kaerl/ar-553/99 review of the critical heat flux

KR0000232

KAERl/AR-553/99

Review of the Critical Heat Flux Correlationsfor Liquid Metals

*

3 1 / 40

Please be aware that all of the Missing Pages in this document wereoriginally blank pages

1999. 10.

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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


potassium 25


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


(Katto correlation) 34

Fig. 3.8 Predicted flow characteristics corresponding to

ORNL test conditions 38


JNC LHF123 test conditions 39


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,

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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

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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.

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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


(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


(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


° 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


- 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


° 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 -


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


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


Mass flux,kg/m2s

79.085.099.0105.0129.0150.0154.0163.0202.0208.0208.0

Saturationtemp., K

10181026101610201018102810261019102810301029


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


Mass flux,kg/m2s

155.6187.0207.5212.0334.0

Saturationtemp., K

10431043102510481081

Critical flux,W/m2xKT6

1.011.261.281.461.69


0.1450.0830.0720.1740.084

Outlet vaporquality, x 2

0.670.780.710.680.52


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


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


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 -


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


0.270.410.430.580.450.540.500.510.530.540.600.670.790.780.830.951.03


0.0730.0480.0550.0710.1240.0740.0540.0520.0450.0680.0580.0580.0690.0290.0800.0680.069


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


0.1920.1480.1680.1390.1340.1870.1530.0940.1100.0970.0720.0480.1660.0910.1460.1160.0750.118


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


0.350.350.710.660.701.131.101.09

Inlet vaporquality, %\

0.0430.1100.1390.0280.0600.0250.0220.044


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


0.410.720.77


0.0350.0450.053


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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3. Y.Y. Hsu and R.W. Graham, Transport process in boiling and two-phase

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4. G.F. Hewitt, Burnout in: Handbook of multiphase systems, G. Hetsroni,

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11. V. Marinelli, "Critical heat flux: A review of recent publication," Nucl.

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13. M.A. Styrikovich, E.I. Nevstruera, and G.M. Dvorina, "The effect of

- 53 -

two-phase flow pattern on the nature of heat transfer crisis in boiling,"

Proc. 4th Int. Heat Transfer Conf., Paris (1970).

14. J. Weisman and B.S. Pei, "Prediction of critical heat flux in flow boiling

at low qualities," Int. J. Heat Mass Transfer 26, pp. 1463-1477 (1983).

15. J. Weisman and S.H. Ying, "Theoretically based CHF prediction at low

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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

IMS

KAERI/AR-553/99

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=?• (KALIMER

(KALIMER

(KALIMER

1999. 9

°\ 56 p. O 3. 71 29.7 Cm.

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kaerl/ar-553/99 review of the critical heat flux

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