Improvement and numerical validation of quasi-steady-state frosting model based on thermal and mass transfer effect

doi:10.11949/0438-1157.20250003

Abstract

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

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

CLC Number:

TB 61

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.

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.

Figures/Tables 12

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

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

Fig.2 Flowchart on solving the mathematical model

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

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

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

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

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

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

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

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

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

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