Frost Model Research Articles

Experimental and Modeling Analysis of the Tensile Properties of Heavy-Duty Coatings for Steel Structures

Coatings are essential for protecting steel structures from corrosion and mechanical stresses, especially under challenging environmental conditions. To this end, this study systematically examines the effects of temperature (20 °C to 50 °C), strain rate (6.67 × 10−4 s−1 to 1.67 × 10−2 s−1), and intermediate coat thickness (140 μm to 700 μm, the layer between the primer and topcoat) on the uniaxial tensile properties of heavy-duty coatings for steel structures. Experimental and theoretical analyses were conducted to quantitatively assess the influence of these factors on the mechanical properties of the coatings. A multifactor constitutive model was developed based on the Sherwood–Frost model by integrating material characteristics and fitting experimental data, incorporating response functions for temperature, strain rate, and intermediate coat thickness. The results reveal that increased temperature causes temperature-induced softening, while higher strain rates lead to strain rate-dependent strengthening of the coatings. In contrast, the effect of layer thickness on mechanical properties follows a non-monotonic trend, influenced by the structural and material characteristics of the coatings, with the most significant mechanical response occurring at 560 μm thickness. These findings suggest that optimal coating design must consider multiple factors to enhance mechanical performance. Additionally, the correlation coefficients (r) between the model predictions and experimental results are 0.97 or higher, indicating the model’s effectiveness in predicting and optimizing the mechanical performance of heavy-duty coatings under complex conditions.

Numerical investigation of the path-dependent frost heave process in frozen rock under different freezing conditions

Frost heave in water-bearing rock masses poses significant threats to geotechnical engineering. This paper developed a novel three-dimensional (3D) frost model, based on the combined finite-discrete element method (FDEM), to investigate the frost heave process in rock masses where thermal transfer, water migration, water-ice phase transition (ice growth) and ice-rock interaction are explicitly simulated. The proposed model is first validated against existing experimental and analytical solutions, and further applied to investigate path-dependent frost heave behavior under various freezing conditions. Results show that freezing direction plays a vital role in the dynamic ice growth and ice-rock interaction, thus affecting the frost heave behavior. In the top-down freezing regime, ice plugs form first at the crack's top surface, sealing the crack and preventing water migration, which can amplify ice pressure. Parametric studies, including rock Young's modulus, ice-rock friction, and rock hydraulic conductivity, further reveal that the temporal aspects of ice development and rock mechanical response strongly affect ice-rock interaction and hence the frost heave mechanism. Furthermore, some typical phenomena (e.g. water/ice extrusion and frost cracking) can also be well captured in this model. This novel numerical framework sheds new light on frost heave behavior and enriches our understanding of frost heave mechanisms and ice-rock interaction processes within cold environment engineering projects.

Study on the impact of low‐temperature stress on winter wheat based on multi‐model coupling

AbstractCrop growth models, such as the WOrld FOod STudies (WOFOST) model, mimic the mechanistic processes involved in crop development, growth, and yield production. The accuracy of simulation is decreased in unfavorable low‐temperature settings because these models do not accurately represent crop response processes in low‐temperature stress. Enhancing the WOFOST crop growth model's accuracy in simulating crops' responses to cold temperatures is the aim of this work. Given its vulnerability to low temperatures, the inquiry uses winter wheat in Henan Province as a focal point. It integrates the WHEATGROW wheat phenology model with the Frost model of Lethal Temperature 50 (FROSTOL) inside the framework of the crop growth model. This link aims to improve simulation accuracy and supplement the model's mechanisms, particularly when it comes to the impact of low temperatures on crop development. The study uses Long Short‐Term Memory networks to build a yield model that integrates remote sensing data with information from simulated crop models. Under low temperatures, the leaf area index, total above ground biomass, and total weight of storage organs of the model WWF—which combines FROSTOL and WHEATGROW with WOFOST—show a considerable decline. It was discovered that there is a greater improvement in simulation accuracy of the linked model WWF relative to the WOFOST model in frost years than in normal years, based on a comparison analysis between typical frost years and normal years. To be more precise, the improvement is 8.03% in frost years and 1.98% in regular years. When all is said and done, the coupled model advances our knowledge of how winter wheat is impacted by low temperatures.

An Eulerian multiphase frost model based on heat transfer measurements

In this paper, a laminar numerical model is developed to predict frost formation over a horizontal cold flat surface. An Eulerian-Eulerian multiphase approach is followed to model humid air and ice phases separately. Frost accumulation on the cold surface is modeled with an empirical mass source term. Model constants were tuned in a systematic way using experimental heat flux and frost thickness data. A velocity dependent model constant is introduced into the mass source term. The heat flux rise observed experimentally at the initial stages of the frosting could be captured with the use of the velocity dependent model constant and the addition of this term considerably improved the accuracy of the frost model at the initial stages of frosting. It was also observed that the selected particle diameter for the solid ice phase has a considerable effect on the velocity profile over the frost layer. This requires tuning of the velocity dependent model constant parameters according to the selected ice particle diameter. The developed numerical model was tested with three different frost thermal conductivity models. Using the thermal conductivity of solid ice for the frost thermal conductivity resulted in the most accurate prediction at the early stages of the frost growth process indicating a rather column-wise vertical growth of ice crystals with very low lateral branching. However, the overprediction of the numerical heat flux with the thermal conductivity of solid ice points out a decrease in the thermal conductivity of the newly added frost layers indicating a more pronounced lateral branching of ice crystals within the frost layer. The effect of the diffusion coefficient of the water vapor in humid air on frosting is also investigated. An artificial increase in the diffusion coefficient improved the accuracy of the heat flux prediction of the model at the initial stages of frosting which might indicate an eddy-driven enhanced mixing in the boundary layer which might not be captured in the laminar flow model. Finally, the developed numerical model is also tested on another scenario with the surface temperature held at -30 °C. Detailed analysis of the numerical simulations showed a more porous frost layer with the surface temperature at -30 °C as compared to the frost porosity formed on the surface at -20 °C.

Study of frost layer growth process on horizontal cold surfaces in the channels

Based on the layer-by-layer growth phenomenon existing in the actual formation of frost layer, we constructed a frost model with supporting criterion and studied the growth process of the frost layer on the horizontal cold surface at the bottom of the channel. Comparison with relevant experimental data revealed a maximum error of 25.3% in the calculated thickness and 13.1% in the density. The change in density and thickness over time under different working conditions, especially the variation in the thermal resistance under refrigeration conditions, were analyzed from local and overall perspectives. From a local perspective, thickness and density were highest at the frost front and slowly decrease along the flow direction before increase again at the end of the frost layer by 7.3% and 32.9% respectively. The local thermal resistance of the frost layer first increased sharply along the flow direction, reached a local peak and then decreased slowly. From an overall perspective, both the average thickness and average density increased with time, while the average thermal resistance first increased sharply with time, reached a peak, and then decreased slowly.

Analysing the COVID-19 epidemic in Italy through the Reed-Frost model: A methodology to delimit epidemic waves over time.

to set out a method based on the Reed Frost model to delimit over time COVID-19 epidemic waves in Italy. the available national epidemic reports published by the Protezione Civile (Italian civil defence) from 24.02.2020 to 16.022022 were used to collect data on COVID-19 epidemic in Italy. Then, the Reed-Frost model was applied to develop a methodology based on the calculation of the effective contact probability, i.e., the probability of contact. in Italy, a daily report related to the epidemic was immediately available, including main epidemiological data (point and periodic infection prevalence, mortality, etc), which made it possible for researchers from different institutions to perform analyses about the epidemic. an iterative methodology was developed resulting in the identification of the start-of-wave, end-of-wave, and inter-wave periods and of the starting and ending days of the COVID-19 epidemic waves in Italy (first wave: from 26±2 February 2020 to 28±2 June 2020). this study led to the development of an accessible and reproducible method to determine the start-of-wave and end-of-wave dates of an epidemic, starting only from the number of cases and susceptible people. The main implications of the method mainly consist in allowing benchmarking and forecasting analyses of the epidemic trend to be carried out to support policy and decision-making processes.

The frost restraining effect of solar air collector applied to air source heat pump

The air source heat pump has been demonstrated to be an efficient clean space heating technology, but the frosting on the exterior surface of the evaporator will largely decrease its performance. In this paper, the triangular solar air collector is adopted for evaporator frost restraint of the air source heat pump, and the dynamic heat transfer model of the triangular solar air collector and quasi-steady-state frosting model of the evaporator were established and coupled. The effect of frost layer thickness variation on evaporator air flow is considered based on the resistance factor to improve the applicability of the model. The heat flux and water vapor diffusion flux at different frost time and frost thickness were calculated, and the frosting characteristics of the air source heat pump with the triangular solar air collector and the conventional air source heat pump were compared on varying working conditions and typical daily meteorological parameters. Results show that triangular solar air collector can effectively restrain the frosting of the air source heat pump, and when the solar irradiance is 500 W/m2, the triangular solar air collector can reduce the frost thickness by more than 15 %. The triangular solar air collector increases the total heat flux by 101.4 W/m2 under frosting conditions, which reduces half of the defrosting times and increases the heat exchange of the evaporator by 36.6 % during a typical day, indicating that triangular solar air collector significantly improved the energy efficiency of air source heat pump on frosting condition.

A frost model based on the frost layer's supporting function

The existence of frost has adverse effects the normal operation of air source heat pumps. Therefore, establishing an accurate frost model is of great significance to suppressing the formation of frost layers on cold surfaces. Since the frost layer grows gradually and cumulatively layer by layer in the actual physical frosting process, it is important to consider the supporting function of the lower frost layer in the process. This study proposes the use of the ice volume fraction threshold of the frost layer to determine whether the supporting condition is satisfied, in addition to using the threshold to determine the occurrence of frosting. A new frost model is developed with the given volume fraction threshold fitting formula. In order to verify the accuracy of the proposed model, the simulation results were compared with 17 groups of experimental results from four representative experiments. It was found that the simulation results of this model were in good agreement with the experimental data, and the average error of thickness did not exceed 4.9%, while the average error of density was less than 5.5%.

CFD analysis of phase change behaviour and frost growth under various conditions using mass transfer theory

A frosting model based on mass transfer theory was developed using Computational Fluid Dynamics software to investigate frost growth on a horizontal surface. The mass transfer model utilizes dimensionless numbers to calculate the mass transfer coefficient to predict rate of frosting. The predicted frost thickness was generally within 20% of experimental data and was able to show the mass transfer behaviour for the frosting phenomenon. Compared to previous studies, water vapour condensation and frost growth in this study are governed by the 0 °C air temperature iso-surface which in turn is affected by the amount of frost developed as well as the operating conditions. The predictions by model show that mass transfer rates are higher at both the cold surface and the frost-air interface, which represents frost densification and thickness growth, respectively. A larger distinction between the two mass transfer rates is observed as the surface temperature becomes lower. Additionally, the effects of air humidity, velocity and temperature on frost formation at refrigeration conditions are investigated.

Temporal and spatial frost growth prediction of a tube-finned heat exchanger considering frost distribution characteristics

To better understand the frost growth characteristics of a tube-finned heat exchanger, a novel frosting model was developed based on its frosting distribution characteristics. The frosting model considered both the frost growth on the edge of windward fins and the uneven frost distribution on the surfaces of tube-finned segments. Compared to a conventional frosting model, the novel one can improve the prediction accuracy on frost thickness on the surfaces of fins and tubes, and total frost mass of the tube-finned heat exchanger by 5.1%, and 2.0%, respectively. The temporal and spatial frost growth characteristics of the tube-finned heat exchanger were numerically investigated based on the novel frosting model. The results showed that the frost growth on the edge of windward fins impacted more on the entire frost growth of tube-finned heat exchanger as frosting progressed. After a 3,600-s frosting period, the heat transfer rate and frosting rate on the edge of windward fins accounted for 10.4% and 10.3% of the entire heat transfer rate and frosting rate of the tube-finned heat exchanger, respectively. Besides, the relative differences between the frost density at the frost surface and wall surface on the surfaces of fins and tubes, and the edge of windward fins were 68.0%, and 71.7%, respectively. This study is meaningful for the accurate control of defrosting and thus energy saving.

A modeling study of spatial and temporal frost growth on the edge of windward fins for a tube-finned heat exchanger

Frosting on the surface of tube-finned heat exchangers is a serious and common problem in the fields of air source heat pump and vaporization of liquid nitrogen. To reveal the frosting characteristics, a frosting model on the edge of windward fins was developed. Based on the previously reported experimental visualization results, the model was simplified by regarding the flat surface of the edge of windward fins to a half-cylindric surface. The predicted frost thickness and frost mass according to the proposed frosting model agreed well with the previously reported experimental data. The numerical results showed that frost layer on the edge of a windward fin grew the fastest along the opposite airflow direction and gradually slower with the increasing θ, angular position relating to the center axis of fin, showing a streamlined profile. The frost thickness, density, and surface temperature all decreased by 31.9%, 19.0%, and 2.2 °C, respectively, while θ increased from 0° to 90° at the end of a 3,600 s frosting period. Additionally, the average water vapor mass flux, total, sensible, and latent heat flux decreased by 17.6%, 17.9%, 18.1%, and 17.6%, respectively. The frosting surface area, frosting rate, total, sensible, and latent heat transfer rates increased by 141.0 times, 119.6 times, 119.0 times, 118.6 times, and 119.8 times, respectively. This study is meaningful for the accurate control of defrosting and thus energy saving.

Process-based indicators for timely identification of apricot frost disaster on the warm temperate zone, China

Frequent occurrences of late spring frost disaster create severe agricultural/forest damage, even given the background of global warming. In the warm temperate zone of China, which is the largest planting area for fresh apricot, late spring frost disaster has become one of the major meteorological hazards during flowering. To prevent cold weather–induced apricot frost disaster and reduce potential losses in related fruit economic value, it is vital to establish a meteorological indicator for timely and accurate identification of cold weather process–based apricot frost disaster, to provide support for timely apricot frost monitoring and warning in late spring. In this study, daily minimax temperature ( $${T}_{\mathrm{min}}$$ ) and apricot frost disaster data during flowering were combined to establish meteorological identification indicators of apricot frost based on cold weather processes. A process-based apricot frost model $$f(D,{T}_{\mathrm{cum}})$$ was firstly constructed, and characteristics of $${T}_{\mathrm{cum}}$$ (accumulated harmful temperature) were explored under different D (duration days) based on the representation of historical apricot frost processes. Thresholds for the $${T}_{\mathrm{cum}}$$ for apricot frost in 1, 2, 3, 4, and more than 5 days of apricot frost process were determined as − 1.5, − 2.9, − 4.4, − 5.8, and − 7.3 °C, respectively. Validation results by reserved independent disaster samples were generally consistent with the historical records of apricot frost disasters, with 89.00% accuracy for indicator-based identification results. Typical process tracking of the proposed identification indicator to an apricot frost event that occurred in North Hebei during April 3–9, 2018, revealed that the indicator-based identification result basically coincides with the historical disaster record and can reflect more detailed information about the apricot frost process.

Frosting characteristics and prediction of thickness of frost layer on a finned tube in regasification process of cryogenic liquids

Frost frequently forms on cryogenic equipment and is the main reason for the decline in the heat transfer of cryogenic ambient air vaporizers. In this paper, the characteristics of frosting on the surface of a finned tube in the regasification process of liquid nitrogen were investigated by a series of experiments. The experiments were conducted in an air temperature range of 2–12°C and a humidity range of 1.4–4.0 g·kg–1. The results show that frosting of the finned tube is complex, and a new “wisteria-type” frost crystal is observed at the inlet of the finned tube. The “wisteria-type” frost crystal is formed in the area of the fins with an initial temperature drop rate of higher than 2.32°C·min–1. The data on the frost layer thickness show that along the tube, the frost layer thickness first decreases and then increases, which results from the wall temperature and the concentration of water vapor. A comparison of the measured data with the frosting models in the literature is also presented. Moreover, the wall temperature is identified to modify the frosting model. The modified frosting model can predict 62.4% of the present database within a ±25% error band. This work highlights the vital role of the wall temperature in the frost porosity.

Division of Frosting Type and Frosting Degree of the Air Source Heat Pump for Heating in China

The frosting type and frosting degree of the outdoor heat exchanger of air source heat pump (ASHP) in the heating season are greatly affected by the local environmental temperature and humidity. China has a vast territory, and the climate varies greatly in different regions. Therefore, when the ASHP is running in different climate zones for heating in winter, there are significant differences in the frosting type and frosting degree. In order to achieve deeper understanding of frost formation and provide more accurate guidance for the suitability application of antifrosting and defrosting technologies, a study on the division of frosting type and frosting degree was performed in this work. Based on the three-phase diagram of water and combined with the theory of phase change dynamics, the outdoor heat exchanger of the ASHP in the heating season was divided into four states: neither frosting nor condensation, condensation, condensation frosting, and sublimation frosting, and the proportion of each state in a typical city in different climate zones was calculated. The results showed that more than 80% of the heating seasons in Nanjing, Shanghai, Wuhan, Changsha, Xi’an, and Harbin had the frosting phenomenon. Sublimation frosting was the main frosting type in Xi’an, Beijing, and Harbin, while Chongqing was all condensation frosting. Moreover, a frosting model was developed and the frosting degree was divided into mild frosting, moderate frosting, and heavy frosting, according to the performance attenuation of the ASHP under frosting conditions. The proportion of each frosting degree in a typical city was achieved. About 50% of the heating seasons in Nanjing and Changsha were distributed in the heavy frost area and 100% in Chongqing.

A numerical simulation of frosting and condensation in aviation electronic devices based on nielsen dynamic frosting model

A numerical simulation of frosting and condensation in aviation electronic devices based on nielsen dynamic frosting model

A CFD model of frost formation based on dynamic meshes technique via secondary development of ANSYS fluent

To simulate the non-uniform frost growth in flow direction for humid air flowing through a freezing channel, a 2D numerical frosting model based on dynamic meshes technique is developed in the current work via the secondary development of commercial ANSYS Fluent. The computation domain consists of both frost layer and humid air regions, and the local heat and vapor fluxes at the surface of frost layer are determined by numerical temperature and vapor fraction fields in the humid air region rather than by empirical correlations. The frost layer is treated as a growing packed bed with heat and mass transfer dominated by molecular diffusion, where local absorption coefficient of vapor desublimation and local vapor fraction are both determined by solving the pseudo steady vapor diffusion equation with a source term theoretically. The interface of frost layer and humid air regions is treated as two walls for the iteration of its temperature, of which the humid air side is specified with the temperature equal to the frost-side counterpart and the frost side takes the heat flux including the extra latent heat caused by vapor deposit. User-defined functions are compiled to implement the above treatments to ANSYS Fluent. Frosting experiments in the literature are simulated with the current model for validation. How the profile of frost layer evolves with time in the frosting process is explored. The contours and profiles of velocity, temperature and vapor fraction are presented to discuss the effects of heat and mass transfer on frost formation. Numerical results demonstrate that the proposed CFD model can predict the frost growth and densification with a relative deviation less than 5% compared with experiments. Besides, the computation load of current model is small due to no solution of complex multiphase flow. In addition, dynamic meshes help current model to capture the interface of frost layer and humid air regions accurately.

Model and calculation method of frost heaving stress of stagnant water of tunnel in seasonally frozen area

The frost heave caused by the stagnant water may seriously threaten tunnels’ operation safety and service life in seasonally frozen areas. This paper aims to put forward new insights for the accurate evaluation of the frost heaving stress and the prevention of frost damage in seasonally frozen-region tunnels. Firstly, based on the local frost theory and local deformation theory, a new calculation model of the frost heaving stress caused by stagnant water is established. In this model, the space of stagnant water is simplified as the three-axis semi-ellipsoid, which is more in line with the actual situation. Then, the rationality of the new calculation model was verified by comparing it with the results of numerical analysis and previous studies. Finally, the effects of the crucial parameters in the calculation model were also conducted by the univariate method. The results show that the theoretical model is in good agreement with the numerical simulation. The theoretical analysis exhibits the more conservative results, which may provide a practical approach for damage assessments and frost preventions in the case of a lack of observed in-site data. Besides, some significant suggestions about the construction and design of seasonally frozen-region tunnels are obtained.

Effect of non-uniform temperature & humidity distribution in the frontal airflow on evaporator frosting performance of a frost-free refrigerator

Abstract The frost-free refrigerator typically has three compartments, i.e. refrigerating, variable-temperature and freezing ones. The temperature and humidity (T&H) inside each compartment vary dramatically, leading to non-uniform T&H distribution in the overall return air. Therefore, frost maldistribution occurs on the evaporator and further induces airflow redistribution. In this article, the quasi-static 3–2–1–1 frosting model is built considering 3D evaporator, 2D T&H of frontal airflow, 1D frost growth and 1D non-uniform fin spacing. The model is verified by the experiment data in the open literature. Results show that frost mass is similar with non-uniform and uniform T&H distribution in frontal airflow, but frost distribution is much different. The evaporator capacity for non-uniform airflow is lower at the early stage of frosting process than that for uniform airflow, but higher later due to the airflow transverse redistribution when the airflow transfers transversally from higher to lower T&H areas owing to frost maldistribution. The transverse redistribution results in the air velocity increment and heat transfer compensation effect. Moreover, the fan stall for non-uniform airflow arises later and results in the larger airflow rate and evaporator capacity at later frosting process.

Frost modeling under cryogenic conditions

A frost model for predicting frosting behavior under cryogenic conditions was developed. The frosting behavior was visualized through numerical analysis, and the results were compared to experimental data to confirm the validity of the model. It was shown that under cryogenic temperatures, a considerably low-density frost layer was formed owing to the frosting mechanism, which was sublimation-dominant frosting, rather than conventional condensation-freezing. It was qualitatively confirmed through experiments that low-density frost formed near the frost surface, and high-density frost formed near the cryogenic cold plate. Furthermore, the frost density distribution of the interior frost was quantitatively analyzed through a numerical analysis. The surface temperature of frost was seen to rise rapidly during the initial stage of frosting. Thus, it is possible to estimate the time at which the frosting mechanism changes from sublimation to condensation-freezing.

Dynamic Constitutive Model of Ultra-High Molecular Weight Polyethylene (UHMWPE): Considering the Temperature and Strain Rate Effects.

The temperature and strain rate significantly affect the ballistic performance of UHMWPE, but the deformation of UHMWPE under thermo-mechanical coupling has been rarely studied. To investigate the influences of the temperature and the strain rate on the mechanical properties of UHMWPE, a Split Hopkinson Pressure Bar (SHPB) apparatus was used to conduct uniaxial compression experiments on UHMWPE. The stress–strain curves of UHMWPE were obtained at temperatures of 20–100 °C and strain rates of 1300–4300 s−1. Based on the experimental results, the UHMWPE belongs to viscoelastic–plastic material, and a hardening effect occurs once UHMWPE enters the plastic zone. By comparing the stress–strain curves at different temperatures and strain rates, it was found that UHMWPE exhibits strain rate strengthening and temperature softening effects. By modifying the Sherwood–Frost model, a constitutive model was established to describe the dynamic mechanical properties of UHMWPE at different temperatures. The results calculated using the constitutive model were in good agreement with the experimental data. This study provides a reference for the design of UHMWPE as a ballistic-resistant material.