- Email: [email protected]
Melting attack of solid plates by a high temperature liquid jet — effect of crust formation
Nuclear Engineering and Design 121 (1990) 11-23 North-Holland
11
MELTING - EFFECT
ATTACK OF SOLID PLATES OF CRUST FORMATION *
BY A HIGH
TEMPERATURE
M. SAITO
* *, K. S A T O , A. F U R U T A N I ,
M. ISOZAKI,
S. I M A H O R I
LIQUID
JET
a n d Y. H A T T O R I
***
Safety Engineering Division, O-arai Engineering Center, Power Reactor and Nuclear Fuel Development Corporation, 4002 Narita, O-arai-machi, Ibaraki-ken 311-13, Japan Received 10 November 1989
When a molten UO 2 jet impinges on a steel structure in a reactor vessel during a severe accident, the erosion rate of the steel by the molten UO 2 jet is expected to be limited considerably by a UO 2 crust layer forming on a molten steel substrate at the jet/steel plate interface. A series of simulation experiments was performed to study the melting behavior of solid plates by high temperature liquid jets and the effects of crust forming at jet/structure interface. In the first series of experiments, salt (NaCI) was selected as the jet material and tin (Sn) as the solid structure. The experiments were conducted with varying the jet diameter (10 - 30 ram) and jet temperature (900 -1100 o C). The jets were accelerated to a range of 3 - 5 m / s at the nozzle outlet by gravitational force and impinged perpendicularly to the solid plate underneath. Furthermore, to check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were performed by using a molten A1203 jet ( - 2200 ° C) impinging on stainless steel plate at room temperature. The erosion rates obtained in the present experiments were far less than the values predicted by an analytical solution that neglects the existence of a crust layer and its thermal effects. With the inclusion of the crust behavior in the model, the experimental results were predicted fairly well. From the present experiments, a Nusselt number of the turbulent heat transfer, which takes into account simultaneous melting and freezing in the impingement region of a molten jet, is correlated by a Reynolds number and a Prandtl number as follows: Nu,, = 0.0033 Re- Pr. In conclusion, the existence of a crust layer plays an important role in the erosion process of a solid plate by the molten fuel jet with high melting point as in a reactor situation.
1. Introduction
A large technical d a t a b a s e a n d more reliable theoretical models are needed for assessing the i n h e r e n t retention a b i h t y of m o l t e n core materials without leading to vessel failure a n d the release of a large a m o u n t of radioactive materials after p e r m a n e n t neutronic shutd o w n of L M F B R severe accidents. After a p e r m a n e n t s h u t d o w n is achieved by the fuel dispersal from the reactor core region, the m o l t e n core materials r e m a i n i n g
* Originally presented at the 26th ASME/AIChE National Heat Transfer Conference, Philadelphia, PA, August 6-9, 1989. * * Presently with Department of Nuclear Engineering, Faculty of Engineering, Osaka University, Yamada-oka, Suita-shi, Osaka 565, Japan. * * * Presently with Shinko Plant Engineering Company, Inc., 1-20-11 Nishikojiya, Ohta-ku, Tokyo 144, Japan. 0029-5493/90/$03.50
in the region m a y either be encapsuled by the crust a n d cooled d o w n by the a m b i e n t coolant a n d cold structures, or m a y penetrate the lower core assembly in the d o w n w a r d direction by the c o m b i n e d effects of gravity a n d the residual decay heat generation, resulting in a discharge into a lower p l e n u m region. In the P A M R (Post-Accident Materials Relocation) phase in the L M F B R severe accidents, one of the greatest concerns is potential d o w n w a r d release of the m o l t e n material t h r o u g h control rod assembhes which have weaker thermal resistance in the b o t t o m of core region, and subsequent direct contact of m o l t e n fuel jets with structures located u n d e r n e a t h . Particular emphasis should be placed on the investigation of the b r e a k u p or p e n e t r a t i o n b e h a v i o r of a large m o l t e n core material jet in the coolant, a n d also o n the erosion b e h a v i o r of the structures b y a large m o l t e n core material jet. In a n earlier p a p e r [1], the p e n e t r a t i o n b e h a v i o r of a m o l t e n jet into coolant was discussed b a s e d on the experimen-
© 1 9 9 0 - E l s e v i e r S c i e n c e P u b l i s h e r s B.V. ( N o r t h - H o l l a n d )
12
M. Saito et al. / Melting attack of solid plates Molten Jet i TI, {'rmo. i)
Ti
J]l/~ NOpha'~c-h'ng'
Structure Ts, {Trap,s)
[Case 1 ]
Molten Jet Ti, (Trap, i)
Molten Jet } Ti, T~p j) I~
Crust
Structure T,, (Trap s [ Case 2 ]
Molten Jet Tj,
(Trap,i)
ro ,oo L/,I Molten Film Structure Ts (Tmo s
[Case 3]
Film Structure T , (Trap s)
[Case 4]
Fig. 1. H e a t transfer in a m o l t e n j e t i m p i n g e m e n t on structure.
tal results performed with a (hot) water jet injected into a f r e o n - l l or liquid nitrogen pool. The present paper focuses on the erosion behavior of the structures by a high temperature molten jet. The physical and thermal characteristics of a molten jet impinging on a solid surface are classified into four categories shown as Cases 1 through 4 in fig. 1, by the combination of the jet temperature (Tj), the melting point of the jet (Trap0), the melting point of the solid structure (Trap,s), the temperature of the solid structure (T~) and the interface temperature (Ti) at the j e t / s t r u c ture interface. Many studies have been reported on the heat transfer related to liquid jet impingement on a solid surface. They include those by Sitharamayya and Subba Raju [2], Roberts [3], Savino et al. [4], Gilpin [5], Yen and Zehnder [6], Lipsett and Gilpin [7], Swedish et al. [8], Sienicki and Spencer [9], and Furutani et al. [10]. These previous studies, however, were performed for limited conditions of Cases 1 through 3 as illustrated in fig. 1 :, i.e., either no liquid-solid phase change at an impingement surface, non-melting of the solid surface or no liquid jet solidification. When the interface temperature is below the melting point of the molten jet and exceeds that of the colder solid structure, freezing of the molten jet and melting of the wall can take place simultaneously as shown in Case 4 depicted in fig. 1, This combination is very important in the case of the molten U O 2 jet impingement on the stainless steel structure as these are quahtative characteristics on a reactor accident. In this case, the steel melting rate can be reduced by a frozen layer of U O 2.
Epstein et al. [11] carried out the first theoretical and experimental study of impingement heat transfer for the simultaneous occurrence of melting and freezing in the impingement region of a hquid jet. A laminar-axisymmetric flow model was developed to describe the heat transfer in the presence of jet solidification and to predict the threshold jet temperature for the incipient jet solidification. To verify the theoretical predictions, they performed the experiments with an upward water jet (Dj0 = 4.76 mm, Vjo = 1.39 - 3.16 m / s , Tj = 1.0 80 ° C) against the lower end of a meltable rod (solid octane, Tmp.~ = - 56.6 ° C, or solid mercury, T,,w,~ = -38.9°C). Since their theoretical prediction only applies to laminar jet flow and their experimental conditions are not typical of the real reactor accident conditions, it is very important to investigate and extend the jet impingement heat transfer with simultaneous melting and freezing behavior taking place in the impingement region of a molten jet in the more realistic accident conditions. Therefore, in the present paper, a simple turbulent-axisymmetric flow model was developed by extending their theoretical model, and verifying the model with experiments performed using a molten salt (NaC1) jet impinging on tin (Sn) solid plate. The experiments were conducted in the larger jet Reynolds number region for the impinging jet with varying jet diameters (10 - 30 ram) and jet temperatures (900 - 1100 o C). The jet was accelerated to a range of 3 - 5 m / s at the nozzle outlet by the gravitational force and impinged perpendicular to the solid tin plate underneath. Furthermore, to check the more specific effects of thermophysical properties on the erosion behavior, preliminary experiments were preceded by using a molten AI203 jet ( D o = 10 ram, Tj = - 2200° C, Vj0 = - 1.4 m / s ) impinging on stainless steel plate. The experimental results were compared with the values predicted with the laminar jet flow model by Epstein et al. and the present turbulent jet flow model to discuss the applicability of the models to the reactor accident conditions.
2. Theoretical treatments
A schematic analytical model is shown in fig. 2. In the vicinity of a stagnant point in the jet flow, the heat flux q through the upper surface of the crust can be expressed empirically by:
kj q = ~(Tj
- Tmpj)fa(Re)f2(Pr),
(1)
M. Saito et aL / Melting attack of solidplates Molten Jet (Ti, Vi) ~ ' ~ 1 Di I ~
I Ill [ I ~
13
layer thickness (Sm) ,
///
q =ki/Di (Ti- Trap j) fl (Re) f, (Pr)
f'(Re>=C'Rem
~m ,~--2/3[ o ~ ~1/3a [ 24ABkj ] 1/3 Re(m- 2)/3prn/3 (4) for the melting velocity (Vm),
~, Interface Temperature, Ti ~ , ~ C r u s t ~ / g ~ ' , G ~ / ~ ¢ ~ ........... i ~,~ Z f ~m
~/xN/~
~ Melt Flow
Vm
¢l¢2PjCpj(rj - Tmpd) R e m - l P r "-1 Ps(L+cps(rmp,s- rs))
b
Structure (T~)
Fig. 2. Analytical model.
for the temperature at the lower crust surface (Ti), Ti - - Tmp,s
,'~-2/3z
Zj _ Tmpd
/
where f ] ( R e ) = c, Re m
,4/3-- kj [ 2 4 ABkj ] 1/3
~C1C2) A~-m [ ~ ]
X Re (4m 2)/3pr4n/3 (2)
k c ( r m p j - Ti)
= Cl d,j(Tj - rmpa) Re- Pr-" (3)
When the liquid melt film is very thin (called the thin film approximation), the inertia term in the m o m e n t u m equation and the convection term in the energy equation in the melt film layer can be neglected. With the following assumptions and the theoretical treatments done by Epstein et al. [11], the flow and temperature fields in the melt layer can be solved analytically: (1) The initial transient conduction stage is ignored and the melting process is assumed to occur under steady state condition. (2) The analysis is restricted to the vicinity of the stagnation point of the axisymmetric external jet flow. (3) The melt flow is assumed to be laminar and moves radially outward between the crust and the melting surface. (4) The liquid velocities at the upper and lower crust surfaces are set equal to zero. (5) The thickness of the melt layer and the crust are assumed to be spatially uniform. (6) The crust disk is assumed to be rigid. (7) All physical properties are considered constant and the densities of the liquid melt and solid structure plate are assumed to be approximately equal. With these assumptions, theoretical treatments and the thin film approximation done by Epstein et al., the following formulations can be obtained for the melting
(6)
for the crust layer thickness (3c), (~c
and f2(Pr) = c2Pr".
(s)
(7)
and for the critical jet temperature (rj.crit) above which the crust formation will not take place.
Tj,crit- Zmpd _ V~km Zmpd-- Tmp,s c1c2AjA
Prm(t+Cps(Tmps- Ts))] 1/4 2~Cp~((~mpj~pmp, 3 "
X R e ( - 2m+ l)/2 Pr -n ,
(8)
where
/"m("m/lj2
A :
B=
,
Cpm( Tj - rmp,j) L + cps(Vmp.s-
(9)
(lo)
When the jet is assumed to be in a laminar flow,
(la)
f l ( R e ) = ~/2 Re'/2 and f2(Pr) = 0.55Pr °35
(for Pr > 0.5)
(12)
that is, combination of m = ½, n = 0.35, c I = ~/2 and c 2 = 0.55 yields the same solutions for the 3m, Vm, Ti, 3¢ and Tj,mt as obtained by Epstein et al. [111. Figures 3(a) and (b) show the theoretical predictions of erosion rate and crust thickness based on the laminar jet flow model for the cases of a molten U O 2 jet impinging on the stainless steel plate and molten NaC1
14
M. Saito et al. / Melting attack of solid plates * lO-Z
* lo-Z
125
.__ UO~
~- 1 Stainless DI - Z c m
1.25 ~
~
]
___L
.........
t. . . .
~ee]
~ I
Erosion
Crust Thlckness
Crust Thic~aess
~
%
,
o
)
/
v, = 5 m / s
o~ 0.75
/
Rate
~
0.6 ~
~ 0.75
~.4/
~
.= =
.
N
NaC1 - S'n
~
D =Eem 0.2~ 1
000
3100
3300
....
0
3500
Temperature
3700
of Molten UO~ Jet (K)
O~ 700
•
Vl =
5 m/q - -
~-~ 80(]
i
......... 900
Temperature
(a) Molten UO 2 jet-stainless steel plate
~ 1000
llO(]
{k2
~ 0 120(}
o f M o l t e n NaCI J e t (~C')
(b) Molten NaCI jet-tin plate
Fig. 3. prediction of erosion rate and crust thickness (based on the laminar jet flow mode] [] t]).
jet impinging on the tin plate, respectively. It can clearly be seen that the both melting behaviors are quite similar, so that in the first series of the experiments, molten NaC1 was selected as jet material and tin plate as a solid structure.
2200
Thermocoupli
Heating Vessel /(Stainless Steel)
Melting Section
Vessel
3. Experimental facility and conditions
-Molten Material H ~P'ug (NaCl) I = J ~ J
Induction Coil
FL±0
Nozzle Section ¢10,@20.¢30 Jet Sensor High Speed Video Camera
High Speed Camera
/
Thermocouples
Test Section unit
/
/
~--
/
/
Fig. 4. MELT-II experimental facility.
/
: mm
,
/
,
The experiments were conducted in the MELT-II facility (fig. 4), which consists of the melting section, the nozzle section, the test section, the containment vessel and the argon gas cooling system. The test section is exchangeable to perform two types of experiments: a molten jet-structure interaction; and a molten jet-coolant interaction. In the melting section, up to about 30 l of material such as alumina, stainless steel and salt can be melted at a m a x i m u m temperature of about 2300 ° C by the induction heating technique and poured down to the test section as a jet through the nozzle section by pulling out the special plug at the nozzle inlet. The length of the nozzle section is about 2.1 m which is sufficient to attain a fully developed continuous jet. Argon gas is charged in the containment vessel and the test section to avoid the oxidization of the melting section and the test section during the experiment. In the first series of the experiments, molten salt (NaC1, TrapJ = 8 0 0 ° C ) jets of about 900, 1000 and 1 1 0 0 ° C impinged perpendicular to the tin (Sn, Tmp,s = 232 ° C) plates at system temperature. The nozzle diameter (Do) was varied from 10 m m to 30 ram. The nozzle
M. Saito et a L / Melting attack of solid plates
15
Table 1 Experimental conditions of a molten NaCI jet impinging on tin plates Experimental Conditions Diameter Do (mm)
~
SCTN-10-09
10
SCTN-10-11
10
I I I I
SCTN-10-10
10
No.
Plate (Sn)
Molten Jet (NaCI)
Experimental
SCTN-20-02
20
SCTN-20-03
20
SCTN-20-05
20
Temperature Thickness Vjo (m/s)
Tj (°C)
3.1
1110
3,1
1100
3,1
1100
I
i 4.3 r '
1090 4.3
1080
4.5
1090
i
Temperature Ts (°C)
Z (mm)
Reynolds Number
Prandtl Number
Re
Pr
7.09 ×104 7.74×104
0.75 0,75
6.83 Xl04 7,52 ×104 7,08×104 7.61 ×104
0.76 0.76 0.76 0.76
(c) 80
51
(d) 12 80 12 5O 30
50~ 92 (el (f) 33 42-' 63 40 45-* 90
30 50 30 80 12 40 12 4O 12 5O 30 40 12 37
56~200 44 56--' 80 44 69-+116 37 43-'133 20 20-* 53 20 30-~ 41 11 27-* 73 50
1.92 ×10 s 1.78 × 10s 1.88 X105 1.93 × 10s 2.04×10e 1.87 X10s 1.96 X 10s 1.63X10s 1.70 × 10s 1.64X10s 1,77×10s 1.61 ×10 s 1.71 ×105 1.34 Xl0 s
0,78 0.80 0,80 0,76 0.76 0.79 0,79 0.92 0.92 0.92 0.89 0.94 0,93 1.16
44 70-'137 12 12-* 49 17
1,28X10s 1.34X10s 1,37 ×10 s 1,44×10s 1,39 ×10e
1,22 1,2_2 1.13 1,13 1.10
:
SCTN-20-08
20
4.4
1080
SCTN-20-09
20
SCTN-20-10
20
4.3 4.3
1000 1000 1010
SCTN-20-11
20
4.3
990
SCTN-20-04
20
4.3
890
SCTN-20-06
20
4.3
880
SCTN-20-12
20
4.3
900
SCTN-20-13
20
4.3
910
SCTN-30-01
30
5.1
SCTN-30-02
30
5.1
SCTN-30-03
30
5.1
1090 1140 1080 1100 1100
3O 20 50 12 70
25 23-* 51 29 43-'110 20
3.23×10e 3.36x10s 3.20 Xl0 s 3.46X10s 3,30 Xl0 s
0,79 0.70 0,60 0.76 0,76
SCTN-30-05
30
5.0
SCTN-3ff04
30
4.9
980 1030 900 910
3O 12 20 12
20 23-+ 46 18 33-+ 61
2.80 x 10s 3.15×10s 2.35X10s 2,51 x l 0 s
0,94 0.86 1.13 1.09
3O 20 40 12 60
;
(g] (a) : Do is the inner diameter of a nozzle at room temperature. (b) : Vjo is the velocity of a molten jet at the nozzle outlet under the experimental (hot) condition, (c) : Thickness of the upper test plate, (d) : Thickness of the lower test plate. (el : Initial upper surface temperature of the lower test plate just before the jet impingement on an upper test plate. (f) : Upper surface temperature of the lower test plate just before the penetration of an upper test plate by a molten jet. (g) : These values were evaluated by using the physical properties of molten NaCI reported in Reference [12],
diameters in the experimental (hot) conditions were, however, enlarged by the thermal expansion, which was taken into account for the analysis. Two plates were set in a run as the target plates for the efficiency of the experiments. The jet was accelerated by the gravitational force in a range from 3.1 m / s to 5.1 m / s at the nozzle outlet. The jet velocities were evaluated from the correlation curve obtained in the separate calibration tests with water and its extrapolation to high tempera-
ture NaC1 condition and nozzle thermal expansion. The accuracy is estimated to be within a 10% error range. Additional corrections were made for the diameter (Dj) and velocity (Vj) of the jet just before the impingement on the plate, by taking account of the effect of the gravitational acceleration during the travel from the outlet of the nozzle to the plate. The distance from the lower end of the nozzle to the upper surface of the test plate ranges from about 0.10 m to 0.48 m in the
16
M. Saito et al. / Melting attack of solid plates
Table 2 Preliminar experimental conditions of a molten A]203 jet impinging on stainless steel plates Experimental Conditions Experimental No,
, Molten Jet (AI203) ~-Diameter ! Velocity Temperature Do VIo Tj (mm) (m/s) (°C) --
Thickness Z (mm)
10
~1.4
~2200
. (d) 6
(a)
(a) (hi (c) (d) (e)
: : : : :
I __ (b)
R.T. . R, T.
T
__
~ d t I Number l RNeumber
Temperature Ts ('C)
(c) 5 AOSS-IO-02
__
Plate (Stainless Steel)
Re
'
Pr
I
.
1.88 XIO 3 | . 1.95 x l O ~ _
5.46 5.46
(e)
~,
Do the inner diameter of a nozzle at room temperature. Vjo is the velocity of a molten jet at the nozzle outlet under the experimental (hot) condition. Thickness of the upper test plate. Thickness of the lower test plate. The following physical properties of molten AI203 were used in the evaluation: - T h e viscosity and density were used the values reported in Reference [13]. - T h e specific heat and thermal conductivity were estimated by extrapolating the values around the melting point at solid state to those at the melting point.
experimental conditions. The jet Reynolds number ranges from 6.8 x 10 4 to 3.5 x 10 5 in the molten NaCI jet experiments. The experimental conditions of the NaC1 jet impingement on tin plate are shown in table I.
To check the effects of thermo-physical properties on the erosion behaviors, preliminary experiments were performed on the MELT-I facility by using a molten A1203 jet impinging on stainless steel plate. The specifi-
Fig. 5. Typical erosion behavior of tin plate by a molten NaCI jet [SCTN-20-06].
17
M. Saito et al. / Melting attack of solid plates
m (Top View )
(Top View )
Fig. 6. Erosion cavities formed in tin plates in a molten NaCI jet-tin plate interaction experiments [SCTN-20-10]; (a, left) upper tin plate, bottom: A-A cross section; (b, fight) lower tin plate, bottom: B-B cross section.
cations of the MELT-I facility and the experimental technique are basically the same as those of the MELT-II facility mentioned above except for the smaller melting capacity of about 2 l due to the smaller size of the induction coil. The experimental conditions of the molten AI203 jet impingement on the stainless steel plate are shown in table 2. The penetration time was measured by break-through type sensors using thin aluminium film which were set just above and below the test plates. The erosion behaviors at the impingement surface were observed by both a high-speed video camera at 200 fps and a high-speed camera at 300 - 500 fps.
4. Experimental results and discussions Typical erosion behavior of tin plate by the molten NaC1 jet is shown in fig. 5. During the experiment, the molten jet was quite stable. With increasing the erosion depth compared with the jet diameter, however, the jet splashed up at a larger angle from the plate surface. Figure 6 shows, as an example, the shape of erosion
cavities formed in upper and lower plates in the molten NaC1 j e t - t i n plate interaction experiment [SCTN-20-10]. The holes in the plate lower surface of the erosion cavities are approximately 2 to 3 times as large as the jet diameter. Figure 7 shows the relations between the penetration time and the erosion depth (plate thickness) by a molten NaC1 jet with different diameters, DO= 10, 20 and 30 mm. The slope of the experimental data indicates the erosion rate of the plates. As seen in the figure, the erosion rates are far less than the values predicted by the model using a heat flux for a non-freezing laminar jet impinging on a non-melting wall surface. From this discrepancy, it is expected that the solid plate is protected by the insulating effects of the crust and melt layers. Also seen in fig. 7(a), the erosion rates tend to decrease with increasing erosion depth in the cases of smaller jet diameter. This kind of behavior, which has also been observed in the experiments without jet crust formation [10], must be caused by the decrease of the input heat flux of the jet to the solid structure surface due to the interaction of the jet and the stagnant molten pool in the deeply eroded hole, called the 'Pool Effect'.
18
M. Saito et al. / Melting attack of solid plates When the erosion rate is assumed constant with time, the erosion depth can be expressed simply as:
2 = Vj ,
199 ~
. //////, " N
// ~
/,
•
•
•
f •
40~
20-
Do : 10 ro_m Tj : ~ I t O 0 ° C
/
l ,, • //~y]//./
~-i
0
Time (sec) (a) Nozzle diameter IDol : 10 m m I
199
J
Predicted by•LaminarJet Flow ModelD 1l w i t h o u t Crust and Melt Layer(Tj = 1100"E)
89/ s y/
20-
++...:
.+
/,+.-"+. ......... ...........
9
"""
+
+
3
6
+ ++ :++oo++
+
12
15
(13)
where: 2 = Z / D j is the normalized erosion depth, 1~m = V ~ / V j is the normalized erosion rate, and 7 = t V J D j is the normalized erosion time. The normalized erosion depths are plotted as a function of the normalized erosion time in fig. 8. Although it can be predicted from eq. (5) that the normalized erosion rate I)m depends on the jet Reynolds number, i.e., jet velocity and diameter if m ~: 1, fig. 8 shows that I7"m has little dependency on the jet velocity or the jet diameter. This means an index number m may be close to unity. The 'Pool Effect' is also seen clearly in the figure when 2~ is greater than 4. The dependency of the normalized erosion rate I ~ on the jet temperature is shown in fig. 9 with the standard deviation. The experimental results show that the normalized erosion rate decreases as the jet temperature decreases and tends to zero when the jet temperature approaches to the jet freezing point TrapJ ( = 800°C). This tendency provides very important evidence for the existence of the thermally protective crust, which restricts the input heat flux to attack on the plate, as expected from eq. (5): the heat flux is governed and limited by the temperature difference between the jet temperature and jet freezing temperature (instead of the melting point of the structure).
I + T+ :~tooo<'c + . ,+.+r,++ :y,00+ ; 9
Time (sec)
•
I
(b) Nozzle diameter (Do) = 20 m m 109
[
7~
I - -
// /
J L
Predicted by Laminar Jet Flow Model[1~] w i t h o u t Crust and Melt Layer (Tj = 1100"(
84
i
.,.+
i
5-,
/
44
///
ef/
/
uJ
:
~/
=f
20
-
. . . . . . . . . /'".+if'+"
e"'"
• 0
o
~
.
.
~
(c)
.
/I"
Do 30 mm Tj :~ 900=C Tj :~IO00°C Tj : ~ll00"C
.
~ ~ Tim~(~)
~
,/
t~
/'
A
TI
Do
5/'
in' zf
lo
Nozzle diameter(Dg) = 3 0 r n m
Fig. 7. Erosion behavior of a tin plate by a molten NaCI jet.
0 l:')'" I0 s
(= t viol) Fig. 8. Relationship between the normalized erosion depth and time in molten NaC1 jet-tin plate interaction experiments.
19
M. Saito et al. / Melting attack of solid plates
10-a
I
',
Avora0o
ing the jet impingement on upper plates are also shown as the bars in the figures. The experimental results with the 'Pool Effect', however, are excluded in fig. 10. Theoretical prediction by the laminar jet flow model (eq. (16)) is compared with the experimental results in fig. 10(a). Since experimental data have not been obtained to sufficiently cover the wide range of the Prandtl number, the dependency of Nu m on Pr cannot be discussed in full detail in the present paper. By comparing fig. 10(b) with fig. 10(a), it can, however, be concluded that the experimental results of a molten NaC1 jet impinging on a tin plate are better predicted by eq. (15) with m = 1 and n = 1 than by the laminar jet flow
]
: S t a n d a r d Deviation
2
,."+
III
// ./
/i" BOO
700
•
/"
/"
i 900
! 1000
--
1100
1200
,let Temperature Tj (°C) Fig. 9. Dependency of the normalized erosion rate on jet temperature in molten NaCI jet-tin plate interaction experiments.
NaCI-Sn
103 Since the impingement jet heat transfer is controlled by the difference between the jet temperature (Tj) and the temperature at the upper surface of crust, i.e., the jet melting point (Tmpj) as discussed above, a convective heat transfer coefficient h can be defined as: q = h(Tj
-
Tmp,j).
10
20
30
,,-oo0"c
~
o
~I000~C
v
B
T•
~uoo'c • UzOa-S.S. ~2200°C
102
[m=
1 in Eq.(15)]
'~/~'
•
~ ~*
x
.........~
""-~.........
~
•
~.
-
Eq. (16)
[m = 112 in Eq.(15)]
(14) /
Therefore, a Nusselt number defined by Nu m = h D j / k j for the heat transfer with simultaneous freezing and melting at the impingement region is described from eq.
10t 103
i
/"
~
r
llllt
(1):
10'
i
i
i
i
=i~i
i
105
i
i
i
I
I
I 1 I {I
i
llll
IC
( a ) N u m / P r 0.3s vs. R e
NU m = ClC2 Re"Pr".
(15)
When the molten jet is laminar flow, the Nusselt number Nu m can be expressed based on the proposal by Epstein et al. [11]: Nu m = 0.55V~- Re°Spr °'35 (Pr > 0.5).
(16)
104 -
I
t
I iJ Ilii
I
103
I~t.
Re~p
llli
r
~'~
Nurn = 0"0i33
~10z
In the thin film approximation, all the heat is transferred from the jet to melt the solid plate through the crust and melt film. Therefore, the impinging heat transfer coefficient h can be obtained from the energy balance at the melting surface of the solid plate:
L
z
-
-.oo~, • ,-,2200 ~C x
h(Tj
-- Zmpj)
=
VmPs[t+Cps(Zrnp,
s -
Ts)].
(17)
Figure 10 shows the dependency of the Nusselt number for the heat transfer with simultaneous freezing and melting at the impingement region on the jet Reynolds number and Prandtl number. The error bands due to the initial temperature increases of lower plates dur-
~°°
'
......
io"
. . . . . . .
(b) NUm/Pr
io ~
. . . . . . .
io'
vs. Re
Fig. 10. Dependency of the Nusselt number for impingement heat transfer with simultaneous freezing and melting on Reynolds number and Prandtl number.
M. Saito et al. / Melting attack of solid plates
20
.
.
.
.
.
.
.
.
.
.
.
.
.
4
*
.
.
.
.
.
.
.
/
.
.
/
it jJJ/ # ~b~
.
10 t
0t .............
/
&
/
/
r
--
i
Ti
/
/
. . . . . . .
•
/
/
,,
~6 2 o • 0 0 1 mm mm mm
~,
I"/IYI
.oa, 1
:
P 0
....
0
" ,
• ,
i ~
r
'
:
--
5
r
2 .
.
.
L .
l
10
•
1 ,
•
!
/
/ /
t
,/
I:
•
15
. . . .
20
l
5
10
ZOaeo,Z (=
0.0033
20
15
pj Cpj(TTTmPo) ~'/ N L-+Cp,(q;=~,-%) t /
1
Fig. 11. Comparison of normalized erosion depths obtained in the present experiments with theoretical ones predicted by Epstein et al.'s model (laminar jet flow model).
Fig. 12. Comparison of normalized erosion depths obtained in the present experiments with theoretical ones predicted by the present study.
model ( m = 0.5 and n = 0.35). The experimental results of the Nusselt n u m b e r can be correlated by the following equation:
a molten At203 jet i m p i n g e m e n t on the stainless steel plate. F r o m eqs. (5) and (13), the normalized erosion d e p t h is obtained as:
N u m - 0.0033 R e - Pr.
(18)
2=
ClC2PjCpj(rj -- rmpd) R e "
'Pr"
1 (19)
The preliminary experimental results with a molten A1203 jet i m p i n g e m e n t on the stainless steel plate are also plotted in figs. 10(a) and (b). The correlation given by eq. (18) also predicts well the experimental results of
Ps[L+cps(rmp.s_Ts) ]
t.
W h e n for the case with rn = 0.5, n = 0.35 and q c 2 = 0.55 v~-, i.e., the jet is a laminar flow, the normalized erosion
°10 ~ I u0z - Stainless Steel ' , 0.8 1
[
7
i
o.0-
i I .
- --
/
,
,.X
3100
"
"~://
L0, ~ s 04 ~ ~
/
i 0.0
/
~0.4 "
I
'\/ "
o.'e
o0i~:2
/
I o.0~ ~ o.s
~ '
]
O=0.1m
I
-,
0, i
- ~
::":: 2 i, 0.~
/
/
><3300
L
----4
. . . . . . . . , 3,500
T e m p e r a t u r e of M o l t e n U02 J e t ( K ) ( a ) T s = 700 K
o.e ~
3700
o,Z
3100
~/
\ . ~. ' >. - -.[
"-
/ ,
,
3300
. . . . .
i I 02
-'--
,__
i-3500
~--
4 0 3700
T e m p e r a t u r e of M o l t e n U02 J e t ( K ) (b)Ts=
1100 K
Fig. 13. Prediction of erosion rate and crust thickness in a molten U O 2 jet impingement on stainless steel: - - - , laminar jet flow , present work (turbulent jet model without crust and melt film; . . . . . . , laminar jet flow model with crust and melt film; - flow model with crust and melt film).
M. Saito et al. / Melting attack of solid plates depth 2~ is expressed as:
Ztheo,1 = 0.557r2
p j C p j ( T j -- Tmpd)
R e _ 0 . 5 pr_O.65}."
,o~[L + c,,~(Tmp,s- ~)] (20)
On the other hand, for the case with m = 1, n = 1 and
ClCz = 0.0033, Z is expressed as: pjcpj (Tj - Tmpd)
2th~o,z=O.OO33ps[L+cp~(Tmp,s - Ts)] t',
(21)
1
where 2~ is independent of Re and Pr. This means that the erosion rate Vm is proportional to the jet impingement velocity Vj. Using these equations, the experimental results of normalized erosion depth are compared with the theoretical predictions by eqs. (20) and (21) in figs. 11 and 12, respectively. As anticipated, the prediction of experimental results by eq. (21) is better than by eq. (20). Figure 12 shows that the data of molten A1203 jet impingement on a stainless steel plate are also predicted fairly well by eq. (21). Figure 13 compares the erosion rate and crust thickness in a molten UO 2 jet impingement on the stainless
7000
i
J
I
I
.7.7:5,;77;vv:.:.._~___~__.st__f__o_._rm.._atioa : """""vv':; ;~
st f°rraati°n:;'~ :]'';';':"'':;:%%;77"" "''"",',',.,,v
6000
Laminar jet flow model [11]
& 5000 Present work
No Crust f o r m a t i o n
/////////////////0_ ~ f 0 - o r m a t i o n / / / ~ 4000-
3000 700
800
900
1000
1100
1200
Irxi~al T e m p e r a t u r e of b-tainless Steel, T,(K)
Fig. 14. Critical temperature of the molten UO2 jet for crust formation.
21
steel plate predicted by the present model, the Epstein's laminar flow model with crust and melt film, and the simple assumption of suppression for crust and melt film. The present model predicts thinner crust thickness, that is, a higher erosion rate than Epstein's model. Both models, which treat simultaneous freezing and melting phenomena, however, predict significantly smaller erosion rates compared with the model without crust and melt film layers. Figure 14 exemplifies the critical jet temperatures above which the crust formation will not take place for the case of a molten UO 2 jet with a diameter of 0.1 m and a velocity of 5 m / s , which are obtained by the present work and Epstein's model [11] (eq. (8)). The present results give a much lower critical jet temperature than Epstein's model, but are still in the very high temperature region. For example, a molten UO 2 jet needs to be heated well above 4000 K (higher than the UO 2 boiling point at one atmosphere) in order not to solidify as a crust layer on a melting stainless steel plate.
5. Conclusions
To investigate the effect of crust forming on the impingement region on the erosion rate of solid plates by a high temperature molten jet, a series of model experiments was performed using simulation materials. In the first series of experiments, salt (NaC1) was selected as the jet material and tin plate (Sn) as the solid structure. To check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were also performed by using a molten A1203 jet impinged on stainless steel plate at room temperature. The experimental results were compared with the values predicted by Epstein's laminar jet flow model and also by the turbulent jet flow model developed in the present study. The results in the present study are summarized as follows: (1) The erosion rates of the solid plate by the molten jet impingement are far less than the value predicted by an analytical solution that neglects the existence of crust and melting film layers. With the inclusion of the crust behavior in the theoretical model, the experimental results are predicted fairly well. (2) The existence of a thermally protective crust restricts the input heat flux from thermally attacking the solid plate. A Nusselt number for the turbulent heat transfer with the simultaneous occurrence of freezing and melting in the impingement region of a
M. Saito et al. / Melting attack of solid plates
22
molten jet is correlated by a Reynolds number and a Prandtl number as follows: N u m = 0.0033 R e . Pr. (3) In addition to the erosion rate, the present turbulent jet flow model can predict the crust thickness, melthag layer thickness and the threshold jet temperature for the crust formation. (4) When Z / D j > 4, the erosion rate tends to substantially decrease due to the interaction between the jet and the stagnant molten pool in the deep hole called the 'Pool Effect'. In conclusion, the existence of a crust layer plays an important role in the erosion process of the solid plate in the case of a molten fuel jet with a high melting point like a reactor accident situation. However encouraging these results, additional theoretical and experimental efforts are required before the present results can be applied to the reactor accident analysis.
? T
Tmpj Tmp,s
r~
rj Vm
Cm
Vj Z
Z
2
Greek symbols
~m /z
Acknowledgments The authors wish to thank the section manager, Mr N. Tanaka for his valuable comments and support on the subject. We are grateful also to Messrs N. Ushiki, T. Takaha, T. Sekine, K. Shimizu, S. Sato and K. Suganuma of the SAG-3 group of the F B R safety Engineering Section, P N C for their technical and computational contributions to the present study.
p
0 C
exp
J s
dimensionless property ratio defined by eq.
(9) B
Cp
19o h k L Nu m
Pr
q r
Re t
melting parameter defined by eq. (10) heat capacity nozzle inner diameter at r o o m temperature jet diameter heat transfer coefficient thermal conductivity latent heat of fusion of the solid plate Nusselt number for the heat transfer with simultaneous freezing and melting at the jet impingement region Prandtl number ( c m ~ J k j ) heat flux radial coordinate Reynolds number (pjVjjDj//~j) time
crust thickness melt film thickness viscosity kinematic viscosity density
Subscripts
m
Nomenclature
normalized time ( t V y D j ) temperature melting point of the jet melting point of the sohd plate initial temperature of the solid plate interface temperature (temperature of the lower surface of the crust) temperature of the impinging jet erosion rate of the solid plate normalized erosion rate (Vm/Vj) jet velocity coordinate perpendicular to the melting surface erosion depth normalized erosion depth (Z/Dj)
theo
at the nozzle outlet crust experiment molten jet melt film structure plate theoretical prediction
References [1] M. Saito, K. Sato and S. Imahori, Experimental study on penetration behaviors of water jet into freon-11 and liquid nitrogen, ANS Proc. 1988 National Heat Transfer Conf., Houston, TX (July 24-27, 1988) 173-183. [2] S. Sitharamayya and K. Subba Raju, Heat transfer between an axisymmetric jet and a plate held normal to the flow, Can. J. Chem. Eng. 47 (1969) 365. [3] A.L. Roberts, On the melting of a semi-infinite body of ice placed in a hot steam of air, J. Fluid Mech. 4 (1958) 505. [4] J.M. Savino, J.F. Zumdieck and R. Siegel, Experimental study of freezing and melting of flowing warm water at a stagnation point on a cold plate, Fourth Int. Heat Transfer Conf., Cu 2.10 (1970). [5] R.R. Gilpin, The ablation of ice by a water jet, Trans. Can. Soc. Mech. Engrs. 2 (1973) 91.
M. Saito et al. / Melting attack of solid plates [6] Y. Yen and A. Zehnder, Melting heat transfer with water jet, Int. J. Heat Mass Transfer 16 (1973) 219. [7] A.W. Lipsett and R.R. Gilpin, Laminar jet impingement heat transfer including the effects of melting, Int. J. Heat Mass Transfer 21 (1978) 25. [8] M.J. Swedish, M. Epstein, J.H. Linehan, G.A. Lambert, G.M. Hauser and L.J. Stachyra, Surface ablation in the impingement region of a liquid jet, AIChE J. 25 (4) (1979) 630. [9] J.J. Sienicki and B.W. Spencer, Analysis of reactor material experiments investigating corium crust stability and heat transfer in jet impingement flow, ANS Proc. 1985 National Heat Transfer Conf., Denver, Colorado (1985). [10] A. Furutani, S. Imahori, K. Sato and M. Saito, Erosion behavior of solid plate by a liquid jet - effect of molten
23
layer, ANS Proc. 1989 National Heat Transfer Conf., Philadelphia, PA (August 6-10, 1989) 263-271. [11] M. Epstein, M.J. Swedish, J.H. Linehan, G.A. Lambert, G.M. Hauser and L.J. Stachyra, Simultaneous melting and freezing in the impingement region of a liquid jet, AIChE J. 26 (5) (1980) 743. [12] G.J. Janz, C.B. Allen, N.P. Bansal, R.M. Murphy and R.P.T. Tomkins, Physical properties data compilations relevant to energy storage. II. Molten salts: Data on single and multi-component salt systems, NSRDS-NBS (US) 61, Part II (April 1979). [13] V.P. Elyutin, B.C. Mitin and Yu.A. Nagibin, Properties of liquid alumina (Svoystva Zhidkoi Okisi Alyuminiya) ANL-TRANS-987 (August 1975) (Source: Fizika Aerodispersnykh Sistem No. 7 (1972) pp. 104-09).
11
MELTING - EFFECT
ATTACK OF SOLID PLATES OF CRUST FORMATION *
BY A HIGH
TEMPERATURE
M. SAITO
* *, K. S A T O , A. F U R U T A N I ,
M. ISOZAKI,
S. I M A H O R I
LIQUID
JET
a n d Y. H A T T O R I
***
Safety Engineering Division, O-arai Engineering Center, Power Reactor and Nuclear Fuel Development Corporation, 4002 Narita, O-arai-machi, Ibaraki-ken 311-13, Japan Received 10 November 1989
When a molten UO 2 jet impinges on a steel structure in a reactor vessel during a severe accident, the erosion rate of the steel by the molten UO 2 jet is expected to be limited considerably by a UO 2 crust layer forming on a molten steel substrate at the jet/steel plate interface. A series of simulation experiments was performed to study the melting behavior of solid plates by high temperature liquid jets and the effects of crust forming at jet/structure interface. In the first series of experiments, salt (NaCI) was selected as the jet material and tin (Sn) as the solid structure. The experiments were conducted with varying the jet diameter (10 - 30 ram) and jet temperature (900 -1100 o C). The jets were accelerated to a range of 3 - 5 m / s at the nozzle outlet by gravitational force and impinged perpendicularly to the solid plate underneath. Furthermore, to check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were performed by using a molten A1203 jet ( - 2200 ° C) impinging on stainless steel plate at room temperature. The erosion rates obtained in the present experiments were far less than the values predicted by an analytical solution that neglects the existence of a crust layer and its thermal effects. With the inclusion of the crust behavior in the model, the experimental results were predicted fairly well. From the present experiments, a Nusselt number of the turbulent heat transfer, which takes into account simultaneous melting and freezing in the impingement region of a molten jet, is correlated by a Reynolds number and a Prandtl number as follows: Nu,, = 0.0033 Re- Pr. In conclusion, the existence of a crust layer plays an important role in the erosion process of a solid plate by the molten fuel jet with high melting point as in a reactor situation.
1. Introduction
A large technical d a t a b a s e a n d more reliable theoretical models are needed for assessing the i n h e r e n t retention a b i h t y of m o l t e n core materials without leading to vessel failure a n d the release of a large a m o u n t of radioactive materials after p e r m a n e n t neutronic shutd o w n of L M F B R severe accidents. After a p e r m a n e n t s h u t d o w n is achieved by the fuel dispersal from the reactor core region, the m o l t e n core materials r e m a i n i n g
* Originally presented at the 26th ASME/AIChE National Heat Transfer Conference, Philadelphia, PA, August 6-9, 1989. * * Presently with Department of Nuclear Engineering, Faculty of Engineering, Osaka University, Yamada-oka, Suita-shi, Osaka 565, Japan. * * * Presently with Shinko Plant Engineering Company, Inc., 1-20-11 Nishikojiya, Ohta-ku, Tokyo 144, Japan. 0029-5493/90/$03.50
in the region m a y either be encapsuled by the crust a n d cooled d o w n by the a m b i e n t coolant a n d cold structures, or m a y penetrate the lower core assembly in the d o w n w a r d direction by the c o m b i n e d effects of gravity a n d the residual decay heat generation, resulting in a discharge into a lower p l e n u m region. In the P A M R (Post-Accident Materials Relocation) phase in the L M F B R severe accidents, one of the greatest concerns is potential d o w n w a r d release of the m o l t e n material t h r o u g h control rod assembhes which have weaker thermal resistance in the b o t t o m of core region, and subsequent direct contact of m o l t e n fuel jets with structures located u n d e r n e a t h . Particular emphasis should be placed on the investigation of the b r e a k u p or p e n e t r a t i o n b e h a v i o r of a large m o l t e n core material jet in the coolant, a n d also o n the erosion b e h a v i o r of the structures b y a large m o l t e n core material jet. In a n earlier p a p e r [1], the p e n e t r a t i o n b e h a v i o r of a m o l t e n jet into coolant was discussed b a s e d on the experimen-
© 1 9 9 0 - E l s e v i e r S c i e n c e P u b l i s h e r s B.V. ( N o r t h - H o l l a n d )
12
M. Saito et al. / Melting attack of solid plates Molten Jet i TI, {'rmo. i)
Ti
J]l/~ NOpha'~c-h'ng'
Structure Ts, {Trap,s)
[Case 1 ]
Molten Jet Ti, (Trap, i)
Molten Jet } Ti, T~p j) I~
Crust
Structure T,, (Trap s [ Case 2 ]
Molten Jet Tj,
(Trap,i)
ro ,oo L/,I Molten Film Structure Ts (Tmo s
[Case 3]
Film Structure T , (Trap s)
[Case 4]
Fig. 1. H e a t transfer in a m o l t e n j e t i m p i n g e m e n t on structure.
tal results performed with a (hot) water jet injected into a f r e o n - l l or liquid nitrogen pool. The present paper focuses on the erosion behavior of the structures by a high temperature molten jet. The physical and thermal characteristics of a molten jet impinging on a solid surface are classified into four categories shown as Cases 1 through 4 in fig. 1, by the combination of the jet temperature (Tj), the melting point of the jet (Trap0), the melting point of the solid structure (Trap,s), the temperature of the solid structure (T~) and the interface temperature (Ti) at the j e t / s t r u c ture interface. Many studies have been reported on the heat transfer related to liquid jet impingement on a solid surface. They include those by Sitharamayya and Subba Raju [2], Roberts [3], Savino et al. [4], Gilpin [5], Yen and Zehnder [6], Lipsett and Gilpin [7], Swedish et al. [8], Sienicki and Spencer [9], and Furutani et al. [10]. These previous studies, however, were performed for limited conditions of Cases 1 through 3 as illustrated in fig. 1 :, i.e., either no liquid-solid phase change at an impingement surface, non-melting of the solid surface or no liquid jet solidification. When the interface temperature is below the melting point of the molten jet and exceeds that of the colder solid structure, freezing of the molten jet and melting of the wall can take place simultaneously as shown in Case 4 depicted in fig. 1, This combination is very important in the case of the molten U O 2 jet impingement on the stainless steel structure as these are quahtative characteristics on a reactor accident. In this case, the steel melting rate can be reduced by a frozen layer of U O 2.
Epstein et al. [11] carried out the first theoretical and experimental study of impingement heat transfer for the simultaneous occurrence of melting and freezing in the impingement region of a hquid jet. A laminar-axisymmetric flow model was developed to describe the heat transfer in the presence of jet solidification and to predict the threshold jet temperature for the incipient jet solidification. To verify the theoretical predictions, they performed the experiments with an upward water jet (Dj0 = 4.76 mm, Vjo = 1.39 - 3.16 m / s , Tj = 1.0 80 ° C) against the lower end of a meltable rod (solid octane, Tmp.~ = - 56.6 ° C, or solid mercury, T,,w,~ = -38.9°C). Since their theoretical prediction only applies to laminar jet flow and their experimental conditions are not typical of the real reactor accident conditions, it is very important to investigate and extend the jet impingement heat transfer with simultaneous melting and freezing behavior taking place in the impingement region of a molten jet in the more realistic accident conditions. Therefore, in the present paper, a simple turbulent-axisymmetric flow model was developed by extending their theoretical model, and verifying the model with experiments performed using a molten salt (NaC1) jet impinging on tin (Sn) solid plate. The experiments were conducted in the larger jet Reynolds number region for the impinging jet with varying jet diameters (10 - 30 ram) and jet temperatures (900 - 1100 o C). The jet was accelerated to a range of 3 - 5 m / s at the nozzle outlet by the gravitational force and impinged perpendicular to the solid tin plate underneath. Furthermore, to check the more specific effects of thermophysical properties on the erosion behavior, preliminary experiments were preceded by using a molten AI203 jet ( D o = 10 ram, Tj = - 2200° C, Vj0 = - 1.4 m / s ) impinging on stainless steel plate. The experimental results were compared with the values predicted with the laminar jet flow model by Epstein et al. and the present turbulent jet flow model to discuss the applicability of the models to the reactor accident conditions.
2. Theoretical treatments
A schematic analytical model is shown in fig. 2. In the vicinity of a stagnant point in the jet flow, the heat flux q through the upper surface of the crust can be expressed empirically by:
kj q = ~(Tj
- Tmpj)fa(Re)f2(Pr),
(1)
M. Saito et aL / Melting attack of solidplates Molten Jet (Ti, Vi) ~ ' ~ 1 Di I ~
I Ill [ I ~
13
layer thickness (Sm) ,
///
q =ki/Di (Ti- Trap j) fl (Re) f, (Pr)
f'(Re>=C'Rem
~m ,~--2/3[ o ~ ~1/3a [ 24ABkj ] 1/3 Re(m- 2)/3prn/3 (4) for the melting velocity (Vm),
~, Interface Temperature, Ti ~ , ~ C r u s t ~ / g ~ ' , G ~ / ~ ¢ ~ ........... i ~,~ Z f ~m
~/xN/~
~ Melt Flow
Vm
¢l¢2PjCpj(rj - Tmpd) R e m - l P r "-1 Ps(L+cps(rmp,s- rs))
b
Structure (T~)
Fig. 2. Analytical model.
for the temperature at the lower crust surface (Ti), Ti - - Tmp,s
,'~-2/3z
Zj _ Tmpd
/
where f ] ( R e ) = c, Re m
,4/3-- kj [ 2 4 ABkj ] 1/3
~C1C2) A~-m [ ~ ]
X Re (4m 2)/3pr4n/3 (2)
k c ( r m p j - Ti)
= Cl d,j(Tj - rmpa) Re- Pr-" (3)
When the liquid melt film is very thin (called the thin film approximation), the inertia term in the m o m e n t u m equation and the convection term in the energy equation in the melt film layer can be neglected. With the following assumptions and the theoretical treatments done by Epstein et al. [11], the flow and temperature fields in the melt layer can be solved analytically: (1) The initial transient conduction stage is ignored and the melting process is assumed to occur under steady state condition. (2) The analysis is restricted to the vicinity of the stagnation point of the axisymmetric external jet flow. (3) The melt flow is assumed to be laminar and moves radially outward between the crust and the melting surface. (4) The liquid velocities at the upper and lower crust surfaces are set equal to zero. (5) The thickness of the melt layer and the crust are assumed to be spatially uniform. (6) The crust disk is assumed to be rigid. (7) All physical properties are considered constant and the densities of the liquid melt and solid structure plate are assumed to be approximately equal. With these assumptions, theoretical treatments and the thin film approximation done by Epstein et al., the following formulations can be obtained for the melting
(6)
for the crust layer thickness (3c), (~c
and f2(Pr) = c2Pr".
(s)
(7)
and for the critical jet temperature (rj.crit) above which the crust formation will not take place.
Tj,crit- Zmpd _ V~km Zmpd-- Tmp,s c1c2AjA
Prm(t+Cps(Tmps- Ts))] 1/4 2~Cp~((~mpj~pmp, 3 "
X R e ( - 2m+ l)/2 Pr -n ,
(8)
where
/"m("m/lj2
A :
B=
,
Cpm( Tj - rmp,j) L + cps(Vmp.s-
(9)
(lo)
When the jet is assumed to be in a laminar flow,
(la)
f l ( R e ) = ~/2 Re'/2 and f2(Pr) = 0.55Pr °35
(for Pr > 0.5)
(12)
that is, combination of m = ½, n = 0.35, c I = ~/2 and c 2 = 0.55 yields the same solutions for the 3m, Vm, Ti, 3¢ and Tj,mt as obtained by Epstein et al. [111. Figures 3(a) and (b) show the theoretical predictions of erosion rate and crust thickness based on the laminar jet flow model for the cases of a molten U O 2 jet impinging on the stainless steel plate and molten NaC1
14
M. Saito et al. / Melting attack of solid plates * lO-Z
* lo-Z
125
.__ UO~
~- 1 Stainless DI - Z c m
1.25 ~
~
]
___L
.........
t. . . .
~ee]
~ I
Erosion
Crust Thlckness
Crust Thic~aess
~
%
,
o
)
/
v, = 5 m / s
o~ 0.75
/
Rate
~
0.6 ~
~ 0.75
~.4/
~
.= =
.
N
NaC1 - S'n
~
D =Eem 0.2~ 1
000
3100
3300
....
0
3500
Temperature
3700
of Molten UO~ Jet (K)
O~ 700
•
Vl =
5 m/q - -
~-~ 80(]
i
......... 900
Temperature
(a) Molten UO 2 jet-stainless steel plate
~ 1000
llO(]
{k2
~ 0 120(}
o f M o l t e n NaCI J e t (~C')
(b) Molten NaCI jet-tin plate
Fig. 3. prediction of erosion rate and crust thickness (based on the laminar jet flow mode] [] t]).
jet impinging on the tin plate, respectively. It can clearly be seen that the both melting behaviors are quite similar, so that in the first series of the experiments, molten NaC1 was selected as jet material and tin plate as a solid structure.
2200
Thermocoupli
Heating Vessel /(Stainless Steel)
Melting Section
Vessel
3. Experimental facility and conditions
-Molten Material H ~P'ug (NaCl) I = J ~ J
Induction Coil
FL±0
Nozzle Section ¢10,@20.¢30 Jet Sensor High Speed Video Camera
High Speed Camera
/
Thermocouples
Test Section unit
/
/
~--
/
/
Fig. 4. MELT-II experimental facility.
/
: mm
,
/
,
The experiments were conducted in the MELT-II facility (fig. 4), which consists of the melting section, the nozzle section, the test section, the containment vessel and the argon gas cooling system. The test section is exchangeable to perform two types of experiments: a molten jet-structure interaction; and a molten jet-coolant interaction. In the melting section, up to about 30 l of material such as alumina, stainless steel and salt can be melted at a m a x i m u m temperature of about 2300 ° C by the induction heating technique and poured down to the test section as a jet through the nozzle section by pulling out the special plug at the nozzle inlet. The length of the nozzle section is about 2.1 m which is sufficient to attain a fully developed continuous jet. Argon gas is charged in the containment vessel and the test section to avoid the oxidization of the melting section and the test section during the experiment. In the first series of the experiments, molten salt (NaC1, TrapJ = 8 0 0 ° C ) jets of about 900, 1000 and 1 1 0 0 ° C impinged perpendicular to the tin (Sn, Tmp,s = 232 ° C) plates at system temperature. The nozzle diameter (Do) was varied from 10 m m to 30 ram. The nozzle
M. Saito et a L / Melting attack of solid plates
15
Table 1 Experimental conditions of a molten NaCI jet impinging on tin plates Experimental Conditions Diameter Do (mm)
~
SCTN-10-09
10
SCTN-10-11
10
I I I I
SCTN-10-10
10
No.
Plate (Sn)
Molten Jet (NaCI)
Experimental
SCTN-20-02
20
SCTN-20-03
20
SCTN-20-05
20
Temperature Thickness Vjo (m/s)
Tj (°C)
3.1
1110
3,1
1100
3,1
1100
I
i 4.3 r '
1090 4.3
1080
4.5
1090
i
Temperature Ts (°C)
Z (mm)
Reynolds Number
Prandtl Number
Re
Pr
7.09 ×104 7.74×104
0.75 0,75
6.83 Xl04 7,52 ×104 7,08×104 7.61 ×104
0.76 0.76 0.76 0.76
(c) 80
51
(d) 12 80 12 5O 30
50~ 92 (el (f) 33 42-' 63 40 45-* 90
30 50 30 80 12 40 12 4O 12 5O 30 40 12 37
56~200 44 56--' 80 44 69-+116 37 43-'133 20 20-* 53 20 30-~ 41 11 27-* 73 50
1.92 ×10 s 1.78 × 10s 1.88 X105 1.93 × 10s 2.04×10e 1.87 X10s 1.96 X 10s 1.63X10s 1.70 × 10s 1.64X10s 1,77×10s 1.61 ×10 s 1.71 ×105 1.34 Xl0 s
0,78 0.80 0,80 0,76 0.76 0.79 0,79 0.92 0.92 0.92 0.89 0.94 0,93 1.16
44 70-'137 12 12-* 49 17
1,28X10s 1.34X10s 1,37 ×10 s 1,44×10s 1,39 ×10e
1,22 1,2_2 1.13 1,13 1.10
:
SCTN-20-08
20
4.4
1080
SCTN-20-09
20
SCTN-20-10
20
4.3 4.3
1000 1000 1010
SCTN-20-11
20
4.3
990
SCTN-20-04
20
4.3
890
SCTN-20-06
20
4.3
880
SCTN-20-12
20
4.3
900
SCTN-20-13
20
4.3
910
SCTN-30-01
30
5.1
SCTN-30-02
30
5.1
SCTN-30-03
30
5.1
1090 1140 1080 1100 1100
3O 20 50 12 70
25 23-* 51 29 43-'110 20
3.23×10e 3.36x10s 3.20 Xl0 s 3.46X10s 3,30 Xl0 s
0,79 0.70 0,60 0.76 0,76
SCTN-30-05
30
5.0
SCTN-3ff04
30
4.9
980 1030 900 910
3O 12 20 12
20 23-+ 46 18 33-+ 61
2.80 x 10s 3.15×10s 2.35X10s 2,51 x l 0 s
0,94 0.86 1.13 1.09
3O 20 40 12 60
;
(g] (a) : Do is the inner diameter of a nozzle at room temperature. (b) : Vjo is the velocity of a molten jet at the nozzle outlet under the experimental (hot) condition, (c) : Thickness of the upper test plate, (d) : Thickness of the lower test plate. (el : Initial upper surface temperature of the lower test plate just before the jet impingement on an upper test plate. (f) : Upper surface temperature of the lower test plate just before the penetration of an upper test plate by a molten jet. (g) : These values were evaluated by using the physical properties of molten NaCI reported in Reference [12],
diameters in the experimental (hot) conditions were, however, enlarged by the thermal expansion, which was taken into account for the analysis. Two plates were set in a run as the target plates for the efficiency of the experiments. The jet was accelerated by the gravitational force in a range from 3.1 m / s to 5.1 m / s at the nozzle outlet. The jet velocities were evaluated from the correlation curve obtained in the separate calibration tests with water and its extrapolation to high tempera-
ture NaC1 condition and nozzle thermal expansion. The accuracy is estimated to be within a 10% error range. Additional corrections were made for the diameter (Dj) and velocity (Vj) of the jet just before the impingement on the plate, by taking account of the effect of the gravitational acceleration during the travel from the outlet of the nozzle to the plate. The distance from the lower end of the nozzle to the upper surface of the test plate ranges from about 0.10 m to 0.48 m in the
16
M. Saito et al. / Melting attack of solid plates
Table 2 Preliminar experimental conditions of a molten A]203 jet impinging on stainless steel plates Experimental Conditions Experimental No,
, Molten Jet (AI203) ~-Diameter ! Velocity Temperature Do VIo Tj (mm) (m/s) (°C) --
Thickness Z (mm)
10
~1.4
~2200
. (d) 6
(a)
(a) (hi (c) (d) (e)
: : : : :
I __ (b)
R.T. . R, T.
T
__
~ d t I Number l RNeumber
Temperature Ts ('C)
(c) 5 AOSS-IO-02
__
Plate (Stainless Steel)
Re
'
Pr
I
.
1.88 XIO 3 | . 1.95 x l O ~ _
5.46 5.46
(e)
~,
Do the inner diameter of a nozzle at room temperature. Vjo is the velocity of a molten jet at the nozzle outlet under the experimental (hot) condition. Thickness of the upper test plate. Thickness of the lower test plate. The following physical properties of molten AI203 were used in the evaluation: - T h e viscosity and density were used the values reported in Reference [13]. - T h e specific heat and thermal conductivity were estimated by extrapolating the values around the melting point at solid state to those at the melting point.
experimental conditions. The jet Reynolds number ranges from 6.8 x 10 4 to 3.5 x 10 5 in the molten NaCI jet experiments. The experimental conditions of the NaC1 jet impingement on tin plate are shown in table I.
To check the effects of thermo-physical properties on the erosion behaviors, preliminary experiments were performed on the MELT-I facility by using a molten A1203 jet impinging on stainless steel plate. The specifi-
Fig. 5. Typical erosion behavior of tin plate by a molten NaCI jet [SCTN-20-06].
17
M. Saito et al. / Melting attack of solid plates
m (Top View )
(Top View )
Fig. 6. Erosion cavities formed in tin plates in a molten NaCI jet-tin plate interaction experiments [SCTN-20-10]; (a, left) upper tin plate, bottom: A-A cross section; (b, fight) lower tin plate, bottom: B-B cross section.
cations of the MELT-I facility and the experimental technique are basically the same as those of the MELT-II facility mentioned above except for the smaller melting capacity of about 2 l due to the smaller size of the induction coil. The experimental conditions of the molten AI203 jet impingement on the stainless steel plate are shown in table 2. The penetration time was measured by break-through type sensors using thin aluminium film which were set just above and below the test plates. The erosion behaviors at the impingement surface were observed by both a high-speed video camera at 200 fps and a high-speed camera at 300 - 500 fps.
4. Experimental results and discussions Typical erosion behavior of tin plate by the molten NaC1 jet is shown in fig. 5. During the experiment, the molten jet was quite stable. With increasing the erosion depth compared with the jet diameter, however, the jet splashed up at a larger angle from the plate surface. Figure 6 shows, as an example, the shape of erosion
cavities formed in upper and lower plates in the molten NaC1 j e t - t i n plate interaction experiment [SCTN-20-10]. The holes in the plate lower surface of the erosion cavities are approximately 2 to 3 times as large as the jet diameter. Figure 7 shows the relations between the penetration time and the erosion depth (plate thickness) by a molten NaC1 jet with different diameters, DO= 10, 20 and 30 mm. The slope of the experimental data indicates the erosion rate of the plates. As seen in the figure, the erosion rates are far less than the values predicted by the model using a heat flux for a non-freezing laminar jet impinging on a non-melting wall surface. From this discrepancy, it is expected that the solid plate is protected by the insulating effects of the crust and melt layers. Also seen in fig. 7(a), the erosion rates tend to decrease with increasing erosion depth in the cases of smaller jet diameter. This kind of behavior, which has also been observed in the experiments without jet crust formation [10], must be caused by the decrease of the input heat flux of the jet to the solid structure surface due to the interaction of the jet and the stagnant molten pool in the deeply eroded hole, called the 'Pool Effect'.
18
M. Saito et al. / Melting attack of solid plates When the erosion rate is assumed constant with time, the erosion depth can be expressed simply as:
2 = Vj ,
199 ~
. //////, " N
// ~
/,
•
•
•
f •
40~
20-
Do : 10 ro_m Tj : ~ I t O 0 ° C
/
l ,, • //~y]//./
~-i
0
Time (sec) (a) Nozzle diameter IDol : 10 m m I
199
J
Predicted by•LaminarJet Flow ModelD 1l w i t h o u t Crust and Melt Layer(Tj = 1100"E)
89/ s y/
20-
++...:
.+
/,+.-"+. ......... ...........
9
"""
+
+
3
6
+ ++ :++oo++
+
12
15
(13)
where: 2 = Z / D j is the normalized erosion depth, 1~m = V ~ / V j is the normalized erosion rate, and 7 = t V J D j is the normalized erosion time. The normalized erosion depths are plotted as a function of the normalized erosion time in fig. 8. Although it can be predicted from eq. (5) that the normalized erosion rate I)m depends on the jet Reynolds number, i.e., jet velocity and diameter if m ~: 1, fig. 8 shows that I7"m has little dependency on the jet velocity or the jet diameter. This means an index number m may be close to unity. The 'Pool Effect' is also seen clearly in the figure when 2~ is greater than 4. The dependency of the normalized erosion rate I ~ on the jet temperature is shown in fig. 9 with the standard deviation. The experimental results show that the normalized erosion rate decreases as the jet temperature decreases and tends to zero when the jet temperature approaches to the jet freezing point TrapJ ( = 800°C). This tendency provides very important evidence for the existence of the thermally protective crust, which restricts the input heat flux to attack on the plate, as expected from eq. (5): the heat flux is governed and limited by the temperature difference between the jet temperature and jet freezing temperature (instead of the melting point of the structure).
I + T+ :~tooo<'c + . ,+.+r,++ :y,00+ ; 9
Time (sec)
•
I
(b) Nozzle diameter (Do) = 20 m m 109
[
7~
I - -
// /
J L
Predicted by Laminar Jet Flow Model[1~] w i t h o u t Crust and Melt Layer (Tj = 1100"(
84
i
.,.+
i
5-,
/
44
///
ef/
/
uJ
:
~/
=f
20
-
. . . . . . . . . /'".+if'+"
e"'"
• 0
o
~
.
.
~
(c)
.
/I"
Do 30 mm Tj :~ 900=C Tj :~IO00°C Tj : ~ll00"C
.
~ ~ Tim~(~)
~
,/
t~
/'
A
TI
Do
5/'
in' zf
lo
Nozzle diameter(Dg) = 3 0 r n m
Fig. 7. Erosion behavior of a tin plate by a molten NaCI jet.
0 l:')'" I0 s
(= t viol) Fig. 8. Relationship between the normalized erosion depth and time in molten NaC1 jet-tin plate interaction experiments.
19
M. Saito et al. / Melting attack of solid plates
10-a
I
',
Avora0o
ing the jet impingement on upper plates are also shown as the bars in the figures. The experimental results with the 'Pool Effect', however, are excluded in fig. 10. Theoretical prediction by the laminar jet flow model (eq. (16)) is compared with the experimental results in fig. 10(a). Since experimental data have not been obtained to sufficiently cover the wide range of the Prandtl number, the dependency of Nu m on Pr cannot be discussed in full detail in the present paper. By comparing fig. 10(b) with fig. 10(a), it can, however, be concluded that the experimental results of a molten NaC1 jet impinging on a tin plate are better predicted by eq. (15) with m = 1 and n = 1 than by the laminar jet flow
]
: S t a n d a r d Deviation
2
,."+
III
// ./
/i" BOO
700
•
/"
/"
i 900
! 1000
--
1100
1200
,let Temperature Tj (°C) Fig. 9. Dependency of the normalized erosion rate on jet temperature in molten NaCI jet-tin plate interaction experiments.
NaCI-Sn
103 Since the impingement jet heat transfer is controlled by the difference between the jet temperature (Tj) and the temperature at the upper surface of crust, i.e., the jet melting point (Tmpj) as discussed above, a convective heat transfer coefficient h can be defined as: q = h(Tj
-
Tmp,j).
10
20
30
,,-oo0"c
~
o
~I000~C
v
B
T•
~uoo'c • UzOa-S.S. ~2200°C
102
[m=
1 in Eq.(15)]
'~/~'
•
~ ~*
x
.........~
""-~.........
~
•
~.
-
Eq. (16)
[m = 112 in Eq.(15)]
(14) /
Therefore, a Nusselt number defined by Nu m = h D j / k j for the heat transfer with simultaneous freezing and melting at the impingement region is described from eq.
10t 103
i
/"
~
r
llllt
(1):
10'
i
i
i
i
=i~i
i
105
i
i
i
I
I
I 1 I {I
i
llll
IC
( a ) N u m / P r 0.3s vs. R e
NU m = ClC2 Re"Pr".
(15)
When the molten jet is laminar flow, the Nusselt number Nu m can be expressed based on the proposal by Epstein et al. [11]: Nu m = 0.55V~- Re°Spr °'35 (Pr > 0.5).
(16)
104 -
I
t
I iJ Ilii
I
103
I~t.
Re~p
llli
r
~'~
Nurn = 0"0i33
~10z
In the thin film approximation, all the heat is transferred from the jet to melt the solid plate through the crust and melt film. Therefore, the impinging heat transfer coefficient h can be obtained from the energy balance at the melting surface of the solid plate:
L
z
-
-.oo~, • ,-,2200 ~C x
h(Tj
-- Zmpj)
=
VmPs[t+Cps(Zrnp,
s -
Ts)].
(17)
Figure 10 shows the dependency of the Nusselt number for the heat transfer with simultaneous freezing and melting at the impingement region on the jet Reynolds number and Prandtl number. The error bands due to the initial temperature increases of lower plates dur-
~°°
'
......
io"
. . . . . . .
(b) NUm/Pr
io ~
. . . . . . .
io'
vs. Re
Fig. 10. Dependency of the Nusselt number for impingement heat transfer with simultaneous freezing and melting on Reynolds number and Prandtl number.
M. Saito et al. / Melting attack of solid plates
20
.
.
.
.
.
.
.
.
.
.
.
.
.
4
*
.
.
.
.
.
.
.
/
.
.
/
it jJJ/ # ~b~
.
10 t
0t .............
/
&
/
/
r
--
i
Ti
/
/
. . . . . . .
•
/
/
,,
~6 2 o • 0 0 1 mm mm mm
~,
I"/IYI
.oa, 1
:
P 0
....
0
" ,
• ,
i ~
r
'
:
--
5
r
2 .
.
.
L .
l
10
•
1 ,
•
!
/
/ /
t
,/
I:
•
15
. . . .
20
l
5
10
ZOaeo,Z (=
0.0033
20
15
pj Cpj(TTTmPo) ~'/ N L-+Cp,(q;=~,-%) t /
1
Fig. 11. Comparison of normalized erosion depths obtained in the present experiments with theoretical ones predicted by Epstein et al.'s model (laminar jet flow model).
Fig. 12. Comparison of normalized erosion depths obtained in the present experiments with theoretical ones predicted by the present study.
model ( m = 0.5 and n = 0.35). The experimental results of the Nusselt n u m b e r can be correlated by the following equation:
a molten At203 jet i m p i n g e m e n t on the stainless steel plate. F r o m eqs. (5) and (13), the normalized erosion d e p t h is obtained as:
N u m - 0.0033 R e - Pr.
(18)
2=
ClC2PjCpj(rj -- rmpd) R e "
'Pr"
1 (19)
The preliminary experimental results with a molten A1203 jet i m p i n g e m e n t on the stainless steel plate are also plotted in figs. 10(a) and (b). The correlation given by eq. (18) also predicts well the experimental results of
Ps[L+cps(rmp.s_Ts) ]
t.
W h e n for the case with rn = 0.5, n = 0.35 and q c 2 = 0.55 v~-, i.e., the jet is a laminar flow, the normalized erosion
°10 ~ I u0z - Stainless Steel ' , 0.8 1
[
7
i
o.0-
i I .
- --
/
,
,.X
3100
"
"~://
L0, ~ s 04 ~ ~
/
i 0.0
/
~0.4 "
I
'\/ "
o.'e
o0i~:2
/
I o.0~ ~ o.s
~ '
]
O=0.1m
I
-,
0, i
- ~
::":: 2 i, 0.~
/
/
><3300
L
----4
. . . . . . . . , 3,500
T e m p e r a t u r e of M o l t e n U02 J e t ( K ) ( a ) T s = 700 K
o.e ~
3700
o,Z
3100
~/
\ . ~. ' >. - -.[
"-
/ ,
,
3300
. . . . .
i I 02
-'--
,__
i-3500
~--
4 0 3700
T e m p e r a t u r e of M o l t e n U02 J e t ( K ) (b)Ts=
1100 K
Fig. 13. Prediction of erosion rate and crust thickness in a molten U O 2 jet impingement on stainless steel: - - - , laminar jet flow , present work (turbulent jet model without crust and melt film; . . . . . . , laminar jet flow model with crust and melt film; - flow model with crust and melt film).
M. Saito et al. / Melting attack of solid plates depth 2~ is expressed as:
Ztheo,1 = 0.557r2
p j C p j ( T j -- Tmpd)
R e _ 0 . 5 pr_O.65}."
,o~[L + c,,~(Tmp,s- ~)] (20)
On the other hand, for the case with m = 1, n = 1 and
ClCz = 0.0033, Z is expressed as: pjcpj (Tj - Tmpd)
2th~o,z=O.OO33ps[L+cp~(Tmp,s - Ts)] t',
(21)
1
where 2~ is independent of Re and Pr. This means that the erosion rate Vm is proportional to the jet impingement velocity Vj. Using these equations, the experimental results of normalized erosion depth are compared with the theoretical predictions by eqs. (20) and (21) in figs. 11 and 12, respectively. As anticipated, the prediction of experimental results by eq. (21) is better than by eq. (20). Figure 12 shows that the data of molten A1203 jet impingement on a stainless steel plate are also predicted fairly well by eq. (21). Figure 13 compares the erosion rate and crust thickness in a molten UO 2 jet impingement on the stainless
7000
i
J
I
I
.7.7:5,;77;vv:.:.._~___~__.st__f__o_._rm.._atioa : """""vv':; ;~
st f°rraati°n:;'~ :]'';';':"'':;:%%;77"" "''"",',',.,,v
6000
Laminar jet flow model [11]
& 5000 Present work
No Crust f o r m a t i o n
/////////////////0_ ~ f 0 - o r m a t i o n / / / ~ 4000-
3000 700
800
900
1000
1100
1200
Irxi~al T e m p e r a t u r e of b-tainless Steel, T,(K)
Fig. 14. Critical temperature of the molten UO2 jet for crust formation.
21
steel plate predicted by the present model, the Epstein's laminar flow model with crust and melt film, and the simple assumption of suppression for crust and melt film. The present model predicts thinner crust thickness, that is, a higher erosion rate than Epstein's model. Both models, which treat simultaneous freezing and melting phenomena, however, predict significantly smaller erosion rates compared with the model without crust and melt film layers. Figure 14 exemplifies the critical jet temperatures above which the crust formation will not take place for the case of a molten UO 2 jet with a diameter of 0.1 m and a velocity of 5 m / s , which are obtained by the present work and Epstein's model [11] (eq. (8)). The present results give a much lower critical jet temperature than Epstein's model, but are still in the very high temperature region. For example, a molten UO 2 jet needs to be heated well above 4000 K (higher than the UO 2 boiling point at one atmosphere) in order not to solidify as a crust layer on a melting stainless steel plate.
5. Conclusions
To investigate the effect of crust forming on the impingement region on the erosion rate of solid plates by a high temperature molten jet, a series of model experiments was performed using simulation materials. In the first series of experiments, salt (NaC1) was selected as the jet material and tin plate (Sn) as the solid structure. To check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were also performed by using a molten A1203 jet impinged on stainless steel plate at room temperature. The experimental results were compared with the values predicted by Epstein's laminar jet flow model and also by the turbulent jet flow model developed in the present study. The results in the present study are summarized as follows: (1) The erosion rates of the solid plate by the molten jet impingement are far less than the value predicted by an analytical solution that neglects the existence of crust and melting film layers. With the inclusion of the crust behavior in the theoretical model, the experimental results are predicted fairly well. (2) The existence of a thermally protective crust restricts the input heat flux from thermally attacking the solid plate. A Nusselt number for the turbulent heat transfer with the simultaneous occurrence of freezing and melting in the impingement region of a
M. Saito et al. / Melting attack of solid plates
22
molten jet is correlated by a Reynolds number and a Prandtl number as follows: N u m = 0.0033 R e . Pr. (3) In addition to the erosion rate, the present turbulent jet flow model can predict the crust thickness, melthag layer thickness and the threshold jet temperature for the crust formation. (4) When Z / D j > 4, the erosion rate tends to substantially decrease due to the interaction between the jet and the stagnant molten pool in the deep hole called the 'Pool Effect'. In conclusion, the existence of a crust layer plays an important role in the erosion process of the solid plate in the case of a molten fuel jet with a high melting point like a reactor accident situation. However encouraging these results, additional theoretical and experimental efforts are required before the present results can be applied to the reactor accident analysis.
? T
Tmpj Tmp,s
r~
rj Vm
Cm
Vj Z
Z
2
Greek symbols
~m /z
Acknowledgments The authors wish to thank the section manager, Mr N. Tanaka for his valuable comments and support on the subject. We are grateful also to Messrs N. Ushiki, T. Takaha, T. Sekine, K. Shimizu, S. Sato and K. Suganuma of the SAG-3 group of the F B R safety Engineering Section, P N C for their technical and computational contributions to the present study.
p
0 C
exp
J s
dimensionless property ratio defined by eq.
(9) B
Cp
19o h k L Nu m
Pr
q r
Re t
melting parameter defined by eq. (10) heat capacity nozzle inner diameter at r o o m temperature jet diameter heat transfer coefficient thermal conductivity latent heat of fusion of the solid plate Nusselt number for the heat transfer with simultaneous freezing and melting at the jet impingement region Prandtl number ( c m ~ J k j ) heat flux radial coordinate Reynolds number (pjVjjDj//~j) time
crust thickness melt film thickness viscosity kinematic viscosity density
Subscripts
m
Nomenclature
normalized time ( t V y D j ) temperature melting point of the jet melting point of the sohd plate initial temperature of the solid plate interface temperature (temperature of the lower surface of the crust) temperature of the impinging jet erosion rate of the solid plate normalized erosion rate (Vm/Vj) jet velocity coordinate perpendicular to the melting surface erosion depth normalized erosion depth (Z/Dj)
theo
at the nozzle outlet crust experiment molten jet melt film structure plate theoretical prediction
References [1] M. Saito, K. Sato and S. Imahori, Experimental study on penetration behaviors of water jet into freon-11 and liquid nitrogen, ANS Proc. 1988 National Heat Transfer Conf., Houston, TX (July 24-27, 1988) 173-183. [2] S. Sitharamayya and K. Subba Raju, Heat transfer between an axisymmetric jet and a plate held normal to the flow, Can. J. Chem. Eng. 47 (1969) 365. [3] A.L. Roberts, On the melting of a semi-infinite body of ice placed in a hot steam of air, J. Fluid Mech. 4 (1958) 505. [4] J.M. Savino, J.F. Zumdieck and R. Siegel, Experimental study of freezing and melting of flowing warm water at a stagnation point on a cold plate, Fourth Int. Heat Transfer Conf., Cu 2.10 (1970). [5] R.R. Gilpin, The ablation of ice by a water jet, Trans. Can. Soc. Mech. Engrs. 2 (1973) 91.
M. Saito et al. / Melting attack of solid plates [6] Y. Yen and A. Zehnder, Melting heat transfer with water jet, Int. J. Heat Mass Transfer 16 (1973) 219. [7] A.W. Lipsett and R.R. Gilpin, Laminar jet impingement heat transfer including the effects of melting, Int. J. Heat Mass Transfer 21 (1978) 25. [8] M.J. Swedish, M. Epstein, J.H. Linehan, G.A. Lambert, G.M. Hauser and L.J. Stachyra, Surface ablation in the impingement region of a liquid jet, AIChE J. 25 (4) (1979) 630. [9] J.J. Sienicki and B.W. Spencer, Analysis of reactor material experiments investigating corium crust stability and heat transfer in jet impingement flow, ANS Proc. 1985 National Heat Transfer Conf., Denver, Colorado (1985). [10] A. Furutani, S. Imahori, K. Sato and M. Saito, Erosion behavior of solid plate by a liquid jet - effect of molten
23
layer, ANS Proc. 1989 National Heat Transfer Conf., Philadelphia, PA (August 6-10, 1989) 263-271. [11] M. Epstein, M.J. Swedish, J.H. Linehan, G.A. Lambert, G.M. Hauser and L.J. Stachyra, Simultaneous melting and freezing in the impingement region of a liquid jet, AIChE J. 26 (5) (1980) 743. [12] G.J. Janz, C.B. Allen, N.P. Bansal, R.M. Murphy and R.P.T. Tomkins, Physical properties data compilations relevant to energy storage. II. Molten salts: Data on single and multi-component salt systems, NSRDS-NBS (US) 61, Part II (April 1979). [13] V.P. Elyutin, B.C. Mitin and Yu.A. Nagibin, Properties of liquid alumina (Svoystva Zhidkoi Okisi Alyuminiya) ANL-TRANS-987 (August 1975) (Source: Fizika Aerodispersnykh Sistem No. 7 (1972) pp. 104-09).