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Thermal interaction in crusted melt jets with large-scale structures
Nuclear Engineering and Design 189 (1999) 329 – 336
Thermal interaction in crusted melt jets with large-scale structures Ken-ichiro Sugiyama *, Fuminori Sotome, Miciho Ishikawa Department of Nuclear Engineering, Hokkaido Uni6ersity, North 13, West 8, North Ward, Sapporo 060 -8628, Japan Received 3 June 1998; accepted 3 June 1998
Abstract The objective of the present study is to experimentally observe thermal interaction, which is capable of triggering, due to water entrained, or entrapped within crusted melt jets with ‘large-scale structures’. The present experiment was carried out by dropping molten zinc and molten tin of 100 g. These were sufficient to generate large-scale structures of melt jets. The results showed that the entrapment-type thermal interaction occurs in molten-zinc jets with rare probability, and the entrainment-type thermal interaction occurs in molten tin jets with high probability. The difference in thermal interaction between the molten zinc and molten tin is considered to be mainly due to a difference in kinematic viscosity between them. © 1999 Elsevier Science S.A. All rights reserved.
1. Introduction In a severe accident, there is a possibility that molten core drops into water, causing a vapor explosion. The energy of vapor explosion may cause the integrity of the reactor or the containment vessel to fail. However, the physics of vapor explosion is not sufficiently understood yet. It is generally considered that a large-scale vapor explosion involves a progression through four stages of coarse mixing, triggering, propagation, and expansion. This has been accepted as a concept in vapor explosion. Based on this concept, vapor explosion could not occur without spontaneous triggering. Hence, it is important to understand * Corresponding author. Tel./fax: +81-11-706-6663. E-mail address: [email protected] (K.-i. Sugiyama)
what thermal-hydraulic mechanisms between water and high temperature melts cause triggering. Triggering is defined as events that initiate a rapid, local heat transfer and a pressure rise. The objective of the present study is to observe locally caused thermal interaction, which is capable of triggering, due to water entrapped or entrained within crusted melt jets with large-scale structures. It has been recognized in the field of fluid mechanics that jet flows generate large-scale structures (Laufer, 1975). This recognition involves that the Kelvin–Helmholtz instability in jet flows potentially generates large-scale structures. Fig. 1 shows a generation and development of the large-scale structure in a water jet falling through still water, which was reported by Browand and Laufer (1975). The shear layer at nozzle exit (38.1 mm in inner diameter) rolls up into discrete vor-
0029-5493/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 9 8 ) 0 0 2 7 1 - 4
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tices because of its instability, developing into large-scale vertices (large-scale structures) downstream. The size of large-scale structures is generally comparable to the characteristic length in fluid systems (jet diameter in Fig. 1). Many interesting studies on large-scale structures in the field of fluid mechanics have been reported for the last three decades. However, we have not found previous studies on large-scale structure with solidification in our survey of technical papers. Our motivation in carrying out the present study is to experimentally observe whether or not thermal interaction, which is capable of triggering, occurs due to water entrapped or entrained within crusted melts with large-scale structures. The large-scale structures are a subsequent evolu-
Fig. 2. Conceptual setup of experimental apparatus.
Fig. 1. Large-scale structure in water jet visualized by hydrogen bubbles (cited from Browand and Laufer (1975)).
tion of instability. Observation is important in high-temperature melts covered with vapor film to understand the triggering in reactor conditions. However, as a first step, we used molten zinc and tin with low melting points below the minimum film boiling temperatures in the present study. Kinematic viscosity plays a key role for the development of large-scale structures (process of deformation) in melt jets. Kinematic viscosity of molten UO2 is around 0.5 mm2 s − 1, if we take low values reported by Woodley (1974), based on the fact that intensity of vapor explosion increases as the kinematic viscosity of melts decreases (Zimanowski et al., 1993). Since the value of molten zinc is about same as that of molten UO2, it is expected that the behavior of large-scale structures in molten zinc is qualitatively similar than that in molten UO2, when thermal behavior is not taken into consideration. Hence, experiments on molten zinc give some useful aspects on the possibility of spontaneous triggering in jets of molten UO2, even though a large difference of thermal diffusivity between molten zinc and molten UO2 exists (Fink et al., 1981). As it is known that thermal interaction does not usually occur in molten zinc, we also used molten tin. This has a
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331
Fig. 3. Large-scale structure and deformation in mercury jet.
kinematic viscosity equal to half that of molten zinc and easily causes thermal interaction.
2. Experimental apparatus and procedure Experiments were carried out by dropping 100 g masses of molten zinc and tin into sub-cooled water at atmospheric pressure. These are sufficient to generate large-scale melt structures. Melts were dropped through a funnel with 6.5 mm in inner diameter. Conceptual setup is shown in Fig. 2. Zinc and tin were first put in a crucible made of ceramic and then heated by a gas burner. A C – A thermocouple was used to measure the temperature of melts. The initial temperature of molten zinc was between 430 and 470°C, and tin was between 250 and 270°C, where the formation of solid crust was assured during falling through water. The funnel was heated to become the same as the initial temperature of melts. The water tank was made of acrylic plate. The inner size of the tank is 22 cm wide, 10 cm deep,
and 80 cm high. The depth of the water in the tank was kept at 78 cm. The water temperature was always kept at about 15°C. A video camera (Sony, CCD-V700) at a framing rate of 30 pps and high speed video camera (Photron, FASTCAM Rabbit-2) at a framing rate of 400 pps were used to record the behavior of melts falling through water.
3. Observation of genelation of large-scale structure in a high density jet Fig. 3 shows a mercury jet dropping through water using a funnel with an inner diameter of 6.5 mm. The mercury and water were both maintained at room temperature. In Fig. 3, D and X stand for the inner diameter of the funnel exit and the depth from the funnel exit, respectively. The exit of the funnel sits just below the water surface in order to avoid disturbance caused by impact against the water surface. Fig. 3(a) shows regularly generated conical shapes, which are generally categorized as large-
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scale structures in the field of fluid mechanics. Fig. 3(b) shows considerably deformed conical shapes, and Fig. 3(c) shows an irregularly deformed jet just before breaking up. This result indicates that large-scale structures are inevitably generated even in jets with high density which is largely different from that of water, as well as jet systems with same density as shown in Fig. 1 reported in the field of fluid mechanics.
Fig. 4. Large-scale structure in molten-zinc jet.
4. Results and discussion on molten-zinc jet Fig. 4 shows a typical example of large-scale structures in a molten-zinc jet falling through water. The initial temperature of zinc was 430°C. It clearly shows that several conical shapes, which we categorize as large-scale structures, connect to each other. The shape is similar to that of mercury. This characteristic shape was often observed in molten-zinc experiment. It has been reported that thermal interaction does not occur in molten zinc. This fact is applicable to most of zinc runs in our experiment. This means that porous debris or fine fragments generated by locally caused thermal interactions were not observed in most of solidified zinc samples, although generation of large-scale structures was often observed. Fig. 5(a and b) show a zinc sample in which evidence of thermal interaction was observed in a large-scale structure. Fig. 5(a) shows a conical shape that is swollen in the middle. Fig. 5(b) is the cross sectional view. Initial temperature of molten zinc was 450°C. This sample, as shown in Fig. 5(a), has a crater on the left side. This sample was basically a hollow tube with different cross section stopped at top and bottom sides (the bottom is open in Fig. 5(b)). The hollow tube was produced by solidification during the passage through water. A long drop, of which the top is indicated by arrow A, is clearly observed over lower the region in the hollow tube, and the somewhat porous part is locally observed in the upper region of the long drop as indicated by arrow B. From this observation, it is reasonable to consider that the crater was produced by an eruption of high pressure caused by a thermal interaction. The physics of the occurrence of thermal interaction would be as follows. After the solid crust of the leading melt (hollow tube) was formed by cooling, the succeeding molten zinc (long drop inside) could catch up with the leading crusted melt by means of acceleration due to low pressure, hydrodynamically produced, above the leading crusted melt. This means that the succeeding molten zinc enters into the leading crusted melt. This ‘catch up’ phenomenon was observed often in these experiments. The motion of melt mass
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333
Fig. 5. Thermal interaction in crusted molten-zinc jet.
associated with catch-up phenomenon is generally called ‘organized motion’ in the field of fluid mechanics. Under these circumstances, it would be possible that some amount of surrounding water is simultaneously entrained inside the leading crusted zinc (hollow tube). Although the mechanism that the leading crusted zinc makes a closed hollow tube stopped at top and bottom sides has not been clear, a thermal interaction between molten zinc and water entrapped within the hollow tube would be possible to produce a high pressure. When the solid crust (tube wall) does not bear the inner high pressure, the highpressure vapor erupts from a weak region on the solid crust. The crater shown in Fig. 5(a) would be produced in such processes.
5. Results and discussion on molten-tin jet As explained in the previous section, molten zinc is insensitive to thermal interaction. Hence, it is difficult to clearly observed the relation between the large-scale structure and thermal interaction. We therefore carried out an experiment of molten tin to observe the relation in detail. Fig. 6 shows time-sequence pictures of a molten-tin jet. The initial temperature of tin was 270°C. The jet has two conical shapes indicated by arrows A. Many of runs that initial temperatures were from 250 to 270°C showed similar shapes, which we categorize as large-scale structures. It was rare that thermal interaction occurs near the water surface because of a superficial
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Fig. 6. Large-scale structure and thermal interaction in tin jet.
crust of tin jet has already formed in the air. The jet falls through water with almost keeping its shape. At 2.5 ms, thermal interaction occurs inside the upper conical shape indicated by arrow B. At 5.0 ms, the thermal interaction region moves upward as indicated by arrow C. At 7.5 ms, the thermal interaction comes close to the water surface as indicated by arrow D. This phenomenon is regarded as a the ‘propagation’ of thermal interaction. Thermal interaction did not occur in the lower conical shape, because the solidification of molten tin inside the crust had been progressed. This type of thermal interaction is due to the fact that some amount of water is entrained from the opening of the base of conical shapes into the crust due to the low pressure hydrodynamically caused above the conical shapes, and the water is forced into contact with molten tin inside. We now suppose that the opening hydrodynamically produced on the base of conical shapes originates in a low kinematic viscosity of molten tin. This kind of opening was not observed on the base of conical shapes in molten-zinc jets. Fig. 7(a) shows the typical appearance of a solidified tin jet. The initial temperature was 270°C. This sample consists of several conical shapes. Porous debris, which is an evidence of the
occurrence of thermal interaction, is clearly observed in two regions indicated by arrows. Fig. 7(b) shows the cross sectional view of a conical shape with porous debris outside as indicated by the upper arrow in Fig. 7(a). A solid crust, conical in shape, is filled with fine fragment and porous debris. The crust has some cracks, including one indicated by an arrows. These are considered to be caused by a high pressure produced after the crust formed. This result indicates that some amount of water was hydrodynamically entrained inside the crust, and thermal interaction with molten tin produced a high pressure inside. The fine fragment and porous debris as shown in Fig. 7(b) were observed frequently in molten tin experiments. Taking no large difference in thermal diffusivity between zinc and tin into consideration, the difference of thermal interaction between molten tin and zinc is considered to be mainly due to difference in kinematic viscosity between them.
6. Conclusions In order to clarify the relation between largescale structure and thermal interaction capable of triggering, we carried out experiments dropping
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Fig. 7. Thermal interaction in crusted molten-tin jet.
molten zinc and tin into water. The conclusions in the present study are as follows: (1) We observed the large-scale structures that we call conical shapes, which are generated by development of instability in molten zinc and tin jets as well as in mercury jet without phase change. (2) It was infrequently observed that thermal interaction occurs in molten-zinc jets, because of the water entrapped within large-scale structures. (3) It was observed with high probability that thermal interaction occurs in molten-tin jets, because of the water entrained into large-scale structures.
(4) The difference of thermal interaction between molten zinc and tin jets is considered to be mainly due to difference in kinematic viscosity between them.
References Browand, F.K., Laufer, J., 1975. The role of large scale structures in initial development of circular jets, Proceedings of the 4th Biennial Symposium on Turbulence in Liquids. Rolla, pp. 333 – 344. Fink, J.K., Chasanov, M.G., Leibowitz, L., 1981. Thermophysical properties of uranium dioxide. J. Nucl. Mat. 102, 17 – 25.
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K.-i. Sugiyama et al. / Nuclear Engineering and Design 189 (1999) 329–336
Laufer, J., 1975. New trends in experimental turbulence research. Annu. Rev. Fluid Mech. 7, 307–325. Woodley, R.E., 1974. The viscosity of molten uranium dioxide. J. Nucl. Mat. 50, 103–106.
.
Zimanowski, B., Fro¨hlich, G., Lorentz, V., 1993. Experiments on vapor explosion by interaction of water with silicate melts, Proceedings of the International Seminar on the Physics of Vapor Explosions. Tomakomai, pp. 149 –156.
Thermal interaction in crusted melt jets with large-scale structures Ken-ichiro Sugiyama *, Fuminori Sotome, Miciho Ishikawa Department of Nuclear Engineering, Hokkaido Uni6ersity, North 13, West 8, North Ward, Sapporo 060 -8628, Japan Received 3 June 1998; accepted 3 June 1998
Abstract The objective of the present study is to experimentally observe thermal interaction, which is capable of triggering, due to water entrained, or entrapped within crusted melt jets with ‘large-scale structures’. The present experiment was carried out by dropping molten zinc and molten tin of 100 g. These were sufficient to generate large-scale structures of melt jets. The results showed that the entrapment-type thermal interaction occurs in molten-zinc jets with rare probability, and the entrainment-type thermal interaction occurs in molten tin jets with high probability. The difference in thermal interaction between the molten zinc and molten tin is considered to be mainly due to a difference in kinematic viscosity between them. © 1999 Elsevier Science S.A. All rights reserved.
1. Introduction In a severe accident, there is a possibility that molten core drops into water, causing a vapor explosion. The energy of vapor explosion may cause the integrity of the reactor or the containment vessel to fail. However, the physics of vapor explosion is not sufficiently understood yet. It is generally considered that a large-scale vapor explosion involves a progression through four stages of coarse mixing, triggering, propagation, and expansion. This has been accepted as a concept in vapor explosion. Based on this concept, vapor explosion could not occur without spontaneous triggering. Hence, it is important to understand * Corresponding author. Tel./fax: +81-11-706-6663. E-mail address: [email protected] (K.-i. Sugiyama)
what thermal-hydraulic mechanisms between water and high temperature melts cause triggering. Triggering is defined as events that initiate a rapid, local heat transfer and a pressure rise. The objective of the present study is to observe locally caused thermal interaction, which is capable of triggering, due to water entrapped or entrained within crusted melt jets with large-scale structures. It has been recognized in the field of fluid mechanics that jet flows generate large-scale structures (Laufer, 1975). This recognition involves that the Kelvin–Helmholtz instability in jet flows potentially generates large-scale structures. Fig. 1 shows a generation and development of the large-scale structure in a water jet falling through still water, which was reported by Browand and Laufer (1975). The shear layer at nozzle exit (38.1 mm in inner diameter) rolls up into discrete vor-
0029-5493/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 9 8 ) 0 0 2 7 1 - 4
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tices because of its instability, developing into large-scale vertices (large-scale structures) downstream. The size of large-scale structures is generally comparable to the characteristic length in fluid systems (jet diameter in Fig. 1). Many interesting studies on large-scale structures in the field of fluid mechanics have been reported for the last three decades. However, we have not found previous studies on large-scale structure with solidification in our survey of technical papers. Our motivation in carrying out the present study is to experimentally observe whether or not thermal interaction, which is capable of triggering, occurs due to water entrapped or entrained within crusted melts with large-scale structures. The large-scale structures are a subsequent evolu-
Fig. 2. Conceptual setup of experimental apparatus.
Fig. 1. Large-scale structure in water jet visualized by hydrogen bubbles (cited from Browand and Laufer (1975)).
tion of instability. Observation is important in high-temperature melts covered with vapor film to understand the triggering in reactor conditions. However, as a first step, we used molten zinc and tin with low melting points below the minimum film boiling temperatures in the present study. Kinematic viscosity plays a key role for the development of large-scale structures (process of deformation) in melt jets. Kinematic viscosity of molten UO2 is around 0.5 mm2 s − 1, if we take low values reported by Woodley (1974), based on the fact that intensity of vapor explosion increases as the kinematic viscosity of melts decreases (Zimanowski et al., 1993). Since the value of molten zinc is about same as that of molten UO2, it is expected that the behavior of large-scale structures in molten zinc is qualitatively similar than that in molten UO2, when thermal behavior is not taken into consideration. Hence, experiments on molten zinc give some useful aspects on the possibility of spontaneous triggering in jets of molten UO2, even though a large difference of thermal diffusivity between molten zinc and molten UO2 exists (Fink et al., 1981). As it is known that thermal interaction does not usually occur in molten zinc, we also used molten tin. This has a
K.-i. Sugiyama et al. / Nuclear Engineering and Design 189 (1999) 329–336
331
Fig. 3. Large-scale structure and deformation in mercury jet.
kinematic viscosity equal to half that of molten zinc and easily causes thermal interaction.
2. Experimental apparatus and procedure Experiments were carried out by dropping 100 g masses of molten zinc and tin into sub-cooled water at atmospheric pressure. These are sufficient to generate large-scale melt structures. Melts were dropped through a funnel with 6.5 mm in inner diameter. Conceptual setup is shown in Fig. 2. Zinc and tin were first put in a crucible made of ceramic and then heated by a gas burner. A C – A thermocouple was used to measure the temperature of melts. The initial temperature of molten zinc was between 430 and 470°C, and tin was between 250 and 270°C, where the formation of solid crust was assured during falling through water. The funnel was heated to become the same as the initial temperature of melts. The water tank was made of acrylic plate. The inner size of the tank is 22 cm wide, 10 cm deep,
and 80 cm high. The depth of the water in the tank was kept at 78 cm. The water temperature was always kept at about 15°C. A video camera (Sony, CCD-V700) at a framing rate of 30 pps and high speed video camera (Photron, FASTCAM Rabbit-2) at a framing rate of 400 pps were used to record the behavior of melts falling through water.
3. Observation of genelation of large-scale structure in a high density jet Fig. 3 shows a mercury jet dropping through water using a funnel with an inner diameter of 6.5 mm. The mercury and water were both maintained at room temperature. In Fig. 3, D and X stand for the inner diameter of the funnel exit and the depth from the funnel exit, respectively. The exit of the funnel sits just below the water surface in order to avoid disturbance caused by impact against the water surface. Fig. 3(a) shows regularly generated conical shapes, which are generally categorized as large-
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scale structures in the field of fluid mechanics. Fig. 3(b) shows considerably deformed conical shapes, and Fig. 3(c) shows an irregularly deformed jet just before breaking up. This result indicates that large-scale structures are inevitably generated even in jets with high density which is largely different from that of water, as well as jet systems with same density as shown in Fig. 1 reported in the field of fluid mechanics.
Fig. 4. Large-scale structure in molten-zinc jet.
4. Results and discussion on molten-zinc jet Fig. 4 shows a typical example of large-scale structures in a molten-zinc jet falling through water. The initial temperature of zinc was 430°C. It clearly shows that several conical shapes, which we categorize as large-scale structures, connect to each other. The shape is similar to that of mercury. This characteristic shape was often observed in molten-zinc experiment. It has been reported that thermal interaction does not occur in molten zinc. This fact is applicable to most of zinc runs in our experiment. This means that porous debris or fine fragments generated by locally caused thermal interactions were not observed in most of solidified zinc samples, although generation of large-scale structures was often observed. Fig. 5(a and b) show a zinc sample in which evidence of thermal interaction was observed in a large-scale structure. Fig. 5(a) shows a conical shape that is swollen in the middle. Fig. 5(b) is the cross sectional view. Initial temperature of molten zinc was 450°C. This sample, as shown in Fig. 5(a), has a crater on the left side. This sample was basically a hollow tube with different cross section stopped at top and bottom sides (the bottom is open in Fig. 5(b)). The hollow tube was produced by solidification during the passage through water. A long drop, of which the top is indicated by arrow A, is clearly observed over lower the region in the hollow tube, and the somewhat porous part is locally observed in the upper region of the long drop as indicated by arrow B. From this observation, it is reasonable to consider that the crater was produced by an eruption of high pressure caused by a thermal interaction. The physics of the occurrence of thermal interaction would be as follows. After the solid crust of the leading melt (hollow tube) was formed by cooling, the succeeding molten zinc (long drop inside) could catch up with the leading crusted melt by means of acceleration due to low pressure, hydrodynamically produced, above the leading crusted melt. This means that the succeeding molten zinc enters into the leading crusted melt. This ‘catch up’ phenomenon was observed often in these experiments. The motion of melt mass
K.-i. Sugiyama et al. / Nuclear Engineering and Design 189 (1999) 329–336
333
Fig. 5. Thermal interaction in crusted molten-zinc jet.
associated with catch-up phenomenon is generally called ‘organized motion’ in the field of fluid mechanics. Under these circumstances, it would be possible that some amount of surrounding water is simultaneously entrained inside the leading crusted zinc (hollow tube). Although the mechanism that the leading crusted zinc makes a closed hollow tube stopped at top and bottom sides has not been clear, a thermal interaction between molten zinc and water entrapped within the hollow tube would be possible to produce a high pressure. When the solid crust (tube wall) does not bear the inner high pressure, the highpressure vapor erupts from a weak region on the solid crust. The crater shown in Fig. 5(a) would be produced in such processes.
5. Results and discussion on molten-tin jet As explained in the previous section, molten zinc is insensitive to thermal interaction. Hence, it is difficult to clearly observed the relation between the large-scale structure and thermal interaction. We therefore carried out an experiment of molten tin to observe the relation in detail. Fig. 6 shows time-sequence pictures of a molten-tin jet. The initial temperature of tin was 270°C. The jet has two conical shapes indicated by arrows A. Many of runs that initial temperatures were from 250 to 270°C showed similar shapes, which we categorize as large-scale structures. It was rare that thermal interaction occurs near the water surface because of a superficial
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Fig. 6. Large-scale structure and thermal interaction in tin jet.
crust of tin jet has already formed in the air. The jet falls through water with almost keeping its shape. At 2.5 ms, thermal interaction occurs inside the upper conical shape indicated by arrow B. At 5.0 ms, the thermal interaction region moves upward as indicated by arrow C. At 7.5 ms, the thermal interaction comes close to the water surface as indicated by arrow D. This phenomenon is regarded as a the ‘propagation’ of thermal interaction. Thermal interaction did not occur in the lower conical shape, because the solidification of molten tin inside the crust had been progressed. This type of thermal interaction is due to the fact that some amount of water is entrained from the opening of the base of conical shapes into the crust due to the low pressure hydrodynamically caused above the conical shapes, and the water is forced into contact with molten tin inside. We now suppose that the opening hydrodynamically produced on the base of conical shapes originates in a low kinematic viscosity of molten tin. This kind of opening was not observed on the base of conical shapes in molten-zinc jets. Fig. 7(a) shows the typical appearance of a solidified tin jet. The initial temperature was 270°C. This sample consists of several conical shapes. Porous debris, which is an evidence of the
occurrence of thermal interaction, is clearly observed in two regions indicated by arrows. Fig. 7(b) shows the cross sectional view of a conical shape with porous debris outside as indicated by the upper arrow in Fig. 7(a). A solid crust, conical in shape, is filled with fine fragment and porous debris. The crust has some cracks, including one indicated by an arrows. These are considered to be caused by a high pressure produced after the crust formed. This result indicates that some amount of water was hydrodynamically entrained inside the crust, and thermal interaction with molten tin produced a high pressure inside. The fine fragment and porous debris as shown in Fig. 7(b) were observed frequently in molten tin experiments. Taking no large difference in thermal diffusivity between zinc and tin into consideration, the difference of thermal interaction between molten tin and zinc is considered to be mainly due to difference in kinematic viscosity between them.
6. Conclusions In order to clarify the relation between largescale structure and thermal interaction capable of triggering, we carried out experiments dropping
K.-i. Sugiyama et al. / Nuclear Engineering and Design 189 (1999) 329–336
335
Fig. 7. Thermal interaction in crusted molten-tin jet.
molten zinc and tin into water. The conclusions in the present study are as follows: (1) We observed the large-scale structures that we call conical shapes, which are generated by development of instability in molten zinc and tin jets as well as in mercury jet without phase change. (2) It was infrequently observed that thermal interaction occurs in molten-zinc jets, because of the water entrapped within large-scale structures. (3) It was observed with high probability that thermal interaction occurs in molten-tin jets, because of the water entrained into large-scale structures.
(4) The difference of thermal interaction between molten zinc and tin jets is considered to be mainly due to difference in kinematic viscosity between them.
References Browand, F.K., Laufer, J., 1975. The role of large scale structures in initial development of circular jets, Proceedings of the 4th Biennial Symposium on Turbulence in Liquids. Rolla, pp. 333 – 344. Fink, J.K., Chasanov, M.G., Leibowitz, L., 1981. Thermophysical properties of uranium dioxide. J. Nucl. Mat. 102, 17 – 25.
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K.-i. Sugiyama et al. / Nuclear Engineering and Design 189 (1999) 329–336
Laufer, J., 1975. New trends in experimental turbulence research. Annu. Rev. Fluid Mech. 7, 307–325. Woodley, R.E., 1974. The viscosity of molten uranium dioxide. J. Nucl. Mat. 50, 103–106.
.
Zimanowski, B., Fro¨hlich, G., Lorentz, V., 1993. Experiments on vapor explosion by interaction of water with silicate melts, Proceedings of the International Seminar on the Physics of Vapor Explosions. Tomakomai, pp. 149 –156.