Frost Growth Rate Research Articles

Experimental study of relative humidity effect on the edge effect of frosting characteristics on a vertical cold plate surface

As a common phenomenon, frosting often brings negative impacts in various fields. To gain more insight into the frosting process on a vertical cold plate considering the edge effect, a specific experimental system is designed and built to perform frosting experiments under forced convection conditions with relative humidity varying from 40% to 80%. The results show that as the relative humidity increases, the droplet solidification stage period in the unaffected region decreases, but the equivalent width of edge-affected region, area-average equivalent contact diameter of droplets, and coverage area ratio of droplets increases and then decreases. The area-average equivalent diameter of droplets in edge-affected region increases by 41.25%, 214.63%, 137.98%, 159.03%, and 30.30%, when compared to the unaffected region from Case 1 to Case 5, respectively. Besides, the difference between the droplet distribution density in the edge-affected and unaffected regions gradually decreases, but the average frost layer thickness in the edge-affected region increases significantly as the relative humidity increases. The frost layer growth rate decreases first and then increases as relative humidity increases. From Case 1 to Case 5, the frost growth rates at 1,800 s decrease by 90.05%, 70.19%, 56.08%, 62.28%, and 82.39%, respectively, compared to the initial ones. Results of this study can provide a reference for the anti-frosting and defrosting control technologies in the field such as refrigeration and air source heat pump units.

Numerical simulations of frost growth using mixture model on surfaces with different wettability

Frost growth on cold surfaces is a transient process with coupled heat and mass transfer. Due to multiple factors such as humidity, temperature, flow velocity, and constantly changing thermal properties as frost grows, precise prediction can be challenging. Especially when the geometry of the frosting surfaces gets complicated, it requires a balance of computing accuracy and efficiency. In this work, a numerical model is developed to predict frost growth considering the effect of the above parameters. Mixture model is adapted to improve computational efficiency and the unstructured grids add the flexibility to extend the model to complex geometries. The predicted frost growth rate matches well with the experimental data reported in the literature under similar conditions. The model predicts a reasonable growth trend of frost as the surface temperature, air temperature, humidity, and flow velocity vary. The surface wettability effect is well captured at the early stage of frosting and it shows a higher frost growth rate on surfaces with a higher wettability.

Heat transfer in the regenerative heat exchanger

This paper tackles the issue of frost formation in non-hygroscopic rotary heat exchangers used for energy recovery from exhaust air under high-speed rotor conditions by means of numerical simulations and experimental approaches. On the basis of some idealized assumptions, a frost growth submodel is presented to predict the behavior of the rotary heat exchanger under frosting conditions. Frost formation is modeled by considering the mass diffusion of water vapor through the frost layer, taking into account supersaturation phenomena. Calculations were carried out using a three-zone model based on the modified ε-NTU method. The local heat transfer coefficient and the NTU calculation method resulting from the influence of the heat exchanger entrance region were also applied. The obtained correlations for the temperature effectiveness agree with the simulation data within uncertainty bounds. The results of the numerical simulations allowed us to determine the outdoor air conditions that initiated the frost accumulation phenomenon inside the thermal wheel for two values of return air relative humidity: RH2i=20% and RH2i=40%. In both cases, the threshold temperature for unsafe operating conditions increases with increasing relative humidity of the outdoor air. Under ‘frost accumulation’ operating conditions, the frost growth rate is approximately five times higher at RH2i=40% than at RH2i=20%. In this regard, the need to implement frost protection techniques increases significantly with an increase in relative humidity of return airflow. Further analysis conducted for the operation of a thermal wheel’s operation under frosting conditions revealed that a latent heat flux contributed to the local frost density should not be neglected in a compact heat exchanger’s model. Interestingly, the operation time of the rotary heat exchanger, and hence the growth of the thickness of the frost layer, has a significant influence on a local heat transfer coefficient α, however, it does not affect the Number of Transfer Units (NTU) visibly.

Experimental Study on Frost Crystal Morphologies and Frosting Characteristics under Different Working Pressures

Frost usually grows on the cooling surface of heat transfer equipment, which often operates under different working pressures. In such conditions, one of the fundamental influencing factors of frosting, the diffusion coefficient of water vapor around the cooling surface, is different from that in the normal atmosphere pressure. In order to investigate the pressure effect on frosting, a test rig for frosting visualization is designed. The role of working pressure around the cooling surface on the frost crystal morphologies and frost layer characteristics is evaluated under different air parameters and temperatures of cooling surface. The vertical growth and lateral distribution of frost crystals are strongly related to working pressure around the cooling surface. More frost crystal morphologies and faster growth rate of frost layer are presented at a lower pressure. The frost thickness, frost accumulation and density reduce with higher pressure. The dimensionless correlation of frost thickness is proposed considering working pressure around the cooling surface, humid air parameters, and temperature of cooling surface.

Wettability-defined frosting dynamics between plane fins in quiescent air

Finned heat exchangers used in energy applications regularly undergo condensation frosting. Understanding the effects of fin spacing on frost growth with surfaces having differing wettability is important for the design of next-generation heat exchangers. This study presents an experimental investigation using high-resolution optical imaging of frost growth between two parallel vertical plain aluminum fins as a function of surface wettability (hydrophilic, superhydrophilic, superhydrophobic), fin surface temperature (-5 to -15 °C), fin spacing (2 to 8 mm), and relative humidity (≈ 50 and 70%). We observe two distinct regimes of frost growth for all test conditions. The effect of surface wettability on frost growth rate becomes significant for fin spacing ≤ 6 mm at fin surface temperatures below -10 °C. The fin surface temperature plays a significant role for fin spacing > 4 mm. Furthermore, for hydrophilic surfaces, the effect of relative humidity was found to be significant for fin spacing > 4 mm. To explain the frosting physics and mass transfer effects, we developed a three-dimensional finite volume method simulation to characterize the moist air flow field between fins at varying fin spacings. For similar humidity, fin surface temperature, and wettability, larger fin spacing resulted in higher frost growth rate due to higher access to moist air. We use the experimental data to develop an empirical correlation for predicting frost thickness. Furthermore, we develop an artificial neural network independent of predetermined functional form that can be trained with the experimental data to predict frost thickness with high accuracy.

Delayed Frost Growth on Nanoporous Microstructured Surfaces Utilizing Jumping and Sweeping Condensates.

Self-propelled jumping of condensate droplets (dew) enables their easy and efficient removal from surfaces and is essential for enhancing the condensation heat transfer coefficient and for delaying the frost growth rate on supercooled surfaces. Here, we report the droplet-jumping phenomenon using nanoporous vertically aligned carbon nanotube (VA-CNT) microstructures grown on smooth silicon substrates and coated with poly-(1H, 1H, 2H, 2H-perfluorodecylacrylate) (pPFDA). We also report droplet-sweeping phenomenon on horizontally mounted surfaces, concluding that the frost surface coverage area and the frost growth rates observed with the droplet-sweeping phenomenon are much lower than those that are observed with the droplet-jumping phenomenon alone. We also investigate the fundamentals of droplet-jumping and the frost growth phenomena using line-shaped, hollow-cylindrical, and cylindrical microstructures, comparing the frost surface coverage area and the ice-bridging times during condensation-frosting, prolonged condensation-frosting, and direct-frosting. We find that the closely spaced thin line-shaped microstructures and hollow-cylindrical microstructures are optimal for frost coverage reduction because of their ability to exhibit droplet-jumping and droplet-sweeping phenomena. We observe that adding nonuniform roughness on top of the microstructures leads to jumping-associated droplet-sweeping on supercooled surfaces. Here, we report the evaporation of an already frozen droplet because of freezing of a supercooled condensate droplet in its close vicinity, enabling the Cassie-Baxter state frost growth and enhancing defrosting efficiency. Finally, we discuss the dynamic defrosting behavior of the pPFDA-coated VA-CNT microstructures, concluding that the small gaps (spacings) between the microstructures not only enable dewetting transitions of droplets but also promote the Cassie-Baxter state frost formation.

The effects of outdoor air-side fouling on frost growth and heat transfer characteristics of a microchannel heat exchanger: An experimental study

Air source heat pumps have the potential to efficiently heat and cool buildings, but their effectiveness in many climates is limited by frost growth on the outdoor heat exchanger in heating mode. These heat exchanger coils are also subject to fouling from fibers and particulates outdoors. Frost and fouling have each independently been studied extensively, and newly available research on fouling provides a method to realistically foul the air-side of coils in the laboratory. The current paper uses this method to conduct the first laboratory study of the important interactions between fouling and frost growth for a heat pump outdoor coil. A microchannel heat exchanger is tested clean and fouled, with variations in fouling level, humidity, and initial face velocity of air. Air flow rate is allowed to vary with resistance, and a surprising result is that light fouling increases heat transfer and frost growth rates, even with a 3.5% reduction in initial airflow caused by the fouling. However, heavier fouling decreases both rates. When frost growth is normalized to heat transfer, it is found to be increased by fouling; i.e. the coil's sensible heat ratio decreases.

Prediction of the frost growth and performance change of air source heat pump system under various frosting conditions

A numerical model of air source heat pump (ASHP) system under frosting conditions is developed to predict the frost growth rate and performance change of the heat pump system under various frosting conditions. The modified ε-NTU model is introduced to compute the heat transfer rate of the evaporator with latent heat generation from the water vapor sublimation. Local frost growth is considered to obtain the non-uniform airflow distribution, air pressure drop, and heat transfer rate. The effect of the frost deposition on the ASHP system is investigated from the suggested model under various frosting conditions. It is shown that the performance drop mostly occurs in the latter part of the frosting process, and the mass of the deposited frost is not directly related to the performance drop. The experimental set up is set to verify the proposed simulation model. The simulation results are in good agreement with the experimental data.

A study of frost build-up on hydrophilic and hydrophobic surfaces under forced convection conditions

The present study is aimed at investigating, by means of an experimental approach, the effect of surface wettability on the frost accretion over horizontal flat surfaces under forced convection conditions. A purpose-built closed-loop wind-tunnel facility was especially designed and constructed to provide a strict control of the psychrometric conditions at the entrance of the test section, and also of the plate surface temperature. An image acquisition system was used to measure the thickness of the frost layer over time. A dataset comprised of >800 experimental data points spanning different surface temperatures (from −20 to −10 °C), air temperatures (from 5 to 16 °C), modified Jakob numbers (from 1.05 to 2.10), and static contact angles (from 60° to 123°) was gathered and used to investigate both the individual and simultaneous effects of key heat and mass transfer parameters on the frost growth rate. A first-principles modelling approach was used together with the experimental data obtained in-house to come up with a semi-empirical fully-algebraic expression for the frost thickness as a function of the time, the supercooling degree, and the surface contact angle. It was found that the proposed correlation was able to predict most of the experimental data points (>90%) for the frost thickness within ±15% error bounds. Insights on early and delayed nucleation were also obtained from the analysis of the experimental data.

A finite volume method to solve the frost growth using dynamic meshes

The physical mechanisms of frost formation have been widely studied, yet much empirism is still needed in numerical approaches. Indeed, accurate simulations of frost growth can be reached by setting up a specific combination of the model empirical inputs while using a method to accurately track the frost-air interface.This paper presents a finite volume ALE method which captures the air-frost interface using dynamic meshes. It is divided into two main sections. First, the search of a valid set of empirical correlations to correctly emulate frost growth under certain experimental conditions. An assessment of seven reference cases is carried out by comparing solutions using different empirical correlations against experimental data. As a result, a discussion on the performance of such parameters is made, emphasizing the fact of using diffusion resistance factors above 1.0 in order to capture the frost growth. Second, a 2D numerical test consisting of a duct flow with a non-homogeneously cooled lower boundary is performed. Aspects related to the frost thickness and growth rate are analysed, proving the method to be a valid candidate to simulate frost growth.

The role of surface wettability on natural convection frosting: Frost growth data and a new correlation for hydrophilic and hydrophobic surfaces

In refrigeration systems, frost accumulation on the evaporator demands periodic defrosting. Chemical coatings (either hydrophilic or hydrophobic) are sometimes used to mitigate frost build-up and/or improve drainage during the defrost cycle. Although several studies have been performed on frost growth behavior, relatively few studies have specifically examined the effect of surface wettability on the frost growth rate. This paper focuses on the influence of environmental operating conditions on the growth of a frost layer on surfaces which span a wide range of contact angles under natural convection conditions. A new semi-empirical correlation which includes the surface contact angle θ and the modified Jakob number Λ as parameters is reported with an average predictive error of 11.7% (N = 930) for all non-zero experimental data. The correlation was developed using multivariable regression analysis and data which span different surface temperatures (−13 °C to −5°C), relative humidities (40–80%), and static contact angles ranging from 45° (hydrophilic) to 160° (hydrophobic).

A semi-empirical model for predicting frost accretion on hydrophilic and hydrophobic surfaces

A first-principles model was used together with experimental data obtained in-house to validate a semi-empirical modeling approach for predicting frost accretion on hydrophilic and hydrophobic substrates. An algebraic expression for the frost thickness as a function of the time, the modified Jakob number, the humidity gradient, and the surface contact angle was devised from frost formation theory. At this stage, the correlation was fitted to 956 experimental data points for natural convection conditions spanning different surface temperatures and supercooling degrees, with the modified Jakob number ranging from 0.79 to 1.30, and contact angles ranging from 45° (hydrophilic) to 160° (hydrophobic). When compared to the experimental data for the frost thickness, the proposed semi-empirical model showed errors within ±15% bounds, and an average predictive error of 11.7%. Since the model carries the contact angle as an independent parameter, a sensitivity analysis of the frost growth rate in relation to it is also reported.

Numerical Modelling of Frost Formation of Flat Surface

Frost formation begins when humid air comes in contact with a cold surface kept below freezing temperature of water. Objective of the present study is to develop a numerical model which can predict frost formation parameters such as rate of frost growth, frost densification and to study effect of ambient conditions on these parameters. The one-dimensional pure implicit finite difference method is adopted for solving differential equations. Numerical code is written in MATLAB 2013. The proposed numerical model is validated against two independent published experimental data with 6.6 and 16.8% deviation. Effect of ambient parameters like wall temperature, ambient temperature, humidity and Reynolds number on frost growth and densification are investigated. Also effect of variable wall temperature and variable ambient temperature on frost growth rate is discussed.

Experimental study of the characteristic of frosting on low-temperature air cooler

In order to find out the influencing factors of frosting on air coolers, the experiments were conducted for air coolers under frosting, and the frost layer thicknesses under various operating conditions were measured with the aid of microphotography. Experimental results show that the frosting process for air coolers is significantly influenced by those parameters including the fin spacing, coating material over fin surface, air relative humidity, evaporating temperature and air flow rate. It is found out that the smaller the fin spacing is, the earlier frosting occurs and the faster the frost grows. The frosting can be delayed by coating the hydrophilic material over fin surfaces; however, the frost quantity is not obviously affected. Under the condition of large air relative humidity, the frost growth rate increases, and the increasing tendency drops off when the relative humidity is larger than 80%. The starting time of frosting may not be obviously influenced. The lower the evaporating temperature is, the larger the frost growth rate. As the evaporating temperature decreases, the initial morphology of frost layer varies from large and flat shape to needle-shape or column-shape due to the increasing of temperature difference. The occurrence of the frosting is delayed by increasing the air flow rate and the increasing of frost layer thickness can also be delayed due the melting of frost, but the frosting rate is not sensitive to the air flow rate.

Developing empirical correlations for frost thickness and air face velocity degradation for microchannel heat exchangers used in heat pump applications under frosting conditions

This study experimentally investigated the frost growth on louvered folded fins in outdoor microchannel heat exchangers used in air-source heat pump systems. The effects of surface temperature and fin geometries on the performance of the microchannel heat exchangers under frosting condition were studied. Seven fin samples with various fin widths, fin heights, and fin densities and a louver angle of approximately 30° were tested in controlled laboratory conditions that replicated those of actual heat pump systems in the winter season. The fin surface temperature was experimentally measured with the novel methodology developed in the present study. Experimental data of local frost thickness, air pressure drop across the coils, time of frost–defrost cycles, and heat transfer rates were recorded for heat exchangers operating in actual transient frosting conditions. Data showed that frosting time and frost growth rates depended mainly on the local fin surface temperature. A set of empirical correlations were developed to predict the frost thickness on the fin leading edge and the reduction of air face velocity due to air pressure drop across the frosted coil during frosting operation. The correlations were compared against experimental data of frost collected in the present study, and satisfactory agreement was achieved. The frost thickness correlation and air face velocity correlations aid in the calculation of the instantaneous air-side Reynolds numbers during frosting operation of the fin samples. These are critical for predicting the heat transfer rates of the microchannel coils in quasi-steady-state frosting operating conditions.

Effects of surface coating and water retention on frost formation in microchannel evaporators (ASHRAE RP-1589)

This study experimentally investigated frost growth on louvered folded fins in outdoor microchannel heat exchangers when used in air-source heat pump systems. The effects of five surface coatings on the thermal and hydraulic performance of the microchannel heat exchangers under frosting conditions were studied. The overall aim was to provide some guidelines about frosting behavior of microchannel heat exchangers with hydrophilic and hydrophobic coatings. The approach taken was to perform laboratory experiments on small-scale coils and several sample fins that were cut out from commercially available heat exchangers. The sample fins were tested in controlled laboratory conditions that replicated those in actual heat pump systems in the winter season. A better estimation of the fin surface temperature was achieved with the methodology developed in the present study. The experimental value of air pressure drop across the coils, time of frost–defrost cycles, and heat transfer rates were recorded for heat exchangers operating in actual transient frosting conditions. Data showed that the frosting time and frost growth rates depended mainly on the local fin surface temperature. Five surface coatings were investigated, and the data show that the hydrophobic coating had slightly lower frosting performance after a few defrost cycles with respect to hydrophilic surface coating.

Frost growth characteristics of spirally-coiled circular fin-tube heat exchangers under frosting conditions

The objective of this study is to investigate frost formation and growth in a spirally-coiled circular fin-tube heat exchanger. The frost thickness and growth rate were measured in the transverse and circumferential directions by varying the relative humidity (or humidity ratio), air flow rate, inlet air temperature, and fin pitch. The frost thickness was affected primarily by the relative humidity, inlet air temperature, and air flow rate. The relative humidity showed a dominant effect on the frost growth among all parameters tested. An empirical correlation for the frost thickness was developed for the spirally-coiled circular fin-tube heat exchanger as a function of the Reynolds number, Fourier number, humidity ratio, and dimensionless temperature. The mean and average deviations of the predictions using the present correlation from the measured data were 4.32% and 3.96%, respectively.

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.

An analytical solution to the problem of frost growth and densification on flat surfaces

This paper advances an algebraic first-principles simulation model to predict the frost growth and densification on flat surfaces. The model was put forward based on macroscopic heat and mass balances in the frost layer, which were written according to a dimensionless formulation and solved analytically to obtain an algebraic expression for the time evolution of the frost thickness as a function of the Nusselt number, the supersaturation degree and the air-to-surface temperature difference. The model predictions for the frost thickness were compared with experimental data obtained elsewhere, when a very good agreement between calculated and measured counterparts was observed. The sensitivity of the frost growth rate to key heat and mass transfer parameters is also assessed and reported.

Experimental measurements of the surface coating and water retention effects on frosting performance of microchannel heat exchangers for heat pump systems

Frost formation on louvered fin microchannel heat exchangers was experimentally investigated in this paper with the aim of studying the effect of hydrophilic and hydrophobic surface coatings and of water retention on their frosting performance and on their frost growth rates. Frost mass and thickness growth rates, corresponding coil heat transfer rates, capacity degradation, and air-side pressure drop for five microchannel coils with different surface coatings were measured and discussed. The experimental data showed that the hydrophilic and hydrophobic surface coated coils considered in the present work accumulated frost on the heat transfer surfaces with visible difference in the type, appearance, and patterns of the frost. The duration of the frosting cycle, the heat transfer rate, and air-side pressure drop were similar to the ones of a louvered aluminum fin microchannel heat exchanger with uncoated surfaces. For the operating conditions tested in this work, hydrophobic and hydrophilic coatings on microchannel coils affected the heat transfer capacity in frosting conditions by up to 15%.