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Visual investigation on the breakup of high superheated molten metal during FCI process
Applied Thermal Engineering 98 (2016) 962–975
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Visual investigation on the breakup of high superheated molten metal during FCI process Qi Lu, Deqi Chen *, Chong Li Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400044, China
H I G H L I G H T S
• • •
Visual investigation on the breakup process of high superheated molten metal was carried out. The mechanism of the breakup process was analyzed in detail under different working conditions. Two dimensionless parameters were proposed to predict the occurrence of the breakup process.
A R T I C L E
I N F O
Article history: Received 7 September 2015 Accepted 22 December 2015 Available online 14 January 2016 Keywords: FCI Molten metal Breakup Visual investigation
A B S T R A C T
A visual experimental investigation was carried out to study the breakup process as high superheated molten metal falling into the subcooled coolant during the severe accident of a nuclear reactor, namely the FCI (fuel coolant interaction) process. Deionized water was used as the coolant, and the aluminum, lead, and bismuth were used as the metal samples. In this study, the characteristics of FCI process with different molten metals, different molten metal mixtures, different coolant depths, different coolant temperatures and different initial molten metal temperatures were analyzed in detail. The molten metal breakup process was observed by a high speed camera during this experimental study. It was found that the breakup process was restricted significantly by the high melting point of the metal, large surface tension, large viscosity, high thermal conductivity, and low specific heat of the molten metal. Meanwhile, increasing the coolant temperature and the temperature of molten lead could obviously restrict or prevent the breakup process. Finally, two dimensionless parameters were proposed to predict the occurrence of the breakup process. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction As for any potential core disruptive accident (CDA), fuel elements probably burn out due to much core residual heat. During the falling process of molten fuels, the interaction between the molten fuels and coolant will cause violent boiling or flashing of water into vapor, namely the vapor explosion. Meanwhile, the possible breakup process and pressure pulses will threaten the integrity of the nuclear reactor. Over the years, many authors tried to describe clearly the process of FCI (fuel coolant interaction). According to widely accepted concepts, the fundamental process of FCI was molten melt fragmentation increasing the heat transfer area to the coolant. Corradini et al. [1] and Arias [2] described the explosive scenario as follows: (1) quiescent mixing of the fuel and coolant, (2) triggering of the explosion, (3) explosion escalation and propagation, and (4) expansion and work production. Also, Zhou et al. [3] concluded that the fragmentation
* Corresponding author. Tel.: +86 23 65106902; fax: +86 23 65106902. E-mail address: [email protected] (D. Chen). http://dx.doi.org/10.1016/j.applthermaleng.2015.12.118 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
process could be divided into several stages: vapor film collapsing, melt drop-coolant direct contact, formation of high pressure spots, rapid growth of a filament around molten metal drop, rapid fuel coolant interaction area expansion, breaking up of the filament, and mixing of fragments with the coolant. Recently, Tyrpekl et al. [4] suggested that FCI occurred generally in two main phases: a premixing phase, during which the molten melt was fragmented into large droplets and mixed with the coolant; the explosion phase, during which the vapor film that developed around the molten droplets were destabilized and finely fragmented. However, Dinh et al. [5] proposed that the jet fragmentation was a pre-condition for the premixing and the vapor produced, due to mixing of the melt and coolant, affecting jet fragmentation for quasi-steady (long-duration) melt jets. Therefore, a separate-effect description was not suitable for such an integrated and synergistic transient process. In previous studies, it was believed that the breakup of molten metal was depended on the deformation, the boundary layer stripping, and the instability of surface waves on molten metal surface, such as the Rayleigh–Taylor instability and Kelvin–Helmholtz instability. As mentioned by Duan et al. [6], any or all of above three modes might contribute to jet breakup process. Ciccarelli and Frost
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[7] proposed that the breakup of a cold drop was caused by the stripping of fragments due to relative flow, but the fragmentation of a hot drop was dominated by the growth and collapsing of the vapor film. Bang et al. [8] experimentally investigated the jet breakup process in non-boiling conditions to isolate the jet breakup process from the complex interactions. It was found that the Kelvin– Helmholtz instability was the most possible reason for jet breakup. Abe et al. [9] also suggested that the stripped off from the molten material jet due to the Kelvin–Helmholtz instability, which was dominant for the break up process. However, Abe et al. [10] suggested that the molten jet front experienced the conditions to produce Rayleigh–Taylor instability. Also, the stability of the generated fragment was related to critical Weber number theory and that the fragmentation of the molten jet side was related to Kelvin–Helmholtz instability and unstable wavelength. Recently, Arias [2] considered the Kelvin-Helmholtz and Rayleigh-Taylor instabilities at the interface corium–water in his physical model, where the oscillation of the interface transmitted sufficient momentum to the corium so that its surface distorted into waves that could grow until they detached to form small corium fragments (debris). Cao et al. [11] suggested that the growth of filaments on the molten tin drop surface was the essential mechanism of fragment caused by Rayleigh– Taylor instability. Also, Zhou et al. [3] concluded that the growth and breaking up of the filament were the critical mechanism of melt tin drop fragmentation, which were similar to Ciccarelli and Frost [7]. As mentioned by Thakre et al. [12], the molten tin drop initially presented as a circular shape surrounded by a thin vapor film. Then, it gradually evolved to a semicircle, and continued deformation eventually leaded to a crescent shape. During the deformation process, the surrounding vapor was removed to the tail of the molten tin drop due to the buoyancy. Shick and Grace [13] suggested that three possible explanations about the fragmentation were the impact pressure developed as the two liquids coming together, release of superheat at the contact interface, and hydrodynamic instabilities associated with an explosion shock wave. Meanwhile, a ‘splash’ theory for local propagation of vapor explosion was proposed by Ochiai and Bankoff [14]. As a random liquid–liquid contact was made, the explosive growth
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and coalescence of vapor bubbles occurred as soon as the surrounding pressure was relieved, resulting in high-pressure vapor layer at the liquid–liquid contact area. Nevertheless, Tso and Strauss [15] concluded that it was difficult to explain the occurrence of the fragmentation process by assuming the existence of a small pressure pulse (0.3 kPa) measured in their experiment. As mentioned by Abe et al. [16], the spontaneous vapor explosion hardly occurred when the water temperature was near the saturation temperature or the interfacial temperature between molten material and water was lower than the material melting temperature, which was also proposed by Sa et al. [17]. Takashimal and Iida [18] suggested that the full film boiling was eventually established again after the surrounding vapor thickness decreasing, which demonstrated the transient contact between the liquid and solid. Even though lots of studies focusing on FCI have been carried out as discussed in the preceding sections, many mechanisms during FCI do not reached a common agreement due to complications. The subject of this paper is to visually investigate the rapid phase change and fragmentation process during the molten metal coming into contact with the coolant and falling in the coolant. Meanwhile, the theoretical analysis has been carried out to further discuss the breakup mechanism and predict the breakup occurrence by two dimensionless parameters.
2. Experimental apparatus A schematic diagram of the experimental apparatus is shown in Fig. 1. Metal samples are heated by a muffle furnace with the highest temperature of 1200 °C. The molten metal is poured into the water tank through a funnel, which is equipped at the top of a water tank. The coolant depth is 1400 mm, and the distance between the exit of the funnel and coolant surface is 100 mm, so the velocity as the molten metal initially as it comes into contact with the coolant is 1.4 m/s. The water tank is composed of PMMA (polymethyl methacrylate), with the size of 500 mm × 500 mm × 1500 mm. The coolant temperature is adjusted by a preheater and heat exchanger, respectively. The molten metal and coolant temperatures are measured
Fig. 1. The schematic diagram of experimental apparatus.
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Table 2 Properties of metals.
Table 1 Working conditions. Number
Metal sample
m (g)
Tmm (°C)
Tc (°C)
Metal
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Bismuth Lead Lead Lead Lead Lead (small coolant depth) Lead Lead Lead Lead Lead Lead Lead Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Lead–aluminum Lead–aluminum
200 200 400 50 50 50 50 50 50 50 50 50 50 200 200 200 20 50 100 150 200 200 200 200 200 200 360-40 396-4
950 950 950 900 800 800 800 800 800 700 600 500 400 1100 1000 950 950 950 950 950 950 900 850 800 750 700 950 950
20 20 20 20 20 20 30 40 60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
Aluminum
Lead
Bismuth
660 2.39 × 103 −0.35 2.28 × 103 914 −0.35 1.02 × 103 0.1492 16.50 0.7558 1080 103.7 1.4 998 4.70 56.59
327 10.68 × 103 −1.32 9.86 × 103 458 −0.13 0.54 × 103 0.4636 8.61 0.4640 135 19.9 1.4 998 1.91 15.66
271 10.05 × 103 −1.18 9.25 × 103 378 −0.07 0.43 × 103 0.4458 6.45 0.4461 133.6 15.5 1.4 998 1.53 14.48
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
by K-type thermocouples, and the metal mass is measured by electronic scales, with uncertainties of ±0.5 K and ±0.1 g, respectively. The coolant is deionized water, and metal samples include aluminum, lead, and bismuth, which are heated to the specified temperature in a graphite crucible by a muffle furnace. All the working conditions are summarized in Table 1. The experimental study is carried out under an atmosphere of 0.101 MPa and an environmental temperature of 30 °C. During the heating process, the nitrogen is injected into muffle furnace to prevent metals to be oxidized. The breakup process of molten metals in the coolant are captured by a high speed camera (Redlake-HG-100K) with a microlens with a recording speed of 5000 fps (frame per second) to obtain clear fragmentation process with an LED light used for illumination. Meanwhile, the micro-lens of the high speed camera is equipped at the location where the top of view area is the coolant surface, and solidified molten metals are collected from the bottom of the water tank, as shown in Fig. 1. 3. Results and discussion 3.1. The FCI process for different metals In order to study the effect of metal property on FCI process, aluminum, lead and bismuth are used to carry out the experimental investigation. All the melting points of these metals are below 700 °C, and the main physical properties are shown in Table 2. The temperature of molten metal is set up to 950 °C, the temperature of coolant is 20 °C, and the metal mass is 200 g during the experiment. The side of the molten metal is affected by the Kelvin–Helmholtz instability, which is known as follows, i.e. when two immiscible fluids flow relatively to each other along an interface of separation, there is a maximum relative velocity above which a small disturbance of the interface will amplify and grow and thereby distort the flow. According to Abe et al. [9], a critical relative velocity above which
Tm (°C) ρm (kg/m3) Δρ/ΔT (kg/m3) ρmm (kg/m3) Tmm = 950 °C σm (mN/m) Δσ/ΔT mN/mK σmm (mN/m) T = 950 °C μ0 (mN/sm2) E (kJ/mol) μmm (mN/sm2) Tmm = 950 °C cp (J/kgK) k (W/mK) u (m/s) ρc (kg/m3) Tc = 20 °C λK-H (mm) λR-T (mm)
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
some initial disturbances of large wavelength are unstable is presented as
u=
2πσ mm ( ρmm + ρc ) λK -H ρmm ρc
(1)
where ρmm is the density of molten metal (kg/m3); ρc is the density of coolant (kg/m3 ); λ K-H is the critical wavelength for Kelvin– Helmholtz instability (mm). Also, the critical wavelength is given by
λK -H =
2πσ ( ρmm + ρc ) u 2ρmm ρc
(2)
As mentioned by Tong and Tang [20], the Rayleigh–Taylor instability is interfacial instability between two fluids of different densities that are stratified in the gravity field or accelerated normal to the interface. It is commonly observed that the boundary between two stratified fluid layers at rest is not stable if the upper fluid density is larger than the lower-fluid density. Once the wavelength of a disturbance is larger than the critical wavelength, the Rayleigh– Taylor instability can lead to the destruction of the single common interface. Meanwhile, the critical wavelength of the Rayleigh– Taylor instability at the fastest growth rate is expressed as follows, which obviously affects the front of molten metal.
λR -T = 2π
σ mm
(ρmm − ρc ) g
(3)
where g is the gravitational acceleration (m/s2); λR-T is the critical wavelength for Rayleigh–Taylor instability (mm). The evolutions of the liquid–vapor interface during the FCI process for different molten metals are shown in Figs. 2–4, which are sketched by red dotted lines. As shown in Fig. 2, the molten aluminum does not break up during the whole falling process. It is found that the vapor film generates rapidly on the surface as the molten aluminum comes into contact with the coolant, and the vapor film grows quickly during the falling process. In addition, when molten aluminum initially comes into contact with the coolant (t = 1 ms to t = 6 ms), the surface can retain its integrity under shear force. During the falling process, the vapor film attached on the molten aluminum is obviously thick and smooth, so the molten metal boundary can be also considered smooth. The condensation process of the vapor film on the molten aluminum is relatively slow, which continues for more than 26 ms. Meanwhile, the condensation of the
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t=1ms
t=6ms
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t=11ms
12.3 mm
t=16ms
t=21ms
Side
t=26ms
Front
Fig. 2. The evolution of the liquid–vapor interface during the FCI process for the aluminum (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
vapor film gradually enhances with the temperature of the molten metal decreasing, and finally the molten aluminum solidified, as shown in Fig. 5a. In addition, lots of irregular holes are distributed on the surface of the solidified aluminum caused by strong the shock from violent boiling. As for molten lead and bismuth, once these molten metals come into contact with the coolant, the breakup process occurs quickly with the vapor rapidly being generated on the superheated surfaces of the molten metals, as shown in Figs. 3
t=1 ms
and 4. Meanwhile, the solidified residues of lead and bismuth are both particles, and the fragmentation of bismuth is more significant than that of lead, as shown in Fig. 5b and c. As shown in Table 2, the surface tension of molten aluminum at 950 °C is 914 mN/m, which is obviously larger than that of molten lead (σ = 458 mN/m) and bismuth (σ = 378 mN/m) at 950 °C, especially the molten bismuth. Therefore, the surface of molten aluminum can retain its integrity under shear force, namely no premixing
t=11ms
t=6ms
Initial Breakup 12.3 mm
t=16ms
t=21ms
t=26ms
Fig. 3. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
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t=1ms
t=6 ms
t=11 ms
Initial Breakup
12.3 mm
t=16 ms
t=26 ms
t=21ms
Fig. 4. The evolution of the liquid–vapor interface during the FCI process for the bismuth (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
process happening. The critical wavelength of the Rayleigh–Taylor instability for molten aluminum (λR-T = 56.59 mm) is significantly larger than that for molten lead (λR-T = 15.66 mm) and bismuth (λR-T = 14.48 mm). Also, the critical wavelength of Kelvin–Helmholtz instability for molten aluminum (λK-H = 4.70 mm) is obviously larger
than that for molten lead (λ K-H = 1.91 mm) and bismuth (λK-H = 1.53 mm). As mentioned by Abe [10], the front and side of molten jet are affected by Rayleigh–Taylor instability and Kelvin– Helmholtz instability, respectively. Therefore, the front and side of molten aluminum boundary are much stable, as shown in Fig. 2. Al-
a The solidified aluminum
b The solidified lead
c The solidified bismuth
Fig. 5. The coagula of different metals.
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though the specific heat capacity of molten aluminum is relatively large (cp = 1080 J/kgK), its thermal conductivity (k = 103.7 W/mK) is much larger than that of molten lead (k = 19.9 W/mK) and bismuth (k = 15.5 W/mK); hence, the heat can be conducted quickly to the surface from the center of the molten aluminum. Furthermore, the thermal stress acting on the surface of molten aluminum is small, which is not intense enough to damage the surface integrity. As shown in Fig. 2, the vapor film generates immediately on the surface of molten aluminum as the molten aluminum comes into contact with the coolant, and the dominant boiling heat transfer mechanism is stable film boiling due to high heat flux conducted from the center to the surface of molten aluminum, which prevents the interaction between the molten aluminum and coolant. Next, the molten aluminum is gradually cooled by the coolant; the superheat on the surface of molten aluminum decreases during the falling process. What is more, the temperature difference between the center and the surface of molten metal gradually decreases, so the heat transfer amount conducted to the vapor film decreases. Meanwhile, the vapor film thickness at the liquid–vapor interface decreases due to constant condensation, and the dominant heat transfer mechanism transfers from the film boiling to transition boiling. Finally, the vapor film is broken by hydraulic pressure and the effect of dragging from the coolant, and the coolant directly contacts with the molten aluminum. However, the melting point of aluminum is relatively high, so the area coming into contact with the coolant has solidified to solid as the vapor film broken up. Although the superheated aluminum surface contacts with the coolant, the coolant cannot flow into the inside of molten aluminum, and just evaporates quickly on the superheated surface. Also, the explosive boiling generates intense pressure pulses at the metalcoolant interface, which can damage the integrity of solidified surface. Therefore, lots of irregular holes are distributed on the surface of solidified aluminum, as shown in Fig. 5a. As for molten lead and bismuth, when molten metals initially come into contact with the coolant, the shear force caused by relative velocity acts on the surfaces of the molten metals. Meanwhile, surface tension cannot overcome the shear forces to retain the surface integrity; hence, the boundary layer stripping clearly occurs at the beginning of falling process, as shown in Figs. 3 and 4. Lots of fragments on the boundary layer mix with the coolant and the vapor film rapidly generates, namely the premixing process. As mentioned above, the critical wavelengths of Rayleigh–Taylor instability for molten lead (λR-T = 15.66 mm) and bismuth (λR-T = 14.48 mm) are small. Also, the critical wavelengths of Kelvin–Helmholtz instability for molten lead (λK-H = 1.91 mm) and bismuth (λK-H = 1.53 mm) are small. Therefore, the surface wavelengths of molten lead and bismuth can easily exceed critical values. Once unstable wavelengths of the front and side exceed critical values, the interface fluctuation transmits enough momentum to the molten metal so that its surface distorts into waves and detaches to form small fragments, which enhance the premixing process. In addition, the thermal conductivities of molten lead and bismuth are much worse, especially the molten bismuth. Therefore, temperature differences between the center and surface of molten lead and bismuth are very high, which cause the significant thermal stress and make contribution to the fragment process on the boundary layer. What is more, the instantaneous pressure pulses also contribute to the fragmentation during the premixing process, no matter the boundary layer or inner location. Meanwhile, the vapor film is so thin that it can be condensed quickly by the coolant, and the dominant heat transfer mechanism transfers from film boiling to transition boiling, namely the trigger process. As shown in Table 2, the liquidities of molten lead and bismuth above melting points are good due to relatively small viscosities, which can enhance the mixing between the molten metals and coolant. Furthermore, as more fragments come into contact with the coolant again, the violent boiling occurs
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rapidly, and intense pressure pulse generates instantaneously. What is more, the intense pressure pulse damages the integrities of molten metals from the surface to the inside, and finally breaks up all the molten metals. 3.2. The FCI process for different molten metal mixtures In order to investigate the FCI process for different molten metal mixtures, lead (400 g), lead (396 g) – aluminum (4 g), lead (360 g) – aluminum (40 g) are chosen for experimental samples. The temperature of molten metal mixture is set up to 950 °C, and the temperature of coolant is 20 °C. The evolutions of the liquid– vapor interface during FCI process for different molten metal mixtures are shown in Figs. 6–8, which are sketched by red dotted lines. As shown in Fig. 6, the breakup process occurs quickly once the molten lead comes into contact with the coolant, which agrees well with the section 3.1. However, the breakup process does not happen after adding 4 g and 40 g aluminum, respectively. As for lead (396 g) – aluminum (4 g) and lead (360 g) – aluminum (40 g), the vapor film generates rapidly on the surface as molten mixtures initially attaching the coolant, and the vapor film grows quickly during the falling process. The dominant heat transfer mechanism is the film boiling, and the thickness of vapor film for lead (360 g) – aluminum (40 g) is larger and more stable than that for lead (396 g) – aluminum (4 g). The lead–aluminum mixture is the monotectic alloy, which can hardly present the mutual fusion. Also, the density of molten aluminum (ρ = 2.28 × 103 kg/m3) is obviously smaller than that of molten lead (ρ = 9.86 × 103 kg/m3), as shown in Table 1. Therefore, the molten aluminum is located on top of molten lead during the heating process, and the molten aluminum firstly attaches the coolant. During the falling process, the molten aluminum wraps the front of the molten lead due to relatively large viscosity (μ = 0.756 mN/sm2), as shown in Figs. 7 and 8. With the condensation gradually enhancing, the dominant heat transfer mechanism transfers from the film boiling to transition boiling. Finally, the front vapor film is broken by high hydraulic pressure and the effect of dragging from the coolant, and the coolant directly attaches the molten aluminum. However, the molten aluminum surface has solidified due to the high thermal conductivity (k = 103.7 W/mK) and high melting point (Tm = 660 °C), so the coolant cannot flow into the inside of molten aluminum and the breakup process does not happen. In addition, the molten aluminum continuously prevents the front of molten lead from attaching the coolant, and hydrodynamics cannot affect the front of molten lead, such as the shear force and Rayleigh– Taylor instability. However, the Kelvin–Helmholtz instability continuously affects the side of molten lead, and the breakup of molten lead does not happen. Therefore, it is concluded that the breakup process is more likely to be influenced by the Rayleigh– Taylor instability than that of Kelvin–Helmholtz instability. 3.3. The FCI process for different coolant depths In order to investigate the influence of different coolant depths on the FCI process, the lead with a mass of 50 g is chosen for this study. Figs. 9 and 10 show the evolutions of the liquid–vapor interface during the FCI process for different coolant depths, which are sketched by red dotted lines. The temperature of molten lead is set up to 800 °C, and the coolant temperature coolant is 20 °C. As shown in Fig. 9, the breakup process does not rapidly happen as the molten lead just comes into contact with the coolant, and the vapor film generates rapidly on the front of molten lead. Although shear force acts on the front of molten lead, the surface with small volume can well retain its integrity due to surface tension. Meanwhile, the front of molten lead is obviously affected by the Rayleigh–Taylor instability, which distorts into waves and
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t=1 ms
t=6 ms
t=11 ms
Initial Breakup 12.3 mm
t=16 ms
t=26 ms
t=21 ms
Fig. 6. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 400 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
detaches to form small fragments. On account of the bad thermal conductivity of molten lead (k = 19.9 W/mK), the significant thermal stress acts on the molten lead, which contributes to the initial fragmentation on the boundary layer, namely the premixing process. During the falling process, the vapor film on the front is gradually condensed and evolves irregularly, and the dominant boiling heat
t=1 ms
transfer mechanism transfers from the film boiling to the transition boiling. As shown in Table 3, the melting point of lead is relatively low, and the viscosity of it is also bad, so the molten lead presents good liquidity during falling process. When the vapor film is broken by hydraulic pressure and the effect of dragging from the coolant, the coolant directly comes into contact with the front of
t=6 ms
t=11 ms
t=21 ms
t=26 ms
12.3 mm
t=16 ms
Side
Front
Fig. 7. The evolution of the liquid–vapor interface during the FCI process for the lead-aluminum (m = 360 g – 40 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=6 ms
t=11 ms
t=21 ms
t=26 ms
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12.3 mm
t=16 ms
Side
Front
Fig. 8. The evolution of the liquid–vapor interface during the FCI process for the lead-aluminum (m = 396 g – 4 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
molten lead. Furthermore, the violent boiling rapidly occurs and significant pressure pulse acts on the molten lead, namely the trigger process. In addition, the fragmentation of the front increases the contact area between the molten lead and coolant, and the pressure pulse caused by violent boiling rapidly transmits upward, which finally causes the absolute breakup. Meanwhile, the side of molten
lead is continuously affected by Kelvin–Helmholtz instability during the falling process. However, the side of molten lead does not present obvious fragmentation phenomena until initial breakup happens. Therefore, the breakup process is more likely to be influenced by the Rayleigh–Taylor instability than that of Kelvin–Helmholtz instability, which agrees well with section 3.3.
t=40 ms
t=25 ms
t=1 ms
Side
12.3 mm
Front t=90 ms
t=80 ms
t=95 ms Transmit Upward
Initial Breakup
Fig. 9. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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Table 3 Properties of molten lead with different temperatures. Tmm (°C)
500
800
900
Tm (°C) ρm (kg/m3) Δρ/ΔT (kg/m3) ρmm (kg/m3) σm (mN/m) Δσ/ΔT (mN/mK) σmm (mN/m) μ0 (mN/sm2) E (kJ/mol) μmm (mN/sm2) cp (J/kgK) k (W/mK) u (m/s) ρc (kg/m3) Tc = 20 °C λK-H (mm) λR-T (mm) tin, exp (ms)
327 10.68 × 103 −1.32 10.45 × 103 458 −0.13 481 0.4636 8.61 0.4642 137 18.2 1.4 998 1.64 14.01 27
327 10.68 × 103 −1.32 10.05 × 103 458 −0.13 520 0.4636 8.61 0.4640 135 19.9 1.4 998 1.83 15.20 84
327 10.68 × 103 −1.32 9.92 × 103 458 −0.13 533 0.4636 8.61 0.4640 135 19.9 1.4 998 1.88 15.50 147
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
In order to investigate the FCI process with small coolant depth, a metal plate is equipped at the location, which is 90 mm below the coolant surface. As shown in Fig. 10, the breakup process does not happen during the whole falling process. Before the molten lead coming into contact with the metal plate, the boundaries of the front and side are significantly irregular, which are affected by the Rayleigh–Taylor and Kelvin–Helmholtz instability, respectively. Also, the thermal stress contributes to the fragmentation of boundary due to bad heat conduction of molten lead. During the falling process, the vapor film generates rapidly on the molten lead surface, especially fragments from the boundary layer stripping, namely the premixing process. With the front of molten lead firstly coming into contact with the bottom, the molten lead gradually accumulates and spreads out due to good liquidity. Meanwhile, the contact area between the molten lead and metal plate gradually increases, so
t=1 ms
the heat is quickly transferred from the molten lead to the metal plate. What is more, the vapor film on the front is extruded to the top of accumulation due to significant density difference between the molten lead and coolant. The vapor film on the top of accumulation gradually increases, which prevents the molten lead coming into contact with the coolant. Also, the vapor film is continuously condensed and finally broken by the coolant. The coolant again rapidly evaporates on the top of accumulation and causes significant pressure pulse. However, the top of molten lead has solidified, which protects the inside of molten lead from the pressure pulse and prevents the trigger process, as shown in Fig. 10. 3.4. The FCI process for different coolant temperatures In order to research the effect of different coolant temperatures on FCI process, the lead is used to carry out the visual investigation. The evolutions of the liquid–vapor interface during FCI process for different coolant temperatures are shown in Figs. 9, 11, 12, 13, which are sketched by red dotted lines. The temperature of molten lead is set up to 800 °C, and the mass of lead is 50 g during the experiment. As mentioned in section 3.3.1, the front of molten lead firstly presents breakup (t = 80 ms) with the coolant temperature of 20 °C, which rapidly transmits upward and finally causes the absolute breakup, as shown in Fig. 9. As the coolant temperature increases to 30 °C, the breakup process still occurs, but the occurrence time rises to t = 90 ms, as shown in Fig. 11. Also, the final breakup intensity for Tc = 30 °C is obviously weaker than that for Tc = 20 °C, as shown in Fig. 9 (t = 95 ms) and Fig. 11 (t = 140 ms). As the coolant temperature increases to 40 °C and 60 °C, the breakup process does not occur during the whole falling process, as shown in Figs. 12 and 13. As shown in Table 4, the critical wavelengths of the Rayleigh– Taylor and Kelvin–Helmholtz instability changes a little for different coolant temperatures. Also, the density of the coolant varies little with different coolant temperatures, so the influence of hydraulics difference can be neglected. As the coolant temperature increases,
t=40 ms
t=70 ms
Side
12.3 mm Front
Metal Plate t=90 ms
t=130 ms
t=230 ms
Fig. 10. The evolution of the liquid–vapor interface during the FCI process for the lead coming into contact the bottom with small water depth before breakup (m = 50 g, Tmm = 800 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=10 ms
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t=30 ms
Side
Front 12.3 mm
t=90 ms
t=120 ms
t=140 ms
Transmit Upward Initial Breakup
Fig. 11. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 30 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
the vapor film can more quickly generate as the molten lead comes into contact with the coolant. In addition, the vapor film is thicker and the film boiling is more stable. During the falling process, the vapor film is gradually condensed and the dominant boiling heat transfer mechanism transfers from the film boiling to the transition boiling. However, the condensation slows down and the time
t=1 ms
for vapor film initially broken is delayed with increasing the coolant temperature. If the molten lead surface still keeps the liquid state as molten lead again comes into contact with the coolant, the breakup process will consequently occur, as shown in Figs. 9 and 11. However, if the molten lead surface has solidified, the breakup will not occur because the solid surface can prevent the obvious pres-
t=10 ms
t=30 ms
Front 12.3 mm
t=90 ms
t=120 ms
t=140 ms
Side
Fig. 12. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 40 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=10 ms
t=30 ms
Side
12.3 mm Front
t=90 ms
t=120 ms
t=140 ms
Fig. 13. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 60 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
sure pulse of violent boiling, namely no trigger process, as shown in Figs. 12 and 13. Therefore, increasing the coolant temperature can significantly restrict or prevent the breakup process during FCI process. 3.5. The FCI process for different molten metal temperatures In order to study the effect of molten metal temperatures on FCI process, molten leads with different temperatures are chosen for the experiment. Figs. 9, 14, 15 show the evolutions of the liquid– vapor interface during the FCI process for different molten metal temperatures, which are sketched by red dotted lines. The temperatures of molten leads are set up to 500 °C, 800 °C, and 900 °C, respectively. The mass of lead is 50 g, and the coolant temperature is 20 °C. As shown in Figs. 9, 14, 15, the molten leads with different temperatures present breakup. Also, the initial breakup occurs at the front of molten lead, and rapidly transmits upward, finally causes the absolute breakup. However, the occurrence times for the breakup processes are obviously different for different molten metal temperatures. With increasing the temperature from 500 °C to 800 °C to 900 °C, the occurrence time for breakup increases from 21 ms to 80 ms to 147 ms. The solidification time increases as the molten metal temperature increases, which makes for the breakup. However, as shown in Table 3, the critical wavelengths of the Rayleigh– Taylor and Kelvin–Helmholtz instability significantly increase with as the molten metal temperature increases. Therefore, the influence of hydraulics on the front and side of molten lead obviously
Table 4 Hydraulics characteristics for different coolant temperatures. Tc (°C) (kg/m3)
ρc λK-H (mm) λR-T (mm)
20
30
40
60
998 1.833 15.20
996 1.837 15.19
992 1.850 15.19
983 1.859 15.18
decreases with increasing the molten metal temperature. Also, the viscosity decreases only 0.05% as the molten metal temperature increases, as shown in Table 3. As the molten metal temperature increases from 500 °C to 800 °C and 900 °C, the surface tension of molten lead increases from 481 mN/m to 520 mN/m and 533 mN/ m, which enhances the capacity for molten lead to maintain surface integrity and weakens the fragmentation during falling process. Meanwhile, the thermal conductivities for T = 800 °C (k = 19.9 W/ mK) and T = 900 °C (k = 19.9 W/mK) W/mK are larger than T = 500 °C (k = 18.2 W/mK), and the specific heat changes a little with the molten metal temperature increasing from 500 °C to 800 °C to 900 °C. Therefore, the heat can be conducted quickly to the surface from the center, and the thermal stress acting on the surface decreases. In addition, the vapor film is thicker and the film boiling is more stable with the molten metal temperature increasing. Therefore, the occurrence time for breakup increases as the molten metal temperature increases from 500 °C to 800 °C to 900 °C, as shown in Figs. 9, 14, 15. 3.6. The criterion for FCI process In order to predict the breakup occurrence, two dimensionless parameters are proposed in this section. The shear force from relative velocity of fluids is balanced by the surface tension as a molten metal drop existing in a flow. Weber number (We) is derived as
We =
ρcu 2Deq σ mm
(4)
where We is the Weber number; u is the velocity (m/s) as the molten metal just comes into contact with the coolant. σmm is the surface tension of molten metal (N/m); Deq is the equivalent diameter of molten metal (mm), which is defined as
V eq =
m ρmm
(5)
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t=1 ms
t=10 ms
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t=20 ms Side
Initial 12.3 mm Front
t=21 ms
t=22 ms
Breakup
t=24 ms
Transmit Upward
Fig. 14. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 500 °C,Tc = 20 °C).
Deq = 3
6V eq π
(6)
where m is the mass of molten metal (g); Veq is the equivalent volume of molten metal (mm3). As discussed above, the breakup of molten metals is dependent on the initial contact with the coolant and the falling process.
t=1 ms
Once the Weber number for the molten metal exceeds a value, the surface tension cannot keep the front integrity as the molten metal just comes into contact with the coolant. With the contact area increasing, the consequent violent boiling leads to absolute breakup. When the Weber number is small, the molten metal can keep the integrity well as it comes into contact with the coolant and following the breakup during the falling process is mostly dependent on
t=30 ms
t=100 ms
Side
12.3 mm
Front t=147 ms
t=150 ms
t=151
Transmit Upward Initial Breakup
Fig. 15. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 900 °C,Tc = 20 °C).
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Solid circle • : Breakup initially
We (Weber number)
Hollow circle o : Breakup during falling Cross × : No Breakup
(2300)
F (Fragmentation Factor) Fig. 16. The criterion for prediction of molten metal breakup occurrence. The red symbols stand for data of this study; the green symbols stand for data of Abe [16], and the blue symbols stand for data of Kondo [21]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the property of the molten metal. Therefore, the Weber number can be used to estimate the breakup occurrence as the molten metal initially comes into contact with the coolant, and another dimensionless parameter should reflect the influences of the properties of molten metals. According to the discussion above, the molten metal with small thermal diffusivity is more likely to present breakup during falling process, which is derived as
α=
k ρmm c p
(7)
where α is the thermal diffusivity (s/m2); k is the thermal conductivity (W/mK); cp is the specific heat (J/kgK). In addition, the molten metal with a large equivalent diameter and large falling velocity is significantly affected by hydraulics, which should be considered in dimensionless parameter F1 (fragmentation factor 1)
F1 = Dequα = Dequ
ρmm c p k
(8)
As discussed in section 3.4, increasing the coolant temperature can significantly restrict or prevent the breakup. Hence, a dimensionless parameter F2 (fragmentation factor 2) is used to reflect the influence of coolant temperature, which is presented as
F2 =
Tsat Tc
(9)
where Tsat is the saturated temperature (K); Tc is the coolant temperature (K). Meanwhile, the breakup can be restricted by increasing the molten metal temperature due to the increase of vapor film thickness, which can be reflected by a dimensionless parameter F3 (fragmentation factor 3)
F3 =
Tsat Tin − Tsat
(10)
where Tin is the initial temperature of molten metal (K). However, the solidification time increases as the molten metal temperature increases, which makes for breakup. Hence, increasing the molten metal temperature has two sides, and a dimensionless parameter F4 (fragmentation factor 4) should be proposed to reflect this influence
F4 =
Tin Tm
(11)
where Tm is the melting point of metal (K). When all of these factors are considered together, a dimensionless parameter F (fragmentation factor) can be presented as
F = F1F2F3F4 = Dequ
ρmm c p Tsat Tin Tsat k Tc Tm Tin − Tsat
(12)
As analyzed above, high Weber number is favorable for the breakup occurrence as the molten metal initially comes into contact with the coolant, and the possibility for breakup occurrence during falling process is large with high fragmentation factor. According to comparisons with experimental results, the critical Weber number and fragmentation factor are proposed. Once the initial breakup happens due to large Weber number (>120), the violent boiling rapidly spreads and leads to absolute breakup. As for a Weber number of <120, the front of the molten metal can keep the integrity, and subsequent breakup is dependent on the fragmentation factor. As for a fragmentation factor of <2300, the molten metal can keep the integrity during the whole falling process. As for a fragmentation factor of >2300, the breakup initially happens at the front of molten metal, and rapidly transmits upward, and finally leads to absolute breakup. In order to predict the occurrence of molten metal breakup, a scatter diagram with the Weber number for x-axis and fragmentation factor for y-axis is shown as Fig. 16. Meanwhile, the Weber number and fragmentation factor are used for data in Abe [16] (11 working conditions) and Kondo [21] (4 working conditions), which are also shown as Fig. 16. The predicted results agree well with the experimental results proposed by Abe [16] and Kondo [21].
4. Conclusions A visual experimental study is carried out to investigate the breakup as high superheated molten metal comes into contact with the coolant under different working conditions. The obtained conclusions are as follows: (1) The FCI process is significantly affected by properties of molten metals. As the molten aluminum comes into contact with the subcooled coolant (water), the breakup process does not occur, which is attributed to the large critical wavelength of
Q. Lu et al./Applied Thermal Engineering 98 (2016) 962–975
Rayleigh–Taylor and Kelvin–Helmholtz instability, large surface tension, large viscosity, large thermal conductivity and high melting point. As for molten lead and bismuth, the breakup process rapidly occurs once the molten metals come into contact with the subcooled coolant due to the low melting point, and low heat conduction and surface stability capacities. (2) The breakup process is more likely to be influenced by the Rayleigh–Taylor instability than that of Kelvin–Helmholtz instability. Such as for the molten lead during the falling process with the mass of 50 g, the initial breakup always occurs at the front of the molten lead, and then the breakup process transmits upward and leads to a severe breakup. However, the breakup process does not occur with small water depth or with the front of the molten lead protected by a little molten aluminum. (3) As the coolant temperature increases, the thickness of the vapor film increases and the condensation slows down, which restricts or prevents the breakup process. As the initial temperature of molten metal such as lead increases, the surface tension and the thermal conductivity obviously increase, which enhances the surface integrity and heat conduction capacities. In addition, the critical wavelengths of the Rayleigh– Taylor instability and Kelvin–Helmholtz instability obviously increase. Then the influence of the hydraulics weakens. Therefore, the initial time for breakup increases as the initial temperature of molten lead increases. Meanwhile, two dimensionless parameters are proposed to predict the breakup occurrence. The Weber number significantly affects the breakup occurrence at the initial moment when the molten metal just comes into contact with the subcooled coolant. While the breakup occurrence during the falling process within the subcooled coolant obviously depends on the fragmentation factor. Acknowledgement The authors are grateful for the support of the National Natural Science Foundation of China (No. 51206199), Natural Science Foundation of Chongqing (NO. cstc2013jcyjA90013), and the project funded by China Postdoctoral Science Foundation (No. 2014M562337). Nomenclature General symbol u Velocity [m/s] T Temperature [°C] t Time [s] m Mass [g] ρ Density [kg/m3] E Constant We Weber number D Diameter [mm] V Volume [mm] F Fragmentation factor Greek letters σ Surface tension [N/m] μ Dynamic viscous [Pa·s] k Thermal conductivity [W/mK]
cp λ α
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Specific heat [J/kgK] Critical wavelength [mm] Thermal diffusivity [m2/s]
Subscripts mm Molten metal m Melting point c Coolant in Initial exp Explosion sat Saturated eq Equivalent K-H Kelvin–Helmholtz R-T Rayleigh–Taylor
References [1] M.L. Corradini, B.J. Kim, M.D. Oh, Vapor explosions in light water reactors: a review of theory and modeling, Prog. Nucl. Energy 22 (1988) 1–117. [2] F.J. Arias, Vapor explosions: prediction of a critical liquid–corium velocity in vapor destabilization mechanism of corium melt in the fuel–coolant interactions – FCI, Ann. Nucl. Energy 37 (2010) 1236–1240. [3] Y. Zhou, Z. Zhang, M. Lin, Y. Minghao, Y. Xiao, Numerical simulation of fragmentation of melt drop triggered by external pressure pulse in vapor explosions, Ann. Nucl. Energy 57 (2013) 92–99. [4] V. Tyrpekl, P. Piluso, S. Bakardjieva, O. Dugne, Material effect in the nuclear fuel–coolant interaction: analyses of prototypic melt fragmentation and solidification in the KROTOS facility, Nucl. Technol. 186 (2014) 229–240. [5] T.N. Dinh, V.A. Bui, R.R. Nourgaliev, J.A. Green, B.R. Sehgal, Experimental and analytical studies of melt jet–coolant interactions: a synthesis, Nucl. Eng. Des. 189 (1999) 299–327. [6] R.-Q. Duan, S. Koshizuka, Y. Oka, Droplet breakup under impulsive acceleration using moving particle semi-implicit method, in: ICONE-11: Proceedings of the 11th International Conference on Nuclear Engineering, vol. 35, 2003, p. 36029. [7] G. Ciccarelli, D.L. Frost, Fragmentation mechanisms based on single drop steam explosion experiments using flash X-ray radiography, Nucl. Eng. Des. 146 (1994) 109–132. [8] K.H. Bang, J.M. Kim, D.H. Kim, Experimental study of melt jet breakup in water, J. Nucl. Sci. Technol. 40 (2003) 807–813. [9] Y. Abe, T. Kizu, T. Arai, H. Nariai, K. Chitose, K. Koyama, Study on thermalhydraulic behavior during molten material and coolant interaction, Nucl. Eng. Des. 230 (2004) 277–291. [10] Y. Abe, E. Matsuo, T. Arai, H. Nariai, K. Chitose, K. Koyama, et al., Fragmentation behavior during molten material and coolant interactions, Nucl. Eng. Des. 236 (2006) 1668–1681. [11] X. Cao, R. Hajima, K. Furuta, S. Kondo, A numerical analysis of molten metal drop and coolant interaction, J. Nucl. Sci. Technol. 37 (2000) 1049–1055. [12] S. Thakre, W. Ma, L. Li, A numerical analysis on hydrodynamic deformation of molten droplets in a water pool, Ann. Nucl. Energy 53 (2013) 228–237. [13] P.E. Shick, T.M. Grace, Review of smelt-water explosions, The Institute of Paper Chemistry, 1982. [14] M. Ochiai, S.G. Bankoff, Local propagation theory for vapor explosions, in: Proceedings of the Third Specialist Meeting on Sodium/Fuel Interaction in Fast Reactors, vol. 8, 1976, pp. 129–152. [15] C.P. Tso, J.H. Strauss, Quenching of an instrumented sphere in Freon-12 and liquid nitrogen in a vapour explosion study, J. Phys. D Appl. Phys. 16 (1983) 943–953. [16] Y. Abe, H. Nariai, Y. Hamada, The trigger mechanism of vapor explosion, J. Nucl. Sci. Technol. 39 (2002) 845–853. [17] R. Sa, M. Takahashi, K. Moriyama, Study on fragmentation behavior of liquid lead alloy droplet in water, Prog. Nucl. Energy 53 (2011) 895–901. [18] T. Takashima, Y. Iida, Destabilization of film boiling and pressure change in vapor film when an external pressure wave is supplied, Heat Transf. Asian Res. 30 (2001) 689–701. [19] W.F. Gale, T.C. Totemeier, Smithells Metals Reference Book, ButterworthHeinemann, Oxford, 2004. [20] L.S. Tong, Y.S. Tang, Boiling Heat Transfer and Two-Phase Flow, Taylor & Francis, Washington, D.C, 1997. [21] S. Kondo, K. Konishi, M. Isozaki, S. Imahori, A. Furutani, D.J. Brear, Experimental study on simulated molten jet–coolant interactions, Nucl. Eng. Des. 155 (1995) 73–84.
Contents lists available at ScienceDirect
Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Visual investigation on the breakup of high superheated molten metal during FCI process Qi Lu, Deqi Chen *, Chong Li Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400044, China
H I G H L I G H T S
• • •
Visual investigation on the breakup process of high superheated molten metal was carried out. The mechanism of the breakup process was analyzed in detail under different working conditions. Two dimensionless parameters were proposed to predict the occurrence of the breakup process.
A R T I C L E
I N F O
Article history: Received 7 September 2015 Accepted 22 December 2015 Available online 14 January 2016 Keywords: FCI Molten metal Breakup Visual investigation
A B S T R A C T
A visual experimental investigation was carried out to study the breakup process as high superheated molten metal falling into the subcooled coolant during the severe accident of a nuclear reactor, namely the FCI (fuel coolant interaction) process. Deionized water was used as the coolant, and the aluminum, lead, and bismuth were used as the metal samples. In this study, the characteristics of FCI process with different molten metals, different molten metal mixtures, different coolant depths, different coolant temperatures and different initial molten metal temperatures were analyzed in detail. The molten metal breakup process was observed by a high speed camera during this experimental study. It was found that the breakup process was restricted significantly by the high melting point of the metal, large surface tension, large viscosity, high thermal conductivity, and low specific heat of the molten metal. Meanwhile, increasing the coolant temperature and the temperature of molten lead could obviously restrict or prevent the breakup process. Finally, two dimensionless parameters were proposed to predict the occurrence of the breakup process. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction As for any potential core disruptive accident (CDA), fuel elements probably burn out due to much core residual heat. During the falling process of molten fuels, the interaction between the molten fuels and coolant will cause violent boiling or flashing of water into vapor, namely the vapor explosion. Meanwhile, the possible breakup process and pressure pulses will threaten the integrity of the nuclear reactor. Over the years, many authors tried to describe clearly the process of FCI (fuel coolant interaction). According to widely accepted concepts, the fundamental process of FCI was molten melt fragmentation increasing the heat transfer area to the coolant. Corradini et al. [1] and Arias [2] described the explosive scenario as follows: (1) quiescent mixing of the fuel and coolant, (2) triggering of the explosion, (3) explosion escalation and propagation, and (4) expansion and work production. Also, Zhou et al. [3] concluded that the fragmentation
* Corresponding author. Tel.: +86 23 65106902; fax: +86 23 65106902. E-mail address: [email protected] (D. Chen). http://dx.doi.org/10.1016/j.applthermaleng.2015.12.118 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
process could be divided into several stages: vapor film collapsing, melt drop-coolant direct contact, formation of high pressure spots, rapid growth of a filament around molten metal drop, rapid fuel coolant interaction area expansion, breaking up of the filament, and mixing of fragments with the coolant. Recently, Tyrpekl et al. [4] suggested that FCI occurred generally in two main phases: a premixing phase, during which the molten melt was fragmented into large droplets and mixed with the coolant; the explosion phase, during which the vapor film that developed around the molten droplets were destabilized and finely fragmented. However, Dinh et al. [5] proposed that the jet fragmentation was a pre-condition for the premixing and the vapor produced, due to mixing of the melt and coolant, affecting jet fragmentation for quasi-steady (long-duration) melt jets. Therefore, a separate-effect description was not suitable for such an integrated and synergistic transient process. In previous studies, it was believed that the breakup of molten metal was depended on the deformation, the boundary layer stripping, and the instability of surface waves on molten metal surface, such as the Rayleigh–Taylor instability and Kelvin–Helmholtz instability. As mentioned by Duan et al. [6], any or all of above three modes might contribute to jet breakup process. Ciccarelli and Frost
Q. Lu et al./Applied Thermal Engineering 98 (2016) 962–975
[7] proposed that the breakup of a cold drop was caused by the stripping of fragments due to relative flow, but the fragmentation of a hot drop was dominated by the growth and collapsing of the vapor film. Bang et al. [8] experimentally investigated the jet breakup process in non-boiling conditions to isolate the jet breakup process from the complex interactions. It was found that the Kelvin– Helmholtz instability was the most possible reason for jet breakup. Abe et al. [9] also suggested that the stripped off from the molten material jet due to the Kelvin–Helmholtz instability, which was dominant for the break up process. However, Abe et al. [10] suggested that the molten jet front experienced the conditions to produce Rayleigh–Taylor instability. Also, the stability of the generated fragment was related to critical Weber number theory and that the fragmentation of the molten jet side was related to Kelvin–Helmholtz instability and unstable wavelength. Recently, Arias [2] considered the Kelvin-Helmholtz and Rayleigh-Taylor instabilities at the interface corium–water in his physical model, where the oscillation of the interface transmitted sufficient momentum to the corium so that its surface distorted into waves that could grow until they detached to form small corium fragments (debris). Cao et al. [11] suggested that the growth of filaments on the molten tin drop surface was the essential mechanism of fragment caused by Rayleigh– Taylor instability. Also, Zhou et al. [3] concluded that the growth and breaking up of the filament were the critical mechanism of melt tin drop fragmentation, which were similar to Ciccarelli and Frost [7]. As mentioned by Thakre et al. [12], the molten tin drop initially presented as a circular shape surrounded by a thin vapor film. Then, it gradually evolved to a semicircle, and continued deformation eventually leaded to a crescent shape. During the deformation process, the surrounding vapor was removed to the tail of the molten tin drop due to the buoyancy. Shick and Grace [13] suggested that three possible explanations about the fragmentation were the impact pressure developed as the two liquids coming together, release of superheat at the contact interface, and hydrodynamic instabilities associated with an explosion shock wave. Meanwhile, a ‘splash’ theory for local propagation of vapor explosion was proposed by Ochiai and Bankoff [14]. As a random liquid–liquid contact was made, the explosive growth
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and coalescence of vapor bubbles occurred as soon as the surrounding pressure was relieved, resulting in high-pressure vapor layer at the liquid–liquid contact area. Nevertheless, Tso and Strauss [15] concluded that it was difficult to explain the occurrence of the fragmentation process by assuming the existence of a small pressure pulse (0.3 kPa) measured in their experiment. As mentioned by Abe et al. [16], the spontaneous vapor explosion hardly occurred when the water temperature was near the saturation temperature or the interfacial temperature between molten material and water was lower than the material melting temperature, which was also proposed by Sa et al. [17]. Takashimal and Iida [18] suggested that the full film boiling was eventually established again after the surrounding vapor thickness decreasing, which demonstrated the transient contact between the liquid and solid. Even though lots of studies focusing on FCI have been carried out as discussed in the preceding sections, many mechanisms during FCI do not reached a common agreement due to complications. The subject of this paper is to visually investigate the rapid phase change and fragmentation process during the molten metal coming into contact with the coolant and falling in the coolant. Meanwhile, the theoretical analysis has been carried out to further discuss the breakup mechanism and predict the breakup occurrence by two dimensionless parameters.
2. Experimental apparatus A schematic diagram of the experimental apparatus is shown in Fig. 1. Metal samples are heated by a muffle furnace with the highest temperature of 1200 °C. The molten metal is poured into the water tank through a funnel, which is equipped at the top of a water tank. The coolant depth is 1400 mm, and the distance between the exit of the funnel and coolant surface is 100 mm, so the velocity as the molten metal initially as it comes into contact with the coolant is 1.4 m/s. The water tank is composed of PMMA (polymethyl methacrylate), with the size of 500 mm × 500 mm × 1500 mm. The coolant temperature is adjusted by a preheater and heat exchanger, respectively. The molten metal and coolant temperatures are measured
Fig. 1. The schematic diagram of experimental apparatus.
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Table 2 Properties of metals.
Table 1 Working conditions. Number
Metal sample
m (g)
Tmm (°C)
Tc (°C)
Metal
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Bismuth Lead Lead Lead Lead Lead (small coolant depth) Lead Lead Lead Lead Lead Lead Lead Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Lead–aluminum Lead–aluminum
200 200 400 50 50 50 50 50 50 50 50 50 50 200 200 200 20 50 100 150 200 200 200 200 200 200 360-40 396-4
950 950 950 900 800 800 800 800 800 700 600 500 400 1100 1000 950 950 950 950 950 950 900 850 800 750 700 950 950
20 20 20 20 20 20 30 40 60 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
Aluminum
Lead
Bismuth
660 2.39 × 103 −0.35 2.28 × 103 914 −0.35 1.02 × 103 0.1492 16.50 0.7558 1080 103.7 1.4 998 4.70 56.59
327 10.68 × 103 −1.32 9.86 × 103 458 −0.13 0.54 × 103 0.4636 8.61 0.4640 135 19.9 1.4 998 1.91 15.66
271 10.05 × 103 −1.18 9.25 × 103 378 −0.07 0.43 × 103 0.4458 6.45 0.4461 133.6 15.5 1.4 998 1.53 14.48
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
by K-type thermocouples, and the metal mass is measured by electronic scales, with uncertainties of ±0.5 K and ±0.1 g, respectively. The coolant is deionized water, and metal samples include aluminum, lead, and bismuth, which are heated to the specified temperature in a graphite crucible by a muffle furnace. All the working conditions are summarized in Table 1. The experimental study is carried out under an atmosphere of 0.101 MPa and an environmental temperature of 30 °C. During the heating process, the nitrogen is injected into muffle furnace to prevent metals to be oxidized. The breakup process of molten metals in the coolant are captured by a high speed camera (Redlake-HG-100K) with a microlens with a recording speed of 5000 fps (frame per second) to obtain clear fragmentation process with an LED light used for illumination. Meanwhile, the micro-lens of the high speed camera is equipped at the location where the top of view area is the coolant surface, and solidified molten metals are collected from the bottom of the water tank, as shown in Fig. 1. 3. Results and discussion 3.1. The FCI process for different metals In order to study the effect of metal property on FCI process, aluminum, lead and bismuth are used to carry out the experimental investigation. All the melting points of these metals are below 700 °C, and the main physical properties are shown in Table 2. The temperature of molten metal is set up to 950 °C, the temperature of coolant is 20 °C, and the metal mass is 200 g during the experiment. The side of the molten metal is affected by the Kelvin–Helmholtz instability, which is known as follows, i.e. when two immiscible fluids flow relatively to each other along an interface of separation, there is a maximum relative velocity above which a small disturbance of the interface will amplify and grow and thereby distort the flow. According to Abe et al. [9], a critical relative velocity above which
Tm (°C) ρm (kg/m3) Δρ/ΔT (kg/m3) ρmm (kg/m3) Tmm = 950 °C σm (mN/m) Δσ/ΔT mN/mK σmm (mN/m) T = 950 °C μ0 (mN/sm2) E (kJ/mol) μmm (mN/sm2) Tmm = 950 °C cp (J/kgK) k (W/mK) u (m/s) ρc (kg/m3) Tc = 20 °C λK-H (mm) λR-T (mm)
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
some initial disturbances of large wavelength are unstable is presented as
u=
2πσ mm ( ρmm + ρc ) λK -H ρmm ρc
(1)
where ρmm is the density of molten metal (kg/m3); ρc is the density of coolant (kg/m3 ); λ K-H is the critical wavelength for Kelvin– Helmholtz instability (mm). Also, the critical wavelength is given by
λK -H =
2πσ ( ρmm + ρc ) u 2ρmm ρc
(2)
As mentioned by Tong and Tang [20], the Rayleigh–Taylor instability is interfacial instability between two fluids of different densities that are stratified in the gravity field or accelerated normal to the interface. It is commonly observed that the boundary between two stratified fluid layers at rest is not stable if the upper fluid density is larger than the lower-fluid density. Once the wavelength of a disturbance is larger than the critical wavelength, the Rayleigh– Taylor instability can lead to the destruction of the single common interface. Meanwhile, the critical wavelength of the Rayleigh– Taylor instability at the fastest growth rate is expressed as follows, which obviously affects the front of molten metal.
λR -T = 2π
σ mm
(ρmm − ρc ) g
(3)
where g is the gravitational acceleration (m/s2); λR-T is the critical wavelength for Rayleigh–Taylor instability (mm). The evolutions of the liquid–vapor interface during the FCI process for different molten metals are shown in Figs. 2–4, which are sketched by red dotted lines. As shown in Fig. 2, the molten aluminum does not break up during the whole falling process. It is found that the vapor film generates rapidly on the surface as the molten aluminum comes into contact with the coolant, and the vapor film grows quickly during the falling process. In addition, when molten aluminum initially comes into contact with the coolant (t = 1 ms to t = 6 ms), the surface can retain its integrity under shear force. During the falling process, the vapor film attached on the molten aluminum is obviously thick and smooth, so the molten metal boundary can be also considered smooth. The condensation process of the vapor film on the molten aluminum is relatively slow, which continues for more than 26 ms. Meanwhile, the condensation of the
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t=1ms
t=6ms
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t=11ms
12.3 mm
t=16ms
t=21ms
Side
t=26ms
Front
Fig. 2. The evolution of the liquid–vapor interface during the FCI process for the aluminum (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
vapor film gradually enhances with the temperature of the molten metal decreasing, and finally the molten aluminum solidified, as shown in Fig. 5a. In addition, lots of irregular holes are distributed on the surface of the solidified aluminum caused by strong the shock from violent boiling. As for molten lead and bismuth, once these molten metals come into contact with the coolant, the breakup process occurs quickly with the vapor rapidly being generated on the superheated surfaces of the molten metals, as shown in Figs. 3
t=1 ms
and 4. Meanwhile, the solidified residues of lead and bismuth are both particles, and the fragmentation of bismuth is more significant than that of lead, as shown in Fig. 5b and c. As shown in Table 2, the surface tension of molten aluminum at 950 °C is 914 mN/m, which is obviously larger than that of molten lead (σ = 458 mN/m) and bismuth (σ = 378 mN/m) at 950 °C, especially the molten bismuth. Therefore, the surface of molten aluminum can retain its integrity under shear force, namely no premixing
t=11ms
t=6ms
Initial Breakup 12.3 mm
t=16ms
t=21ms
t=26ms
Fig. 3. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
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t=1ms
t=6 ms
t=11 ms
Initial Breakup
12.3 mm
t=16 ms
t=26 ms
t=21ms
Fig. 4. The evolution of the liquid–vapor interface during the FCI process for the bismuth (m = 200 g, Tmm = 950 °C,Tc = 20 °C).
process happening. The critical wavelength of the Rayleigh–Taylor instability for molten aluminum (λR-T = 56.59 mm) is significantly larger than that for molten lead (λR-T = 15.66 mm) and bismuth (λR-T = 14.48 mm). Also, the critical wavelength of Kelvin–Helmholtz instability for molten aluminum (λK-H = 4.70 mm) is obviously larger
than that for molten lead (λ K-H = 1.91 mm) and bismuth (λK-H = 1.53 mm). As mentioned by Abe [10], the front and side of molten jet are affected by Rayleigh–Taylor instability and Kelvin– Helmholtz instability, respectively. Therefore, the front and side of molten aluminum boundary are much stable, as shown in Fig. 2. Al-
a The solidified aluminum
b The solidified lead
c The solidified bismuth
Fig. 5. The coagula of different metals.
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though the specific heat capacity of molten aluminum is relatively large (cp = 1080 J/kgK), its thermal conductivity (k = 103.7 W/mK) is much larger than that of molten lead (k = 19.9 W/mK) and bismuth (k = 15.5 W/mK); hence, the heat can be conducted quickly to the surface from the center of the molten aluminum. Furthermore, the thermal stress acting on the surface of molten aluminum is small, which is not intense enough to damage the surface integrity. As shown in Fig. 2, the vapor film generates immediately on the surface of molten aluminum as the molten aluminum comes into contact with the coolant, and the dominant boiling heat transfer mechanism is stable film boiling due to high heat flux conducted from the center to the surface of molten aluminum, which prevents the interaction between the molten aluminum and coolant. Next, the molten aluminum is gradually cooled by the coolant; the superheat on the surface of molten aluminum decreases during the falling process. What is more, the temperature difference between the center and the surface of molten metal gradually decreases, so the heat transfer amount conducted to the vapor film decreases. Meanwhile, the vapor film thickness at the liquid–vapor interface decreases due to constant condensation, and the dominant heat transfer mechanism transfers from the film boiling to transition boiling. Finally, the vapor film is broken by hydraulic pressure and the effect of dragging from the coolant, and the coolant directly contacts with the molten aluminum. However, the melting point of aluminum is relatively high, so the area coming into contact with the coolant has solidified to solid as the vapor film broken up. Although the superheated aluminum surface contacts with the coolant, the coolant cannot flow into the inside of molten aluminum, and just evaporates quickly on the superheated surface. Also, the explosive boiling generates intense pressure pulses at the metalcoolant interface, which can damage the integrity of solidified surface. Therefore, lots of irregular holes are distributed on the surface of solidified aluminum, as shown in Fig. 5a. As for molten lead and bismuth, when molten metals initially come into contact with the coolant, the shear force caused by relative velocity acts on the surfaces of the molten metals. Meanwhile, surface tension cannot overcome the shear forces to retain the surface integrity; hence, the boundary layer stripping clearly occurs at the beginning of falling process, as shown in Figs. 3 and 4. Lots of fragments on the boundary layer mix with the coolant and the vapor film rapidly generates, namely the premixing process. As mentioned above, the critical wavelengths of Rayleigh–Taylor instability for molten lead (λR-T = 15.66 mm) and bismuth (λR-T = 14.48 mm) are small. Also, the critical wavelengths of Kelvin–Helmholtz instability for molten lead (λK-H = 1.91 mm) and bismuth (λK-H = 1.53 mm) are small. Therefore, the surface wavelengths of molten lead and bismuth can easily exceed critical values. Once unstable wavelengths of the front and side exceed critical values, the interface fluctuation transmits enough momentum to the molten metal so that its surface distorts into waves and detaches to form small fragments, which enhance the premixing process. In addition, the thermal conductivities of molten lead and bismuth are much worse, especially the molten bismuth. Therefore, temperature differences between the center and surface of molten lead and bismuth are very high, which cause the significant thermal stress and make contribution to the fragment process on the boundary layer. What is more, the instantaneous pressure pulses also contribute to the fragmentation during the premixing process, no matter the boundary layer or inner location. Meanwhile, the vapor film is so thin that it can be condensed quickly by the coolant, and the dominant heat transfer mechanism transfers from film boiling to transition boiling, namely the trigger process. As shown in Table 2, the liquidities of molten lead and bismuth above melting points are good due to relatively small viscosities, which can enhance the mixing between the molten metals and coolant. Furthermore, as more fragments come into contact with the coolant again, the violent boiling occurs
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rapidly, and intense pressure pulse generates instantaneously. What is more, the intense pressure pulse damages the integrities of molten metals from the surface to the inside, and finally breaks up all the molten metals. 3.2. The FCI process for different molten metal mixtures In order to investigate the FCI process for different molten metal mixtures, lead (400 g), lead (396 g) – aluminum (4 g), lead (360 g) – aluminum (40 g) are chosen for experimental samples. The temperature of molten metal mixture is set up to 950 °C, and the temperature of coolant is 20 °C. The evolutions of the liquid– vapor interface during FCI process for different molten metal mixtures are shown in Figs. 6–8, which are sketched by red dotted lines. As shown in Fig. 6, the breakup process occurs quickly once the molten lead comes into contact with the coolant, which agrees well with the section 3.1. However, the breakup process does not happen after adding 4 g and 40 g aluminum, respectively. As for lead (396 g) – aluminum (4 g) and lead (360 g) – aluminum (40 g), the vapor film generates rapidly on the surface as molten mixtures initially attaching the coolant, and the vapor film grows quickly during the falling process. The dominant heat transfer mechanism is the film boiling, and the thickness of vapor film for lead (360 g) – aluminum (40 g) is larger and more stable than that for lead (396 g) – aluminum (4 g). The lead–aluminum mixture is the monotectic alloy, which can hardly present the mutual fusion. Also, the density of molten aluminum (ρ = 2.28 × 103 kg/m3) is obviously smaller than that of molten lead (ρ = 9.86 × 103 kg/m3), as shown in Table 1. Therefore, the molten aluminum is located on top of molten lead during the heating process, and the molten aluminum firstly attaches the coolant. During the falling process, the molten aluminum wraps the front of the molten lead due to relatively large viscosity (μ = 0.756 mN/sm2), as shown in Figs. 7 and 8. With the condensation gradually enhancing, the dominant heat transfer mechanism transfers from the film boiling to transition boiling. Finally, the front vapor film is broken by high hydraulic pressure and the effect of dragging from the coolant, and the coolant directly attaches the molten aluminum. However, the molten aluminum surface has solidified due to the high thermal conductivity (k = 103.7 W/mK) and high melting point (Tm = 660 °C), so the coolant cannot flow into the inside of molten aluminum and the breakup process does not happen. In addition, the molten aluminum continuously prevents the front of molten lead from attaching the coolant, and hydrodynamics cannot affect the front of molten lead, such as the shear force and Rayleigh– Taylor instability. However, the Kelvin–Helmholtz instability continuously affects the side of molten lead, and the breakup of molten lead does not happen. Therefore, it is concluded that the breakup process is more likely to be influenced by the Rayleigh– Taylor instability than that of Kelvin–Helmholtz instability. 3.3. The FCI process for different coolant depths In order to investigate the influence of different coolant depths on the FCI process, the lead with a mass of 50 g is chosen for this study. Figs. 9 and 10 show the evolutions of the liquid–vapor interface during the FCI process for different coolant depths, which are sketched by red dotted lines. The temperature of molten lead is set up to 800 °C, and the coolant temperature coolant is 20 °C. As shown in Fig. 9, the breakup process does not rapidly happen as the molten lead just comes into contact with the coolant, and the vapor film generates rapidly on the front of molten lead. Although shear force acts on the front of molten lead, the surface with small volume can well retain its integrity due to surface tension. Meanwhile, the front of molten lead is obviously affected by the Rayleigh–Taylor instability, which distorts into waves and
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t=1 ms
t=6 ms
t=11 ms
Initial Breakup 12.3 mm
t=16 ms
t=26 ms
t=21 ms
Fig. 6. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 400 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
detaches to form small fragments. On account of the bad thermal conductivity of molten lead (k = 19.9 W/mK), the significant thermal stress acts on the molten lead, which contributes to the initial fragmentation on the boundary layer, namely the premixing process. During the falling process, the vapor film on the front is gradually condensed and evolves irregularly, and the dominant boiling heat
t=1 ms
transfer mechanism transfers from the film boiling to the transition boiling. As shown in Table 3, the melting point of lead is relatively low, and the viscosity of it is also bad, so the molten lead presents good liquidity during falling process. When the vapor film is broken by hydraulic pressure and the effect of dragging from the coolant, the coolant directly comes into contact with the front of
t=6 ms
t=11 ms
t=21 ms
t=26 ms
12.3 mm
t=16 ms
Side
Front
Fig. 7. The evolution of the liquid–vapor interface during the FCI process for the lead-aluminum (m = 360 g – 40 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=6 ms
t=11 ms
t=21 ms
t=26 ms
969
12.3 mm
t=16 ms
Side
Front
Fig. 8. The evolution of the liquid–vapor interface during the FCI process for the lead-aluminum (m = 396 g – 4 g, Tmm = 950 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
molten lead. Furthermore, the violent boiling rapidly occurs and significant pressure pulse acts on the molten lead, namely the trigger process. In addition, the fragmentation of the front increases the contact area between the molten lead and coolant, and the pressure pulse caused by violent boiling rapidly transmits upward, which finally causes the absolute breakup. Meanwhile, the side of molten
lead is continuously affected by Kelvin–Helmholtz instability during the falling process. However, the side of molten lead does not present obvious fragmentation phenomena until initial breakup happens. Therefore, the breakup process is more likely to be influenced by the Rayleigh–Taylor instability than that of Kelvin–Helmholtz instability, which agrees well with section 3.3.
t=40 ms
t=25 ms
t=1 ms
Side
12.3 mm
Front t=90 ms
t=80 ms
t=95 ms Transmit Upward
Initial Breakup
Fig. 9. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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Table 3 Properties of molten lead with different temperatures. Tmm (°C)
500
800
900
Tm (°C) ρm (kg/m3) Δρ/ΔT (kg/m3) ρmm (kg/m3) σm (mN/m) Δσ/ΔT (mN/mK) σmm (mN/m) μ0 (mN/sm2) E (kJ/mol) μmm (mN/sm2) cp (J/kgK) k (W/mK) u (m/s) ρc (kg/m3) Tc = 20 °C λK-H (mm) λR-T (mm) tin, exp (ms)
327 10.68 × 103 −1.32 10.45 × 103 458 −0.13 481 0.4636 8.61 0.4642 137 18.2 1.4 998 1.64 14.01 27
327 10.68 × 103 −1.32 10.05 × 103 458 −0.13 520 0.4636 8.61 0.4640 135 19.9 1.4 998 1.83 15.20 84
327 10.68 × 103 −1.32 9.92 × 103 458 −0.13 533 0.4636 8.61 0.4640 135 19.9 1.4 998 1.88 15.50 147
All the properties of molten metals are referenced from Gale and Totemeier [19] under the same working condition.
In order to investigate the FCI process with small coolant depth, a metal plate is equipped at the location, which is 90 mm below the coolant surface. As shown in Fig. 10, the breakup process does not happen during the whole falling process. Before the molten lead coming into contact with the metal plate, the boundaries of the front and side are significantly irregular, which are affected by the Rayleigh–Taylor and Kelvin–Helmholtz instability, respectively. Also, the thermal stress contributes to the fragmentation of boundary due to bad heat conduction of molten lead. During the falling process, the vapor film generates rapidly on the molten lead surface, especially fragments from the boundary layer stripping, namely the premixing process. With the front of molten lead firstly coming into contact with the bottom, the molten lead gradually accumulates and spreads out due to good liquidity. Meanwhile, the contact area between the molten lead and metal plate gradually increases, so
t=1 ms
the heat is quickly transferred from the molten lead to the metal plate. What is more, the vapor film on the front is extruded to the top of accumulation due to significant density difference between the molten lead and coolant. The vapor film on the top of accumulation gradually increases, which prevents the molten lead coming into contact with the coolant. Also, the vapor film is continuously condensed and finally broken by the coolant. The coolant again rapidly evaporates on the top of accumulation and causes significant pressure pulse. However, the top of molten lead has solidified, which protects the inside of molten lead from the pressure pulse and prevents the trigger process, as shown in Fig. 10. 3.4. The FCI process for different coolant temperatures In order to research the effect of different coolant temperatures on FCI process, the lead is used to carry out the visual investigation. The evolutions of the liquid–vapor interface during FCI process for different coolant temperatures are shown in Figs. 9, 11, 12, 13, which are sketched by red dotted lines. The temperature of molten lead is set up to 800 °C, and the mass of lead is 50 g during the experiment. As mentioned in section 3.3.1, the front of molten lead firstly presents breakup (t = 80 ms) with the coolant temperature of 20 °C, which rapidly transmits upward and finally causes the absolute breakup, as shown in Fig. 9. As the coolant temperature increases to 30 °C, the breakup process still occurs, but the occurrence time rises to t = 90 ms, as shown in Fig. 11. Also, the final breakup intensity for Tc = 30 °C is obviously weaker than that for Tc = 20 °C, as shown in Fig. 9 (t = 95 ms) and Fig. 11 (t = 140 ms). As the coolant temperature increases to 40 °C and 60 °C, the breakup process does not occur during the whole falling process, as shown in Figs. 12 and 13. As shown in Table 4, the critical wavelengths of the Rayleigh– Taylor and Kelvin–Helmholtz instability changes a little for different coolant temperatures. Also, the density of the coolant varies little with different coolant temperatures, so the influence of hydraulics difference can be neglected. As the coolant temperature increases,
t=40 ms
t=70 ms
Side
12.3 mm Front
Metal Plate t=90 ms
t=130 ms
t=230 ms
Fig. 10. The evolution of the liquid–vapor interface during the FCI process for the lead coming into contact the bottom with small water depth before breakup (m = 50 g, Tmm = 800 °C, Tc = 20 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=10 ms
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t=30 ms
Side
Front 12.3 mm
t=90 ms
t=120 ms
t=140 ms
Transmit Upward Initial Breakup
Fig. 11. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 30 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
the vapor film can more quickly generate as the molten lead comes into contact with the coolant. In addition, the vapor film is thicker and the film boiling is more stable. During the falling process, the vapor film is gradually condensed and the dominant boiling heat transfer mechanism transfers from the film boiling to the transition boiling. However, the condensation slows down and the time
t=1 ms
for vapor film initially broken is delayed with increasing the coolant temperature. If the molten lead surface still keeps the liquid state as molten lead again comes into contact with the coolant, the breakup process will consequently occur, as shown in Figs. 9 and 11. However, if the molten lead surface has solidified, the breakup will not occur because the solid surface can prevent the obvious pres-
t=10 ms
t=30 ms
Front 12.3 mm
t=90 ms
t=120 ms
t=140 ms
Side
Fig. 12. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 40 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
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t=1 ms
t=10 ms
t=30 ms
Side
12.3 mm Front
t=90 ms
t=120 ms
t=140 ms
Fig. 13. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 800 °C, Tc = 60 °C). (For interpretation of the references to color in the citations to this figure, the reader is referred to the web version of this article.)
sure pulse of violent boiling, namely no trigger process, as shown in Figs. 12 and 13. Therefore, increasing the coolant temperature can significantly restrict or prevent the breakup process during FCI process. 3.5. The FCI process for different molten metal temperatures In order to study the effect of molten metal temperatures on FCI process, molten leads with different temperatures are chosen for the experiment. Figs. 9, 14, 15 show the evolutions of the liquid– vapor interface during the FCI process for different molten metal temperatures, which are sketched by red dotted lines. The temperatures of molten leads are set up to 500 °C, 800 °C, and 900 °C, respectively. The mass of lead is 50 g, and the coolant temperature is 20 °C. As shown in Figs. 9, 14, 15, the molten leads with different temperatures present breakup. Also, the initial breakup occurs at the front of molten lead, and rapidly transmits upward, finally causes the absolute breakup. However, the occurrence times for the breakup processes are obviously different for different molten metal temperatures. With increasing the temperature from 500 °C to 800 °C to 900 °C, the occurrence time for breakup increases from 21 ms to 80 ms to 147 ms. The solidification time increases as the molten metal temperature increases, which makes for the breakup. However, as shown in Table 3, the critical wavelengths of the Rayleigh– Taylor and Kelvin–Helmholtz instability significantly increase with as the molten metal temperature increases. Therefore, the influence of hydraulics on the front and side of molten lead obviously
Table 4 Hydraulics characteristics for different coolant temperatures. Tc (°C) (kg/m3)
ρc λK-H (mm) λR-T (mm)
20
30
40
60
998 1.833 15.20
996 1.837 15.19
992 1.850 15.19
983 1.859 15.18
decreases with increasing the molten metal temperature. Also, the viscosity decreases only 0.05% as the molten metal temperature increases, as shown in Table 3. As the molten metal temperature increases from 500 °C to 800 °C and 900 °C, the surface tension of molten lead increases from 481 mN/m to 520 mN/m and 533 mN/ m, which enhances the capacity for molten lead to maintain surface integrity and weakens the fragmentation during falling process. Meanwhile, the thermal conductivities for T = 800 °C (k = 19.9 W/ mK) and T = 900 °C (k = 19.9 W/mK) W/mK are larger than T = 500 °C (k = 18.2 W/mK), and the specific heat changes a little with the molten metal temperature increasing from 500 °C to 800 °C to 900 °C. Therefore, the heat can be conducted quickly to the surface from the center, and the thermal stress acting on the surface decreases. In addition, the vapor film is thicker and the film boiling is more stable with the molten metal temperature increasing. Therefore, the occurrence time for breakup increases as the molten metal temperature increases from 500 °C to 800 °C to 900 °C, as shown in Figs. 9, 14, 15. 3.6. The criterion for FCI process In order to predict the breakup occurrence, two dimensionless parameters are proposed in this section. The shear force from relative velocity of fluids is balanced by the surface tension as a molten metal drop existing in a flow. Weber number (We) is derived as
We =
ρcu 2Deq σ mm
(4)
where We is the Weber number; u is the velocity (m/s) as the molten metal just comes into contact with the coolant. σmm is the surface tension of molten metal (N/m); Deq is the equivalent diameter of molten metal (mm), which is defined as
V eq =
m ρmm
(5)
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t=1 ms
t=10 ms
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t=20 ms Side
Initial 12.3 mm Front
t=21 ms
t=22 ms
Breakup
t=24 ms
Transmit Upward
Fig. 14. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 500 °C,Tc = 20 °C).
Deq = 3
6V eq π
(6)
where m is the mass of molten metal (g); Veq is the equivalent volume of molten metal (mm3). As discussed above, the breakup of molten metals is dependent on the initial contact with the coolant and the falling process.
t=1 ms
Once the Weber number for the molten metal exceeds a value, the surface tension cannot keep the front integrity as the molten metal just comes into contact with the coolant. With the contact area increasing, the consequent violent boiling leads to absolute breakup. When the Weber number is small, the molten metal can keep the integrity well as it comes into contact with the coolant and following the breakup during the falling process is mostly dependent on
t=30 ms
t=100 ms
Side
12.3 mm
Front t=147 ms
t=150 ms
t=151
Transmit Upward Initial Breakup
Fig. 15. The evolution of the liquid–vapor interface during the FCI process for the lead (m = 50 g, Tmm = 900 °C,Tc = 20 °C).
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Solid circle • : Breakup initially
We (Weber number)
Hollow circle o : Breakup during falling Cross × : No Breakup
(2300)
F (Fragmentation Factor) Fig. 16. The criterion for prediction of molten metal breakup occurrence. The red symbols stand for data of this study; the green symbols stand for data of Abe [16], and the blue symbols stand for data of Kondo [21]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the property of the molten metal. Therefore, the Weber number can be used to estimate the breakup occurrence as the molten metal initially comes into contact with the coolant, and another dimensionless parameter should reflect the influences of the properties of molten metals. According to the discussion above, the molten metal with small thermal diffusivity is more likely to present breakup during falling process, which is derived as
α=
k ρmm c p
(7)
where α is the thermal diffusivity (s/m2); k is the thermal conductivity (W/mK); cp is the specific heat (J/kgK). In addition, the molten metal with a large equivalent diameter and large falling velocity is significantly affected by hydraulics, which should be considered in dimensionless parameter F1 (fragmentation factor 1)
F1 = Dequα = Dequ
ρmm c p k
(8)
As discussed in section 3.4, increasing the coolant temperature can significantly restrict or prevent the breakup. Hence, a dimensionless parameter F2 (fragmentation factor 2) is used to reflect the influence of coolant temperature, which is presented as
F2 =
Tsat Tc
(9)
where Tsat is the saturated temperature (K); Tc is the coolant temperature (K). Meanwhile, the breakup can be restricted by increasing the molten metal temperature due to the increase of vapor film thickness, which can be reflected by a dimensionless parameter F3 (fragmentation factor 3)
F3 =
Tsat Tin − Tsat
(10)
where Tin is the initial temperature of molten metal (K). However, the solidification time increases as the molten metal temperature increases, which makes for breakup. Hence, increasing the molten metal temperature has two sides, and a dimensionless parameter F4 (fragmentation factor 4) should be proposed to reflect this influence
F4 =
Tin Tm
(11)
where Tm is the melting point of metal (K). When all of these factors are considered together, a dimensionless parameter F (fragmentation factor) can be presented as
F = F1F2F3F4 = Dequ
ρmm c p Tsat Tin Tsat k Tc Tm Tin − Tsat
(12)
As analyzed above, high Weber number is favorable for the breakup occurrence as the molten metal initially comes into contact with the coolant, and the possibility for breakup occurrence during falling process is large with high fragmentation factor. According to comparisons with experimental results, the critical Weber number and fragmentation factor are proposed. Once the initial breakup happens due to large Weber number (>120), the violent boiling rapidly spreads and leads to absolute breakup. As for a Weber number of <120, the front of the molten metal can keep the integrity, and subsequent breakup is dependent on the fragmentation factor. As for a fragmentation factor of <2300, the molten metal can keep the integrity during the whole falling process. As for a fragmentation factor of >2300, the breakup initially happens at the front of molten metal, and rapidly transmits upward, and finally leads to absolute breakup. In order to predict the occurrence of molten metal breakup, a scatter diagram with the Weber number for x-axis and fragmentation factor for y-axis is shown as Fig. 16. Meanwhile, the Weber number and fragmentation factor are used for data in Abe [16] (11 working conditions) and Kondo [21] (4 working conditions), which are also shown as Fig. 16. The predicted results agree well with the experimental results proposed by Abe [16] and Kondo [21].
4. Conclusions A visual experimental study is carried out to investigate the breakup as high superheated molten metal comes into contact with the coolant under different working conditions. The obtained conclusions are as follows: (1) The FCI process is significantly affected by properties of molten metals. As the molten aluminum comes into contact with the subcooled coolant (water), the breakup process does not occur, which is attributed to the large critical wavelength of
Q. Lu et al./Applied Thermal Engineering 98 (2016) 962–975
Rayleigh–Taylor and Kelvin–Helmholtz instability, large surface tension, large viscosity, large thermal conductivity and high melting point. As for molten lead and bismuth, the breakup process rapidly occurs once the molten metals come into contact with the subcooled coolant due to the low melting point, and low heat conduction and surface stability capacities. (2) The breakup process is more likely to be influenced by the Rayleigh–Taylor instability than that of Kelvin–Helmholtz instability. Such as for the molten lead during the falling process with the mass of 50 g, the initial breakup always occurs at the front of the molten lead, and then the breakup process transmits upward and leads to a severe breakup. However, the breakup process does not occur with small water depth or with the front of the molten lead protected by a little molten aluminum. (3) As the coolant temperature increases, the thickness of the vapor film increases and the condensation slows down, which restricts or prevents the breakup process. As the initial temperature of molten metal such as lead increases, the surface tension and the thermal conductivity obviously increase, which enhances the surface integrity and heat conduction capacities. In addition, the critical wavelengths of the Rayleigh– Taylor instability and Kelvin–Helmholtz instability obviously increase. Then the influence of the hydraulics weakens. Therefore, the initial time for breakup increases as the initial temperature of molten lead increases. Meanwhile, two dimensionless parameters are proposed to predict the breakup occurrence. The Weber number significantly affects the breakup occurrence at the initial moment when the molten metal just comes into contact with the subcooled coolant. While the breakup occurrence during the falling process within the subcooled coolant obviously depends on the fragmentation factor. Acknowledgement The authors are grateful for the support of the National Natural Science Foundation of China (No. 51206199), Natural Science Foundation of Chongqing (NO. cstc2013jcyjA90013), and the project funded by China Postdoctoral Science Foundation (No. 2014M562337). Nomenclature General symbol u Velocity [m/s] T Temperature [°C] t Time [s] m Mass [g] ρ Density [kg/m3] E Constant We Weber number D Diameter [mm] V Volume [mm] F Fragmentation factor Greek letters σ Surface tension [N/m] μ Dynamic viscous [Pa·s] k Thermal conductivity [W/mK]
cp λ α
975
Specific heat [J/kgK] Critical wavelength [mm] Thermal diffusivity [m2/s]
Subscripts mm Molten metal m Melting point c Coolant in Initial exp Explosion sat Saturated eq Equivalent K-H Kelvin–Helmholtz R-T Rayleigh–Taylor
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