基于等效热容法的水域冰盖生长过程的数值模拟

郭雅勋; 李星; 章青

doi:10.21656/1000-0887.460151

基于等效热容法的水域冰盖生长过程的数值模拟

doi: 10.21656/1000-0887.460151

郭雅勋^1,,
李星²,
章青^1, ,

1.
河海大学力学与工程科学学院，南京 211100
2.
河西学院土木工程学院，甘肃张掖 734000

(我刊编委章青来稿)

基金项目:

国家自然科学基金 12472200

甘肃省高校教师创新基金 2025B-192

详细信息

作者简介:
郭雅勋(1997—)，男，硕士生(E-mail: guo_yaxun2315@163.com)

通讯作者:
章青(1963—)，男，教授，博士，博士生导师(通信作者. E-mail: lxzhangqing@hhu.edu.cn)

中图分类号: TV124
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- 被引次数: 0
出版历程
- 收稿日期: 2025-08-26
- 修回日期: 2025-10-12
- 刊出日期: 2026-04-01

Numerical Simulation of Ice Cover Growth in Water Bodies Based on the Equivalent Heat Capacity Method

GUO Yaxun^1
,,
LI Xing²,
ZHANG Qing^{1
, ,}

1.
School of Mechanics and Engineering Science, Hohai University, Nanjing 211100, P.R.China
2.
College of Civil Engineering, Hexi University, Zhangye, Gansu 734000, P.R.China

(Contributed by ZHANG Qing, M.AMM Editorial Board)

摘要

摘要: 寒区水域在冬季常形成冰盖，冰盖的不断生长会对人类活动产生显著影响，理解与预测冰盖生长行为对预防冰害具有重要的实际意义. 冰盖生长受到众多要素的影响，目前尚未完全认识其中的机制. 为深入研究冰盖生长行为的复杂现象，建立了冰盖生长的有限元计算模型，采用等效热容法进行了冰盖生长过程的数值模拟. 通过与实验数据的对比，验证了所建模型和方法的准确性，并对是否考虑自然对流两种情况的数值计算结果进行比较分析. 应用本文方法和冻冰度日法计算了松花江某断面河冰生长的冰盖厚度，给出了两种方法的均方根误差，进一步证实了等效热容法在实际河流环境中的有效性. 研究结果表明，本文所建立的冰盖生长计算模型和数值方法能够反映热传递和流体运动等物理过程，可有效处理冰水相变问题，为考虑多物理场耦合效应进行冰盖生长过程模拟提供了一种有效方法.
- 冰盖 /
- 生长过程 /
- 数值模拟 /
- 等效热容法 /
- 多物理场耦合
Abstract: In cold regions, the formation of ice covers over water bodies during winter is a common phenomenon. The continuous growth of ice covers significantly impacts human activities, making it practically important to understand and predict ice growth behavior for the prevention of ice-related hazards. Ice cover growth is influenced by multiple factors, and the underlying mechanisms have not yet been fully elucidated. To investigate the complexity of ice cover growth, a finite element computational model was established, and the equivalent heat capacity method was employed to numerically simulate the ice growth process. The accuracy of the proposed model and method was validated through comparison with experimental data. A comparative analysis was conducted between numerical results considering and neglecting natural convection. Furthermore, both the proposed method and the freezing degree-day method were applied to estimate the ice thickness at a specific cross section of the Songhua River. The root mean square errors of the 2 methods were provided, further confirming the effectiveness of the equivalent heat capacity method in real river environments. The results demonstrate that, the established computational model and the numerical approach can effectively represent physical processes such as heat transfer and fluid motion, and handle water-ice phase transition problems. This study provides an effective method for simulating ice cover growth under multi-physics coupling effects.
- ice cover /
- growth process /
- numerical simulation /
- equivalent heat capacity method /
- multi-physics coupling
edited-by

edited-by
注释:

1) (我刊编委章青来稿)

HTML全文

图 1 冰盖生长过程三相状态示意图

Figure 1. Schematic diagram of 3 phase states during the ice sheet growth

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图 2 数值模拟流程

Figure 2. Numerical simulation process

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图 3 几何模型和网格划分

Figure 3. The calculation model and the finite element mesh

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图 4 冰厚实测值与等效热容法计算所得冰厚值的比较

Figure 4. Comparison between measured ice thicknesses and calculated ice thicknesses with the equivalent heat capacity method

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图 5 冰盖生长过程中的固液相分布、温度和流体流动速度

Figure 5. Solid-liquid 2-phase distributions, temperature contours, fluid flow velocity contours during the ice sheet growth process

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图 6 冰厚实测值与考虑自然对流和忽略自然对流计算所得冰厚值的比较

Figure 6. Comparison of measured ice thickness versus calculated results with and without natural convection effects

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图 7 大顶子山断面河冰冰厚实测值和计算值的比较

Figure 7. Comparison of measured and calculated ice thickness values at the Dadingzi mountain cross section

下载: 全尺寸图片幻灯片

表 1 计算参数

Table 1. Calculation parameters

parameter	value
specific heat capacity of ice c_{p, s}/(J/(kg·K))	2 052
specific heat capacity of water c_{p, l}/(J/(kg·K))	4 202
latent heat of phase change L/(J/kg)	3.35×10⁵
dynamic viscosity η/(Pa·s)	1.788×10^-3
phase change temperature T_pc/℃	0
thermal conductivity of ice λ_s/(W/(m·K))	2.26
thermal conductivity of water λ_l/(W/(m·K))	0.56
mushy zone constant A_m/(kg/(m³·s))	10⁵
coefficient of thermal expansion β/(1/K)	10^-7
density of ice ρ_s/(kg/m³)	917
density of water ρ_l/(kg/m³)	1 000

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表 2 不同试验温度下的均方根误差

Table 2. Root mean square errors at different experimental temperatures

temperature/℃	with natural convection effects	without natural convection effects
-18	1.63	2.14
-20	2.99	5.57
-25	2.49	4.47
-30	0.64	0.96

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表 3 2005年11—12月大顶子山断面封冻后地面平均温度

Table 3. Average ground temperatures after freezing of the Dadingzi mountain section from november to december 2005

date	temperature/℃	date	temperature/℃
11-18	-7.5	12-03	-11.8
11-19	-6.3	12-04	-5.8
11-20	-3.6	12-05	-5.6
11-21	-4.4	12-06	-9.4
11-22	-4.0	12-07	-11.5
11-23	-3.7	12-08	-13.1
11-24	-6.5	12-09	-12.1
11-25	-3.7	12-10	-13.0
11-26	-6.8	12-11	-13.7
11-27	-8.7	12-12	-14.2
11-28	-8.4	12-13	-12.6
11-29	-11.3	12-14	-12.7
11-30	-10.1	12-15	-11.9
12-01	-11.6	12-16	-13.6
12-02	-13.3	12-17	-14.6

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表 4 不同方法计算大顶子山断面河冰冰厚的均方根误差

Table 4. Root mean square errors of river ice thicknesses calculated with different methods at the Dadingzi mountain cross section

method	equivalent heat capacity method	freezing degree-day method
RMSE/cm	4.92	8.05

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