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Summary
The CHF phenomenon in the two-phase convective flows has been an
important issue in the fields of design and safety analysis of light water
reactor(LWR) as well as sodium cooled liquid metal reactor(LMR). Especially
in the LWR application, many physical aspects of the CHF phenomenon are
understood and reliable correlations and mechanistic models to predict the
CHF condition have been proposed over the past three decades.
Most of the existing CHF correlations have been developed for light water
reactor core applications. Compared with water, liquid metals show a
divergent picture of boiling pattern. This can be attributed to the
consequence that special CHF conditions obtained from investigations with
water cannot be applied to liquid metals. Numerous liquid metal boiling heat
transfer and two-phase flow studies have put emphasis on development of
models and understanding of the mechanism for improving the CHF
predictions. Thus far, no overall analytical solution method has been obtained
and the reliable prediction method has remained empirical.
The principal objectives of the present report are to review the state of
the art in connection with liquid metal critical heat flux under low pressure
and low flow conditions and to discuss the basic mechanisms.
- iv -
Table of Contents
Summary iv
Table of contents v
List of figures vi
1. Introduction 1
2. Background 5
2.1 Definition of the CHF 5
2.2 Classification of the CHF mechanisms 5
2.2.1 The CHF of water 5
2.2.2 The CHF of liquid metal 10
2.3 Parametric trends of the CHF 14
2.4 Prediction methods of the CHF 14
3. Generalized empirical CHF correlations for alkali metals 19
3.1 Nucleate pool boiling CHF 19
3.1.1 Noyes correlations 19
3.1.2 Caswell and Balzhiser correlation 20
3.1.3 Kirillov correlation 20
3.1.4 Subbotin correlation 22
3.1.5 Assessment of the correlations 23
3.2 Flooding limited CHF 27
3.2.1 Criteria for flooding 27
3.2.2 Mishima and Ishii correlation 29
3.3 Low flow convection CHF 31
3.3.1 Kottowski correlation 31
3.3.2 Katto correlation 33
3.4 Flow excursion CHF 34
3.4.1 General consideration 34
3.4.2 CHF prediction and simulation experiments 36
4. Conclusions 41
Appendix 45
References 53
- v -
List of Figures
Fig. 2.1 Typical flow boiling curve 6
Fig. 2.2 Mechanisms of CHF for subcooled and low quality boiling ••• 9
Fig. 2.3 Flow excursion and flow versus pressure drop stability
consideration 13
Fig. 2.4 Parametric trends of CHF for uniformly heated tubes 15
Fig. 3.1 Correlation of CHF data by Eq.(3.2) for stable nucleate pool
boiling of liquid metals on horizontal cylindrical heaters 21
Fig. 3.2 Comparisons of generalized empirical correlations for
sodium 24
Fig. 3.3 Comparisons of generalized empirical correlations for
potassium 25
Fig. 3.4 Comparisons of generalized empirical correlations for
cesium 26
Fig. 3.5 Non-dimensional critical heat flux versus K 30
Fig. 3.6 Comparison of predicted and measured CHF
(Kottowski correlation) 32
Fig. 3.7 Comparison of predicted and measured CHF
(Katto correlation) 34
Fig. 3.8 Predicted flow characteristics corresponding to
ORNL test conditions 38
Fig. 3.9 Predicted flow characteristics corresponding to
JNC LHF123 test conditions 39
Fig. 3.10 Predicted flow characteristics corresponding to
JNC LHF124 test conditions 40
- vi -
1. Introduction
The critical heat flux(CHF) is a condition in which a small increase in
wall temperature leads to a sharp reduction of heat flux or heat transfer
coefficient. The CHF phenomenon has been researched extensively especially
in relation to high heat flux application such as nuclear power reactors,
fossil-fueled boilers, steam generators, etc., to operate them with optimum
heat transfer rates without the risk of physical burnout.
The CHF phenomenon in the two-phase convective flows has been an
important issue in the fields of design and safety analysis of light water
reactor(LWR) as well as sodium cooled liquid metal reactor(LMR). In a
LWR, hypothetical transient conditions generally lead to CHF in the subcooled
or low quality region. Most LWR reactor design is accomplished using
empirical, dimensional CHF correlations carefully tested by application to
experimental data obtained under conditions similar to those of LWR
operation. Especially in the LWR application, many physical aspects of the
CHF phenomenon are understood and reliable correlations and mechanistic
models to predict the CHF condition have been proposed over the past three
decades. A number of excellent surveys of the water application CHF are
available in books[l-5] and papers[6-8].
Also for the design and safety analysis of LMR, the prediction of the
critical heat flux(CHF) in the two-phase convective flow is an important
consideration. The sodium coolant typically remains highly subcooled for
normal reactor steady state operation and design transient, even for those
considered to be major incidents. However, for certain postulated severe
accident conditions such as loss of piping integrity(LOPI) and a loss of heat
sink(LOHS) in connection with LMR safety analysis, the process of decay
heat removal can lead to coolant boiling. For such low-heat-flux/low-flow
conditions, CHF criterion is required in order to assess the potential for fuel
pin failure and melting.
Most of the existing CHF correlations have been developed for light water
reactor core applications. Compared with water, liquid metals show a
- 1 -
divergent picture of boiling pattern. This can be attributed to the
consequence that special CHF conditions obtained from investigations with
water cannot be applied to liquid metals. Numerous liquid metal boiling heat
transfer and two-phase flow studies have put emphasis on development of
models and understanding of the mechanism for improving the CHF
predictions. Thus far, no overall analytical solution method has been obtained
and the reliable prediction method has remained empirical.
In general the CHF of water under forced convective condition is classified
into two types, i.e., departure from nucleate boiling(DNB) at low qualities and
liquid film dryout(LFD) at high qualities based on physical mechanisms. In
the LFD case, the CHF occurs when the flow rate of liquid film on the
heated surface falls to zero, which can be modeled by considering
evaporation, entrainment and deposition. However, the detailed physical
mechanism of DNB at low quality condition is not clearly understood.
Generally, the following three DNB mechanisms have been identified:
- bubble boundary layer dryout,
- local nucleation initiated dryout, and
- evaporation of liquid film surrounding a vapor slug.
Among these mechanisms, bubble boundary layer dryout has been of
paramount interest to the nuclear power reactor designers. Typical
phenomenological models of the DNB type CHF corresponding to bubble
boundary layer dryout are as followstl]:
- boundary layer separation,
- near-wall bubble crowding, and
- sublayer dryout under a vapor blanket.
On the other hand, the CHF of liquid metal under low-heat-flux/ low-flow
conditions several different CHF mechanisms are possible because of the
coupling and the existence of the hydrodynamic instabilities such as flooding
and flow excursions. From the examinations of relevant experimental data,
Ishii classified the CHF condition of liquid metals under low flow into 4
categories as [9]:
- 2 -
- pool boiling CHF,
- flooding limited CHF,
- low flow convection CHF, and
- flow excursion CHF.
The principal objectives of the present report are to review the state of
the art in connection with liquid metal critical heat flux under low pressure
and low flow conditions and to discuss the basic mechanisms.
_ O _
2. Background
2.1 Definition of the CHF
The phenomenon of the critical heat flux(CHF) consists of the deterioration
of the local heat transfer coefficient which occurs when the thermohydraulic
parameters, such as steam quality, thermal flux, specific flow rate, etc., reach
certain critical values. Figure 2.1 shows a typical boiling curve for a boiling
system. The CHF also constitutes the most important boundary in
considering the two-phase flow regimes. Pressure drop as well as heat
transfer generally decreases when flow undergoes transition from pre-CHF to
post-CHF regimes. The CHF is defined as follows[10, 11]:
For a surface with a controlled heat flux, such as electrical heating,
radiant heating or nuclear heating, the CHF is defined as that condition under
which a small increase in the surface heat flux leads to an inordinate
increase in wall temperature.
For a surface whose wall temperature is controlled, such as one heated by
a condensing vapor, the CHF is defined as that condition in which a small
increase in wall temperature leads to an inordinate decrease in heat flux or
heat transfer coefficient.
The CHF phenomenon has been researched extensively especially in
relation to high heat flux application such as nuclear reactors, fossil-fueled
boilers, steam generators, etc., to operate them with optimum heat transfer
rates without risk of physical burnout.
2.2 Classification of the CHF mechanisms
2.2.1 The CHF of water
The CHF condition is classified into pool boiling CHF and flow boiling
CHF according to the flow condition. The pool boiling is defined as boiling
from a surface positioned in a static pool of liquid. In pool boiling, the CHF
occurs when the conditions are no longer such as to allow the vapor
- 5 -
SurfaceHeat Flux
CHF
MinimumHeat Flux
AB Single-phase forced convection to liquidBD Nucleate boiling or forced convective evaporationDE Transition boilingEG Film boiling
SurfaceTemperature
Fig. 2.1 Typical flow boiling curve
— fi —
generated in nucleate boiling to be removed from the vicinity of the heated
surface. When the pool boiling CHF occurs, part or all of the heated surface
is covered by a poorly conducting film of vapor and this leads to a
deterioration in the heat transfer.
The flow boiling CHF is again classified into the departure from nucleate
boiling (DNB) at low qualities and liquid film dryout (LFD) at high qualities
based on the physical mechanism. In the LFD case, the CHF occurs when
the flow rate of liquid film on the heated surface falls to zero, which can be
modeled by considering evaporation, entrainment and deposition. However, the
detailed physical mechanism of DNB at low quality condition is not clearly
understood. Generally, the following three DNB mechanisms have been
identified:
(1) Bubble boundary layer dryout.
At moderate subcooling, a boundary layer of bubbles may grow to the
point where it restricts the access of liquid to the heated surface. At some
point, if access is seriously affected, then overheating occurs with the
formation of a continuous vapor layer adjacent to the wall.
(2) Local nucleadon initiated dryout.
As a result of evaporation of the micro-layer a dry patch tends to form
on the heating surface under a growing vapor bubble. When the bubble
departs from the surface this dry patch is rewetted. A stable situation
results from an alternate heating and quenching of the surface at the dry
spot. If the heat flux is high, the dry patch cannot be easily wetted
following bubble departure and therefore a progress increase in the surface
temperature leads to the CHF condition.
(3) Evaporation of liquid film surrounding- a vapor slup.
At low mass flux the slug flow pattern may occur with a liquid film
initially remaining between the vapor bubble and the heated wall. If,
- 7 -
however, the heat flux is high, this film may be completely evaporated and a
form of dryout with consequent overheating of the tube wall may occur.
These mechanisms are schematically shown in Fig. 2.2. Among these
mechanisms, bubble boundary layer dryout has been of paramount interest to
the nuclear power reactor designers.
Typical phenomenological models of the DNB type CHF corresponding to
bubble boundary layer dryout are as follows:
(3) Boundary layer separation.
The boundary layer separation models are based on the assumption that
vapor injection into the liquid stream reduces the liquid velocity gradient near
the wall. The liquid separates from the wall, resulting in a transition from
nucleate to film boiling when the rate of vapor effusion increases beyond a
critical level. Semi-empirical CHF correlations, based on the bubble boundary
layer separation concepts, have been developed by Kutateladze[12] and others.
But this mechanism has lost its popularity in recent years.
(b) Near-wall bubble crowding.
Here, a bubble boundary layer builds up on the surface and vapor
generated by boiling at the wall surface must escape through this boundary
layer. When the boundary layer becomes too crowded with bubbles, outward
vapor flow away from the wall is impossible. The surface becomes dry and
overheats which leads to burnout. This mechanism has been developed by
Styrikovich[13], Weisman & Pei[14], Weisman & Ying[15] and others.
(c) Sublayer dryout under a vapor blanket.
Here, the CHF is assumed to occur when a vapor blanket isolates the
liquid sublayer from bulk liquid and the liquid entering the sublayer falls
short of balancing the rate of sublayer dryout by evaporation. This
mechanism has been developed by Lee & Mudawwar[16], Katto[17, 18] and
others.
- 8 -
Position of critical phenomenon
o
-o - - ' . "
(A) (B) (C)
Mass flux, G
(A)
Onset ofannular flow
Subcooling 0 Quality, X
(A) Local nucleation initiated dryout(B) Bubble boundary layer dryout(C) Evaporation of liquid film surrounding a vapor slug
Fig. 2.2 Mechanisms of CHF for subcooled and low quality boiling
- 9 -
The sublayer dryout models have become popular in recent years. The
observations by Mesler (1976), Molen & Galjee (1978), Bhat et al. (1983),
Serizawa (1983), Hino & Ueda (1985) and Mudawwar et al. (1987) represent
strong evidence that, just before CHF, a very thin liquid sublayer is trapped
beneath a vapor blanket. Recently, Katto[17,18] presented a physical model of
the CHF of subcooled flow boiling based on the liquid sublayer dryout
mechanism, showing good accuracy to predict CHF of various kinds of fluids.
He derived a coefficient correlation to evaluate the vapor blanket velocity by
relating it to the local velocity of the two-phase flow at the boundary of
liquid sublayer.
2.2.2 The CHF of liquid metal
The CHF mechanism of liquid metal is influenced by the coupling of the
heat transfer, vapor generation, and driving head. Because of this coupling
and the existence of hydrodynamic instabilities such as flooding and flow
excursions, several different CHF mechanisms are possible.
Careful examination of relevant experimental data in terms of the
controlling physical mechanisms leading to CHF suggest that the following
four different mechanisms should be considered: pool-boiling CHF, flooding or
film flow limited CHF, low flow convection CHF, and flow excursion CHF.
It follows that the values of CHF can vary widely from one data source to
the next if the mechanism of CHF is different.
(1) Pool Boiline CHF.
Pool boiling is defined as boiling from a surface positioned in a static pool
of liquid. In pool boiling, burnout occurs when the conditions are no longer
such as to allow the vapor generated in nucleate boiling to be removed from
the vicinity of the heated surface. When burnout occurs, part or all of the
heated surface is covered by a poorly conducting film of vapor and this leads
to a deterioration in the heat transfer.
For a boiling pool, the flow pattern is basically established by natural
- 10 -
circulation induced by the lighter vapor phase as a result of boiling. The
heat transfer mechanism and local flow near the heated surface are governed
by the microscale convection due to the nucleation, bubble growth, and
bubble departure.
In general, it can be said that the pool boiling CHF is very high. And in
the viewpoint of LMFBR application, the pool boiling CHF will not occur in a
rod bundle even with a complete inlet blockage. In such a case, the
flooding-limited CHF is the dominant mechanism, which gives a far smaller
CHF value.
(2) Flooding Limited CHF.
The design philosophy of LMFBR is to prevent flow blockage. There are
two kinds of potential blockages - gross flow blockage at the inlet of core
assemblies and local flow blockages within assemblies. The sequence of
these events following the flow blockage was reported as sodium boiling and
fuel cladding failure. In this case, the flooding limited CHF is the dominant
mechanism.
Except for very short tubes where the pool boiling CHF is important, the
flooding-limited CHF occurs consistently for a vertical tube with an inlet
blockage. In a vertical system with an inlet blockage, liquid flows down
from the top and evaporated in the heated section. If the generated vapor is
flowing upward at a low rate, a countercurrent flow takes place in the tube.
For a high vapor flux the liquid becomes unstable and waves of large
amplitudes appear. When the vapor is increased further the critical vapor
flux for the onset of flooding is exceeded, and the liquid penetration into the
heated section is considerably reduced. At this point, dryout occurs anywhere
in the heated section as a result of the flooding.
(3) Low Flow Convection CHF.
Aladyev performed CHF tests using potassium at low flow forced
convection conditions[19]. The experiments were carried out with 4 and 6mm
tubes and heated length to diameter ratios from 30 to 100. The mass flux
- 11 -
ranged from 20 to 325kg/m2sec and the pressure, from 0.013 to 0.41MPa.
The burnout always occurred at the tube outlet when uniform heating was
applied. The exit quality under these conditions was in the range of 0.5 to
1.0. He concluded that the Prandtl number has no effect on the CHF and
that CHF is essentially determined by the hydrodynamics of the high quality
two-phase flow.
The observed quality of Aladyev experimental data at the time of CHF
was very high, approaching a value of 0.8. For such high qualities, the
annular flow regime prevails, and liquid film dryout is likely to be closely
related to entrainment of liquid into the vapor stream[20]. Similar trends
were observed in the experiments of Fisher using rubidium and cesium[21].
(4) Flow Excursion CHF.
From the physical properties of sodium, the variation of pressure drop
versus the inlet mass flow rate under constant power and constant outlet
pressure can be expected to have "S" shape as shown in Fig. 2.3. During
the rundown of the pumps and as long as the coolant is subcooled, the flow
decreases monotonically with decreasing pressure drop, i.e., from A to B in
Fig. 2.3.
At the onset of boiling point, point B in Fig. 2.3, the large liquid to
vapor density ratio for sodium at low pressure causes a large volume
change and rapid increase in local pressure drop. However, since there is
insufficient pressure supply, the flow further decelerates to compensate for the
deficiency in the pressure supply until the another stable point C is reached.
When this flow excursion from low quality flow to high quality flow
occurs, it probably will also trigger CHF, because a steady-state calculation
may show that at the next stable point C, the exit quality will exceed one, in
which case a simple enthalpy burnout occurs. Even if the exit quality is
below one, it can be high enough to exceed the critical exit quality (Xec)
corresponding to the high quality CHF for low flow convection conditions.
- 12 -
AP
Pressure head
quality\ R T 1 LOW j AllI i quality J liqui
Interalcharacteristic
. WorkingI pointII
Fig. 2.3 Flow excursion and flow versus pressure dropstability consideration
- 13 -
2.3 Parametric trends of the CHF
For uniformly heated tubes, the following parameters mainly affect the
steady-state CHF: tube diameter (D), tube heated length (Lh), system
pressure (P), mass flux (G) and inlet subcooling (zJhi). Fig. 2.4 shows
conceptually the effect of the various system parameters.
(a) For fixed pressure, tube diameter and tube length the CHF value
varies approximately linearly with the inlet subcooling. This linear
relationship is obeyed over fairly wide ranges, but it has no fundamental
significance. If a very wide range of inlet subcooling is used, then
departures from linearity are observed.
(b) For fixed pressure, tube diameter and inlet subcooling the CHF value
decreases with increasing tube length. However, the power input required for
burnout increases at first rapidly, and then less rapidly. For very long tubes,
the power to burnout may appear to asymptote to a constant value
independent of tube length in some cases. Again, this only applies over a
limited range of length.
(c) For fixed pressure, mass flux and tube length the CHF value increases
with tube diameter. The rate of increase decreases as the diameter increases.
(d) For fixed inlet subcooling, tube diameter and tube length the CHF
value increases with pressure, passes through a maximum, and then drops
off. This effect, however, is not clearly identified.
2.4 Prediction methods of the CHF
Up to the present the following three approaches to predict the critical
heat flux are available:
- empirical correlation,
- graphical or look-up table, and
- theoretical prediction.
- 14 -
CHFj
•-Ah;P, D, A^ = const.
CHF
j
P, G, L,, = const.
CHF/
Ah; , 0 ,1^ , = const.
Fig. 2.4 Parametric trends of CHF for uniformly heated tubes
- 15 -
The empirical correlation approach commonly used in the analysis of heat
transfer equipment is subdivided into two main groups:
(1) local condition type correlation in the form of
Qc = AP,G,%, cross — section geometry), and
(2) global condition type correlation in the form of
Qc = KP,G,Lh, AHin, cross — section geometry).
The former is more commonly used on the ground of its flexibility and
convenience for predicting the location of the CHF and for reflecting the
effects of axial flux distribution, spacers, flux spikes, flow transients, etc. On
the other hand, the latter is primarily used to predict critical power during
steady-state operation and would be more accurate for a given geometry and
axial heat flux distribution.
Typically W-3 correlation and Biasi correlation are commonly used in the
analysis of DNB type CHF and LFD type CHF, respectively, and the other
important correlations may be found in literatures[l, 26, 27]. On the other
hand, for the prediction of the CHF in liquid metal the Kottowski correlation
is commonly used.
The graphical or look-up table technique has been partially employed to
overcome the limitations concerned with the empirical correlation method. In
the graphical method the CHF value can be found in a graph as a function
of flow and fluid properties. It would be excellent for handbook application or
for obtaining a first estimate of the CHF.
The look-up table technique is accurate, simple to use, and easily shows
the correct parametric and asymptotic trends. The U.S.S.R. Academy of
Sciences constructed a series of standard CHF tables of water for 8mm i.d.
tubes based on the local condition concepts[28]. Recently, Groeneveld et al.
presented an important version of the CHF look-up table of water for the
same tube as a function of pressure, mass flux and equilibrium quality[29].
- 16 -
However, graphical or look-up table technique appears to be nothing but the
generalization of various experimental data and correlations proposed
previously. The requirement for the fundamental understanding of the CHF
phenomenon is still not satisfied.
One alternative approach is the theoretical prediction method. Theoretical
CHF models of water for LFD type are successful in understanding of the
CHF mechanism and attaining reliable prediction. These models are found in
many literatures[30~36]. In comparison with the LFD type CHF, the
theoretical model for DNB type CHF is unsatisfactory since there is no
common consent for the crucial mechanism of the DNB phenomenon.
Typically three categories of the mechanism which initiates the DNB type
CHF have been suggested'-
- bubble boundary layer dryout,
- local nucleation initiated dryout, and
- evaporation of liquid film surrounding a vapor slug.
These models are found in the literatures[12~18]. The theoretical
prediction methods are valuable indeed in improving the understanding of the
physical mechanism leading to the CHF.
- 17 -
3. Greneralized empirical CHF correlations for alkali metals
3.1 Nucleate pool boiling CHF
3.1.1 Noyes correlations
The first empirical equation proposed for correlating CHF data on liquid
metals was Eq.(3.1.a) by Noyes[37], for horizontal cylindrical heaters. This
equation usually predicts CHF values that are more nearly correct than the
theoretical correlations, but it is not recommended because it is based on a
few results obtained by Noyes on sodium and others on water and
hydrocarbons, and it predicts a much higher pressure dependence on the CHF
than is generally observed. However, Noyes was the first to call attention to
the metal boiling.
where gc is critical heat flux, Btu/ft2hr
A is latent heat of vaporization, Btu/lbm
pv is density of saturated vapor, lbm/ft3
pL is density of saturated liquid, lbm/ft3
g is acceleration due to gravitational field, ft/hr2
gc is conversion factor, 4.170x108 lbmft/lbfhr2
a is surface tension, lbt/ft
PrL is Prandtl number of liquid C P L ^ I A L
Later, Noyes and Lurie recommended Eq.(3.1.b) for predicting CHF values
for nucleate boiling sodium. They correlated the CHF results on sodium,
along with those of Subbotin et al. and Carbon, by adding a conduction-
convection flux quantity to the Kutateladze equation. This equation is much
more reliable than Eq.(3.1.a), with regard to both the magnitude of the
predicted CHF and its dependence on the boiling pressure.
Qc= 4X105 + 0.16 A (gc g a pL p\)Vi (3.1.b)
- 19 -
3.1.2 Caswell and Balzhiser correlation
The Eq.(3.2) was proposed by Caswell and Balzhizer[38]. They took the
sodium results of Noyes and Carbon, the potassium results of Colver and
Balzhiser, and their own sodium and rubidium results and correlated them by
the empirical two-dimensionless-group equation.
(3.2)i h r 1.18i(rfA PvkLJ \ Pv
where CPL is specific heat of liquid, Btu/lbm°F
J is mechanical equivalent of heat, 778.16 lbf-ft/Btu
This is illustrated in Fig. 3.1. Ninety-five percent of the data points fall,
within a ±6% deviation, along the straight line given by Eq.(3.2). This is
very good, but, as the authors cautioned, it is probably risky to apply the
equation to systems and conditions appreciably different from those for which
the correlated data were obtained. For example, the equation neglects the
acceleration effect and is therefore restricted to boiling under conditions where
the body force is close to that corresponding to the earth's normal
gravitational force.
3.1.3 Kirillov correlation
By assuming that the critical heat flux is proportional to the rate of
growth of a vapor bubble, Kirillov concluded that it should be approximately
proportional to the 0.6 power of ki!39]. Then, by invoking the law of
corresponding stages, he arrived at the simple Eq.(3.3) in which the
coefficient and the power on the reduced pressure were obtained from
published CHF data on sodium, potassium, and cesium, over the reduced
pressure range 10 4 to 3 x 10"2.
<fc=3.12xl05 k°£6 (PjPcr)m (3.3)
where PL is static pressure in liquid at boiling surface, psia
- 20 -
10
10 r
10
-5
-7
; . i
Symbol ^ g j Investigators
• K Colver & BalzhiserA Na Noyes & Luriex Na Carbon• Na Caswell & Balzhisero Rb Caswell & Balzhiser
I I
10J 107
PL~ P I
Fig. 3.1 Correlation of CHF data by Eq.(3.2) for stable nucleate pool boiling
of liquid metals on horizontal cylindrical heaters
- 21 -
Per is critical pressure, psia
The data points, from both horizontal disk and horizontal cylindrical
heaters, showed an average deviation of ±15% from the line of the equation;
the higher the reduced pressure, the better the fit.
3.1.4 Subbotin correlation
Subbotine et al. developed a CHF correlation by starting out with the
same postulate as that initiated by Noyes and Lurie, i.e.,
Qc= Qevap+ Qc-c (3.4a)
which can be put in the form of
Qevap (3Ab)Qevap
They expressed the relation Qc-Cl Qevap by the empirical relation
(3.4.0
on the basis of experimental CHF data on sodium, potassium, rubidium, and
cesium from six different sources obtained with both horizontal flat-disk and
horizontal cylindrical heaters. The final correlation of Subbotin et al. is
therefore
where Per in the ratio 45/Pcr is in atmospheres. This equation possesses the
anomaly that, although derived on the promise of a liquid-phase conduction-
convection contribution to the total CHF, it contains no kL term.
- 22 -
3.1.5 Assessment of the correlations
Three generalized empirical correlations, Eq.(3.2) by Caswell and Balzhiser,
Eq.(3.3) by Kirillov and Eq.(3.5) by Subbotin et al., are plotted in Figs. 3.2,
3.3 and 3.4, along with experimental results on sodium, potassium, and
cesium, for comparison[40]. From the results in Fig. 3.2 through 3.4, we
would judge that Kirillov's equation is somewhat superior to the other two,
and that both it and the equation of Subottin et al. are superior to Caswell
and Balzhiser's. Kirillov's equation has the additional advantage of being
very simple. However, it does not meet the theoretical requirement that the
CHF should approach zero as Pi^Pcr, as do Eq.(3.2) and (3.5), which means
that it is not applicable as the higher values of reduced pressure, but it is
hardly a worry with liquid metals.
We observed that much of the sodium data in Fig. 3.2 falls below the
generalized correlation curves at the lower pressures. This could result from
unstable boiling, which often occurs when sodium boils at the lower
pressures because of the relatively high nucleation superheats required.
Borishansky successfully applied the law of corresponding state to correlate
the effect of pressure on the nucleate-boiling critical heat flux for water and
several organic liquids. He proposed the relation
(3.6)Qc
in which q „. is the value of the CHF at a particular value of the reduced
pressure, which we shall write as PLPCY • Subbotin et al. later applied
Eq.(3.6) to liquid metals with excellent results. Their values of q &. were
arbitrarily taken at a common P*LPCT value of 0.003. Apparently, the value
of this ratio is not critical, but a better correlation will be obtained if it is
chosen well within the PJ Per range of the data to be correlated. Subbotin
et al. found that Na, K, and Cs data obtained with horizontal disk heaters, as
well as the data obtained with a horizontal cylindrical heater, defined a
- 23 -
1Oe
szCM
Z3-•—>
CD
o
10*
Sodium c
-^r-^--~ B
1Q-1
Curve
1234ABC
Type of curve
experimentalexperimentalexperimentalexperimentalgen. emp. Cor.gen. emp. Cor.gen. emp. Cor.
Authors
Subbotin et al.Subbotin et al.Noyes & Lurie
CarbonKirillov
Subbotin et al.
Heating surface
Ni alloyS.S. & MoS.S. &Mo
Mo
Caswell & Balzhiser
10c 102
PL, psia
Fig. 3.2 Comparisons of generalized empirical correlations for sodium
- 24 -
10 -
CD
b
Potassium
B _
• 2•
Curve Type of curve Authors
1 experimental Colver & Balzhiser2 experimental Subbotin et al.A gen. emp. Cor. KirillovB gen. emp. Cor. Subbotin et al.C gen. emp. Cor. Caswell & Balzhiser
. i . i . .
10-1 10c 102
Pi, psia
Fig. 3.3 Comparisons of generalized empirical correlations for potassium
- 25 -
10 -
<M
CD
o:cr 10 -
Cesium
1&A "2
-
•
— - —
Curve
12ABC
— —
Type of curve
experimentalexperimentalgen. emp. Cor.gen. emp. Cor.gen. emp. Cor.
Authors
Subbotin et al.Avksentyuk
KirillovSubbotin et al.Caswell & Balzhiser
. . . i . . .
A
"Bc
10-1 10c
PL, psia
Fig. 3.4 Comparisons of generalized empirical correlations for cesium
- 26 -
common straight line on a log-log plot of qc-f q cr versus PjPcr. The
data points covered the reduced pressure range 5X10"4 to 3xlO~2, and a
straight line drawn through them gave the relation
0.125L » (3.7)
An obvious limitation of this equation is that a dependable values of q „. at
the reference value of the reduced pressure must be available for predicting
Qcr at some other value of the reduced pressure. Otherwise, it is a very
simple and dependable tool. Note that Eq.(3.7) says that the CHF was found
to vary only as the 0.125 power of the boiling pressure, when the data for
the alkali metals were pooled.
3.2 Flooding limited CHF
3.2.1 Criteria for flooding
A number of experiments have been conducted to demonstrate the
existence of such a phenomenon as well as to examine various parametric
dependencies. Except for very short tubes where the pool boiling CHF was
important, the flooding-limited CHF occurred consistently for a vertical tube
with an inlet blockage. The experimental data clearly showed that the total
heat input rather than the local heat flux was the governing parameters, as
expected. The observed CHF values were inversely proportional to L/D.
This indicated that the exit vapor flux was approximately constant at the
point of CHF.
The flooding-limited CHF occurs for a heated vertical channel with a
complete inlet blockage. The critical power to the test section can be
calculated from the standard flooding criterion. The flooding criterion of
Wallis is given by
- 27 -
Jg + Jf =1 (3.8)
where the nondimensional volumetric fluxes are defined by
and
j g = vapor volumetric flux
jf = liquid volumetric flux
pg = saturation vapor density
Ap =density difference(pf-pg)
D = hydraulic diameter
Assuming that the incoming liquid is saturated, the total heat input Q can
be expressed as
Q=Ah/g pgjg
where A and hfg are the flow area and latent heat of vaporization. Then by
using the continuity balance for counter-current flow given by pg jg — p/ j/,
one obtains
Q=
If this criterion is applied to a typical LMR subassembly with a complete
inlet blockage, the counter-current cooling limit is only ~0.18kW/pin or 0.9%
of the normal average power of 20kW/pin. Note that limit does not include
the possible cooling by superheated vapor or by radiation heat transfer; thus,
it is considered to be conservative.
- 28 -
3.2.2 Mishima and Ishii correlation
Mishima and Ishii demonstrated that a similar CHF mechanism occurs in
the absence of a complete inlet blockage[41]. It was observed that CHF at
low mass flow occurred due to a transition from chun to annular flow.
Based on the flow regime transition correlation, the CHF criterion for the
total heat input was given as
Q=A\G/lhi+[-?r-Q.ll)-k/k(pgg4pD)'i\ (3.10)L \ ̂ o I
where Co is the distribution parameter given by
r — 1 9 — 0 '
and G and zJhi are the mass velocity and the inlet subcooling, respectively.
Note that, as low pressures typical of LMR conditions, the second term of
Eq.(3.10) is very close to the flooding-limited criterion by Eq.(3.9). The
difference between these two criteria is basically the heat removal by
subcooling present in the film-flow-limited criterion, Eq.(3.10)
A resonable agreement between Eq.(3.10) and the experimental data for
various conditions is shown in Fig. 3.5. In this figure the non-dimensional
critical heat flux versus f for flooding limited CHF is illustrated. As Block
and Wallis pointed out, the critical heat flux tends to a constant for small
L/D which means that the burnout is limited by wall heat flux. Then it may
be deduced that pool boiling type burnout will occur in very short tubes.
Even at very low flow rates the exit quality implied by the second term
in Eq.(3.10) is generally very small. This means that if sufficient subcooling
exists at the inlet, the main portion of heat removal is due to the subcooling
effect rather than to the latent heat transport. Therefore, for this type of
CHF, the subcooling plays a major role in determining the CHF value.
- 29 -
POOL 6OH.INQ BURNOUT
to•s
•4
t
FLUIO
WATERWATERWATER
ecuecun-HEXAMEETHANOLFREON-113WATERETMANOUn-HEXANEWATER
GEOMETRYANNULUSROUND TUBE
m
-
„ANNULUS
ROUNO TUBE
Iff4 10-
Fig. 3.5 Non-dimensional critical heat flux versus
- 30 -
3.3 Low flow convection CHF
3.3.1 Kottowski correlation
Gorlov, Rzayev, and Khudyakov developed a CHF correlation in terms of
thermal and hydraulic variables for the flow of potassium in tubes.
Kottowski modified this correlation, also taking into account measurements
with sodium as follows[42];
Qc = a- ( L / ^ ) 0 . 8 (1 - 2xd hfg (3.11)
where
hfg = latent heat of evporation
L = heated length of the test section
D = hydraulic diameter
G = mass flux
Xi = inlet vapor quality
Its application to other alkali metals also seems possible. The terms a and
b are determined from a least-squares fitting of the measurements. For tube
geometries, these parameters are a=0.216 and b=0.807. For x\, the negative
value of the relative subcooling enthalpy has to be used.
The most surprising finding is that the CHF is best correlated by the
term (1-2 Zi), and not by the calorimetric term (1- xO- The CHF increases
linearly with the subcooling. However, when normalized by the term (1-2%;),
it becomes independent of the vapor number. Note that, according to
two-phase flow terminology, the term referring to the inlet subcooling is
so-called "vapor number," expressed as
CP'(T,-T,)
The correlation of these terms leads to Eq.(3.11), which accurately
represents the physical terms determining the critical heat flux at forced
- 31 -
2.2
2.0
1.8
1.6
1.4
Meana
oKottowski
1.1580.209
*Katto1.1060.212
1.4 176 T78 T T 5 2 7 2
Measured CHF, MW/m2
Fig. 3.6 Comparison of predicted and measured CHF
(Kottowski correlation)
- 32 -
convection. Its application to tubes bas been validated for the following
range of parameters:
30 < L/D < 125
-0.4 < xi < 0
50 < G < 800 kg/m2s.
3.3.2 Katto correlation
Some experimental data indicating annular flow dryout at low flow rates
were correlated by Katto[43] as follows:
The first term in Eq.C3.il) is associated with the latent heat transport and
the second term with the subcooling effect. On the other hand, the critical
exit quality can be calculated from the energy balance; thus,
0.043
Also, note that Eq.O.ll) is applicable for G>( a pt/Lh)^, since, beyond this
value, the exit quality reaches one and the enthalpy burnout occurs. The
above correlation is compared to the experimental data in Fig. 3.7, and the
agreement is shown to be good.
The applicability of the above CHF criterion is limited to low flow
conditions bounded by
apf ) ^ D/Lh+0.003l
Beyond this limit, a forced convection CHF criterion should be used. This is
given by
- 33 -
-2.0
1.8
14
L2IEO-o i.oCD
-•—»
oCL
Meana
oKottowski
1.1580.209
Katto1.1060.212
' • _ ' • ' • '_ • . ' _ I , I. • . ' r . 11 I .0.4 0̂ 8 0̂ 8 U) K2 1-4
Measured CHF, MW/m2
Fig. 3.7 Comparison of predicted and measured CHF
(Katto correlation)
- 34 -
0-133
When the inequality is applied to typical LMR conditions, the low flow
convection CHF is applicable for G<1900kg/m2s, or, in terms of the inlet
liquid velocity, for Vfi<260cm/s. Therefore, for natural circulation boiling
conditions, it is safe to assume that the forced convection CHF regime given
by Eq.(3.12) will not be encountered for LMR conditions.
3.4 Flow excursion CHF
3.4.1 General consideration
The flow excursion CHF for sodium under LMFBR conditions has been
recognized and studied by Costa[22], Costa and Charlety[23], and Costa and
Menant[24]. In their experiments, the flow excursion was not induced by a
reduction of the pressure head simulating the pump rundown but rather by a
small increase in the power starting from the single-phase region. This
process is very similar to the PNC, Japan, natural circulation CHF tests [25].
From the experiments performed by Costa et al, covering a wide range of
parameters, it has been concluded that the flow excursion is a slow process
lasting for a period of several seconds. Two distinct phases have been
observed. The first phase consists of progressive voiding of the channel
accompanied by a quiet boiling regime. The second phase involves a
chugging flow pattern resulting in local dryout. The relatively slow decrease
of flow during the flow excursion can be directly related to the thermal
inertia of the structural materials and the heated pins.
The flow excursion stability criterion can be obtained from the internal
characteristic and external characteristic. The internal characteristic is the
variations of pressure drop that would be induced by two-phase flow when
the inlet mass flow rate is varied under constant power and constant outlet
pressure. And the external characteristic is the variations of pressure drop
induced by the external circuit when inlet mass flow rate is varied.
- 35 -
According to the Ledinegg criterion, a stable point can be found on the "S"
curve in Fig. 2.3 when the intersection point between internal and external
characteristic has satisfied following condition.
If the above criterion is not satisfied, a two-phase flow instability will
develop and then trigger flow excursion CHF.
3.4.2 CHF prediction and simulation experiments
Several simulation experiments have been examined in terms of the flow
excursion phenomena. The results are illustrated in Fig. 3.8 through Fig.
3.10. For the ORNL test, the experimental CHF occurred at 17W/cm2;
whereas, the predicted flow excursion point is 21W/cm2. Furthermore, the
calculation indicates that the flow excursion leads to enthalpy burnout. In an
actual system a premature excursion cannot be ruled out due to closeness of
the velocity solutions between the stable low quality mode and the unstable
mode. Experimentally, this is confirmed by the existence of considerable flow
oscillations prior to the CHF occurrence. From these considerations, it can be
concluded that CHF occurred as a result of the flow excursion. The
predicted value is reasonably close to the data.
A very similar observation can be made in the case of the LNC LHF123
test shown in Fig. 3.9. The flow excursion CHF of 73.5W/cm2 was predicted
against the experimental data of 62W/cm2. The higher heat flux of this case
compared to the ORNL data is due mainly to the shorter heated length of the
JNC test section.
On the other hand, the prediction for the JNC LHF124 test is quite
different from the abobe two cases. Due to the large inlet flow restriction
used for this test, the system was very stable as shown in Fig. 3.10. Only a
very small unstable regiopn exists. Futhermore, the jump from the low to
- 36 -
the high quality mode is not as dramatic as in the previous cases. At the
first excursion point, the quality increases to only 0.22, which is much lower
than that for the low flow convection CHF. Therefore, continued operation
beyond this excursion point is possible as confirmed by the experiment. The
subsequent CHF due to the low flow convection CHF was predicted at
32W/cm2 ; whereas, the experimental CHF value occurred between 37 and
43W/cm2. Both the predicted CHF value and the predicted mechanism
leading to CHF are very satisfactory.
The ORNL THORS experiment using a 61-pin bundle also showed the
significant effect of the flow excursion on the occurrence of CHF. In this
experiment there is a considerable two-dimensional effect that results in a
delayed timing for CHF. However, when the entire cross section of the
bundle reaches the sodium boiling condition, the inlet flow is significantly
reduced by the flow excursion to the higher quality mode. This generally
leads to the occurrence of the dryout.
- 37 -
100
E 80
I I I I IORNL DATABOILING INITIATION = 13.1 W/cm2
CHF = 17W/cma "
6 X 10r-4
10 15 20 25 30HEAT FLUX, q" (W/cm2)
35 40
Fig. 3.8 Predicted flow characteristics corresponding to ORNL test conditions
- 38 -
100
PNC LHF123BOILING INITIATION = 27 W/cm*CHF«52to64W/cm2
40 60 80 100 120 140 160HEAT FLUX, q"(W/cm2)
Fig. 3.9 Predicted flow characteristics corresponding to JNC LHF123 test
conditions
- 39 -
100
Eu
> •
OOUJ
HUJ_JZ
80
60
40
20
T
PNC LHF124BOILING INITIATION = 6.5 W/cm2
CHF = 37 to 43 W/cm?
- Xe = 3.8 X 10"4
LOW FLOW CONVECTION CHF (32 W/cm2)t I I I I I
0 20 40 60 80 100 120 140 160HEAT FLUX, q" (W/cm2)
Fig. 3.10 Predicted flow characteristics corresponding to JNC LHF124 test
conditions
- 40 -
4. Conclusions
The CHF mechanism of liquid metal is influenced by the coupling of the
heat transfer, vapor generation, and driving head. Because of this coupling
and the existence of hydrodynamic instabilities such as flooding and flow
excursions, several different CHF mechanisms are possible.
Careful examination of relevant experimental data in terms of the
controlling physical mechanisms leading to CHF suggest that the following
four different mechanisms should be considered: pool-boiling CHF, flooding or
film flow limited CHF, low flow convection CHF, and flow excursion CHF.
(1) Pool-boiling CHF
• Condition: low pressure & low flow / boiling from a surface in a
static pool of sodium
• Mechanism'- pool boiling -» burnout —* heated surface is covered by
vapor film —* deterioration in heat transfer
• Model/correlation/criterion
° Noyes correlation
. -0.245L
° Caswell correlation
1' r^+. - / „ „ \ 0.71Qc <-PL 6 ,
A 2 P v k L J L—~ \ P v
° Kirrilov correlation
^ c =3.12x l0 5 ^ 6 (P L /P c ) 1 / 6
° Subbotin empirical correlation
P, ^°-4
- 41 -
(2) Flooding or film flow limited CHF
• Condition: low pressure & low flow / in a vertical system with an
inlet blockage
• Mechanism: stable cooling (counter-current flow) —• liquid film
becomes unstable -» critical vapor flux for the onset of flooding is
exceeded —»• dryout anywhere in heated region
• Model/correlation/criterion
° Mishima & Ishii
2gc= G AA.-+ (-£- -O.l l) • h/e • (Pgg Ap D)
o 4 2
where C o =1.2 -0 .2 ( -^
(3) Low flow convection CHF
• Condition: low pressure & low flow / forced convection
• Mechanism
0 dryout under a slug or vapor clot
° film dryout in annular flow
° near-wall bubble crowding
• Model/correlation/criterion
- Katto
, 0 . 0 4 3 , ,
GW-a,0.4(p,/P/)apf
0.133, . „
otherwise
- 42 -
Kottowski correlation
WJ.807
QC = 0.216
(4) Flow excursion CHF
• Condition: low pressure & low flow
• Mechanism: exceed stability criterion -» flow excursion —» trigger
CHF
• Model/correlation/criterion
° Costa (CEA)
c JNC natural circulation CHF test
j_ =
9 vfi d vfi
- 43 -
Appendix : CHF for Alkali Liquid Metals in Tube
A.1 Critical heat flux for sodium in tubes with L/D=21.55. 43.33. and 30.64Critical heat flux anr=1/7.37xiQ6W/m2
Outlet vapor quality y?= 1/0.5Saturation temperature Ts=1214/1099K
Mass fluxkg/m2s
38.540.047.558.584.083.090.0100.0101.0108.0112.0121.0155.0167.0
Ml-2z,-)
4.134.625.426.849.299.039.429.0311.3511.3511.3511.3513.4213.42
Mass fluxkg/m s
60.061.069.070.0154.0166.0170.0180.0181.0191.0210.0240.0245.0285.0
Qcr{LlD)™Mi-2*,0
7.027.257.487.2214.9614.9614.9614.9613.4215.7415.7417.5515.7418.06
Ref.) A. Kaiser, W. Peppier, and L. Voross, "Type of flow, pressuredrop and critical heat flow of two phase sodium flow," presentedat Liquid Metal Boiling Working Group Mtg., Grenible, France,April 1974.
A.2 Critical heat flux for sodium in a 6-mm tube with L/D=166.6
Mass flux,kg/m2s
401.8352.6287270246
Saturationtemp., K
14531373137313621355
Critical flux,W/m2xi0"6
2.011.851.641.541.38
Inlet vaporquality, %\
0.2030.1700.1840.1800.198
Outlet vaporquality, x 2
0.8250.8830.9790.9770.956
Ref.) H.M. Kottowski, "Sodium Boiling," Nuclea Reactor SafetyHeat transfer, p. 813, O.C. JOENS, ed., HermispherePublishing Corporation (1981)
- 45 -
A.3 Critical heat flux for potassium in a 4-mm tube with L/D=100
Mass flux,kg/m2s
154177177177177190199205205214229232254264276281282286288308320347
Saturationtemp., K
1369141314181419115614261233139214101386118814691134119812391296117414061433143014181419
Critical flux,W/m2xl0"6
0.820.940.930.970.710.880.841.191.271.000.811.211.191.141.241.350.991.591.161.501.691.73
Inlet vaporquality, Xi
0.200.260.240.230.140.130.170.310.330.290.160.370.130.160.180.170.140.260.100.270.260.25
Outlet vapor
quality, X2
0.900.870.880.920.600.850.670.850.910.700.560.860.730.680.720.820.540.950.780.880.940.85
Ref.) I.G. Gorlov, A.I. Rzayev, and V.F. Khudyakov, Sov. Res., 7,4(1975)
- 46 -
A.4 Critical heat flux for potassium in a 4-mm tube with L/D=30
Mass flux,kg/m2s
65.570.570.589.095.095.095.095.095.0102.0115.0118.0130.0141.0141.0141.0153.0
Saturationtemp., K
10321064105110411063106510641058105310431044105710591058105710591062
Critical flux,W/m2xi0~6
0.840.840.781.141.091.241.131.131.141.201.201.381.411.561.541.541.41
Inlet vaporquality, Xi
0.0380.0670.0800.0440.0600.1220.0570.0790.0670.0570.0590.0720.0690.0550.0770.0720.038
Outlet vaporquality, xz
0.710.670.570.720.620.660.640.630.640.630.560.620.570.600.560.570.50
A.5 Critical heat flux for potassium in a 4-mm tube with L/D=50
Mass flux,kg/m2s
79.085.099.0105.0129.0150.0154.0163.0202.0208.0208.0
Saturationtemp., K
10181026101610201018102810261019102810301029
Critical flux,W/m2xi0"6
0.540.670.670.760.820.991.121.241.221.481.37
Inlet vaporquality, x\
0.0750.0860.0610.0740.0610.0590.0610.0740.0570.0580.054
Outlet vapor
quality, x 2
0.670.740.670.730.630.630.630.790.600.630.68
- 47
A.6 Critical heat flux for potassium in a 4-mm tube with L/D=69
Mass flux,kg/m2s
155.6187.0207.5212.0334.0
Saturationtemp., K
10431043102510481081
Critical flux,W/m2xKT6
1.011.261.281.461.69
Inlet vaporquality, x\
0.1450.0830.0720.1740.084
Outlet vaporquality, x 2
0.670.780.710.680.52
A.7 Critical heat flux for potassium in a 4-mm tube with L/D=80
Mass flux,kg/m2s
75.575.575.5100.0100.0132.0132.0151.0151.0151.0
Saturationtemp., K
873985102410051037903869904874995
Critical flux,W/m2xl0"6
0.390.340.330.500.500.580.560.710.740.71
Inlet vaporquality, X\
0.0470.1060.1010.0840.0930.0460.0270.0440.0340.076
Outlet vaporquality, %2
0.780.760.730.640.650.760.760.700.740.69
- 48 -
A.8 Critical heat flux for potassium in a 4-mm tube with LYD=82
Mass flux,kg/m2s
22.322.322.334.244.644.666.966.967.067.067.067.067.067.067.067.068.468.468.468.468.468.468.468.468.4325.0
Saturationtemp., K
853853101910238751022113284710261099113710998581174861110281881891095398510761182121010251025
Critical flux,W/m2xi0~6
0.150.150.170.220.270.250.410.420.380.430.440.370.360.450.370.320.350.330.350.370.300.350.430.410.341.20
Inlet vaporquality, Xi
0.0190.0270.0980.1120.0200.0470.0700.0870.1160.1500.1800.1500.0100.1800.4400.0010.1190.1120.1090.1110.1110.1130.1120.1120.1120.110
Outlet vaporquality, X2
1.001.020.990.970.890.790.850.860.730.840.810.780.670.920.770.700.690.690.740.780.640.781.000.920.730.53
- 49 -
A.9 Critical heat flux for potassium in a 4-mm tube with L/D=100
Mass flux,kg/m2s
68.0101.0115.0128.0129.0130.0130.0130.0131.0133.0169.0169.0197.0204.0236.0236.0270.0
Saturationtemp., K
104310011044880109396292393790310561042104110441015101410491043
Critical flux,W/m2xi0~6
0.270.410.430.580.450.540.500.510.530.540.600.670.790.780.830.951.03
Inlet vaporquality, Xi
0.0730.0480.0550.0710.1240.0740.0540.0520.0450.0680.0580.0580.0690.0290.0800.0680.069
Outlet vaporquality, X2
0.780.730.680.770.610.730.670.700.730.710.640.710.690.730.570.680.67
A. 10 Critical heat flux for Dotassium in a 6-mm tube with L/D=46.6
Mass flux,kg/m2s
38.638.738.839.063.968.268.668.768.7102.2106.3106.3130.0135.3135.5136.2136.2194.5
Saturationtemp., K
103110431028104110431043104310431043107310431043104310911063104310431123
Critical flux,W/m 2xl0" 6
0.470.450.460.420.670.700.730.670.640.970.790.891.071.041.010.970.891.43
Inlet vaporquality, Xi
0.1920.1480.1680.1390.1340.1870.1530.0940.1100.0970.0720.0480.1660.0910.1460.1160.0750.118
Outlet vaporquality, X2
0.940.960.950.880.870.780.880.810.790.820.640.720.600.670.590.550.540.61
- 50 -
A. 11 Critical heat flux for potassium in a 6-mm tube with L7D=48
Mass flux,kg/m2s
40.540.580.380.380.3119.3119.3120.3
Saturationtemp., K
12011202120312021042120712031042
Critical flux,W/m2xi0"6
0.350.350.710.660.701.131.101.09
Inlet vaporquality, %\
0.0430.1100.1390.0280.0600.0250.0220.044
Outlet vaporquality, X2
0.820.890.900.870.790.930.910.86
A.12 Critical heat flux for potassium in a 6-mm tube with L/D=10Q
Mass flux,kg/m2s
110.7166.0253.0
Saturationtemp., K
104110551050
Critical flux,W/m2xi0"6
0.410.720.77
Inlet vaporquality, x\
0.0350.0450.053
Outlet vaporquality, X2
0.620.730.46
A.5-A.11 :Ref.) I.I. Aladyev, et al., "The effect of a unform axial heat flux
distribution on critical heat flux with potassium in tubes,"presented at 4th Int. Heat Transfer Conf., Paris, France,Aug. 31 - Sep. 5, 1970
- 51 -
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(1977).
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and Low Flow Conditions," Nucl. Sci. and Eng., 84, pp. 131-146 (1983).
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BIBLIOGRAPHIC INFORMATION SHEET
Performing Org.
Report No.
Sponsoring Org.
Report No.Stamdard Report No. INIS Subject Code
KAERI/AR-553/99
Title / Subtitle
Review of the critical heat flux correlations for liquid metals
Main Author LEE, YONG-BUM (KALIMER Technology development)
Researcher andDepartment
H.D Hahn (KALIMER Technology development)
W.P. Chang (KALIMER Technology development)Y.M. Kwon (KALIMER Technology development)
Publication
PlaceTaejon Publisher KAERI
Publication
Date1999. 9
Page 56 p. 111. & Tab. Yes( O ), No ( ) Size 29.7 Cm.
Note
Classified Open( O ), Restricted ),
Class DocumentReport Type State-of-the-Art Report
Sponsoring Org. Contract No.
Abstract (15-20 Lines)
The CHF phenomenon in the two-phase convective flows has been an important issuein the fields of design and safety analysis of light water reactor(LWR) as well as sodiumcooled liquid metal reactor(LMR). Especially in the LWR application, many physicalaspects of the CHF phenomenon are understood and reliable correlations and mechanisticmodels to predict the CHF condition have been proposed over the past three decades.
Most of the existing CHF correlations have been developed for light water reactor coreapplications. Compared with water, liquid metals show a divergent picture of boilingpattern. This can be attributed to the consequence that special CHF conditions obtainedfrom investigations with water cannot be applied to liquid metals. Numerous liquid metalboiling heat transfer and two-phase flow studies have put emphasis on development ofmodels and understanding of the mechanism for improving the CHF predictions. Thusfar, no overall analytical solution method has been obtained and the reliable predictionmethod has remained empirical.
The principal objectives of the present report are to review the state of the art inconnection with liquid metal critical heat flux under low pressure and low flow conditionsand to discuss the basic mechanisms.
Subject Keywords(About 10 words) liquid metal, sodium CHF, critical heat flux