As schematically shown in Figure 1, the three-dimensional ellipsoidal test section (COPRA-ROC) is composed of an ellipsoidal lower head, a cylinder, an upper cover plate, a layered partition and a cooling channel. The ellipsoidal lower head, whose inner diameter and depth are 1,150 mm and 286 mm respectively, is welded with cylinder. A layered partition made of stainless steel with a thickness of 20 mm or 30 mm is placed in the test section to simulate the stratified corium pools. The heating wires are arranged in the lower part to simulate the homogenously decay heat in the lower oxide layer, while no heat is generated in the upper metal layer. An approximately isothermal cooling boundary condition is offered by the cooling channel, whose outer wall is welded with the upper cylinder to form a shell cooling path with a width of 120 mm. An adiabatic boundary condition is adopted to the top wall. Cylindrical openings with a diameter of 60 mm are designed in the top lid and layered partition for the injection or discharge of the molten salt. Furthermore, the same cylindrical openings are designed in the middle of two plates as the outlet of fixed bracket.

As mentioned above, five layers of spiral heating wires are evenly installed in the test section to simulate the homogeneous decay heat generated within the oxide layer. The test section is divided into six areas by the five layers of heating wire, as shown in Figure 2. In the height direction, the distance between adjacent heating wires is 80mm, and the bottom heating wire is 40 mm from the bottom of the test section. In order to avoid affecting the temperature distribution on the wall of the molten pool, the minimum distance between the heating wire and the inner wall of the pressure vessel should be greater than 50 mm. The heating wire with a diameter of 6 mm can provide a maximum heating power of 4 kW, and the total power of the test section is 20 kW. The heating power of heating wire can be adjusted continuously according to different experimental conditions. Before each experiment, the power of each layer of electric heating wire is adjusted based on the heating volume of each layer, while maintaining a constant total heating power, to provide an approximately uniform volumetric power. The heating wires are positioned through a solid stainless steel skeleton, which is welded on the central shaft of the molten pool. For the sake of minimizing the impact on the flow field of the molten pool, the cables of heating wires are led out at the edge of the molten pool.

Inside the three-dimensional ellipsoidal test section, to obtain the temperature field inside the molten pool, thermocouples with a total number of 72 are uniformly positioned along the radial and height directions at four azimuth angles of 0°, 90°, 180° and 270°, as shown in Figure 3. The detailed positions of these thermocouples are listed in Table 1. As can be seen from Figure 4, in order to obtain the wall heat flux of the molten pool, nine groups of thermocouples are arranged on the inner and outer walls of the test section at four azimuth angles to measure the inner and outer wall temperature of the molten pool. The heat flux of ellipsoidal lower head is calculated by Equation 1 and the heat flux of upper cylinder is calculated by Equation 2. q = λ w a l l T i − T o δ ⋅ R i R o (1) q = λ w a l l R o T i − T o ln R o / R i (2) Where, R _i and R _o represent the curvature radius of the inner and outer wall of the ellipsoid and the inner and outer radius of the cylinder respectively; λ _wall is the thermal conductivity of wall material; T _i and T _o are the temperatures of inner wall and outer wall respectively; δ is the wall thickness.

In addition, 8 groups of thermocouples are arranged on the layered partition to measure the upper and lower surfaces temperature of the layered partition, which is used to calculate the heat flux transmitted from the lower oxide layer to the upper metal layer. The heat flux can be calculated as follows: q p a r t i t i o n = − λ p a r t i t i o n T d n − T u p δ p a r t i t i o n Where, λ _partition is thermal conductivity of layered partition; T _dn and T _up are temperatures of the lower and upper surfaces of layered partition respectively; δ _partition is thickness of layered partition.

In order to obtain the crust thickness of the inner wall of the test section, 12 multipoint thermocouples are arranged at four azimuth angles for calculation. The schematic diagram of multipoint thermocouples arrangement is shown in Figure 5.

In the experiment, the direct measurement parameters and their uncertainties are shown in Table 2. The direct measurement parameters include temperature parameters, height parameters, water flow rate in the coolant channel and heating power. The measuring uncertainty ( U ) can be calculated based on the instruments error ( Δ 1 ) and acquisition system error ( Δ 2 ), the equation is as follows: U = Δ 1 + Δ 2 3

As we know, many factors such as heating power and molten pool height will have a certain impact on the heat transfer characteristics of molten pool. In this two-layer molten pool experiment, the layered molten pool is realized by placing a layered partition in the test section. Therefore, considering the effects of different heating power, different oxide layer height and layered partition thickness, a total of 10 groups of test conditions were carried out, as shown in Table 3. In tests with different heights of oxide layers, the layered partition will be moved and rewelded.

Referring to the molten pool heat transfer experiments such as COPRA and LIVE, the binary mixture of 20 mol%NaNO₃–80 mol%KNO₃ is selected as the simulant material for both molten pools. The solidus temperature and liquidus temperature of mixture are 224°C and 284°C respectively. The molten nitrate mixture is injected into the test section to the required height, and the heating power is adjusted to the required power. Meanwhile, the temperature of cooling water is approximately maintained near the room temperature during the experiment. Finally, the molten pool will reach a stable state under the joint action of internal heating and external cooling, that is, the temperature of the molten pool will vary no more than 1°C for 2 h. Then, the experimental data are collected, processed and analyzed.

With the temperature distributions obtained under the above 10 tests normalized, the dimensionless temperature distributions of oxide molten pool with dimensionless height are obtained, as shown in Figure 14. It can be seen from the figure that the dimensionless temperature distributions obtained from different tests are in good agreement, ignoring the effects of heating power, oxide layer height and layered partition thickness. The dimensionless temperature increases with the height of the molten pool, and the peak value is about 1.18. The relationship between dimensionless temperature and height is as follows: T T a v e = 1.162 − 0.95 ⁡ exp − 6.185 ⋅ H H max

Similarly, the wall heat flux is normalized to obtain the distribution of dimensionless heat flux with arc length ratio, as shown in Figure 15. It can be found that when the arc length ratio is less than 0.8, the dimensionless heat fluxes under different tests change little. Then, with arc length ratio increasing, the dimensionless heat fluxes increase sharply. The maximum value can reach about 2.51. The relationship between dimensionless heat flux and arc length ratio is given by: q q a v e = 2.287 − 1.753 1 + 11.406 ⋅ L i / L max 15.714

As shown in Figures 16, 17, the distributions of downward heat transfer Nu_dn and upward heat transfer Nu_up with Ra’ are presented respectively. The heat transfer Nu of molten pool increases exponentially with Ra’. In the range of Ra’ from 3.43 × 10¹² to 1.54 × 10¹³, the ranges of downward heat transfer Nu_dn and upward heat transfer Nu_up are 106.97–211.18 and 227.62–334.12, respectively. The relationships of downward heat transfer Nu_dn and upward heat transfer Nu_up with Ra’ are as follows: N u u p = 1.669 R a ′ 0.171 N u d n = 0.011 R a ′ 0.315

The relationships obtained from the ACOPO experiment (Theofanous et al., 1997) are also added to in Figures 16, 17 for comparison, and its predicted values are relatively higher than the experimental values.