- Email: [email protected]
The top-down reflooding model in the CATHARE code
Nuclear Engineenng ELSEVIER
Nuclear Engineering and Design 149 (1994) 141 152
The top-down reflooding model in the
CATHARE
and Design
code
J. Bartak, D. Bestion, T. Haapalehto * Centre d'Etudes Nucldaires de Grenoble, S T R / L M L , 17 Rue des Martyrs, F-38054 Grenoble Cedex 9, France
Abstract
A top-down reflooding model was developed for the French best-estimate thermal hydraulic code CATHARE. The paper presents the current state of development of this model. Based on a literature survey and on compatibility considerations with respect to the existing CATHARE bottom reflooding package, a falling film top-down reflooding model was developed and implemented into CATHARE version 1.3U. Following a brief review of previous work, the paper describes the most important features of the model. The model was validated with the Winfrith single-tube top-down reflooding experiment and with the REWET-II simultaneous bottom and top-down reflooding experiment in a rod bundle geometry. The results demonstrate the ability of the new package to describe the falling film rewetting phenomena and the main parametric trends both in a simple analytical experimental set-up and in a much more complex rod bundle reflooding experiment.
1. Introduction
Reflooding of a heated core is a complex phenomenon generally encountered in a large-break loss-of-coolant accident (LOCA) scenario some time after the accumulator injection. There is a significant energy release from the hot wall. As a consequence, a large variation in the thermal hydraulic conditions of the flow occurs in the immediate vicinity of the quench front, on a scale which is usually much smaller than the characteristic scale of the calculation scheme used in the two-fluid model. In the French best-estimate code CATHARE a special model was developed to represent this * Present address: Department of Energy Technology, Lappeenranta University of Technology, PO Box 20, SF-53851 Lappeenranta, Finland.
situation (Housiadas, 1987). It is a two-dimensional heat conduction model solved on a local fine mesh moving along the wall with the quench front velocity. An important restriction on the use of this model is the fact that it was developed only for b o t t o m reflood and cannot be used for topdown rewetting. There are two basic reasons for this restriction. Firstly, the possibility to have a unique quench front moving from the bottom to the top of an axial element was intrinsically embedded into the computational and decision-making logic of CATIJARE as well as into the language structure used to specify the input data. Secondly, the specific physical models employed in the quench front region and downstream of it use correlations developed on the basis of data derived exclusively from forced flow bottom reflood experiments in tubes and rod bundles. To remove the restriction, a top-down reflooding
0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSD1 0029-5493(94)00682-0
142
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
model was developed and implemented into the CATHARE code. The objective of this paper is to describe the basic physical features of the model and to present the results of the first validation calculations. A more complete assessment programme for the top-down reflooding model is currently in progress. Quenching of a hot surface is the transition from a regime in which heat transfer takes place predominantly to vapour, to a regime in which liquid is in direct contact with a large fraction of the wall. In top-down rewetting a liquid film flows down along the wall. With decreasing distance from the quench front the wall-to-film heat transfer develops from convective cooling to subcooled boiling, nucleate boiling and very violent nucleate and/or transition boiling at the quench front. At the quench front the liquid is violently sputtered off the wall and a spray of droplets is ejected into the vapour field. The droplets bounce against the pipe walls or adjacent rods and may contribute significantly to the heat transfer downstream of the quench front. The large amount of vapour generated in the quench front region has a tendency to rise, exposing the liquid film to a countercurrent flow situation. The film hydrodynamics are thus affected, the film is retarded and may eventually stop or even start to climb (flooding). This is further accentuated if there is vapour upflow from the bottom of the pipe or rod bundle, as is the case e.g. in combined reflooding. On the other hand, the generated vapour can condense on the surface of the film in the case of subcooled reflooding. Another problem encountered in top-down rewetting is that, except for very low liquid flows, there is always some liquid fallover, i.e. only a part of the total liquid flow contributes to the film flow. The liquid falling over improves the heat transfer in the dry region, causing additional precooling.
2. Review of previous work A large amount of work has been carried out world wide on the investigation of the reflooding phenomena and top-down reflooding in particular, both in the experimental and theoretical fields.
Review papers by Butterworth and Owen (1975), Sawan and Carbon (1975), Elias and Yadigaroglu (1978), Carbajo and Siegel (1980) and Collier (1982) summarize this work and the knowledge acquired and provide references to most of the original contributions. More recent theoretical works were mainly refinements and enhancements of the existing models; recent experimental studies were devoted to the influence of special effects such as countercurrent flow conditions (Duffey, 1978). A variety of methods have been proposed for the solution of the conduction equation for a wall in reflooding conditions. Several basic assumptions are common to almost all of them. By invoking commonly used simplifications, the theoretical models have served as an important tool for understanding the basic mechanisms, the influencing variables and the main parametric trends in the rewetting of a hot surface. For the same reasons they are not very well fitted for use for realistic (best-estimate) calculations in which various interacting phenomena are present and which render the generally accepted assumptions inapplicable. The common feature of most of the theoretical models is the necessity to specify the heat transfer coefficients in the wet and dry regions and the rewetting temperature as boundary conditions. Important differences in the values of these parameters exist between the models in order to obtain reasonable agreement with experimental data. This, together with different simplifying assumptions, makes the use of analytical models in best-estimate codes difficult to justify. The large amount of experimental work on top-down reflooding will be summarized briefly by analysing the major effects influencing the rewetting phenomenon.
2. I. Effect of initial wall temperature All the experiments document a decrease in the rewetting velocity with an increase in the initial wall temperature (Yamanouchi, 1968; Elliott, 1970, 1971; Duffey, 1973; Butterworth, 1975; Ueda, 1983). The inverse rewetting velocity increases almost linearly with increasing wall temperature.
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141-152
2.2. Effect of pressure The quench front velocity increases with increasing pressure, though the exact functional dependence may be rather complex (Elliott, 1970, 1971; Butterworth, 1975). It is given by the improved heat transfer to the fluid (both in the wet and dry regions) and depends on the wall material, wall thickness and other factors.
2.3. Effect of reflooding flow rate and liquid subcooling These effects are quite complicated and ambiguous. Some experimental data exhibit a flow rate dependence while others do not. Bennett et al. (1966), Elliott and Rose (1970, 1971) and Ueda et al. (1983) conclude from their data that there is no flow rate effect, whereas Yamanouchi (1968), Duffey and Porthouse (1973) and Piggott and Duffey (1975) observed an increase in the rewetting rate with increased liquid flow rate. The flow rate effect is obviously linked with the liquid subcooling at the quench front. For a given subcooling at the injection point the subcooling at the quench front level should remain higher for higher flow rates. The data of Yoshioka and Hasegawa (1970) and Piggott and Duffey (1975) show a significant increase in quench front velocity with increased subcooling. Another possible effect of high liquid flow rates is a higher liquid fallover to the region below the quench front, causing higher precursory cooling and increasing the quench front velocity.
143
the material heat conductivity is twofold in this case. Increasing the heat conductivity in the axial direction increases the quench front velocity, whereas decreasing the heat conductivity in the radial direction also increases the quench front velocity. Thus a rod with a gap will quench faster than a rod without a gap, and a hollow rod will quench faster than a rod filled with a filler. This was clearly shown in the tests by Piggott and Duffey (1975), in the tests on the REWET-II facility (Kervinen, 1989) and on the LOFT test support facility (Birchley, 1991). This behaviour is well predicted by the numerical 2-D conduction model used in CATHARE. The wall thickness influences only the conduction pattern in the wall. The decrease in the quench front velocity with the square root of the wall thickness predicted by the analytical models e.g. (Yamanouchi, 1968; Yoshioka, 1970) should thus be a good approximation of this effect.
2.5. Effect of countercurrent flow Duffey et al. (1978) performed an experimental and theoretical investigation of falling film rewetting in the presence of countercurrent flow. A single heated rod was placed in a tube. The falling film quench rate was significantly retarded by an air, steam or two-phase upflow, even before the point of flow reversal (flooding). Effects of surface roughness and deposits and effects of irradiation of fuel pins are not discussed here since they are not taken into account in current models, though they can be quite important in practice.
2.4. Effect of wall material and wall thickness In the case of reflooding of a single material wall the experimental results for various materials confirm the theoretical predictions. The quench front velocity is proportional to the parameter 2 ~/~-/pc(Yamanouchi, 1968; Yoshioka, 1970). This gives a quench speed of zircaloy about two times higher than that of stainless steel. This was shown e.g. in the tests performed by Elliott and Rose (1970) and Piggott and Duffey (1975). However, the situation becomes more complex in the case of a rod with a filler and/or a gap. The influence of
3. The CATHARE top-down reflooding model
3. I. General description The CATHARE top-down reflooding model assumes a wetted wall with a descending liquid film upstream of the quench front, a steep wall temperature gradient in the quench front region and a hot dry wall downstream of the quench front. The two-dimensional transient heat conduction problem in a multilayer wall is solved numerically. A
144
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
fine 2-D mesh is moving along the wall with the quench front velocity. This mesh movement introduces a convective term into the heat conduction equation. Together with the boundary conditions and an additional condition at the quench front, the discretized equations are solved for the temperature field in the fine mesh and the quench front velocity (Housiadas, 1987). The condition at the quench front imposes the wall temperature to be equal to the local burn-out temperature. The total length of the fine mesh region is typically around 8 cm and contains about 30 axial meshes. The size of these meshes varies from about 5 x 10-Sm at the quench front to 5 x 10 3m at the extremities. The boundary conditions necessary to perform a heat conduction calculation within the fine mesh are the following: zero radial heat flux on the rod axis or on the outer surface of a tube; wall-to-fluid heat transfer correlations on the wall facing the fluid; zero axial conduction heat flux on the horizontal boundary within the wetted region; a temperature boundary condition on the horizontal boundary within the dry region. The solution method is the N e w t o n - R a p h s o n iteration with a direct solver of the linearized equations. As a result of this solution procedure, the temperature field within the fine mesh region and the quench front velocity are obtained. The convergence criteria used are 1 0 - 4 m s -1 for the quench front velocity and 0.1°C for the temperatures.
3.2. Thermal hydraulics in the vicinity of the top-down quench front The following heat transfer mechanisms in the quench front region are taken into account: nucleate boiling in the descending film upstream of the quench front; critical heat flux at the quench front; transition boiling immediately downstream of the quench front; heat transfer to droplets sputtered off the film in the quench front region; dispersed flow film boiling further downstream of the quench front.
3.2. I. Region upstream of the quench front In this region Thorn et al.'s (1966) correlation is used to calculate the nucleate boiling heat trans-
fer. The critical heat flux (CHF) is calculated with Zuber et al.'s (1963) C H F correlation with the Ivey and Morris (1962) correction for subcooling. The equality of these two heat fluxes at the C H F point provides the condition for the burn-out temperature which is used as the imposed wall temperature at the quench front. Since the CATHARE code uses only one liquid field, it is impossible to distinguish between the liquid present in the film and in the gas core. The top-down reflooding model assumes that there is always a liquid film on the wall in the wet region. This film is entirely vaporized at the quench front. The amount of liquid which was not vaporized and passes the quench front defines the total liquid fallover. This liquid is assumed to be in the form of droplets which are treated with standard CATnARE wall and interface heat transfer and interfacial shear correlations used in dispersed flow. In the case of countercurrent flow the droplets sputtered off the film can be entrained by the vapour flow and the film itself can be retarded, stopped or forced to move upwards (CCFL). The model is unable to take these effects into account on a phenomenological basis. Instead, a local CCFL criterion of the Wallis (1969) type is applied at the quench front. If the rising vapour velocity exceeds the value of the critical velocity given by this criterion, the top-down quench front is stopped and cannot proceed any further until the vapour velocity decreases again below the critical value.
3.2.2. Region immediately downstream of the quench front This region is the most difficult to describe. It is the region of violent boiling and disintegration of the liquid film with the formation of a jet of droplets of various sizes sputtered off the liquid film. Owing to the steep temperature gradients in the wall, a complete change in the boiling mechanism from nucleate boiling to dispersed flow film boiling occurs within no more than a few centimetres along the wall. The transition boiling region is the least understood part of the boiling curve owing to its inherently unstable nature (negative slope of the boiling curve) and extremely difficult experimental realization. Recent developments in
J. Bartak et al. / Nuclear Engineering and Design 149 0994) 141-152
this field are discussed by Auracher (1990a,b). The heat flux in the transition boiling (TB) region is always anchored between the two characteristic points of the boiling curve, namely the critical heat flux and the minimum stable film boiling (MSF) heat flux. It is therefore usually correlated as qTB = ~ q C H F ~- ( l - - ~ ) q M S F
= (_
w_y
(1)
\T~s~- T~n~/ or
qTB _ ( Tw -- Ts .'y7 qc.v \Tony-- TsJ
(2)
The second method seems preferable since it uses only the parameters at the CHF point which are known with better accuracy. The problem resides in the correct value of the exponent n, since the shape of the transition boiling curve is quite sensitive to this value. Large differences in the proposed values for the exponent n can be found in the literature, ranging from - 0 . 5 to -5.3. Under flow boiling conditions of water, values of the exponent close to - 1 were found to fit the data best at low pressures and flow rates (Weber, 1990). The value of the exponent is not constant in the whole transition boiling region but decreases with increasing wall superheat. It also depends on the regime parameters (pressure, flow rate, subcooling). Based on an experimental study, Johannsen et al. (1990) proposed empirical correlations for CHF, Tcnv and the exponent n. The correlations are valid in the following ranges of parameters: pressure, 0.1-1.2 MPa; mass flux, 25-200 kgm -2 s-l; inlet subcooling, 3-30 K; flow direction, upflow. The correlation (Johannsen, 1990) for the exponent n has the form /~
\1/2
n = -0.3412 + 1 3 . 0 5 [ ~ )
--0.000127G .2
_
ATcH~--~
\/LG/t
(3)
where G* -
rh p~2[g~r(p L __ p~)]o25 '
ATw = T w - Ts,
ATcHF=
A i s = iLS - - i L TCHF --
Ts
(4)
145
The effects of mass flux and subcooling are of rather little importance compared with the effects of wall superheat and pressure (Weber, 1990) and have been omitted in the model. Liquid subcooling is taken into account in the CHF correlation (see Section 3.2.1) where its effect is much more important than in the equation for the transition boiling exponent n. The pressure dependence of n implies the extension of the transition boiling region to higher wall superheats with increasing pressure. Obviously the reflooding process is different from the quasi-steady-state experiments. Significant deformations of the boiling curve were observed in transient experiments as compared with the steady state boiling curves (Auracher, 1990a) owing to the influence of process history. The large amount of droplets sputtered off the liquid film at the quench front may also improve the heat transfer in this region. Recent experimental investigations of liquid droplet evaporation when hitting a hot wall (Xiong, 1991) have shown that the heat transfer to water doplets is extremely efficient in the wall temperature range corresponding to the transition boiling region. Being unable to take into account all these effects on a phenomenological basis in the framework of CATHARE, the coefficient of the wall superheat term in the correlation for the exponent n was adjusted on the basis of the Winfrith single-tube experimental data (see Section 4), giving a value of 0.225 instead of 0.4319. As expected, the heat transfer just downstream of the quench front is higher than predicted by the original correlation. The heat transfer coefficient downstream of the quench front in the whole fine mesh is calculated as
h
= hTB -+- hDS ,
hTB _
qxB
T w - Ts
(5)
where h D s is the heat transfer coefficient in the dispersed flow film boiling further downstream of the quench front. 3.2.3. Wall heat transfer in the film boiling region The heat transfer coefficient hDs mentioned above is calculated as the ratio of the total wall heat flux in the dry wall region and the temperature difference Tw -- Ts. The total wall heat flux is
146
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
the sum of the wall-to-interface, wall-to-vapour and wall-to-liquid heat fluxes. The wall-to-interface heat flux is the part of the wall heat flux used for mass transfer. It figures along with the vapour-to-interface and liquid-to-interface heat fluxes in the mass transfer closure relationship of CATHARE. To calculate the components of the total wall heat flux, the standard CATHARE heat transfer package is used (Bestion, 1990). (a) Wall-to-interface heat transfer. A Berensontype correlation is used with a void modifier and an enhancement factor taking into account liquid subcooling. (b) Heat transfer to vapour. This is the sum of the convective (the larger of forced or natural convection) and radiative components. (c) Heat transfer to the liquid. Radiation to liquid droplets is the only contribution to this heat flux.
4. Validation of the top-down reflooding model Two experimental programmes were selected for the validation of the new top-down reflooding model. The first one is the Winfrith single-tube reflooding experiment documented by Elliott and Rose (1970, 1971). The advantage of this experiment is its relative simplicity. It is well suited to test the functionality of the new model and assess the heat transfer correlations in the absence of complex system effects, CCFL, etc. The second experiment selected was the Finnish REWET-II facility (Kervinen, 1989). It is a 19-rod bundle reflooding experiment in the VVER-440 geometry. Experiments with downcomer, upper plenum and combined injection were performed on this facility. This makes it suitable to validate the new reflooding package and the overall behaviour of the code in much more complex situations close enough to reality.
4,1. The AEE Winfrith single-tube top-down reflooding experiment The test facility and test procedure are described in detail in the original papers (Elliott, 1970, 1971). Basically it consists of the nozzle
TEST SECT:ON BY PASS LNE
kATER TCP f ENT~'~~PE
PLATE SPRAY NOZZLE~ CHAMBER
SHROUO TUBE SECT~GN
T
O
O
CONNECTION
SLOTS AT BOTTOM ~ OF TEST SECTION
TERMfNAL CLAMP
/IBOTTOM ORIOPLATE
j TO RIG MAIN I PRESSUREVESSEL
Fig. l. The AEE Winfrith top-down refloodingtest facility.
chamber, the instrumented heated pipe and a large volume below. The facility is closed at the top. A drawing of the test section is shown in Fig. 1. The length of the test section was 965 mm, the pipe i.d. 13.36mm and the wall thickness 1.27 mm. Four different test sections were used: two were made of stainless steel (SS4# 1 and SS4~2), one of inconel and one of zircaloy. Water at saturation temperature was injected into the nozzle chamber through six 1.6 mm i.d. jets equally spaced around the periphery of the nozzle. The test section temperature was measured by six sheathed chromelalumel thermocouples brazed on to the wall. They were arranged in a spiral around the test section at a distance of 152 mm from each other. At the same moment when the injection was started, the power supply to the test section (40 kW) was switched off. For all test sections, experiments were performed in the following ranges of regime parameters: pressure, 0.343, 0.787, 2.17 and 5.28 MPa;
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
initial wall temperature, 350-750°C; liquid injection flow rate, 7.5, 15.0, 22.5 and 30.0 g s i. The test results are presented as plots of the inverse quench front velocity vs. the wall temperature. In the experiments the differences between inconel and stainless steel tests (the first test section) were negligible. The differences between the two different stainless steel test sections were much more pronounced. The reason for this was probably the difference in thermocouple attachment in the two test series. The first stainless steel test section SS ~ 1 had the thermocouples brazed against the outer wall of the tube. For the second stainless steel test section SS 4~2 the thermocouple ends were embedded into the wall of the tube. With the inconel test section the thermocouples were again embedded into the wall of the tube but also had small stainless steel shims spot welded across the thermocouple ends. This means that the thermocouples on the first stainless steel and inconel test sections were probably more affected by radial heat losses than those on the second stainless steel test section. This is why the experimental results and their evaluation for these two wall materials were divided into two groups. The first group contains the data from the first stainless steel and inconel test sections, the second group the data from the second stainless steel test section. To cover the whole range of the experimental regime parameters and to analyse the most important parametric trends (effects of material, pressure, mass flow rate, initial temperature) and compare them with experimental and/or theoretical trends, a total of 18 computations were performed. The difference in calculated results for stainless steel and inconel is practically negligible (they have almost the same thermal diffusivities). Special inconel calculations were therefore not performed. The calculation results will be analysed in terms of the important parametric trends which were well established in the experiments and/or in the top-down reflooding theory.
4. I. 1. Effect of wall material The experiments clearly indicated a higher rewetting rate for zircaloy tubes compared with
147
l/Uqf (s/m) 140-1 [] CATHARE - ZIRC
• CATHARE - SS
J
120-1--.BEST FIT ZIRC
J
100-1 - " BEST FIT SS#2 80-~
BEST FIT SS#1 ...........
f
/
60t 4020-
t
0
/ 0
. . . . .
. . . . . . . . . . . . . .
at,
. . . . . . . . . . . . . . . .
,i'
/
100
150
.....- / : I i' i " i 50
..................... :
. . . . . . . . . . .
i 200
i 250
300
350
400
450
500
Tw - Ts (°C)
Fig. 2. Effect of wall material on quench front velocity (p =0.343MPa, M=15gs 1). stainless steel tubes. From the theory it follows that the quench front velocity is proportional to the material properties combination 21/2/pc. The ratio of these for zircaloy and stainless steel is 1.7-2.0 (depends on temperature). Fig. 2 shows the calculated and measured data for stainless steel and zircaloy at 0.343MPa and 15.0gs -~ injection rate. The ratio of calculated reflooding times is 1.9 in this case. For all the calculations performed for stainless steel and zircaloy under identical conditions the reflooding time ratio was between 1.8 and 1.9.
4.1.2. Effect of pressure Calculated results are compared with the data best fits for three different pressures (Fig. 3). It can be seen that the calculated results are fully consistent with the data and demonstrate an increase in rewetting velocity with increased pressure.
4.1.3. Effect of injection flow rate It was already noted that Elliott and Rose (1970) conclude in their paper that they observed no dependence of the rewetting rate on the injection rate. Other investigators, however, did observe such a dependence (see Section 2.3). On the basis of the calculated results, the following interpretation of the flow rate dependence can be made. The calculated reflooding time decreases with increased injection flow rate. However, once
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
148 1/uqf
(s/m)
Twall (°C) 700 . . . . . . .
140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1,o ......
i~
• ~ ........................
....
'.'.
I DO . . . . . .
~
1
.
t ............... ............ ............ T............... ! ............... :........... :. . . . . . . . . .
!
"~...
~ o o ............... : ~ : , ~ . .
- \ .......ji . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -., .......
I]~ "llltr soo
. . . . . .
............
i"~
BESTF,T 60-
,~.,~" ~i~-
40-~
ilIIP~"
.,~"
. - ~ i "~"
~ /
--
......
p=0.787
J 0 200
i 500
250
• .~
• i 400
i 450 Tw - Ts
CATHARE i 500
.
.
200-
[
.
~
.
~
M
:~
i .................. .......... ...... •% "..~... • .~
300
................
~
CATHARE ~ = 2 . 1 7 0 MPo, DATA BEST FIT
350
"! ....
400 ..........................
MPo, DATA BEST FIT
(3
20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.......
.......... i< .... i .............. i .......................................... • ~ .......
"'~
CATHARE
..........
.....
i
.
=
g / 3s
0 .................... 0 i .................
" . . . . . ................... . I :
('C)
90
Fig. 3. Effect o f pressure: c o m p a r i s o n o f calculated a n d measured results.
100
110
120
130
140
150
160 Time
170 (s)
Fig. 5. C a l c u l a t e d wall t e m p e r a t u r e e v o l u t i o n s for three different injection flow rates. I/Uqf
(s/m)
16o ..................
i ................... : ....................................
i ................
zc (m) .....
o . 9 0 - ~ 120 .
.
.
.
.
.
i
o ,o
............,,~:" ............... i............
,
J - -
. . .~.
.
, -~-
• \.~... ...~-
.............. . . . . .....
....
.......
o.7o ..............................
oo
0.60
80-
.
.
.
.
x.
.
:'\.:"~,~
....
60g/s
40 ............. . . . .
2o. . . . . . . . . . . . . O
1 O0
o. o.,o
~ I- c~.~,
. . . . . . . . . I
150
200
I
[
I
I
250
300
350
400
~=~o.o I
~/,
I
o_ .................................. . . . .
o.2o .
...
. . . . . . . . . . . . .
\.
".....
I
450 500 Tw - Ts ('C)
Fig. 4. Inverse quench front velocity as a function of downs t r e a m wall t e m p e r a t u r e for three different injection flow rates.
plotted as a function of the wall temperature, the quench front velocities show no dependence on the injection flow rate (Fig. 4). For a given wall temperature the quench front velocity has a certain value which does not depend on the injection rate. This indicates that conditions downstream of the quench front are responsible for the faster rewetting. For higher injection flow rates there is more liquid falling over below the quench front, causing increased precursory cooling downstream of the quench front. The rates of wall temperature decrease prior to quenching (Fig. 5) clearly indicate higher precursory cooling with increasing injection flow rate.
0
10
20
30
40
50
60
70
80
Time (s)
Fig. 6. Effect of initial wall t e m p e r a t u r e on quench front progression.
4.I.4. Effect of initial wall temperature The quench front position vs. time is plotted in Fig. 6 for initial wall temperatures of 500, 600 and 700°C at p = 0 . 3 4 3 M P a and M = 1 5 g s -~. As expected, the rewetting time increases with increasing initial wall temperature. 4.2. The R E W E T - H reflooding experiment The REWET-II facility was designed for the investigation of the reflooding phase of a LOCA for the VVER-type reactors. In these reactors,
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
emergency core cooling (ECC) water can be injected to the downcomer as well as to the upper plenum. The facility consisted of a downcomer, a lower plenum, a 19-rod core with a heated length of 2.4 m and an upper plenum. The rest of the primary loops were modelled in a simplified manner with the steam generators and primary pumps simulated with flow resistances. The pressure losses in the loops were simulated with the use of special throttling valves. The elevations of the VVER-440 geometry were preserved; the scaling of volumes and flow areas was 1:2333. A simplified drawing of the test facility is presented in Fig. 7.
STE~ PRE~
F i g . 7. T h e
REWET-II
experimental
facility.
~.2.50
£
149
......... ~.................................. :..... ~ .......~ ........... ~
l i
i
'
o
~
~
i
i
zoo
"
!
i
:.
:.
i ................... !......... i ....i......... ~ !....
o
~
u-
i
i
:
!
'
~
i
i
i
i
¢,
++
1.00 . . . . . . . . . . . . . . . . .
0.50-
i
..... ~ + T ~
i
+ ............ T
"
!...... !
:~
:
i
i
4
o+o+
o ...... '. ....
o EXP. INNER
0.00 50
100 ~50 200 250 300 350 400 450 500 550
Time F i g . 8. C a l c u l a t e d
and measured
in the REWET-II
EXP3
progression
(s)
of quench
fronts
test.
Experiments were performed with all possible types of water injection (to the downcomer, to the upper plenum and to the downcomer and upper plenum simultaneously) at pressures of 0.1, 0.3 and 0.4 MPa. The heater rods had a chopped cosine power profile. The injection rates varied from 34.5 to 3 4 5 g s - ' . The temperature of the injected water was 10, 50 or 100°C. It should be pointed out that the reflooding pattern observed in the experiments was extremely complex and largely multidimensional, especially in the upper part of the core where certain rods were reflooded at the beginning of the transient by top-down quench while others at the same elevation were rewetted several hundred seconds later by the arriving bottom quench front (see Fig. 8). Even in the lower part of the core the differences in rewetting times for the central and peripheral rods could reach 150 s. It is obvious that a 1-D model cannot describe quantitatively this kind of behaviour. Thus the most important objective was to describe qualitatively the averaged behaviour of the two quench fronts and the form of the cladding temperature vs. time curves and to provide a good quantitative estimate of the time and elevation of the position where the two quench fronts meet as well as of the m a x i m u m cladding temperature. Calculation of the test EXP3 with upper plenum injection at 0.1 MPa is presented here.
150
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 -152
The experimental results of this test (see Fig. 8) indicate that the top-down quench front rewetted the upper part of the rods (about 1 m). At the same time the bottom quench front was rewetting the core from the bottom. It might have been fed either by liquid falling over the top-down quench or by liquid carried over by the rising vapour through the intact loop simulator to the downcomer. Unfortunately, the exact values of the hydraulic resistances of the broken and intact loop simulators in the experiments were not reported. They are, however, extremely important to predict correctly the liquid flow to the intact loop, hence the liquid flow at the bottom of the core, the vapour generation rate at the bottom quench front and the CCFL conditions at the top quench front. Sensitivity calculations had confirmed the sensibility of the results to the value of pressure loss coefficients in the broken and intact loops. The calculation presented here was performed with a pressure loss coefficient equal to 100 in the intact loop (simulating a partial closure of the throttling valve; see Fig. 7) and to 4 in the broken loop. The calculation proved the functionality of the new model and the modified logic for two simultaneous quench fronts. It should be noted that the previous version of CATHARE was unable to predict even the bottom quench front progression in the case of upper plenum injection. Fig. 8 shows the simultaneous progression of the two quench fronts. The length of the upper part of the core rewetted by the top-down quench front (about 1 m) as well as the total rewetting time are well predicted. After 200 s of the transient the bottom quench front progression is slightly too fast. The top-down quench front progresses throughout the transient, indicating that the local CCFL limit calculated within the reflooding module had not been reached. While the progression of the quench fronts is well calculated, the maximum cladding temperatures are generally overpredicted (Fig. 9). The maximum cladding temperature is overpredicted by 100c'C; the turnaround times are delayed by 50-90 s. In the experiments it was observed that when the ECC water is injected to the upper plenum the shape of the rod surface temperature
[ • ExP 00m Io ExP. 1.2m I. EXP 12m I l" EXP' 1'7m I EXP' "TmI--0A'C0 T'ONI 800n
............
700 .
.
,
:
:
.
.
.
.
-
,
.t., .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2 600
~-
.
500 .
.
.
.
.
.
.
. .
. .
.
. .
. .
.
. .
.
.
.
AA~
%
.
400
•~.....:
. . . . . . . :. . . . i •
300
200
:
100
oo
0
0
50
100
150
200
250
300
350
400
core
cladding
o~
.....
i
i
i
450
500
55 5 50
Time
Fig. 9. R E W E T - 1 I EXP3: z = 0.9, 1.2 a n d 1.7 m .
,
(s)
temperatures
at
curves is flatter and the quenching temperature seems to be higher than when the water is injected into the downcomer (Kervinen, 1984). This can be explained by the presence of liquid penetrating into the core from the upper plenum, probably more easily in the core periphery, while CCFL conditions existed in the central part of the core. In the calculation there is no or very little liquid flow from the upper plenum to the core, the void fraction in the dry region remains close to unity and consequently the wall-to-fluid heat transfer is underpredicted.
5. Conclusions
This paper summarizes the development work on the CATHARE top-down reflooding model. Based on a literature survey of the state-of-the-art knowledge of falling film reflooding and on compatibility considerations with the existing bottom reflooding model, a top-down reflooding model was developed and implemented into CATHARE 2, version 1.3U. Some new physical models, numerical improvements and a considerable amount of coding were required for the implementation. Calculations of a simple single-tube reflooding experiment demonstrated the functionality of the new
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141-152 model and n o m e n a in results o f quenching the a b i l i t y p a c k a g e to situation.
its a b i l i t y to c o r r e c t l y p r e d i c t the p h e falling film r e w e t t i n g . F i r s t c a l c u l a t i o n simultaneous bottom and top-down in a r o d b u n d l e g e o m e t r y h a v e s h o w n o f CATHARE w i t h the n e w r e f l o o d i n g d e s c r i b e r e a s o n a b l y well this c o m p l e x
Appendix A: Nomenclature c g h i rh M P q T z
thermal capacity (J kg I K-1) a c c e l e r a t i o n d u e t o g r a v i t y ( m e S-l) h e a t t r a n s f e r coefficient ( W m 2 K - l ) specific e n t h a l p y ( J k g - l ) m a s s flux ( k g m -2 s - l ) m a s s f l o w r a t e ( k g s t) pressure (Pa) h e a t flux ( W m z) temperature (K) q u e n c h f r o n t v e l o c i t y ( m s -~) axial c o o r d i n a t e ( m )
G r e e k letters 2 thermal conductivity (W m-l p d e n s i t y ( k g m 3) ~r s u r f a c e t e n s i o n ( N m -1) Indices CHF DS G L MSF qf S TB W
K-l)
critical h e a t flux downstream gas p h a s e liquid phase m i n i m u m stable film b o i l i n g quench front saturation transition boiling wall
References H. Auracher, Transition boiling, Proc. 9th Int. Heat Transfer Conf., Jerusalem, 1990a, Vol. 1, pp. 69-90. H. Auracher, Recent advances in transition boiling research, Proc. Eur. Two-Phase Flow Group Meeting, Ispra, 1990b, Paper DI. A.W. Bennett, G.F. Hewitt, H.A. Kearsey and R.K.F. Keeys, The wetting of hot surfaces by water in a steam environment at high pressure, Rep. AERE-R5146, 1966.
151
D. Bestion, The physical closure laws in the CATHAREcode, Nucl. Eng. Design 124 (1990) 229-245. J.C. Birchley, G.F. Hewitt and C.G. Richards, LOFT dataset review, Rep. AEA-TRS-1061, 1991. D. Butterworth and R.G. Owen, RS 133: the quenching of hot surfaces by top and bottom flooding. A review, Rep. AERER799, 1975. J.J. Carbajo and A.D. Siegel, Review and comparison among the different models for rewetting in LWRs, Nucl. Eng. Design 58 (1980) 33 44. J.G. Collier, Heat transfer in the postburnout region and during quenching and reflooding, in G. Hetsroni (ed.), Handbook of Multiphase Systems, McGraw-Hill, New York, 1982, pp. 6.142-6.188. R.B. Duffey, M.C. Ackerman, B.D.G. Piggott and S.A. Fairbairn, The effects of countercurrent single and two-phase flows on the quenching rate of hot surfaces, Int. J. Multiphase Flow4 (1978) ll7 140. R.B. Duffey and D.T.C. Porthouse, The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Design 25 (1973) 379-394. E. Elias and G. Yadigaroglu, The reflooding phase of the LOCA in PWRs. Part II: Rewetting and liquid entrainment, Nucl. Safety 19 (1978) 160 175. D.F. Elliott and P.W. Rose, The quenching of a heated surface by a film of water in a steam environment at pressures up to 53 bar, Rep. AEEW-M976, 1970. D.F. Elliott and P.W. Rose, The quenching of a heated zircaloy surface by a film of water in a steam environment at pressures up to 53 bar, Rep. AEEW-M1027, 1971. C. Housiadas, Contribution ~ l'analyse des ph6nom6nes bidimensionnels intervenant lors du renoyage d'un coeur de r6acteur a eau sous pression, Ph.D. Thesis, Institut National Polytechnique de Grenoble, 1987. H.J. Ivey and D.J. Morris, On the relevance of the vapour liquid exchange mechanism for subcooled boiling heat transfer at high pressure, Rep. AEEW-R137, 1962. K. Johannsen, P. Weber and Q. Feng, Experimental investigation of heat transfer in the transition region. CEC shared cost action Reactor Safety Program 1985-1987, Final Rep. EUR 13235 EN, 1990. T. Kervinen, H. Purhonen and T. Haapalehto, REWET-II and REWET-III facilities for PWR LOCA experiments, VTT Res. Notes 929, 1989. T. Kervinen, H. Purhonen and H. Kalli, REWET-II experiments to determine the effects of spacer grids on the reflooding process, Proc. 5th Int. Meet. on Thermal Nuclear Reactor Safety, Karlsruhe, 1984. B.D.G. Piggott and R.B. Duffey, The quenching of irradiated fuel pins, Nucl. Eng. Design 32 (1975) 182 190. M.E. Sawan and M.W. Carbon, A review of spray-cooling and bottom-flooding work for LWR cores, Nucl. Eng. Design 32 (1975) 191 207. J.R.S. Thom, W.M. Walker, T.A. Fallon and G.F.S. Reising, Boiling in subcooled water during flow up heated tubes or annuli, Proc. Inst. Mech. Eng. 180 (1966) Pt. 3C, 226 246.
152
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
T. Ueda, M. Inoue, Y. lwata and Y. Sogawa, Rewetting of a hot surface by a falling film, Int. J. Heat Mass Transfer 26 (1983) 401 410. G.B. Wallis, One Dimensional Two-Phase Flow, McGrawHill, New York, 1969. P. Weber and K. Johannsen, Convective transition boiling of water at medium pressure, Proc. 9th Int. Heat Transfer Conf., Jerusalem, 1990, Vol. 6, pp. 35-40. T.Y. Xiong and M.C. Yuen, Evaporation of a liquid droplet on a hot plate, Int. J. Heat Mass Transfer 34 (1991) 1881 1894.
A. Yamanouchi, Effect of core spray cooling in transient state after loss of coolant accident, J. Nucl. Sci. Technol. 5 (1968) 547- 558. K. Yoshioka and S. Hasegawa, A correlation on displacement velocity of liquid film boundary formed on a heated vertical surface in emergency cooling, J. Nucl. Sci. Technol. 7 (1970) 418--425. N. Zuber, M. Tribus and J.W. Westwater, The hydrodynamic crisis in pool boiling of saturated liquid, in International Developments in Heat Transfer, ASME~ New York, 1963, pp. 230 236.
Nuclear Engineering and Design 149 (1994) 141 152
The top-down reflooding model in the
CATHARE
and Design
code
J. Bartak, D. Bestion, T. Haapalehto * Centre d'Etudes Nucldaires de Grenoble, S T R / L M L , 17 Rue des Martyrs, F-38054 Grenoble Cedex 9, France
Abstract
A top-down reflooding model was developed for the French best-estimate thermal hydraulic code CATHARE. The paper presents the current state of development of this model. Based on a literature survey and on compatibility considerations with respect to the existing CATHARE bottom reflooding package, a falling film top-down reflooding model was developed and implemented into CATHARE version 1.3U. Following a brief review of previous work, the paper describes the most important features of the model. The model was validated with the Winfrith single-tube top-down reflooding experiment and with the REWET-II simultaneous bottom and top-down reflooding experiment in a rod bundle geometry. The results demonstrate the ability of the new package to describe the falling film rewetting phenomena and the main parametric trends both in a simple analytical experimental set-up and in a much more complex rod bundle reflooding experiment.
1. Introduction
Reflooding of a heated core is a complex phenomenon generally encountered in a large-break loss-of-coolant accident (LOCA) scenario some time after the accumulator injection. There is a significant energy release from the hot wall. As a consequence, a large variation in the thermal hydraulic conditions of the flow occurs in the immediate vicinity of the quench front, on a scale which is usually much smaller than the characteristic scale of the calculation scheme used in the two-fluid model. In the French best-estimate code CATHARE a special model was developed to represent this * Present address: Department of Energy Technology, Lappeenranta University of Technology, PO Box 20, SF-53851 Lappeenranta, Finland.
situation (Housiadas, 1987). It is a two-dimensional heat conduction model solved on a local fine mesh moving along the wall with the quench front velocity. An important restriction on the use of this model is the fact that it was developed only for b o t t o m reflood and cannot be used for topdown rewetting. There are two basic reasons for this restriction. Firstly, the possibility to have a unique quench front moving from the bottom to the top of an axial element was intrinsically embedded into the computational and decision-making logic of CATIJARE as well as into the language structure used to specify the input data. Secondly, the specific physical models employed in the quench front region and downstream of it use correlations developed on the basis of data derived exclusively from forced flow bottom reflood experiments in tubes and rod bundles. To remove the restriction, a top-down reflooding
0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSD1 0029-5493(94)00682-0
142
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
model was developed and implemented into the CATHARE code. The objective of this paper is to describe the basic physical features of the model and to present the results of the first validation calculations. A more complete assessment programme for the top-down reflooding model is currently in progress. Quenching of a hot surface is the transition from a regime in which heat transfer takes place predominantly to vapour, to a regime in which liquid is in direct contact with a large fraction of the wall. In top-down rewetting a liquid film flows down along the wall. With decreasing distance from the quench front the wall-to-film heat transfer develops from convective cooling to subcooled boiling, nucleate boiling and very violent nucleate and/or transition boiling at the quench front. At the quench front the liquid is violently sputtered off the wall and a spray of droplets is ejected into the vapour field. The droplets bounce against the pipe walls or adjacent rods and may contribute significantly to the heat transfer downstream of the quench front. The large amount of vapour generated in the quench front region has a tendency to rise, exposing the liquid film to a countercurrent flow situation. The film hydrodynamics are thus affected, the film is retarded and may eventually stop or even start to climb (flooding). This is further accentuated if there is vapour upflow from the bottom of the pipe or rod bundle, as is the case e.g. in combined reflooding. On the other hand, the generated vapour can condense on the surface of the film in the case of subcooled reflooding. Another problem encountered in top-down rewetting is that, except for very low liquid flows, there is always some liquid fallover, i.e. only a part of the total liquid flow contributes to the film flow. The liquid falling over improves the heat transfer in the dry region, causing additional precooling.
2. Review of previous work A large amount of work has been carried out world wide on the investigation of the reflooding phenomena and top-down reflooding in particular, both in the experimental and theoretical fields.
Review papers by Butterworth and Owen (1975), Sawan and Carbon (1975), Elias and Yadigaroglu (1978), Carbajo and Siegel (1980) and Collier (1982) summarize this work and the knowledge acquired and provide references to most of the original contributions. More recent theoretical works were mainly refinements and enhancements of the existing models; recent experimental studies were devoted to the influence of special effects such as countercurrent flow conditions (Duffey, 1978). A variety of methods have been proposed for the solution of the conduction equation for a wall in reflooding conditions. Several basic assumptions are common to almost all of them. By invoking commonly used simplifications, the theoretical models have served as an important tool for understanding the basic mechanisms, the influencing variables and the main parametric trends in the rewetting of a hot surface. For the same reasons they are not very well fitted for use for realistic (best-estimate) calculations in which various interacting phenomena are present and which render the generally accepted assumptions inapplicable. The common feature of most of the theoretical models is the necessity to specify the heat transfer coefficients in the wet and dry regions and the rewetting temperature as boundary conditions. Important differences in the values of these parameters exist between the models in order to obtain reasonable agreement with experimental data. This, together with different simplifying assumptions, makes the use of analytical models in best-estimate codes difficult to justify. The large amount of experimental work on top-down reflooding will be summarized briefly by analysing the major effects influencing the rewetting phenomenon.
2. I. Effect of initial wall temperature All the experiments document a decrease in the rewetting velocity with an increase in the initial wall temperature (Yamanouchi, 1968; Elliott, 1970, 1971; Duffey, 1973; Butterworth, 1975; Ueda, 1983). The inverse rewetting velocity increases almost linearly with increasing wall temperature.
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141-152
2.2. Effect of pressure The quench front velocity increases with increasing pressure, though the exact functional dependence may be rather complex (Elliott, 1970, 1971; Butterworth, 1975). It is given by the improved heat transfer to the fluid (both in the wet and dry regions) and depends on the wall material, wall thickness and other factors.
2.3. Effect of reflooding flow rate and liquid subcooling These effects are quite complicated and ambiguous. Some experimental data exhibit a flow rate dependence while others do not. Bennett et al. (1966), Elliott and Rose (1970, 1971) and Ueda et al. (1983) conclude from their data that there is no flow rate effect, whereas Yamanouchi (1968), Duffey and Porthouse (1973) and Piggott and Duffey (1975) observed an increase in the rewetting rate with increased liquid flow rate. The flow rate effect is obviously linked with the liquid subcooling at the quench front. For a given subcooling at the injection point the subcooling at the quench front level should remain higher for higher flow rates. The data of Yoshioka and Hasegawa (1970) and Piggott and Duffey (1975) show a significant increase in quench front velocity with increased subcooling. Another possible effect of high liquid flow rates is a higher liquid fallover to the region below the quench front, causing higher precursory cooling and increasing the quench front velocity.
143
the material heat conductivity is twofold in this case. Increasing the heat conductivity in the axial direction increases the quench front velocity, whereas decreasing the heat conductivity in the radial direction also increases the quench front velocity. Thus a rod with a gap will quench faster than a rod without a gap, and a hollow rod will quench faster than a rod filled with a filler. This was clearly shown in the tests by Piggott and Duffey (1975), in the tests on the REWET-II facility (Kervinen, 1989) and on the LOFT test support facility (Birchley, 1991). This behaviour is well predicted by the numerical 2-D conduction model used in CATHARE. The wall thickness influences only the conduction pattern in the wall. The decrease in the quench front velocity with the square root of the wall thickness predicted by the analytical models e.g. (Yamanouchi, 1968; Yoshioka, 1970) should thus be a good approximation of this effect.
2.5. Effect of countercurrent flow Duffey et al. (1978) performed an experimental and theoretical investigation of falling film rewetting in the presence of countercurrent flow. A single heated rod was placed in a tube. The falling film quench rate was significantly retarded by an air, steam or two-phase upflow, even before the point of flow reversal (flooding). Effects of surface roughness and deposits and effects of irradiation of fuel pins are not discussed here since they are not taken into account in current models, though they can be quite important in practice.
2.4. Effect of wall material and wall thickness In the case of reflooding of a single material wall the experimental results for various materials confirm the theoretical predictions. The quench front velocity is proportional to the parameter 2 ~/~-/pc(Yamanouchi, 1968; Yoshioka, 1970). This gives a quench speed of zircaloy about two times higher than that of stainless steel. This was shown e.g. in the tests performed by Elliott and Rose (1970) and Piggott and Duffey (1975). However, the situation becomes more complex in the case of a rod with a filler and/or a gap. The influence of
3. The CATHARE top-down reflooding model
3. I. General description The CATHARE top-down reflooding model assumes a wetted wall with a descending liquid film upstream of the quench front, a steep wall temperature gradient in the quench front region and a hot dry wall downstream of the quench front. The two-dimensional transient heat conduction problem in a multilayer wall is solved numerically. A
144
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
fine 2-D mesh is moving along the wall with the quench front velocity. This mesh movement introduces a convective term into the heat conduction equation. Together with the boundary conditions and an additional condition at the quench front, the discretized equations are solved for the temperature field in the fine mesh and the quench front velocity (Housiadas, 1987). The condition at the quench front imposes the wall temperature to be equal to the local burn-out temperature. The total length of the fine mesh region is typically around 8 cm and contains about 30 axial meshes. The size of these meshes varies from about 5 x 10-Sm at the quench front to 5 x 10 3m at the extremities. The boundary conditions necessary to perform a heat conduction calculation within the fine mesh are the following: zero radial heat flux on the rod axis or on the outer surface of a tube; wall-to-fluid heat transfer correlations on the wall facing the fluid; zero axial conduction heat flux on the horizontal boundary within the wetted region; a temperature boundary condition on the horizontal boundary within the dry region. The solution method is the N e w t o n - R a p h s o n iteration with a direct solver of the linearized equations. As a result of this solution procedure, the temperature field within the fine mesh region and the quench front velocity are obtained. The convergence criteria used are 1 0 - 4 m s -1 for the quench front velocity and 0.1°C for the temperatures.
3.2. Thermal hydraulics in the vicinity of the top-down quench front The following heat transfer mechanisms in the quench front region are taken into account: nucleate boiling in the descending film upstream of the quench front; critical heat flux at the quench front; transition boiling immediately downstream of the quench front; heat transfer to droplets sputtered off the film in the quench front region; dispersed flow film boiling further downstream of the quench front.
3.2. I. Region upstream of the quench front In this region Thorn et al.'s (1966) correlation is used to calculate the nucleate boiling heat trans-
fer. The critical heat flux (CHF) is calculated with Zuber et al.'s (1963) C H F correlation with the Ivey and Morris (1962) correction for subcooling. The equality of these two heat fluxes at the C H F point provides the condition for the burn-out temperature which is used as the imposed wall temperature at the quench front. Since the CATHARE code uses only one liquid field, it is impossible to distinguish between the liquid present in the film and in the gas core. The top-down reflooding model assumes that there is always a liquid film on the wall in the wet region. This film is entirely vaporized at the quench front. The amount of liquid which was not vaporized and passes the quench front defines the total liquid fallover. This liquid is assumed to be in the form of droplets which are treated with standard CATnARE wall and interface heat transfer and interfacial shear correlations used in dispersed flow. In the case of countercurrent flow the droplets sputtered off the film can be entrained by the vapour flow and the film itself can be retarded, stopped or forced to move upwards (CCFL). The model is unable to take these effects into account on a phenomenological basis. Instead, a local CCFL criterion of the Wallis (1969) type is applied at the quench front. If the rising vapour velocity exceeds the value of the critical velocity given by this criterion, the top-down quench front is stopped and cannot proceed any further until the vapour velocity decreases again below the critical value.
3.2.2. Region immediately downstream of the quench front This region is the most difficult to describe. It is the region of violent boiling and disintegration of the liquid film with the formation of a jet of droplets of various sizes sputtered off the liquid film. Owing to the steep temperature gradients in the wall, a complete change in the boiling mechanism from nucleate boiling to dispersed flow film boiling occurs within no more than a few centimetres along the wall. The transition boiling region is the least understood part of the boiling curve owing to its inherently unstable nature (negative slope of the boiling curve) and extremely difficult experimental realization. Recent developments in
J. Bartak et al. / Nuclear Engineering and Design 149 0994) 141-152
this field are discussed by Auracher (1990a,b). The heat flux in the transition boiling (TB) region is always anchored between the two characteristic points of the boiling curve, namely the critical heat flux and the minimum stable film boiling (MSF) heat flux. It is therefore usually correlated as qTB = ~ q C H F ~- ( l - - ~ ) q M S F
= (_
w_y
(1)
\T~s~- T~n~/ or
qTB _ ( Tw -- Ts .'y7 qc.v \Tony-- TsJ
(2)
The second method seems preferable since it uses only the parameters at the CHF point which are known with better accuracy. The problem resides in the correct value of the exponent n, since the shape of the transition boiling curve is quite sensitive to this value. Large differences in the proposed values for the exponent n can be found in the literature, ranging from - 0 . 5 to -5.3. Under flow boiling conditions of water, values of the exponent close to - 1 were found to fit the data best at low pressures and flow rates (Weber, 1990). The value of the exponent is not constant in the whole transition boiling region but decreases with increasing wall superheat. It also depends on the regime parameters (pressure, flow rate, subcooling). Based on an experimental study, Johannsen et al. (1990) proposed empirical correlations for CHF, Tcnv and the exponent n. The correlations are valid in the following ranges of parameters: pressure, 0.1-1.2 MPa; mass flux, 25-200 kgm -2 s-l; inlet subcooling, 3-30 K; flow direction, upflow. The correlation (Johannsen, 1990) for the exponent n has the form /~
\1/2
n = -0.3412 + 1 3 . 0 5 [ ~ )
--0.000127G .2
_
ATcH~--~
\/LG/t
(3)
where G* -
rh p~2[g~r(p L __ p~)]o25 '
ATw = T w - Ts,
ATcHF=
A i s = iLS - - i L TCHF --
Ts
(4)
145
The effects of mass flux and subcooling are of rather little importance compared with the effects of wall superheat and pressure (Weber, 1990) and have been omitted in the model. Liquid subcooling is taken into account in the CHF correlation (see Section 3.2.1) where its effect is much more important than in the equation for the transition boiling exponent n. The pressure dependence of n implies the extension of the transition boiling region to higher wall superheats with increasing pressure. Obviously the reflooding process is different from the quasi-steady-state experiments. Significant deformations of the boiling curve were observed in transient experiments as compared with the steady state boiling curves (Auracher, 1990a) owing to the influence of process history. The large amount of droplets sputtered off the liquid film at the quench front may also improve the heat transfer in this region. Recent experimental investigations of liquid droplet evaporation when hitting a hot wall (Xiong, 1991) have shown that the heat transfer to water doplets is extremely efficient in the wall temperature range corresponding to the transition boiling region. Being unable to take into account all these effects on a phenomenological basis in the framework of CATHARE, the coefficient of the wall superheat term in the correlation for the exponent n was adjusted on the basis of the Winfrith single-tube experimental data (see Section 4), giving a value of 0.225 instead of 0.4319. As expected, the heat transfer just downstream of the quench front is higher than predicted by the original correlation. The heat transfer coefficient downstream of the quench front in the whole fine mesh is calculated as
h
= hTB -+- hDS ,
hTB _
qxB
T w - Ts
(5)
where h D s is the heat transfer coefficient in the dispersed flow film boiling further downstream of the quench front. 3.2.3. Wall heat transfer in the film boiling region The heat transfer coefficient hDs mentioned above is calculated as the ratio of the total wall heat flux in the dry wall region and the temperature difference Tw -- Ts. The total wall heat flux is
146
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
the sum of the wall-to-interface, wall-to-vapour and wall-to-liquid heat fluxes. The wall-to-interface heat flux is the part of the wall heat flux used for mass transfer. It figures along with the vapour-to-interface and liquid-to-interface heat fluxes in the mass transfer closure relationship of CATHARE. To calculate the components of the total wall heat flux, the standard CATHARE heat transfer package is used (Bestion, 1990). (a) Wall-to-interface heat transfer. A Berensontype correlation is used with a void modifier and an enhancement factor taking into account liquid subcooling. (b) Heat transfer to vapour. This is the sum of the convective (the larger of forced or natural convection) and radiative components. (c) Heat transfer to the liquid. Radiation to liquid droplets is the only contribution to this heat flux.
4. Validation of the top-down reflooding model Two experimental programmes were selected for the validation of the new top-down reflooding model. The first one is the Winfrith single-tube reflooding experiment documented by Elliott and Rose (1970, 1971). The advantage of this experiment is its relative simplicity. It is well suited to test the functionality of the new model and assess the heat transfer correlations in the absence of complex system effects, CCFL, etc. The second experiment selected was the Finnish REWET-II facility (Kervinen, 1989). It is a 19-rod bundle reflooding experiment in the VVER-440 geometry. Experiments with downcomer, upper plenum and combined injection were performed on this facility. This makes it suitable to validate the new reflooding package and the overall behaviour of the code in much more complex situations close enough to reality.
4,1. The AEE Winfrith single-tube top-down reflooding experiment The test facility and test procedure are described in detail in the original papers (Elliott, 1970, 1971). Basically it consists of the nozzle
TEST SECT:ON BY PASS LNE
kATER TCP f ENT~'~~PE
PLATE SPRAY NOZZLE~ CHAMBER
SHROUO TUBE SECT~GN
T
O
O
CONNECTION
SLOTS AT BOTTOM ~ OF TEST SECTION
TERMfNAL CLAMP
/IBOTTOM ORIOPLATE
j TO RIG MAIN I PRESSUREVESSEL
Fig. l. The AEE Winfrith top-down refloodingtest facility.
chamber, the instrumented heated pipe and a large volume below. The facility is closed at the top. A drawing of the test section is shown in Fig. 1. The length of the test section was 965 mm, the pipe i.d. 13.36mm and the wall thickness 1.27 mm. Four different test sections were used: two were made of stainless steel (SS4# 1 and SS4~2), one of inconel and one of zircaloy. Water at saturation temperature was injected into the nozzle chamber through six 1.6 mm i.d. jets equally spaced around the periphery of the nozzle. The test section temperature was measured by six sheathed chromelalumel thermocouples brazed on to the wall. They were arranged in a spiral around the test section at a distance of 152 mm from each other. At the same moment when the injection was started, the power supply to the test section (40 kW) was switched off. For all test sections, experiments were performed in the following ranges of regime parameters: pressure, 0.343, 0.787, 2.17 and 5.28 MPa;
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
initial wall temperature, 350-750°C; liquid injection flow rate, 7.5, 15.0, 22.5 and 30.0 g s i. The test results are presented as plots of the inverse quench front velocity vs. the wall temperature. In the experiments the differences between inconel and stainless steel tests (the first test section) were negligible. The differences between the two different stainless steel test sections were much more pronounced. The reason for this was probably the difference in thermocouple attachment in the two test series. The first stainless steel test section SS ~ 1 had the thermocouples brazed against the outer wall of the tube. For the second stainless steel test section SS 4~2 the thermocouple ends were embedded into the wall of the tube. With the inconel test section the thermocouples were again embedded into the wall of the tube but also had small stainless steel shims spot welded across the thermocouple ends. This means that the thermocouples on the first stainless steel and inconel test sections were probably more affected by radial heat losses than those on the second stainless steel test section. This is why the experimental results and their evaluation for these two wall materials were divided into two groups. The first group contains the data from the first stainless steel and inconel test sections, the second group the data from the second stainless steel test section. To cover the whole range of the experimental regime parameters and to analyse the most important parametric trends (effects of material, pressure, mass flow rate, initial temperature) and compare them with experimental and/or theoretical trends, a total of 18 computations were performed. The difference in calculated results for stainless steel and inconel is practically negligible (they have almost the same thermal diffusivities). Special inconel calculations were therefore not performed. The calculation results will be analysed in terms of the important parametric trends which were well established in the experiments and/or in the top-down reflooding theory.
4. I. 1. Effect of wall material The experiments clearly indicated a higher rewetting rate for zircaloy tubes compared with
147
l/Uqf (s/m) 140-1 [] CATHARE - ZIRC
• CATHARE - SS
J
120-1--.BEST FIT ZIRC
J
100-1 - " BEST FIT SS#2 80-~
BEST FIT SS#1 ...........
f
/
60t 4020-
t
0
/ 0
. . . . .
. . . . . . . . . . . . . .
at,
. . . . . . . . . . . . . . . .
,i'
/
100
150
.....- / : I i' i " i 50
..................... :
. . . . . . . . . . .
i 200
i 250
300
350
400
450
500
Tw - Ts (°C)
Fig. 2. Effect of wall material on quench front velocity (p =0.343MPa, M=15gs 1). stainless steel tubes. From the theory it follows that the quench front velocity is proportional to the material properties combination 21/2/pc. The ratio of these for zircaloy and stainless steel is 1.7-2.0 (depends on temperature). Fig. 2 shows the calculated and measured data for stainless steel and zircaloy at 0.343MPa and 15.0gs -~ injection rate. The ratio of calculated reflooding times is 1.9 in this case. For all the calculations performed for stainless steel and zircaloy under identical conditions the reflooding time ratio was between 1.8 and 1.9.
4.1.2. Effect of pressure Calculated results are compared with the data best fits for three different pressures (Fig. 3). It can be seen that the calculated results are fully consistent with the data and demonstrate an increase in rewetting velocity with increased pressure.
4.1.3. Effect of injection flow rate It was already noted that Elliott and Rose (1970) conclude in their paper that they observed no dependence of the rewetting rate on the injection rate. Other investigators, however, did observe such a dependence (see Section 2.3). On the basis of the calculated results, the following interpretation of the flow rate dependence can be made. The calculated reflooding time decreases with increased injection flow rate. However, once
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
148 1/uqf
(s/m)
Twall (°C) 700 . . . . . . .
140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1,o ......
i~
• ~ ........................
....
'.'.
I DO . . . . . .
~
1
.
t ............... ............ ............ T............... ! ............... :........... :. . . . . . . . . .
!
"~...
~ o o ............... : ~ : , ~ . .
- \ .......ji . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -., .......
I]~ "llltr soo
. . . . . .
............
i"~
BESTF,T 60-
,~.,~" ~i~-
40-~
ilIIP~"
.,~"
. - ~ i "~"
~ /
--
......
p=0.787
J 0 200
i 500
250
• .~
• i 400
i 450 Tw - Ts
CATHARE i 500
.
.
200-
[
.
~
.
~
M
:~
i .................. .......... ...... •% "..~... • .~
300
................
~
CATHARE ~ = 2 . 1 7 0 MPo, DATA BEST FIT
350
"! ....
400 ..........................
MPo, DATA BEST FIT
(3
20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.......
.......... i< .... i .............. i .......................................... • ~ .......
"'~
CATHARE
..........
.....
i
.
=
g / 3s
0 .................... 0 i .................
" . . . . . ................... . I :
('C)
90
Fig. 3. Effect o f pressure: c o m p a r i s o n o f calculated a n d measured results.
100
110
120
130
140
150
160 Time
170 (s)
Fig. 5. C a l c u l a t e d wall t e m p e r a t u r e e v o l u t i o n s for three different injection flow rates. I/Uqf
(s/m)
16o ..................
i ................... : ....................................
i ................
zc (m) .....
o . 9 0 - ~ 120 .
.
.
.
.
.
i
o ,o
............,,~:" ............... i............
,
J - -
. . .~.
.
, -~-
• \.~... ...~-
.............. . . . . .....
....
.......
o.7o ..............................
oo
0.60
80-
.
.
.
.
x.
.
:'\.:"~,~
....
60g/s
40 ............. . . . .
2o. . . . . . . . . . . . . O
1 O0
o. o.,o
~ I- c~.~,
. . . . . . . . . I
150
200
I
[
I
I
250
300
350
400
~=~o.o I
~/,
I
o_ .................................. . . . .
o.2o .
...
. . . . . . . . . . . . .
\.
".....
I
450 500 Tw - Ts ('C)
Fig. 4. Inverse quench front velocity as a function of downs t r e a m wall t e m p e r a t u r e for three different injection flow rates.
plotted as a function of the wall temperature, the quench front velocities show no dependence on the injection flow rate (Fig. 4). For a given wall temperature the quench front velocity has a certain value which does not depend on the injection rate. This indicates that conditions downstream of the quench front are responsible for the faster rewetting. For higher injection flow rates there is more liquid falling over below the quench front, causing increased precursory cooling downstream of the quench front. The rates of wall temperature decrease prior to quenching (Fig. 5) clearly indicate higher precursory cooling with increasing injection flow rate.
0
10
20
30
40
50
60
70
80
Time (s)
Fig. 6. Effect of initial wall t e m p e r a t u r e on quench front progression.
4.I.4. Effect of initial wall temperature The quench front position vs. time is plotted in Fig. 6 for initial wall temperatures of 500, 600 and 700°C at p = 0 . 3 4 3 M P a and M = 1 5 g s -~. As expected, the rewetting time increases with increasing initial wall temperature. 4.2. The R E W E T - H reflooding experiment The REWET-II facility was designed for the investigation of the reflooding phase of a LOCA for the VVER-type reactors. In these reactors,
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
emergency core cooling (ECC) water can be injected to the downcomer as well as to the upper plenum. The facility consisted of a downcomer, a lower plenum, a 19-rod core with a heated length of 2.4 m and an upper plenum. The rest of the primary loops were modelled in a simplified manner with the steam generators and primary pumps simulated with flow resistances. The pressure losses in the loops were simulated with the use of special throttling valves. The elevations of the VVER-440 geometry were preserved; the scaling of volumes and flow areas was 1:2333. A simplified drawing of the test facility is presented in Fig. 7.
STE~ PRE~
F i g . 7. T h e
REWET-II
experimental
facility.
~.2.50
£
149
......... ~.................................. :..... ~ .......~ ........... ~
l i
i
'
o
~
~
i
i
zoo
"
!
i
:.
:.
i ................... !......... i ....i......... ~ !....
o
~
u-
i
i
:
!
'
~
i
i
i
i
¢,
++
1.00 . . . . . . . . . . . . . . . . .
0.50-
i
..... ~ + T ~
i
+ ............ T
"
!...... !
:~
:
i
i
4
o+o+
o ...... '. ....
o EXP. INNER
0.00 50
100 ~50 200 250 300 350 400 450 500 550
Time F i g . 8. C a l c u l a t e d
and measured
in the REWET-II
EXP3
progression
(s)
of quench
fronts
test.
Experiments were performed with all possible types of water injection (to the downcomer, to the upper plenum and to the downcomer and upper plenum simultaneously) at pressures of 0.1, 0.3 and 0.4 MPa. The heater rods had a chopped cosine power profile. The injection rates varied from 34.5 to 3 4 5 g s - ' . The temperature of the injected water was 10, 50 or 100°C. It should be pointed out that the reflooding pattern observed in the experiments was extremely complex and largely multidimensional, especially in the upper part of the core where certain rods were reflooded at the beginning of the transient by top-down quench while others at the same elevation were rewetted several hundred seconds later by the arriving bottom quench front (see Fig. 8). Even in the lower part of the core the differences in rewetting times for the central and peripheral rods could reach 150 s. It is obvious that a 1-D model cannot describe quantitatively this kind of behaviour. Thus the most important objective was to describe qualitatively the averaged behaviour of the two quench fronts and the form of the cladding temperature vs. time curves and to provide a good quantitative estimate of the time and elevation of the position where the two quench fronts meet as well as of the m a x i m u m cladding temperature. Calculation of the test EXP3 with upper plenum injection at 0.1 MPa is presented here.
150
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 -152
The experimental results of this test (see Fig. 8) indicate that the top-down quench front rewetted the upper part of the rods (about 1 m). At the same time the bottom quench front was rewetting the core from the bottom. It might have been fed either by liquid falling over the top-down quench or by liquid carried over by the rising vapour through the intact loop simulator to the downcomer. Unfortunately, the exact values of the hydraulic resistances of the broken and intact loop simulators in the experiments were not reported. They are, however, extremely important to predict correctly the liquid flow to the intact loop, hence the liquid flow at the bottom of the core, the vapour generation rate at the bottom quench front and the CCFL conditions at the top quench front. Sensitivity calculations had confirmed the sensibility of the results to the value of pressure loss coefficients in the broken and intact loops. The calculation presented here was performed with a pressure loss coefficient equal to 100 in the intact loop (simulating a partial closure of the throttling valve; see Fig. 7) and to 4 in the broken loop. The calculation proved the functionality of the new model and the modified logic for two simultaneous quench fronts. It should be noted that the previous version of CATHARE was unable to predict even the bottom quench front progression in the case of upper plenum injection. Fig. 8 shows the simultaneous progression of the two quench fronts. The length of the upper part of the core rewetted by the top-down quench front (about 1 m) as well as the total rewetting time are well predicted. After 200 s of the transient the bottom quench front progression is slightly too fast. The top-down quench front progresses throughout the transient, indicating that the local CCFL limit calculated within the reflooding module had not been reached. While the progression of the quench fronts is well calculated, the maximum cladding temperatures are generally overpredicted (Fig. 9). The maximum cladding temperature is overpredicted by 100c'C; the turnaround times are delayed by 50-90 s. In the experiments it was observed that when the ECC water is injected to the upper plenum the shape of the rod surface temperature
[ • ExP 00m Io ExP. 1.2m I. EXP 12m I l" EXP' 1'7m I EXP' "TmI--0A'C0 T'ONI 800n
............
700 .
.
,
:
:
.
.
.
.
-
,
.t., .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2 600
~-
.
500 .
.
.
.
.
.
.
. .
. .
.
. .
. .
.
. .
.
.
.
AA~
%
.
400
•~.....:
. . . . . . . :. . . . i •
300
200
:
100
oo
0
0
50
100
150
200
250
300
350
400
core
cladding
o~
.....
i
i
i
450
500
55 5 50
Time
Fig. 9. R E W E T - 1 I EXP3: z = 0.9, 1.2 a n d 1.7 m .
,
(s)
temperatures
at
curves is flatter and the quenching temperature seems to be higher than when the water is injected into the downcomer (Kervinen, 1984). This can be explained by the presence of liquid penetrating into the core from the upper plenum, probably more easily in the core periphery, while CCFL conditions existed in the central part of the core. In the calculation there is no or very little liquid flow from the upper plenum to the core, the void fraction in the dry region remains close to unity and consequently the wall-to-fluid heat transfer is underpredicted.
5. Conclusions
This paper summarizes the development work on the CATHARE top-down reflooding model. Based on a literature survey of the state-of-the-art knowledge of falling film reflooding and on compatibility considerations with the existing bottom reflooding model, a top-down reflooding model was developed and implemented into CATHARE 2, version 1.3U. Some new physical models, numerical improvements and a considerable amount of coding were required for the implementation. Calculations of a simple single-tube reflooding experiment demonstrated the functionality of the new
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141-152 model and n o m e n a in results o f quenching the a b i l i t y p a c k a g e to situation.
its a b i l i t y to c o r r e c t l y p r e d i c t the p h e falling film r e w e t t i n g . F i r s t c a l c u l a t i o n simultaneous bottom and top-down in a r o d b u n d l e g e o m e t r y h a v e s h o w n o f CATHARE w i t h the n e w r e f l o o d i n g d e s c r i b e r e a s o n a b l y well this c o m p l e x
Appendix A: Nomenclature c g h i rh M P q T z
thermal capacity (J kg I K-1) a c c e l e r a t i o n d u e t o g r a v i t y ( m e S-l) h e a t t r a n s f e r coefficient ( W m 2 K - l ) specific e n t h a l p y ( J k g - l ) m a s s flux ( k g m -2 s - l ) m a s s f l o w r a t e ( k g s t) pressure (Pa) h e a t flux ( W m z) temperature (K) q u e n c h f r o n t v e l o c i t y ( m s -~) axial c o o r d i n a t e ( m )
G r e e k letters 2 thermal conductivity (W m-l p d e n s i t y ( k g m 3) ~r s u r f a c e t e n s i o n ( N m -1) Indices CHF DS G L MSF qf S TB W
K-l)
critical h e a t flux downstream gas p h a s e liquid phase m i n i m u m stable film b o i l i n g quench front saturation transition boiling wall
References H. Auracher, Transition boiling, Proc. 9th Int. Heat Transfer Conf., Jerusalem, 1990a, Vol. 1, pp. 69-90. H. Auracher, Recent advances in transition boiling research, Proc. Eur. Two-Phase Flow Group Meeting, Ispra, 1990b, Paper DI. A.W. Bennett, G.F. Hewitt, H.A. Kearsey and R.K.F. Keeys, The wetting of hot surfaces by water in a steam environment at high pressure, Rep. AERE-R5146, 1966.
151
D. Bestion, The physical closure laws in the CATHAREcode, Nucl. Eng. Design 124 (1990) 229-245. J.C. Birchley, G.F. Hewitt and C.G. Richards, LOFT dataset review, Rep. AEA-TRS-1061, 1991. D. Butterworth and R.G. Owen, RS 133: the quenching of hot surfaces by top and bottom flooding. A review, Rep. AERER799, 1975. J.J. Carbajo and A.D. Siegel, Review and comparison among the different models for rewetting in LWRs, Nucl. Eng. Design 58 (1980) 33 44. J.G. Collier, Heat transfer in the postburnout region and during quenching and reflooding, in G. Hetsroni (ed.), Handbook of Multiphase Systems, McGraw-Hill, New York, 1982, pp. 6.142-6.188. R.B. Duffey, M.C. Ackerman, B.D.G. Piggott and S.A. Fairbairn, The effects of countercurrent single and two-phase flows on the quenching rate of hot surfaces, Int. J. Multiphase Flow4 (1978) ll7 140. R.B. Duffey and D.T.C. Porthouse, The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Design 25 (1973) 379-394. E. Elias and G. Yadigaroglu, The reflooding phase of the LOCA in PWRs. Part II: Rewetting and liquid entrainment, Nucl. Safety 19 (1978) 160 175. D.F. Elliott and P.W. Rose, The quenching of a heated surface by a film of water in a steam environment at pressures up to 53 bar, Rep. AEEW-M976, 1970. D.F. Elliott and P.W. Rose, The quenching of a heated zircaloy surface by a film of water in a steam environment at pressures up to 53 bar, Rep. AEEW-M1027, 1971. C. Housiadas, Contribution ~ l'analyse des ph6nom6nes bidimensionnels intervenant lors du renoyage d'un coeur de r6acteur a eau sous pression, Ph.D. Thesis, Institut National Polytechnique de Grenoble, 1987. H.J. Ivey and D.J. Morris, On the relevance of the vapour liquid exchange mechanism for subcooled boiling heat transfer at high pressure, Rep. AEEW-R137, 1962. K. Johannsen, P. Weber and Q. Feng, Experimental investigation of heat transfer in the transition region. CEC shared cost action Reactor Safety Program 1985-1987, Final Rep. EUR 13235 EN, 1990. T. Kervinen, H. Purhonen and T. Haapalehto, REWET-II and REWET-III facilities for PWR LOCA experiments, VTT Res. Notes 929, 1989. T. Kervinen, H. Purhonen and H. Kalli, REWET-II experiments to determine the effects of spacer grids on the reflooding process, Proc. 5th Int. Meet. on Thermal Nuclear Reactor Safety, Karlsruhe, 1984. B.D.G. Piggott and R.B. Duffey, The quenching of irradiated fuel pins, Nucl. Eng. Design 32 (1975) 182 190. M.E. Sawan and M.W. Carbon, A review of spray-cooling and bottom-flooding work for LWR cores, Nucl. Eng. Design 32 (1975) 191 207. J.R.S. Thom, W.M. Walker, T.A. Fallon and G.F.S. Reising, Boiling in subcooled water during flow up heated tubes or annuli, Proc. Inst. Mech. Eng. 180 (1966) Pt. 3C, 226 246.
152
J. Bartak et al. / Nuclear Engineering and Design 149 (1994) 141 152
T. Ueda, M. Inoue, Y. lwata and Y. Sogawa, Rewetting of a hot surface by a falling film, Int. J. Heat Mass Transfer 26 (1983) 401 410. G.B. Wallis, One Dimensional Two-Phase Flow, McGrawHill, New York, 1969. P. Weber and K. Johannsen, Convective transition boiling of water at medium pressure, Proc. 9th Int. Heat Transfer Conf., Jerusalem, 1990, Vol. 6, pp. 35-40. T.Y. Xiong and M.C. Yuen, Evaporation of a liquid droplet on a hot plate, Int. J. Heat Mass Transfer 34 (1991) 1881 1894.
A. Yamanouchi, Effect of core spray cooling in transient state after loss of coolant accident, J. Nucl. Sci. Technol. 5 (1968) 547- 558. K. Yoshioka and S. Hasegawa, A correlation on displacement velocity of liquid film boundary formed on a heated vertical surface in emergency cooling, J. Nucl. Sci. Technol. 7 (1970) 418--425. N. Zuber, M. Tribus and J.W. Westwater, The hydrodynamic crisis in pool boiling of saturated liquid, in International Developments in Heat Transfer, ASME~ New York, 1963, pp. 230 236.