Abstract A distributed parameter model has been proposed for the transient heat transfer calculation of IVR in this paper. The model, composed by the free convection model based on empirical correlations and the isothermal solidification model based on the moving boundary method, has been verified with the LIVE-L5L experiment. The result deviations of key parameters, including the average temperature of molten pool, the heat flux distribution on boundary, and the growth rate of solidified crust, are evaluated by comparing with the experimental data. The validation indicates that, for LIVE-L5L experiment within the Ra’ magnitude of 10 12 - 10 14 , Asfia-Dhir formula is optimal to calculate the averaged Nusselt number ( Nu ¯ ). And the errors caused by using the empirical correlations to calculating the transient free convection are acceptable. Besides, the moving boundary method under the isothermal assumption is also applicable for calculating the dynamic solidification on the pool boundary. When the internal heat changes, both the thermal non-equilibrium on the solid–liquid interface and the pulse shape of the crust’s growth rate can be well simulated. And a stable result for interface tracking (or thickness change) can also be obtained. Next, to show the model performance, the work chooses an IVR scenario in SMR (220 MW thermal power) for test. The calculation results show that, the maximum estimation result for the molten pool’s internal heat ( Q m ) is 0.42 MW/m3. And the corresponding peak heat flux ( q m θ ) can reach 267.5 kW/m2. Even in the maximum heat load moment, the maximum temperature on inner wall ( T w , i n θ ) only reaches 1318.1 K. When the molten pool enters into the long-term cooling, the peak heat flux will remain around 170.5 kW/m2. Another, At the upper position with large circumferential angle, the higher heat flux will make the crust form thinner. Thus, the local wall temperature of vessel will be higher by this combined effect of large heat load and small thermal resistance. But it can’t destroy the integrity of the pressure vessel. Research of this paper can provide references for the safety design of SMR.

中文翻译：

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真皮池中瞬态传热的模型开发

摘要 本文提出了一种用于IVR瞬态传热计算的分布参数模型。该模型由基于经验相关性的自由对流模型和基于移动边界法的等温凝固模型组成，已通过 LIVE-L5L 实验验证。通过与实验数据对比，评估熔池平均温度、边界热通量分布、凝固结壳生长速率等关键参数的结果偏差。验证表明，对于在Ra' 10 12 - 10 14 范围内的LIVE-L5L 实验，Asfia-Dhir 公式是计算平均努塞尔数(Nu¯ ) 的最佳方法。使用经验相关性计算瞬态自由对流造成的误差是可以接受的。此外，等温假设下的移动边界法也适用于计算熔池边界上的动态凝固。当内部热量发生变化时，固液界面上的热非平衡和地壳生长速度的脉冲形状都可以很好地模拟出来。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 并且也可以获得界面跟踪（或厚度变化）的稳定结果。接下来，为了展示模型性能，工作选择了 SMR（220 MW 火电）中的 IVR 场景进行测试。计算结果表明，熔池内热（Q m ）的最大估算结果为0.42 MW/m3。并且相应的峰值热通量（ qm θ ）可以达到267.5 kW/m2。即使在最大热负荷时刻，内壁的最高温度（T w ，在 θ 中）也仅达到 1318.1 K。当熔池进入长期冷却时，峰值热通量将保持在 170.5 kW/m2 左右。另外，在圆周角大的上部位置，较高的热通量会使地壳形成更薄。因此，在这种大热负荷和小热阻的共同作用下，容器的局部壁温会更高。但不能破坏压力容器的完整性。本文的研究可为SMR的安全设计提供参考。但不能破坏压力容器的完整性。本文的研究可为SMR的安全设计提供参考。但不能破坏压力容器的完整性。本文的研究可为SMR的安全设计提供参考。