- Email: [email protected]
Simulation of molten metal freezing behavior on to a structure
Nuclear Engineering and Design 238 (2008) 2706–2717
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Simulation of molten metal freezing behavior on to a structure M. Mizanur Rahman a,∗ , Yoshiyuki Ege a , Koji Morita a , Kiyoshi Nakagawa a , Kenji Fukuda a , Werner Maschek b a b
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan Institute for Nuclear and Energy Technologies, Forschungszentrum Karlsruhe, IKET, Postfach 3640, D-76021, Karlsruhe, Germany
a r t i c l e
i n f o
Article history: Received 3 October 2007 Received in revised form 31 March 2008 Accepted 1 April 2008
a b s t r a c t In the severe accident analysis of liquid metal reactors (LMRs), understanding the freezing behavior of molten metal onto the core structure during the core disruptive accidents (CDAs) is of importance for the design of next-generation reactor. CDA can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated. Material distribution and relocation of molten metal are the key study areas during CDA. In order to model the freezing behavior of molten metal of the postulated disrupted core in a CDA of an LMR and provide data for the verification of the safety analysis code, SIMMER-III, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure. The numerical simulation was performed by SIMMER-III with a mixed freezing model, which represents both bulk freezing and crust formation. The comparison between SIMMER-III simulation and its corresponding experiment indicates that SIMMER-III can reproduce the freezing behavior observed on different structure materials and under various cooling conditions. SIMMER-III also shows encouraging agreement with experimental results of melt penetration on structures and particle formation. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In a hypothetical core disruptive accident (CDA) of a liquid metal reactor (LMR), the molten core metal of the reactor may relocate through flow paths in the core (Kondo et al., 1995). This would cause a molten metal, coolant and structure interactions, in which the heat is transferred from the molten metal to the coolant and core structure, would cause freezing of the molten metal onto the core structure. In assessing the safety of LMRs, it is important to know the consequences of such freezing phenomena during interactions of molten metal with the coolant and core structure. Interactions between molten metal and the reactor structure can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated (Theofanous and Bell, 1986), which are often called CDAs. These include fuel-pin disruption, phase transition or subassembly disruption and the escape of fuel. Fig. 1 shows the postulated CDA events of a heavy liquid metal reactor whereas Fig. 2 represents the schematic view of key CDA phenomena in a heavy liquid metal reactor. It is anticipated that during CDA of LMR molten cladding and disrupted fuel pass through the coolant channel and due to interaction of the molten metal with coolant and
∗ Corresponding author. Tel.: +81 92 802 3502; fax: +81 92 802 3502. E-mail address: [email protected] (M.M. Rahman). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.04.008
structure, heat is transferred from the molten metal to the coolant and structure and as a result molten metal becomes freeze and relocates onto the structure. Due to this relocation of molten metal onto the structure, coolant channel becomes narrow and finally the possibility of the channel blockages is increased. Though the occurrence of CDA is extremely unrealistic due to the denying actuations of all multiple safety systems, it is still emphasized from the viewpoint of safety designs and evaluation. This is because CDAs potentially lead to significant mechanical energy release as a result of recriticality (Epstein et al., 1976). This potential consequence of energetic recriticality is regarded as one of the most important risk contributors to the environments (El-genk and Cronenberg, 1978). Therefore, it is very important to evaluate adequately the sequences of CDA of LMR; SIMMER-III code has been developed for this purpose. SIMMER-III, an advanced safety analysis computer code (Kondo et al., 1992; Tobita et al., 2000) has been developed to investigate the severe transients and CDAs of LMRs. The development of SIMMERIII has been conducted at JAEA (Japan Atomic Energy Agency) formerly JNC (Japan Nuclear Cycle Development Institute), initially in collaboration with FZK (Forschungszentrum Karlsruhe) in Germany, and CEA (Commissariat a` I’Energie Atomique) which also ˆ e´ Nucleaire) ´ includes IRSN (Institute de Radioprotection et de Suret in France. The objective of SIMMER-III is to alleviate some of the limitations of SIMMER-II and thereby to provide a next-generation
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2707
Fig. 2. Schematic view of key CDA phenomena of heavy liquid metal reactor. Fig. 1. Postulated CDA events of heavy liquid metal reactor.
tool for more reliable analysis of severe transients and CDAs. Material distribution and relocation of molten fuel is one of the key study areas in the SIMMER-III assessment program. In particular, freezing of molten fuel on the core structure surface is a key phenomenon because the dynamics of freezing plays an important role in determining the fuel removal from the active core region. In order to reasonably evaluate the mass distribution of molten fuel in the core region and the consequences of recriticality, it is important especially for the code to evaluate the freezing and blockage formation phenomena inside the escape path adequately (Kamiyama et al., 2006). The main purpose of the SIMMER-III code is to provide a numerical simulation of complex multi-phase, multi-component flow problems essential to investigate CDAs in LMRs. However, the code is designed to be sufficiently flexible to be applied to a variety of multi-phase flows, in addition to LMR safety issues. In order to apply SIMMER-III to LMR safety analysis, the code must be demonstrated to be sufficiently robust and reliable. Therefore, it has to be tested and validated extensively. In our previous study (Rahman et al., 2007) a series of molten metal freezing experiments were performed in order to figure out the basic physical characteristics in freezing mode of molten metal and to determine some of the characteristics parameters of the freezing of molten metal during penetrating onto the structure. In these experiments, freezing characteristics were investigated using Wood’s metal as a molten metal material and the experiments were conducted using a copper or stainless-steel plate of flat shaped in design as the freezing structure in air and water coolant systems. Experimental results such as penetration length and width of frozen metal on stainless steel and brass structures were compared under the air and water coolant conditions. In the air coolant experiments, most of the molten metal froze to the structure in thin, wide frozen shapes of metal with good adherence, whereas in the water coolant experiments, it was found that most of the frozen metal broke up and were swept downstream as debris with only a very small fraction of the melt that adhered to the structure without a uniform shape. Different freezing modes dependent on experimental conditions were observed in the water coolant experiments, whereas with air as the coolant, the freezing mode did not change. The present work is an extension of our previous study, which was undertaken to provide quantitative experimental information
with the verification of the models and methods for the numerical simulation of the freezing behavior of molten metal. In these experiments, although the similar experimental system to one used in the first series of experiments was also used, L-shaped flow channels for brass and stainless steel were used to realize more uniform melt flow than on the flat plate. In the present study, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure under various cooling conditions. The numerical simulation of the experimental results was performed by the SIMMER-III code using a mixed freezing model involving both bulk freezing and crust formation on the structure. The experimental results were compared with the simulation results to demonstrate that the code is applicable to such complex, transient multi-phase flow situations. 2. Molten metal freezing experiments 2.1. Experimental apparatus The present molten metal freezing experiment is conducted using Wood’s metal as a molten metal stimulant in air and water coolant conditions. A schematic diagram of the experimental setup is shown in Fig. 3. The facility consists of a cylindrical melt tank and a water pool, in which molten metal is poured. A circular nozzle is connected to the bottom of the melt tank to enable a smooth ejection of melt flow onto the metal structure, which is immersed in the water pool. The melt tank and nozzle, which are made of stainless steel, are heated by an electric heater and their temperature is adjusted using the temperature controller. Fourteen K-type thermocouples are connected to the melt tank, nozzle and metal structure to measure the temperature of the melt as it falls onto the metal structure. The inner diameter of the upper part of the melt tank is 75 mm, whereas the inner and outer diameters of the lower part of the melt tank are 12.5 mm and 37.5 mm, respectively. Two nozzles of diameters 1.9 mm and 2.2 mm, respectively, are used to eject the molten metal with different melt flow rates. The water pool, which is a rectangular open-topped box (1500 mm in height × 300 mm in width), is made of stainless steel and with two of the side-walls made of transparent glass for the purpose of observation. An electric heater with temperature controller and
338 g (6.7 s) 340 g (5.7 s)
338 g (6.7 s) 340 g (5.7 s) 1.9 mm (50.5 g/s) 2.2 mm (59.7 g/s)
Nozzle diameter (melt flow rate)
1.9 mm (50.5 g/s) 2.2 mm (59.7 g/s) 20 C 35 C and 52 C
20 ◦ C 35 ◦ C and 52 ◦ C 1.9 mm (51.5 g/s), 2.2 mm (60.1 g/s)
335 g (6.5 s), 337 g (5.6 s) 1.9 mm (51.5 g/s), 2.2 mm (60.1 g/s) 17 C
17 ◦ C
Stainless steel
Brass
335 g (6.5 s), 337 g (5.6 s)
◦
Coolant temperature
Metal plate
Table 1 Conditions of experimental cases
The experiment is conducted in two steps using two types of coolant, namely air and water. The freezing phenomena are investigated experimentally using two structures made of stainless steel and brass, of which thermal conductivities are 16 W/(m K) and 125 W/(m K) respectively, at room temperature. In both air and water coolant experiments, simulant Wood’s metal is melted down by an electric furnace, and then transferred to the test section; the temperature of the melt is monitored using a digital thermometer and poured into the melt tank. In this tank, the temperature is measured to achieve the desired temperature. At the desired temperature, the melt is ejected onto the structure by opening the plug of the nozzle. In air coolant experiment, the structure is supported with the stand and the tank and its nozzle section are installed above the stand and secured. In water coolant experiment, the structure is set-up within the water pool and then tank and its nozzle section are installed above the water pool and secured. The temperature of the water pool is kept constant by the electric heater and a stainless-steel stirrer with three fans positioned at the top, middle and bottom of the stirrer is employed to create a uniform water temperature throughout the pool. The experiments were carried out at water temperatures of 20.2 ◦ C, 35 ◦ C and 50 ◦ C. The molten metal is prepared as of air coolant experiment described above and poured into the cylindrical tank. The melt penetration length stands for the length of the frozen metal adhered on the structure. Distribution of frozen metal adhered on the structures was measured for both in air and water coolant conditions. Effects on melt freezing behavior were observed by changing the structure material, coolant, coolant temperature and melt temperature.
Nozzle diameter (melt flow rate)
2.2. Experimental procedure
◦
Water coolant
Ejected mass (duration) Air coolant
a thermocouple sensor are used to control the water temperature at a desired level. An L-shaped metal structure 800-mm long and 5-mm thick is inclined at an angle of 72.5◦ to the horizontal line, and is supported on a stainless-steel stand. The initial temperature of the metal structure is equivalent to that of the atmosphere. A fragment collector is also present inside the horizontal part of the stand. During experiments where air was the only coolant, the water pool was absent. A high-speed video camera (SONY, Model: DCR-TRV900) was used to record video images of the melt as it falls onto the metal structure.
Coolant temperature
Fig. 3. Schematic of experimental set-up.
◦
Ejected mass (duration)
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
◦
2708
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2709
going into melting. For example, Fig. 4 shows interface (A, B) where the interface is undergoing a net loss energy to component B. This energy is either coming from freezing of component A. The resulting product will be either more of component B depending on the process involved. When the phase transition is predicted, the interface I is defined as the melting temperature of a phasetemperature TA,B transition species. Otherwise, in the case of no mass transfer, the interface temperature is defined so that qIA,B becomes zero: I = TA,B
hA,B TA + hB,A TB hA,B + hB,A
(2)
The M/F mass-transfer rate is determined from energy balance at the interface. If qIA,B is zero, sensible heat is exchanged without mass transfer. If qIA,B is positive, namely the energy is lost at the interface, a liquid component freezes. Then the mass-transfer rate for this case is determined from qIA,B
Fig. 4. Basis of heat-transfer limited process. I = A,B
The melt flow and distribution were observed with a high-speed video camera. In both the air and water-cooled conditions, experiments are carried out at atmospheric pressure. The experimental conditions are summarized in Table 1. 3. Numerical simulation by SIMMER-III
SIMMER-III is a two-dimensional, three-velocity-field, multiphase, multi-component, Eulerian, fluid-dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model (Kondo et al., 1992; Tobita et al., 2000). The fundamental equations of the fluid dynamics are based on a so-called multi-fluid model. The code models the melting/freezing (M/F) phase transition as non-equilibrium processes occurring at fluid interfaces and equilibrium processes occurring when the bulk temperatures exceed or drop below the melting temperature (Morita et al., 2003). The overall fluid-dynamics solution algorithm is based on a time-factorization (time-splitting) approach, in which intracell heat and mass transfer is determined separately from inter-cell fluid convection. The followings describe the general heat and mass-transfer model associated with the M/F processes. In SIMMER-III, the M/F processes occurring at interfaces are described by a heat-transfer limited model. These are nonequilibrium processes because the bulk temperature does not generally satisfy the phase-transition condition when the mass transfer occurs at the interface. The basic concept of this model is described using Fig. 4, in which a binary contact interface of the energy components A and B is shown. Each energy component interfaces with the other energy components simultaneously, and each interface has a uniquely defined interfacial area. Energy transfers between components are based on the interfacial area and heat-transfer coefficients determined from engineering correlations. A specified temperature is assigned to each possible interface to calculate heat flows from/to each interface into/from the respective bulk materials. These heat flows are summed to give the net interfacial energy loss or gain. The net energy transfer rate from the interface is defined as
I I qIA,B = aA,B hA,B (TA,B − TA ) + hB,A (TA,B − TB )
(1)
where a is the interfacial area per unit volume, h is the heat-transfer coefficient, T is the temperature and the superscript I stands for interface. An interfacial energy loss is defined as positive and means freezing must occur to conserve (provide) energy. An interfacial energy gain, which is defined as negative, means the energy is
(3)
where i is the enthalpy and the subscript sol means the solidus point. If qIA,B is negative, on the other hand, namely the energy is gained at the interface, a solid component melts. Then the masstransfer rate for this case is determined from I =− B,A
3.1. Phase-transition model of SIMMER-III
iA − isol
qIA,B iLiq − iB
(4)
where the subscript Liq stands for liquidus point. The equilibrium M/F model calculates equilibrium processes resulting from the non-equilibrium heat and mass transfer. If the internal energy of a solid component A exceeds its solidus energy (eA > esol ), the component A melts into the component B with the mass-transfer rate: EQ A,B =
1 eA − esol ¯ A t hf
(5)
where the superscript EQ means the equilibrium process, ¯ is the macroscopic density and hf is the heat of fusion. If the internal energy of a liquid component B drops below its liquids energy (eB
1 eLiq − eB ¯ B t hf
(6)
The non-equilibrium M/F transfers can include the crust formation on a structure wall (conduction-limited freezing) and particle formation in the melt flow that contribute to equilibrium (bulk) freezing. The M/F transfers at the liquid/particle interfaces are also included which is analogous to the liquid/structure M/F transfers for consistency. In addition, equilibrium M/F transfers are performed to eliminate subcooled liquids or metastable solids as the result of heat transfer. 3.2. Modeling for experimental analyses The present analytical model for freezing phenomena of molten metal describes the heat and mass transfer among molten metal, structure (metal plate) and coolant. The concept of the heat and mass-transfer model for the present experimental analyses using SIMMER-III is illustrated in Fig. 5 schematically. In this model for freezing phenomena of molten metal, five components such as molten metal, coolant, solid particles, crust and structure surface are assigned to mass and energy components. Here, crust is frozen metal adhered on the structure, while molten metal solidified in fluids is treated as solid particles. In the case of water coolant experiments, these five components are expressed as L1 (molten metal),
2710
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
EQ EQ EQ + S3,L1 + L4,L1 esol − L1,L4 eLiq
I I +aS3,L1 hL1,S3 TS3,L1 − TL1 + aS7,L1 hL1,S7 TL1,S7 − TL1 I I +aL1,L3 hL1,L3 TL1,L3 − TL1 + aL1,L4 hL1,L4 TL1,L4 − TL1
(8) Particles
∂¯ L4 I (L1/L3) I(L1/L4) I(L1/L4) = L1,L4 − L4,L1 − L1,L4 ∂t ∂¯ L4 eL4 = ∂t
I(L1/L3)
L1,L4
I(L1/L4)
+ L1,L4
EQ EQ − L4,L1 − L1,L4
I(L1/L4)
esol − L4,L1
∂¯ S3 I(L1/S3) I(L1/S3) = − S3,L1 − L1,S3 ∂t
L3 (water), L4 (solid particles), S3 (crust) and S7 (structure surface), respectively, according to the indexes commonly used in SIMMERIII models. The molten metal interacts with structure, crust, coolant and particles at four interfaces of S3/L1, S7/L1, L1/L3 and L1/L4, respectively. There can also exist an interface of S3/S7 after the crust formation. Both non-equilibrium and equilibrium freezing processes of molten metal are considered in this model as described in Section 3.1. In the present analyses, freezing behaviors of molten metal in the water coolant system are represented by the five massI(S3/L1) I(S7/L1) I(L1/L3) I(L1/L4) EQ transfer rates: L1,S3 , L1,S3 , L1,L4 , L1,L4 and L1,L4 . On the other hand, although re-melting of the frozen metal from the crust and the particles might have minor effects on the general freezing behavior under the present experimental conditions, four I(S3/L1) I(L1/L4) melting mass-transfer rates are also considered: S3,L1 , L4,L1 , EQ EQ S3,L1 and L4,L1 . Here, the superscripts I(S3/L1), I(S7/L1), I(L1/L3) and I(L1/L4) mean non-equilibrium mass transfers at the interfaces of S3/L1, S7/L1, L1/L3 and L1/L4, respectively (Table 2). The intra-cell heat and mass transfers for molten metal, particles and crust components are expressed by the following conservation equations without convection terms:
∂¯ L1 = ∂t
I(S3/L1)
S3,L1
I(L1/L4)
+ L4,L1 ∂¯ L1 eL1 = ∂t
I(S3/L1)
− L1,S3
I(L1/L4)
− L1,L4
I(S3/L1)
S3,L1
I(L1/L4)
EQ EQ EQ + S3,L1 + L4,L1 − L1,L4
I(S8/L1)
+ L1,S3
(7)
esol I(L1/L3)
+ L1,L4
I(L1/L4)
+ L1,L4
eL1
Table 2 Non-equilibrium mass-transfer paths Interface
Freezing Melting
(10)
EQ + S3,L1
(11)
I I +aS3,S7 hS3,S7 TS3,S7 −TS3 + aS3,L1 hS3,L1 TS3,L1 −TS3
I I +aS3,L3 hS3,L3 TS3,L3 − TS3 + aS3,L3 hS3,L3 TS3,L3 − TS3
(12) For the coolant and the structure, the following energy equations only with heat-transfer terms are solved as the intra-cell heat transfer: Water
I I ∂¯ L3 eL3 = aL1,L3 hL3,L1 TL1,L3 − TL3 + aS3,L3 hL3,S3 TS3,L3 − TL3 ∂t
I +aS7,L3 hL3,S7 TS7,L3 − TL3
(13)
Structure
I I ∂¯ S7 eS7 = aS3,S7 hS7,S3 TS3,S7 − TS7 + aL1,S7 hS7,L1 TL1,S7 − TS7 ∂t
I +aL3,S7 hS7,L3 TL3,S7 − TS7
(14)
In addition to the above, the heat conduction inside the structure and the heat transfer from the other side of the structure to the coolant are calculated separately. 3.3. Analytical geometry of SIMMER-III simulation
I(L1/L3)
− L1,L4
+ L4,L1
I(S3/L1)
− L1,S3
I(S7/L1)
− L1,S3
∂¯ S3 eS3 I(L1/S3) I(L1/S3) EQ esol = L1,S3 esol − S3,L1 eS3 + S3,L1 ∂t
Fig. 5. Modeling concept of melt freezing behavior.
Molten metal
(9)
EQ eL4 + L1,L4 esol
EQ I −L1,L4 eLiq + aL1,L4 hL4,L1 TL1,L4 − TL4
Crust
Melt/crust
Melt/structure
Melt/coolant
Melt/particle
Melt ⇒ crust Crust ⇒ melt
Melt ⇒ crust X
Melt ⇒ particles X
Melt ⇒ particles Particles ⇒ melt
A two-dimensional mesh of Cartesian geometry was adopted for the numerical simulation using SIMMER-III. The analytical geometry of SIMMER-III simulation is shown in Fig. 6. The melt reservoir is located at the top of the first column by one mesh cell of size 20 mm and 50 mm in the x and z directions, respectively. Here, the x-direction is along with the melt flow on the structure surface, while the z-direction is taken as the vertical to the structure surface. The melt was injected downward due to gravity ‘g’ at constant pressure of 1 atm from the melt reservoir and passes through the coolant channel. The structure on which the frozen metal is adhered, is assigned a mesh cells can wall. Since the present SIMMER-III simulation is modeled in the x–z two-dimensional co-ordinate, the geometrical configuration in the y direction is considered as the difference in binary contact area between melt/structure and melt/coolant. The mesh cell size of 20 mm in the x direction and 20 mm in the z direction was used
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2711
Fig. 7. Photographs of adhered frozen metal observed on stainless-steel structure in air coolant condition by varying nozzle diameter.
Fig. 6. Analytical geometry of SIMMER-III simulation.
in the coolant (air/water) pool where two meshes in the x direction and 50 meshes in the z direction were defined. The calculation starts just after the contact of melt with the structure. 4. Results and discussion 4.1. Experimental observation In the experiment, molten Wood’s metal (melting point 78.8 ◦ C) was used as a simulant melt, while stainless steel and brass were used as freezing structures. The L-shaped structure with 5-mm thickness and 80-cm length was inclined at an angle of 72.5◦ to the horizontal line in a bath filled with stagnant coolant. The simulant melt was ejected onto the inclined freezing structure in the bath through a stainless-steel nozzle with 1.9-mm and 2.2-mm diameter, respectively, by gravity. Effects on melt freezing behavior were observed by changing the structure material and coolant at melt temperature of 102–105 ◦ C. The reason of considering this melt temperature range is that relatively longer penetration of melt onto the structure is observed at this melt temperature range. The melt flow and distribution were observed for both the experiments with a high-speed video camera. The typical freezing behaviors of molten metal at air coolant conditions are shown in Figs. 7 and 8. In air coolant condition, it is clearly seen from the figures that when hot melt falls onto the stainless-steel structure, the frozen layer becomes thin and strip but the length of the frozen metal adhered onto the structure was observed to be longer at nozzle diameter (ND) of 2.2 mm than that of the nozzle diameter of 1.9 mm. Whereas, in the case of brass structure, the frozen layer becomes a bit more thicker specially at the downstream than the frozen layer observed on stainless-steel structure. The length of adhered frozen metal on brass structure was also found to be longer at nozzle diameter of 2.2 mm than that of nozzle diameter of 1.9 mm. But
the length of frozen metal adhered onto the structure is found to be shorter for brass structure than that of the stainless-steel structure. This difference is due to the high thermal conductivity of brass than stainless steel. This can be explained by the fact that during passing on the brass structure, the molten metal losses significant amount of its latent heat; thus for a very short period of time, the temperature decreased near to its freezing point and become more rapid rate of solidification than the stainless-steel structure. In water coolant condition, the experiments were conducted at water coolant temperatures of 20.2 ◦ C, 35 ◦ C and 52 ◦ C and the results are shown in Figs. 9 and 10 for stainless steel and brass structures, respectively. It is observed from both the figures that when hot melt falls on the structure, a part of the molten metal is frozen and quenched on the structure and a significant amount of molten metal is broken and fall down as different fragments called debris. Beside these some frozen metal is broken and fall down due to rapid increase of viscosity. The heat transfer of molten metal is occurred between water coolant and structure as a result debris is observed. For both stainless steel and brass structures it is found that the length of the adhered frozen metal is observed to be longer at nozzle diameter of 2.2 mm than that of the nozzle diameter of 1.9 mm. Comparing with respect to water coolant temperature, it is viewed that the length of the adhered frozen metal is found to be maximum at water coolant temperature of 20.2 ◦ C and then further increased of water coolant temperature at 35 ◦ C and 52 ◦ C, the length of the adhered frozen metal is found to be decreased gradually. Beside these some differences of the sizes of the debris are also observed for both structures at different coolant temperatures and nozzle diameter. It is clearly seen from the observed photographs that the length of the adhered frozen metal becomes shorter in brass structure than that of the stainless-steel structure but the
Fig. 8. Photographs of adhered frozen metal observed on brass structure in air coolant condition by varying nozzle diameter.
2712
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 9. Photographs of adhered frozen metal and debris observed on stainless-steel structure at melt temperature of 102 ◦ C by varying water coolant temperature and nozzle diameter.
adhered frozen metal is observed to be thicker on brass structure than that of the stainless-steel structure. It is also viewed from both figures of air and water coolant conditions, the lower part of frozen metal becomes thicker than that
of the upper part. This is observed due to the re-melting of frozen metal at the upstream for further falling of hot melt from the nozzle to the upper part of the melt and finally re-melting metal is accumulated at the downstream. Beside these some instability is also
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2713
Fig. 10. Photographs of adhered frozen metal and debris observed on stainless-steel structure at melt temperature of 102 ◦ C by varying water coolant temperature and nozzle diameter.
2714
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 11. Transient penetration length of molten metal on stainless-steel structure in the presence of air coolant at different nozzle diameter.
found for both the cases, which might be due to the melt initial inertia and other hydrodynamic interaction forces. 4.2. Melt penetration length The penetration length is defined as the length of the melt flow along the metal plate. The penetration length of different experimental cases is compared with their corresponding SIMMER-III simulation results. The comparison of penetration length for all the cases shows similar transient trends. In this paper, the experimental cases such as penetration length on stainless steel and brass structures in presence of air and water coolant with different nozzle diameter will be mainly presented and compared with the SIMMER-III simulation results. The transient penetration length of molten metal on stainless steel and brass structures are plotted in the presence of air coolant, for nozzle diameter of 1.9 mm and 2.2 mm as shown in Figs. 11 and 12. From these figures it can be seen that the transient penetration length in the experiments increases with the increase of melt flow rate (by changing nozzle diameter) and the SIMMERIII simulation results also successfully reproduce similar trend of transient penetration length observed in the experiments for both stainless steel and brass structures. These two figures also illustrate that the total time of freezing of molten metal is observed to be earlier at higher melt flow rate (ND = 2.2 mm) than the lower melt flow rate (ND = 1.9 mm) in both experiments and SIMMERIII simulation, although a small difference of total freezing time of molten metal is observed in experiment and SIMMER-III simulation in stainless-steel structure at nozzle diameter of 2.2 mm.
Fig. 12. Transient penetration length of molten metal on brass structure in the presence of air coolant at different nozzle diameter.
Fig. 13. Transient penetration length of molten metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in the presence of water coolant at different coolant temperatures.
Comparing the transient penetration length of stainless steel and brass structures it can be predicted that maximum penetration length is found to be longer in stainless-steel structure than brass structure for nozzle diameter of 1.9 mm and 2.2 mm for both experiments and SIMMER-III simulation. From the early stage of transient penetration of molten metal shown in Figs. 11 and 12, it is also observed experimentally that in stainless-steel structure, the molten metal penetrates longer distance within a short period of time than the brass structure. SIMMER-III simulation results also reproduce the same behavior for both stainless steel and brass structures. This difference of freezing behavior on stainless steel and brass structure is observed due to the high thermal conductivity of brass than stainless steel. Figs. 13 and 14 show the transient penetration length of molten metal on stainless-steel structure and Figs. 15 and 16 represent the transients penetration length on brass structure during falling through nozzles of diameter 1.9 mm and 2.2 mm, respectively, in the presence of water coolant at coolant temperatures of 20.2 ◦ C, 35 ◦ C and 52 ◦ C. It is worth noting here from these figures that the transient penetration length decreases with the increase of coolant temperature and increase with the increase of melt flow rate (by changing the nozzle diameter). At low coolant temperature, structure temperature also becomes low and heat transfer from molten metal to the structure is dominant at low structure temperature, which results in more crust formation on the structure and thus increases the penetration length. In SIMMER-III simulation of water coolant experiments, we find that the code reproduces the transient penetration length observed in the experiments well by increas-
Fig. 14. Transient penetration length of molten metal on stainless-steel structure during falling through a nozzle of diameter 2.2 mm in the presence of water coolant at different coolant temperatures.
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 15. Transient penetration length of molten metal on brass structure during falling through a nozzle of diameter 1.9 mm in the presence of water coolant at different coolant temperatures.
ing the heat transfer between melt and water coolant. This might be because in the experiment the ripples on the melt flow surface enhances heat-transfer areas between the melt and the coolant. In the present simulation, the binary contact area was increased about 16% between the melt and the coolant, compared with the uniform melt flow. Figs. 13 and 14 also show no observable differences of transient penetration length at melt temperatures of 35 ◦ C and 52 ◦ C but it differs a bit only at melt temperatures of 20.2 ◦ C at nozzle diameter of 1.9 mm (Fig. 13) while obvious difference is clearly observed at melt temperature of 20.2 ◦ C at nozzle diameter of 2.2 mm (Fig. 14). This similar behavior of transient penetration length of molten metal at coolant temperature of 35 ◦ C and 52 ◦ C indicates that these temperatures have less effect on change of penetration length. Similar trend of transient penetration length also observed in SIMMER-III simulation for the above-mentioned cases. Fig. 15 predicts that at early stage of transient melt penetration of molten metal on brass structure at nozzle diameter of 1.9 mm shows no clear difference at melt temperature of 35 ◦ C and 52 ◦ C for both the result of experiment and SIMMER-III simulation while clear difference is observed at maximum penetration length. On the other hand, Fig. 16 depicts very encouraging agreement of transient penetration length of molten metal on brass structure for different coolant temperatures at nozzle diameter of 2.2 mm. Comparing the transient penetration length of stainless steel and brass structures in the presence of water coolant, it can be predicted that maximum penetration length is found to be longer in stainless-steel plate than brass structure for nozzle diameter of
Fig. 16. Transient penetration length of molten metal on brass structure during falling through a nozzle of diameter 2.2 mm in the presence of water coolant at different coolant temperatures.
2715
Fig. 17. Transient mass distribution of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm.
1.9 mm and 2.2 mm for both experiments and SIMMER-III simulation. From the early stage of transient penetration of molten metal it is also observed experimentally that in stainless-steel plate, the molten metal penetrates longer distance within a short period of time than the brass structure. SIMMER-III simulation results also reproduce the same behavior for both stainless steel and brass structures. This difference of freezing behavior on stainless steel and brass structure is observed due to the high thermal conductivity of brass than stainless steel. 4.3. Mass distribution Figs. 17 and 18 depict the transient mass distribution of SIMMER-III simulation results for stainless steel and brass structure, respectively, in the presence of air and water coolant. It can be seen from these two figures that in air coolant condition, most of the molten metal become crust after freezing and no particle is observed. Whereas, in the presence of water coolant, SIMMERIII simulation results a significant amount of particle formation as debris along with the crust formation. In both the cases of stainless steel and brass structures, the amount of particle formation is found to be higher than the crust formation. The formation of debris was observed in water coolant system due to the high heat transfer of molten metal to water. The SIMMER-III simulation results of crust formation on plate and particle formation as debris represent an important sequence of non-equilibrium heat-transfer model that contributes to melt quenching and bulk freezing. Comparing the final mass distribution into crust and solid particle with the experimental results, it is observed from the experiments that in air coolant system about 96% of the molten
Fig. 18. Transient mass distribution of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm.
2716
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 19. Transient mass-transfer rate of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
metal becomes crust for both on stainless steel and brass structures. On the other hand, in the water coolant system, crust is formed on stainless steel and brass structure, with about 40% of the molten metal, while the rest of the molten metal is observed as solid particles. Simulation results of final mass distribution into crust and solid particle (Figs. 17 and 18) revels the comparable results with the experiments of reference cases on both stainless steel and brass structures for both in air and water coolant conditions. Figs. 19 and 20 represent the dominant transient mass-transfer rates on stainless steel and brass structures, respectively in water coolant condition. These two figures also revels the comparison of freezing rates between crust formation at L1/S3 (molten metal/crust) and L1/S7 (molten metal/structure surface) contact and particle formation at L1/L3 (molten metal/water) contact on stainless steel and brass structures. It can be observed from Fig. 19 that at early stage of freezing, the rate of crust and particle formations are almost comparable but at later stage, the rate of particle formation is higher than that of crust formation. On the other hand, Fig. 20 predicts that at early stage of freezing, the rate of crust formation is little bit higher than that of particle formation, while at later stage, the rate of particle formation is little bit higher than that of crust formation. These two figures also show that not only crust formation but also particle formations at L1/L3 contact are dominant freezing processes. 4.4. Sensitivity of particle formation effects Figs. 21 and 22 illustrate the transient penetration length of Wood’s metal on stainless steel and brass structures, respectively,
Fig. 21. Transient penetration length of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
Fig. 22. Transient penetration length of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
in water coolant condition with and without considering particle formation effects at the contact of L1/L3 (molten metal/water) in SIMMER-III simulation. These two figures revels the effects of particle formation on penetration length in water coolant condition. It can be seen from these two figures that with considering particle formation effect at L1/L3 contact (reference case of SIMMER-III), SIMMER-III result shows well comparable with the experimental result, while on the other hand, without considering the particle formation effect at L1/L3 contact, SIMMER-III overestimates the melt penetration on both stainless steel and brass structures. 5. Conclusion
Fig. 20. Transient mass-transfer rate of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
In this work, a series of fundamental experiments was conducted to simulate the freezing behavior of molten Wood’s metal observed onto metal structures to verify the basic validity of the SIMMER-III code on simulating freezing behavior of molten metal onto the core structure. The experiments show that longer penetration length and good adherence on structure were found in the air coolant than in the water coolant. In both air and water coolant experiments, penetration length was found to be a bit longer on the stainless-steel plate than on the brass structure due to the lower thermal conductivity of stainless steel than brass. In air coolant condition, most of the molten metal was adhered on the plate and no particle formation due to melt solidification was observed as debris. On the other hand, in water coolant condition, only a small part of molten metal was adhered onto the plate and a significant amount of melt froze as debris. The
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
formation of debris was observed in water coolant system due to the high heat transfer of molten metal to water. The numerical simulation of molten metal freezing was performed with the SIMMER-III code using a mixed freezing model involving both bulk freezing and crust formation on the plate. In the air coolant condition, SIMMER-III simulation shows good agreement with the transient penetration length measured on both stainless steel and brass structures. In the water coolant conditions, simulation results suggest that melt cooling was enhanced by the effective increase of the contact area between melt and water. From the transient mass distribution of molten metal, SIMMER-III also resulted in the significant amount of particle formation as debris in water coolant condition, whereas, in air coolant condition no particle formation was observed and most of the frozen metal was adhered on the plate. These behaviors are also in good agreement with the experimental results. Results of transient mass-transfer rate of molten metal in water coolant condition revels that not only crust formation but also particle formations at melt coolant contact are dominant freezing process. The SIMMER-III simulation results of crust formation on plate and particle formation as debris represent an important sequence of non-equilibrium heat-transfer model that contributes to melt quenching and bulk freezing. Sensitivity study of particle formation effects at melt and coolant contact shows that without considering particle formation effect at melt and coolant contact, SIMMER-III overestimates the melt penetration on both brass and stainless steel structures. The present study advances the experimental verification of SIMMER-III in terms of freezing phenomena of molten metal for the disrupted core. Though the further code verification would be necessary, we anticipate that the present results will contribute to the improvement of reliability in accident analysis of LMR.
2717
Acknowledgements Part of this work was performed as a joint research project between Kyushu University and FZK, Germany. One of the authors, M. Mizanur Rahman gratefully acknowledges the Ministry of Education, Culture, Sports, Science and Technology, Japan, for the support by providing Monbukagakusho scholarship. References El-genk, M., Cronenberg, W.A., 1978. An assessment of fuel freezing and drainage phenomena in a reactor shield plug following a core disruptive accident. Nucl. Eng. Des. 47 (2), 195–225. Epstein, M., Grolmes, M.A., Henry, R.E., Fauske, H.K., 1976. Transient freezing of a flow ceramic fuel in a steel channel. Nucl. Sci. Eng. 61, 310–323. Kamiyama, K., Brear, D.J., Tobita, Y., Kondo, S., 2006. Establishment of freezing model for reactor safety analysis. J. Nucl. Sci. Technol. 43 (10), 1206– 1217. Kondo, S., Tobita, Y., Morita, K., Shirakawa, N., 1992. SIMMER-III: An advanced computer program for LMFBR severe accident analysis. In: Proceedings of the International Conference on Design and Safety of Advanced Nuclear Power Plant (ANP’92), vol. IV, Tokyo, pp. 40.5.1–40.5.11. Kondo, S., Konishi, K., Isozaki, M., Imahori, S., Furutani, A., Bear, D.J., 1995. Experimental study on simulated molten jet–coolant interactions. Nucl. Eng. Des. 155 (1–2), 73–84. Morita, K., Yamano, H., Tobita, Y., Kondo, S., 2003. SIMMER-III/IV heat- and masstransfer model—model and method description-, JNC report, JNC TN9400 2003047, Japan. Rahman, M.M., Hino, T., Morita, K., Matsumoto, T., Nakagawa, K., Fukuda, K., Maschek, W., 2007. Experimental investigation of molten metal freezing onto a structure. Exp. Therm. Fluid Sci. 32, 198–213. Theofanous, T.G., Bell, C.R., 1986. An assessment of clinch river breeder reactor core disruptive accident energetics. Nucl. Sci. Eng. 93, 215–228. Tobita, Y., Kondo, S., Yamano, H., Fujita, S., Morita, K., Maschek, W., Louvet, J., Coste, P., Pingy, S., 2000. Current status and application of SIMMER-III, an advanced computer program for LMFR safety analysis. In: Second Japan– Korea Symposium on Nuclear Thermal Hydraulics and Safety (NTHAS-2), Fukuoka, pp. 65–72.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Simulation of molten metal freezing behavior on to a structure M. Mizanur Rahman a,∗ , Yoshiyuki Ege a , Koji Morita a , Kiyoshi Nakagawa a , Kenji Fukuda a , Werner Maschek b a b
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan Institute for Nuclear and Energy Technologies, Forschungszentrum Karlsruhe, IKET, Postfach 3640, D-76021, Karlsruhe, Germany
a r t i c l e
i n f o
Article history: Received 3 October 2007 Received in revised form 31 March 2008 Accepted 1 April 2008
a b s t r a c t In the severe accident analysis of liquid metal reactors (LMRs), understanding the freezing behavior of molten metal onto the core structure during the core disruptive accidents (CDAs) is of importance for the design of next-generation reactor. CDA can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated. Material distribution and relocation of molten metal are the key study areas during CDA. In order to model the freezing behavior of molten metal of the postulated disrupted core in a CDA of an LMR and provide data for the verification of the safety analysis code, SIMMER-III, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure. The numerical simulation was performed by SIMMER-III with a mixed freezing model, which represents both bulk freezing and crust formation. The comparison between SIMMER-III simulation and its corresponding experiment indicates that SIMMER-III can reproduce the freezing behavior observed on different structure materials and under various cooling conditions. SIMMER-III also shows encouraging agreement with experimental results of melt penetration on structures and particle formation. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In a hypothetical core disruptive accident (CDA) of a liquid metal reactor (LMR), the molten core metal of the reactor may relocate through flow paths in the core (Kondo et al., 1995). This would cause a molten metal, coolant and structure interactions, in which the heat is transferred from the molten metal to the coolant and core structure, would cause freezing of the molten metal onto the core structure. In assessing the safety of LMRs, it is important to know the consequences of such freezing phenomena during interactions of molten metal with the coolant and core structure. Interactions between molten metal and the reactor structure can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated (Theofanous and Bell, 1986), which are often called CDAs. These include fuel-pin disruption, phase transition or subassembly disruption and the escape of fuel. Fig. 1 shows the postulated CDA events of a heavy liquid metal reactor whereas Fig. 2 represents the schematic view of key CDA phenomena in a heavy liquid metal reactor. It is anticipated that during CDA of LMR molten cladding and disrupted fuel pass through the coolant channel and due to interaction of the molten metal with coolant and
∗ Corresponding author. Tel.: +81 92 802 3502; fax: +81 92 802 3502. E-mail address: [email protected] (M.M. Rahman). 0029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.04.008
structure, heat is transferred from the molten metal to the coolant and structure and as a result molten metal becomes freeze and relocates onto the structure. Due to this relocation of molten metal onto the structure, coolant channel becomes narrow and finally the possibility of the channel blockages is increased. Though the occurrence of CDA is extremely unrealistic due to the denying actuations of all multiple safety systems, it is still emphasized from the viewpoint of safety designs and evaluation. This is because CDAs potentially lead to significant mechanical energy release as a result of recriticality (Epstein et al., 1976). This potential consequence of energetic recriticality is regarded as one of the most important risk contributors to the environments (El-genk and Cronenberg, 1978). Therefore, it is very important to evaluate adequately the sequences of CDA of LMR; SIMMER-III code has been developed for this purpose. SIMMER-III, an advanced safety analysis computer code (Kondo et al., 1992; Tobita et al., 2000) has been developed to investigate the severe transients and CDAs of LMRs. The development of SIMMERIII has been conducted at JAEA (Japan Atomic Energy Agency) formerly JNC (Japan Nuclear Cycle Development Institute), initially in collaboration with FZK (Forschungszentrum Karlsruhe) in Germany, and CEA (Commissariat a` I’Energie Atomique) which also ˆ e´ Nucleaire) ´ includes IRSN (Institute de Radioprotection et de Suret in France. The objective of SIMMER-III is to alleviate some of the limitations of SIMMER-II and thereby to provide a next-generation
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2707
Fig. 2. Schematic view of key CDA phenomena of heavy liquid metal reactor. Fig. 1. Postulated CDA events of heavy liquid metal reactor.
tool for more reliable analysis of severe transients and CDAs. Material distribution and relocation of molten fuel is one of the key study areas in the SIMMER-III assessment program. In particular, freezing of molten fuel on the core structure surface is a key phenomenon because the dynamics of freezing plays an important role in determining the fuel removal from the active core region. In order to reasonably evaluate the mass distribution of molten fuel in the core region and the consequences of recriticality, it is important especially for the code to evaluate the freezing and blockage formation phenomena inside the escape path adequately (Kamiyama et al., 2006). The main purpose of the SIMMER-III code is to provide a numerical simulation of complex multi-phase, multi-component flow problems essential to investigate CDAs in LMRs. However, the code is designed to be sufficiently flexible to be applied to a variety of multi-phase flows, in addition to LMR safety issues. In order to apply SIMMER-III to LMR safety analysis, the code must be demonstrated to be sufficiently robust and reliable. Therefore, it has to be tested and validated extensively. In our previous study (Rahman et al., 2007) a series of molten metal freezing experiments were performed in order to figure out the basic physical characteristics in freezing mode of molten metal and to determine some of the characteristics parameters of the freezing of molten metal during penetrating onto the structure. In these experiments, freezing characteristics were investigated using Wood’s metal as a molten metal material and the experiments were conducted using a copper or stainless-steel plate of flat shaped in design as the freezing structure in air and water coolant systems. Experimental results such as penetration length and width of frozen metal on stainless steel and brass structures were compared under the air and water coolant conditions. In the air coolant experiments, most of the molten metal froze to the structure in thin, wide frozen shapes of metal with good adherence, whereas in the water coolant experiments, it was found that most of the frozen metal broke up and were swept downstream as debris with only a very small fraction of the melt that adhered to the structure without a uniform shape. Different freezing modes dependent on experimental conditions were observed in the water coolant experiments, whereas with air as the coolant, the freezing mode did not change. The present work is an extension of our previous study, which was undertaken to provide quantitative experimental information
with the verification of the models and methods for the numerical simulation of the freezing behavior of molten metal. In these experiments, although the similar experimental system to one used in the first series of experiments was also used, L-shaped flow channels for brass and stainless steel were used to realize more uniform melt flow than on the flat plate. In the present study, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure under various cooling conditions. The numerical simulation of the experimental results was performed by the SIMMER-III code using a mixed freezing model involving both bulk freezing and crust formation on the structure. The experimental results were compared with the simulation results to demonstrate that the code is applicable to such complex, transient multi-phase flow situations. 2. Molten metal freezing experiments 2.1. Experimental apparatus The present molten metal freezing experiment is conducted using Wood’s metal as a molten metal stimulant in air and water coolant conditions. A schematic diagram of the experimental setup is shown in Fig. 3. The facility consists of a cylindrical melt tank and a water pool, in which molten metal is poured. A circular nozzle is connected to the bottom of the melt tank to enable a smooth ejection of melt flow onto the metal structure, which is immersed in the water pool. The melt tank and nozzle, which are made of stainless steel, are heated by an electric heater and their temperature is adjusted using the temperature controller. Fourteen K-type thermocouples are connected to the melt tank, nozzle and metal structure to measure the temperature of the melt as it falls onto the metal structure. The inner diameter of the upper part of the melt tank is 75 mm, whereas the inner and outer diameters of the lower part of the melt tank are 12.5 mm and 37.5 mm, respectively. Two nozzles of diameters 1.9 mm and 2.2 mm, respectively, are used to eject the molten metal with different melt flow rates. The water pool, which is a rectangular open-topped box (1500 mm in height × 300 mm in width), is made of stainless steel and with two of the side-walls made of transparent glass for the purpose of observation. An electric heater with temperature controller and
338 g (6.7 s) 340 g (5.7 s)
338 g (6.7 s) 340 g (5.7 s) 1.9 mm (50.5 g/s) 2.2 mm (59.7 g/s)
Nozzle diameter (melt flow rate)
1.9 mm (50.5 g/s) 2.2 mm (59.7 g/s) 20 C 35 C and 52 C
20 ◦ C 35 ◦ C and 52 ◦ C 1.9 mm (51.5 g/s), 2.2 mm (60.1 g/s)
335 g (6.5 s), 337 g (5.6 s) 1.9 mm (51.5 g/s), 2.2 mm (60.1 g/s) 17 C
17 ◦ C
Stainless steel
Brass
335 g (6.5 s), 337 g (5.6 s)
◦
Coolant temperature
Metal plate
Table 1 Conditions of experimental cases
The experiment is conducted in two steps using two types of coolant, namely air and water. The freezing phenomena are investigated experimentally using two structures made of stainless steel and brass, of which thermal conductivities are 16 W/(m K) and 125 W/(m K) respectively, at room temperature. In both air and water coolant experiments, simulant Wood’s metal is melted down by an electric furnace, and then transferred to the test section; the temperature of the melt is monitored using a digital thermometer and poured into the melt tank. In this tank, the temperature is measured to achieve the desired temperature. At the desired temperature, the melt is ejected onto the structure by opening the plug of the nozzle. In air coolant experiment, the structure is supported with the stand and the tank and its nozzle section are installed above the stand and secured. In water coolant experiment, the structure is set-up within the water pool and then tank and its nozzle section are installed above the water pool and secured. The temperature of the water pool is kept constant by the electric heater and a stainless-steel stirrer with three fans positioned at the top, middle and bottom of the stirrer is employed to create a uniform water temperature throughout the pool. The experiments were carried out at water temperatures of 20.2 ◦ C, 35 ◦ C and 50 ◦ C. The molten metal is prepared as of air coolant experiment described above and poured into the cylindrical tank. The melt penetration length stands for the length of the frozen metal adhered on the structure. Distribution of frozen metal adhered on the structures was measured for both in air and water coolant conditions. Effects on melt freezing behavior were observed by changing the structure material, coolant, coolant temperature and melt temperature.
Nozzle diameter (melt flow rate)
2.2. Experimental procedure
◦
Water coolant
Ejected mass (duration) Air coolant
a thermocouple sensor are used to control the water temperature at a desired level. An L-shaped metal structure 800-mm long and 5-mm thick is inclined at an angle of 72.5◦ to the horizontal line, and is supported on a stainless-steel stand. The initial temperature of the metal structure is equivalent to that of the atmosphere. A fragment collector is also present inside the horizontal part of the stand. During experiments where air was the only coolant, the water pool was absent. A high-speed video camera (SONY, Model: DCR-TRV900) was used to record video images of the melt as it falls onto the metal structure.
Coolant temperature
Fig. 3. Schematic of experimental set-up.
◦
Ejected mass (duration)
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
◦
2708
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2709
going into melting. For example, Fig. 4 shows interface (A, B) where the interface is undergoing a net loss energy to component B. This energy is either coming from freezing of component A. The resulting product will be either more of component B depending on the process involved. When the phase transition is predicted, the interface I is defined as the melting temperature of a phasetemperature TA,B transition species. Otherwise, in the case of no mass transfer, the interface temperature is defined so that qIA,B becomes zero: I = TA,B
hA,B TA + hB,A TB hA,B + hB,A
(2)
The M/F mass-transfer rate is determined from energy balance at the interface. If qIA,B is zero, sensible heat is exchanged without mass transfer. If qIA,B is positive, namely the energy is lost at the interface, a liquid component freezes. Then the mass-transfer rate for this case is determined from qIA,B
Fig. 4. Basis of heat-transfer limited process. I = A,B
The melt flow and distribution were observed with a high-speed video camera. In both the air and water-cooled conditions, experiments are carried out at atmospheric pressure. The experimental conditions are summarized in Table 1. 3. Numerical simulation by SIMMER-III
SIMMER-III is a two-dimensional, three-velocity-field, multiphase, multi-component, Eulerian, fluid-dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model (Kondo et al., 1992; Tobita et al., 2000). The fundamental equations of the fluid dynamics are based on a so-called multi-fluid model. The code models the melting/freezing (M/F) phase transition as non-equilibrium processes occurring at fluid interfaces and equilibrium processes occurring when the bulk temperatures exceed or drop below the melting temperature (Morita et al., 2003). The overall fluid-dynamics solution algorithm is based on a time-factorization (time-splitting) approach, in which intracell heat and mass transfer is determined separately from inter-cell fluid convection. The followings describe the general heat and mass-transfer model associated with the M/F processes. In SIMMER-III, the M/F processes occurring at interfaces are described by a heat-transfer limited model. These are nonequilibrium processes because the bulk temperature does not generally satisfy the phase-transition condition when the mass transfer occurs at the interface. The basic concept of this model is described using Fig. 4, in which a binary contact interface of the energy components A and B is shown. Each energy component interfaces with the other energy components simultaneously, and each interface has a uniquely defined interfacial area. Energy transfers between components are based on the interfacial area and heat-transfer coefficients determined from engineering correlations. A specified temperature is assigned to each possible interface to calculate heat flows from/to each interface into/from the respective bulk materials. These heat flows are summed to give the net interfacial energy loss or gain. The net energy transfer rate from the interface is defined as
I I qIA,B = aA,B hA,B (TA,B − TA ) + hB,A (TA,B − TB )
(1)
where a is the interfacial area per unit volume, h is the heat-transfer coefficient, T is the temperature and the superscript I stands for interface. An interfacial energy loss is defined as positive and means freezing must occur to conserve (provide) energy. An interfacial energy gain, which is defined as negative, means the energy is
(3)
where i is the enthalpy and the subscript sol means the solidus point. If qIA,B is negative, on the other hand, namely the energy is gained at the interface, a solid component melts. Then the masstransfer rate for this case is determined from I =− B,A
3.1. Phase-transition model of SIMMER-III
iA − isol
qIA,B iLiq − iB
(4)
where the subscript Liq stands for liquidus point. The equilibrium M/F model calculates equilibrium processes resulting from the non-equilibrium heat and mass transfer. If the internal energy of a solid component A exceeds its solidus energy (eA > esol ), the component A melts into the component B with the mass-transfer rate: EQ A,B =
1 eA − esol ¯ A t hf
(5)
where the superscript EQ means the equilibrium process, ¯ is the macroscopic density and hf is the heat of fusion. If the internal energy of a liquid component B drops below its liquids energy (eB
1 eLiq − eB ¯ B t hf
(6)
The non-equilibrium M/F transfers can include the crust formation on a structure wall (conduction-limited freezing) and particle formation in the melt flow that contribute to equilibrium (bulk) freezing. The M/F transfers at the liquid/particle interfaces are also included which is analogous to the liquid/structure M/F transfers for consistency. In addition, equilibrium M/F transfers are performed to eliminate subcooled liquids or metastable solids as the result of heat transfer. 3.2. Modeling for experimental analyses The present analytical model for freezing phenomena of molten metal describes the heat and mass transfer among molten metal, structure (metal plate) and coolant. The concept of the heat and mass-transfer model for the present experimental analyses using SIMMER-III is illustrated in Fig. 5 schematically. In this model for freezing phenomena of molten metal, five components such as molten metal, coolant, solid particles, crust and structure surface are assigned to mass and energy components. Here, crust is frozen metal adhered on the structure, while molten metal solidified in fluids is treated as solid particles. In the case of water coolant experiments, these five components are expressed as L1 (molten metal),
2710
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
EQ EQ EQ + S3,L1 + L4,L1 esol − L1,L4 eLiq
I I +aS3,L1 hL1,S3 TS3,L1 − TL1 + aS7,L1 hL1,S7 TL1,S7 − TL1 I I +aL1,L3 hL1,L3 TL1,L3 − TL1 + aL1,L4 hL1,L4 TL1,L4 − TL1
(8) Particles
∂¯ L4 I (L1/L3) I(L1/L4) I(L1/L4) = L1,L4 − L4,L1 − L1,L4 ∂t ∂¯ L4 eL4 = ∂t
I(L1/L3)
L1,L4
I(L1/L4)
+ L1,L4
EQ EQ − L4,L1 − L1,L4
I(L1/L4)
esol − L4,L1
∂¯ S3 I(L1/S3) I(L1/S3) = − S3,L1 − L1,S3 ∂t
L3 (water), L4 (solid particles), S3 (crust) and S7 (structure surface), respectively, according to the indexes commonly used in SIMMERIII models. The molten metal interacts with structure, crust, coolant and particles at four interfaces of S3/L1, S7/L1, L1/L3 and L1/L4, respectively. There can also exist an interface of S3/S7 after the crust formation. Both non-equilibrium and equilibrium freezing processes of molten metal are considered in this model as described in Section 3.1. In the present analyses, freezing behaviors of molten metal in the water coolant system are represented by the five massI(S3/L1) I(S7/L1) I(L1/L3) I(L1/L4) EQ transfer rates: L1,S3 , L1,S3 , L1,L4 , L1,L4 and L1,L4 . On the other hand, although re-melting of the frozen metal from the crust and the particles might have minor effects on the general freezing behavior under the present experimental conditions, four I(S3/L1) I(L1/L4) melting mass-transfer rates are also considered: S3,L1 , L4,L1 , EQ EQ S3,L1 and L4,L1 . Here, the superscripts I(S3/L1), I(S7/L1), I(L1/L3) and I(L1/L4) mean non-equilibrium mass transfers at the interfaces of S3/L1, S7/L1, L1/L3 and L1/L4, respectively (Table 2). The intra-cell heat and mass transfers for molten metal, particles and crust components are expressed by the following conservation equations without convection terms:
∂¯ L1 = ∂t
I(S3/L1)
S3,L1
I(L1/L4)
+ L4,L1 ∂¯ L1 eL1 = ∂t
I(S3/L1)
− L1,S3
I(L1/L4)
− L1,L4
I(S3/L1)
S3,L1
I(L1/L4)
EQ EQ EQ + S3,L1 + L4,L1 − L1,L4
I(S8/L1)
+ L1,S3
(7)
esol I(L1/L3)
+ L1,L4
I(L1/L4)
+ L1,L4
eL1
Table 2 Non-equilibrium mass-transfer paths Interface
Freezing Melting
(10)
EQ + S3,L1
(11)
I I +aS3,S7 hS3,S7 TS3,S7 −TS3 + aS3,L1 hS3,L1 TS3,L1 −TS3
I I +aS3,L3 hS3,L3 TS3,L3 − TS3 + aS3,L3 hS3,L3 TS3,L3 − TS3
(12) For the coolant and the structure, the following energy equations only with heat-transfer terms are solved as the intra-cell heat transfer: Water
I I ∂¯ L3 eL3 = aL1,L3 hL3,L1 TL1,L3 − TL3 + aS3,L3 hL3,S3 TS3,L3 − TL3 ∂t
I +aS7,L3 hL3,S7 TS7,L3 − TL3
(13)
Structure
I I ∂¯ S7 eS7 = aS3,S7 hS7,S3 TS3,S7 − TS7 + aL1,S7 hS7,L1 TL1,S7 − TS7 ∂t
I +aL3,S7 hS7,L3 TL3,S7 − TS7
(14)
In addition to the above, the heat conduction inside the structure and the heat transfer from the other side of the structure to the coolant are calculated separately. 3.3. Analytical geometry of SIMMER-III simulation
I(L1/L3)
− L1,L4
+ L4,L1
I(S3/L1)
− L1,S3
I(S7/L1)
− L1,S3
∂¯ S3 eS3 I(L1/S3) I(L1/S3) EQ esol = L1,S3 esol − S3,L1 eS3 + S3,L1 ∂t
Fig. 5. Modeling concept of melt freezing behavior.
Molten metal
(9)
EQ eL4 + L1,L4 esol
EQ I −L1,L4 eLiq + aL1,L4 hL4,L1 TL1,L4 − TL4
Crust
Melt/crust
Melt/structure
Melt/coolant
Melt/particle
Melt ⇒ crust Crust ⇒ melt
Melt ⇒ crust X
Melt ⇒ particles X
Melt ⇒ particles Particles ⇒ melt
A two-dimensional mesh of Cartesian geometry was adopted for the numerical simulation using SIMMER-III. The analytical geometry of SIMMER-III simulation is shown in Fig. 6. The melt reservoir is located at the top of the first column by one mesh cell of size 20 mm and 50 mm in the x and z directions, respectively. Here, the x-direction is along with the melt flow on the structure surface, while the z-direction is taken as the vertical to the structure surface. The melt was injected downward due to gravity ‘g’ at constant pressure of 1 atm from the melt reservoir and passes through the coolant channel. The structure on which the frozen metal is adhered, is assigned a mesh cells can wall. Since the present SIMMER-III simulation is modeled in the x–z two-dimensional co-ordinate, the geometrical configuration in the y direction is considered as the difference in binary contact area between melt/structure and melt/coolant. The mesh cell size of 20 mm in the x direction and 20 mm in the z direction was used
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2711
Fig. 7. Photographs of adhered frozen metal observed on stainless-steel structure in air coolant condition by varying nozzle diameter.
Fig. 6. Analytical geometry of SIMMER-III simulation.
in the coolant (air/water) pool where two meshes in the x direction and 50 meshes in the z direction were defined. The calculation starts just after the contact of melt with the structure. 4. Results and discussion 4.1. Experimental observation In the experiment, molten Wood’s metal (melting point 78.8 ◦ C) was used as a simulant melt, while stainless steel and brass were used as freezing structures. The L-shaped structure with 5-mm thickness and 80-cm length was inclined at an angle of 72.5◦ to the horizontal line in a bath filled with stagnant coolant. The simulant melt was ejected onto the inclined freezing structure in the bath through a stainless-steel nozzle with 1.9-mm and 2.2-mm diameter, respectively, by gravity. Effects on melt freezing behavior were observed by changing the structure material and coolant at melt temperature of 102–105 ◦ C. The reason of considering this melt temperature range is that relatively longer penetration of melt onto the structure is observed at this melt temperature range. The melt flow and distribution were observed for both the experiments with a high-speed video camera. The typical freezing behaviors of molten metal at air coolant conditions are shown in Figs. 7 and 8. In air coolant condition, it is clearly seen from the figures that when hot melt falls onto the stainless-steel structure, the frozen layer becomes thin and strip but the length of the frozen metal adhered onto the structure was observed to be longer at nozzle diameter (ND) of 2.2 mm than that of the nozzle diameter of 1.9 mm. Whereas, in the case of brass structure, the frozen layer becomes a bit more thicker specially at the downstream than the frozen layer observed on stainless-steel structure. The length of adhered frozen metal on brass structure was also found to be longer at nozzle diameter of 2.2 mm than that of nozzle diameter of 1.9 mm. But
the length of frozen metal adhered onto the structure is found to be shorter for brass structure than that of the stainless-steel structure. This difference is due to the high thermal conductivity of brass than stainless steel. This can be explained by the fact that during passing on the brass structure, the molten metal losses significant amount of its latent heat; thus for a very short period of time, the temperature decreased near to its freezing point and become more rapid rate of solidification than the stainless-steel structure. In water coolant condition, the experiments were conducted at water coolant temperatures of 20.2 ◦ C, 35 ◦ C and 52 ◦ C and the results are shown in Figs. 9 and 10 for stainless steel and brass structures, respectively. It is observed from both the figures that when hot melt falls on the structure, a part of the molten metal is frozen and quenched on the structure and a significant amount of molten metal is broken and fall down as different fragments called debris. Beside these some frozen metal is broken and fall down due to rapid increase of viscosity. The heat transfer of molten metal is occurred between water coolant and structure as a result debris is observed. For both stainless steel and brass structures it is found that the length of the adhered frozen metal is observed to be longer at nozzle diameter of 2.2 mm than that of the nozzle diameter of 1.9 mm. Comparing with respect to water coolant temperature, it is viewed that the length of the adhered frozen metal is found to be maximum at water coolant temperature of 20.2 ◦ C and then further increased of water coolant temperature at 35 ◦ C and 52 ◦ C, the length of the adhered frozen metal is found to be decreased gradually. Beside these some differences of the sizes of the debris are also observed for both structures at different coolant temperatures and nozzle diameter. It is clearly seen from the observed photographs that the length of the adhered frozen metal becomes shorter in brass structure than that of the stainless-steel structure but the
Fig. 8. Photographs of adhered frozen metal observed on brass structure in air coolant condition by varying nozzle diameter.
2712
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 9. Photographs of adhered frozen metal and debris observed on stainless-steel structure at melt temperature of 102 ◦ C by varying water coolant temperature and nozzle diameter.
adhered frozen metal is observed to be thicker on brass structure than that of the stainless-steel structure. It is also viewed from both figures of air and water coolant conditions, the lower part of frozen metal becomes thicker than that
of the upper part. This is observed due to the re-melting of frozen metal at the upstream for further falling of hot melt from the nozzle to the upper part of the melt and finally re-melting metal is accumulated at the downstream. Beside these some instability is also
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
2713
Fig. 10. Photographs of adhered frozen metal and debris observed on stainless-steel structure at melt temperature of 102 ◦ C by varying water coolant temperature and nozzle diameter.
2714
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 11. Transient penetration length of molten metal on stainless-steel structure in the presence of air coolant at different nozzle diameter.
found for both the cases, which might be due to the melt initial inertia and other hydrodynamic interaction forces. 4.2. Melt penetration length The penetration length is defined as the length of the melt flow along the metal plate. The penetration length of different experimental cases is compared with their corresponding SIMMER-III simulation results. The comparison of penetration length for all the cases shows similar transient trends. In this paper, the experimental cases such as penetration length on stainless steel and brass structures in presence of air and water coolant with different nozzle diameter will be mainly presented and compared with the SIMMER-III simulation results. The transient penetration length of molten metal on stainless steel and brass structures are plotted in the presence of air coolant, for nozzle diameter of 1.9 mm and 2.2 mm as shown in Figs. 11 and 12. From these figures it can be seen that the transient penetration length in the experiments increases with the increase of melt flow rate (by changing nozzle diameter) and the SIMMERIII simulation results also successfully reproduce similar trend of transient penetration length observed in the experiments for both stainless steel and brass structures. These two figures also illustrate that the total time of freezing of molten metal is observed to be earlier at higher melt flow rate (ND = 2.2 mm) than the lower melt flow rate (ND = 1.9 mm) in both experiments and SIMMERIII simulation, although a small difference of total freezing time of molten metal is observed in experiment and SIMMER-III simulation in stainless-steel structure at nozzle diameter of 2.2 mm.
Fig. 12. Transient penetration length of molten metal on brass structure in the presence of air coolant at different nozzle diameter.
Fig. 13. Transient penetration length of molten metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in the presence of water coolant at different coolant temperatures.
Comparing the transient penetration length of stainless steel and brass structures it can be predicted that maximum penetration length is found to be longer in stainless-steel structure than brass structure for nozzle diameter of 1.9 mm and 2.2 mm for both experiments and SIMMER-III simulation. From the early stage of transient penetration of molten metal shown in Figs. 11 and 12, it is also observed experimentally that in stainless-steel structure, the molten metal penetrates longer distance within a short period of time than the brass structure. SIMMER-III simulation results also reproduce the same behavior for both stainless steel and brass structures. This difference of freezing behavior on stainless steel and brass structure is observed due to the high thermal conductivity of brass than stainless steel. Figs. 13 and 14 show the transient penetration length of molten metal on stainless-steel structure and Figs. 15 and 16 represent the transients penetration length on brass structure during falling through nozzles of diameter 1.9 mm and 2.2 mm, respectively, in the presence of water coolant at coolant temperatures of 20.2 ◦ C, 35 ◦ C and 52 ◦ C. It is worth noting here from these figures that the transient penetration length decreases with the increase of coolant temperature and increase with the increase of melt flow rate (by changing the nozzle diameter). At low coolant temperature, structure temperature also becomes low and heat transfer from molten metal to the structure is dominant at low structure temperature, which results in more crust formation on the structure and thus increases the penetration length. In SIMMER-III simulation of water coolant experiments, we find that the code reproduces the transient penetration length observed in the experiments well by increas-
Fig. 14. Transient penetration length of molten metal on stainless-steel structure during falling through a nozzle of diameter 2.2 mm in the presence of water coolant at different coolant temperatures.
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 15. Transient penetration length of molten metal on brass structure during falling through a nozzle of diameter 1.9 mm in the presence of water coolant at different coolant temperatures.
ing the heat transfer between melt and water coolant. This might be because in the experiment the ripples on the melt flow surface enhances heat-transfer areas between the melt and the coolant. In the present simulation, the binary contact area was increased about 16% between the melt and the coolant, compared with the uniform melt flow. Figs. 13 and 14 also show no observable differences of transient penetration length at melt temperatures of 35 ◦ C and 52 ◦ C but it differs a bit only at melt temperatures of 20.2 ◦ C at nozzle diameter of 1.9 mm (Fig. 13) while obvious difference is clearly observed at melt temperature of 20.2 ◦ C at nozzle diameter of 2.2 mm (Fig. 14). This similar behavior of transient penetration length of molten metal at coolant temperature of 35 ◦ C and 52 ◦ C indicates that these temperatures have less effect on change of penetration length. Similar trend of transient penetration length also observed in SIMMER-III simulation for the above-mentioned cases. Fig. 15 predicts that at early stage of transient melt penetration of molten metal on brass structure at nozzle diameter of 1.9 mm shows no clear difference at melt temperature of 35 ◦ C and 52 ◦ C for both the result of experiment and SIMMER-III simulation while clear difference is observed at maximum penetration length. On the other hand, Fig. 16 depicts very encouraging agreement of transient penetration length of molten metal on brass structure for different coolant temperatures at nozzle diameter of 2.2 mm. Comparing the transient penetration length of stainless steel and brass structures in the presence of water coolant, it can be predicted that maximum penetration length is found to be longer in stainless-steel plate than brass structure for nozzle diameter of
Fig. 16. Transient penetration length of molten metal on brass structure during falling through a nozzle of diameter 2.2 mm in the presence of water coolant at different coolant temperatures.
2715
Fig. 17. Transient mass distribution of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm.
1.9 mm and 2.2 mm for both experiments and SIMMER-III simulation. From the early stage of transient penetration of molten metal it is also observed experimentally that in stainless-steel plate, the molten metal penetrates longer distance within a short period of time than the brass structure. SIMMER-III simulation results also reproduce the same behavior for both stainless steel and brass structures. This difference of freezing behavior on stainless steel and brass structure is observed due to the high thermal conductivity of brass than stainless steel. 4.3. Mass distribution Figs. 17 and 18 depict the transient mass distribution of SIMMER-III simulation results for stainless steel and brass structure, respectively, in the presence of air and water coolant. It can be seen from these two figures that in air coolant condition, most of the molten metal become crust after freezing and no particle is observed. Whereas, in the presence of water coolant, SIMMERIII simulation results a significant amount of particle formation as debris along with the crust formation. In both the cases of stainless steel and brass structures, the amount of particle formation is found to be higher than the crust formation. The formation of debris was observed in water coolant system due to the high heat transfer of molten metal to water. The SIMMER-III simulation results of crust formation on plate and particle formation as debris represent an important sequence of non-equilibrium heat-transfer model that contributes to melt quenching and bulk freezing. Comparing the final mass distribution into crust and solid particle with the experimental results, it is observed from the experiments that in air coolant system about 96% of the molten
Fig. 18. Transient mass distribution of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm.
2716
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
Fig. 19. Transient mass-transfer rate of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
metal becomes crust for both on stainless steel and brass structures. On the other hand, in the water coolant system, crust is formed on stainless steel and brass structure, with about 40% of the molten metal, while the rest of the molten metal is observed as solid particles. Simulation results of final mass distribution into crust and solid particle (Figs. 17 and 18) revels the comparable results with the experiments of reference cases on both stainless steel and brass structures for both in air and water coolant conditions. Figs. 19 and 20 represent the dominant transient mass-transfer rates on stainless steel and brass structures, respectively in water coolant condition. These two figures also revels the comparison of freezing rates between crust formation at L1/S3 (molten metal/crust) and L1/S7 (molten metal/structure surface) contact and particle formation at L1/L3 (molten metal/water) contact on stainless steel and brass structures. It can be observed from Fig. 19 that at early stage of freezing, the rate of crust and particle formations are almost comparable but at later stage, the rate of particle formation is higher than that of crust formation. On the other hand, Fig. 20 predicts that at early stage of freezing, the rate of crust formation is little bit higher than that of particle formation, while at later stage, the rate of particle formation is little bit higher than that of crust formation. These two figures also show that not only crust formation but also particle formations at L1/L3 contact are dominant freezing processes. 4.4. Sensitivity of particle formation effects Figs. 21 and 22 illustrate the transient penetration length of Wood’s metal on stainless steel and brass structures, respectively,
Fig. 21. Transient penetration length of Wood’s metal on stainless-steel structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
Fig. 22. Transient penetration length of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
in water coolant condition with and without considering particle formation effects at the contact of L1/L3 (molten metal/water) in SIMMER-III simulation. These two figures revels the effects of particle formation on penetration length in water coolant condition. It can be seen from these two figures that with considering particle formation effect at L1/L3 contact (reference case of SIMMER-III), SIMMER-III result shows well comparable with the experimental result, while on the other hand, without considering the particle formation effect at L1/L3 contact, SIMMER-III overestimates the melt penetration on both stainless steel and brass structures. 5. Conclusion
Fig. 20. Transient mass-transfer rate of Wood’s metal on brass structure during falling through a nozzle of diameter 1.9 mm in presence of water coolant at coolant temperature of 20 ◦ C.
In this work, a series of fundamental experiments was conducted to simulate the freezing behavior of molten Wood’s metal observed onto metal structures to verify the basic validity of the SIMMER-III code on simulating freezing behavior of molten metal onto the core structure. The experiments show that longer penetration length and good adherence on structure were found in the air coolant than in the water coolant. In both air and water coolant experiments, penetration length was found to be a bit longer on the stainless-steel plate than on the brass structure due to the lower thermal conductivity of stainless steel than brass. In air coolant condition, most of the molten metal was adhered on the plate and no particle formation due to melt solidification was observed as debris. On the other hand, in water coolant condition, only a small part of molten metal was adhered onto the plate and a significant amount of melt froze as debris. The
M.M. Rahman et al. / Nuclear Engineering and Design 238 (2008) 2706–2717
formation of debris was observed in water coolant system due to the high heat transfer of molten metal to water. The numerical simulation of molten metal freezing was performed with the SIMMER-III code using a mixed freezing model involving both bulk freezing and crust formation on the plate. In the air coolant condition, SIMMER-III simulation shows good agreement with the transient penetration length measured on both stainless steel and brass structures. In the water coolant conditions, simulation results suggest that melt cooling was enhanced by the effective increase of the contact area between melt and water. From the transient mass distribution of molten metal, SIMMER-III also resulted in the significant amount of particle formation as debris in water coolant condition, whereas, in air coolant condition no particle formation was observed and most of the frozen metal was adhered on the plate. These behaviors are also in good agreement with the experimental results. Results of transient mass-transfer rate of molten metal in water coolant condition revels that not only crust formation but also particle formations at melt coolant contact are dominant freezing process. The SIMMER-III simulation results of crust formation on plate and particle formation as debris represent an important sequence of non-equilibrium heat-transfer model that contributes to melt quenching and bulk freezing. Sensitivity study of particle formation effects at melt and coolant contact shows that without considering particle formation effect at melt and coolant contact, SIMMER-III overestimates the melt penetration on both brass and stainless steel structures. The present study advances the experimental verification of SIMMER-III in terms of freezing phenomena of molten metal for the disrupted core. Though the further code verification would be necessary, we anticipate that the present results will contribute to the improvement of reliability in accident analysis of LMR.
2717
Acknowledgements Part of this work was performed as a joint research project between Kyushu University and FZK, Germany. One of the authors, M. Mizanur Rahman gratefully acknowledges the Ministry of Education, Culture, Sports, Science and Technology, Japan, for the support by providing Monbukagakusho scholarship. References El-genk, M., Cronenberg, W.A., 1978. An assessment of fuel freezing and drainage phenomena in a reactor shield plug following a core disruptive accident. Nucl. Eng. Des. 47 (2), 195–225. Epstein, M., Grolmes, M.A., Henry, R.E., Fauske, H.K., 1976. Transient freezing of a flow ceramic fuel in a steel channel. Nucl. Sci. Eng. 61, 310–323. Kamiyama, K., Brear, D.J., Tobita, Y., Kondo, S., 2006. Establishment of freezing model for reactor safety analysis. J. Nucl. Sci. Technol. 43 (10), 1206– 1217. Kondo, S., Tobita, Y., Morita, K., Shirakawa, N., 1992. SIMMER-III: An advanced computer program for LMFBR severe accident analysis. In: Proceedings of the International Conference on Design and Safety of Advanced Nuclear Power Plant (ANP’92), vol. IV, Tokyo, pp. 40.5.1–40.5.11. Kondo, S., Konishi, K., Isozaki, M., Imahori, S., Furutani, A., Bear, D.J., 1995. Experimental study on simulated molten jet–coolant interactions. Nucl. Eng. Des. 155 (1–2), 73–84. Morita, K., Yamano, H., Tobita, Y., Kondo, S., 2003. SIMMER-III/IV heat- and masstransfer model—model and method description-, JNC report, JNC TN9400 2003047, Japan. Rahman, M.M., Hino, T., Morita, K., Matsumoto, T., Nakagawa, K., Fukuda, K., Maschek, W., 2007. Experimental investigation of molten metal freezing onto a structure. Exp. Therm. Fluid Sci. 32, 198–213. Theofanous, T.G., Bell, C.R., 1986. An assessment of clinch river breeder reactor core disruptive accident energetics. Nucl. Sci. Eng. 93, 215–228. Tobita, Y., Kondo, S., Yamano, H., Fujita, S., Morita, K., Maschek, W., Louvet, J., Coste, P., Pingy, S., 2000. Current status and application of SIMMER-III, an advanced computer program for LMFR safety analysis. In: Second Japan– Korea Symposium on Nuclear Thermal Hydraulics and Safety (NTHAS-2), Fukuoka, pp. 65–72.