Fig. 1. Calculation model

Fig. 2. Grid independence verification (a) Bubble phase profile at 50 ms, (b) Bubble trajectory

Fig. 3. Comparison of bubble migrations (a) Experimental results, (b) Simulation results

Fig. 4. Comparisons of bubble behaviors (a) Cross-sectional area comparison, (b) Perimeter comparison, (c) Trajectory comparison

Fig. 5. Deformation of bubbles in LBE under different conditions (a) Jet process, (b) Deformation of bubbles under different jet pressures (T_LBE = 573 K, P_inlet = 5 MPa; T_LBE = 573 K, P_inlet = 20 MPa), (c) Deformation of bubbles under different LBE temperatures (T_LBE = 573 K, P_inlet = 10 MPa; T_LBE = 773 K, P_inlet = 10 MPa)

Fig. 6. Velocities of bubbles in LBE under different conditions (a) Effect of jet pressure on bubble velocity (T_LBE = 573 K), (b) Effect of LBE temperature on bubble velocity (P_inlet = 10 MPa)

Fig. 7. Trajectories of bubbles in LBE under different conditions (a) Effect of jet pressure on bubble trajectory (T_LBE = 573 K), (b) Effect of LBE temperature on bubble trajectory (P_inlet = 10 MPa)

Fig. 8. Aspect ratios of bubbles in LBE under different conditions (a) Effect of jet pressure on bubble aspect ratio (T_LBE = 573 K), (b) Effect of LBE temperature on bubble aspect ratio (P_inlet = 10 MPa)

Fig. 9. Force analysis of bubbles in LBE

Fig. 10. Diagram of the relationship between bubble equivalent particle size and terminal velocity

Fig. 11. Drag coefficients of different bubbles(a) Relationship between drag coefficient and bubble diameter, (b) Relationship between drag coefficient and Re

Fig. 12. Comparison between simulated drag coefficients and existing model results: models proposed by (a) Ishii and Chawla^[6], (b) Tomiyama et al.^[9], (c) Wallis et al.^[22], (d) Peebles and Garber^[7], (e) Mei and Klausner^[8], and (f) Turton and Levenspiel^[23]

Fig. 13. Applicability analysis of the optimized drag coefficient model