Mass transfer on and within a frost layer

This paper investigates fundamental phenomena related to understanding of frost deposition and growth. The water vapor mass transfer rate from the air stream to a frost surface was tested and the results analyzed. The water vapor pressure at the frost surface was found to be supersaturated, and this phenomenon is explained using laminar concentration boundary layer analysis. A simple equation for calculating the supersaturated water vapor density at the frost surface was developed using boundary layer analysis, and it was compared to the experimental data. The comparison showed that the proposed equation for the water vapor supersaturation degree at the frost surface agrees well with the experimental data. The physical meaning of the tortuosity factor, which is related to mass diffusion within the frost layer, is mathematically explained, and published correlations were reviewed. It was found that some existing correlations are basically empirical curve fits that force agreement of the frost growth rate with the measured values. Further, these empirical curve fits do not satisfy the known physical bounds on the tortuosity factor. This deficiency further supports the existence of supersaturation at the frost surface. The effect of uncertainty in tortuosity factor on the heat transfer rate through a frost layer was quantitatively analyzed, and it was found that its uncertainty does not significantly affect the heat transfer rate through the frost layer in typical frosting conditions.     

New model for frost growth rate

Many models have been published to predict frost growth. These may be divided into empirical and theoretical models. All prior theoretical models assume the water vapor is saturated at the interface between the air stream and frost layer. This paper provides a new theoretically based numerical model of frost deposition and growth. The present model: (1) uses supersaturated water vapor at the frost surface, which is fundamentally correct; (2) improved correlations for frost thermal conductivity; (3) uses a rationally based tortuosity factor; and (4) calculates the local frost density variation. For numerical simulation of the frost growth rate, the measured thermal conductivity was used. Frost growth rate on a cold surface was measured, and the experimental data were compared to the numerical model and agreed within 15%. The proposed supersaturation model was also compared to previous investigators’ experimental data, and it was found that the supersaturation model is superior to analytical or numerical models that assume the water vapor at the frost surface to be saturated.     

An experimental study of the effect of air quality on frosting on cold flat surface

The effects of air quality in the freezing process of droplets and the frost crystal growth on cold flat plate are studied experimentally. It is found that the air quality has important influence in the frosting process. The supercooling degree and freezing time change with solution concentration on different solutes. When supercooled droplets are in the instability state, the composition and concentration of solution can affect the nucleation and heat transfer, and most of the solute can increase the degree of supercooling and accelerate the freezing process. Solutions with cation of strong electrolyte have higher supercooling degree because the weak cation will hydrolyze. The hydrated ion can accelerate the formation of ice crystal. In addition, the frosting process on cold flat plate under different fine particle (PM2.5) concentrations is also studied in form of frost height and mass variations. The result shows that the greater the PM2.5 concentration is, the thicker the frost layer is and the greater the amount of the frost crystal is. This is because suspended particles in the air that can act as nucleating substrate to promote heterogeneous nucleation and the frost crystals are more easily deposited.     

An experimental investigation on frosting characteristics of a microchannel outdoor heat exchanger in an air conditioning heat pump system for electric vehicles

To increase the driving range of electric vehicles in cold climate, air conditioning heat pump (ACHP) system is supposed to be the most effective solution. Working near 0°C with high humidity, the microchannel outdoor heat exchanger (OHX) in system would experience badly frosting process, like traditional residential heat pump system. It would lead to a significant reduction of system performance without defrosting in time. In this article, experimental investigation has been implemented on the frosting process of ACHP system of electric vehicles which is with a microchannel OHX. The phenomenon of frosting distribution was observed, the frosted part on surface shows uneven with various flows paths. The typical frosting characteristics of an outdoor microchannel heat exchanger were also obtained. In a self-designed three-heat exchanger ACHP system, the inlet and outlet refrigerant temperature of OHX as well as the outlet air temperature of system decrease with increasing frosting coverage rate. The frosting phenomenon was analyzed with variation of ambient temperature and humidity. System influence by frosting was also studied with under different ambient conditions. When OHX begins to frost, the heating capacity reduction of system under different ambient conditions were both increased but the differences in the coefficient of performance (COP) variations under different ambient conditions were small as frosting progressed.     

Experimental investigations of frost release by hydrophilic surfaces

Frost formation occurs when water vapor in the surrounding air comes into contact with cold surfaces through heat and mass transfer. It is usually an undesirable phenomenon in most refrigeration and cryogenic systems. A few studies have shown that changing the surface energy, such as increasing the surface hydrophilicity or hydrophobicity, has significant effects on frost growth. In this paper, a kind of hydrophilic polymer paint is formulated to counteract frost deposition on cold surfaces. The coated surface can retard frost formation up to three hours under low plate temperatures (− 15.3°C) and high air humidity (72%). To test the antifrosting performance of the hydrophilic paint under more practical conditions, it is applied to a fin-and-tube heat exchanger and a domestic refrigerator at a coating thickness of 30 μm. Comparisons of frost deposition, pressure drops, and outlet temperatures are made between uncoated and coated heat exchangers. Under conditions of high air temperature (2.2°C) and relative high air humidity (90%), the paint prolongs the defrosting interval from 80 to 137 min. Experimental observations also show that the coated hydrophilic fins are free of frost deposition during the entire course of the test and that the coating has no significant additional thermal resistance.     

翅片管式蒸发器结霜性能的仿真与实验研究

建立了结霜条件下翅片管蒸发器空气侧流动和换热的分布参数仿真模型,模型考虑了蒸发器结构、霜层厚度以及湿空气状态等参数在气流方向的沿程变化.对冰箱冷冻室蒸发器结霜条件下的动态性能进行了试验研究和数值模拟.结果表明,蒸发器结霜过程中的结霜量、能量传递系数和空气侧压降的计算值和试验值吻合良好,证明模型可以应用于翅片管蒸发器结霜性能的正确预测和优化设计分析.     

Frosting of heat pump with heat recovery facility

This paper aims to prolong the heat pump frost time and reduce its growth with heat recovery facility, which should mix the exhausted indoor and outdoor air before entering the evaporator. An ideal mathematic model is developed for heat transfer, frost generation and airside pressure drop. The properties of the mixture would be obtained by solving the mass and energy conservation equations. A parametric analysis is performed to investigate the effects of air inlet temperature, relative humidity and air mass flow rate on total heat transfer coefficient, frost thickness and airside pressure drop, respectively. The results show that rationalizing the ratio of indoor and outdoor air could prolong frosting time and reduce the frost thickness greatly. The total heat transfer coefficient, frost thickness and airside pressure drop increase monotonically with time going, but are not proportional. Decreasing the mixture inlet air temperature and relative humidity could essentially reduce frost growth on the tube surfaces. This can also be observed when increasing the air mass flow rate.     

Visualization of Effects of Ultrasound on Liquid Droplet Solidification and Frost Formation on Cold Flat Surface

An experimental study was conducted to study the effect of ultrasonic vibrations on frost suppression on a cold flat surface in atmospheric air flow. A microscopic visualization on the liquid droplet solidification and frost formation process with and without the effect of 20-kHz ultrasound was made. The water droplets solidification and frost crystal growth on the solidified water droplet surface were comparatively observed. Meanwhile, the frost thickness variations were comparatively analyzed. It was found that almost no difference can be seen between the water droplet solidification onset time with the effect of ultrasound and that without the effect of ultrasound. However, after the water droplet solidifies, almost no growth of the frost crystal can be observed on the solidified water droplets surface with the effect of ultrasound. In addition, during the whole frost formation progress, very small growth of the frost layer can be seen on the flat surface with the effect of ultrasound. The experimental results showed that the frost growth process on the cold flat surface can be significantly restrained due to the effect of ultrasound.     

Frosting and defrosting characteristics of a fin according to surface contact angle

We investigated the characteristics of frosting and defrosting on a fin according to its surface contact angle under the winter operating conditions of a heat pump. The static contact angles were 2.5°, 75°, and 142° for hydrophilic, bare, and hydrophobic surfaces, respectively. The frost layer exhibited different frost formations for different surface contact angles during the early stages of frost formation. Frost retardation was observed on the hydrophobic fin, but the effect was not significant. The frost layer was thinner and the average frost density was higher on the hydrophilic surface than on the other surface-treated fins. The effect of surface treatment on defrosting time was found to be insignificant. However, the ratio of residual water on the hydrophilic surface was significantly smaller than those on the other surfaces. Because of this, in repeated frosting/defrosting experiments, the fin of the hydrophilic surface was found to show almost the same frosting/defrosting behaviors as those of the first run.     

Dimensionless correlations of frost properties on a cold cylinder surface

We propose dimensionless correlations for frost properties on a cold cylinder surface. Frosting experiments were performed while changing various frosting parameters such as the air temperature, cold cylinder surface temperature, air velocity, and absolute humidity. The experimental data showed that a uniform frost layer grew around the circumference of the cylinder at a high air velocity. Dimensionless correlations for the thickness, density, and surface temperature of the frost layer, and for the heat transfer coefficient were obtained as functions of the Reynolds number, Fourier number, absolute humidity, and dimensionless temperature. The applicable ranges of these correlations are Reynolds number of 700–3000 (air velocities of 0.5–2.0 m/s), Fourier number of 56.8–295.7 (operating time of 0–100 min), absolute humidity of 0.00280–0.00568 kg/kg_a, air temperatures of 3–9 °C, and cold cylinder surface temperatures of ?32 to ?20 °C. The proposed correlations agreed with the experimental data within an error of 15%.     

肋片管式换热器过饱和假设下结霜数学模型的建立

在空气和霜层之间为过饱和空气假设的基础上，针对平肋肋片管式换热器的结霜过程，建立了数学模型，考虑了霜层密度变化和霜层阻力引起空气流量减小等因素，并将结霜模型与换热器传热特性模型有机地结合起来。     

Prediction of the frost formation on a cold flat surface

A mathematical model is presented to predict the behavior of frost formation by simultaneously considering the air flow and the frost layer. The present model is validated by comparing with several other analytical models and our experiments. It is found that most of the previous models cause considerable errors depending on the working conditions or the correlations used in predicting the frost thickness growth, whereas the model in this work estimates the thickness, density, and surface temperature of the frost layer more accurately within an error of 10% except the early stage of frosting in comparison with the experimental data. Numerical results are presented for the variations of heat and mass transfer during the frost formation and for the behavior of frost layer growth along the direction of air flow. Also, a correlation between the convective heat and mass transfer is obtained as Le⁽¹⁻ⁿ⁾=0.905±0.005 in this work.     

A fundamental understanding of factors affecting frost nucleation

Theoretical analysis of the nucleation process for frost formation on a cold surface shows that the air at the cold surface should be supersaturated in order for frost nucleation to occur. This understanding is new, relative to previously published frost growth models. Further, the supersaturation degree is dependent on the surface energy, which is related to the water contact angle. The theoretical predictions were compared to experimental results, and reasonable agreement was obtained. Qualitatively, a low energy surface (high contact angle) requires higher supersaturation degree for frost nucleation than a high energy surface. Quantitatively, the experimental data shows that the low energy surface requires approximately 10 times higher supersaturation degree than the high energy surface when the contact angle difference is approximately 80° at −20 °C surface temperature. The factors affecting the surface energy such energy such as temperature, surface roughness, and foreign particles are discussed in this paper.     

Frost distribution characteristics of laminar airflow on cold surface of mini-channels

This study was performed for simulating frosting characteristics that occurred on the surface of plate fins of the outside heat exchanger. Test section with local cooling modules at the central part was made as the rectangular cross sectional passage to imitate the outside heat exchanger. Local frost thickness distributions for test conditions having three experimental parameters (plate wall temperature, air humidity and velocity) were presented. Leading edge effect of the plate was clearly confirmed from the measured frost thickness distributions. The central part of the plate had the highest frost thickness because cooling devices were installed at the center of the plate. Due to different heat and mass transfer characteristics of upstream flow and downstream flow, the frost thickness of upstream area was much higher than that of downstream. The effects of plate surface temperature, humidity and velocity of inlet flow on frost thickness, and sensible and latent heat fluxes were analyzed.     

Experimental study on behavior of initial frost crystal formation under lower water vapor pressures

This paper studies the fashion in which the initial ice crystals form on the surface under lower water vapor pressures. The fashion affects greatly the ensuing frost growth. A unique fashion of ice crystal formation was observed. Some kind of unknown surface property, but not roughness and maybe more microscopic than roughness, determined the possibility of the surface to induce frosting. There were a limited number of sites with such kind of property on the surface. Improving the conditions of those sites is possible to avoid or delay the induction of deposition.     

Effects of air flow maldistribution on refrigeration system dynamics of air source heat pump chiller under frosting conditions

The effects of air flow maldistribution on the performance of an air source heat pump chiller under frosting conditions were investigated experimentally. The results indicated that air flow maldistribution was the dominant factor leading to hunting of the thermostatic expansion valve for medium and/or large size finned tube evaporators. With air flow maldistribution degree (AMD) increasing, frost occurred earlier, and the frost layer grew faster. The operating characteristics became lower when AMD was increased. We found such phenomenon seemed to be related to both the difference of refrigerant outlet superheat and the frosting velocity. In the hunting stage, the frost block effect became the main factor degrading the refrigeration system performance. With AMD increasing, the heat pump system pertinent performance data (suction pressure, evaporation temperature, discharge pressure, refrigerant outlet temperature, etc.) were degraded more dramatically.     

Experimental investigation on the performance of air cooler under frosting conditions

Evaluation of heat transfer performance of the air cooler under frosting conditions is of great importance for the refrigeration industry. In this paper, effects of frost growth on the performance of the air cooler have been studied with an experimental air cooler of industrial size with different fin spacings, i.e., 6, 8 and 10 mm. Results showed that factors affecting the heat transfer performance of the air cooler include the evaporation temperature, the frost height, the fin spacing and the air velocity. The overall heat transfer coefficients based on a logarithmic mean temperature difference (LMTD) and the energy transfer coefficients based on a logarithmic mean enthalpy difference (LMED) were calculated. As the frost accumulated on the air cooler, the overall heat transfer coefficient and energy transfer coefficient will drop gradually.     

Experimental study of natural frost formation over a horizontal tube with annular compact fins under natural convection

This paper presents experimental measurements of natural convection heat transfer and frost deposition over a horizontal fin‐tube. Measurements are made for a fin‐tube of diameter 25.4 mm, fin thickness 0.4 mm, fin center diameter 56 mm, and fin spacing 2 mm. For measurements the ambient air temperature and relative humidity are changed from 18 to 25°C and from 35% to 55%, respectively. The tube surface temperature is changed from –5 to –9 °C, and super cooling degrees of 7.5 to 24.5 °C. Results include a visualization of frost deposition growth, frost accumulation rate, and heat transfer rate with respect to time for each experiment. The results show that cold air starts from the upper point and moves downward and frost deposition starts on the fin tips, and grows with time both radially and angularly. Frost growth thickness changes significantly from top to bottom, where the boundary layers of both thermal and concentration increase at the bottom of the fin‐tube section without considerable separation. Frost growth only takes place on the fin's tip and it blocks the heat and mass transfer from the fin surfaces and the tube base which reduces convection and frost growth considerably. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20397     

Modeling for predicting frosting behavior of a fin–tube heat exchanger

A mathematical model is proposed to evaluate the frosting behavior of a fin–tube heat exchanger under frosting conditions. Empirical correlations of the heat transfer coefficients for the plate and tube surfaces and a diffusion equation for the frost layer are used to establish the model. The correlations for the heat transfer coefficients, derived from various experimental data, were obtained as functions of the Reynolds number and Prandtl number. The proposed model is validated by comparing the numerical results with experimental data for the frost thickness, frost accumulation, and heat transfer rate. The numerical results agree well with the experimental data. It is also found that this model can be applied to evaluate the thermal performance of a common fin–tube heat exchanger under frosting conditions.     

Frost formation on a bionic super‐hydrophobic surface under natural convection conditions

A bionic super‐hydrophobic surface has a multiple micro‐nano‐binary structure (MNBS) similar to the lotus leaf surface microstructure. This kind of surface has a contact angle of water greater than 150^° and a roll angle smaller than 5^°. In this paper, the frost deposition phenomena on a bionic super‐hydrophobic surface were observed. The surface has many micro bumps and its contact angle is 162^°. The formation of water droplets, the droplet freezing process, the formation of initial frost crystals and the frost layer structure on a cold bionic super‐hydrophobic surface under natural convection conditions were closely observed. The frost layer structure formed on the super‐hydrophobic surface shows remarkable differences to that on a plain copper surface: the structure is weaker, looser, thin, and easily removed and most importantly, it is of a very special pattern, a pattern similar to a chrysanthemum, a frost layer structure that has not been reported before to the best of the present authors knowledge. The experimental results also show that a super‐hydrophobic surface has a strong ability to restrain frost growth. The frost deposition on this bionic surface was delayed 55 minutes when compared with a plain copper surface under the conditions of a cold plate temperature of ?10.1^°C, air temperature of 18.4^°C, and relative humidity of 40%. A theoretical analysis was also presented to explain the observed phenomena. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 412–420, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20216