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.     

Heat and mass transfer on a cylinder surface in cross flow under supersaturated frosting conditions

In this paper a semi-empirical model describing heat and mass transfer on a cylinder surface in humid air cross flow under supersaturated frosting conditions is presented. The lack of psychrometric data in the supersaturated zone of the psychrometric chart has historically impeded the ability of researchers to accurately predict heat and mass transfer in supersaturated air. The work described in this paper has been partially made possible by developing a systematic procedure to compute the properties of supersaturated moist air, especially in the low temperature zone of the psychrometric chart. Development of such a capability will allow us to predict the amount of frost collected on a coil, the frost deposition and coil heat transfer rates, frost thickness and frost surface temperature, and other important coil frost parameters under supersaturated conditions.     

Experimental investigation of the surface temperature and water retention effects on the frosting performance of a compact microchannel heat exchanger for heat pump systems

Frost formation on a louvered fin microchannel heat exchanger was experimentally investigated in this paper with the aim of determining the dominant factors affecting the time of frosting and frost growth rate. A novel methodology was developed to measure frost thickness and frost weight at intervals during the frosting period. Frost mass and thickness growth rates, corresponding coil heat transfer, capacity degradations and air pressure drop are measured and discussed. The experimental data showed that at a given air dry bulb temperature, the fin surface temperature and air humidity are the primary parameters that influence the frost growth rates. Water retention and air velocity had a secondary impact on the frosting performance. From digital images of the frost growth it was observed that frost does not nucleate from the water droplets retained in between fins but it developed from the leading edges of the fins.     

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.     

室外环境参数对空气源热泵翅片管蒸发器动态结霜特性的影响

对一台空气源热泵空调器在不同环境条件下室外换热器的动态结霜性能进行了实验研究，分析了进风温、湿度对热泵空调器结霜量及霜层厚度的影响。实验中考虑了结霜引起的热泵系统蒸发温度及风机流量的变化，采用显微照相法测量翅片表面霜层厚度，结霜量则通过测量蒸发器进出口含湿量的方法来获得。实验结果表明，室外换热器结霜量随时间线性增长，而翅片表面霜层厚度则分为初始段、匀速增长段和快速增长段三个阶段；在结霜循环的最后20％～30％的快速增长段内霜层生长速率大大加快，可达匀速生长段霜层生长速率的2．4，3．3倍。对于不同的工况，蒸发器均在进风温度0～3℃附近时结霜最为严重，且相对湿度对霜层厚度的影响要大于对结霜量的影响。     

Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry

The development of frost is a phenomenon that deteriorates thermohydraulic performance on heat exchangers. In this study, several heat-transfer area distributions on a fin-and-tube geometry are proposed and their performances as frost develops are compared using simulation. The frost development at a specific location is determined using a segment analysis. In each segment, a semiempirical model to predict the frost growth based on air temperature, velocity, relative humidity and surface temperature is applied. The analysis considers airflow redistribution among channels, leading to changes in heat transfer and frosting rates with time. Results show that a geometry that allows even flow distribution along the operation time is less sensitive to thermohydraulic deterioration. An area distribution with larger fin spacing and fin length presents an advantage, particularly on the pressure drop, which allows longer operation time between defrost cycles.     

空气源热泵蒸发器表面霜层生长特性实验研究

在室外环境空气温度-15℃~5℃、相对湿度65%~90%范围内,对一台空气源热泵室外换热器表面霜层生长特性及热泵系统动态性能进行了实验研究。实验结果表明,翅片表面霜层厚度呈分段增长模式,在结霜初始段,霜层主要由粒状冰晶组成,并逐渐形成柱状冰晶,其厚度增长较快;在第二阶段为柱状冰晶主要在其半径方向生长,霜层厚度增长速度减慢;而在第三阶段,柱状冰晶主要在其高度方向生长,逐渐形成针状冰晶,霜层厚度增长速度迅速增大至第二阶段的3~5.8倍。对实验结果的分析表明,热泵机组性能恶化主要是由于蒸发器表面温度下降、霜晶形态变化引起霜层厚度快速增长及空气流动阻力增加导致风机流量下降三个因素之间形成的恶性循环所致,其中换热器表面温度下降引起的霜晶形态变化起到了至关重要的作用。     

三排变片距翅片盘管换热器结霜特性实验研究

为改善空气源热泵室外翅片盘管换热器在低环境温度下沿空气流动方向结霜不均匀、首排结霜量较大进而导致热泵除霜间隔较短、制热能力下降等问题,对不同翅片片距组合的变片距翅片盘管换热器在低环温工况下运行及结霜的情况进行实验研究。结果表明：变片距翅片盘管换热器在低环温条件下可有效延长迎风面管排发生结霜堵塞的时间、对于结霜生长速度和结霜质量也有抑制作用。变片距翅片盘管换热器在结霜中后期阶段换热功率更高,在合理的翅片间距组合下,变片距翅片盘管换热器可以在不损失过多换热功率的情况下延长换热器迎风面管排结霜堵塞的时间,如样品4的平均换热功率比样品1低6.02%,而除霜间隔延长了37 min。     

翅片结构对换热器结霜特性影响的实验研究

本文对空气源热泵的翅片管换热器表面霜层生长特性进行实验研究,通过红外热像仪对霜层表面温度进行测量,并用热电偶直接测量装置进行校核.分析了平片、波纹片、条缝片3种翅片类型及翅片节距对霜层厚度、结霜量、换热量的影响,并用霜层-湿空气界面条件等作为传热及传质驱动力分析了霜层生长规律.实验结果表明,波纹片及条缝片翅片换热器界面...     

低温罩表面结霜过程数值模拟

对低温罩表面结霜过程进行了数值模拟研究。通过能量和质量平衡方程建立了低温罩结霜的物理模型,考虑了霜层厚度增加的传质和传热过程。据此分析了来流空气的温度、相对湿度、速度及冷壁面温度对霜层表面温度和霜层厚度的影响。计算结果表明,来流空气的温度及冷壁面温度对结霜的影响较大,而来流空气的速度和相对湿度对结霜的影响则较小。最后指出了对低温罩在加注低温液体时采取隔热防霜措施的必要性。     

Distributed steady and dynamic modelling of dry-expansion evaporators: Modèlisation du régime stable et du régime transitoire des évaporateurs à détente sèche

A general distributed parameter model is presented to describe both steady and dynamic behaviors of dry-expansion evaporators. The homogeneous and three different non-homogeneous two-phase flow models are used to evaluate the impact of different flow models on the accuracy of the simulation. The experimental work was carried out on a full-scale refrigeration system with R-134a as the working fluid and without frost formation at the evaporator. Comparison between the modelling and experimental measurements shows that the drift flux flow models give satisfactory predictions. The simulation results indicate that an even air temperature distribution off the evaporator may be obtained by controlling liquid dry-out point at the two ends of the coil. The study also indicates that the counterflow configuration provides a higher heat exchange efficiency with a slower transient response compared with the cocurrent-flow configuration. A general distributed parameter model is presented to describe both steady and dynamic behaviors of dry-expansion evaporators. The homogeneous and three different non-homogeneous two-phase flow models are used to evaluate the impact of different flow models on the accuracy of the simulation. The experimental work was carried out on a full-scale refrigeration system with R-134a as the working fluid and without frost formation at the evaporator. Comparison between the modelling and experimental measurements shows that the drift flux flow models give satisfactory predictions. The simulation results indicate that an even air temperature distribution off the evaporator may be obtained by controlling liquid dry-out point at the two ends of the coil. The study also indicates that the counterflow configuration provides a higher heat exchange efficiency with a slower transient response compared with the cocurrent-flow configuration.     

Dynamic behavior of a direct expansion evaporator under frosting condition. Part I. Distributed model

A general distributed model with two-phase flow for refrigerant coupled with a frost model is developed for studying the dynamic behavior of an evaporator. The equations are derived in non-steady-state manner for the refrigerant and a quasi-steady state model with permeation for the frost. The complex flow and geometry of the finned tube evaporator lead to uneven wall and air temperature distributions, which in turn affect the rate of frost growth and densification along the coil depth. Results include frost accumulation and its effect on energy transfer, air off-coil temperature, refrigerant liquid dry-out position and propagation of frost formation along the coil.     

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.     

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.     

冻藏间冷却排管霜层传热效应的研究

本文实地凋研了冻结物冷藏间冷却排管的结霜速度和相应的霜层密度及影响结霜速度的主要因素.在此基础上进一步研究分析了:(1)在蒸发温度不变条件下霜层厚度与传热系数的关系.(2)在保证排管冷量不变和库温恒定的条件下,蒸发温度、传热系数和制冷系统COP等重要性能指标随霜层厚度的变化关系.分析计算结果表明:冻藏间的冷却排管霜层厚度的过度增加会严重地影响排管本身的传热性能和制冷能力,降低制冷系统的COP.     

结霜工况下热泵空调器性能的数值模拟

本文对热泵空调器在结霜工况下的运行性能进行了理论模拟,建立了热泵空调器制冷系统稳态分布参数模型和结霜过程的动态分布参数模型.在系统模型建立中把结霜过程视为准稳态过程.计算结果表明在霜刚开始形成时,有助于增大管壁和空气之间的换热系数,当霜层达到一定厚度时热泵的制热能力,性能系数等讯速下降.经与其他已发表的文献比较计算结果合理.     

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.     

低温冷风机结霜特性的研究及其融霜方法的改进

以华中地区某禽类加工厂冻结间的冷风机为研究对象，建立数学模型，对结霜工况下冷风机运行特性进行了理论分析。模型和实验测得的霜层厚度的平均偏差8．99％，吻合较好。阐述了随着霜层的生长，空气冷却器的传热面积、传热系数以及空气侧压降的变化规律。进一步分析了冻结间内空气相对湿度、冷风机进口空气干球温度以及迎面风速等对霜层生长的影响。并遵循尽量减少初投资、节能、实用为选择改进的原则，结合企业生产工序及冻结间运行的实际情况，对原融霜方式提出改进方案。     

空气热源热泵动态结霜过程研究

建立了空气热源热泵动态结霜过程的物理模型,对热泵机组在结霜工况下的供热特性和霜在空气盘管翅片表面的集聚过程进行了动态模拟,分析了环境温湿度,翅片间距,管排数对结霜特性和机组供热性能的影响。     

Frost formation on a cold surface under turbulent flow

This study presents a mathematical model to predict the frosting behavior on a cold surface under turbulent flow. The model consists of the standard κ–ε model for turbulent flow and the diffusion equation for the frost layer. The numerical results show that turbulent flow promotes the growth of the frost layer on the cold surface, compared to the laminar flow. Increase in air velocity has little effect on mass transfer under turbulent flow, while frost growth under laminar flow is influenced by the air velocity. With constant air humidity, the frost layer thickness increases with decreasing air temperature, while the relationship for the frost density is reversed. The effect of the air temperature on the mass flux is negligible, compared to the other frosting parameters.