Modeling of frosting behavior on a cold plate

This paper proposes a mathematical model to predict the frost properties and heat and mass transfer within the frost layer formed on a cold plate. Laminar flow equations for moist air and empirical correlations for local frost properties are employed to predict the frost layer growth. Correlations for local frost density and effective thermal conductivity of the frost layer, derived from various experimental data, are expressed as a function of the various frosting parameters: the Reynolds number, frost surface temperature, absolute humidity and temperature of the moist air, cooling plate temperature, and frost density. The numerical results are compared with experimental data to validate the proposed model, and those agree well with the experimental data within a maximum error of 10%. Heat and mass transfer coefficients obtained from the numerical analyses are also presented. The results show that the model for the frost growth using the correlation of the heat transfer coefficient without considering the air flow has a limitation in its application.     

Modeling of frost growth and frost properties with airflow over a flat plate

A physical model of frost layer growth and frost properties with airflow over a flat plate at subfreezing temperature was developed. Frost roughness was measured, and an empirical correlation for the average frost roughness was suggested. Heat and mass transfer coefficients were calculated using the modified Prandtl mixing-length scheme containing the effects of both frost roughness and turbulent boundary layer thickness. Frost thermal conductivity was theoretically analyzed by solving the combined equations of air equivalent conductivity and thermal conductivity of the frost inner layer. Based on the present model, heat and mass transfer coefficient, frost thermal conductivity, frost thickness, frost mass concentration and frost density with time and space were estimated. The model showed good agreement with the basic trends of the test data taken from other literature. Spatial and temporal changes of heat flux and frost surface temperature were also investigated.     

间冷式冰箱蒸发器结霜模拟

针对间冷式冰箱蒸发器的结霜工况进行了模拟。在改进现有的计算霜表面水蒸气过饱和度公式的基础上,建立了适用于间冷式冰箱蒸发器的霜层生长模型,并模拟出结霜过程中的结霜量,空气侧压降,霜的密度和厚度随时间的变化。通过与实验数据的比较,结霜量的误差在10％以内,空气侧压降在25％以内,该模型能够有效的模拟间冷式冰箱蒸发器的结霜过程。     

Analysis of early-stage frost formation in natural convection over a horizontal cylinder

Frost growth process on a cold surface consists of two stages: The early-stage or one-dimensional growth of ice columns and multidimensional growth in the form of a porous structure. The transition time which marking these two stages is important for any numerical modeling of frost formation. This paper proposes a mathematical model to predict the transition time and frost properties in natural convection of frost formation over a cooled horizontal cylinder in the first stage of growth period. Comparison is performed among the results of this model and experimental observations reported in the literatures. It is observed that the presented model can be used more efficiently to determine transition time and frost properties in the early-stage of frost formation. Based on the obtained results a new correlation is developed for the duration time of early-stage of frost formation process (transition time) in natural convection.     

Modeling of a fan-supplied flat-tube heat exchanger exposed to non-uniform frost growth

Reversible heat pumps for electric vehicles are being developed by the car industry to address cabin heating and improve energy efficiency compared to electric heaters. For this new application, the front, louvered-fin, microchannel heat exchanger (MCHX or flat-tube heat exchanger) of the A/C system happens to operate as an evaporator under frosting conditions. MCHX are particularly sensitive to frosting, and a model is required to improve the design. This paper presents a dynamic pseudo 3D model of a fan-supplied MCHX which predicts non-uniform frost growth, air pressure losses, airflow rate and thus, thermal performances. The air pressure losses are computed considering the maximum frost thickness along each air channel. A correlation was developed to take into account frost effects on the friction factor. The model was validated against ad hoc experimental data and was also able to predict experimental data from the literature.     

翅片管式换热器表面结霜特性的数值分析和实验研究

换热器表面结霜会增加传热热阻和流动阻力，为了合理确定融霜周期，必须对其结霜特性做深入地了解。本文采用了数值求解方法预测了翅片管式换热器的结霜量和霜层密度的变化过程。翅片管结霜是一个瞬变问题，为了计算方便，将其简化为准稳态过程，即在时间步长内，认为该过程是稳定的，然后把所得的霜层厚度以及霜层的表面温度作为下一时间步长内传热传质的边界条件。在研究中考虑了霜层阻力引起风量下降这一因素，计算结果与翅片管式换热器结霜的实际工况相符。     

翅片管式换热器表面结霜特性的数值分析和实验研究

换热器表面结霜会增加传热热阻和流动阻力,为合理确定融霜周期,必须对其结霜特性作深入的了解。文中采用了数值求解方法预测了平翅翅片管式换热器的结霜量和霜层密度的变化过程。翅片管结霜是一个瞬变问题,为了计算方便,将其简化为准稳态过程,即在时间步长内,认为该过程是稳定的,然后把所得的霜层厚度以及霜层的表面温度作为下一时间步长内传热传质的边界条件。在研究中考虑了霜层阻力引起风量下降这一因素,模型的计算结果与翅片管式换热器结霜的实际工况相符。     

Frost formation and heat transfer on circular cylinders in cross-flow

When humid air comes into contact with a surface whose temperature is below the dew point of water vapour in air and also below the freezing point, frost deposition takes place over the surface. Previous studies indicate that the heat transfer rate increases at the initial stages of deposition since the rough frost surface acts as a finned one. As the frost thickens, however, the insulating effect of the frost layer predominates resulting in a reduction in the heat transfer rate. This paper presents a transient model to predict the frosting process over a circular cylinder in a cross-flow of humid air. the transfer parameters are computed employing a numerical solution of the momentum, energy and diffusion boundary-layer equations along with the continuity equation, using a finite difference scheme. Empirical correlations for thermal conductivity and density are utilized for closure purposes. Model results are compared with existing experimental data and with numerical data of previous investigators and are found to agree well in the applicable temperature and humidity ranges of the frost density and conductivity correlations.     

基于分形论的深冷翅片管气化器结霜数值模拟

利用分形理论DLA模型,建立翅片管气化器深冷表面霜层生长模型,通过控制程序循环次数模拟了深冷表面霜层生长不同阶段。结合实验观测到的深冷表面霜层生长过程,从分形维数和霜层密度两个方面验证数值模拟的合理性。结果表明,结霜初期随着初始霜枝晶上不断长出分枝晶,霜层密度随厚度的增大而减小,且深冷表面上霜层分形维数较一般冷表面分形维数大,说明深冷表面霜的生长更加复杂,充满空间的能力更大。这对进一步理解空温式深冷翅片管气化器表面结霜机理,探索有效除霜方法,提高气化器换热特性有重要意义。     

A semi-empirical correlation for predicting the frost density on hydrophilic and hydrophobic substrates

A new semi-empirical correlation for the prediction of frost density on hydrophilic and hydrophobic surfaces is proposed. The proposed correlation is a function of the modified Jakob number and contains two correction terms, one for surface contact angle and another for relative humidity. Whereas most frost correlations exclude surface wettability as a parameter, our research has shown that the surface contact angle can be important when trying to accurately predict the properties of a growing frost layer. The correlation was developed using data from three different surfaces. On each surface, the frost was grown for three hours and then defrosted. The proposed correlation predicted more than 93% of the data to within a ±20% error band and is proposed for use on surfaces with contact angles 45° < θ < 160°, relative humidity 0.40 < ϕ < 0.80, and plate temperatures −13 °C < T_w < −5 °C under natural convection conditions.     

Modeling of frost formation over parallel cold platesModélisation de la formation de givre sur les plaques froides parallèles

This paper numerically evaluates some of the parameters involved in modeling the process of frost formation on flat cold surfaces subject to the flow of humid air. The model employs one-dimensional transient formulation based upon the local volume averaging technique. The modeling process was validated by comparison with available experimental data. Numerical experiments were realized to determine the best initial values of the diffusivity, initial radius and geometry of the ice crystals. This model was applied to the known case of flow of humid air over a single flat cold plate to predict the frost temperature, density and thickness distribution along the flow direction and also the void fraction. The results were compared with available results in the literature. The model was then extended to solve the case of flow of humid air between two parallel cold plates for which there are no available results.     

Heat and mass transfer under frosting conditions

The effect of frost formation on heat transfer between a test cylinder and its gaseous environment was studied experimentally. The main parameters discussed in the paper are: the total heat flux, the steady-state convective heat transfer coefficient, and the mass of frost adhering to the test cylinder. The emphasis of the paper is on the thermal conducivity of frost. The data indicate that the diffusion mechanisms of moisture transfer within the frost layer causes the frost density and thermal conductivity to increase with time. Frost thermal conductivity is a function of the local temperature and average density. The can be used by designers of low temperature systems with uninsulated surfaces.     

结霜过程的变密度分析

采用分子扩散模型对结霜过程进行数学描述。在支配方程推导及求解过程中，采用了霜层变密度分析并了据试验数据拟合的传质系数。计算结果表明，霜层厚度及霜层密度，与试验数吻合较好。     

Modeling spatial and temporal frost formation with distributed properties on a flat plate using the orthogonal collocation method

In this paper the orthogonal collocation method is used to solve the equations that describe the frost formation process when a cold flat plate is exposed to a humid air stream. The proposed scheme combines a front-fixing method to handle the moving boundary with the orthogonal collocation method to discretize and solve the resulting set of partial differential equations. Time and spatial variations of frost properties such as porosity and density as well as other relevant variables such as the frost thickness, frost temperature, and heat flux through the frost layer – are predicted with the proposed method. Model results were found to agree closely with available experimental data.     

Electronic expansion valve mass flow rate prediction based on dimensionless correlation and ANN model

Refrigerant mass flow rate through electronic expansion valve (EEV) makes significant sense for refrigeration system intelligent control and energy conservation. Objectives of this study were to present experimental data of R134a mass flow rate through EEV and to develop models for EEV mass flow rate prediction via two approaches: dimensionless correlation based on Buckingham π-theorem and artificial neural network (ANN) model based on dimensionless parameters. The database utilized for model training and test was comprised of our experimental data and data available in open literatures including R22, R407C, R410A and R134a. Compared with three existing dimensionless correlations, the proposed dimensionless correlation and ANN model demonstrated higher accuracy. The proposed dimensionless correlation gave mean relative error (MRE) of 6.60%, relative mean square error of (RMSE) 12.05 kg h⁻¹ and correlation coefficient (R²) of 0.9810. The ANN model with the configuration of 8-6-1 showed MRE, RMSE and R² of 3.97%, 7.59 kg h⁻¹ and 0.9924, respectively.     

Dynamic modeling and characteristic analysis of a two-stage vapor injection heat pump system under frosting conditions

This paper presents a distributed-parameter dynamic heat exchanger model integrated with a detailed frost growth model to account for non-uniform frost formation on a fan-supplied finned-tube coil. A novel, iteration-free approach is proposed to solve the air flow redistribution by linearizing a system of non-linear air pressure drop equalization equations, resulting in a significant improvement in the computational efficiency. As a continuation and extension of our previous work, the developed models along with the component models described in Qiao et al. (2015a) are applied for the first time to explore the frosting dynamics of a two-stage flash tank vapor injection heat pump system. It is found that frost formation degrades the heating performance of the system substantially. Meanwhile, the simulation indicates that air and refrigerant flow maldistribution, resulting from non-uniform frost growth on the outdoor heat exchanger, can lead to unstable system hunting behavior. Comparisons between the simulation results and experimental data indicate that the proposed models can reasonably predict the time-dependent heat transfer and fluid flow phenomena of the system.     

Simulation based identification of the ideal defrost start time for a heat pump system for electric vehicles

Resistance heating with PTC elements to cover the heat demand of electric vehicles reduces significantly the cruising range at low outside temperatures. Reversible heat pump systems are one of the most promising solutions for this problem. However, in heat pump mode the frost formation on the exterior heat exchanger reduces the performance and efficiency of the system. Therefore, an efficient defrost method is crucial to benefit from the heat pump also under frosting conditions. In the present paper, a transient Modelica simulation model of a reversible CO₂-heat pump system with hot gas defrost was set up in order to assess the impact of different defrost start times. The model is able to handle frost growth on the exterior heat exchanger as well as defrosting. The simulation results showed an optimal point of time to conduct defrost at chosen operating conditions in order to maximize the average COP including the frosting and defrost period.     

Experimental investigation of adverse effect of frost formation on microchannel evaporators,part 1: Effect of fin geometry and environmental effects

This study experimentally investigated the frost growth on louvered folded fins in microchannel heat exchangers when used in outdoor air-source heat pump systems. The effects of surface temperature, fin geometries, and air environmental conditions were studied. The overall aim was to isolate and quantify the effect of geometry from surface temperature effects. Experimental data of frost weight, local frost thickness, air pressure drop across the coils, time of frost–defrost cycles and heat transfer rates were recorded. Data showed that the frosting time and the frost growth rates depended mainly on the local fin surface temperature. Lower fin density was beneficial because it delayed the blockage of the air flow. The fin length and fin depth had minor effects on frosting performance. The air humidity had a fairly significant effect on rate of frost formation while air velocity seemed to have a small effect on the frost growth rate.     

Prediction of frost deposition on a horizontal circular cylinder under natural convection using artificial neural networks

In the present work Artificial Neural Network is used to predict frost thickness and density around a cooled horizontal circular cylinder having constant surface temperature under natural convection for different ambient conditions. The database for ANN generated from the experimental measurements. In the present work a multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth due to accurate and faster training procedure. Experimental measurements are used for training and testing the ANN approach and comparison is performed among the soft programming ANN and experimental measurements. It is observed that ANN soft programming code can be used more efficiently to determine frost thickness and density around a cold horizontal cylinder. Based on the developed ANN wide range of frost formation over various cylinder diameters are determined and presented for various conditions.     

A generalized dimensionless local power-law correlation for refrigerant flow through adiabatic capillary tubes and short tube orifices

This paper presents a new method to obtain generalized dimensionless correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. The dimensionless Pi groups were derived from the homogeneous equilibrium model, which is available for different refrigerants entering adiabatic capillary tubes or short tube orifices as the subcooled liquid, two-phase mixture, or supercritical fluid. To mitigate the potential over-fitting risk in neural network, a new “local” power-law correlation reformed from the homogeneous equilibrium model was proposed and compared with the conventional “global” power-law correlation and recently developed neural network model. About 2000 sets of experimental mass flow rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions were collected for the model development. The comparison between the recommended six-coefficient correlation and experimental data reports 0.80% average and 8.98% standard deviations, which is comparable with the previously developed neural network and much better than the “global” power-law correlation.