Fig. 1. Structural diagram of geometric model for molten salt filling pipeline with the initial boundary conditions

Fig. 2. Schematic diagram of the grid size

Fig. 3. Variation of flow distance with time for different grid sizes

Fig. 4. Diagram of the basic phase interface structure and initial solidification behavior (t=0.4s) (color online)

Fig. 5. Diagram of solidification and melting behaviors in horizontal sections during filling process (x=0)

Fig. 6. Solidification and melting behaviors in z=0 section during filling process(a) Liquid fraction contours (z=0), (b) Liquid fraction at t=0.4~1.2 s, (c)Liquid fraction at t=2.0~4.0 s

Fig. 7. Velocity field contours of the fluid zone at different time moments during filling process (x=0) (color online)

Fig. 8. Velocity distribution across the pipe cross-section at different time moments (color online) (a) t=0.4 s, (b) t=4.0 s

Fig. 9. Temperature field contours of the fluid zone at different time moments during filling process (x=0) (color online)

Fig. 10. Temperature distribution across the pipe cross-section at different time moments (color online) (a) t=0.4 s, (b) t=4.0 s

Fig. 11. Variations of total heat transfer from molten salt to cold pipe (a) and the average temperature in the cold pipe (b) with time (color online)

Fig. 12. Liquid fraction contours at different time moments during filling process for various Amush(a) 5×10⁵, (b) 10⁵, (c) 5×10⁴, (d) 2×10⁴, (e) 10⁴, (f) 5×10³

Fig. 13. Variations of the temperature (a), velocity (b) and flow distance (c) with time at the characteristic interface (color online)

Fig. 14. Variation of penetration distance with Amush values

Fig. 15. Comparison of the penetration distances between the simulation results and the experimental data^[23]