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.

中文翻译：

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压力对H13模具钢锭凝固过程中夹杂物数分布的影响

为了阐明高压对夹杂物数量分布的影响机制，研究了相变序列、关键性质和传热边界条件随压力的变化。此外，利用冷却速率和参数ηn的实验结果验证了数学模型，对H13模具钢锭在不同压力（0.1、1和2 MPa）下的夹杂物数量分布进行了数值模拟。Thermo-Calc 软件研究了关键特性和相变序列随压力的变化。随着压力从 0.1 增加到 1000 MPa，铁素体相（δ）形成的抑制和液相线/固相线温度的提高是明显的，但密度、热膨胀系数、比热、凝固潜热几乎没有变化。同时，通过实验测量和数值计算提出的公式，定量揭示了压力对传热边界条件的影响：hf,0.1 = 1137.4t−0.23 (for 0.1 MPa), hf,1.0 = 1294.3t−0.23 (for 1 MPa) 和 hf,2.0 = 1501.6t-0.23（对于 2 MPa）。在凝固过程中，重力、浮力和阻力在影响夹杂物的运动行为中起着关键作用。此外，它们的合力驱使夹杂物在柱状枝晶尖端附近下沉，并逆时针移动。随着压力从 0.1 增加到 2 MPa，钢锭中夹杂物的富集度降低，