In order to clarify the influence mechanism of high pressure on inclusion number distribution, the changes in phase transition sequences, key properties, and heat transfer boundary conditions with pressure have been investigated. Furthermore, the inclusion number distribution of H13 die steel ingot under different pressures (0.1, 1, and 2 MPa) has been numerically simulated by the mathematical model verified using the experimental results of cooling rate and the parameter ηn. The changes in key properties and phase transition sequences with pressure were investigated by Thermo-Calc software. With increasing pressure from 0.1 to 1000 MPa, the suppression of ferritic phase (δ) formation and improvement of liquidus/solidus temperature are obvious, but the density, thermal expansion coefficient, specific heat, and latent heat of solidification barely change. Meanwhile, the effect of pressure on heat transfer boundary conditions has been quantitatively revealed with formulas proposed by experimental measurement and numerical calculation: hf,0.1 = 1137.4t−0.23 (for 0.1 MPa), hf,1.0 = 1294.3t−0.23 (for 1 MPa), and hf,2.0 = 1501.6t−0.23 (for 2 MPa). During solidification process, gravity, buoyancy, and drag forces play the key roles in affecting the movement behavior of inclusions. Moreover, their net force drives inclusions to sink downward near the tip of columnar dendrite, and move counterclockwise. With increasing pressure from 0.1 to 2 MPa, the enrichment degrees of inclusions in ingot decrease, and the distribution of inclusion number becomes more uniform due to the stronger escaping ability of inclusions and the weaker inclusion trapping ability of the mushy zone.
