1 Introduction

Heat transfer from a molten metal with phase change is an important phenomenon that has been the subject of various research fields such as nuclear safety, heat storage, and material processing technologies. Molten core concrete interaction (MCCI) is an advanced phase of the nuclear severe accident encountered after the molten reactor core materials (corium) are ejected into the concrete reactor cavity following the reactor pressure vessel (RPV) failure. Upon reaching the reactor cavity, molten corium interacts with the concrete thermo-chemically, and erodes the concrete by the continuous internal decay heat generation. In the literature, several experimental and computational efforts exist investigating that phenomenon. Recent reviews reported by Foit et al. (2014) and Cranga et al. (2014) describe the MCCI experiments and relevant problems encountered in understanding of the phenomenon. Advancement of molten corium inside the concrete towards the lateral and vertical directions occasionally demonstrates unsymmetrical and inconsistent behaviors in the experiments (Farmer et al. 2006). An MCCI event with the moving boundary of corium resembles the Stefan problem and involves challenging tasks for the computational codes (Mitchell and Vynnycky 2014).

In this study, we performed an experiment with molten metal alloy moving inside the gel wax due to the phase change of wax. We measured transient velocities of liquid wax flow sweeping the metal interface boundary and above the molten metal with time-resolved particle image velocimetry (TR-PIV) to investigate the buoyancy-driven flow. We think that the progression of molten metal and buoyant flow in the wake of the molten metal constitute a challenging exercise for the MCCI simulation codes. The insights obtained from a simulation of this kind of simple experiments might be extrapolated to models of large-scale experiments or the real MCCI events.

2 Experimental method

As illustrated in the schematic layout of the experimental setup (Fig. 1), transparent gel wax fills the transparent glass container. A cylindrical cavity having 30 mm diameter was created at the center of the solidified wax. The U-alloy was melted and heated up to 190 °C in a pot, and poured gently into the cavity. The condition after pouring the liquid metal alloy is shown in Fig. 2. The U-alloy has a low temperature melting point and it is composed of Bi, Pb, Cd and Sn. The properties of U-alloy and the wax are listed in Table 1.

Fig. 1
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Schematic of experimental setup

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Fig. 2
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Initial condition

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Table 1 Properties of U-alloy and gel wax
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Mechanical pencil lead particles were used as the tracer particles inside the wax. Cylindrical pencil leads having 0.5 mm diameter were crushed into small fine particles and dispersed in the melted gel wax inside a hot pot. After the solidification of wax, a homogenous particle distribution was obtained. Gel wax was illuminated with 1-mm-thick green laser light sheet and moving particle images were recorded with Photron SA5 high-speed camera at 500 frames/s. Recorded images were analyzed with in-house PIV code (Erkan et al. 2008).

3 Results and discussion

Three snapshots of original images are illustrated with dimensional axes in Fig. 3. At the beginning, metal temperature is high; hence, a rapid progression takes place towards favorably to the lateral directions. After a while, lateral progression slows down because of the sustained heat loss from the molten metal. Melted wax from the bottom interface of the metal flows upwards through the pathways sweeping lateral interface. That hot liquid wax supply from the bottom interface enhances the lateral erosion of solid wax compared to the bottom interface.

Fig. 3
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Raw images: a t = 0.54 s, b t = 0.94 s, c t = 1.34 s

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Vector maps resolved from the same snapshots are presented in Fig. 4. As a general tendency, velocities decay in the wake region by the time because of the temperature decrease and solidification of liquid metal. The hot liquid wax rises upward along the central region, cools down when it reaches the air interface at the top, and it flows downward through the outer regions. When the downward stream reaches the upper surface of molten metal, it comes across the flow stream coming from the bottom interface and they mix. This mixture moves toward the central region. By the heat transfer from the molten metal’s upper interface, heated up liquid wax accelerates in the upward direction due to buoyancy force. This flow pattern can be observed clearly in Fig. 4b. Stronger upward motion on the left side is observed occasionally (Fig. 4a) that demonstrates a nonsymmetrical flow pattern relative to the central axis; nevertheless, an overall natural circulation pattern can still be visualized. By the time molten metal moves downward and cool down, the magnitude of velocities decrease (Fig. 4c). Measured velocity profiles along the horizontal x axis are plotted in Fig. 5 for several elevations on the y axis. Here, predominant upward flow of liquid wax in the central region can be discerned from the two peaks of velocity magnitudes. The magnitudes decay in time because of the decline in the heat transfer from the molten metal to the wax (Fig. 5c). In some occasions during the test such as at t = 0.54 s (Fig. 5a), a large peak appears at around x = −15 mm that might be caused by two reasons. One is the air bubbles spurting out from the bottom at which they were trapped prior to the test startup. Another one is non-uniformity of heat flux from the molten metal surface because of the crust formation and the internal flows of liquid metal.

Fig. 4
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Vector maps, 2D. a t = 0.54 s, b t = 0.94 s, c t = 1.34 s

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Fig. 5
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2D velocity profiles at different heights along the vertical y axis

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4 Conclusions

Downward progression of the molten U-alloy and natural convection in the wake region inside the wax were investigated with a simple experiment. Time-resolved 2D velocity vector maps of liquid wax were extracted with PIV analysis. Flow characteristics of the melted wax demonstrate buoyancy-driven flow. The velocity magnitudes decay in the time is attributed to the continuous heat loss from the molten U-alloy for the phase change of gel wax. The flow patterns demonstrate a symmetric characteristic around the central vertical axis (x = 0 mm) except the case earlier in time which is characterized by large velocity magnitude upward motions.