Modeling non-uniform frost growth on a fin-and-tube heat exchanger

Abstract

A semi-empirical model that predicts non-uniform frost growth on heat exchangers is developed and experimentally validated. The model is based on a scaling approach that uses the average frost layer properties to predict growth in a quasi-steady state, heat and mass balance based segment-by-segment coil simulation. The air redistribution algorithm in the model improved frost thickness predictions by 20%–50% and coil capacity predictions by 42% compared to the same model without air redistribution. The model along with an empirical frost delay predicted the frost thickness for different inlet refrigerant temperatures, air relative humidities and air velocities under non-uniform frosting with a root mean square error of 3.7%, 9.8% and 5.2% respectively.

Introduction

Air source heat pump systems are used for heating and cooling buildings all year around. They are energy efficient, compact and have low installation cost. An air source heat pump exchanges heat directly from the indoor environment to the outdoor ambient air, and during winter operation, the outdoor coil might accumulate frost on its surface. Defrost cycles are periodically executed in between the heating time to melt the ice, drain the water from the outdoor coil, and free its surface from accumulated frost before the heating service could start again. Thus, air source heat pumps suffer from a drop in energy efficiency, that is, a degradation of the actual heating seasonal performance factor. Due to the fact that frost and defrost are inherently transient phenomena, steady state models, which are often employed to predict the performance of heat pump systems, do not adequately describe heat pump behavior when operating in frosting conditions.

This paper presents an experimentally validated quasi-steady state heat exchanger frost growth model that is both computationally efficient and sufficiently accurate to be useful in practical engineering design of heat pump outdoor coils. The heat exchanger frost growth model is modular and when integrated with a whole vapor compression system simulation program assists in predicting the time-dependent heat transfer rate, air, frost, and refrigerant properties, and air pressure drop across the outdoor coil due to flow blockage from frost accumulation.

Frost growth is a coupled heat transfer, mass transfer, and fluid dynamic phenomenon. The performance of a heat exchanger working in frosting conditions is difficult to estimate because the rate of frost growth varies from inlet to outlet of the heat exchanger circuits. This results in a continuous redistribution of the airflow over the frontal face of the heat exchanger during the frost accumulation process. In addition, as frost grows on the fin and tube surfaces, the heat transfer area changes along with the free flow area. The direct effect of frost is increased air side resistance to both flow and heat transfer thereby reducing heat transfer performance. Previous models have either neglected the dynamic redistribution of airflow due to non-uniformity of frost thickness at various locations or assumed uniform frost thickness over the entire surface of the heat exchanger. Such assumptions introduce significant error if the fin/tube temperatures vary considerably. In order to effectively integrate the frost growth model in a heat exchanger simulation algorithm, all variables of interest should be solved with the boundary conditions set on the air and refrigerant side. Typically this means that air and refrigerant inlet flow rates and temperatures are the only direct inputs to the heat exchanger model; the surface temperature of the fins is not used as the control variable. A unique feature of our model is the ability to simultaneously update fin and tube heat transfer areas, air free flow area and the air flow map across the face of the coil due to the direct and indirect effects of frost growth on the heat exchanger during each time step of the frosting simulation period.

Previous studies pertaining to frost growth on simple geometries such as flat plates and cylinders focused either on the development of empirical correlations for frost properties or on modeling the heat and mass transfer within the frost layer. Yonko and Sepsy (1967) presented empirical correlations for frost thermal properties as a function of frost density. The relation of Hayashi et al. (1977) which expressed the density of frost as a functions of the frost surface temperature is used in this study. Schneider (1978) claimed that the properties of the frost layer were not affected by the Reynolds number or the difference in vapor pressure water in the air and frost layers. Their conclusion that the water vapor pressure differential did not affect the frost growth did not agree with the observations of other researchers. Jones and Parker (1974) developed an analytical model for the rate of frost growth on a heat exchanger. They provided closed form solutions for the frost surface temperature and the temperature gradient inside the frost layer. The model was able to predict the frost growth for varying environmental parameters, but was not validated for a heat exchanger. Yun et al. (2002) proposed an empirical model for frost parameters and heat and mass transfer rate based on the average frost roughness. They compared the results from the model to experimental data. The trends predicted by the model matched the experiments well. However, for some parameters like frost density and frost surface temperature, the values predicted by the model did not match the experimental data. Frost growth on cylinders in cross flow has been studied and reported in literature (Raju and Sherif, 1993, Mago and Sherif, 2003, Lee and Ro, 2001).

Stoecker (1957) studied the performance of a fin-and-tube heat exchanger under frosting conditions. He studied the performance under both constant air flow and variable air flow conditions. Frost growth models for heat exchangers have also been previously reported in the literature. Padki et al. (1989) presented a quais-steady state model applicable for both flat plate and round tubes. However, the approach of Padki et al. (1989) requires the knowledge of heat transfer coefficients for the fin and the tube separately which are difficult to obtain. Kondepudi and ONeal, 1991, Kondepudi and ONeal, 1993 presented expressions for fin efficiency and overall heat transfer coefficients for heat exchangers, but they did not implement the correlations in a simulation model. Yang et al. (2006) presented a time marching model for frost growth in heat exchangers which can be used with a segmentation model. This model, however, does not calculate the surface temperature, but requires it as an input to the model during the frosting process. A finite difference model was presented by Chen et al. (2000). This model significantly increases the computation time of the overall heat pump simulation. A frost growth model for heat exchangers based on scaling was presented by Storey and Jacobi (1999). One shortcoming of this model was that it did not consider diffusion in the frost layer and assumed that heat and mass transfer coefficients remain constant throughout the entire frosting period. The work however demonstrated an approach of using the average frost layer properties instead of local frost properties in heat exchanger applications. Due to the simplicity of the model, it will be used as a basis for the work presented in this paper. In the authors’ opinion, frost models available in the literature generally lacked the ability to simulate the effect of time-delayed onset of frost nucleation due to the effects of local fin temperature and the subsequent redistribution of airflow across the heat exchanger during the frosting process. This might be due to the fact that experimental data for model validation are difficult to obtain.