AN EXPERIMENTAL STUDY OF THE FROST FORMATION ON A COLD SURFACE IN FREE CONVECTIVE FLOW

Transcription

1 AN EXPERIMENTAL STUDY OF THE FROST FORMATION ON A COLD SURFACE IN FREE CONVECTIVE FLOW Giovanni Tanda, Marco Fossa DITEC, Università degli Studi di Genova via all Opera Pia 15a, I Genova, ITALY tanda@ditec.unige.it, mfossa@ditec.unige.it ABSTRACT The frost growth on a vertical cold plate exposed to a free convective flow has been experimentally investigated. The plate is placed in a vertical channel open at the top and bottom in order to permit the natural circulation of ambient air. The cold surface temperature has been varied in the -13 to 4 C range, while the ambient air relative humidity resulted in the range percent at the temperature of C. The measured quantities during the frost formation included the frost thickness (in three different spots), the frost surface temperature and the mass of frost deposited. The frost thickness was found to depend mainly on time and on the frost to plate temperature difference. The frost mass increased linearly with time and was mainly affected by the difference between the air humidity ratio and the saturated humidity ratio of the frost surface. INTRODUCTION Processes involving heat transfer from a humid air stream to a cold surface, with the simultaneous deposition of frost, are of great importance in a variety of refrigeration equipment. As the frost layer grows thicker, the heat transfer is affected in part because of the insulating effect of the frost layer. This can adversely affect the performance of the cooling equipment. The frost formation process is complex due to the fact that the frost properties vary continuously during the frost growth and also because of the temporal and spatial changes of the air-frost interface temperature. Typical frost formation periods have been described by Hayashi et al. [1]: an initial one-dimensional crystal growth is followed by a frost layer growth period and, finally, a socalled frost layer full-growth period characterises the long time processes, where the frost surface can reach the melting temperature. Each growth mode is characterised by peculiar values of the frost density which in turns affects the other frost parameters (thickness, apparent conductivity). Furthermore, as observed in several studies [2-5], the features of the heat transfer rate (through the wall-to-air temperature difference) and of the mass transfer rate (which depends on air moisture content too) affect the frost structure and control the length of the growth periods. As a consequence of the complexity of the phenomenon, the development of reliable frost formation models as well as of correlations for frost properties evaluation is a demanding task and experimental data are required to check the assumptions done in the theoretical analyses as well as the predicted results. Despite the large mass of studies devoted to the frost formation process, only a limited number of investigations deals with the mass-heat transfer on a surface at subfreezing temperatures for a natural convection airflow. This problem was tackled by Kennedy and Goodman ([6], study of frost formation on a vertical plate), Tajima et al. ([7], plane surface with different orientations), Cremers and Mehra ([3], outside surface of vertical cylinders), Tokura et al. ([4], vertical plate). To the authors knowledge, no data are available for the natural convection in channels, despite this situation has practical significance in such devices as evaporative heat exchangers for cryogenic liquid gasification. The present study aims to investigate some aspects of the transient process of frost formation on a vertical plate inside a rectangular channel where ambient air is flowing due to natural convection. Attention was focused on the thickness and the surface temperature of the growing frost layer and to the total mass of frost deposited on the cold surface. The experiments were conducted in the range of low and intermediate values of the of relative humidity (31-58 percent) for which the frost temperature, during the frost growth, is well below the triple-point temperature, thus acting as an additional parameter of the study. The measured data have been analysed in order to obtain correlations for the thickness and the frost mass as functions of the most important parameters. THE EXPERIMENT A schematic view of the experimental apparatus is shown in Figure 1. The entire apparatus and the measurement instrumentation were placed in a large laboratory where the relative humidity could be regulated over the percent range at 27±1 C. The channel, made of Plexiglas and rectangular in shape, had a section of 20 mm x 360 mm and is 2.4 m long: it was open at the top and bottom in order to

2 95 mm 77 mm Refrigeration unit Cold surface Polystyrene guard hygro-mete r Cold surface 17 mm 282 mm 50 mm Thermocouple arrays permit the natural circulation of ambient air. The test section, located 1.3m from the channel top section and m from the bottom section, consisted of the cooled plate, 95 mm long and 282 mm wide, and three Plexiglas walls to form a channel as deep and wide as the entrance and exit channels. The plate was made of copper and cooled by the internal circulation of a glycol solution coming from a thermostatic bath. The plate was framed inside a Plexiglas wall and separated from it by 10 mm-thick polystyrene strips in order to minimise the thermal conduction at the plate boundaries and thus avoid the frost (and dew) formation on surfaces different from the test surface. During the experiments, the buoyancy-induced humid air entered the channel from the top section and flows along the cold plate causing the progressive formation of a frost layer. The surface temperature of the copper plate was measured by five pre-calibrated thermocouples, fitted inside small holes drilled into the wall material positioned as close as possible to the exposed surface. Two of them were able to move inside the frost layer driven by micrometers. The relative humidity of the convective air flow was measured by capacitance hygrometers, carefully calibrated in the percent range, positioned at the inlet and outlet of the test section. Additional thermocouples were located in the material framing the cooled plate (in order to check the thermal conduction to the plate from the surrounding). An infrared, pre-calibrated temperature detector was used for the A C B Multiplexer & multimeter Test section Figure 1. Schematic layout of the vertical channel and of the cold plate measurement of the average frost layer surface temperature, with an estimated uncertainty of 0.4 C. The thickness of the frost layer was continuously monitored at three different locations (A, B, C) as shown in Fig.1. The employed sensors were mounted on micrometers in order to carefully check their position when moved from the Plexiglas wall facing the cooled plate towards the frost surface. Two alternative types of sensors were used: impedance sensors and nylon sensors. The impedance probes were realised by eliminating the junction in a shielded thermocouple in order to obtain a pair of closely spaced electrodes (at a distance of about 0.3 mm). A DC low voltage, applied to the thermocouple wires, gave rise to a small current circulation when the probe tip was in contact with the frost layer; this kind of measurement was particularly suitable in the presence of a rather compact layer of frost. In the presence of a fragile structure of the frost layer, a probe with the tip made of nylon (to prevent the melting of the frost) was employed and the contact with the frost surface was visually observed. The estimated uncertainty of the frost layer thickness was 0.1 mm, regardless of the type of probe employed. Each experiment was conducted by keeping fixed the temperature and relative humidity of the ambient air and for a given value of the surface temperature of the cooled plate. The experimental runs were performed by maintaining the temperature of the ambient air at a constant temperature (±0.5 C). Typically, the ambient temperature was set at C and with a relative humidity varying over the range of 31 to 58 percent (with maximum variations of 1 percent during each test run). The surface temperature of the cooled plate was varied from 13 to 4 C, with variations in time and along the surface, relative to the average value, within ±0.3 C. Before cooling the test plate, the surface had been covered by a thin polyethylene film in order to prevent the deposition of dew on the test plate. After the prescribed temperature of the plate was reached, the test was started by taking off the film. The typical duration of each test was 7.5 hours; the monitored quantities (air, plate and frost temperatures, frost thickness) were measured at regular time intervals (typically every 45 min) after starting the test. At the end of the test, additional measurements of frost thickness were made by using the two shielded, 0.5mm-dia, thermocouples travelling through the cooling plate and connected to a micrometer. These were also used to check the frost temperature given by the infra-red thermometer. For measuring the frost mass deposited on the test plate, additional runs were performed after which the frost was scraped off the plate and weighed by a precision balance. RESULTS AND DISCUSSION Figures 2 and 3 show the thickness of the frost layer measured at three different spots A, B, C (as shown in Fig.1). In particular, the position A is in the upper part of the plate, B is in the plate midheight and C is in the lower part of the plate. As found by other Authors [3, 4, 8], the thickness of the frost layer is slightly affected by the location. Largest differences in local values were found at low relative humidity (31 percent) and high plate temperature (-4 C): for these conditions the frost growth is not uniform over the cooled plate and a large scatter of data recorded at different positions is reasonable. The mean thickness (evaluated as the average

3 Tw=-13, (A) Tw=-13, (B) Tw=-13, (C) Tw=-8, (A) Tw=-8, (B) Tw=-8, (C) Tw=-4, (A) Tw=-4, (B) Tw=-4(C) Figure 2. Thickness of the frost layer versus time at different locations (A,B,C) on the cold plate. Air relative humidity: 31 percent, T w =-13, -8, -4 C; T a 27 C T w = -13 C Figure 4. Average thickness of the frost layer versus time for T w =-13 C and different values of the air humidity. Tw=-13, (A) Tw=-13, (B) Tw=-13, (C) Tw=-8, (A) Tw=-8, (B) Tw=-8, (C) Tw=-4, (A) Tw=-4, (B) Tw=-4, (C) Figure 3. Thickness of the frost layer versus time at different locations (A,B,C) on the cold plate. Air relative humidity: 58 percent, T w =-13, -8, -4 C; T a 27 C T w = -8 C Figure 5. Average thickness of the frost layer versus time for T w =-8 C and different values of the air humidity. of the three local measurements) versus time is reported, for different values of the relative humidity, in Figures 4-6. Each graph reports the frost thickness measured for two experimental runs performed under the same operating conditions (wall and ambient air temperatures, air relative humidity), this in order to assess the reproducibility of the measurements. Generally speaking, the frost layer grows quickly during the first one-two hours, after that the slope of the growth curve decreases with time owing to the frost densification processes. Previous studies [3,8] showed the possibility to correlate the frost thickness to the product of time (measured from the inception of growth) and the temperature difference between the frost surface and the cooled plate. The relationship has the following form: S = A [τ (T f -T w )] n (1) where S is the frost thickness, τ is the time, T f and T w denote the frost surface and the cooled plate temperature, respectively, while the coefficient A derives from ambient parameters (humidity and temperature of air). Results reported in the literature for a variety of geometries under forced and free convective airflow and in a wide range of differences between frost surface and plate temperatures indicated for the exponent n a range of variation from 0.40 to Figure 7 shows the measured mean thickness S of the frost layer against the parameter [τ (T f -T w )] for values of time exceeding 90 mins. From a least-squares analysis, two distinct empirical equations for the frost growth were obtained depending on the air humidity conditions: S = 0.21 [τ (T f -T w )] (Rh = percent) (2) S = 0.45 [τ (T f -T w )] (Rh = percent) (3)

4 280 Tw=-13, Tw=-13, T w = -4 C Frost surface temperature [K] Tw=-8, Tw=-4, melting line Tw=-8, Tw=-4, 260 Figure 6. Average thickness of the frost layer versus time for T w =-4 C and different values of the air humidity. 1 Rh 31% Rh 35% Rh 52% Rh 58% y = x Power fit (RH>50%) Power fit (RH<50%) Cremers & Mehra y =0.2123x Frost growth parameter [min K] Frost mass per unit area [kg/m²] Figure 8. Surface temperature of frost versus time: effects of the air humidity and the cold plate temperature Tw=-13, Tw=-8, Tw=-4, Tw=-13, Tw=-8, Tw=-4, Figure 7. Frost growth correlations with S expressed in mm and the τ in min. A comparison with previous results reveals that the exponents found here are lower than those reported in the literature. However, if only data for values of the frost growth parameter [τ (T f -T w )] higher than 1000 are considered (as done by Cremers and Mehra, [3]), all data differ by only 3 percent from the Cremers-Mehra equation S = 0.20 [τ (T f -T w )] 0.40 (4) Figure 8 shows the mean frost surface temperatures as functions of time, for two different values of the relative humidity (31 and 58 percent) and three values of the cooled plate temperature (13, -8, and -4 C). It is apparent from the figure that, when the humidity is relatively high, the frost surface temperature approaches a value close to the triplepoint value in a rather short time (about two hours). Conversely, for the lower value of the relative humidity, the surface temperature of the frost increases very slowly with time; moreover, a visual observation revealed a frost growth not regular over the cooled plate. Figure 9. Mass of frost deposited (per unit surface area) on the cold surface. Air humidity: 31 and 58 percent. Frost mass per unit area [kg/m²] Linear Fit y =0.4945x Mass deposition parameter [min] Figure 10. Correlation for the mass of frost deposited (per unit surface area).

5 Finally, the mass of frost (per unit of surface area) deposited onto the cooled surface is plotted in Figure 9 for air humidity values of 31 and 58 percent. Inspection of the figure reveals a linear increase of the deposited mass of frost with time, as found by Tokura et al. [4] and by Östin and Andersson [9]. The rate of increase of frost mass with time is markedly affected by the air humidity, while the cooled plate temperature seems to exert a little effect, especially when the humidity is relatively high. Indeed, in these conditions, the temperature difference (from the air to the frost surface) rapidly tends to a common value independent on the cooled plate temperature (as previously seen in Fig. 8). When the relative humidity is low, the surface temperature of the frost layer increases slowly, especially when it starts from the lowest value (-13 C); thus the effect of the cooled plate temperature on the deposited mass is more pronounced, especially during the initial transient of period of frost formation. Frost mass data have been plotted in Fig.10 against the product between the time τ and the difference (ω a - ω f ), where ω a is the air humidity ratio and ω f is the saturated humidity ratio at the frost surface temperature. Plotted data satisfactory agree with the equation M = τ (ω a - ω f ) (5) with M expressed in kg/m 2, τ in min and ω in kg (vapour) /kg (air). CONCLUSIONS The growth of a frost layer on a cold surface in free convection was experimentally investigated. The surface was placed inside a long vertical channel open at the top and bottom to permit the natural convective, laminar, flow of air at controlled temperature and relative humidity. Experiments were conducted by varying the temperature of the cooled plate between 13 and 4 C and the relative humidity of ambient air from 31 to 58 percent. The temperature of the ambient was maintained at C. For these parameter ranges, the frost thickness was found to uniformly grow over the cold plate, except for situations involving low air humidity and high cold plate temperatures in which the frost formation is less regular. The average thickness of the frost layer was correlated by a power law to the product between time and the temperature drop from the frost to the plate surface. Coefficients and exponents of the correlations were found to depend on the relative humidity of the ambient air. The surface temperature of the frost exhibited a different behaviour on the basis of the relative humidity of air. When the relative humidity is medium-high (51-58 percent), the surface temperature of the frost layer rapidly attain a common, asymptotic value close to the melting temperature; as a consequence, the total mass of vapour sublimated onto the cooled plate at a given time is scarcely dependent on the cooled plate temperature. At the lowest values of the air humidity, the frost surface temperature increases slowly with time and the driving force of the mass transfer to the layer is also affected by the cooled plate temperature. A relationship for the mass of frost deposited, fitting the experimental data, was given as a function of time and the difference between the air humidity ratio and the saturated humidity ratio of the frost surface. NOMENCLATURE M frost mass per unit area, kg/m 2 S frost thickness, mm Rh relative humidity, dimensionless T temperature, K τ ω subscripts a f w time, min air humidity ratio, kg (vapour) /kg (air) air frost wall REFERENCES 1. Y. Hayashi, A. Aoki, S. Adachi, and K. Hori, Study of frost properties correlating with frost formation types, ASME Journal of Heat Transfer, vol. 99, pp , B.W. Jones and J.D. Parker, Frost formation with varying environmental parameters, ASME.Journal of Heat Transfer, vol. 97, pp , C.J. Cremers and V.K. Mehra, Frost formation on vertical cylinders in free convection, ASME Journal of Heat Transfer, vol. 104, pp.3-7, I. Tokura, H. Saito, and K.Kishinami, Study on properties and growth rate of frost layers on cold surfaces, ASME Journal of Heat Transfer, vol. 105, pp , D.L. O Neal and D.R.Tree, Measurement of frost growth and density in a parallel plate geometry, ASHRAE Transactions, vol. 90, Part. 2, pp , L.A. Kennedy and J. Goodman, Free convection heat and mass transfer under conditions of frost deposition, Int. Journal of Heat and Mass Transfer, vol. 17, pp , O. Tajima, E. Naito, K. Nakashima, and H. Yamamoto, Frost formation on air coolers, part III: natural convection for a cooled vertical plate, Heat Transfer Jap. Research, vol.3, pp.55-66, H.W. Schneider, Equation of the growth rate of frost forming on cooled surfaces, Int. Journal of Heat Mass Transfer, vol.21, pp , R. Östin and S. Andersson, Frost growth parameters in a forced air stream, Int. Journal of Heat and Mass Transfer, vol. 34, pp , 1991.