Applied Thermal Engineering

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1 Applied Thermal Engineering 31 (2011) 3084e3091 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: Case Study In-situ evaluation of a criterion to predict frost formation on liners of refrigerated cabinets Robson O. Piucco a, Christian J.L. Hermes b, *, Cláudio Melo c a Whirlpool S.A. - Home Appliances Unit, , Rua Dona Francisca 7200, Joinville-SC, Brazil b Applied Thermodynamics Research Center, Department of Mechanical Engineering, Federal University of Paraná, PO Box 19011, , Curitiba-PR, Brazil c POLO Research Laboratories in Cooling and Thermophysics, Department of Mechanical Engineering, Federal University of Santa Catarina, , Florianópolis-SC, Brazil article info abstract Article history: Received 1 March 2011 Accepted 4 May 2011 Available online 12 May 2011 Keywords: Frost formation Design criterion Refrigerated cabinet This paper evaluates a theoretical criterion to predict whether frost will form on the inner liners of refrigerated compartments. In-situ experiments were carried out using a Combi top-mount refrigerator tested within a climatized chamber with rigid control of the temperature and humidity. Two experimental tests were performed, one keeping the doors closed and another using an automatic dooropening device. During the tests, both the liner surface temperature and supercooling degree were monitored at different locations within the refrigerated cabinet. After the test period, the cabinet was opened and photographed to identify the sites of frost nucleation. In addition, samples of different liner materials were extracted from the refrigerated cabinet in order to measure the contact angle. For each surface, the maximum supercooling degree observed experimentally was plotted as a function of the contact angle and thus compared to the nucleation limits provided by a theoretical model introduced in a previous study [1]. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction In most refrigerating appliances, frost is supposed to form on the evaporator coil only. Nonetheless, under certain environmental, operating and constructive conditions, frost is sometimes found on the cabinet liners, increasing the field call rates and consequently the maintenance and quality costs. In order to avoid this drawback, manufacturers have been pushed to consider new refrigerator concepts, while maintaining or even reducing the product costs and energy consumption. Although several distinguishing publications in the field of frost formation can be found in the open literature [2e8], none of them were actually aimed at predicting the frost formation on liners of refrigerated cabinets focusing on the most important factors that drive the frost nucleation process, namely air temperature, humidity and velocity, and surface conditions (temperature, roughness and contact angle). In a previous study [1], the ice crystal nucleation process was investigated both theoretically and experimentally in order to provide the physical basis upon which to forecast whether frost nucleation will occur under different psychrometric and surface conditions. A mathematical model for the heterogeneous frost * Corresponding author. Tel.: þ address: chermes@ufpr.br (C.J.L. Hermes). nucleation on smooth surfaces was put forward based on the classical nucleation theory [9,10]. Experiments were additionally carried out using a purpose-built testing facility to provide data for the model validation exercise. The model predictions were compared to the experimental data showing a good level of accuracy. In the present paper, the model accuracy was assessed in real application conditions by testing a typical household refrigerator using an automatic door-opening device installed in a climatized test chamber with rigid control of the temperature and humidity. Samples of different liner materials were extracted from the refrigerated cabinet in order to measure the contact angle. For each surface, the maximum supercooling degree was plotted as a function of the contact angle and then compared to the nucleation limits provided by the theoretical model introduced by Piucco et al. [1]. 2. Nucleation model Certain temperature and humidity conditions are required for the onset of frost nucleation. In cases where the surface temperature is above the dew-point, only sensible heat transfer occurs. If the surface temperature is below the dew-point but above 0 C, vapor condensation may take place. On the other hand, if the surface temperature is below 0 C, the condensed vapor might /$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.applthermaleng

2 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e Nomenclature Roman G Gibbs free energy [J] I Embryo formation rate [m 2 s 1 ] I 0 Kinetic constant [m 2 s 1 ] k Boltzmann constant [J K 1 ] M Molar mass of water [kg mol 1 ] R Ideal gas constant [J mol 1 K 1 ] T Temperature [K] V Volume [m 3 ] Greek g Surface energy [J m 2 ] r Density [kg m 3 ] q Contact angle [degrees] u Humidity ratio [kg steam /kg dry-air ] Subscripts e embryo se interface embryo-surroundings ew interface embryo-wall s surroundings sat saturation sw interface surroundings-wall w wall freeze. Finally, in cases where both surface and dew-point temperatures are below 0 C, vapor desublimation may occur, i.e., vapor changes directly into solid. In this case, a difference between the dew-point and surface temperatures, DT sup, known as the supercooling degree, is required for the onset of nucleation. The transformation of water vapor into frost follows a heterogeneous nucleation process. In this case, the minimum energy required to trigger the nucleation process, DG, is obtained from [1]: Fig. 2. Schematic representation of the climatized chamber. gas constant, g se is the surface energy at the embryo-surrounding interface, u s is the humidity ratio at the surrounding temperature T s, and u sat,e is the saturated humidity ratio at the embryo temperature, T e. As reported by Volmer and Flood [11], a minimum rate of embryo formation of 2.2 embryo/cm 2 s is required for a homogeneous nucleation process to begin. For heterogeneous nucleation, Becker and Doring [12] proposed the following exponential function for the rate of embryo formation, I, I ¼ I + exp DG (2) kt w DG ¼ 4p 3 rrte M ln g 3 se usat;e u s 2 ð1 cosqþ 2 ð2 þ cosqþ (1) where q is the contact angle, r, V and M are, respectively, the density, volume and molar mass of ice (in the case of desublimation) or water (in the case of condensation), R is the universal Fig. 1. Minimum supercooling degree required for the onset of nucleation [1]. Fig. 3. Schematic representation of the door opening device.

3 3086 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e3091 Fig. 5. Schematic representation of the surface instrumentation. thresholds for a smooth surface in terms of the supercooling degree as a function of the contact angle. It can be seen that unless q is zero, there must be a certain supercooling degree to trigger the phase change process. More details can be found in [1,13]. 3. In-situ measurements Fig. 4. Refrigerator instrumentation: (a) freezer compartment, (b) freezer door, and (c) ice tray compartment. where I o ¼ embryo/cm 2 s is the kinetic constant of desublimation, k ¼ J/K is the Boltzmann constant, and T w is the surface temperature. Combining the Becker and Doring [12] equation and the minimum rate of embryo formation observed by Volmer and Flood [11], the limit energy barrier required for the onset of nucleation can be expressed in terms of the supercooling degree as a function of the contact angle. Fig. 1 plots the nucleation Refrigerators are usually designed for a standardized test condition according to which the refrigerator must be tested with the doors closed [14,15]. Assuming that there is no moisture infiltration through the gaskets, the probability of frost formation on the cabinet walls is quite low when the doors are closed as the air is kept dry. However, in cases where the door is periodically opened, home usage for instance, the amount of moisture inside the freezer compartment is considerable, and the supercooling degree required for the onset of nucleation is usually surpassed. In order to compare both close and opening door situations, two experiments were carried out, one keeping the refrigerator doors closed and another opening both the freezer and fresh-food doors according to a preset pattern. Tests were performed with the refrigerator placed inside a climatized chamber with a strict control of the operating conditions (air humidity and temperature), as depicted in Fig. 2. The experiments were carried out with a Combi top-mount 432-L refrigerator, whose refrigeration capacity is controlled by switching the compressor on and off through an electronic thermostat. In this particular refrigerator, the cold air is conveyed to each of the refrigerated compartments (freezer and fresh-food) through two independent fans. After a predefined period of time, the refrigerator is switched off and a defrost heater melts the frost deposited along the evaporator coil. The opening of the door was performed using purpose-built devices attached to the freezer and fresh-food doors, as depicted in Fig. 3, which could be operated independently. Each of these devices permits the time between door openings and the period of time during which the door remains open to be programmed. During the test, the freezer door was opened every 12 min for 10 s over a 1-h period, while the fresh-food door was opened every 3 min for 30 s over the same period. This procedure was repeated 4 times a day at 3 h intervals. This program was adopted since it has been used regularly in the industrial environment to access product robustness in terms of frost formation and defrosting strategy [13]. Table 1 Measured velocities [m/s]. Surface # I II III IV V VI VII VIII IX Door closed Door openings

4 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e Fig. 6. Contact angle measurement apparatus. Table 2 Measured contact angles [degrees]. Surface # I II III IV V VI VII VIII IX Contact angle During the tests, the temperatures of nine different surfaces of the freezer compartment were instrumented as illustrated in Fig. 4: top (I), center (II) and bottom (III) of the plenum cover (the wall placed in between the freezer compartment and the evaporator Fig. 8. Test with doors opened periodically. Surface I: (a) supercooling degree and (b) surface temperature. region); top (IV) and center (V) of the door liner; freezer drawer (VI) and shelf (VII); water reservoir (VIII); and left wall (IX). Both the surface temperature and the supercooling degree were monitored over time. The former was measured using stick-on T-type thermocouples, while the latter was calculated based on the measurements of air temperature and humidity at 20 mm from the surface by T-type thermocouples and capacitive relative humidity transducers (uncertainty of 2%), respectively (see Fig. 5). All thermocouples used in this study have an uncertainty of 0.2 C. In addition, the air velocity parallel to each surface was evaluated using a hot-wire anemometer with a measurement uncertainty of 0.1 m/s. Velocity measurements were performed a priori at the maximum air flow rate and the results are summarized in Table 1.It should be noted that the regions near surfaces I and VIII presented the highest velocities, while the regions close to surfaces IV and VI presented the lowest velocities. The contact angles were characterized by depositing and photographing a water droplet with a known volume on the horizontal surface [13] (see Fig. 6). The measurement uncertainty of the contact angles lies within a band of 5. As can be seen in Table 2, all nine surfaces presented similar contact angles since they were made from the same raw material and processed according to the same manufacturing technique. 4. Discussion Fig. 7. Test with doors closed. Surface I: (a) supercooling degree and (b) surface temperature. Two of the nine surfaces investigated during the experiments merit particular attention. One is the plenum cover (surface I),

5 3088 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e3091 Fig. 9. Surface V during test with doors closed: (a) supercooling degree and (b) surface temperature. Fig. 10. Surface V during test with doors opened periodically: (a) supercooling degree and (b) surface temperature. i.e., the wall placed in between the freezer compartment and the evaporator region (see Fig. 4a), which is chilled by the extremely cold air flowing through the evaporator coil on one side, whilst it is warmed by freezer air on the other side. In addition, during the door opening period, its central and bottom regions are reached by an external air stream, while the top region is practically encapsulated by the freezer drawer. Fig. 7 shows the variation in the supercooling degree (Fig. 7a) and the surface temperature (Fig. 7b) at the plenum cover during the test with the doors closed, where supercooling degrees of up to 5 C can be observed during the defrost period, when the surface temperature increased from 25 to 5 C. Considering that the contact angle is 72 and the surface temperature was kept below the freezing point, 5 C of supercooling should be sufficient to trigger the nucleation process (see Fig. 1), thus a favorable condition for droplet condensation and freezing was observed. Fig. 8 plots the variation of the supercooling degree (Fig. 8a) and the surface temperature (Fig. 8b) at the plenum cover (top region) during the test with the door opened periodically. Surprisingly, the supercooling degree did not surpass 7 C, a value similar to that observed with the doors closed, which is due to the flow confinement provoked by the freezer drawer. The surface temperatures varied from 25 to 10 C, being below the freeing point most of the time. Again, there is a favorable condition for droplet condensation and freezing, as can be observed in Fig. 1. In addition, four temperature peaks are noted in Fig. 8b instead of the two peaks observed during the test with the doors closed (Fig. 7b), indicating that the refrigerator control regime changed to ensure a proper evaporator defrosting. Interesting results were also observed for the door liner (surface V), as its temperature is usually warmer than the internal air because of the heat gained from the surroundings (see Fig. 4b). During the tests with the doors closed, the air velocity close to surface V is high, which reduces its temperature. As can be seen in Fig. 9, supercooling degrees of up to 7 C can be observed (Fig. 9a) with surface temperatures varying from 25 to 12 C(Fig. 9b). Associating this with a contact angle of 78 indicates that a favorable condition for frost nucleation occurs (Fig. 1). During the test with doors opened periodically (see Fig. 10) the peaks of supercooling degree were observed up to 20 C (Fig. 10a) for surface temperatures of 5 C(Fig. 10b), which is an extremely favorable condition in terms of triggering the frost nucleation process. Fig. 11 compares both the experimental results obtained from the tests with the doors closed (Fig. 11a) and with the doors opened periodically (Fig. 11b) with the predictions of the theoretical model presented by Piucco et al. [1]. Fig. 11a shows that, except for surface III, there are favorable conditions for droplet condensation and freezing on the internal walls even when the doors are kept closed. However, no frost formation on the inner walls was actually observed at the end of the test, probably because there was no significant air infiltration to the cabinet, in such a way that the air humidity was reduced substantially during the test and, therefore, the ice has turned back into vapor (i.e., sublimation) during the compressor off period, when the cabinet liners are warmer.

6 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e Fig. 11. Frost formation with the doors (a) closed and (b) periodically opened. For the tests with periodic opening of the doors the conditions were favorable for frost formation by vapor desublimation for all surfaces except I and VIII which presented favorable conditions for droplet condensation and freezing. The theoretical predictions were corroborated by visual inspection of the surfaces at the end of the test, as shown in Fig. 12. As can be noted, most surfaces presented sites with frost or ice, according to the model predictions. It was found that surfaces II and III presented the thickest frost layers, while surfaces IV, V and VII had the thinnest ones. Also, frost layers were also noted on surfaces VI and IX, whereas a large amount of ice was formed over surface VIII. On the other hand, surface I did not present ice nucleation, which is due to its proximity to the nucleation threshold (i.e., theoretical uncertainties), and also to the ice sublimation when the compressor is off.

7 3090 R.O. Piucco et al. / Applied Thermal Engineering 31 (2011) 3084e3091 Fig. 12. Visual appearance of surfaces after the test period. 5. Conclusions This study assessed the accuracy of a theoretical model for predicting frost formation on the inner liners of refrigerated compartments. A Combi top-mount refrigerator was tested within an environmental test chamber with rigid control of the temperature and humidity. The inspection of the cabinet liners after the test with periodic opening of the doors showed that the predictions of the theoretical model can be used to qualitatively forecast whether or not frost will form. Moreover, the following methodology for the analysis of frost and ice nucleation on the inner walls of refrigerated cabinets was proposed. Firstly, experimental tests with the refrigerator using a door opening device must be carried out in order to identify the sites where frost or ice form. The contact angles of the critical surfaces must be measured. Based on the operating (supercooling degree) and surface conditions (contact angle and temperature), the model can be used to determine the proximity of the actual conditions to the nucleation limit. Based on this information, the contact angle and/or the supercooling degree needs to be reduced (without increasing the roughness) in order to improve the surface robustness to the frost formation. After modifications, the refrigerator must be re-tested to confirm the model predictions. The procedure is then repeated until the desired condition is achieved. It is worthy of note that the nucleation limits established by the theoretical model of Piucco et al. [1] are valid for smooth surfaces only. In case of real surfaces, the minimum supercooling degree required for the onset of nucleation is lower than its counterpart for smooth surfaces and, therefore, real surfaces show more favorable conditions for frost formation than smooth ones. A model suitable to predict the nucleation limits for real, non-smooth surfaces is still to be developed. Acknowledgements This study was carried out at the POLO Labs under grant no / (Brazilian National Institute of Science and Technology in Refrigeration and Thermophysics) funded by the CNPq Agency. Financial support from Whirlpool S.A. is also duly acknowledged.

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