欧拉-拉格朗日迭代固-液相变算法

doi:10.11949/0438-1157.20240273

摘要/Abstract

摘要：

在固-液相变过程中，外力可导致固体相变材料在液体相变材料中产生相对运动并严重影响相变流动传热。提出一种欧拉-拉格朗日迭代固-液相变算法，创新地将预测固体相对运动的拉格朗日迭代外置耦合于预测相变流动传热的欧拉迭代，能够稳定准确地耦合计算固-液相变的流动传热和固体相变材料的相对运动。采用本算法研究了方腔内的接触熔化过程，探讨不同糊状区系数和重力加速度对本算法的影响规律。结果表明，本算法预测液相体积分数的平均误差为4.93%，固体相对运动预测数值振荡降低51.42%。对于石蜡材料，推荐使用的糊状区系数为10¹⁰。增大重力加速度会提高熔化速率并加快相对运动，但对整体趋势影响较小。研究结果可作为相变储能装置的设计参考。

关键词: 相变, 传热, 算法, 数值模拟, 接触熔化, 相对运动, 内外迭代

Abstract:

During the solid-liquid phase change process, the external force can cause relative motion of the solid phase change material within the liquid phase change material, which can seriously affect the flow and heat transfer. An Euler-Lagrange iterative solid-liquid phase change algorithm is proposed to numerically solve the above problem. The Lagrange iteration for predicting the solid relative motion is externally coupled to the Euler iteration for calculating the phase change flow and heat transfer, which can stably and accurately simulate the flow and heat transfer of the solid-liquid phase change and the relative motion of the solid phase change material. Based on the present algorithm, the close-contact melting processes in the square cavity are investigated under gravity. Furthermore, the influence of different mushy zone coefficients and gravity accelerations on this algorithm is explored. The results show that the average error of the algorithm in predicting the liquid phase volume fraction is 4.93%, and the numerical oscillation of the solid relative motion prediction is reduced by 51.42%. For paraffin materials, the mushy zone coefficient of 10¹⁰ is recommended for this algorithm. The increase of the gravity acceleration can improve the melting rate and accelerate the relative downward motion, yet has less impact on the overall trends of liquid phase fraction and solid phase relative motion. The results can be used as the theoretical guideline for the design and optimization of the efficient solid-liquid phase change energy storage devices.

Key words: phase change, heat transfer, algorithm, numerical simulation, close-contact melting, relative motion, internal-external iteration

中图分类号:

TK 02

朱子良, 王爽, 姜宇昂, 林梅, 王秋旺. 欧拉-拉格朗日迭代固-液相变算法[J]. 化工学报, 2024, 75(8): 2763-2776.

Ziliang ZHU, Shuang WANG, Yu'ang JIANG, Mei LIN, Qiuwang WANG. Solid-liquid phase change algorithm with Euler-Lagrange iteration[J]. CIESC Journal, 2024, 75(8): 2763-2776.

图/表 12

图1 固-液相变储能装置几何模型

Fig.1 Geometry of solid-liquid phase change energy storage device

表1 数值模拟工况

Table 1 Working conditions of numerical simulations

工况	A_m / (kg/(m³·s))	g/(m/s²)	算法
案例0	10¹⁰	9.81	焓-多孔
案例1	10¹⁰	9.81	欧拉-拉格朗日
案例2	10⁸	9.81	欧拉-拉格朗日
案例3	10⁵	9.81	欧拉-拉格朗日
案例4	10¹⁰	29.43	欧拉-拉格朗日
案例5	10¹⁰	3.72(火星)	欧拉-拉格朗日

表2 流动传热无量纲数

Table 2 Dimensionless numbers of flow and heat transfer

T_s / K	T_l / K	T_w / K	Pr	Ste	Gr	Ra
307.65	309.15	313.15	53.30	9.55×10^-2	7.41×10⁴	3.95×10⁶

图2 欧拉-拉格朗日迭代算法流程

Fig.2 Flowchart of Euler-Lagrange iterative algorithm

图3 连续性方程残差曲线

Fig.3 Residual curves for continuity equation

图4 实验和数值结果中相分布对比

Fig.4 Comparison of phase distributions in experimental and numerical results

图5 实验和数值结果中液相体积分数和相对运动速度对比

Fig.5 Comparison of liquid phase volume fraction and relative velocity in experimental and numerical results

图6 速度云图和矢量以及流线分布(案例1)

Fig.6 Distributions of velocity magnitude, vector and streamline (Case 1)

图7 不同糊状区系数下相分布对比(t = 800 s)

Fig.7 Comparison of phase distributions with different mushy zone coefficients (t = 800 s)

图8 不同糊状区系数下液相体积分数和固体相对运动速度对比

Fig.8 Liquid phase volume fraction and relative velocity with different mushy zone coefficients

图9 不同重力加速度下相分布对比(t = 800 s)

Fig.9 Comparison of phase distributions with different gravity accelerations (t = 800 s)

图10 不同重力加速度下液相体积分数和固体相对运动速度对比

Fig.10 Liquid phase volume fraction and relative velocity with gravity accelerations

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