DECOBI: investigation of melt coolability with bottom coolant injection

Pergamon Progress in Nuclear Energy, Vol. 40, No. 2, pp. 161-206, 2002

0 2002 Elsevier Science Ltd. All rights reserved Printed in Great Britain

www.elsevier.com/locatelpnucene PII: SO149-1970(01)00022-1

0149-1970/02/$ - see front matter

DECOBI: INVESTIGATION OF MELT COOLABILITY

WITH BOTTOM COOLANT INJECTION

D. PALADINO, S.A. THEERTHAN and B.R. SEHGAL

Royal Institute of Technology @IT)

Division of Nuclear Power Safety (NPS)

Brinellvlgen 60, 10044 STOCKHOLM, SWEDEN

Fax + (46)(8) 790-9252, e-mail: [email protected]

Keywords: severe accident, core-catcher, coolability, direct contact heat transfer.

ABSTRACT

This paper describes the results obtained in the DECOBI program at RIT/NPS, which is

concerned with the ex-vessel melt coolability by bottom coolant injection through embed-

ded nozzles. Experiments have been performed with metallic simulants as well as with

three different binary oxidic simulants, so that a substantial range of coolant melt inter-

action and its influence on the debris structure has been investigated. Experiments reveal

that, through this scheme of coolant injection, the high temperature melt debris, arriving

in the containment as a result of vessel failure, can be quenched in a short time. Sufficient

porosity is created in the debris so that water flow from the bottom can access the heat

generating melt (debris) to cool and stabilize it permanently. Analysis performed, based

on the insights gained from the experiments, estimates the amount of porosity that can

be obtained with a single nozzle. 0 2002 Elsevier Science Ltd. All rights reserved.

161

162 D. Paladino et al.

1 INTRODUCTION

1.1 Background

Ex-vessel melt (debris) coolability is a critical safety issue for the current and the future

light water reactor plants (LWRs), with respect to stabilization and termination of a pos-

tulated severe (core melt down) accident. The late phase of a severe accident progression

is associated with melt discharge from the RPV and spreading on the concrete basemat

in the current plants, or on a core-catcher in future plants e.g. EPR, forming a melt pool

and/or a particulate bed which generates decay heat and reacts with the containment

structures. The accident would be considered stabilized when the coolability (quenching

and solidification) of the melt/debris bed is assured for all time.

The most convenient accident management measure to cool the debris is to establish

a water layer on top of the melt pool. This coolability scheme has been investigated

extensively in the MACE experimental program (Sehgal et al. 1992, Merilo et al. 1997)

where it was found that a tough crust is formed on the upper surface of the melt pool,

which limits the access of the water overlayer to the melt pool, below the crust.

The top crust formation together with the separation of the melt pool from the crust

due to the concrete erosion marks a sharp decline in the corium coolability. In this

situation, the decay heat is higher than the cooling by the water layer and the ablation

of the basemat would continue.

Recently, achieving coolability by injecting coolant water from the bottom of the

core melt pool has been investigated in the COMET experiments (Tromm et al. 1993,

Alsmeyer and Tromm 1995, Tromm and Alsmeyer 1995, Alsmeyer et al. 1998) performed

in Germany at the Forschungszentrun Karlsruhe. In this scheme, molten corium material,

after release from the RPV, spreads onto a layer of sacrificial concrete material (core-

catcher) located in the containment cavity, erodes this layer and finally reaches a matrix

of plastic water injectors buried in this layer. Upon contact with the molten core material,

the plastic plugs melt and water is injected into the molten corium. The driving water

DECO3I 163

pressure is due to the location of the water reservoir above the containment cavity, In

the COMET expe~ments, the melt was found to quench, in a relatively short time, to

a porous, easily penetrable debris, with continued access of water to the regions of the

solidified debris. Recently, the mode of the water injection has been changed from nozzles

to percolation through a layer of porous concrete.

1.2 Accident progression

When analyzing severe accident progression, one has to identify the phenomena occurring

during inter~tion of melt with in-vessel and ex- vessel structures and with the coolant.

A great number of research programs have been devoted in the last twenty years to

resolve relevant phenomenological issues and to mitigate a severe accident in the extremely

unlikely case it happens. Usually, the experimental approach is coupled with analytical

models and numerical simulations in order to develop the knowledge base on the relevant

physical processes and phenomena. In Figure 1 a schematic of the accident progression

and termination is shown. In the current work, we focus on the ex-vessel melt coolability

by bottom injection of coolant.

After the reactor pressure vessel lower head fails the melt will collect in the reactor

cavity. Several experimental programs have been performed to investigate the melt release

behaviour by the ablating vessel (Sehgal et al. 1997), and the dispersion in the reactor

cavity (Meyer 1999, Sehgal et al. 1997, Dinh et aZ. 2000). After leaving the reactor cavity,

the melt flows onto the spreading compartment of the core catcher. The design of the

EPR includes a spreading compartment of about 170 m2 (Figure 2). Initially, the floor of

the core-catcher will be dry so that a good spreading efficiency can be obtained. The melt

spreading process was the subject of intense research in the EU 4th framework. Several

experimental (Engel et al. 1999, Cognet et al. 1999, Steinwartz et al. 1999, Sehgal et al.

1998) and analytical studies (Spindler et al. 1999, Wittmaack 1999) have been performed

in order to understand spreading mechanisms and to estimate the final thickness of the

melt layer in the core catcher. As soon as the high temperature corium melt begins to

spread on the cor~catcher floor, it will interact with the sacrificial layer and will ablate it.

As the erosion of the s~rifici~ layer reaches the nozzles, in the bottom injection scheme,

164 D. Paladin0 et al.

PHENOMENA

Melt spreading in the cweatcher

Figure 1: A flow chart of the accident progression and termination

the coolant water starts to enter the melt from below. At first, the inflowing water is

evaporated immediately, and completely, due to the high temperature difference between

coolant and melt. The production of steam creates pressure inside the melt and creates

porosity. This process is controlled by the steaming process.

After complete quenching of the melt the long term cooling of the solidified decay-

heated debris should be guaranteed. The efficiency of cooling will depend upon the

structure of the debris and the distance between the nozzles. If a porous structure is

formed, as consequence of the solidification process, and if the distance between the nozzles

is properly maintained, the continuous water inflow will ensure long term coolability.

1.3 A review of the COMET experiments

Up till now, four major series of COMET experiments have been performed. In Table

1 and in the text below the specific objectives and the main findings for each series of

experiments are briefly summarized.

165

Figure 2: The COMET concept

In the COMET-T expe~msnts iron and oxide melt in different percentages (initial

temperature about N 1800 “C) were used as melt simulants. The decay heat was not

simulated. Two possible melt configurations are considered: (i) a stratified configuration

with a layer of the lighter oxide melt located above the metallic melt, (ii) an uniform

configuration, in which metal is dispersed inside the oxide melt due to the strong agitation

of the melt by gas release from the sacrificial layer. The main conclusion that has been

drawn from the transient cooling of thermite melts is that the behavior of the pure oxide

melts does not differ very much from that of the stratified metal and oxide melts as far

as the coolability is concerned. The average porosity obtained was 30% for the metal

portion and 50 % for the oxide portion.

The COMET-U experiments were performed at the ANL in USA and were aimed

at investigating the coolability of corium melts with a high content of UOz. The major

constituents of the melt are 52 % UOz, 16 % ZrOs, 13 % SiOs, 4% CaO and 11% Cr.

The composition of the oxide fraction corresponds to the situation that proceeds after the

erosion of the sacrificial concrete layer. The decay heat was not simulated. In this series

it was confirmed that corium melts behaved in the same way as the thermite melts in the

experiments at FZK.

The COMET-H experiments were large-scale tests performed with thermite melts of


up to 1300 Kg. A decay heat of 450 W/m2 (surface power density) was simulated during

the experiments. This value for the decay heat represents the highest level of decay heat

that has to be managed in the EPR. In some experiments, due to the partial or total

closure of several nozzles by solid debris, the low water flow rate through the cooling

channels to the lower side was insufficient to cool some portion of the melt pool. The

parameters for safe operation of the cooling device were determined.

Table 1: THE COMET EXPERIMENTS

EXPERIMENT INVESTIGATION ON CONDITIONS

COMET-T coolant water pressure simul~t melt of = 60 Kg

Iron+ medium scale with‘5 plugs

oxide-test water supply pressure:

0.2, 0.4 bar

possibility of steam high melt temperature

like-explosion high water supply temperature

melt composition addition of Zr

COMET-U transferability to corium melts of 110 Kg with

real corium melt U02/ZrOa and addition

of sacrificial concrete,

medium scale with 9 plugs

COMET-H large scale with area of N 1 m I.D. with 100

continuous D.H.S. plugs; D.H.S. = 300 KW

COMET-PC possibility to replace the thermite melts of

array of flow channels by a 54-180 Kg

layer of porous concrete

As the COMET concept is under evolution for plant application, the possibility to re-

place the array of flow channels by a layer of Porous Concrete (see Figure 3 for CometPC

concept) through which the coolant water could be supplied to the melt is under inves-

tigation. Up to now three tr~sient experiments have been carried out using thermite

melts of 54 and 180 Kg with an initial temperature of 1800 “C. As the radial erosion of

DECOBI 16’7

the sacrificial layer was higher than expected, flooding started from the side instead from

the bottom and therefore resulted in a typical top flooding scen~io. Due to the existing

sideward bypass for the coolant water, cooling of the bottom melt was however incom-

plete and parts of the melt continued downward propagation, resulting in an erosion of

the porous water-filled concrete layer.

Water lnfioW

Figure 3: CometPC for Bottom Flooding through Porous Concrete

1.4 DECOBI experimental program

A research program named DECOBI (DEbris COolability by Bottom Injection) was ini-

tiated in, and is being pursued at the Nuclear Power Safety Division of Royal Institute

of Technology (Paladin0 et al. 1999a, Paladin0 et al. 1999b). The DECOBI program ad-

dresses the issue of the ex-vessel debris coolability by bottom injection, with the objective

to understand and model the processes of porosity formation and coolability observed in

the COMET experimental program. Research approach of the present work is to perform

small scale experiments covering a wide range of parameters. A series of experiments was

performed at medium (- 600 “C) and at high temperature (- 1100-1400 “C) conditions.

The coolant used was water and the pool simulants were pure molten metal (Pb) and

binary oxide mixtures (CaO-BsOs, CaO-WOs & MnOa-TiOn). The difference in cooling

behaviour and porosity formation during solidification, between the molten metal and

the binary oxide mixtures are rationalized. Parametric models have been developed to

evaluate cooling characteristics for the bottom injection scheme, in particular, to assess


the the amount of melt that can be cooled efficiently with one nozzle, and to assess the

cooling behaviour of less porous debris.

The main objectives of the DECOBI experiments are,

1. to verify whether it is possible to obtain a uniformly interconnected porosity in the

melt pool,

2. to determine the effect of melt material properties on the formation of interconnected

porosity in the melt pool,

3. to determine if with the bottom injection scheme, it is possible to quench the melt

and,

4. to obtain experimental data for developing, models and for the coolability assess-

ment during the prototypic accident scenario.

2 TEST FACILITY

A schematic diagram of the experimental setup used in both MT (Medium Temperature)

and HT (High Temperature) experiments is shown in Figure 4. The setup consisted

mainly of a cylindrical test section, a water supply system to provide the coolant water

to the test apparatus, an inductive furnace for producing the melt and a DAS (Data

Acquisition System). With the exception of the DAS, the entire system is housed in a

containment. The test apparatus is in modular form and the test section consisted of two

cylindrical halves made of stainless steel sheet material (2 mm thick, 200 mm ID, 500 mm

height), the bottom and upper side were made from 4 mm thick stainless steel sheet. A

drainage line for water, during the coolability process, is attached on one of the halves,

at the top. The test section walls were covered with insulation material to minimize the

heat loss to the environment. The nozzles for the supply of coolant, extend from a lower

plenum to the bottom plate stick out into the test section. The nozzles on the periphery

have 4 mm internal di~eter (ID) w h ere the nozzle at the center has 5 mm I.D. The

positions of the nozzles are as shown in Figure 5. Each nozzle sticks out, about, 10 mm

DECOBl 169

A: lower plenum B: water Injection pipe C: nozzles D: melt pouring pipe E: waterdminline F: steam line. G: sacrificial material

ii. giiE%nSd”cer Z: computer 1-8: thermocouples

Figure 4: DECOBI-HT Test Apparatus

above the bottom plate and its mouth was covered by a small sacrificial layer to avoid

melt dropping inside the nozzle during the pouring of melt into the test section. The

nozzles are made of carbon steel and copper pipes were used for their connection to the

plenum. Thermocouples were inserted into the test section through the upper plate and

were kept in the desired locations in the test section with the help of guide tubes in the

upper plate (see Figure 4). The melt was poured into the funnel and a pipe (D) attached

with the top plate guided the melt into the test section. A tube is also attached onto

the top plate to guide the steam out of the test section. The sidewalls were dissembled

after each experiment and the debris were photographed and analysed for the porosity

distribution. To ensure human safety, the experiments were carried out from within a

concrete containment. The coolant was supplied from the main supply line through a

pipe-line connected to the lower plenum. A valve controlled the supply of water to the

test section at a prescribed flow rate. The inlet water flow rate to the test section was

monitored with a flow meter.

170 0. Paladin0 et al.

Figure 5: Lower Section

2.1 Experimental procedure

In each experiment, before the melt was poured in, differents blocks of the test apparatus

were assembled and the nozzles were covered with a small piece of the sacrificial layer.

In the HT experiments, the sacrificial layer, was made of BzOa and of Sn and in the MT

experiments it was made of Pb-Bi. The lower plenum and all the connecting tubes to the

nozzles, were filled with coolant so as to avoid any air pockets. This ensured the immediate

injection of coolant into the melt once the control valves are opened, that is, as soon as the

melt is poured in. The thermocouples were fixed in their respective locations and tested

with the data acqu~ition system (DAS). In the mean time the melt was heated to the

desired temperature in a Sic crucible using an induction furnace. The temperature of the

melt inside the crucible was constantly monitored by means of K-type thermocouple. The

time to obtain the melt at the desired temperature was different for each experiment l.

Once the melt had been generated and the desired superheat was obtained, the funnel was

heated by a gas flame to avoid crust formation during the pouring process. The apparatus

was monitored by a video camera located outside the containment. The picture from this

video camera was helpful to control the pouring process from outside the containment.

After pm-heating the funnel, the door to the containment was closed and the DAS was

‘It took approximately 70 min for each liter of melt produced.

DECOBI 171

started. Prom outside the containment, the furnace was remotely tipped by looking at

the video image and melt was poured into the test section2 The injection of coolant was

controlled from outside the containment and the desired flow rate was set by monitoring

the flow meter through another video camera kept inside the containment. The coolant

injection was stopped once the coolant started to flow out from the condensate pipe. After

each experiment, the apparatus was carefully dissembled for observing the solidified melt

debris. The upper lid and one half of the cylindrical shell were removed, which allowed

direct examination of the top and the middle sections of the solidified debris. After the

melt was removed from the test section, the nozzles were checked for any blockages due

to the melt dropping inside because of late coolant injection. The average porosity, after

the solidification process, E was estimated from the change of the melt height, from before

cooling, Lbcr to after cooling, L,,.

E = La, - Lbc L 00

The thermo-physical properties of the simulants employed are reported in Table 2 and

are compared to the corium properties (Okkonen 1998 and Asmolov et al. 2000).

Two DECOBI-MT experiments were performed using molten metal (Pb) as a melt simu-

lant and water as coolant. In the first experiment 48.5 Kg of liquid lead was poured inside

the test section. The melt temperature inside the Sic crucible before the pouring was

about 550 “C. There was no sacrificial cover to the nozzles in this test. The coolant water

was injected almost simultaneous to the pouring process. Due to the intense melt-coolant

interaction, the lead solidified and cooled down quickly. The post test examination of the

debris showed that about 5.5 kg of debris were expelled to the upper plenum of the test

section. This portion of debris solidified with a high porosity. The porosity measured

for rest of the debris was about 20 %. There was a cavity present in the debris that

‘Pouring times from the furnace to test section are 10 seconds or less. This pouring time must be kept

small in order to minimize the water interaction with only a part of the melt, instead of the complete

melt pool.


Table 2: MATE~AL PROPERTIES USED IN THE PRESENT STUDY

Property Lead CaO-320s CaO-WOa MnOz-Ti02 Corium

Tli, (K) 600 1300 1410 1723 2850

Tsol (K) 600 1250 1410 1600 2800

A& (KJ/Kg) 23.3 460 ? ? 360

k6 (W/mK) 15.6 3.0 ? ? 3.0

k, (WImK) 35.3 2.0 ? ? 2.5

P (Kg/m3) 10500 2500 6500 4300 7450

C&t (J/k Kl 155 2200 ? ? 540

C,,s (J/k K) 129 1530 520 N 900 (?) 410

CaO-BzOa has 30-70 wt-% composition (non eutectic)

CaO-WOs has 75-25 mol-% composition (eutectic)

MnO~-TiO~ has 80-20 mol-% composition (non eute~tic)

Corium is a UOz-ZrOs mixture of 80-20 wt-% composition

? to be experimentally determined

occupied about 6 % of the volume, and presumably this was created by steam jetting out

from the closest nozzle. After the test, only two nozzles were found open, one nozzle was

completely closed and the other two were partially open.

In the next experiment, about 68 Kg of molten lead were poured inside the test section.

The nozzles were initially closed with a sacrificial plug, made of Pb-Bi. The coolant water

was injected at room temperature. The nozzles were found to open themselves 4-5 set

after completion of the pouring. Again, due to the intense melt-coolant interactions

about 20 kg of lead was ejected to the upper plenum of the test section. This part of

the melt solidified with a high porosity (see Figure 6). The melt solidified very quickly

and the cooling of solidified debris was very rapid (see Figure 7). The experiments, with

a metallic melt suggest that intense melt-water interactions may take place, owing to

high conductivity of the melt. Also, the melt temperature may not be high enough to

preclude nucleate boiling. The porosity observed was relatively high in the upper portions

of debris. The debris were “cemented” into a continuum of hard, though porous material.

DECOBI 173

Figure 6: The post-test cross section of the Pb-Bi debris cake.

600.0 I I 1

i 1’

- TC1 (Melt bulk. Above the nozzle) l ----+ Tcz Melt bulk. Away from the nozzle)

500.0 I, ’ i

g 400.0

3 3000

! .

i-” 200.0

100.0

i 0.0 L

0.0 I

200.0 I

400.0 Time (set)

I 600.0 600.0

Figure 7: The temperature history of the second experiment with Pb-Bi as melt simulant.


4 RESULTS FROM DECOBI-HT EXPERIMENTS

A total of twenty expe~ments were performed using water as coolant and the three binary

oxide mixtures: CaO-&OS, CaO-WOa and MnOz-TiOz as the meltsimulants for corium.

With the use of these three binary oxide melts, we have attempted to simulate the pro-

totypic conditions in which the UOz-ZrOz-Zr melt, which initially has very low viscosity

and ceramic structure , ablates the concrete, resulting in mixing of the glass-forming SiOz

in the melt pool, which changes its structure to that of a glass-type material and incresses

its viscosity greatly.

4.1 CaO-B203 as melt simulant

A total of fifteen experiments were performed using water as coolant and the binary

oxide mixture 30wt%CaO-70wt%&Oa as the simulant melt for corium. Table 3 lists

the experimental conditions for each experiment and also some of the main experimental

results. It should be noted that some of the experiments were repeated to be assured

of the test conditions. The main parameters that were varied are the coolant flow rate

and its temperature, the number of injection nozzles and the melt volume (or the layer

height). The results are organized in two categories as one-nozzle experiments and five-

nozzle experiments.

4.1 .l one-no5sle experiments

Five experiments (CBl, CB2, CB13, CB14 and CB15) were performed with coolant in-

jection from the central nozzle only. In all of these experiments a small piece of debris

from the previous experiment was used as sacrificial layer on the nozzle.

The CBl was a scoping experiment to test the instrumentation. The post-test cross

section of the debris from the CB2 is shown in Figure 8. The results indicated that there

were two distinct regions present in the solidified debris. In and around the coolant flow,

the melt was quenched rapidly and the debris looked darker. The surrounding regions,

DIXOBI 175

Table 3: Experimental conditions and results

-

CB4 CaO-B&s 5 ‘4 4.0 12.7 1157 130 27 1.5 41

CB5 CaO-B@s 5 4 4.0 12.7 1157 130 90 1.2 16

CB6 CaO-B$& 5 4 4.0 12.7 1070 47 90 0.8 -

CB7 C&O-B&$ 5 4 6.0 19.1 1157 130 27 1.5 38

CB8 CaO-B203 5 4 6.0 19.1 1157 130 27 2.3 44

CB9 CaO-B&s 5 4 6.0 19.1 1200 173 27 2 30

CBlO CaO-BzOs 5 4 6.0 19.1 1250 223 27 2 20

CBll CaO-B203 5 4 5.1 16.2 1200 173 27 1.2 29

CB12 CaO-B203 5 4 5.0 15.9 1250 223 27 1.6 32

CB13 CaO-B&a 1 4 6.0 19.1 1250 223 27 0.3 10

CB14 CaO-B&3 1 4 4.5 14.3 1250 223 27 0.38 10

CB15 CaO-B&3 1 4 5.5 17.5 1250 223 27 0.85 17 - which look bright, cooled quite slowly.

Figure 9 shows the temperature history for the two main regions of the solidified debris,

wiz, the quenched region close the nozzle and the surrounding slowly-cooled region. The

coolant flow rate was varied among the experiments CB13, CB14 and CB15. The initial

volume and height of melt were almost the same for each of these three experiments and

were approximately twice that of CB2. It was found that for low coolant flow rates (CB13

and CB14) the evaporation process occurred in a “eruptive way” and a portion of debris

was finely fra~ented and was partially expelled out of the test section. The post-test

debris showed again the formation of a quenched region above the nozzle and fine porosity

in the upper portion (Figure 11). The experiment CB15 was performed by injecting the

D. Paladin0 et al.

_- .-... -

Figure 8: The post test section for the experiment CB2.

coolant at a higher flow rate. In this experiment, intense melt-coolant interactions leading

to eruptions did not occur. It seems that at low flow rates, a water accumulation occurs in

the lower part of the melt and a steam spike results in p~hing part of the melt upwards,

and fra~enting it in this process. Figure lob, shows the pressure spike at low flow

rates which is due to water accumulation and subsequent eruption creating the flow path.

At higher flow rates (> 0.4 lit/min/nozzle), the coolant creates its flow path through

the melt, without generation of excessive steam (Figure 10a). Somewhat less melt-water

contact occurs and there is a greater fraction of melt volume which remains unquenched

(Figure 12).

DECOBI 177

.w I I

1 500.0 1000.0 15 Time (set)

Figure 9: Temperature history for the experiment CB14

0.40 4.9 -

0.20 3.0

8 0.20

I 2.0

a. 0.10

1.a 0.00

,,,a 0.0 200.0 ” 4w#O Boa0 300.0

0-a

Figure IO: Pressure in the coolant injection chamber


20 cm

Figure 11: The post-test cross section for the experiment CB 14.

20 cm

12: The post-test cross section for the exneriment CB15.

DECOBI 179

4.1.2 five-nozzles experiments with cold water for coolant

A total of eight experiments (CB3, CB4, CB7, CB8, CB9 , CBlO , CBll and CB12) were

performed injecting cold water through all the fives nozzles into the hot melt. As before,

each nozzle was initially covered at the top by a small piece of debris from the previous

experiments. The salient results from these experiments are:

l the post-test observations of the debris (Figure 13) show a highly porous region,

above each coolant nozzle and a non-porous region surro.unding these porous regions.

l the measured temperature history indicated rapid solidification and, then, quenching

of the melt, to near saturation temperature of the coolant, in the regions above the

nozzle exit, extending N 3 cm (see, for example, thermocouple TCl in Figure 15

from the experiment CBEI). The adjacent region cooled slowly by conduction to the

surroundings (as shown by thermocouple TC2 in Figure 15).

l the average pressure reading indicated an initial peak of overpressure due to the

steam formation during the coolant path formation and then the pressure decreased

to 0.1-0.2 bar (depending on the coolant flow rate), once the paths are opened up

for the flow (Figure 16),

l the average porosity measured, by the increase in volume after solidification, was

about 20-40%. The porosity (see Figure 13) in the upper part of the debris was

uniformly distributed. Large interconnected holes were found in the debris, formed

possibly due to the sloshing of the melt during the melt-coolant interactions. In the

lower part of the debris the formation of an interconnected channel like structure

was noticed. As shown in Figure 13, this region, extending radially away from

the nozzles, is darker due to the rapid solidification. outside this region the debris

appear more bright and has no porosity. These regions seems to have had no contact

with the coolant. These observations are quite similar to the observations made from

the single nozzle experiments.

When the coolant flow rate was varied, a tendency similar to that observed in the one-

nozzle experiments was found. In these experiments, for intermediate coolant flow rates


(0.3-0.4 1X/ * / 1 mm nozzle) branched channels were formed inside the debris, while for higher

flow rates, the coolant traverses the melt pool rapidly and the expansion due to the phase

change (which cause the formation of channels) is less pronounced. As shown in Figure 16

(compare it with Figure lob), in the experiment performed at a flow rate of 1.6 lit/min into

five nozzles, the steam accumulation resulted in a eruption of the coolant and subsequent

well mixing of the pool in the upper part (see Figure 14). Large interconnected holes are

also seen in many parts of the debris.

20.0 cm 4 *

Figure 13: The post test section of CB7 showing a porous debris above the nozzles (darker

region) and a non-porous region (bright) adjacent to the porous regions.

Figure 14: The post test section from the experiment CB9.

DECOBI 181

1500.0

1000.0

500.0

I f

H TCl (Melt bulk. Above the nozzle) U TC2 (Melt bulk. Away from the nozzle)

200.0 400.0 600.0 time, s

Figure 15: The temperature history for the experiment CB8

2.5

1.5

0.5

-0.5 fOOO.O

Time’ (MC)

Figure 16: The pressure history from the experiment CB12


4.1.3 five-nozzles experiments with hot water as the coolant

The experiments CB4 and CB5 were performed injecting hot water (90 “C) in the super-

heated melt. The following characteristic events were observed from these experiments.

l In both of the experiments, quenching of the melt did not occur and the coolability

of the solidified debris proceeded very slowly.

o The pressure during the injection was undergoing large oscillation, probably due to

high steam generation in the coolant line itself, since the temperature of the coolant

was near its saturation temperature.

l The post-test cross section (see Figure 17) showed that the porosity formed, did

not spread radially sufficiently, or in other words, a large fraction of the melt did

not come in contact with water and cooled slowly by conducting heat to the small

regions where porosity was formed and water flow was maintained.

Figure 17: The post test section from the experiment CB5.

DECOBI 183

4.2 CaO-W03 and, Md3pTiO~ as melt simulants

A total of six experiments were performed with, CaO-WOs and MnOs-TiOs as melt simu-

lants (see Table4). The melt simwiantn Ca@WO3 and MnO-TiOs are ceramic-type oxides

where as CaO-B&s is a gl*Ejipe oxide. The viscosity of CaO-BsOs near its liquidus

is much higher when corn&red to a ceramic-type oxide melt and increases rapidly with

cooling. In the experimtits with MnO-TiOs, whose melting point is the highest among ’

the three oxide simulants that we used, an intense melt coolant interaction resulted in

some parts of the debris getting thrown out of the test section. In all the six experiments,

the pressure history indic&ed ‘an over-pressure of only 0.3-0.3 bars (see Figure 21) and

there was no indication& an “eruption” as found in some cases with CaO-BsOs. The

Table 4: Experiment conditions

TEST MELT N, D, Vmelt Lbc T’,i mm,, T,i G &

(mm) liters (cm) (“C) (“C) (“C) (lit/min) %

post-test section of the solidified debris showed a different morphology compared to that

obtained with CaO-B2Os. All the thermocouples conkting the melt (see Figure 20), at

different positions show ripid solidification and quenching, in about 40 sec. The post test

examination of the solidifkd &&is (@gums 18 and 19) shows the formation of a well

distributed porosity, estimated to be about 40 %.


Figure 18: The post-test cross section from the experiment CWl

Figure 19: The post test section from the experiment MT1

1500.0

E looo.o

s ti $ e t- 500.0

DECOBI

I /

HTC1 (Melt bulk. Away from the nozzle) H TC2 (Melt bulk. Above the nozzle)

500.0 1000.0 1 Go.0 Time (SW)

Figure 20: The t~mp~rature history of the experiment MT1

Time (SW)

185

Figure 21: The pressure history from the experiment MT1

186

5 ANALYSIS

D. Paladin0 et al.

The analysis reported in this section aims to obtain quantitative information on the

channel formation observed in the the expe~ments with CaO-BzOs melt simulant, and

on the coolability by conduction for the non porous portion of debris. The ~sumptions

in the models are based on the observations obtained in the experiments performed.

5.1 Modeling of the porous region (branched-channel)

According to the observations made in the CaO-BzOs experiments, the solidified debris

had two distinct regions, vk,

l a branch-channeled region (gray) in which a number of branched channels, with

diameters of the same order of magnitude as the nozzle diameter, are distributed

across and this region was quenched.

l a non-porous region (white) in which direct contact of the coolant with the coolant

with the melt did not occur and it solidifi~ quite slowly.

In this section, an energy balance between the

branched regions and an expression to assess

obtained.

coolant and the melt is performed for the

this proportion in the solidified debris is

The schematic representation of the solidified debris is shown in Figure (22). The

distance between the nozzles (I;n) is the sum of the non-porous region (L,,) and the

branched regions (Lb),

.&, = L,, + a$,. (2)

The objective of this analysis is to obtain a relationship for Lb with the parameters of the

coolability process.

The coolant expansion while rising inside the melt, due to its phase change results

in an increase in the interfacial contact area with the melt, and due to this effect, the

DECOBI 187

Figure 22: Schematic representation of the debris

convective heat transfer becomes very effective. The energy removed by the coolant is

expressed as I’ - [C,,, . AT,,, + h, + Cp,#t * AT&,]c where I’ is the flow rate of the coolant.

For conservation of energy, this should be equated to energy removed from the melt

!P~h~Aeh.Nn~~,,,+“. Here we introduced a factor Q‘, which accounts for the increased

interfacial area, due to expansion by phase change. The Ad = (7r - II,. L,) is the contact

area corresponding to a branch whose diameter is assumed to be equal to the nozzle

diameter and its height equal to the melt layer height. The factor 9 is greater than one.

This was done in an effort to obtain the amount of the melt that can be cooled due to

direct contact heat transfer with the coolant (the proportion of the branched regions),

~Z%,W is the averaged temperature difference between the melt and the coolant. By

equating, the \k can be evaluated as

The expansion factor (@I) can be interpreted as an average number of channels, of sizes

comparable to the injection nozzle, that are formed inside the solidified debris.

188 LX Paladin0 et al.

Now, an appropriate heat transfer coefficient h has to be found. Our case correspond

to boiling heat transfer to a gas from a high temperature vertical surface. Chu (1993)

has reported the heat transfer coefficient for turbulent film boiling on a vertical surface.

Analogous to turbulent convective heat transfer, this can be expressed as,

Nu=C.R$ . (4

The above correlation was tested by Chu (1993) against data on nitrogen and helium and

for a large range of the wall-coolant temperature difference, a constant value of 200W/m2

for h can be assumed.

Once XP is known, the next step is to determine the distribution of these Q number of

channels in the quenched portion of melt. This will, in turn determine the span of the

branched channels region, Lb, which is the primary objective. A simple way is to use the .

information on porosity, E, obtained from the experiments. The volume occupied by the

channeled bed region is Q - * - L,. Then, the porosity3 is simply (see Figure 23),

hr-D;-L, vL;*L,

=e (5)

and the extension of the branched region becomes,

Lb,mod = & - (6)

The above model uses the porosity information obtained through experiments to estimate

the optimal distance between the nozzles. The values of the parameters used to calculate

Lb on the DECOBI-HT experiments are reported in the Table 5 and it is seen that the

values obtained by the model are close to the values measured in the experiments from

the debris.

The formation of channels was also observed in the top flooding coolability scheme.

Stubos and Buchlin (1994) explained that the channel formation was due to the fact that

the large amount of vapour generated suddenly resulted in a boiling lift, in a piston-like

manner, in the upper part of the bed _.I sod resulted in formation of channel-like structure in

the overlying bed. They found that the number of channels formed and their distribution

3This is based on the assumption that porosity is confined to the branched channels region only

DECOBI 189

is optimized to minimize the pressure drop requirements, while their final lateral length is

determined by factors that are functions of the bed and of the fluid characteristics. The

channel which is defined as the number of channels randomly distributed per ,*-- _------__ **

.’ -.

,’ *.

0

‘\

‘\\

I’ .’

/” r\ 0 0 ‘\\*

I

:

;O "0

, L

0 \ 0 t \ \ ‘P \ \ \ 0 0 \ ‘.

\

0 \ L I I ,

Figure 23: Schematic top view of the bed surface

unit cross-sectional area (similar to Figure 23) of the bed was found experimentally by

Jones et a$. (1984) and it depends very weakly on the bed height. They can be calculated

as

where the spacing between channels < corresponds to the,

Taylor wavelength, as given by ‘Zuber (1958)

Now another estimate for Lb can be obtained by combining the new distribution factor,

(7) following, modified critical

Y and the channel number, Q that we obtained. The final expression is,

L (9)

To estimate Lb*, the value of am,=, the inter-facial tension between the melt pool and the

gas coolant should be known. As it was not found in the literature, a reasonable estimate

of 0.029 N/m, for the inter-facial tension for superheated vapor in a liquid, provided a good

comparison between the results from the calculations and the experiments (see Table 5).


Both the approaches described in this paper predict the porosity reasonably well,

which can be employed for the assessment of long term coolability of the debris.

Table 5: PARAMETERS FOR DECOBI EXPERIMENTS

Exp. CB4 Exp. CB7 Exp. CB8

5.2 Modeling of non-porous portion

As stated in the previous section, the bottom injection scheme resulted into a region

with porous debris and another with non-porous debris. Also the temperature data from

the five nozzle cold water experiments indicates a slow cooling down of some portion of

melt. The reason for these different cooling rates is that the coolant contacts only a

portion of the melt and the other portion of the solidified debris is is not quenched into

a branched-channel configuration.

DECOBI 191

This non-porous region has a span given by (see Figure 22),

L, = 1;, - Lb (10)

and it would lose heat only by conduction to the coolant passing through the adjacent

channels. To estimate the cooling of the non-porous region, the unsteady conduction

equation, with or without heat generation included was solved with appropriate boundary

conditions, to account for the heat exchange with the adjacent coolant flow. In the present

formulation, the co-ordinate system is fixed in the center of L,. Since the problem is

axi-symmetric, only one-half of the domain, L,, is considered. The formulation of the

problem in terms of 8 = T - T, is

The initial condition is,

and the boundary conditions are,

_K, . se(p) =: h. e($t); In the above equations cr, is the thermal diffusivity of the melt in the solid state and ps,

C& and K, are its density, specific heat and thermal conductivity respectively.

The heat transfer from the sides, to the coolant in the channels, is represented by

a convective bounds condition with h the heat transfer coe~cient associated with the

heat removal. The above system of equations are parametrized by these variables.

Since the term containing qr is added to the homogeneous part, the solution to the

present problem can be written as,

wx, t) = 1/)(x4 + 9x4 (15)

so that the heat generation is included in the formulation of one-dimensional, steady state

problem, (b(z) (Arpaci 1966). The first term on the RI33 is a solution for the homogeneous

part, which is without the term containing q’f’v. The particular solution, 4(x), satisfies,

(16)


with, w4 = 0.

6x ’

c&q = 0

The solution to the above equation is,

W q:’ . G&n

= ; * [I - (2!$

The solution to the homogeneous part, $(x,t) satisfies,

W a2+ -=Q@ at

09)

(20)

with,

+h, 0) = 0, - 4t4 (21) ~~~o~t) = 0

_K~wv$i (22)

= h.$(+q) (23) Since the above system is linear, a solution of the type $(s, t) = X(Z) - 7(t) can be

obtained. The final solution is of the form,

IlrW) = c;=p=, a, e-f: Fo cos(& X)

where, X =&. The &‘s are the zeros of the ~h~~teristic tr~~endenta~,

&, sin[, = Bi cos&.

where Bi = hL,,/k and Fo = cQ/L2_ are, respectively, the Biot number and Fourier

number, the characteristic parameters of the conduction heat transfer. The coefficients

a, were obtained in the present work employing the corresponding boundary conditions.

The details on how to obtain these coefficients for a series of orthogonal functions, like

~2~), are given in Arpaci, (1966). Using this method a solution was obtund following,

(25)

(26)

DECOEI 193

where, 0, is ‘the initial temperature difference between the hot solid debris and the coolant

(= To - T,). The final expression for the coefficients, h, is then obtained as,

(27)

The expression for the temperature change due to the coolant passage on its sides was

finally obtained by combining equations (15), (19), (24) and (27). As can be seen, it is a

function of the width of slowly cooled region, L,, the decay heat generation, q”“,, and

the melt properties. The results from this analysis. can be used to assess the long term

0 100 200 300 '440 500 600 time(sec)

Figure 24: Long term cooling of the non-porous regions in the experiments. The ex-

perimental results are shown as points and the model results are shown as lines. Model

calculations are done for qy =0

coolability.

The comparison of the results from DECOBI ~calculated with qy=O) are presented in

the Figure 24. The decrease in temperature of the solidified debris due to the continuous

passage of the coolant in the ~joining regions is predicted quite well by the model. The

nature of cooling or the shape of the cooling curve, which depend on the flow rate is also

predicted well. The results for the corium case in order to assess the prototypic scenario

are reported in the next section.


6 MELT COOLA~~L~~Y IN A

NARIO

PRO~O~Y~~C SCE-

In this section, the coolability of the liquid melt is analysed with known coolability mech-

anisms.

6.1 Time to solidify a melt pool

In a proposed design, the water supply system is to be buried in a layer of sacrificial

concrete. The water can be injected into the melt pool only after part of the sacrificial

concrete layer is ablated. Water can also contact the melt pool from top, if top flooding

cooling scheme is also employed. Figure 25 represents the scheme of such a cooling process.

The energy balance for coolability and quenching of a melt pool can be expressed as,

Overlying water

Coolant water injection ’

Figure 25: The identification of heat transfer regimes in the bottom coolability

(the distances are out of proportion)

scheme

(28)

DECOBI 195

In the left hand side of this equation the first two terms expresses the energy that is

removed to solidify the unit mass of melt, the third term is the decay heat produced by

the melt and it depends on fuel content, accident scenario and time after the accident.

We can express the decay heat as,

The right hand side of the equation (28), is made up of different heat transfer coolability

mechanisms and can be expressed as:

Qloss = Qc + Qt + f?& (30)

The heat removed by the bottom injected coolant (qc) is a function of the flow-rate,

residence time, melt pool height and cooling efficiency.

AH the experiments performed in DECOBI program, showed that for melt pool height

in the range lo-25 cm the exit temperature of the steam was almost constant during the

coolability process. Thus,

f31)

Regarding the heat removed by the top layer, we have two cases,

l a dry case (no water overlayer),

m a wet case (water overlayer).

In the first case the heat is removed by radiation and in the second case the heat is taken

out from the top surface of the crust layer through film boiling and radiation. In the

second case we can express the heat transfer as (Bui 1998),

qt = qfb + Gad = fhfb * (%r - %)cP + %n(~; - 1”,>] * A, (32)

where T, is the crust temperature at the outside edge, hfa is the heat transfer coefficient

for film boiling, ~7 is the coefficient ~count~g for the au~entation of film boiling heat

transfer due to bubbling, u is the Stefan-Boltzmann constant (a = 5.71. 10-8TV/m2(“K)4)

1% D. Paladin0 et al.

and cem is the crust surface emissivity. The element of area which is considered for the

heat transfer is A,. The film boiling heat transfer coefficient hfa can be evaluated using

Berenson’s co~elation (Bui 1998))

where sub~ripts w and v denote water and vapor, respectively.

Ah,, = huv + 0.5C,,v(T, - T,,t) (34)

The third term on the RI-IS of equation (30) represents the heat lost by corium to the

underlying concrete.

Following Bradley (1988) model, the heat transfer rate qa, from the molten pool to

concrete in the presence of a slag growth, is modeled as,

q. = 0.29. h~u m (Tp - T,) . A,, (35)

where TP is the pool temperature, T, is the concrete ablation temperature, and hK,, is the

Kutatel~ze heat transfer coe~cient obtained from tests with gas blowing into various

fluids through perforated plates.

The heat transfer coefficient hKu is correlated ss function of several parameters in the

form,

hK,, = 1.5 . 10c3 - ( Cp,m ’ h ’ P)2/3 . K1/3 . [

9

where C&,, is the specific heat for the pool; jo is the gas superficial velocity; p

pressure at the concrete/co~um interface; g is the cavitations const~t; K,, pm,

are the. thermal conductivity, density, and surface tension, respectively.

The transition velocity, j,, is indicative of a change in the gas bubbling behavior

obtained from

jT? = 4.3 * lo-‘2

(38)

is the

and CT

and is

(37)

The time scale for the complete solidification of the melt is then obtained from the equation

(28) as:

TN M + [CP s ATOP + Ahfus]m

Qc + Qt + Qa - a (38)

DECOBI 197

Figure 26 shows the plot of the solidification time scale for the case of corium and the case

of the oxide mixture (Ca)-B&). Note that the tendency is similar for both materials

and a sharp difference appears only at very low coolant flow rates due to higher values

of heat of fusion and specific heat for the oxide which yields longer solidification time.

The concrete will ablate even after the nozzles are open, but until the melt drops in

Melt mass 100 Kg, Superheat 180 K I”““’ ” ” t : ’ “, - I

500.0

- P

400.0

B p 300.0

8 I! (d 200.0

100.0

0.0 0.0 500.0 1000.0 1!500.0 2000.0

~li~~~~n t&l8 -18 (WC)

Figure 26: Comparison of solidification time scale between the oxide and the corium melts.

The decay heat, q& is chosen to be zero.

temperature to below the concrete ablation temperature (which is 1100 to 1300 “C).

Now we want to compare the decay heat qd with the heat qc removed by the injected

coolant. Let us take a scenario where the nozzles are embedded in the core catcher in a

square grid ‘with a separation of 8 cm, the melt layer thickness is 25 cm, having a porosity

(E) of 30 % due to the bottom coolant injection, the average decay heat is qv N lMMr.rr~-~.

Then the decay heat power to be removed by each nozzle is,

!?d N 9: ’ Vm,ln * (1 -E) N l.lKW. (39)

If the coolant water flow rate I’ is 0.5 kg/min per nozzle and with complete vaporization


and an exit steam temperature of 800 “C, we obtain the energy removal rate by the coolant

[equation(31)] to be,

qc - 28.7KW (40)

So the energy removed by the coolant injected is much higher than the decay heat to be

removed by a single nozzle and there is no doubt that, from heat transfer point of view,

the corium will be quenched.

6.2 Non porous region coolability

To conclude this study, the analysis of the non-porous region was extended to evaluate

the effects of local heat transfer coefficient h and the effective nozzle distance. A situation

can arise where some nozzles do not open (as found in the experiments)

distance between two working nozzle becomes large.

and the effective

As seen in the DECOBI-HT experiments during the melt-coolant interaction only

a region of the melt about 5-6 cm diameter interacted directly with the coolant and

solidified into a porous debris. The remaining regions of the debris did not demonstrate

any porosity and in the long term they will be cooled by conduction heat transfer to the

porous regions which gets continuous passage of the coolant flow.

The effect of the heat transfer coefficient h (between coolant in the branched channel

region and the non-porous region) is shown to be negligible in Figure 27.

The temperature history of the solidified debris is shown in Figure 28 for a location

at the center line between two nozzles and the decay heat, qy , is kept at 1 MW/m3. The

effect of the nozzle pitch is shown (the L, increases with nozzle pitch).

It should be noted that the choice of the distance between the nozzles is fundamental

for the effective stabilization of the hot corium melt and how, for large values of L,,

( for example N 16.0 cm in Figure 28) the cooling of non-porous debris, by conduction,

would proceed very slowly. In this case, this region of melt pool will keep ablating the

concrete.

2500-

s 2000-

0 e

9500- II! d E s!

lOOO-

500-

DECOBI 199

, I

- h=lOOO

El-

--h=500 .-.-h=250

Figure 27: Effect of the variation in heat transfer coefficient, h on coolability (Lcon=8

3500- 1 I

3OOQ- .,-'-'-'-.___, _..@ ._ \ -._ \ -.w. \ -._, -.-, 2500- \ -,.._, \ -4.w. -._,

o^ \ -.-._. \ -.-._.

iiT g2000

f

~l500-

0

WOO- . .

-. --..._ 500- --.__ ----_______

o- I L I 0 1000 2ooo 3Oca 4ooO 5000 6000

time(B)

Figure 28: Effect of the variation in the width of the non-cooled regions, denoted as L,

(qr=l MW/m3 and h= 500 W/m2K).


7 SUMMARY AND CONCLUSIONS

This paper presents the experimental results obtained and analysis performed in a research

program named DECOBI, ongoing at RIT/NPS to investigate ex-vessel melt coolability

by coolant injection from bottom of the melt pool. The analyses performed are one dimen-

sional and do not consider the phenomena of multidimensional mixing and entrainment.

They, are, however, phenomenological and are based on experimental observations and

the measured data. In the medium temperature (DECOBI-MT) experiments the melt-

coolant interaction characteristics were investigated with a pure molten metal pool. In

the high temperature experiments (DECOBI-HT), binary non-eutectic oxides were em-

ployed whose compositions were chosen to simulate the corium (UOs - ZrOz) as closely

as possible.

The low viscosity and high conductivity of the liquid metal allowed mixing of the

coolant with the melt and high rates of heat transfer. As a consequence, the solidification

occurred quickly and high steam pressure was generated in the test section. The upper

portion of debris had higher porosity in comparison to the lower portion. The first set

of high temperature experiments (DECOBI-HT) employed CaO-BsOa melt at 1100-1300

“C which has a glass type structure with low conductivity and high viscosity. Later

experiments were performed with the binary oxide mixtures CaO-W03 and MnOs -TiO:!,

both of which have ceramic type (similar to UOs - 22-0s) structure, with low conductivity

and relatively low viscosity which does not increase greatly as the melt superheat decreases

and when the temperature decreases below the liquidus temperature. With the use of

these three binary oxide melts, we have attempted to simulate the prototypic conditions

in which the UOp-Zr02 melt, which initially has very low viscosity, ablates concrete,

resulting in mixing of the glass-forming SiOs in the melt pool, which changes its material

structure and increases its viscosity greatly.

The data obtained from the high temperature experiments with ceramic structure

melts show that for the low viscosity binary oxide melts, there is substantial mixing of

the melt with the coolant. The high temperature and low conductivity lead to film boiling,

fragmentation and solidification of the melt pool and creation of highly porous (40 to 50

DECOBI 201

%) debris. The melt is quenched quite readily. The cooling scenario is similar to that for

~oolability of the metallic melt, however much more benign and the pressure ~uctuation

due to steam formation and quenching are not very violent.

Contrary to the complete coolability and quenching obtained for the high temperature

ceramic type low viscosity melts, the CaO-B&a melt pool cooled in a channel-like volume

above each open nozzle where the coolant came in contact with the melt and solidification

and quenching took place. The regions of the melt beyond the channel did not come in

contact with coolant and those regions cooled down slowly. The post-test examination

showed that substantial porosity was created in the channel regions but very little in the

other regions. The melt in the non-channel regions cooled by conduction to the cooled

channel regions. This was modeled in the analysis by the unste~y heat conduction

equation and the cooling rate of the unquen~ed regions of the melt wad5 found to be

described quite well by this analysis. It was found expe~mentally that the cooled and

porous channeled region extended 2.5-3 cm around each nozzle. When the flow rate was

decreased, the melt-coolant interaction was found to be more energetic and resulted in an

eruptive ejection of melt from the test section. This lead to the creation of high porosity

at the upper portion of the debris.

Considering the prototypic case of

bottom injection of water, it appears

cooling and quenching a large corium pool with

that the melt pool will be much easier to cool,

solidify and quench if water is delivered as early as possible so that as few concrete

products are mixed in the melt as possible. However, even later on, if the pitch of the

delivery nozzles is kept below 8 cm, and the nozzles remain open melt could be quenched

and the accident stabilized.

The melt viscosity seems to play an important part in the bottom coolant injection

phenomenology. Low viscosity melts mix more easily with the vaporized coolant and would

quench earlier. This would also lead to high steam pressures. High melt temperature

enforces film boiling which leads to a much more orderly coolability scenario.

Creation of porosity in the melt by the generation of vapor and its radial and axial

movement due to the local pressure generation, appears to be the controlling mechanism

202 I). Paladin0 et al.

of coolability. The continued accessibility of the coolant in these porous regions leads

to melt coolability, solidification and quenching to the coolant temperature. The regions

of melt which do not get in contact with coolant are cooled by heat conduction to the

regions which are in contact with the coolant. By provision of a large number of nozzles,

bottom injection ensures that (a) there are large regions of melt which are quenched, (b)

there is a large surface area for conducting heat away from the uncooled regions of the

melt to the cooled regions. These two factors provide the success of the melt coolability

with bottom injection of the coolant.

ACKNOWLEDGMENTS. This work was supposed by the Swedish Nuclear Power

Inspectorate, the European Union, the US Nuclear Regulatory Commi~ion, Swedish and

Finish Power Companies, Nordic Nuclear Safety Project and Swiss Nuclear Inspectorate.

8 Nomenclature

ARABrC an A aPr

Bi

c

CP Ll

Fo

9

G

Gf23

h

hb K

L

iv

Fourier coefficients,

Spreading area,

Biot number, &

co~t~t,

specific heat, J/kg . K

diameter, m

Fourier number, $

gravity acceleration, 9.8 m/s2

volumetric flow rate, lit/min

boiling Grashof number, ?~~~ 0 Z3

local heat transfer coefficient, W/m2 K

heat of vaporization, J/Kg

thermal conductivity, _wlm. K

length, m

number of nozzle,

LlEcoBI 203

boiling Prandt number, w

decay heat, W/m3

heat removed, W

RayIeigh number, Grg - Prs

temperature, K

radial coordinate, m

length scale, m

the thermal diffusivity (A), m2/sec

heat of fusion, J/kg

dynamic viscosity, Kg/m - set

kinematic viscosity, m/s2

multiplication factor for channels

surface tension, N/m

density, Kg/m3

channels density, rnw2

porosity,

parametric temperature, K

modified critical Taylor wavelength, m

eigen~u~,

SUBSCRIPTS

a

ac

b

bC

b, mod

b*

.o .

c, i

ch

average,

after cooling,

pertains to the branched portion,

before cooling,

model for branched channel portion,

pertains to the branched portion from channel theory,

coolant,

coolant initial condition,

channel,

204

con

m

mod

m,s

n

s

st

sub

sup

w

wn

D. Paladino et al.

pertains to the conductivity portion,

melt,

model,

melt superheat,

pertains to the nozzle,

pertains to the solid phase,

steam,

subcooling,

superheat,

water,

working nozzles,

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DECOBI 205

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Documents

DECOBI: investigation of melt coolability with bottom coolant injection