherland (1969)
where vfg vG - vL, and C2 is a constant
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LOCAL PRESSURE DROP
Bends and fittings
a) Bends
b) Tees
C2 1.75
c) Valves
C2 1.5 for gate valves 2.3 for
globe valves
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ACCELERATION PRESSURE DROP
Reversible component of pressure drop caused by a
change in flow area or density. Expansion,
contraction and fluid flowing through a heated
section are the examples.
Area Change
A0 smaller flow area. ? 1 for single-phase
and for two-phase ? is given by
Density change
Two phase
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HEAT TRANSFER IN SOURCE
Film Heat Transfer Coefficient (h)
h, is normally expressed in terms of Nusselt
Number Nu hd / k
Single phase Laminar flow

• Constant wall temperature local Nusselt Number
  reaches a value of 3.65 asymptotically

• Constant heat flux local Nusselt number reaches
  a value of 4.36 asymptotically

Single phase Turbulent flow
Dittus Boelter equation Nu 0.023 Re0.8 .
Pr0.4
Sieder Tate equation Nu 0.023 Re0.8 .
Pr0.4.( ?w/ ?b )0.14
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HEAT TRANSFER IN SOURCE
Two phase flow
Complexities of the flow boiling mechanisms

• bubble growth and departure
• distribution of the two phases
• departure from thermodynamic
• equilibrium
• characteristics of the heat transfer
• surface
• effect of fluid properties

Saturated flow boiling correlations
Kandlikars Correlation (Kandlikar, 1990)
Co is the convection number and Bo is the boiling
number. Ffl is the fluid dependent Parameter.
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HEAT TRANSFER IN SOURCE
Constants in Kandlikars correlation
C50 for vertical tubes, and for horizontal
tubes with FrLO ? 0.04
h, is evaluated using the two sets of constants
the higher of the two values represents the
predicted value
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HEAT TRANSFER IN SOURCE
Chens Correlation (Chen, 1966)
h TP h mic h mac
hmic is the nucleate boiling part and hmac is the
convective part
h mic hFoster-Zuber .S h mac
hDittus Boelter . F
S, suppression factor is the ratio of effective
superheat to wall superheat
F, the enhancement factor is a function of the
Martinelli Parameter ?tt
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HEAT TRANSFER IN SOURCE
Forster Zuber Correlation (Forster-Zuber, 1955)
Subcooled flow
Chens correlation (Chen, 1963)
hsubhmachmic where, hmachdittus-boelter
hmichforster-zuber.S
Jens and Lottes (1951)
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CRITICAL HEAT FLUX (CHF)
Boiling crisis occurs when the heat flux is
raised to such a high level that the heated
surface can no longer support continuous liquid
contact. This heat flux is usually referred to
as the critical heat flux (CHF).Failure of the
heated surface may occur once the CHF is exceeded

CHF mechanisms
a)DNB (departure from nucleate boiling)

• In subcooled and saturated nucleate boiling
  (approximate quality range from 5 to 5)
• The bubble population density near the heated
  surface increases with increasing heat flux and a
  so-called bubble boundary layer often forms
• If this layer is sufficiently thick it can impede
  the flow of coolant to the heated surface
• This in turn leads to a further increase in
  bubble population until the wall becomes so hot
  that a vapour patch forms over the heated surface

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CRITICAL HEAT FLUX (CHF)
b) Dryout

• In the annular dispersed flow regime (high void
  fraction) Continuous thinning of the liquid film
  takes place due to the combined effect of
  entrainment and evaporation
• If the net droplet deposition rate does not
  balance the evaporation rate the liquid film
  breaks down

CHF Prediction Methodology
A uniformly heated tube cooled internally by a
fluid flowing at a steady rate vertically upwards
CHF (De ,G , ?H in P, E)
E takes into account effect of the surface
Over 400 correlations for CHF in tubes are
currently in existence that indicates the complex
state-of-the-art of predicting CHF phenomena.
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CRITICAL HEAT FLUX (CHF)
Analytical Models

• Annular film dryout model
• Bubbly layer model
• Helmholtz instability model

the models are still less accurate than empirical
correlations
Empirical methods
Inlet-conditions-type prediction methods
N DO (P in, G in, T in, c/s, L H)
NDO Critical Power
cannot be used for predicting the location and
magnitude of CHF
Local-conditions type prediction methods
CHF ?(P,G,X DO, c/s )

• the local CHF is dependent only on the local
  conditions and not on upstream history
• the most common method for predicting CHF
• over 400 empirical correlations of this type
• limited range of application

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CRITICAL HEAT FLUX (CHF)
CHF look-up Table Method

• The CHF look up table is basically a normalized
  data bank
• International CHF look up table Groeneveld et
  al. (1996)

• pressure (P) 0.1 20 Mpa
• mass flux (G) 0-7500 kg.m 2.s-1
• quality (X) 50 to 100

The CHF needs to be modified to account for
bundle specific effects
CHFbundle CHFtable x K1 x K2 x K3 xK4 x K5 x
K6 x K7 x K8
K1 to K8 are correction factors to account for
specific bundle effects
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CRITICAL HEAT FLUX (CHF)
Table-3 The 1995 CHF Look-Up Table for CHF in 8
mm Tubes (in kW/m2)
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CHF LOOK-UP TABLE CORRECTION FACTORS
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CHF LOOK-UP TABLE CORRECTION FACTORS
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HEAT TRANSFER IN SINK
BOILING
Boiling takes place on the secondary side of
steam generators. Correlations for h given
earlier can be used.

CONDENSATION
Vapor starts condensing on the surface when the
surface is cooled below the saturation
temperature of vapor
Two distinct forms of condensation
Film condensation condensate wets the surface
and forms a liquid film on the surface
Dropwise condensation condensed vapor forms
droplets on the surface
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CONDENSATION
Dropwise condensation part of the surface is in
contact with vapor leading to higher heat
transfer rates.
Film condensation the surface is blanketed by a
liquid film of increasing thickness and this
liquid wall between solid surface and the vapor
serves as a resistance to heat transfer
Flow regimes in condensation heat transfer
Re
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Re1800 flow is turbulent
disagreement exists about the value of Re at
which the flow becomes wavy-laminar
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CONDENSATION
Vertical Plates
Laminar Flow on a smooth vertical plate
Does not take into account

• nonlinear temperature profile in the liquid film
• cooling of the liquid below the saturation
  temperature

Wavy Laminar Flow on Vertical Plates

• Waves make it difficult to obtain analytical
  solutions
• Increase in heat transfer due to wave is on an
  average about 20 percent

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CONDENSATION
Turbulent Flow on Vertical Plates
Vertical Tubes Above equation with length of
tube as characteristic length
Horizontal Tubes and spheres
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CONDENSATION
Comparison of Vertical (L) and Horizontal Tube (D)
Setting hvert hhoriz, L 1.294 D 2.77D
For L2.77D,heat transfer coefficient will be
higher in horizontal position
It is common practice to place the tubes in a
condenser horizontally
Horizontal Tube Banks
Horizontal tubes on top of each other
N No. of tubes
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CONDENSATION
Condensation Inside Horizontal Tubes
Strongly influenced by

• vapor velocity
• rate of liquid accumulation on the walls

For low vapor velocities-
TL average of the wall and saturated steam
temperatures
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EFFECT OF NON-CONDENSABLES
Effect of the presence of noncondensable gases
When the vapor mixed with a noncondensable gas
condenses, the noncondensable gas remains in the
vicinity of the condensate layer and acts as a
barrier between the vapor and the condensate
layer
Vapor now must diffuse through the noncondensable
gas first before reaching the surface
Most condensers used in power plants operate at
pressure below the atmospheric pressure and
operation at such a low pressure raises the
possibility of air leaking into the condensers
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EFFECT OF NON-CONDENSABLES
Condensation when steam/noncondensable mixture is
nonflowing
Uchida(1956)
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EFFECT OF NON-CONDENSABLES
Condensation when steam/noncondensable mixture is
nonflowing
Condensation when steam / noncondensable gas
flowing inside vertical tube
Wa air mass fraction in the steam/air mixture
Ja CpG (Tb-Twi)/hfg
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THERMAL STRATIFICATION
THERMAL STRATIFICATION
Formation of horizontal layers of fluid of
varying temperature with the warmer layers of
fluid placed above the cooler ones Large pool of
water is increasingly being used as heat sink in
new generation of advanced reactors Stratificatio
n influences heat transfer to pool to a great
extent and heat storage capacity of the pool in
the form of sensible heat is significantly
reduced
The forces involved are

• - buoyancy force
• viscous force
• - inertia force

In many cases, one has to consider surface
tension and turbulence. In case of free surface,
mass transfer and heat transfer are to be
considered at the free surface
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THERMAL STRATIFICATION
Transient CFD models are being developed for the
prediction of flow patterns temperature
profiles. Stress is on developing better
turbulence models. For validation of theoretical
results,experimental data are being generated.
In most of the region there is no flow indicating
thermal stratification In the region.
Velocity Plots in a side heated cavity
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THERMAL STRATIFICATION IN LARGE POOLS
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OTHER RELEVANT PHENOMENA
CARRYOVER

• Two-phase mixture leaving the of the reactor
  enters the steam drum.
• water separation is effected by gravity in steam
  drum.
• Carryover is a phenomenon associated with droplet
  entrainment.
• Carryover is to be restricted to about 0.2, by
  appropriate measures and should be predicted
  accurately.

Film entrainment

• entrainment of droplets by mechanisms like roll
  wave shear-off and is typified by presence of a
  wavy interface of liquid film and vapor along the
  direction of flow.
• Dispersed annular flow is the typical flow regime
  exemplifying the film entrainment

Pool entrainment

• entrainment of droplets from the surface of pool
  due to bursting of bubbles and break-up of liquid
  jet
• is typified by the presence of liquid pool and
  turbulent liquid vapor flow

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CARRYOVER
Modeling requires droplet formation mechanism and
prediction of average or maximum droplet size
distribution
Entrainment is found to be a function of steam
velocity and height from the free surface
Schematic of steam drum depicting carryover
carryunder
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CARRYUNDER
Carryunder is the entrainment of gas bubbles
with the recirculating liquid

• undesirable in a natural circulation system

- Carryunder depends on bubble dynamics and
configuration
Bubble dynamics

• governed by various forces of which the drag
  force is most significant and most uncertain
• researchers have empirically obtained the drag
  coefficient for various flow regimes

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CARRYUNDER
Configuration

• Baffle spacing and liquid level with respect to
  baffle tip
• Increasing the baffle spacing first increases
  Carryunder due to large inter-baffle space
  then decreases due to very low liquid velocity in
  the inter-baffle space

- with regard to baffle space, Carryunder may be
attributed to area dominated regime and velocity
dominated regime
Schematic of steam drum depicting carryover
carryunder
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OTHER RELEVANT PHENOMENA
Parallel Channel Effect

• Interaction between multiple parallel flow paths
  may become a critical
• phenomenon mainly in respect of instability
• oscillation in one group of channels 180? out of
  phase with oscillation in another group
• - instability may not be detectable by
  monitoring total flow in the loop

• possibility of number of flow configurations in
  which some channels may have flow direction
  opposite to others and some may even stagnate

Effect of Non-condensable Gases
Containment
Containment is the final physical barrier to
prevent release of radioactivity to environment

• it is necessary to remove energy released into
  the containment under accidental condition
• Passive containment coolers are commonly used

• building condensers provided at the top of the
  containment
• is an example

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PASSIVE CONTAINMENT COOLER
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OTHER RELEVANT PHENOMENA
Effect of Non-condensable Gases
Containment

• The performance is highly impaired by the
  presence of non-condensables

• Besides air present, depending on the severity of
  accident, hydrogen may also get released

• It is necessary to predict distribution of
  hydrogen, steam and air in the containment to
  assess the performance of the condensers

• Potential stratification and separation of steam
  and non-condensables constitute an important
  factor for containment cooling

- Theoretical and experimental studies are
being conducted
Primary Loop

• Non-condensables, if released may get accumulated
  at specific locations
• In a PHWR non-condensables may accumulate at the
  top of the inverted U tubes of steam generators
• This may reduce or completely stop flow through
  the tube

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OTHER RELEVANT PHENOMENA
Vortex Formation in Pool

• In many advanced reactor design a large pool of
  water is provided which acts as

• heat sink
• source for low pressure injection of coolant

• Gravity flow through small outlet pipes may lead
  to vortex formation.Depending on the
  orientation of the outlet port and depth of
  water, air or gas may get entrained

Fluid Mixing

• coolant entering the pressure vessel may have
  different temperature and boron concentration
• In absence of proper mixing

• difference in temperature may lead to
  unacceptable thermal gradient
• Difference in boron concentration may cause
  boron-diluted coolant to enter the core

In recent years, more emphasis is placed on fluid
mixing phenomena to avoid boron dilution and
thermal gradient.
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OTHER RELEVANT PHENOMENA
Counter-Current Flow Limitation (CCFL)

• countercurrent flow limitation (CCFL) determines
  the maximum rate at which one phase can flow
  countercurrently to another phase
• It is of great importance in connection with the
  safety analysis of reactor systems

• steam produced in the core of a PWR flows upward
  through the hot leg
• countercurrently flows the injected emergency
  core cooling water
• Steam condensed in steam generator also flows
  back to the core
• Steam going out of core partly or totally
  inhibits the water flow into the core

• The CCFL has been studied by a large number of
  researchers, both experimentally and
  analytically, mostly in vertical pipes. The CCFL
  in horizontal or nearly horizontal geometries has
  received comparatively little attention
• H.T. Kim (2002) has studied CCFL and the study
  revealed the effect of L/D of pipes on CCFL
  phenomena

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COUNTER CURRENT FLOW LIMITATION
Countercurrent Flow of Steam and Cooling
Water in Hot Leg of PWR
63
CONCLUSIONS
An account of various phenomena encountered in
the natural circulation systems of a nuclear
reactor is provided. Thermohydraulic
relationships related to these phenomena are
given as examples. References are given that
contain more relationships covering wider range
of parameters to choose from. Some of the
phenomena are very briefly described. For these
phenomena, references are given which will
provide deeper insight into these phenomena.