基于热质传递效应的准稳态结霜模型改进及数值验证

doi:10.11949/0438-1157.20250003

摘要/Abstract

摘要：

基于相变结霜本质为热质传递的原理，进一步考虑霜层孔隙率逐渐降低和热阻增大分别致使水蒸气扩散能力和换热效果下降的实际情况，进而引入有效扩散系数D_eff和当量传热系数h_eq。同时，修正了传质因子j_m和传热因子j_h的计算式，将无量纲参数J（j_m/j_h）耦合至准稳态结霜模型中，从而对霜层特性参数进行了合理修正。为验证改进模型的预测准确性，与Lee模型、Lenic模型和Wong模型的计算结果以及7个典型实验工况的38组测量数据进行了对比验证。结果表明，该模型预测精度相较上述模型分别提升了31.81%、64.57%和50.64%。此外，模型预测值与典型工况下的实验数据吻合较好，所有工况下霜层厚度的平均误差小于6.57%，霜层密度的平均误差不足7.10%，霜层表面温度及结霜量的平均误差分别为8.41%和9.59%。

关键词: 相变, 传热, 传质, 准稳态结霜模型, 数值模拟

Abstract:

Based on the principle that phase change frosting is essentially heat and mass transfer, this study further considered the practical phenomena where the gradual reduction in frost layer porosity and the increase in thermal resistance leads to decreased water vapor diffusion capacity and heat transfer efficiency. To address these effects, the study introduced the concepts of effective diffusion coefficient (D_eff) and the equivalent heat transfer coefficient (h_eq). Additionally, the calculation formulas for the mass transfer factor (j_m) and heat transfer factor (j_h) were revised, and the dimensionless parameter J(j_m/j_h) was coupled into the quasi-steady frost formation model, leading to a reasonable correction of frost layer characteristic parameters. To verify the prediction accuracy of the improved model, comparisons were made between this model, the Lee model, the Lenic model, and the Wong model, as well as with 38 measured data sets from seven representative experimental conditions. The results show that the prediction accuracy of the improved model increased by 31.81%, 64.57% and 50.64%, respectively, compared to the aforementioned models. Furthermore, the predicted values of the improved model closely match the experimental data under typical conditions, with the average error of frost layer thickness below 6.57%, the average error of frost density under 7.10%, and the average errors of frost surface temperature and frost mass being 8.41% and 9.59%, respectively.

Key words: phase change, heat transfer, mass transfer, quasi-steady-state frosting model, numerical simulation

中图分类号:

TB 61

吴林凯, 林志敏, 王良璧. 基于热质传递效应的准稳态结霜模型改进及数值验证[J]. 化工学报, 2025, 76(8): 4004-4016.

Linkai WU, Zhimin LIN, Liangbi WANG. Improvement and numerical validation of quasi-steady-state frosting model based on thermal and mass transfer effect[J]. CIESC Journal, 2025, 76(8): 4004-4016.

图/表 12

图1 冷表面结霜解析域示意图

Fig.1 Schematic of the analytical domain of frosting on the cold surface

表1 关联式中经验参数的取值

Table 1 Values of empirical parameters in the correlation formula

参数	数值	参数	数值
a₀	-5.675×10³	b₀	-5.800×10³
a₁	6.393	b₁	1.391
a₂	-9.678×10^-3	b₂	-4.864×10^-2
a₃	6.212×10^-7	b₃	4.176×10^-5
a₄	2.075×10^-9	b₄	-1.445×10^-8
a₅	-9.484×10^-13	b₅	6.546
a₆	4.164

图2 数学模型求解流程图

Fig.2 Flowchart on solving the mathematical model

图3 霜厚模型值与Lenic模型[9]及实验[9-10,23]的对比

Fig.3 Comparison of calculated results of frost thickness against Lenic's model[9] and experiments[9-10,23]

图4 各修正项对霜厚预测精度的影响

Fig.4 Effect of each correction term on the accuracy of frost thickness prediction

图5 霜厚迭代计算值与Lee模型及实验[19]的对比

Fig.5 Comparison of iterative results of frost thickness against Lee’s model and experiments[19]

图6 霜厚计算值与Wong模型[31]及实验[25]的对比

Fig.6 Comparison of calculated frost thickness against Wong’s model[31] and experiments[25]

图7 霜厚模拟值与实验数据[30,32]的对比

Fig.7 Comparison of frost thickness between simulated and experimental results[30,32]

图8 霜密度模型值与实验值[25,32]的对比

Fig.8 Comparison of frost density between model’s results and experimental results[25,32]

图9 霜层表面温度计算值与实验值[19]的对比

Fig.9 Comparison of frost surface temperature between calculated and experimental results[19]

表2 不同工况下结霜量模拟值与实验数据［25］的对比

Table 2 Comparison of frost mass between the simulated and experimental results［25］ for different conditions

Run.	t/min	T_a/℃	φ/%	u_a/(m/s)	T_w/℃	传统模型		改进模型
Run.	t/min	T_a/℃	φ/%	u_a/(m/s)	T_w/℃	m_fr/g	Δm_fr/%	m_fr/g	Δm_fr/%
1	60	16	50	0.7	-5	0.84	24.77	1.04	6.31
2					-10	1.24	6.76	1.41	6.02
3					-15	1.56	1.62	1.66	7.79
4		22	80		-5	4.31	18.60	3.86	6.34
5					-10	4.88	26.88	4.25	10.39
6					-15	5.28	38.81	4.49	18.16
1*	120	16	50		-5	1.45	30.04	1.94	6.73
2*					-10	2.29	11.09	2.72	5.84
3*					-15	2.96	3.67	3.27	14.34
4*		22	80		-5	8.73	22.54	7.64	7.30
5*					-10	9.84	29.03	8.48	11.14
6*					-15	10.70	36.65	8.98	14.69

图10 不同参数工况下计算值与实验值的误差图

Fig.10 Error plots of the calculated results vs the experimental results for different operating conditions

参考文献 32

[1]	张毅, 张冠敏, 冷学礼, 等. 无霜空气源热泵技术研究进展[J]. 化工学报, 2020, 71(12): 5400-5419.
	Zhang Y, Zhang G M, Leng X L, et al. Research progress on frost-free air source heat pump technology[J]. CIESC Journal, 2020, 71(12): 5400-5419.
[2]	Zhu J H, Sun Y Y, Wang W, et al. A novel temperature-humidity-time defrosting control method based on a frosting map for air-source heat pumps[J]. International Journal of Refrigeration, 2015, 54: 45-54.
[3]	Jones B W, Parker J D. Frost formation with varying environmental parameters[J]. Journal of Heat Transfer, 1975, 97(2): 255-259.
[4]	童钧耕, 杨志斌. 结霜过程的变密度分析[J]. 低温工程, 1996(2): 14-18.
	Tong J G, Yang Z B. Variable density analysis of frost process[J]. Cryogenics, 1996(2): 14-18.
[5]	Yun R, Kim Y, Min M K. Modeling of frost growth and frost properties with airflow over a flat plate[J]. International Journal of Refrigeration, 2002, 25(3): 362-371.
[6]	Yang D K, Lee K S. Modeling of frosting behavior on a cold plate[J]. International Journal of Refrigeration, 2005, 28(3): 396-402.
[7]	张龙, 宋孟杰, 邵苛苛, 等. 管翅式换热器迎风侧翅片末端霜层生长模拟研究[J]. 化工学报, 2023, 74(S1): 179-182.
	Zhang L, Song M J, Shao K K, et al. Simulation study on frosting at windward fin end of heat exchanger[J]. CIESC Journal, 2023, 74(S1): 179-182.
[8]	Lüer A, Beer H. Frost deposition in a parallel plate channel under laminar flow conditions[J]. International Journal of Thermal Sciences, 2000, 39(1): 85-95.
[9]	Lenic K, Trp A, Frankovic B. Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger[J]. International Journal of Heat and Mass Transfer, 2009, 52(1/2): 22-32.
[10]	Armengol J M, Salinas C T, Xamán J, et al. Modeling of frost formation over parallel cold plates considering a two-dimensional growth rate[J]. International Journal of Thermal Sciences, 2016, 104: 245-256.
[11]	崔静. 结霜与抑霜机理研究及数值模拟[D]. 大连: 大连理工大学, 2011.
	Cui J. Study and numerical simulation of frost formation and frost suppression mechanism[D]. Dalian: Dalian University of Technology, 2011.
[12]	Wang Z P, Cui W Z, Li L J, et al. A numerical study of heterogeneous nucleation of ice crystals and frost layer growth on horizontal cold surfaces[J]. International Journal of Heat and Mass Transfer, 2024, 228: 125604.
[13]	Kim C, Lee J, Lee K S. Numerical modeling of frost growth and densification on a cold plate using frost formation resistance[J]. International Journal of Heat and Mass Transfer, 2017, 115: 1055-1063.
[14]	Wu X M, Chu F Q, Ma Q. Frosting model based on phase change driving force[J]. International Journal of Heat and Mass Transfer, 2017, 110: 760-767.
[15]	Hayashi Y, Aoki A, Adachi S, et al. Study of frost properties correlating with frost formation types[J]. Journal of Heat Transfer, 1977, 99(2): 239-245.
[16]	Padhmanabhan S K, Fisher D E, Cremaschi L, et al. Modeling non-uniform frost growth on a fin-and-tube heat exchanger[J]. International Journal of Refrigeration, 2011, 34(8): 2018-2030.
[17]	Na B, Webb R L. Mass transfer on and within a frost layer[J]. International Journal of Heat and Mass Transfer, 2004, 47(5): 899-911.
[18]	Yao Y, Jiang Y Q, Deng S M, et al. A study on the performance of the airside heat exchanger under frosting in an air source heat pump water heater/chiller unit[J]. International Journal of Heat and Mass Transfer, 2004, 47(17/18): 3745-3756.
[19]	Lee K S, Kim W S, Lee T H. A one-dimensional model for frost formation on a cold flat surface[J]. International Journal of Heat and Mass Transfer, 1997, 40(18): 4359-4365.
[20]	Wang C C, Chi K Y. Heat transfer and friction characteristics of plain fin-and-tube heat exchangers(part Ⅰ): New experimental data[J]. International Journal of Heat and Mass Transfer, 2000, 43(15): 2681-2691.
[21]	Yang D K, Lee K S. Dimensionless correlations of frost properties on a cold plate[J]. International Journal of Refrigeration, 2004, 27(1): 89-96.
[22]	Breque F, Nemer M. Modeling of a fan-supplied flat-tube heat exchanger exposed to non-uniform frost growth[J]. International Journal of Refrigeration, 2017, 75: 129-140.
[23]	Yang D K, Lee K S, Song S. Modeling for predicting frosting behavior of a fin-tube heat exchanger[J]. International Journal of Heat and Mass Transfer, 2006, 49(7/8): 1472-1479.
[24]	Zhang L, Song M J, Deng S M, et al. Frosting mechanism and behaviors on surfaces with simple geometries: a state-of-the-art literature review[J]. Applied Thermal Engineering, 2022, 215: 118984.
[25]	Hermes C J L, Piucco R O, Barbosa J R, et al. A study of frost growth and densification on flat surfaces[J]. Experimental Thermal and Fluid Science, 2009, 33(2): 371-379.
[26]	Wu X M, Ma Q, Chu F Q, et al. Phase change mass transfer model for frost growth and densification[J]. International Journal of Heat and Mass Transfer, 2016, 96: 11-19.
[27]	Chen G, Deng X Z, Zhang G, et al. Simulation of frost growth and densification on horizontal plates with supersaturated interface condition[J]. International Journal of Heat and Mass Transfer, 2019, 133: 426-434.
[28]	范晨, 梁彩华, 江楚遥, 等. 空气源热泵结霜/除霜特性的数值模拟[J]. 制冷技术, 2014, 34(1): 18-25.
	Fan C, Liang C H, Jiang C Y, et al. Numerical simulation of frosting/defrosting characteristics of air source heat pump[J]. Chinese Journal of Refrigeration Technology, 2014, 34(1): 18-25.
[29]	Xu Z M, Wang Z P, Liang Z, et al. A frost model based on the frost layer's supporting function[J]. International Journal of Heat and Mass Transfer, 2023, 202: 123741.
[30]	Zhang L, Jiang Y Q, Dong J K, et al. An experimental study on the effects of frosting conditions on frost distribution and growth on finned tube heat exchangers[J]. International Journal of Heat and Mass Transfer, 2019, 128: 748-761.
[31]	Wong J C Q, Pareek V K, Sun B. CFD analysis of phase change behaviour and frost growth under various conditions using mass transfer theory[J]. International Journal of Heat and Mass Transfer, 2022, 198: 123396.
[32]	Lee K S, Kim W S. The effects of design and operating factors on the frost growth and thermal performance of a flat plate fin-tube heat exchanger under the frosting condition[J]. KSME International Journal, 1999, 13(12): 973-981.