1、 International Journal of Heating, Ventilating, Air-conditioning and Refrigerating Research Editor Reinhard Radermacher, Ph.D., Professor and Director, Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, College Park, USA Associate Editors James
2、 E. Braun, Ph.D., P.E., Professor, Ray W. Herrick Laboratories, Alberto Cavallini, Ph.D., Professor, Dipartmento di Fisicia Tecnica, University of Padova, Italy Qingyan van) Chen, Ph.D., Professor of Mechanical Engineering, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana
3、, USA Arthur L. Dexter, D.Phil., C.Eng., Professor of Engineering Science, Department of Engineering Science, University of Oxford, United Kingdom Srinivas Garimella, Ph.D., Associate Professor and Director, Advanced Thermal Systems Laboratory, Department of Mechanical Engineering, Iowa State Univer
4、sity, Ames, Iowa, USA Leon R. Giicksman, Ph.D., Professor, Departments of Architecture and Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, USA Anthony M. Jacobi, Ph.D., Professor and Co-Director ACRC, Department of Mechanical and Industrial Engineering, University of Illino
5、is, Urbana-Champaign, USA Bjarne W. Olesen, Ph.D., Professor, Intemational Centre for Indoor Environment and Energy Technical University of Denmark Nils Koppels All, Lyngby, Denmark Jeffrey D. Spitler, Ph.D., P.E., Professor, School of Mechanical and Aerospace Engineering, Oklahoma State University,
6、 Stillwater, Oklahoma, USA School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA Editorial Assistant Lon Puente, CEEE OfficeiMechanical Engineering, University of Maryland (301 -405-5439) Policy Committee Special Publications Staff Daryl Boyce, Chair, Member ASHRAE P. Ole
7、 Fanger, Fellow/Life Member ASHRAE Curtis O. Pedersen, Fellow ASHRAE Reinhard Rademacher, Member ASHRAE Jeff Littleton, Associate Member ASHRAE W. Stephen Comstock, AssociateMember ASHRAE Mildred Geshwiler, Editor Erin S. Howard, Associate Editor Christina Helms, Associate Editor Michshell Phillips,
8、 Secretary Barry Kurian, Manager W. Stephen Comstock Publishing SeMces Publisher 02004 by the American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc., 1791 Tullie Circle, Atlanta, Georgia 30329. All rights reserved. Periodicals postage paid at Atlanta, Georgia, passages or r
9、eproduce illustrations in a review with appropriate credit; nor may any part of this book be reproduced, stored in a retrieval system, and additional mailing offices. HVAC Ei (Engineering Information, inc.) Ei Compendex and Engineering Index; IS1 (institute for Scientific Information) Web Science an
10、d Research Alert; and BSNA (Building Services Research accepted July 19,2004 There has been a continuing effort to advance the understanding and modeling ofpost forma- tion on refrigerated surfaces during the last two decades for better design of air-to-refrigerant heat transfer equipment and effect
11、ive and energy-saving control of depostng processes. A review and comparative analysis of the available literature concerning frost properties, correla- tions, and mathematical models are presented in this study to provide an overview of the analyt- ical tools for researchers, product developers, an
12、d designers. The frost research can be divided into two general groups-experimental correlations and mathematical models. In general, the properties correlated are the frost thermal conductivity, the frost average densiv, and air-frost heat transfer coeficient (Nusselt number). A limited operational
13、 range of these relations is observed. The mathematical models include both differential and integral approaches, which are, in general, solved numerically. These models are class$ed based on the geometrical con- figuration of cold surface. A comprehensive comparison of the models is given to assist
14、 the reader in making their decisions for design analysis. The existing gaps in the frost research are dentijed and recommendations are made. INTRODUCTION Frost formation on evaporator surfaces under operating conditions of various freezers and refrigeration systems occurs inevitably, and its conseq
15、uence is well known; that is, frost forma- tion results in a reduction in the heat transfer rate and the blockage of air passage and ultimately decreases the design capacity of the equipment that is rated at the dry condition. To keep the refrigeration systems in a desired operating condition, vario
16、us defrosting devices with their con- trol strategies must be built as the integral part of the system. To accurately predict and control the defrost cycle, one needs to understand the complex relation between the frost formation pro- cess and operating conditions of the system. In the 1970s and 198
17、0s, many researchers focused on the fundamental understanding and characterization of frost properties and their functional relations to various frost formation processes. ONeal and Tree (1 985) reported a review sum- marizing the available correlations in the literature that characterizes frost thi
18、ckness, frost ther- mal conductivity, and heat transfer coefficient on frosting surfaces. During the last two decades, the advance in computational methods prompted more advanced development of analytical and numerical models along with more experimental correlations describing various benchmark con
19、figurations, such as frost formation on flat surfaces as well as on limited types of fin sur- faces. The results have not only just contributed further to the frost properties but also, more importantly, presented various degrees of capabilities in predicting or, more precisely, simulat- Jose Iragor
20、ry is a Ph.D. candidate and Yong-Xin Tao is an associate professor in the Department of Mechanical and Materials Engineering, Florida International University, Miami, Fla. Shaobo Jia is a senior research engineer at Heatcraft Refigeration Products, Inc., Stone Mountain, Ga. 393 394 HVAC Kaviany 1993
21、) shows the definition of a typical frost +yx,t)= +(x,t), d - c Densification and I Bulk-Growth Period I I 1 I tc tt ct Figure 1. (a) Definition of frost growth periods (Tao et al. 1993), and (b) a model of the initial conditions for the solidification and tip-growth (STG) period (Ha0 et al. 2004).
22、VOLUME 10, NUMBER 4, OCTOBER 2004 395 Figure 2. Surface feature comparison (side view) between (a) natural and (b) forced con- vection (Re = 1,400) during the STG period: Tair = -5OC; T, = -3OOC. Frost growth time = 60 minutes. formation process under natural convection during which the temperature
23、of the cooling plate decreases from an initial ambient temperature to a steady-state temperature. The ambient can be either above or below freezing. The initial cooling period is called the drop-wise condensation (DWC) period, during which the condensing droplets in a subcooling state form on the co
24、ld sur- face and all of the coalescent droplets turn into ice particles after a characteristic time (called critical time) tc is reached. This time scale is a function of ambient conditions (temperature, nat- ural or forced convection) and cold surface temperature and roughness. In Figure 1, the mea
25、n droplet diameter, d, and the mean length scale, 1, of the nucleation site, are defined at the critical time, where $I is the areal fraction of droplets. L= The moment at tc is often the actual initial time for many models, as will be discussed later. Once the DWC period reaches the critical time,
26、the solidification and tip-growth period (STG) starts and continues until a transitional time, t, is reached when a relatively uniform porous layer of frost forms. Because of the nature of nonuniform tip-growth on individual drop- lets, especially for tiny ones that are still in the liquid phase, th
27、e average value of !, based on the areal droplet fraction (Equation 1) is not representative of the actual volumetric fraction of frost, = pipi. Therefore, Equation 1 could be modified as where !,fand defare defined in Figure lb in such a way that the total mass of ice accumulation is equal for both
28、 definitions. After t, the frost layer enters the densification and bulk-growth (DBG) period when the frost layer appears globally homogeneous and possesses characteristics of a porous media, with its structure and characteristics depending on the physical and thermodynamic frost properties of a spe
29、cific application. Frost formation under forced convection deviates fiom the above-defined three-period forma- tion process mainly in the STG period. Depending on the speed of the airflow, the pattern of tip growth might be replaced by a tree-growth pattern or other patterns. Figure 2 shows a typica
30、l 396 HVAC= Tr,-Tw (Theoretical) K6 FLATPLATE universal 800 kg/m3 K, = Cl I-c -+1 Kperp Kpar Pf) C1 = 0.042 + 0.42 x 0.995 (Theoretical) K7 FLATPLATE W/mK T, = -5C to Max. density 1992 Mao et al. -15C 200 kg/m3 Ta = 15C to Assumed 23C qs = oc u=1.15to2.67 mis (Empirical) k = 0.132+ 3.13 x iO-4p / +
31、1.6 x w7p2 / / (Empirical) -=cI+1. L=2+2 universal 800 kg/m3 kpor = (1 - K8 FLATPLATE WImK T, = -15T Max. density 1994 Lee et al. Ta = 25OC 400 kg/m u = 0.5 to 2.0 mis K9 FLATPLATE I I-c I-E E WImK Assumed Max. density 1997 Le Gall et al. 9 kperp kpa, kperp *a Lice + sakice %is equivalent toke. 398
32、Table 1. Thermal Conductivity Correlations (kt, (Continued) HVAC j). The layer growth mass flux will determine the frost thickness incremental for each time step. This model was validated with experimental work, giving an average deviation in frost thick- ness of 5.5%. A sensibility study of the eff
33、ects of varying humidity ratio and air velocity gave a direct relation between these parameters and the frost surface temperature and the frost layer thickness. Nevertheless, this modei does not take into account the early stage of frost nucleation, and it uses the standard Fick?s diffusion coeffici
34、ent for water vapor in air; therefore, it will over- estimate the rate of frost growth. Ismail and Salinas (1 999) M7 presented a revision of Tao?s two-stage model using a prede- termined transition time for the configuration of parallel flat plates. In this differential approach, a modified vapor p
35、hase temperature is used in the first stage, and the initiai values for density and thickness are functions of the material and temperature of the cold plate. The transition time and coupling equation were determined based on the studies of Hayashi et ai. (i 977) and Tao et al. (1993). The local vol
36、ume averaging technique is used in the layer growth period, where con- stant thermal conductivities are used for the solid and vapor phase across the frost layer, and the effective diffusion coefficient is obtained using the diffusion factor by Tao et al. (1993). The growth rate equations for the fi
37、rst and second stages are, as in the case of Tao et al.?s model, the boundary conditions for the energy and mass transfer equations. First stage: Second Stage: Chen et. a. (1999) M8 modified the differential model by Tao et al. (1993), replacing the early growth period by modified initial conditions
38、 and setting the boundary condition for the solid phase volumetric fraction at the plate to a constant value. Additionally, they changed the correla- tions used for the calculation of the heat and mass transfer coefficients in order to account for frost surface roughness m4 (see Table 4). The layer
39、growth rate is obtained, as in Tao et al.3 model, from the mass and energy boundary conditions at the frost surface (see Equation 12). VOLUME 10, NUMBER 4, OCTOBER 2004 411 Further modification of this model was performed for the simulation of frost growth on heat exchanger fins M9. A simplification
40、 of the three-dimensional governing equations was per- formed based on previous experimental and numerical results, eliminating terms with a rela- tively low order of magnitude compared to the dominant term, which is the mass accumulation rate (source term). Finally, the same governing equations (of
41、 the previous model) were used for the temperature and vapor density distribution in the direction perpendicular to the fin surface. The boundary and initial conditions are maintained, with the exception of the temperature at the plate (boundary condition), which is obtained with a heat conduction m
42、odel for the fin. Therefore, the frost growth model and the fin heat conduction model are coupled by the plate temperature and temperature gradient. Additionally, based on experimental results, the initial ice volumetric fraction (EP) depends on the position on the fin. Therefore, a two-dimensional
43、linear function was used so that the values for &Po are set between 0.01 and 0.21. X Y Epo(X,Y) = 0.01 + o. 1 - + 0.1 - fin $in The model was validated against experimental data for the frost thickness at reffigeration con- ditions, resulting in acceptable agreement between results. However, a notic
44、eable overprediction was obtained at the upper fin section, due mainly to the effect of the insulation cover on the experimental results. Another negative aspect of the simulation is the consideration of the frost growth near the base as a one-dimensional problem in the direction perpendicular to th
45、e plate. A system of subdomain coupled transient partial differential equations was developed by Ler and Beer (2000) MlO for the frost growth during the DBG period, in which the parallel plates geometry is divided into two subdomains (humid air and frost) connected by the thermal and mass balance at
46、 the interface. The properties for the humid air are evaluated at entrance con- ditions, while volume average and mass average are used for the frost density and specific heat, respectively. The temporal layer thickness is obtained with the evaluation of the coupling condi- tions for air velocity, t
47、emperature, and density as follows: u = -Ls,x“ 3 Similar to previous models, the initial conditions for the frost are the wall temperature and porosity (volume fraction) at the surface. No initial thickness to account for early growth is used, and an iteration process is required to determine the ap
48、propriate value of local porosity at the surface (which varies with position). This model was validated using experimental results obtained in this study, with satisfactory results. Limitations of the model are the requirement of iterative processes for thickness and frost surface porosity, which ha
49、s to be confirmed by experimental results and the relatively high temperature for the airstream used in experiments. The effect of frost surface roughness on the convective heat transfer coefficient and thermal conductivity was introduced by Yun et. al (2002) M12, who developed a correlation for the frost roughness as a function of time. The surface friction coefficient and heat transfer coeffi- cient is calculated as presented in Table 5 ml i, and Woodsides equation is used in the calcu- lation of thermal conductivi
