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Quenching of debris beds having variable permeability in the axial and radial directions
Nuclear Engineering and Design 99 (1987) 275-284 North-Holland, Amsterdam
275
QUENCHING OF DEBRIS BEDS HAVING VARIABLE PERMEABILITY IN T H E A X I A L A N D R A D I A L D I R E C T I O N S * V.X. T U N G a n d V.K. D H I R School of Engineering and Applied Science, University of California, Los Angeles, Los Angeles, CA 90024, USA
In this paper experiments and analyses for the cooling conditions of debris beds with variable permeability in the axial and radial directions are performed. In the experiments steel particles varying in diameter from 1.6 mm to 6.35 mm were used to simulate the core debris beds. The particles were heated inductively to temperatures up to 630°C in an inert atmosphere. Thereafter, the particulate beds were flooded either from the top or from the bottom. In the experiments water at room temperature was used as the coolant. Several configurations of the particulate bed yielding extreme variations in permeability were studied. Analyses to establish the coolability limits have been performed.
I. Introduction The cooling conditions in a Light Water Reactor can be significantly impaired in a loss of coolant accident. Continued undercooling of the core will result in overheating of the fuel elements with an eventual loss of integrity. Such a severely degraded core may behave as a porous layer composed of heated particles of different sizes and shapes. Before continuous cooling of this layer of very hot particles can be established, the particles need to be quenched either by flooding from the top or by flooding from the bottom. In the event the reactor vessel fails, the debris will drop into the reactor cavity and interact with the concrete underneath. As a result, gas is generated at the bottom during quenching and will flow through the debris bed. Several studies on quenching of debris beds by top flooding have been reported in the literature. Armstrong et al. [1] studied top quenching of 75 cm deep beds composed of 3.1 mm diameter steel particles at a maximum temperature of 550°C. By assuming that the steel particles were completely quenched and cooled to saturation temperature of water as water penetrated into the bed, the quench front velocity was found to remain constant with time. For water at an inlet temperature of 24°C the quench front velocity was found to be 0.21 m / s compared to a prediction of 0.26 m / s based on counter current flooding limit. The agreement * Work supported by EPRI, Palo Alto, California, USA
between predictions and experimental results is indeed good considering the simplicity of the model. However, it must be pointed out that as the particle size is increased, heat transfer will be limited by radial conduction in the particles and the quench front may lag behind the liquid penetration front. Cho and Bova [2] have reported that during flooding from the top, liquid penetrated faster in the middle of the bed than in the outer regions. This is indeed an interesting observation. Intuitively one would expect the liquid to penetrate faster near the wall due to higher permeability there. It is possible that the large thermal mass of the wall kept the adjoining region of the bed hot for a longer period of time. Ginsberg et al. [3] also studied heat transfer rate and frontal propagation during flooding from the top of a hot porous layer. They found that the particulate bed was quenched by a bi-frontal process composed of an initial downward front followed by upward front after the downward front has reached the bottom. About 30-40% of the energy initially stored in the particles was released during the downward quenching period and the rest was released during the upward filling period. However, the rate of heat transfer was found to be nearly constant with time and was independent of the mass of the particles and the initial temperature. This is an indication that the rate of heat transfer is limited by the counter-current flooding limit in the particulate layer. Tung et al. [4] studied the quenching characteristics of a particulate bed during top flooding with internal
0 0 2 9 - 5 4 9 3 / 8 7 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
276
I/.X. Tung, I~:K. Dhtr / Quenching o~ debris be,l~
heat generation and gas injection at the bottom. It was found that the quench front could be arrested with high internal energy generation rate and with high rate of gas injection at the bottom. It was also observed that the liquid was seeping down the side wall during the quenching process in contradiction with the observations made by Cho and Bova [2]. Hall and Hall [5] studied quenching of a particulate bed by bottom flooding. In their study, 45 cm deep beds formed with 0.3-2 mm diameter iron particles were used. From experiments it was concluded that the quenching rate increased with increasing particle size and driving head. In their model the particulate bed was divided into three distinct regions: single phase liquid, two-phase and single phase vapor. However, the frictional pressure drop across the two phase region was ignored in the momentum balance and it is not clear how the height of the two phase region was specified, Steam cooling of the unquenched region was also ignored in the energy equation. Tung and Dhir [6] studied bottom quenching of a hot particulate bed with either constant liquid flowrate or constant driving head. It was observed that bottom quenching could be categorized according to flow rates as low flow rates, moderate flow rates and high flow rates. At very low flow rates, the vapor volume flux was insufficient to carry liquid droplets far beyond the quench front. Consequently, the height of the two phase region was negligible. At moderate flow rates, an initial surge of liquid was observed to enter the bed. Upon contact with the particles the liquid vaporized almost instantly forming a recognizable two phase region. The resulted pressure pulse was enough to cause an oscillation of the liquid front at the bottom of the porous layer. The oscillations however died out with time and no fluidization of the bed was observed. At higher flow rates, essentially the same phenomenon was observed. However the pressure pulse created was enough to fluidize the upper portion of the porous layer. In their study Tung and Dhir also proposed a model to predict the quench front history during bottom quenching with fixed beds. In the model, the energy equation in the unquenched portion of the bed was included to account for steam cooling. In a subsequent work, Tung and Dhir [7] studied the quenching behavior of a fluidized bed during bottom quenching. It was found that very high heat transfer rates could be achieved ih this quenching mode. They also proposed a model to predict the conditions leading to the onset of fluidization.
Tutu et al. [8] performed a study on quenching of hot debris bed during bottom reflood with constant liquid flow rate. From their study it was concluded that for small liquid flow rates and low initial temperatures the quenching process is generally one-dimensional. Furthermore, the numerical computations clearly showed an acute need for more reliable information c~n the particle to fluid heat transfer coefficient~ It should be noted that all these previous studies were carried out under somewhat idealized conditions with porous layers composed of single size particles. To simulate more prototypical conditions the present experiments were performed with porous layers stratified in both axial and radial directions. Both top and bottom flooding modes were employed in the experiments.
2. Experimental apparatus and procedures 2.1. Experimental apparatus
The experimental apparatus was designed so that axial distribution of fluid and particle temperatures during quenching could be determined. Water at room temperature was used as the coolant while stainless steel particles were used to form the porous layers. The porous layers were supported by a 16 cm deep layer of 6 mm diameter glass particles contained inside a stainless steel cylinder. In the bottom flooding experiments, water entered the porous layer from the bottom via a 1". PVC pipe. A larger reservoir of water was used to maintain constant driving pressure at the inlet. In the top flooding experiments water entered the test section from a 3 / 8 " pipe located at about 14 cm from the top of the porous layer. The water inlet was connected to a large reservoir to maintain the two phase overlying layer at about 40 cm above the top of the porous layer. Two test sections were employed. Fig. 1 shows the test section employed in experiments involving vertical stratification of the porous layer. The test section in this case is a one meter long stainless steel tube with 73 mm ID and 1.6 mm wall thickness. The porous layers were formed inside this cylinder. The test section was mounted on an aluminum base. The insulation around the test section was made out of fiberglass insuiation sheets 1 / 2 " thick with an average thermal conductivity of 0.15 W / m - K . Instrumentation consisted of two sets of fixed thermocouples located at different axial locations. The first set of thermocouples was located at the center of the test section and the second set of thermo-
V.X. Tung, V.K. Dhir/ Quenching of debris beds
].
73mm
J
277
2.2. Experimental procedure
I
I b°o°o°o°oq 9!
Stainless Steel Particles
50.8mm ~;~
Fixed Thermocouples
p~-~ GlassParticles To X-Y Recorders
Fig. 1. Test section used in experiments involving vertically stratified porous layers.
couples was located at a radial position 25.4 mm from the center. The thermocouple outputs were continuously recorded by x - y recorders during the quenching process. The particles were heated prior to quenching using a 450 kHz induction heater. Fig. 2 shows the test section employed in experiments involving radial stratification of the porous layer. The test section in this case is the same as for the previous case except that the inner diameter is 85 mm. The test section was instrumented in the same manner except that an additional set of thermocouples was located at a radial position 37 mm from the center. Radial stratification of the porous layers was achieved by placing a thin walled, 60 mm OD tube inside the test section. Stainless steel particles of different sizes were then poured into the inner tube and in the annular region respectively. The inner tube then was pulled out of the test section. This procedure produced a porous layer with different permeabilities in the central and outer regions.
At the beginning of each experimental run the porous layer was heated inductively to a desired temperature. Once this temperature had been reached, power to the induction coil was cut off and the temperatures at different axial and radial positions were noted. Thereafter water was injected either from the top or the bottom. In the case of bottom injection, a screen was placed on top of the porous layer to prevent fluidization. The position of the quench front was recovered from the thermocouple output records. In reducing the data, the quench front was assumed to have reached a certain location when the temperature indicated by the thermocouple dropped to nearly the saturation temperature of water.
3. Analysis 3.1. One dimensional model for quenching by flooding from the bottom The model employed in the present work is essentially the same as that proposed by Tung and Dhir in ref. [6]. The height of the two phase region is assumed to be negligible and the bed is divided into two regions - single phase liquid and single phase vapor regions as shown in fig. 3. The mass and energy balances at the quench front can be combined to yield the following relations at
Z = Zq dZ_~q =
Cth~'~
(1)
dt and
85mm
I"
LI
a , = (1 - , ) p ~ c ~ ( ~
- TJ
+ ~p,hT~ '
(2)
Stainless Steel Particles
Fixed Thermocouples
--
Single Phase Vapor Region
5.5mm
Quench Front Single Phase Liquid Region
Glass Particles ~
To X-Y Recorders
Fig. 2. Test section used in experiments involving radially stratified porous layers.
1 Fig. 3. Flow configuration during quenching by bottom flooding.
278
F.X. Tung, V.K. Dhir / Quenching qf detvis hedv
region can be written as
where htg = hfg 4- Cp/(Tsa t - T/lzq ).
(3)
In obtaining eqs. (1) and (2), it has been assumed that all the heat stored in the particles is released instantaneously and is used in converting liquid into vapor. For a given material, this is equivalent to the assumptions of an infinite heat transfer coefficient between the solid and the fluid and very small size of the particles. In reality, these assumptions will not be true and a certain amount of time will elapse before all of the energy initially stored in the particles is released. If conduction is ignored in the single phase region occupied by vapor, the rate of change of particle temperature and vapor temperature as a result of steam cooling can be described by
OT~ OTv ,o~Cp~- = - a v C p v ~ + hv(rs - Tv),
-
,)O~Cp~
~T~ O--t- =
-
h ~ ( ~"-
rv).
The volumetric heat transfer coefficient used in eqs. (4) and (5) can be obtained from a correlation proposed by Choudhury and E1-Wakil [91 as Nu = ReO.65 [[ (1~ - l¢)11133
(63
In eq. (6), the numerical constant 0.00115 has units of length (m), l is the characteristic length and is defined as the ratio of the inertial coefficient, b, and viscous coefficient, a, in the Kozeny-Carman equation for single phase pressure drop. The coefficients a and b are defined as a = 150(1 - ,)2/,3dp2
-h,(r,- L),
(12)
aviGl+ --Gz2 + pig' OI
A edriving =
(aVv6 v+ b~G2+p~g dZ.
Zq \
Pv v
(13)
The integrations in eq. (13) allow for the inclusion of variable fluid properties due to temperature variations as well as the inclusion of the effect of vertical stratification of the porous layer. Eqs. (1)-(5), and (11)-(13) yield a closed set of 8 equations and 8 unknowns namely Zq, htg, Gv, Gt, Tv, ~ and the particle temperature TS in the single phase vapor and liquid regions. They thus can be solved simultaneously for a given bed configuration and a given driving pressure.
3.2. One dimensional model for quenching by flooding from the top The process of top quenching can be modeled by a quasi-steady process using the counter-current flooding limit as a boundary condition. The mass and energy balances at the quench front can be combined to yield
d Zq
Gih ~
dt
(1 - ,)psCm(T~ - T,a,) + cp,htg*
(14)
and (1 - ¢) p~Cp~(T~ - Tsat)G l
(8)
av =
(1 - , ) p , c p s ( r ~
- r~,) + ,p,ht2
while the Nusselt number, Nu, and the Reynolds number, Re, are defined as
where
Nu = h vl2/kv
h&* = h,~ + Cp,(r~a,- r,.i°).
(9)
and Re = Gvl/I~ ~.
(11)
where the volumetric heat transfer coefficient h/ can again be given by eqs. (6)-(10) using thermophysical properties of liquid. A momentum balance can now be made b y adding the pressure drop across each of the two regions
(7)
and b = 1.75(1 - c)/,3dp,
0T,
( 1 - e)o,Cm O-~-=
+f
(5)
.... T,)
and
(4)
and
(1
ep/Cp,-;-~~ . . . . GICp, ~ ~ r+[ .h,(
(10)
Similarly, the energy equation in the single phase liquid
'
(15)
(16)
Eqs. (1,1) and (15) when used in conjunction with the flooding relation
f(Gl,a~,dp) =0
(17)
V.X. Tung, V.K. Dhir / Quenchingof debris beds yields a set of 3 equations and 3 unknowns namely Zq, G/ and Gv and can thus be solved simultaneously for the quench front position as a function of time. It should be noted that the particle diameter dp employed in eq. (17) should be taken as the smallest particle size in the quenched region if the bed is vertically stratified. In the present work the flooding correlation proposed by Marshall and Dhir [10] was employed in eq. (17) as:
j.1/2 _bjl.l/2
=
0.875,
50
I
Gv
'3dpPv(P/-Pv)g
I
I
=400C 6.35rnm Part.
3.t8mm Part. 0
R~mm)
1
I
0
6(1 - , )
] AP = 50cm
V
=
I
(18)
where
Jv*
279
(19)
I Time (min)
I
I 6
Fig. 4. Quench front history during bottom flooding - Vertically stratified porous layer.
and 6(1 - c )
j~ = a/
c3dppl(Pt - Pv)g
(20)
Strictly speaking, the above correlation was based on the inertia of the two phases alone and thus should only be applied to beds composed of large diameter particles. For beds composed of smaller particles, the viscous drags on the fluid becomes dominant and eq. (18) will tend to overpredict the flooding limit. Therefore an overprediction of the quench front velocity is expected for beds composed of smaller particles.
4. Results and discussion A total of 8 experimental runs were made with vertically stratified beds and with bottom flooding. The bed configuration and experimental parameters are given in table 1.
Figs. 4-7 shows the progression of the quench front with time at constant driving pressure. The porous layers in these cases were formed with a 25 cm layer of 3.18 mm diameter stainless steel particles at the bottom and a 25 cm layer of 6.35 mm diameter stainless steel particles on top. In figs. 4-7, the open circles represent the quench front history recorded by the thermocouples located at the center of the test section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location of 25.4 mm from the center. The solid lines represent the predictions made by using the present model, In carrying out the analysis the actual initial temperature profile had been employed in the model to obtain the predictions plotted in figs. 4-7. From these figures it can be seen that the total quench time increased with increasing initial temperature and decreasing driving pressure. Furthermore, the quench front generally travelled faster near the wall of the cylinder due to the higher permeability there. This observation in fact contradicts Cho
Table 1 Bed configuration and parameters in vertically stratified porous layer flooded from bottom under constant driving pressure Figure
Top layer (25 cm)
bottom layer (25 cm)
Ap (cm of water)
~ti~a (°C)
4 5 6 7 8 9 10 11
6.35 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles
3.18 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles
50 50 80 80 50 50 80 80
400 525 400 525 480 525 400 620
280 50
P:XI Tung, KK. Dhtr /" Quenchtng o/dehrts bed~ I
I
A ,mm,
/
O-d~
i-,~..J
[ F i
g
6.35mm Part.
vo
i
3.18mm Part.
, ~
d
l
t
I
1- = 5 2 5 C
I
I
I
,
J
J 6
Time (rain)
Fig. 5. Quench front history during bottom flooding - Vertically stratified porous layer.
F
I
I
Part.
6.35mm
3.18mm Part.
I.,mm> O
Ap = 80cm
o
I
=400C
I
I
t
I
Time (rain)
0
Fig. 6. Quench front history during bottom flooding - Vertically stratified porous layer.
50
I
1 $-j
l
r~
I
I
and Bova's assertion that the liquid front travels faster near the center. However it should be noted that the relatively thin wall 0,6 mm) of the cylinder employed in the present experiments offered little thermal resis tance to the quench front progression, Therefore it ie, reasonable to expect the quench front to travel faster near the wall where permeability is the highest. Fhe predicted quench front histories made by using the present model can be seen to compare well with experimental results, It should be pointed out that the present model assumed a one dimensional quench front. The predictions thus represent only the average location of the quench front at any given time, Figs. 8-11 show the progression of the quench front with time when the porous layers were formed with a 25 cm layer of 6.35 mm diameter particles at the bottom and a 25 cm layer of 3.18 mm diameter particles on top. Again the open circles represent the quench front history recorded by the thermocouples located at the center of the last section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location of 25.4 mm from the center and the solid lines represent the predictions made by using the present model for bottom quenching. Again it can be seen that the total quench time generally increased with increasing initial temperature and decreasing driving pressure. Furthermore a comparison between the two cases plotted in figs. 5 and 9 shows that. for a driving heat of 50 em of water and initial temperature of 525°C, the total quench time is 350 s when the small particles (3.18 ram) are at the top but it is only 200 s when the big particles (6.35 ram) made up the top half of the porous layer. This is a clear indication that vapor friction in the unquenched region dominates the
50
I
i
I
I
---q- ~
"
I R'mm
AP = 80cm
0
o
/ / ~
-
7 = 525 C 6.35mm Part.
i
"~
-
o
r.
.
.
/J-
.
.
3.t8mm Part.
~
e
l
~
0
l
I
Time (rain)
I
.
/ / .
of"
-
6
Fig. 7. Quench front history during bottom flooding - Vertically stratified porous layer.
0
.
t
J
I
.
3.18ramPart. -j
.
.
.
.
.
.
.
.
.
"2 = °cm
/ /
1 I
.
I
i
J
i
=480C
I
L
t
Time (rain)
Fig. 8. Quench front history during bottom flooding cally stratified porous layer.
.. 6
Verti-
281
KX. Tung, V.K. Dhir / Quenching of debris beds 50
I
I
I
I
I ~.~
I RCmm
N
_
/
i/
I
/
~
)
.....
I
6.35mm Part. __
1
I
I
,
Time (rain)
Fig. 9. Quench front history during bottom flooding - Vertically stratified porous layer.
50 L
I
~
I
I
I
&P = 80cm
3.18mm Part. 6.35mm Part.
/¢)
et I
V
2~4 I
l
I
I
0 Time (min) 6 Fig, 10. Quench front history during bottom flooding - Vertically stratified porous layer.
50
I
I
I
R (ram)
/
/
v
I
quenching process by limiting the liquid flow into the porous layer. The present model for bottom quenching however tends to slightly underpredict the quench times in figs. 8-11. This was probably caused by a slight overprediction of steam cooling in the unquenched region. Fig. 12 shows the quench front histories obtained under top quenching when the bed was formed with a 17 cm layer of 1.6 mm diameter particles on top, a 17 cm layer of 3.18 mm diameter particles in the middle and a 16 cm layer of 6.35 mm diameter particles at the bottom. The initial temperature of the bed was 580°C. In this figure, the open circles represent the quench front history recorded by the thermocouple located at the center of the test section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location 25.4 mm from the center. The solid line represents predictions made by using the present one dimensional model. Again, it can be seen that the liquid penetrated faster into the bed near the wall as was the case with bottom quenching. In time, a pool of liquid is formed at the bottom of the test section due to this liquid seepage and an upward moving quench front is observed. This is consistent with the earlier observation made by Tung et al. [4]. Even though there exists a possibility for pockets of unquenched particles to remain as liquid penetrates into the bed, it is not substantiated by the quench behavior shown by the last six thermocouples. It is interesting to note that no sudden change in the quench front velocity is observed as the quench front moved from one layer of particles to the next. This is an indication that the quenching process is controlled by the flooding limit in the small particles which occupied
50 ~
I
I
I
/ 1.6mm Part. _
3.18mm Part.
oN
/d /
0
3.t8mm Part.
6.35mm Part.
I
O
o :m,
O I 25.4
I
I
I
I
Time (min)
Fig, 11. Quench front history during b o t t o m flooding - Vertically stratified porous layer.
\
o
-
"~ 6.35mm Part. I I I \ 0 Time (min) 30 Fig. 12. Quench front history during top flooding - Vertically stratified porous layer.
282
l( X. Tung, V.K. Dhtr / Quenching ~/ ,lebrA~.hed~
the upper portion of the porous layer. The time for complete quenching of the bed is 26.4 min. For an initial temperature of 580°C, this time for complete quenching represents an average heat flux of 33 W / c m 2. The counter current flooding correlation equation (18) would have given for 1.6 mm diameter particles a heat flux of 53 W / c m 2. As anticipated, eq. (18) overpredicts the heat removal rate since it is based on the turbulent flow model. For 1.6 mm particles the flow lies in the transition between laminar and inertia dominated flows. Fig. 13 shows the quench front histories obtained under top flooding when the bed was formed with a 17 cm layer of 6.35 mm diameter particles on top, a 17 cm layer of 3.18 mm diameter particles in the middle and a 16 cm layer of 1.6 mm diameter particles at the bottom. The initial temperature of the bed was again 580 ° C. In fig. 13 the open circles again represent the quench front history recorded by thermocouples located at the center of the test section and the solid circles represent the quench front histories recorded by thermocouples located at 25.4 mm front the center. The solid line represents prediction made by using the present one dimensional model. Essentially the same observation can be made that the liquid penetrated faster near the wall and thus induced an upward quench front after enough liquid had been accumulated at the bottom. The quenching process appears to be one dimensional in the interior of the bed. However preferential downward movement of liquid near the walt leads to two dimensional effects in the outer region. It is interesting to note that the quench front velocity decreased uniformly as the quench front penetrated into layers of smaller diameter particles as shown in fig. 13. This clearly indicates that the process
of top flooding is controlled by the smallest particles present in the quenched region. Also, the predicted quench front history can be seen to be in fair agreement with experimental observation as shown in fig. 13. It should be noted the upward quench front caused by liquid seepage near the side wall has not been represented in the model. Therefore, the predictions do not display an upward moving quench front near the end of the quenching process. Even though the initial temperature remained the same as for the case plotted in fig. 12, simply by switching the order of stratification of the particles the total quench time is reduced to 12.3 rain compared to a value of 26.4 min obtained for the case plotted in fig. 12. This total quench time of 12.3 min represents an average heat flux of 70 W / c m 2 compared to values of 53, 75 and 106 W / c m ~ calculated using the countercurrent flooding correlation (18) with particle diameters of 1.6 mm, 3.18 mm and 6.35 mm respectively. Fig. 14 shows the quench front histories obtained under top flooding of a radially stratified layer. In this case the bed was formed with an inner region 55 mm in diameter containing 3.18 mm diameter particles and an annular region 85 mm in diameter containing 6.35 mm diameter particles. In fig. 14 the open circles represent the quench front history recorded by thermocouples located at the center of the test section, the solid circles represent the quench front history recorded by thermocouples located at 25.4 mm from the center and the squares represent the quench front history recorded by I
5 0 -~
I
[] 50~'
I\
I
f
l
I
I "'ram'
(3
I
O.
mm P a . . T
=630C
O v O" N
E ..~° I
I-:2o ~
T
=580C
3.18mm
I_ I-
I
0
Part,
Fig. 13. Quench front history during top flooding stratified porous layer.
I
I
Time (rain)
30 -
85mm
Vertically
_t
! I
A~-~I
Time (min)
10
Fig. 14. Quench front history during top flooding - Radially stratified porous layer.
V.X. Tung, V.K. Dhir / Quenching of debris beds
thermocouples located at 37 mm from the center. It is interesting to note that the quench front penetrated very quickly in the annular region where permeability is the highest. After liquid had accumulated at the bottom, an upward quench front is observed to go through the inner region. During the upward movement of the quench front, the frictional resistance encountered by vapor in the inner region is balanced by the hydrostatic head of liquid in the quenched outer region. The data suggest that very little crossflow occurs at the koundary of the two regions. From the data the average heat removal rate based on an observed initial temperature of 630°C and a total quench time of 9.45 min is calculated to be 100 W / m 2. The dryout heat flux based on counter-current flooding limit is calculated to be 75 W / c m 2 for 3.18 mm diameter particles and 106 W / c m 2 for 6.35 mm diameter particles. Although the observed time averaged heat flux lies between the two limits based on counter current flooding model, a precise prediction will require use of both top and bottom flooding models simultaneously. Fig. 15 shows the quench front histories during top flooding of a radially stratified porous layer containing 6.35 mm diameter particles in the central region and 3.18 mm diameter particles in the outer region. The open circles, solid circles and squares represent the quench front histories recorded by thermocouples located at radial locations of 0 mm, 25.4 mm and 37 mm respectively from the center. It is noted that the
50
o•R
(ram)
DI 3;'.0
T = 580 C O v
283
liquid penetrates very rapidly into the region with higher permeability. However before complete quenching of the inner region occurs a liquid pool forms at the bottom due to downflow of liquid from the side. This leads to nearly uniform upward flooding in the lower region of the bed. Even though the radially stratified beds configurations shown in figs. 14 and 15 show different hydraulic behaviors the average heat flux for both cases is about 100 W / c m 2.
5. C o n c l u s i o n s
(1) Data obtained with vertically stratified porous layers under both top and bottom flooding indicate that during quenching the quench front generally travels faster near the sidewall due to higher permeability in this region. (2) It is found that the quench front velocity decreases with decreasing driving pressure and increasing initial temperature during bottom quenching. (3) It is observed that during bottom quenching vapor friction dominates the quenching process. Consequently the quench front velocity is lower for the case in which a layer of small particles is on top of another layer of bigger particles in comparison to the case in which orientation of these layers is switched. (4) During top flooding of a vertically stratified porous layer, it is found that the quench front velocity is controlled by the counter-current flooding limit imposed by the smallest particles in the quenched region. (5) During top flooding of a radially stratified porous layer, the data suggest that little crossflow occurs at the boundary of the two regions of different permeabilities. The liquid is found to penetrate quickly into the region with higher permeability while the lower permeability region is quenched mostly by a bottom flooding mode due to the in flow of liquid from the quenched high permeability region.
1:7 N
Nomenclature
Roman letters
3] a
85ram
I 0
Io'~ Time (rain)
1
b 10
Fig. 15. Quench front history during top flooding - Radially stratified porous layer.
Cp dD
viscous coefficient in the Kozeny-Carman equation [m- 2], inertial coefficient in the Kozeny-Carman equation [m- 1], constant pressure specific heat [J/kg-K], particle diameter [m],
284
O b
h rg h
V.X. Tung, V.K. Dhir / Quenching o/debris betA' mass flow rate of fluid per unit area ( k g / m 2s], bed height [m], latent heat of vaporization [J/kg], volumetric heat transfer coefficient [W/m 3-
[3]
K], t T Z
time [s], temperature [K], axial position measured from bottom of porous layer [m], quench front location [m].
[4]
[5] Greek symbols A Pdriving ( p
P
driving pressure [ N / m 2 ], bed porosity, dynamic viscosity [kg/m-s], kinematic viscosity [m2/s], density [ k g / m 3].
[6]
[7]
Subscripts liquid, solid (particles), vapor.
[8]
[9]
References [1] D.R. Armstrong, D.H. Cho, L. Bova, S.H. Chan and G.R. Thomas, Quenching of a high temperature particle bed, Trans. ANS 39 (1981) 1048. [2] D.H. Cho and L. Bova, Formation of dry pockets during
[10]
water penetration into a hot particle bed. ]'rans ANS 43 (1982) 418. T. Ginsberg, J. Klein, J. Klages, C.E. Schwarz and 3.C. Chen, Transient core debris bed heat removal experiments and analysis, presented at the International Meeting on Thermal Nuclear Reactor Safety, Chicago, Illinois, Aug. 29-Sept. 2, 1982. V.X. Tung, V.K. Dhir and D. Squarer, Quenching by top flooding of a heat generating particulate bed with gas injection at the bottom, Proc. Sixth. Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7 9. 1984 P.C. Hall and C.M. Hall, Quenching of heated particulatc beds by bottom flooding: Preliminary. results and analysis, presented at the European Two-Phase Flow Group Meeting, Eindhoven, Holland, June 1981. V.X Tung and VK. Dhir, Quenching of a hot particulate bed by bottom flooding, Proc. ASME-JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, March 20-24, 1983. V.X. Tung and V.K. Dhir, On fluidization of a particulate bed during quenching by flooding from bottom, Proc. Sixth Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7-9, 1984. N.K Tutu, T. Ginsberg, J. Klein, C.E Schwarz and J. Klages, Transient quenching of superheated debris beds during bottom reflood, Proc. Sixth Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7-9, 1984. W.V. Choudhury and M.M. El-Wakil, Heat transfer and flow characteristics in conductive porous media with heat generation, Proc. Int. Heat Transfer Conf., Versailles, France 1970. J. Marshall and V.K. Dhir, On the counter-current flow limitations in porous media, Proc. Int. Meeting on Light Water Reactor Severe Accident Evaluation, Vol. 2, pp. 18.5-1 to 18.5-7 (1983).
275
QUENCHING OF DEBRIS BEDS HAVING VARIABLE PERMEABILITY IN T H E A X I A L A N D R A D I A L D I R E C T I O N S * V.X. T U N G a n d V.K. D H I R School of Engineering and Applied Science, University of California, Los Angeles, Los Angeles, CA 90024, USA
In this paper experiments and analyses for the cooling conditions of debris beds with variable permeability in the axial and radial directions are performed. In the experiments steel particles varying in diameter from 1.6 mm to 6.35 mm were used to simulate the core debris beds. The particles were heated inductively to temperatures up to 630°C in an inert atmosphere. Thereafter, the particulate beds were flooded either from the top or from the bottom. In the experiments water at room temperature was used as the coolant. Several configurations of the particulate bed yielding extreme variations in permeability were studied. Analyses to establish the coolability limits have been performed.
I. Introduction The cooling conditions in a Light Water Reactor can be significantly impaired in a loss of coolant accident. Continued undercooling of the core will result in overheating of the fuel elements with an eventual loss of integrity. Such a severely degraded core may behave as a porous layer composed of heated particles of different sizes and shapes. Before continuous cooling of this layer of very hot particles can be established, the particles need to be quenched either by flooding from the top or by flooding from the bottom. In the event the reactor vessel fails, the debris will drop into the reactor cavity and interact with the concrete underneath. As a result, gas is generated at the bottom during quenching and will flow through the debris bed. Several studies on quenching of debris beds by top flooding have been reported in the literature. Armstrong et al. [1] studied top quenching of 75 cm deep beds composed of 3.1 mm diameter steel particles at a maximum temperature of 550°C. By assuming that the steel particles were completely quenched and cooled to saturation temperature of water as water penetrated into the bed, the quench front velocity was found to remain constant with time. For water at an inlet temperature of 24°C the quench front velocity was found to be 0.21 m / s compared to a prediction of 0.26 m / s based on counter current flooding limit. The agreement * Work supported by EPRI, Palo Alto, California, USA
between predictions and experimental results is indeed good considering the simplicity of the model. However, it must be pointed out that as the particle size is increased, heat transfer will be limited by radial conduction in the particles and the quench front may lag behind the liquid penetration front. Cho and Bova [2] have reported that during flooding from the top, liquid penetrated faster in the middle of the bed than in the outer regions. This is indeed an interesting observation. Intuitively one would expect the liquid to penetrate faster near the wall due to higher permeability there. It is possible that the large thermal mass of the wall kept the adjoining region of the bed hot for a longer period of time. Ginsberg et al. [3] also studied heat transfer rate and frontal propagation during flooding from the top of a hot porous layer. They found that the particulate bed was quenched by a bi-frontal process composed of an initial downward front followed by upward front after the downward front has reached the bottom. About 30-40% of the energy initially stored in the particles was released during the downward quenching period and the rest was released during the upward filling period. However, the rate of heat transfer was found to be nearly constant with time and was independent of the mass of the particles and the initial temperature. This is an indication that the rate of heat transfer is limited by the counter-current flooding limit in the particulate layer. Tung et al. [4] studied the quenching characteristics of a particulate bed during top flooding with internal
0 0 2 9 - 5 4 9 3 / 8 7 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)
276
I/.X. Tung, I~:K. Dhtr / Quenching o~ debris be,l~
heat generation and gas injection at the bottom. It was found that the quench front could be arrested with high internal energy generation rate and with high rate of gas injection at the bottom. It was also observed that the liquid was seeping down the side wall during the quenching process in contradiction with the observations made by Cho and Bova [2]. Hall and Hall [5] studied quenching of a particulate bed by bottom flooding. In their study, 45 cm deep beds formed with 0.3-2 mm diameter iron particles were used. From experiments it was concluded that the quenching rate increased with increasing particle size and driving head. In their model the particulate bed was divided into three distinct regions: single phase liquid, two-phase and single phase vapor. However, the frictional pressure drop across the two phase region was ignored in the momentum balance and it is not clear how the height of the two phase region was specified, Steam cooling of the unquenched region was also ignored in the energy equation. Tung and Dhir [6] studied bottom quenching of a hot particulate bed with either constant liquid flowrate or constant driving head. It was observed that bottom quenching could be categorized according to flow rates as low flow rates, moderate flow rates and high flow rates. At very low flow rates, the vapor volume flux was insufficient to carry liquid droplets far beyond the quench front. Consequently, the height of the two phase region was negligible. At moderate flow rates, an initial surge of liquid was observed to enter the bed. Upon contact with the particles the liquid vaporized almost instantly forming a recognizable two phase region. The resulted pressure pulse was enough to cause an oscillation of the liquid front at the bottom of the porous layer. The oscillations however died out with time and no fluidization of the bed was observed. At higher flow rates, essentially the same phenomenon was observed. However the pressure pulse created was enough to fluidize the upper portion of the porous layer. In their study Tung and Dhir also proposed a model to predict the quench front history during bottom quenching with fixed beds. In the model, the energy equation in the unquenched portion of the bed was included to account for steam cooling. In a subsequent work, Tung and Dhir [7] studied the quenching behavior of a fluidized bed during bottom quenching. It was found that very high heat transfer rates could be achieved ih this quenching mode. They also proposed a model to predict the conditions leading to the onset of fluidization.
Tutu et al. [8] performed a study on quenching of hot debris bed during bottom reflood with constant liquid flow rate. From their study it was concluded that for small liquid flow rates and low initial temperatures the quenching process is generally one-dimensional. Furthermore, the numerical computations clearly showed an acute need for more reliable information c~n the particle to fluid heat transfer coefficient~ It should be noted that all these previous studies were carried out under somewhat idealized conditions with porous layers composed of single size particles. To simulate more prototypical conditions the present experiments were performed with porous layers stratified in both axial and radial directions. Both top and bottom flooding modes were employed in the experiments.
2. Experimental apparatus and procedures 2.1. Experimental apparatus
The experimental apparatus was designed so that axial distribution of fluid and particle temperatures during quenching could be determined. Water at room temperature was used as the coolant while stainless steel particles were used to form the porous layers. The porous layers were supported by a 16 cm deep layer of 6 mm diameter glass particles contained inside a stainless steel cylinder. In the bottom flooding experiments, water entered the porous layer from the bottom via a 1". PVC pipe. A larger reservoir of water was used to maintain constant driving pressure at the inlet. In the top flooding experiments water entered the test section from a 3 / 8 " pipe located at about 14 cm from the top of the porous layer. The water inlet was connected to a large reservoir to maintain the two phase overlying layer at about 40 cm above the top of the porous layer. Two test sections were employed. Fig. 1 shows the test section employed in experiments involving vertical stratification of the porous layer. The test section in this case is a one meter long stainless steel tube with 73 mm ID and 1.6 mm wall thickness. The porous layers were formed inside this cylinder. The test section was mounted on an aluminum base. The insulation around the test section was made out of fiberglass insuiation sheets 1 / 2 " thick with an average thermal conductivity of 0.15 W / m - K . Instrumentation consisted of two sets of fixed thermocouples located at different axial locations. The first set of thermocouples was located at the center of the test section and the second set of thermo-
V.X. Tung, V.K. Dhir/ Quenching of debris beds
].
73mm
J
277
2.2. Experimental procedure
I
I b°o°o°o°oq 9!
Stainless Steel Particles
50.8mm ~;~
Fixed Thermocouples
p~-~ GlassParticles To X-Y Recorders
Fig. 1. Test section used in experiments involving vertically stratified porous layers.
couples was located at a radial position 25.4 mm from the center. The thermocouple outputs were continuously recorded by x - y recorders during the quenching process. The particles were heated prior to quenching using a 450 kHz induction heater. Fig. 2 shows the test section employed in experiments involving radial stratification of the porous layer. The test section in this case is the same as for the previous case except that the inner diameter is 85 mm. The test section was instrumented in the same manner except that an additional set of thermocouples was located at a radial position 37 mm from the center. Radial stratification of the porous layers was achieved by placing a thin walled, 60 mm OD tube inside the test section. Stainless steel particles of different sizes were then poured into the inner tube and in the annular region respectively. The inner tube then was pulled out of the test section. This procedure produced a porous layer with different permeabilities in the central and outer regions.
At the beginning of each experimental run the porous layer was heated inductively to a desired temperature. Once this temperature had been reached, power to the induction coil was cut off and the temperatures at different axial and radial positions were noted. Thereafter water was injected either from the top or the bottom. In the case of bottom injection, a screen was placed on top of the porous layer to prevent fluidization. The position of the quench front was recovered from the thermocouple output records. In reducing the data, the quench front was assumed to have reached a certain location when the temperature indicated by the thermocouple dropped to nearly the saturation temperature of water.
3. Analysis 3.1. One dimensional model for quenching by flooding from the bottom The model employed in the present work is essentially the same as that proposed by Tung and Dhir in ref. [6]. The height of the two phase region is assumed to be negligible and the bed is divided into two regions - single phase liquid and single phase vapor regions as shown in fig. 3. The mass and energy balances at the quench front can be combined to yield the following relations at
Z = Zq dZ_~q =
Cth~'~
(1)
dt and
85mm
I"
LI
a , = (1 - , ) p ~ c ~ ( ~
- TJ
+ ~p,hT~ '
(2)
Stainless Steel Particles
Fixed Thermocouples
--
Single Phase Vapor Region
5.5mm
Quench Front Single Phase Liquid Region
Glass Particles ~
To X-Y Recorders
Fig. 2. Test section used in experiments involving radially stratified porous layers.
1 Fig. 3. Flow configuration during quenching by bottom flooding.
278
F.X. Tung, V.K. Dhir / Quenching qf detvis hedv
region can be written as
where htg = hfg 4- Cp/(Tsa t - T/lzq ).
(3)
In obtaining eqs. (1) and (2), it has been assumed that all the heat stored in the particles is released instantaneously and is used in converting liquid into vapor. For a given material, this is equivalent to the assumptions of an infinite heat transfer coefficient between the solid and the fluid and very small size of the particles. In reality, these assumptions will not be true and a certain amount of time will elapse before all of the energy initially stored in the particles is released. If conduction is ignored in the single phase region occupied by vapor, the rate of change of particle temperature and vapor temperature as a result of steam cooling can be described by
OT~ OTv ,o~Cp~- = - a v C p v ~ + hv(rs - Tv),
-
,)O~Cp~
~T~ O--t- =
-
h ~ ( ~"-
rv).
The volumetric heat transfer coefficient used in eqs. (4) and (5) can be obtained from a correlation proposed by Choudhury and E1-Wakil [91 as Nu = ReO.65 [[ (1~ - l¢)11133
(63
In eq. (6), the numerical constant 0.00115 has units of length (m), l is the characteristic length and is defined as the ratio of the inertial coefficient, b, and viscous coefficient, a, in the Kozeny-Carman equation for single phase pressure drop. The coefficients a and b are defined as a = 150(1 - ,)2/,3dp2
-h,(r,- L),
(12)
aviGl+ --Gz2 + pig' OI
A edriving =
(aVv6 v+ b~G2+p~g dZ.
Zq \
Pv v
(13)
The integrations in eq. (13) allow for the inclusion of variable fluid properties due to temperature variations as well as the inclusion of the effect of vertical stratification of the porous layer. Eqs. (1)-(5), and (11)-(13) yield a closed set of 8 equations and 8 unknowns namely Zq, htg, Gv, Gt, Tv, ~ and the particle temperature TS in the single phase vapor and liquid regions. They thus can be solved simultaneously for a given bed configuration and a given driving pressure.
3.2. One dimensional model for quenching by flooding from the top The process of top quenching can be modeled by a quasi-steady process using the counter-current flooding limit as a boundary condition. The mass and energy balances at the quench front can be combined to yield
d Zq
Gih ~
dt
(1 - ,)psCm(T~ - T,a,) + cp,htg*
(14)
and (1 - ¢) p~Cp~(T~ - Tsat)G l
(8)
av =
(1 - , ) p , c p s ( r ~
- r~,) + ,p,ht2
while the Nusselt number, Nu, and the Reynolds number, Re, are defined as
where
Nu = h vl2/kv
h&* = h,~ + Cp,(r~a,- r,.i°).
(9)
and Re = Gvl/I~ ~.
(11)
where the volumetric heat transfer coefficient h/ can again be given by eqs. (6)-(10) using thermophysical properties of liquid. A momentum balance can now be made b y adding the pressure drop across each of the two regions
(7)
and b = 1.75(1 - c)/,3dp,
0T,
( 1 - e)o,Cm O-~-=
+f
(5)
.... T,)
and
(4)
and
(1
ep/Cp,-;-~~ . . . . GICp, ~ ~ r+[ .h,(
(10)
Similarly, the energy equation in the single phase liquid
'
(15)
(16)
Eqs. (1,1) and (15) when used in conjunction with the flooding relation
f(Gl,a~,dp) =0
(17)
V.X. Tung, V.K. Dhir / Quenchingof debris beds yields a set of 3 equations and 3 unknowns namely Zq, G/ and Gv and can thus be solved simultaneously for the quench front position as a function of time. It should be noted that the particle diameter dp employed in eq. (17) should be taken as the smallest particle size in the quenched region if the bed is vertically stratified. In the present work the flooding correlation proposed by Marshall and Dhir [10] was employed in eq. (17) as:
j.1/2 _bjl.l/2
=
0.875,
50
I
Gv
'3dpPv(P/-Pv)g
I
I
=400C 6.35rnm Part.
3.t8mm Part. 0
R~mm)
1
I
0
6(1 - , )
] AP = 50cm
V
=
I
(18)
where
Jv*
279
(19)
I Time (min)
I
I 6
Fig. 4. Quench front history during bottom flooding - Vertically stratified porous layer.
and 6(1 - c )
j~ = a/
c3dppl(Pt - Pv)g
(20)
Strictly speaking, the above correlation was based on the inertia of the two phases alone and thus should only be applied to beds composed of large diameter particles. For beds composed of smaller particles, the viscous drags on the fluid becomes dominant and eq. (18) will tend to overpredict the flooding limit. Therefore an overprediction of the quench front velocity is expected for beds composed of smaller particles.
4. Results and discussion A total of 8 experimental runs were made with vertically stratified beds and with bottom flooding. The bed configuration and experimental parameters are given in table 1.
Figs. 4-7 shows the progression of the quench front with time at constant driving pressure. The porous layers in these cases were formed with a 25 cm layer of 3.18 mm diameter stainless steel particles at the bottom and a 25 cm layer of 6.35 mm diameter stainless steel particles on top. In figs. 4-7, the open circles represent the quench front history recorded by the thermocouples located at the center of the test section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location of 25.4 mm from the center. The solid lines represent the predictions made by using the present model, In carrying out the analysis the actual initial temperature profile had been employed in the model to obtain the predictions plotted in figs. 4-7. From these figures it can be seen that the total quench time increased with increasing initial temperature and decreasing driving pressure. Furthermore, the quench front generally travelled faster near the wall of the cylinder due to the higher permeability there. This observation in fact contradicts Cho
Table 1 Bed configuration and parameters in vertically stratified porous layer flooded from bottom under constant driving pressure Figure
Top layer (25 cm)
bottom layer (25 cm)
Ap (cm of water)
~ti~a (°C)
4 5 6 7 8 9 10 11
6.35 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles
3.18 mm particles 3.18 mm particles 3.18 mm particles 3.18 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles 6.35 mm particles
50 50 80 80 50 50 80 80
400 525 400 525 480 525 400 620
280 50
P:XI Tung, KK. Dhtr /" Quenchtng o/dehrts bed~ I
I
A ,mm,
/
O-d~
i-,~..J
[ F i
g
6.35mm Part.
vo
i
3.18mm Part.
, ~
d
l
t
I
1- = 5 2 5 C
I
I
I
,
J
J 6
Time (rain)
Fig. 5. Quench front history during bottom flooding - Vertically stratified porous layer.
F
I
I
Part.
6.35mm
3.18mm Part.
I.,mm> O
Ap = 80cm
o
I
=400C
I
I
t
I
Time (rain)
0
Fig. 6. Quench front history during bottom flooding - Vertically stratified porous layer.
50
I
1 $-j
l
r~
I
I
and Bova's assertion that the liquid front travels faster near the center. However it should be noted that the relatively thin wall 0,6 mm) of the cylinder employed in the present experiments offered little thermal resis tance to the quench front progression, Therefore it ie, reasonable to expect the quench front to travel faster near the wall where permeability is the highest. Fhe predicted quench front histories made by using the present model can be seen to compare well with experimental results, It should be pointed out that the present model assumed a one dimensional quench front. The predictions thus represent only the average location of the quench front at any given time, Figs. 8-11 show the progression of the quench front with time when the porous layers were formed with a 25 cm layer of 6.35 mm diameter particles at the bottom and a 25 cm layer of 3.18 mm diameter particles on top. Again the open circles represent the quench front history recorded by the thermocouples located at the center of the last section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location of 25.4 mm from the center and the solid lines represent the predictions made by using the present model for bottom quenching. Again it can be seen that the total quench time generally increased with increasing initial temperature and decreasing driving pressure. Furthermore a comparison between the two cases plotted in figs. 5 and 9 shows that. for a driving heat of 50 em of water and initial temperature of 525°C, the total quench time is 350 s when the small particles (3.18 ram) are at the top but it is only 200 s when the big particles (6.35 ram) made up the top half of the porous layer. This is a clear indication that vapor friction in the unquenched region dominates the
50
I
i
I
I
---q- ~
"
I R'mm
AP = 80cm
0
o
/ / ~
-
7 = 525 C 6.35mm Part.
i
"~
-
o
r.
.
.
/J-
.
.
3.t8mm Part.
~
e
l
~
0
l
I
Time (rain)
I
.
/ / .
of"
-
6
Fig. 7. Quench front history during bottom flooding - Vertically stratified porous layer.
0
.
t
J
I
.
3.18ramPart. -j
.
.
.
.
.
.
.
.
.
"2 = °cm
/ /
1 I
.
I
i
J
i
=480C
I
L
t
Time (rain)
Fig. 8. Quench front history during bottom flooding cally stratified porous layer.
.. 6
Verti-
281
KX. Tung, V.K. Dhir / Quenching of debris beds 50
I
I
I
I
I ~.~
I RCmm
N
_
/
i/
I
/
~
)
.....
I
6.35mm Part. __
1
I
I
,
Time (rain)
Fig. 9. Quench front history during bottom flooding - Vertically stratified porous layer.
50 L
I
~
I
I
I
&P = 80cm
3.18mm Part. 6.35mm Part.
/¢)
et I
V
2~4 I
l
I
I
0 Time (min) 6 Fig, 10. Quench front history during bottom flooding - Vertically stratified porous layer.
50
I
I
I
R (ram)
/
/
v
I
quenching process by limiting the liquid flow into the porous layer. The present model for bottom quenching however tends to slightly underpredict the quench times in figs. 8-11. This was probably caused by a slight overprediction of steam cooling in the unquenched region. Fig. 12 shows the quench front histories obtained under top quenching when the bed was formed with a 17 cm layer of 1.6 mm diameter particles on top, a 17 cm layer of 3.18 mm diameter particles in the middle and a 16 cm layer of 6.35 mm diameter particles at the bottom. The initial temperature of the bed was 580°C. In this figure, the open circles represent the quench front history recorded by the thermocouple located at the center of the test section and the solid circles represent the quench front history recorded by the thermocouples located at a radial location 25.4 mm from the center. The solid line represents predictions made by using the present one dimensional model. Again, it can be seen that the liquid penetrated faster into the bed near the wall as was the case with bottom quenching. In time, a pool of liquid is formed at the bottom of the test section due to this liquid seepage and an upward moving quench front is observed. This is consistent with the earlier observation made by Tung et al. [4]. Even though there exists a possibility for pockets of unquenched particles to remain as liquid penetrates into the bed, it is not substantiated by the quench behavior shown by the last six thermocouples. It is interesting to note that no sudden change in the quench front velocity is observed as the quench front moved from one layer of particles to the next. This is an indication that the quenching process is controlled by the flooding limit in the small particles which occupied
50 ~
I
I
I
/ 1.6mm Part. _
3.18mm Part.
oN
/d /
0
3.t8mm Part.
6.35mm Part.
I
O
o :m,
O I 25.4
I
I
I
I
Time (min)
Fig, 11. Quench front history during b o t t o m flooding - Vertically stratified porous layer.
\
o
-
"~ 6.35mm Part. I I I \ 0 Time (min) 30 Fig. 12. Quench front history during top flooding - Vertically stratified porous layer.
282
l( X. Tung, V.K. Dhtr / Quenching ~/ ,lebrA~.hed~
the upper portion of the porous layer. The time for complete quenching of the bed is 26.4 min. For an initial temperature of 580°C, this time for complete quenching represents an average heat flux of 33 W / c m 2. The counter current flooding correlation equation (18) would have given for 1.6 mm diameter particles a heat flux of 53 W / c m 2. As anticipated, eq. (18) overpredicts the heat removal rate since it is based on the turbulent flow model. For 1.6 mm particles the flow lies in the transition between laminar and inertia dominated flows. Fig. 13 shows the quench front histories obtained under top flooding when the bed was formed with a 17 cm layer of 6.35 mm diameter particles on top, a 17 cm layer of 3.18 mm diameter particles in the middle and a 16 cm layer of 1.6 mm diameter particles at the bottom. The initial temperature of the bed was again 580 ° C. In fig. 13 the open circles again represent the quench front history recorded by thermocouples located at the center of the test section and the solid circles represent the quench front histories recorded by thermocouples located at 25.4 mm front the center. The solid line represents prediction made by using the present one dimensional model. Essentially the same observation can be made that the liquid penetrated faster near the wall and thus induced an upward quench front after enough liquid had been accumulated at the bottom. The quenching process appears to be one dimensional in the interior of the bed. However preferential downward movement of liquid near the walt leads to two dimensional effects in the outer region. It is interesting to note that the quench front velocity decreased uniformly as the quench front penetrated into layers of smaller diameter particles as shown in fig. 13. This clearly indicates that the process
of top flooding is controlled by the smallest particles present in the quenched region. Also, the predicted quench front history can be seen to be in fair agreement with experimental observation as shown in fig. 13. It should be noted the upward quench front caused by liquid seepage near the side wall has not been represented in the model. Therefore, the predictions do not display an upward moving quench front near the end of the quenching process. Even though the initial temperature remained the same as for the case plotted in fig. 12, simply by switching the order of stratification of the particles the total quench time is reduced to 12.3 rain compared to a value of 26.4 min obtained for the case plotted in fig. 12. This total quench time of 12.3 min represents an average heat flux of 70 W / c m 2 compared to values of 53, 75 and 106 W / c m ~ calculated using the countercurrent flooding correlation (18) with particle diameters of 1.6 mm, 3.18 mm and 6.35 mm respectively. Fig. 14 shows the quench front histories obtained under top flooding of a radially stratified layer. In this case the bed was formed with an inner region 55 mm in diameter containing 3.18 mm diameter particles and an annular region 85 mm in diameter containing 6.35 mm diameter particles. In fig. 14 the open circles represent the quench front history recorded by thermocouples located at the center of the test section, the solid circles represent the quench front history recorded by thermocouples located at 25.4 mm from the center and the squares represent the quench front history recorded by I
5 0 -~
I
[] 50~'
I\
I
f
l
I
I "'ram'
(3
I
O.
mm P a . . T
=630C
O v O" N
E ..~° I
I-:2o ~
T
=580C
3.18mm
I_ I-
I
0
Part,
Fig. 13. Quench front history during top flooding stratified porous layer.
I
I
Time (rain)
30 -
85mm
Vertically
_t
! I
A~-~I
Time (min)
10
Fig. 14. Quench front history during top flooding - Radially stratified porous layer.
V.X. Tung, V.K. Dhir / Quenching of debris beds
thermocouples located at 37 mm from the center. It is interesting to note that the quench front penetrated very quickly in the annular region where permeability is the highest. After liquid had accumulated at the bottom, an upward quench front is observed to go through the inner region. During the upward movement of the quench front, the frictional resistance encountered by vapor in the inner region is balanced by the hydrostatic head of liquid in the quenched outer region. The data suggest that very little crossflow occurs at the koundary of the two regions. From the data the average heat removal rate based on an observed initial temperature of 630°C and a total quench time of 9.45 min is calculated to be 100 W / m 2. The dryout heat flux based on counter-current flooding limit is calculated to be 75 W / c m 2 for 3.18 mm diameter particles and 106 W / c m 2 for 6.35 mm diameter particles. Although the observed time averaged heat flux lies between the two limits based on counter current flooding model, a precise prediction will require use of both top and bottom flooding models simultaneously. Fig. 15 shows the quench front histories during top flooding of a radially stratified porous layer containing 6.35 mm diameter particles in the central region and 3.18 mm diameter particles in the outer region. The open circles, solid circles and squares represent the quench front histories recorded by thermocouples located at radial locations of 0 mm, 25.4 mm and 37 mm respectively from the center. It is noted that the
50
o•R
(ram)
DI 3;'.0
T = 580 C O v
283
liquid penetrates very rapidly into the region with higher permeability. However before complete quenching of the inner region occurs a liquid pool forms at the bottom due to downflow of liquid from the side. This leads to nearly uniform upward flooding in the lower region of the bed. Even though the radially stratified beds configurations shown in figs. 14 and 15 show different hydraulic behaviors the average heat flux for both cases is about 100 W / c m 2.
5. C o n c l u s i o n s
(1) Data obtained with vertically stratified porous layers under both top and bottom flooding indicate that during quenching the quench front generally travels faster near the sidewall due to higher permeability in this region. (2) It is found that the quench front velocity decreases with decreasing driving pressure and increasing initial temperature during bottom quenching. (3) It is observed that during bottom quenching vapor friction dominates the quenching process. Consequently the quench front velocity is lower for the case in which a layer of small particles is on top of another layer of bigger particles in comparison to the case in which orientation of these layers is switched. (4) During top flooding of a vertically stratified porous layer, it is found that the quench front velocity is controlled by the counter-current flooding limit imposed by the smallest particles in the quenched region. (5) During top flooding of a radially stratified porous layer, the data suggest that little crossflow occurs at the boundary of the two regions of different permeabilities. The liquid is found to penetrate quickly into the region with higher permeability while the lower permeability region is quenched mostly by a bottom flooding mode due to the in flow of liquid from the quenched high permeability region.
1:7 N
Nomenclature
Roman letters
3] a
85ram
I 0
Io'~ Time (rain)
1
b 10
Fig. 15. Quench front history during top flooding - Radially stratified porous layer.
Cp dD
viscous coefficient in the Kozeny-Carman equation [m- 2], inertial coefficient in the Kozeny-Carman equation [m- 1], constant pressure specific heat [J/kg-K], particle diameter [m],
284
O b
h rg h
V.X. Tung, V.K. Dhir / Quenching o/debris betA' mass flow rate of fluid per unit area ( k g / m 2s], bed height [m], latent heat of vaporization [J/kg], volumetric heat transfer coefficient [W/m 3-
[3]
K], t T Z
time [s], temperature [K], axial position measured from bottom of porous layer [m], quench front location [m].
[4]
[5] Greek symbols A Pdriving ( p
P
driving pressure [ N / m 2 ], bed porosity, dynamic viscosity [kg/m-s], kinematic viscosity [m2/s], density [ k g / m 3].
[6]
[7]
Subscripts liquid, solid (particles), vapor.
[8]
[9]
References [1] D.R. Armstrong, D.H. Cho, L. Bova, S.H. Chan and G.R. Thomas, Quenching of a high temperature particle bed, Trans. ANS 39 (1981) 1048. [2] D.H. Cho and L. Bova, Formation of dry pockets during
[10]
water penetration into a hot particle bed. ]'rans ANS 43 (1982) 418. T. Ginsberg, J. Klein, J. Klages, C.E. Schwarz and 3.C. Chen, Transient core debris bed heat removal experiments and analysis, presented at the International Meeting on Thermal Nuclear Reactor Safety, Chicago, Illinois, Aug. 29-Sept. 2, 1982. V.X. Tung, V.K. Dhir and D. Squarer, Quenching by top flooding of a heat generating particulate bed with gas injection at the bottom, Proc. Sixth. Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7 9. 1984 P.C. Hall and C.M. Hall, Quenching of heated particulatc beds by bottom flooding: Preliminary. results and analysis, presented at the European Two-Phase Flow Group Meeting, Eindhoven, Holland, June 1981. V.X Tung and VK. Dhir, Quenching of a hot particulate bed by bottom flooding, Proc. ASME-JSME Thermal Engineering Joint Conference, Honolulu, Hawaii, March 20-24, 1983. V.X. Tung and V.K. Dhir, On fluidization of a particulate bed during quenching by flooding from bottom, Proc. Sixth Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7-9, 1984. N.K Tutu, T. Ginsberg, J. Klein, C.E Schwarz and J. Klages, Transient quenching of superheated debris beds during bottom reflood, Proc. Sixth Information Exchange Meeting on Debris Coolability, UCLA, Nov. 7-9, 1984. W.V. Choudhury and M.M. El-Wakil, Heat transfer and flow characteristics in conductive porous media with heat generation, Proc. Int. Heat Transfer Conf., Versailles, France 1970. J. Marshall and V.K. Dhir, On the counter-current flow limitations in porous media, Proc. Int. Meeting on Light Water Reactor Severe Accident Evaluation, Vol. 2, pp. 18.5-1 to 18.5-7 (1983).