Kaerl/AR-553/99 Review of the Critical Heat Flux Correlations For

KR0000232 KAERl/AR-553/99

Review of the Critical Heat Flux Correlations for Liquid Metals

31/ 40 Please be aware that all of the Missing Pages in this document were originally blank pages 1999. 10.

s] - iii - Summary

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.

_ 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 - Surface Heat Flux

CHF

Minimum Heat Flux

Surface Temperature AB Single-phase forced convection to liquid BD Nucleate boiling or forced convective evaporation DE Transition boiling EG Film boiling

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.

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 - -'."

(A) (B) (C)

Mass flux, G

Onset of annular flow

(A)

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 Interal characteristic

Pressure head

. Working I point I I

\ R T 1 LOW j All quality I i quality J liqui

Fig. 2.3 Flow excursion and flow versus pressure drop stability 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 - CHF

P, D, A^ = const. •-Ah;

CHF CHF

j /

P, G, L,, = const. 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.

2 where gc is critical heat flux, Btu/ft hr

A is latent heat of vaporization, Btu/lbm 3 pv is density of saturated vapor, lbm/ft

3 pL is density of saturated liquid, lbm/ft g is acceleration due to gravitational field, ft/hr2 2 gc is conversion factor, 4.170x108 lbmft/lbfhr a is surface tension, lbt/ft PrL is Prandtl number of liquid CPL^IAL 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.

5 Vi Qc= 4X10 + 0.16 A (gc g a pL p\) (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.

ih r 1.18i(rf (3.2) A 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.

5 6 m

- 20 - 10 ; . i

10 -5 r

Symbol ^gj Investigators

• K Colver & Balzhiser A Na Noyes & Lurie x Na Carbon • Na Caswell & Balzhiser o Rb Caswell & Balzhiser 10-7 I I 10J 107 PL~ PI

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 - c Sodium 1Oe -^r-^--~ B

sz CM

Z3 -•—> CD o 10* Curve Type of curve Authors Heating surface 1 experimental Subbotin et al. Ni alloy 2 experimental Subbotin et al. S.S. & Mo 3 experimental Noyes & Lurie S.S. &Mo 4 experimental Carbon Mo A gen. emp. Cor. Kirillov B gen. emp. Cor. Subbotin et al. C gen. emp. Cor. Caswell & Balzhiser

1Q-1 10c 102 PL, psia

Fig. 3.2 Comparisons of generalized empirical correlations for sodium

- 24 - Potassium 10 -

B _

CD b Curve Type of curve Authors • 1 experimental Colver & Balzhiser • 2 2 experimental Subbotin et al. A gen. emp. Cor. Kirillov B 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 - Cesium 10 - A "B

o :cr 10 - Curve Type of curve Authors 1 experimental Subbotin et al. 2 experimental Avksentyuk A gen. emp. Cor. Kirillov

• B gen. emp. Cor. Subbotin et al. C gen. emp. Cor. Caswell & Balzhiser

. . . i . . . 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

0.125 L » (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

jg = 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

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

i Q=A\G/lhi+[-?r-Q.ll)-k/k(pgg4pD)' \ (3.10) L \ ^o I

where Co is the distribution parameter given by

r —19—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

FLUIO GEOMETRY t WATER ANNULUS o WATER ROUND TUBE • WATER m s ecu ecu n-HEXAME - ETHANOL „ • FREON-113 4 WATER ANNULUS ETMANOU t n-HEXANE WATER 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 o * Kottowski Katto 1.8 Mean 1.158 1.106 a 0.209 0.212 1.6

1.4

1.4 176 T78 TT5272 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 o Kottowski Katto 1.8 Mean 1.158 1.106 a 0.209 0.212

L2 IE O -o i.o CD -•—» o CL

' • _ ' • ' • '_ • .'_ I , I. • . ' r . 11 I . 0.4 0^8 0^8 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 I I I I I ORNL DATA 2 E 80 BOILING INITIATION = 13.1 W/cm CHF = 17W/cma "

6 X 10r-4

10 15 20 25 30 35 40 HEAT FLUX, q" (W/cm2)

Fig. 3.8 Predicted flow characteristics corresponding to ORNL test conditions

- 38 - 100 PNC LHF123 BOILING INITIATION = 27 W/cm* CHF«52to64W/cm2

40 60 80 100 120 140 160 HEAT FLUX, q"(W/cm2)

Fig. 3.9 Predicted flow characteristics corresponding to JNC LHF123 test conditions

- 39 - 100 T

E 80 PNC LHF124 u BOILING INITIATION = 6.5 W/cm2 ?

>• CHF = 37 to 43 W/cm 60 O O UJ 40

H UJ 4 _J 20 - Xe = 3.8 X 10" Z LOW FLOW CONVECTION CHF (32 W/cm2) t I I I I I 0 20 40 60 80 100 120 140 160 HEAT FLUX, q" (W/cm2)

Fig. 3.10 Predicted flow characteristics corresponding to JNC LHF124 test conditions

- 40 - 4. Conclusions

(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

. -0.245 L

° Caswell correlation

1' r^+. - / „ „ \ 0.71 Qc <-PL 6 , 2 L A PvkLJ —~ \ Pv

° Kirrilov correlation

5 6 1/6 ^c=3.12xl0 ^ (PL/Pc)

° 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

2 gc= G AA.-+ (-£- -O.ll) • h/e • (Pgg Ap D)

o 4 2 where Co=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

,0.043, ,

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 30.64 Critical heat flux anr=1/7.37xiQ6W/m2 Outlet vapor quality y?= 1/0.5

Saturation temperature Ts=1214/1099K

Mass flux Mass flux Qcr{LlD)™ kg/m2s Ml-2z,-) kg/m s Mi-2*,0 38.5 4.13 60.0 7.02 40.0 4.62 61.0 7.25 47.5 5.42 69.0 7.48 58.5 6.84 70.0 7.22 84.0 9.29 154.0 14.96 83.0 9.03 166.0 14.96 90.0 9.42 170.0 14.96 100.0 9.03 180.0 14.96 101.0 11.35 181.0 13.42 108.0 11.35 191.0 15.74 112.0 11.35 210.0 15.74 121.0 11.35 240.0 17.55 155.0 13.42 245.0 15.74 167.0 13.42 285.0 18.06 Ref.) A. Kaiser, W. Peppier, and L. Voross, "Type of flow, pressure drop and critical heat flow of two phase sodium flow," presented at 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, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xi0"6 quality, %\ quality, x 2 401.8 1453 2.01 0.203 0.825 352.6 1373 1.85 0.170 0.883 287 1373 1.64 0.184 0.979 270 1362 1.54 0.180 0.977 246 1355 1.38 0.198 0.956 Ref.) H.M. Kottowski, "Sodium Boiling," Nuclea Reactor Safety Heat transfer, p. 813, O.C. JOENS, ed., Hermisphere Publishing Corporation (1981)

- 45 - A.3 Critical heat flux for potassium in a 4-mm tube with L/D=100

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xl0"6 quality, Xi quality, X2

154 1369 0.82 0.20 0.90 177 1413 0.94 0.26 0.87 177 1418 0.93 0.24 0.88 177 1419 0.97 0.23 0.92 177 1156 0.71 0.14 0.60 190 1426 0.88 0.13 0.85 199 1233 0.84 0.17 0.67 205 1392 1.19 0.31 0.85 205 1410 1.27 0.33 0.91 214 1386 1.00 0.29 0.70 229 1188 0.81 0.16 0.56 232 1469 1.21 0.37 0.86 254 1134 1.19 0.13 0.73 264 1198 1.14 0.16 0.68 276 1239 1.24 0.18 0.72 281 1296 1.35 0.17 0.82 282 1174 0.99 0.14 0.54 286 1406 1.59 0.26 0.95 288 1433 1.16 0.10 0.78 308 1430 1.50 0.27 0.88 320 1418 1.69 0.26 0.94 347 1419 1.73 0.25 0.85 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, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xi0~6 quality, Xi quality, xz 65.5 1032 0.84 0.038 0.71 70.5 1064 0.84 0.067 0.67 70.5 1051 0.78 0.080 0.57 89.0 1041 1.14 0.044 0.72 95.0 1063 1.09 0.060 0.62 95.0 1065 1.24 0.122 0.66 95.0 1064 1.13 0.057 0.64 95.0 1058 1.13 0.079 0.63 95.0 1053 1.14 0.067 0.64 102.0 1043 1.20 0.057 0.63 115.0 1044 1.20 0.059 0.56 118.0 1057 1.38 0.072 0.62 130.0 1059 1.41 0.069 0.57 141.0 1058 1.56 0.055 0.60 141.0 1057 1.54 0.077 0.56 141.0 1059 1.54 0.072 0.57 153.0 1062 1.41 0.038 0.50

A.5 Critical heat flux for potassium in a 4-mm tube with L/D=50

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor 2 2 6 kg/m s temp., K W/m xi0" quality, x\ quality, x 2 79.0 1018 0.54 0.075 0.67 85.0 1026 0.67 0.086 0.74 99.0 1016 0.67 0.061 0.67 105.0 1020 0.76 0.074 0.73 129.0 1018 0.82 0.061 0.63 150.0 1028 0.99 0.059 0.63 154.0 1026 1.12 0.061 0.63 163.0 1019 1.24 0.074 0.79 202.0 1028 1.22 0.057 0.60 208.0 1030 1.48 0.058 0.63 208.0 1029 1.37 0.054 0.68

- 47 A.6 Critical heat flux for potassium in a 4-mm tube with L/D=69

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xKT6 quality, x\ quality, x 2 155.6 1043 1.01 0.145 0.67 187.0 1043 1.26 0.083 0.78 207.5 1025 1.28 0.072 0.71 212.0 1048 1.46 0.174 0.68 334.0 1081 1.69 0.084 0.52

A.7 Critical heat flux for potassium in a 4-mm tube with L/D=80

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xl0"6 quality, X\ quality, %2 75.5 873 0.39 0.047 0.78 75.5 985 0.34 0.106 0.76 75.5 1024 0.33 0.101 0.73 100.0 1005 0.50 0.084 0.64 100.0 1037 0.50 0.093 0.65 132.0 903 0.58 0.046 0.76 132.0 869 0.56 0.027 0.76 151.0 904 0.71 0.044 0.70 151.0 874 0.74 0.034 0.74 151.0 995 0.71 0.076 0.69

- 48 - A.8 Critical heat flux for potassium in a 4-mm tube with LYD=82

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xi0~6 quality, Xi quality, X2 22.3 853 0.15 0.019 1.00 22.3 853 0.15 0.027 1.02 22.3 1019 0.17 0.098 0.99 34.2 1023 0.22 0.112 0.97 44.6 875 0.27 0.020 0.89 44.6 1022 0.25 0.047 0.79 66.9 1132 0.41 0.070 0.85 66.9 847 0.42 0.087 0.86 67.0 1026 0.38 0.116 0.73 67.0 1099 0.43 0.150 0.84 67.0 1137 0.44 0.180 0.81 67.0 1099 0.37 0.150 0.78 67.0 858 0.36 0.010 0.67 67.0 1174 0.45 0.180 0.92 67.0 861 0.37 0.440 0.77 67.0 1102 0.32 0.001 0.70 68.4 818 0.35 0.119 0.69 68.4 818 0.33 0.112 0.69 68.4 910 0.35 0.109 0.74 68.4 953 0.37 0.111 0.78 68.4 985 0.30 0.111 0.64 68.4 1076 0.35 0.113 0.78 68.4 1182 0.43 0.112 1.00 68.4 1210 0.41 0.112 0.92 68.4 1025 0.34 0.112 0.73 325.0 1025 1.20 0.110 0.53

- 49 - A.9 Critical heat flux for potassium in a 4-mm tube with L/D=100

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor 2 6 kg/m2s temp., K W/m xi0~ quality, Xi quality, X2 68.0 1043 0.27 0.073 0.78 101.0 1001 0.41 0.048 0.73 115.0 1044 0.43 0.055 0.68 128.0 880 0.58 0.071 0.77 129.0 1093 0.45 0.124 0.61 130.0 962 0.54 0.074 0.73 130.0 923 0.50 0.054 0.67 130.0 937 0.51 0.052 0.70 131.0 903 0.53 0.045 0.73 133.0 1056 0.54 0.068 0.71 169.0 1042 0.60 0.058 0.64 169.0 1041 0.67 0.058 0.71 197.0 1044 0.79 0.069 0.69 204.0 1015 0.78 0.029 0.73 236.0 1014 0.83 0.080 0.57 236.0 1049 0.95 0.068 0.68 270.0 1043 1.03 0.069 0.67

A. 10 Critical heat flux for Dotassium in a 6-mm tube with L/D=46.6

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xl0"6 quality, Xi quality, X2 38.6 1031 0.47 0.192 0.94 38.7 1043 0.45 0.148 0.96 38.8 1028 0.46 0.168 0.95 39.0 1041 0.42 0.139 0.88 63.9 1043 0.67 0.134 0.87 68.2 1043 0.70 0.187 0.78 68.6 1043 0.73 0.153 0.88 68.7 1043 0.67 0.094 0.81 68.7 1043 0.64 0.110 0.79 102.2 1073 0.97 0.097 0.82 106.3 1043 0.79 0.072 0.64 106.3 1043 0.89 0.048 0.72 130.0 1043 1.07 0.166 0.60 135.3 1091 1.04 0.091 0.67 135.5 1063 1.01 0.146 0.59 136.2 1043 0.97 0.116 0.55 136.2 1043 0.89 0.075 0.54 194.5 1123 1.43 0.118 0.61

- 50 - A. 11 Critical heat flux for potassium in a 6-mm tube with L7D=48

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xi0"6 quality, %\ quality, X2 40.5 1201 0.35 0.043 0.82 40.5 1202 0.35 0.110 0.89 80.3 1203 0.71 0.139 0.90 80.3 1202 0.66 0.028 0.87 80.3 1042 0.70 0.060 0.79 119.3 1207 1.13 0.025 0.93 119.3 1203 1.10 0.022 0.91 120.3 1042 1.09 0.044 0.86

A.12 Critical heat flux for potassium in a 6-mm tube with L/D=10Q

Mass flux, Saturation Critical flux, Inlet vapor Outlet vapor kg/m2s temp., K W/m2xi0"6 quality, x\ quality, X2 110.7 1041 0.41 0.035 0.62 166.0 1055 0.72 0.045 0.73 253.0 1050 0.77 0.053 0.46

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

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- 56 - BIBLIOGRAPHIC INFORMATION SHEET

Performing Org. Sponsoring Org. Stamdard Report No. INIS Subject Code Report No. Report No. 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 and H.D Hahn (KALIMER Technology development) Department W.P. Chang (KALIMER Technology development) Y.M. Kwon (KALIMER Technology development) Publication Publication Taejon Publisher KAERI 1999. 9 Place Date

Page 56 p. 111. & Tab. Yes( O ), No ( ) Size 29.7 Cm.

Note

Classified Open( O ), Restricted ), Report Type State-of-the-Art Report Class Document

Sponsoring Org. Contract No.

Abstract (15-20 Lines)

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.

Subject Keywords (About 10 words) liquid metal, sodium CHF, critical heat flux IMS

KAERI/AR-553/99

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1999. 9

°\ 56 p. O 3. 71 29.7 Cm.

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