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Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry
Accepted Manuscript Title: Analysis of the heat transfer area distribution in a frosted plain fin-andtube geometry Author: A. Morales-Fuentes, O.M. Chapa-Contreras, S. Méndez-Díaz, J.M. Belman-Flores PII: DOI: Reference:
S0140-7007(17)30036-1 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.016 JIJR 3528
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
18-10-2016 17-1-2017 17-1-2017
Please cite this article as: A. Morales-Fuentes, O.M. Chapa-Contreras, S. Méndez-Díaz, J.M. Belman-Flores, Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry a*
a
a
A. Morales-Fuentes , O. M. Chapa-Contreras , S. Méndez-Díaz , J. M. Belman-Flores a
b
School of Mechanical and Electrical Engineering, Autonomous University of Nuevo León, México b Engineering Division, Campus Irapuato-Salamanca, University of Guanajuato, México
Highlights Thermohydraulic analysis of a domestic evaporator during frost formation is studied The humid airflow is re-distributed among channels as frost layer develops The geometry performance is dictated by fin spacing, length and flow distribution A rapid frost development leads to restriction in pressure drop rather than thermal Abstract 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 performance 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 present an advantage, particularly on the pressure drop, which allows longer operation time between defrost cycles. Keywords: Area distribution, Blockage ratio, Frost, Airflow redistribution Nomenclature A Cp
Surface area [m2] Heat capacity [J kg-1 K-1] Binary diffusivity [m2 s-1] Effective diffusivity [m2 s-1] External tube diameter [m] Friction factor Air side heat transfer coefficient [W m-1 K-1] Mass transfer coefficient [m s-1] Latent heat of ablimation [J kg-1] Thermal conductivity [W m-1 K-1] Segment length [m] Characteristic fin length [m]
*
Corresponding author. FIME, Av. Universidad s/n, Ciudad Universitaria, C.P.66451 Tel.: +(52) 811 340 4020, Ext. 1619; Fax: +(52) 811 052 3321 e-mail address: [email protected]
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Lewis number [-] Mass flow [kg s-1] Fin parameter Prandtl number Vapor pressure [Pa] Ideal gas constant [kJ mol-1 K-1] Reynolds number Temperature [K] Time [s] Direction [m] Vapor fraction Greek symbols Frost thickness [m] Fin and tube areas relation [-] Density [kg m-3] Physical property Absolute humidity [kg kga-1] Subscripts a Humid air f Frost i Ice sat Saturation s Surface Bulk conditions
1. Introduction The refrigeration cycle by vapor compression is used widespread in industrial and household appliances in products such as refrigerators, heat pumps and air conditioners. The system efficiency is an issue that attracts the attention of researchers due to the increasing energy consumption in recent years. An important phenomenon that deteriorates the performance of heat exchangers used as evaporator in household refrigerators is frost development on its surface. This does not only act as thermal insulator but also reduces the free airflow area increasing pressure drop. The air side thermal resistance between the frost surface and air might contribute up to 90% of the total thermal resistance (Ye and Lee, 2013). In order to overcome such undesirable effects, defrost cycles are implemented periodically during operation. The defrost process is accelerated using an electric heater while the cooling system is off. It is estimated that only 15 to 20 % of the heat supplied for defrosting is withdrawn by the condensate (Chen et al., 2003). The remaining heat load is rejected in the following cooling cycle, which decreases the system efficiency. According to the fridge capacity, the period of the defrost cycle might last from 30 to 60 min and the electric heater might use about 1 kW per foot of evaporator length (ACHR, 2011). Therefore, the mitigation or delaying of frost formation has important implications in energy savings. The frost formation is a complex process where mass transfer, heat transfer and fluid dynamic phenomenon occurs simultaneously. It is produced when humid air circulates over cold surfaces which temperature is below the freezing point of water. If the frosted surface 2 Page 2 of 19
temperature remains below the freezing point of water, the moisture from the air keeps depositing upon the surface, increasing the frost thickness. Additionally, some of the moisture might diffuse into the frost layer increasing its density and modifying the physical properties. Frost formation on refrigeration coils has been studied for long time (Kondepudi and O'Neal, 1989; Stocker, 1960). The main objectives have been the development of frost models and the study of process conditions. Seker et al. (2004a) present a model for frost formation on finand-tube heat exchangers and discuss operating conditions such as inlet temperature, relative humidity, air mass flowrate and refrigerant temperature. Latter, a comparison between numerical results and experimental data for the same geometry is shown (Seker et al., 2004b). Yan et al. (2003) observe that frost formation is greater for a lower airflow rate and higher relative humidity. Through an experimental study on large size air coolers, Deng et al. (2003) report that the wall temperature, fin spacing, frost height and air velocity are the main factors affecting the heater performance. Gao and Gong (2011) report that the temperature difference between air and tube surface is the main driving force for frosting. They also observe that the frost thickness at the fin base is thicker than at the fin tip due to the temperature profile in the fin. Wang et al. (2012) use a modified correlation for the initial frost density in a simple model for predicting frost growth on cold flat plate, the results are compared with experimental data. Lee et al. (2013) investigate the relative humidity, airflow rate, inlet temperature and fin pitch in a spirally-coiled circular fin-tube heat exchanger. Wang et al. (2013) present a theoretical study where the critical heat and mass transfer characteristic on a frosting tube are identified. Due to manufacture implications and the facility to drain melted water and ice particles, plain fin-and-tube geometries have been widely used as evaporator in household refrigerators. Open literature studies for design considerations of plain fin-tube heat exchangers under frost conditions are limited. Fin spacing under frosting conditions have mostly been determined empirically (Yang et al., 2006a). Watters et al. (2002) tested a coil with 6, 8 and 10 fins per centimeter on the front, second, and third row respectively. They found that the coefficient of performance of the staged coil was 8.7% lower than that of the base coil at 95% relative humidity and 1.7 °C. However its defrost cycle time could be shortened from 6% to 30% depending on the airflow rate. Using a mathematical model validated with experimental data, Yang, et al. (2006b) observed that thermal performance of the heat exchanger could be improved by a proper adjustment of fin spacing reducing the air-flow blockage. Yang et al. (2006a) present an optimum design study for heat exchanger performance, using the response surface and Taguchi method for a fin and tube heat exchanger with variable fin spacing. They also observe that operating conditions had little effect on the choice of an optimum design for the heat exchanger. Coleman (2009) presents low-temperature freezing systems where coils design have fin spacing that varies from the air-inlet side to the air-outlet side to more effectively manage the effects of frost accumulation. As a guidance, they suggest 0 to 3 fins per inch (fpi) under heavy moisture content, 3 to 4 fpi under a moderate to light conditions and 4 to 6 fpi under a light condition of humidity. Kim et al. (2010) present a CFD study of a plain fin-and-tube heat exchanger geometry where fin density increase as the humid air goes across the tube rows. In most heat transfer and pressure drop calculation of heat exchangers, it is assumed that the inlet flow and temperature distributions across the exchanger channels are uniform. Recent studies show that consideration of air redistribution due to frost growth improves frost thickness prediction and coil capacity compared to models where it is not considered (Padhmanabhan et al., 2011). Ye and Lee (2013) describe a numerical model for predicting the performance of a fin and tube heat exchanger considering airflow reduction due to frost accumulation. 3 Page 3 of 19
The objective of this study is to show the importance of the heat-transfer area distribution for design and operation of a plain fin-and-tube evaporator, when frost is developed on its surface. A model previously studied (Padhmanabhan et al., 2011), is adapted and results are compared with data in open literature. First, a geometry with fin spacing that increase or decrease from the centerline is proposed. Then additional heat transfer area is analyzed by increasing the fin density or fin length. Finally, the use of an airflow distributor is studied as a frost mitigation device. A simulation is carried out assuming a quasi-steady-state with small time steps and air redistribution as the frost develops. The frost growth is determined assuming a semi-empirical model.
2. Development of thermohydraulic simulation Local conditions such as air temperature, velocity, relative humidity and surface temperature cause a frost formation at different rates from inlet to outlet in a plain fin-and-tube geometry. When a channel is partially blocked (under a constant total mass flowrate), the airflow is redirected to other channels that offer less resistance. As a result, the pressure drop increases. A plain fin-and-tube geometry is studied on the airside by an integrated segment-by-segment thermohydraulic model. Each segment consists of a central tube and a fin attached to its surface, therefore the tube row in the direction of air flow correspond to the segment numbering as shown in Figure 1. Channels formed by fin separation are numbered starting from the closest to the fan. The formation of frost is simulated using a semi-empirical model based on the scaling approach which include the frost layer (Padhmanabhan et al., 2011). Using an effective diffusivity and the Clausius-Clapeyron equation into the Fick’s law of diffusion, the mass flow that densifies the layer can be expressed as: (1)
The effective diffusivity can be determined from a binary diffusion coefficient density ratio as shown in equation (2).
D AB
and a
(2)
The frost thickness is determined from the difference between the total mass of water sublimated and the mass that densifies the frost layer. The total mass is determined from the difference in absolute humidity of air at entrance and outlet of each segment. At the frost-air interphase, an energy balance (neglecting heat transfer by radiation and heat sinks or sources) equates the sensible and latent heat on the airside with the heat conducted through the frost layer and the latent heat by diffusion as shown in equation (3). (3)
The clean or frosted surface temperature T S is determined once the air outlet condition is known. The heat and mass transfer coefficient are related by the Lewis analogy as: (4)
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The heat transfer coefficient is determined using a correlation previously developed by Seker et al. (2004a) for an evaporator of a household refrigerator as follows: (5)
The heat transferred in fins is determined using a fin efficiency. As frost develops, the additional heat transfer resistance is incorporated to determine an average surface temperature. Using a characteristic fin length l * , the Schmidt method allows to extend the circular fin efficiency shown in equation (6) for different tube layout (Thulukkanam, 2013). (6)
The overall heat surface efficiency is determined using the equation (7) (Incropera et al., 2006). (7)
In order to determine a frost growth in the direction perpendicular to the surface for the following time step, in each segment an equivalent average temperature over the fin surface is used. The change in frost density presented in equation (8) is determined from the water vapor that undergoes a diffusion process (equation (1)) and the frost thickness in the segment . The change in frost thickness is determined from the remaining water vapor that undergoes a phase change and the actual frost density in the segment as in equation (9). (8)
(9)
The mass airflow distributes among channels according to its pressure drop. Neglecting the effects due to acceleration, entrance and exit losses, the pressure drop in each segment is determined by (Kays and London, 1984): (10)
The friction factor is determined as in equation (11), this correlation was previously derived for a similar geometry (Seker et al., 2004a). (11)
The initial flowrate delivered by the fan is given. The fan distributes the air among the channels formed by the fins in such a way that the pressure drop in all channels is equal. The flowrate is determined using the tool solver in Microsoft Excel 2013 spreadsheet, based on a non-linear method for equal pressure drop in channels as restriction. In each segment, the outlet air temperature is initially guessed. It is recalculated through a heat and mass balance at the frost layer interphase using the Newton-Rapson method. The air outlet condition in a segment is the inlet condition for the following one. The process repeats for all segments in a channel and for 5 Page 5 of 19
all channels. Then a hydraulic simulation is carried out to adjust the flowrate in channels due to the frost deposition. If necessary, the airflow is redistributed among channels to retrieve an equal pressure drop. The thermohydraulic simulation is repeated in the segments and channels until convergence is achieved. The next time step, starts with an airflow distribution among channels using the hydraulic diameter of the frosted surface that resulted in the previous time step. The thermohydraulic model has been coded using an Excel-VBA programming according to the flowchart presented in Figure 2. Regarding the physical properties of humid air, the density and heat capacity are determined from the vapor fraction as in equation (12). Where pure component properties are determine as in
.
(12)
The moist air viscosity and thermal conductivity are determined as in ASHRAE (2009). The partial
pressure of saturated humid air is determined as a function of temperature using the correlation in equation (13), which is valid in a range of 243 to 303 K, and was derived from Aspen plus ver. 8.8.1 software. (13)
In each segment, the physical properties of the frost layer are considered constant. The frost density is determined using an empirical correlation as function of surface temperature as presented in equation (14) (Hayashi et al., 1977). Thermal conductivity is determined using Sanders correlation as in equation (15) (Seker et al., 2004a). As frost density increases, its thermal conductivity also increases enhancing the heat transfer by conduction. (14) (15)
3. Results and discussion 3.1. Comparison with other models There are few studies in open literature showing the development of frost thickness with time for a plain fin-and-tube geometry. Two recent numerical studies (Armengol et al., 2016; Cui et al., 2011) compare their predictions with experimental data (Lenic et al., 2009). The operating condition of the experimental study are velocity (0.6 m s-1), air temperature (21.4 °C), absolute humidity (6.2 g kg-1) and surface temperature (-19.5°C). The development of frost with time predicted in this study, is compared in Figure 3 with the works previously mentioned. Error 6 Page 6 of 19
bars with a deviation of 15% from experimental data (Lenic et al., 2009) are included. The model underpredicts the frost growth for the time span. For a 120 min of operation, the deviation from experimental data is the largest 21%, however it is reduced to 9% at 250 min of operation. The recent numerical simulation results (Armengol et al., 2016), overpredicts the frost growth in a range from 9-12% in most of the time span. However at 60 min of operation the deviation observed is around 20%. Although the model describe more in detail the shape of the curve of experimental results, the present simultaion using a semi-epirical model under one-dimensional frost growth assumption, have a good agreement with experimental data and other simulations in literature, avoiding the complexity of numerical models. 3.2. Case study The heat exchanger under study is an evaporator of a household refrigerator made up of four rows of tubes with plain fins attached to the main surface as shown in Figure 1. Inside the tubes, refrigerant evaporates at a constant pressure and temperature. The pressure is considered such that inner surface temperature results in -15°C. A fan is located on top and at the centerline of the evaporator. The air flows through the channels formed by the fins from top to bottom. The air inlet condition used for simulation is 5°C with a relative humidity of 90%. This condition occurs during normal operation. da Silva et al. (2011) present a commercial fan curve that can handle up to 280 m3h-1 under no pump head, and a maximum pressure loss of 105 Pa. This study assumes an airflow rate of 170 m3 h-1, which is distributed to both sides of the exchanger in a symmetric way. The geometry (a) consists of ten fins from the fan centerline to both sides, with a fin spacing of 10 mm as shown on top of Figure 4. Initially the channels closer to the fan with shorter air paths present larger flowrates. Time steps of 1 second allow capturing the thermohydraulic behavior of the evaporator at different locations as the frost layer grows. As time passes, the frost layer in channels reduces the air flowrate in channels 1 to 4 and increases in channels 6 to 10 as shown in Figure 4. The flowrate in the central channel (channel 5) remains constant for the whole operation time. From the minute 2 to 9, an inversion in the flowrate trend in channels can be observed. In channels 1 to 4 the flowrate increases while there is a decrease in channels 6 to 10. This change is given due to the uneven frost allocation in segment 1, which is discussed next. The Figure 5 shows the blockage ratio (defined as the ratio of the cross section area of the frosted surface to the clean airflow area) for 10 minutes of operation in a 2-minutes intervals. During the initial two minutes of operation, in segment 1 of all channels, a frost layer is developed which results in a blockage ratio below the 2%. The heat transferred in the second time interval (2 to 4 minutes) does not yield frost formation in segment 1 of channel 1. However, the air temperature is reduced and the relative humidity increases to the saturation point. The segment 1 of the following channels (2 to 10) show a blockage ratio that increases as the channel is further away from the fan. In the third time interval (4 to 6 min) the frost is first observed in channel 4. The onset of frost formation in the fourth (6 to 8 min) and fifth (8 to 10 min) time intervals are the channels 6 and 8 respectively. Due to the airflow mal-distribution in the evaporator, for the initial 10 minutes of operation, the blockage ratio ranges from 1.7% in segment 1-channel 1, to 5.9% in segment 1-channel 10. In the first segment, the channel with lower flowrate develops a larger frost layer. At the following segments, the heat transfer leads to the frost deposition in all intervals of time as observed in Figure 5. The blockage ratio is larger in the channel with larger flowrate (channel 1). This indicates that the frost deposition is dominated by a mass transport mechanism. As the air flows from segment 2 to 3 and 4, the amount of vapor water in air decreases due to the frost deposition in previous segment. The air temperature becomes even lower, thus reducing the air saturation temperature and mitigating the formation of frost in subsequent segments. It is also observed that frost accumulated in the initial two-minute interval is larger than in the subsequent ones. As time 7 Page 7 of 19
passes, the frost layer gets thicker increasing the heat transfer resistance. Then the frost layer temperature increases promoting mass that diffuses instead of increasing its thickness, as presented in equation (1). The blockage ratio value in channels 1, 5 and 10 are reported in Table 2 for an operation time of 240 min, in 48-minutes intervals. During initial operation, the frost developed at the first segments of all channels, introduces a heat transfer resistance such that further frost deposition is reduced or nil. At the segments 2, 3 and 4, the frost continues developing as in the initial period. Results show that the segment 2 is the most affected by the frost development. Similar frost growth behavior have been observed (Armengol et al., 2016; Cui et al., 2011; Lenic et al., 2009). In Figure 6, the thermohydraulic behavior of the evaporator under two different air flowrates (170 m3 h-1 and 85 m3 h-1) is presented. During the initial 10 minutes, there is a sharp drop in heat load that represents 25% and 10% of the initial heat load for the initial and reduced flowrates respectively. At this point, the frost thickness is only 0.35 mm and 0.25 mm (at the segment most likely to frost) and pressure drop is 29.3 Pa and 7.36 Pa respectively. This thin frost layer contributes significantly to heat transfer. Therefore, an effective clean-up during defrost process is necessary to restore the exchanger performance. The allowable pressure drop of 100 Pa is reached after 80 min and 216 min of operation. If a specific application requires a heat flow of 50 W, then for 170 m3 h-1 the pressure drop restricts the operation at 80 min. For a volumetric flowrate of 85 m 3 h-1 there is not a pressure drop restriction and the evaporator can be operated for 120 min. Due to the flow maldistribution, the frost develops at different rates in segments of the channels, leading to premature deterioration of thermohydraulic performance at locations where the frost accumulates faster. In the next section, the fin spacing is analyzed looking at the airflow distribution among channels that brings benefits on the thermohydraulic performance.
3.3. Analysis of fin spacing The plain fin-and tube geometry is analyzed under three fin spacing scenarios and compared with the constant fin spacing geometry (a) of 10 mm. All of them under the same total airflow and heat transfer area forming 10 channels. The second geometry (b) assumes a fin spacing that increases for channels that are further away from the fan. Since the frost formation is conducted by the air flowrate, this scenario sets the fin spacing such that the same air flowrate is conducted through all channels. The third geometry (c) assumes a fin spacing that decreases for channels that are further away from the fan. It is created by reversing the fin spacing in geometry (b). This geometry allows larger frost deposition in channels closer to the fan with lower pressure drops. The geometry (d) assumes a constant fin spacing of 11 mm instead of 10 mm. The flow distribution in geometries (a) to (d) through channels 1, 5 and 10 are shown in Figure 7. It is observed that in all scenarios the flowrate in the central channel remains constant during the operation time. The flowrate in channel 1 tends to decrease with time and in channel 10 to increase. In geometry (b) the airflow among channels varies little and the flow in channel 10 is larger due to the formation of frost in the channels closer to the fan. The largest flow difference among channels occurs in the geometry (c). In geometry (d) the flowrate behaves very similar as in geometry (a), however the fin separation mitigates the blockage ratio. The blockage ratio in channels 1, 5 and 10 in segment 2 for the geometries (a) to (d) are shown in Figure 8. The operation time is 100 min in intervals of 20 min. As expected, the blockage ratio in channel 1, in geometry (b) is the largest due to the reduced fin spacing. On the other hand, the blockage ratio is nearly the same in all channels of geometry (c) which has a decreasing fin spacing. 8 Page 8 of 19
The total heat load and pressure drop for the four geometries during operation time are shown in Figure 9. The heat load curves show a very similar trend, however it can be observed a delay of 1.8 min and 4.6 min for a load of 75 W in the geometries (b) and (d) respectively. The thermal performance is slightly enhanced due to the frost distribution among channels. On the other hand, a pressure drop of 100 Pa is reached at different operation times: 80 min, 87 min, 89 min and 100 min for the geometries (a), (b), (c) and (d) respectively.
Relative to the geometry (a), the geometry (b) allows an additional operation time of 7 min before the pressure drop constraint is reached. During this time, there is a heat transfer of 3.3 W. The pressure drop in the geometry (c) behaves very similar to the observed in geometry (b) and its heat transfer performance curve does not show differences from the geometry (a). The geometry (d) allows an additional operation time of 20 min in which a heat transfer of 4.9 W occurs. An inconvenient of this geometry is that additional space is required to set the same number of fins. This analysis demonstrate that fin spacing and distribution are important parameters to consider when designing an evaporator subject to frost formation. In the next section, the thermohydraulic performance of additional surface area is analyzed when the number of fins and the fin length are considered.
3.4. Increased heat transfer area Three geometries with additional surface area (equivalent to 5 fins) are compared to the geometry (a) under the same total airflow. The additional area allows a larger heat load and the frost distributes over the fin surface in such a way that thermohydraulic benefits might be observed. The geometry (e) increases the fin density by allocating 15 fins in the same length. The geometry (f) distributes 15 fins keeping the original fin density therefore the total length increases. The geometry (g) use the original 10 fins and fin density as in geometry (a), however the fin length is increased in order to result with an additional equivalent surface of 5 fins. The flowrate through three representative channels are presented in Figure 10. The air is distributed among a greater number of channels in the geometries (e) and (f), therefore the local flowrate is reduced when compared to the 10-fin geometries (a) and (g). In Figure 11, it is observed again, that the blockage ratio in the geometry with reduced fin spacing is the largest (geometry (e)). A larger fin separation reduces the blockage ratio as observed in geometry (f). Finally the frost developed in geometry (g) with fins 12 mm longer, shows the lowest blockage ratio in all channels. The thermohydraulic performances of geometries (e), (f) and (g) show important differences as observed in Figure 12. The geometries (e) and (g) show an enhanced heat transfer and the curves present a crossover at about 90 min of operation. The heat load curve for geometry (f) is considerably above the others. The time at which the pressure drop reaches 100 Pa also increases considerably from 80 min in geometry (a) to 140 min and 180 min for geometry (f) and (g) respectively. Due to the increased fin density, geometry (e) reaches the allowable pressure drop in only 50 min of operation. Between the geometries (f) and (g), the geometry (g) can operate for additional 40 min in which 5.4 W of heat are transferred. On the other hand, at 140 min of operation, the geometry (f) has transferred 79.6 W compared to 75.1 W of the geometry (g). The heat transferred during the extended operation time of 40 min in geometry (g) is 0.9 W larger than the heat transferred by geometry (f) at 140 min of operation. Moreover, due to the extended operation time in geometry (g), the number of defrost cycles in one-year operation can be reduced considerably. 9 Page 9 of 19
3.5. Use of a flow distributor The geometry (b) shows that the thermohydraulic deterioration is less affected due to the homogeneous airflow distribution among the channels. In this section, a flow distributor is included to geometry (a) and named as geometry (h). Under an unfrosted surface condition, the air is distributed evenly in all channels as shown in Figure 13. As time passes and the frost develops, the air flowrate is redistributed among the channels in a non-uniform way.
The flowrate in channels 1 to 4 tends to increase while in the channels 6 to 10 decreases. This is an inverse behavior from that observed in previous simulations. Nevertheles, the flowrate through channels located closer to the fan is still larger. As a result, the blockage ratio in geometry (h) when compared to geometry (a), is slightly lower in channel 1, the same in central channel and slightly larger in channel 10. The thermohydraulic behavior is very similar to curves shown for geometry (a) and omitted for simplicity. The pressure drop results using a flow distributor, shows that a 100 Pa reading is reached four minutes sooner than in geometry (a). Therefore, there is not a thermohydraulic benefit from the use of this strategy.
4. Conclusion In this work, it is highlighted the importance of the heat transfer area distribution on the performance of a plain fin-and-tube evaporator as frost develops on its surface. The fin spacing, length and distribution are used to propose several evaporator designs for equal heat transfer area and compared using a thermohydraulic simulation. It is observed that a larger flowrate is related to thicker frost formation and initial frost layer deposit reduces the heat transfer considerably. A geometry with larger fin spacing shows the largest improvement on the thermohydraulic performance; however, it requires a larger space to set a specific number of fins. When fins are fixed such that flowrate among channels is initially evenly distributed, the performance of the evaporator shows an improved thermohydraulic behavior. When additional heat transfer area is evaluated, an advantage on the thermohydraulic performance is observed when longer fins are used instead of extra fins. Finally, the use of an air distributor shows an increase on pressure drop without any evident benefit on the thermal performance. The results of this study can be used as a guidance for evaporators design and operation, leading to a continued thermohydraulic performance or extended operation periods when frost develops over its surface.
Acknowledgements The authors greatly appreciate the financial support of the National Council for Science and Technology (CONACYT), México, under the grant No. 179181. References ACHR, 2011. Frost and Defrost: How It Happens and Why It Is Needed - A White Paper. The Air Conditioning Heating Refrigeration NEWS, September 5. Armengol, J.M., Salinas, C.T., Xamán, J., Ismail, K.A.R., 2016. Modeling of frost formation over parallel cold plates considering a two-dimensional growth rate. International Journal of Thermal Sciences 104, 245-256. 10 Page 10 of 19
ASHRAE, 2009. ASHRAE Handbook-Fundamentals, pp. 1.2-1.15. Coleman, R., 2009. Frost on Air-Cooling Evaporators. Ashrae J. 51, 27-33. Cui, J., Li, W.Z., Liu, Y., Jiang, Z.Y., 2011. A new time- and space-dependent model for predicting frost formation. Applied Thermal Engineering 31, 447-457. Chen, H., Thomas, L., Besant, R.W., 2003. Fan supplied heat exchanger fin performance under frosting conditions. International Journal of Refrigeration 26, 140-149. da Silva, D.L., Hermes, C.J.L., Melo, C., 2011. Experimental study of frost accumulation on fansupplied tube-fin evaporators. Applied Thermal Engineering 31, 1013-1020. Deng, D.-q., Xu, L., Xu, S.-q., 2003. Experimental investigation on the performance of air cooler under frosting conditions. Applied Thermal Engineering 23, 905-912. Gao, T., Gong, J., 2011. Modeling the airside dynamic behavior of a heat exchanger under frosting conditions. Journal of Mechanical Science and Technology 25, 2719-2728. Hayashi, Y., Aoki, A., Adachi, S., Hori, K., 1977. Study of Frost Properties Correlating With Frost Formation Types. Journal of Heat Transfer 99, 239-245. Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S., 2006. Fundamentals of Heat and Mass Transfer, Sixth ed. Wiley. Kays, W.M., London, A.L., 1984. Compact Heat Exchangers, third ed. McGraw-Hill, Inc, New York. Kim, S.-j., Choi, H.-j., Ha, M.-y., Kim, S.-r., Bang, S.-w., 2010. Heat transfer and pressure drop amidst frost layer presence for the full geometry of fin-tube heat exchanger. 24, 961-969. Kondepudi, S.N., O'Neal, D.L., 1989. Effect of frost growth on the performance of louvered finned tube heat exchangers. International Journal of Refrigeration 12, 151-158. Lee, S.H., Lee, M., Yoon, W.J., Kim, Y., 2013. Frost growth characteristics of spirally-coiled circular fin-tube heat exchangers under frosting conditions. International Journal of Heat and Mass Transfer 64, 1-9. Lenic, K., Trp, A., Frankovic, B., 2009. Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger. International Journal of Heat and Mass Transfer 52, 22-32. Padhmanabhan, S.K., Fisher, D.E., Cremaschi, L., Moallem, E., 2011. Modeling non-uniform frost growth on a fin-and-tube heat exchanger. International Journal of Refrigeration 34, 20182030. Seker, D., Karatas, H., Egrican, N., 2004a. Frost formation on fin-and-tube heat exchangers. Part I—Modeling of frost formation on fin-and-tube heat exchangers. International Journal of Refrigeration 27, 367-374. Seker, D., Karatas, H., Egrican, P.D.N., 2004b. Frost formation on fin- and- tube heat exchangers. Part II—Experimental investigation of frost formation on fin- and- tube heat exchangers. International Journal of Refrigeration 27, 375-377. Stocker, W.F., 1960. Frost formation on refrigeration coils. ASHRAE Transactions 66. Thulukkanam, K., 2013. Heat Exchanges Design Handbook, Second Edition. CRC Press. Wang, W., Guo, Q.C., Feng, Y.C., Lu, W.P., Dong, X.G., Zhu, J.H., 2013. Theoretical study on the critical heat and mass transfer characteristics of a frosting tube. Applied Thermal Engineering 54, 153-160.
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Wang, W., Guo, Q.C., Lu, W.P., Feng, Y.C., Na, W., 2012. A generalized simple model for predicting frost growth on cold flat plate. International Journal of Refrigeration-Revue Internationale Du Froid 35, 475-486. Watters, R.J., O’Neal, D.L., Yang, J.X., 2002. Frost/defrost performance of a three-row fin staged heat pump evaporator. ASHRAE Transactions, 318-329. Yan, W.-M., Li, H.-Y., Wu, Y.-J., Lin, J.-Y., Chang, W.-R., 2003. Performance of finned tube heat exchangers operating under frosting conditions. International Journal of Heat and Mass Transfer 46, 871-877. Yang, D.-K., Lee, K.-S., Song, S., 2006a. Fin spacing optimization of a fin-tube heat exchanger under frosting conditions. International Journal of Heat and Mass Transfer 49, 2619-2625. Yang, D.-K., Lee, K.-S., Song, S., 2006b. Modeling for predicting frosting behavior of a fin–tube heat exchanger. International Journal of Heat and Mass Transfer 49, 1472-1479. Ye, H.-y., Lee, K.-s., 2013. Performance prediction of a fin-and-tube heat exchanger considering air-flow reduction due to the frost accumulation. International Journal of Heat and Mass Transfer 67, 225-233.
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Figure 1. Plain fin-and-tube geometry subject to frost formation.
Figure 2. Flowchart for thermohydraulic simulation of plain fin-and-tube heat exchanger under frost condition.
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Figure 3. Comparison of frost thickness between the present study and others in open literature.
Fin spacing
Fan
Channels 1 2 3 4 5
6 7 8 9 10
Centerline
Figure 4. Geometry (a), flowrate variation through channels as frost develops over time.
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Figure 5. Geometry (a), blockage ratio for several segments and channels during 10 minutes of operation.
Figure 6. Geometry (a), heat load and pressure drop vs. time for air flowrates of 170 and 85 m3h-1.
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Fan
Fin spacing
Fan
Channels 1
5
Channels
Fin spacing 10
1
5
10
Centerline
Centerline
(a) Even fin spacing 10 mm
(b) Increasing fin spacing
Fan
Channels
Fin spacing 1
Fin spacing
Channels 1
5
Centerline
Fan
10
5
10
Centerline
(c) Decreasing fin spacing
(d) Even fin spacing 11 mm
Figure 7. Flow distribution in channels 1, 5 and 10 for plain fin-and-tube geometries with different fin spacing.
Figure 8. Blockage ratio in segment two, for plain fin-and tube geometries with different fin spacing. 16 Page 16 of 19
Figure 9. Heat load and Pressure drop for plain fin-and tube geometries with different fin spacing.
(a) 10 fin with a fin spacing 10 mm
(e) 15 fins with an increased fin density
(f) 15 fins with an increased total length
(g) 10 fins with an equivalent surface area as 15 fins
Figure 10. Flow distribution for plain fin-and-tube geometries with increased heat transfer area.
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Figure 11. Blockage ratio at segment 2, for plain fin-and-tube geometries with increased heat transfer area.
Figure 12. Heat load and Pressure drop for geometries with increased surface area.
Figure 13. Geometry (h), airflow distribution using a flow distributor.
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Table 1. Correlations for Physical properties in dry air and water vapor as function of temperature (in Kelvin).
Dry air
Water vapor
Units
Table 2. Development of the blockage ratio [%] in channels 1, 5 and 10 during an operation of 240 min. CHANNEL 1
Time [min]
Segment
CHANNEL 5
CHANNEL 10
1
2
3
4
1
2
3
4
1
2
3
4
48
1.78
23.45
22.21
21.02
3.90
22.27
20.94
19.65
6.53
21.13
19.70
18.34
96
0.16
15.44
15.09
14.74
0.00
14.95
14.57
14.16
0.00
14.45
14.03
13.57
144
0.14
12.86
12.71
12.54
0.00
12.56
12.38
12.18
0.00
12.22
12.04
11.80
192
0.14
11.34
11.28
11.21
0.00
11.13
11.06
10.96
0.00
10.89
10.83
10.71
240
0.15
10.26
10.31
10.34
0.00
10.13
10.15
10.14
0.00
9.95
9.98
9.94
2.38
73.35
71.61
69.85
3.90
71.04
69.10
67.09
6.53
68.64
66.60
64.37
Accumulated
19 Page 19 of 19
S0140-7007(17)30036-1 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.016 JIJR 3528
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
18-10-2016 17-1-2017 17-1-2017
Please cite this article as: A. Morales-Fuentes, O.M. Chapa-Contreras, S. Méndez-Díaz, J.M. Belman-Flores, Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.01.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry a*
a
a
A. Morales-Fuentes , O. M. Chapa-Contreras , S. Méndez-Díaz , J. M. Belman-Flores a
b
School of Mechanical and Electrical Engineering, Autonomous University of Nuevo León, México b Engineering Division, Campus Irapuato-Salamanca, University of Guanajuato, México
Highlights Thermohydraulic analysis of a domestic evaporator during frost formation is studied The humid airflow is re-distributed among channels as frost layer develops The geometry performance is dictated by fin spacing, length and flow distribution A rapid frost development leads to restriction in pressure drop rather than thermal Abstract 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 performance 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 present an advantage, particularly on the pressure drop, which allows longer operation time between defrost cycles. Keywords: Area distribution, Blockage ratio, Frost, Airflow redistribution Nomenclature A Cp
Surface area [m2] Heat capacity [J kg-1 K-1] Binary diffusivity [m2 s-1] Effective diffusivity [m2 s-1] External tube diameter [m] Friction factor Air side heat transfer coefficient [W m-1 K-1] Mass transfer coefficient [m s-1] Latent heat of ablimation [J kg-1] Thermal conductivity [W m-1 K-1] Segment length [m] Characteristic fin length [m]
*
Corresponding author. FIME, Av. Universidad s/n, Ciudad Universitaria, C.P.66451 Tel.: +(52) 811 340 4020, Ext. 1619; Fax: +(52) 811 052 3321 e-mail address: [email protected]
1 Page 1 of 19
Lewis number [-] Mass flow [kg s-1] Fin parameter Prandtl number Vapor pressure [Pa] Ideal gas constant [kJ mol-1 K-1] Reynolds number Temperature [K] Time [s] Direction [m] Vapor fraction Greek symbols Frost thickness [m] Fin and tube areas relation [-] Density [kg m-3] Physical property Absolute humidity [kg kga-1] Subscripts a Humid air f Frost i Ice sat Saturation s Surface Bulk conditions
1. Introduction The refrigeration cycle by vapor compression is used widespread in industrial and household appliances in products such as refrigerators, heat pumps and air conditioners. The system efficiency is an issue that attracts the attention of researchers due to the increasing energy consumption in recent years. An important phenomenon that deteriorates the performance of heat exchangers used as evaporator in household refrigerators is frost development on its surface. This does not only act as thermal insulator but also reduces the free airflow area increasing pressure drop. The air side thermal resistance between the frost surface and air might contribute up to 90% of the total thermal resistance (Ye and Lee, 2013). In order to overcome such undesirable effects, defrost cycles are implemented periodically during operation. The defrost process is accelerated using an electric heater while the cooling system is off. It is estimated that only 15 to 20 % of the heat supplied for defrosting is withdrawn by the condensate (Chen et al., 2003). The remaining heat load is rejected in the following cooling cycle, which decreases the system efficiency. According to the fridge capacity, the period of the defrost cycle might last from 30 to 60 min and the electric heater might use about 1 kW per foot of evaporator length (ACHR, 2011). Therefore, the mitigation or delaying of frost formation has important implications in energy savings. The frost formation is a complex process where mass transfer, heat transfer and fluid dynamic phenomenon occurs simultaneously. It is produced when humid air circulates over cold surfaces which temperature is below the freezing point of water. If the frosted surface 2 Page 2 of 19
temperature remains below the freezing point of water, the moisture from the air keeps depositing upon the surface, increasing the frost thickness. Additionally, some of the moisture might diffuse into the frost layer increasing its density and modifying the physical properties. Frost formation on refrigeration coils has been studied for long time (Kondepudi and O'Neal, 1989; Stocker, 1960). The main objectives have been the development of frost models and the study of process conditions. Seker et al. (2004a) present a model for frost formation on finand-tube heat exchangers and discuss operating conditions such as inlet temperature, relative humidity, air mass flowrate and refrigerant temperature. Latter, a comparison between numerical results and experimental data for the same geometry is shown (Seker et al., 2004b). Yan et al. (2003) observe that frost formation is greater for a lower airflow rate and higher relative humidity. Through an experimental study on large size air coolers, Deng et al. (2003) report that the wall temperature, fin spacing, frost height and air velocity are the main factors affecting the heater performance. Gao and Gong (2011) report that the temperature difference between air and tube surface is the main driving force for frosting. They also observe that the frost thickness at the fin base is thicker than at the fin tip due to the temperature profile in the fin. Wang et al. (2012) use a modified correlation for the initial frost density in a simple model for predicting frost growth on cold flat plate, the results are compared with experimental data. Lee et al. (2013) investigate the relative humidity, airflow rate, inlet temperature and fin pitch in a spirally-coiled circular fin-tube heat exchanger. Wang et al. (2013) present a theoretical study where the critical heat and mass transfer characteristic on a frosting tube are identified. Due to manufacture implications and the facility to drain melted water and ice particles, plain fin-and-tube geometries have been widely used as evaporator in household refrigerators. Open literature studies for design considerations of plain fin-tube heat exchangers under frost conditions are limited. Fin spacing under frosting conditions have mostly been determined empirically (Yang et al., 2006a). Watters et al. (2002) tested a coil with 6, 8 and 10 fins per centimeter on the front, second, and third row respectively. They found that the coefficient of performance of the staged coil was 8.7% lower than that of the base coil at 95% relative humidity and 1.7 °C. However its defrost cycle time could be shortened from 6% to 30% depending on the airflow rate. Using a mathematical model validated with experimental data, Yang, et al. (2006b) observed that thermal performance of the heat exchanger could be improved by a proper adjustment of fin spacing reducing the air-flow blockage. Yang et al. (2006a) present an optimum design study for heat exchanger performance, using the response surface and Taguchi method for a fin and tube heat exchanger with variable fin spacing. They also observe that operating conditions had little effect on the choice of an optimum design for the heat exchanger. Coleman (2009) presents low-temperature freezing systems where coils design have fin spacing that varies from the air-inlet side to the air-outlet side to more effectively manage the effects of frost accumulation. As a guidance, they suggest 0 to 3 fins per inch (fpi) under heavy moisture content, 3 to 4 fpi under a moderate to light conditions and 4 to 6 fpi under a light condition of humidity. Kim et al. (2010) present a CFD study of a plain fin-and-tube heat exchanger geometry where fin density increase as the humid air goes across the tube rows. In most heat transfer and pressure drop calculation of heat exchangers, it is assumed that the inlet flow and temperature distributions across the exchanger channels are uniform. Recent studies show that consideration of air redistribution due to frost growth improves frost thickness prediction and coil capacity compared to models where it is not considered (Padhmanabhan et al., 2011). Ye and Lee (2013) describe a numerical model for predicting the performance of a fin and tube heat exchanger considering airflow reduction due to frost accumulation. 3 Page 3 of 19
The objective of this study is to show the importance of the heat-transfer area distribution for design and operation of a plain fin-and-tube evaporator, when frost is developed on its surface. A model previously studied (Padhmanabhan et al., 2011), is adapted and results are compared with data in open literature. First, a geometry with fin spacing that increase or decrease from the centerline is proposed. Then additional heat transfer area is analyzed by increasing the fin density or fin length. Finally, the use of an airflow distributor is studied as a frost mitigation device. A simulation is carried out assuming a quasi-steady-state with small time steps and air redistribution as the frost develops. The frost growth is determined assuming a semi-empirical model.
2. Development of thermohydraulic simulation Local conditions such as air temperature, velocity, relative humidity and surface temperature cause a frost formation at different rates from inlet to outlet in a plain fin-and-tube geometry. When a channel is partially blocked (under a constant total mass flowrate), the airflow is redirected to other channels that offer less resistance. As a result, the pressure drop increases. A plain fin-and-tube geometry is studied on the airside by an integrated segment-by-segment thermohydraulic model. Each segment consists of a central tube and a fin attached to its surface, therefore the tube row in the direction of air flow correspond to the segment numbering as shown in Figure 1. Channels formed by fin separation are numbered starting from the closest to the fan. The formation of frost is simulated using a semi-empirical model based on the scaling approach which include the frost layer (Padhmanabhan et al., 2011). Using an effective diffusivity and the Clausius-Clapeyron equation into the Fick’s law of diffusion, the mass flow that densifies the layer can be expressed as: (1)
The effective diffusivity can be determined from a binary diffusion coefficient density ratio as shown in equation (2).
D AB
and a
(2)
The frost thickness is determined from the difference between the total mass of water sublimated and the mass that densifies the frost layer. The total mass is determined from the difference in absolute humidity of air at entrance and outlet of each segment. At the frost-air interphase, an energy balance (neglecting heat transfer by radiation and heat sinks or sources) equates the sensible and latent heat on the airside with the heat conducted through the frost layer and the latent heat by diffusion as shown in equation (3). (3)
The clean or frosted surface temperature T S is determined once the air outlet condition is known. The heat and mass transfer coefficient are related by the Lewis analogy as: (4)
4 Page 4 of 19
The heat transfer coefficient is determined using a correlation previously developed by Seker et al. (2004a) for an evaporator of a household refrigerator as follows: (5)
The heat transferred in fins is determined using a fin efficiency. As frost develops, the additional heat transfer resistance is incorporated to determine an average surface temperature. Using a characteristic fin length l * , the Schmidt method allows to extend the circular fin efficiency shown in equation (6) for different tube layout (Thulukkanam, 2013). (6)
The overall heat surface efficiency is determined using the equation (7) (Incropera et al., 2006). (7)
In order to determine a frost growth in the direction perpendicular to the surface for the following time step, in each segment an equivalent average temperature over the fin surface is used. The change in frost density presented in equation (8) is determined from the water vapor that undergoes a diffusion process (equation (1)) and the frost thickness in the segment . The change in frost thickness is determined from the remaining water vapor that undergoes a phase change and the actual frost density in the segment as in equation (9). (8)
(9)
The mass airflow distributes among channels according to its pressure drop. Neglecting the effects due to acceleration, entrance and exit losses, the pressure drop in each segment is determined by (Kays and London, 1984): (10)
The friction factor is determined as in equation (11), this correlation was previously derived for a similar geometry (Seker et al., 2004a). (11)
The initial flowrate delivered by the fan is given. The fan distributes the air among the channels formed by the fins in such a way that the pressure drop in all channels is equal. The flowrate is determined using the tool solver in Microsoft Excel 2013 spreadsheet, based on a non-linear method for equal pressure drop in channels as restriction. In each segment, the outlet air temperature is initially guessed. It is recalculated through a heat and mass balance at the frost layer interphase using the Newton-Rapson method. The air outlet condition in a segment is the inlet condition for the following one. The process repeats for all segments in a channel and for 5 Page 5 of 19
all channels. Then a hydraulic simulation is carried out to adjust the flowrate in channels due to the frost deposition. If necessary, the airflow is redistributed among channels to retrieve an equal pressure drop. The thermohydraulic simulation is repeated in the segments and channels until convergence is achieved. The next time step, starts with an airflow distribution among channels using the hydraulic diameter of the frosted surface that resulted in the previous time step. The thermohydraulic model has been coded using an Excel-VBA programming according to the flowchart presented in Figure 2. Regarding the physical properties of humid air, the density and heat capacity are determined from the vapor fraction as in equation (12). Where pure component properties are determine as in
.
(12)
The moist air viscosity and thermal conductivity are determined as in ASHRAE (2009). The partial
pressure of saturated humid air is determined as a function of temperature using the correlation in equation (13), which is valid in a range of 243 to 303 K, and was derived from Aspen plus ver. 8.8.1 software. (13)
In each segment, the physical properties of the frost layer are considered constant. The frost density is determined using an empirical correlation as function of surface temperature as presented in equation (14) (Hayashi et al., 1977). Thermal conductivity is determined using Sanders correlation as in equation (15) (Seker et al., 2004a). As frost density increases, its thermal conductivity also increases enhancing the heat transfer by conduction. (14) (15)
3. Results and discussion 3.1. Comparison with other models There are few studies in open literature showing the development of frost thickness with time for a plain fin-and-tube geometry. Two recent numerical studies (Armengol et al., 2016; Cui et al., 2011) compare their predictions with experimental data (Lenic et al., 2009). The operating condition of the experimental study are velocity (0.6 m s-1), air temperature (21.4 °C), absolute humidity (6.2 g kg-1) and surface temperature (-19.5°C). The development of frost with time predicted in this study, is compared in Figure 3 with the works previously mentioned. Error 6 Page 6 of 19
bars with a deviation of 15% from experimental data (Lenic et al., 2009) are included. The model underpredicts the frost growth for the time span. For a 120 min of operation, the deviation from experimental data is the largest 21%, however it is reduced to 9% at 250 min of operation. The recent numerical simulation results (Armengol et al., 2016), overpredicts the frost growth in a range from 9-12% in most of the time span. However at 60 min of operation the deviation observed is around 20%. Although the model describe more in detail the shape of the curve of experimental results, the present simultaion using a semi-epirical model under one-dimensional frost growth assumption, have a good agreement with experimental data and other simulations in literature, avoiding the complexity of numerical models. 3.2. Case study The heat exchanger under study is an evaporator of a household refrigerator made up of four rows of tubes with plain fins attached to the main surface as shown in Figure 1. Inside the tubes, refrigerant evaporates at a constant pressure and temperature. The pressure is considered such that inner surface temperature results in -15°C. A fan is located on top and at the centerline of the evaporator. The air flows through the channels formed by the fins from top to bottom. The air inlet condition used for simulation is 5°C with a relative humidity of 90%. This condition occurs during normal operation. da Silva et al. (2011) present a commercial fan curve that can handle up to 280 m3h-1 under no pump head, and a maximum pressure loss of 105 Pa. This study assumes an airflow rate of 170 m3 h-1, which is distributed to both sides of the exchanger in a symmetric way. The geometry (a) consists of ten fins from the fan centerline to both sides, with a fin spacing of 10 mm as shown on top of Figure 4. Initially the channels closer to the fan with shorter air paths present larger flowrates. Time steps of 1 second allow capturing the thermohydraulic behavior of the evaporator at different locations as the frost layer grows. As time passes, the frost layer in channels reduces the air flowrate in channels 1 to 4 and increases in channels 6 to 10 as shown in Figure 4. The flowrate in the central channel (channel 5) remains constant for the whole operation time. From the minute 2 to 9, an inversion in the flowrate trend in channels can be observed. In channels 1 to 4 the flowrate increases while there is a decrease in channels 6 to 10. This change is given due to the uneven frost allocation in segment 1, which is discussed next. The Figure 5 shows the blockage ratio (defined as the ratio of the cross section area of the frosted surface to the clean airflow area) for 10 minutes of operation in a 2-minutes intervals. During the initial two minutes of operation, in segment 1 of all channels, a frost layer is developed which results in a blockage ratio below the 2%. The heat transferred in the second time interval (2 to 4 minutes) does not yield frost formation in segment 1 of channel 1. However, the air temperature is reduced and the relative humidity increases to the saturation point. The segment 1 of the following channels (2 to 10) show a blockage ratio that increases as the channel is further away from the fan. In the third time interval (4 to 6 min) the frost is first observed in channel 4. The onset of frost formation in the fourth (6 to 8 min) and fifth (8 to 10 min) time intervals are the channels 6 and 8 respectively. Due to the airflow mal-distribution in the evaporator, for the initial 10 minutes of operation, the blockage ratio ranges from 1.7% in segment 1-channel 1, to 5.9% in segment 1-channel 10. In the first segment, the channel with lower flowrate develops a larger frost layer. At the following segments, the heat transfer leads to the frost deposition in all intervals of time as observed in Figure 5. The blockage ratio is larger in the channel with larger flowrate (channel 1). This indicates that the frost deposition is dominated by a mass transport mechanism. As the air flows from segment 2 to 3 and 4, the amount of vapor water in air decreases due to the frost deposition in previous segment. The air temperature becomes even lower, thus reducing the air saturation temperature and mitigating the formation of frost in subsequent segments. It is also observed that frost accumulated in the initial two-minute interval is larger than in the subsequent ones. As time 7 Page 7 of 19
passes, the frost layer gets thicker increasing the heat transfer resistance. Then the frost layer temperature increases promoting mass that diffuses instead of increasing its thickness, as presented in equation (1). The blockage ratio value in channels 1, 5 and 10 are reported in Table 2 for an operation time of 240 min, in 48-minutes intervals. During initial operation, the frost developed at the first segments of all channels, introduces a heat transfer resistance such that further frost deposition is reduced or nil. At the segments 2, 3 and 4, the frost continues developing as in the initial period. Results show that the segment 2 is the most affected by the frost development. Similar frost growth behavior have been observed (Armengol et al., 2016; Cui et al., 2011; Lenic et al., 2009). In Figure 6, the thermohydraulic behavior of the evaporator under two different air flowrates (170 m3 h-1 and 85 m3 h-1) is presented. During the initial 10 minutes, there is a sharp drop in heat load that represents 25% and 10% of the initial heat load for the initial and reduced flowrates respectively. At this point, the frost thickness is only 0.35 mm and 0.25 mm (at the segment most likely to frost) and pressure drop is 29.3 Pa and 7.36 Pa respectively. This thin frost layer contributes significantly to heat transfer. Therefore, an effective clean-up during defrost process is necessary to restore the exchanger performance. The allowable pressure drop of 100 Pa is reached after 80 min and 216 min of operation. If a specific application requires a heat flow of 50 W, then for 170 m3 h-1 the pressure drop restricts the operation at 80 min. For a volumetric flowrate of 85 m 3 h-1 there is not a pressure drop restriction and the evaporator can be operated for 120 min. Due to the flow maldistribution, the frost develops at different rates in segments of the channels, leading to premature deterioration of thermohydraulic performance at locations where the frost accumulates faster. In the next section, the fin spacing is analyzed looking at the airflow distribution among channels that brings benefits on the thermohydraulic performance.
3.3. Analysis of fin spacing The plain fin-and tube geometry is analyzed under three fin spacing scenarios and compared with the constant fin spacing geometry (a) of 10 mm. All of them under the same total airflow and heat transfer area forming 10 channels. The second geometry (b) assumes a fin spacing that increases for channels that are further away from the fan. Since the frost formation is conducted by the air flowrate, this scenario sets the fin spacing such that the same air flowrate is conducted through all channels. The third geometry (c) assumes a fin spacing that decreases for channels that are further away from the fan. It is created by reversing the fin spacing in geometry (b). This geometry allows larger frost deposition in channels closer to the fan with lower pressure drops. The geometry (d) assumes a constant fin spacing of 11 mm instead of 10 mm. The flow distribution in geometries (a) to (d) through channels 1, 5 and 10 are shown in Figure 7. It is observed that in all scenarios the flowrate in the central channel remains constant during the operation time. The flowrate in channel 1 tends to decrease with time and in channel 10 to increase. In geometry (b) the airflow among channels varies little and the flow in channel 10 is larger due to the formation of frost in the channels closer to the fan. The largest flow difference among channels occurs in the geometry (c). In geometry (d) the flowrate behaves very similar as in geometry (a), however the fin separation mitigates the blockage ratio. The blockage ratio in channels 1, 5 and 10 in segment 2 for the geometries (a) to (d) are shown in Figure 8. The operation time is 100 min in intervals of 20 min. As expected, the blockage ratio in channel 1, in geometry (b) is the largest due to the reduced fin spacing. On the other hand, the blockage ratio is nearly the same in all channels of geometry (c) which has a decreasing fin spacing. 8 Page 8 of 19
The total heat load and pressure drop for the four geometries during operation time are shown in Figure 9. The heat load curves show a very similar trend, however it can be observed a delay of 1.8 min and 4.6 min for a load of 75 W in the geometries (b) and (d) respectively. The thermal performance is slightly enhanced due to the frost distribution among channels. On the other hand, a pressure drop of 100 Pa is reached at different operation times: 80 min, 87 min, 89 min and 100 min for the geometries (a), (b), (c) and (d) respectively.
Relative to the geometry (a), the geometry (b) allows an additional operation time of 7 min before the pressure drop constraint is reached. During this time, there is a heat transfer of 3.3 W. The pressure drop in the geometry (c) behaves very similar to the observed in geometry (b) and its heat transfer performance curve does not show differences from the geometry (a). The geometry (d) allows an additional operation time of 20 min in which a heat transfer of 4.9 W occurs. An inconvenient of this geometry is that additional space is required to set the same number of fins. This analysis demonstrate that fin spacing and distribution are important parameters to consider when designing an evaporator subject to frost formation. In the next section, the thermohydraulic performance of additional surface area is analyzed when the number of fins and the fin length are considered.
3.4. Increased heat transfer area Three geometries with additional surface area (equivalent to 5 fins) are compared to the geometry (a) under the same total airflow. The additional area allows a larger heat load and the frost distributes over the fin surface in such a way that thermohydraulic benefits might be observed. The geometry (e) increases the fin density by allocating 15 fins in the same length. The geometry (f) distributes 15 fins keeping the original fin density therefore the total length increases. The geometry (g) use the original 10 fins and fin density as in geometry (a), however the fin length is increased in order to result with an additional equivalent surface of 5 fins. The flowrate through three representative channels are presented in Figure 10. The air is distributed among a greater number of channels in the geometries (e) and (f), therefore the local flowrate is reduced when compared to the 10-fin geometries (a) and (g). In Figure 11, it is observed again, that the blockage ratio in the geometry with reduced fin spacing is the largest (geometry (e)). A larger fin separation reduces the blockage ratio as observed in geometry (f). Finally the frost developed in geometry (g) with fins 12 mm longer, shows the lowest blockage ratio in all channels. The thermohydraulic performances of geometries (e), (f) and (g) show important differences as observed in Figure 12. The geometries (e) and (g) show an enhanced heat transfer and the curves present a crossover at about 90 min of operation. The heat load curve for geometry (f) is considerably above the others. The time at which the pressure drop reaches 100 Pa also increases considerably from 80 min in geometry (a) to 140 min and 180 min for geometry (f) and (g) respectively. Due to the increased fin density, geometry (e) reaches the allowable pressure drop in only 50 min of operation. Between the geometries (f) and (g), the geometry (g) can operate for additional 40 min in which 5.4 W of heat are transferred. On the other hand, at 140 min of operation, the geometry (f) has transferred 79.6 W compared to 75.1 W of the geometry (g). The heat transferred during the extended operation time of 40 min in geometry (g) is 0.9 W larger than the heat transferred by geometry (f) at 140 min of operation. Moreover, due to the extended operation time in geometry (g), the number of defrost cycles in one-year operation can be reduced considerably. 9 Page 9 of 19
3.5. Use of a flow distributor The geometry (b) shows that the thermohydraulic deterioration is less affected due to the homogeneous airflow distribution among the channels. In this section, a flow distributor is included to geometry (a) and named as geometry (h). Under an unfrosted surface condition, the air is distributed evenly in all channels as shown in Figure 13. As time passes and the frost develops, the air flowrate is redistributed among the channels in a non-uniform way.
The flowrate in channels 1 to 4 tends to increase while in the channels 6 to 10 decreases. This is an inverse behavior from that observed in previous simulations. Nevertheles, the flowrate through channels located closer to the fan is still larger. As a result, the blockage ratio in geometry (h) when compared to geometry (a), is slightly lower in channel 1, the same in central channel and slightly larger in channel 10. The thermohydraulic behavior is very similar to curves shown for geometry (a) and omitted for simplicity. The pressure drop results using a flow distributor, shows that a 100 Pa reading is reached four minutes sooner than in geometry (a). Therefore, there is not a thermohydraulic benefit from the use of this strategy.
4. Conclusion In this work, it is highlighted the importance of the heat transfer area distribution on the performance of a plain fin-and-tube evaporator as frost develops on its surface. The fin spacing, length and distribution are used to propose several evaporator designs for equal heat transfer area and compared using a thermohydraulic simulation. It is observed that a larger flowrate is related to thicker frost formation and initial frost layer deposit reduces the heat transfer considerably. A geometry with larger fin spacing shows the largest improvement on the thermohydraulic performance; however, it requires a larger space to set a specific number of fins. When fins are fixed such that flowrate among channels is initially evenly distributed, the performance of the evaporator shows an improved thermohydraulic behavior. When additional heat transfer area is evaluated, an advantage on the thermohydraulic performance is observed when longer fins are used instead of extra fins. Finally, the use of an air distributor shows an increase on pressure drop without any evident benefit on the thermal performance. The results of this study can be used as a guidance for evaporators design and operation, leading to a continued thermohydraulic performance or extended operation periods when frost develops over its surface.
Acknowledgements The authors greatly appreciate the financial support of the National Council for Science and Technology (CONACYT), México, under the grant No. 179181. References ACHR, 2011. Frost and Defrost: How It Happens and Why It Is Needed - A White Paper. The Air Conditioning Heating Refrigeration NEWS, September 5. Armengol, J.M., Salinas, C.T., Xamán, J., Ismail, K.A.R., 2016. Modeling of frost formation over parallel cold plates considering a two-dimensional growth rate. International Journal of Thermal Sciences 104, 245-256. 10 Page 10 of 19
ASHRAE, 2009. ASHRAE Handbook-Fundamentals, pp. 1.2-1.15. Coleman, R., 2009. Frost on Air-Cooling Evaporators. Ashrae J. 51, 27-33. Cui, J., Li, W.Z., Liu, Y., Jiang, Z.Y., 2011. A new time- and space-dependent model for predicting frost formation. Applied Thermal Engineering 31, 447-457. Chen, H., Thomas, L., Besant, R.W., 2003. Fan supplied heat exchanger fin performance under frosting conditions. International Journal of Refrigeration 26, 140-149. da Silva, D.L., Hermes, C.J.L., Melo, C., 2011. Experimental study of frost accumulation on fansupplied tube-fin evaporators. Applied Thermal Engineering 31, 1013-1020. Deng, D.-q., Xu, L., Xu, S.-q., 2003. Experimental investigation on the performance of air cooler under frosting conditions. Applied Thermal Engineering 23, 905-912. Gao, T., Gong, J., 2011. Modeling the airside dynamic behavior of a heat exchanger under frosting conditions. Journal of Mechanical Science and Technology 25, 2719-2728. Hayashi, Y., Aoki, A., Adachi, S., Hori, K., 1977. Study of Frost Properties Correlating With Frost Formation Types. Journal of Heat Transfer 99, 239-245. Incropera, F.P., DeWitt, D.P., Bergman, T.L., Lavine, A.S., 2006. Fundamentals of Heat and Mass Transfer, Sixth ed. Wiley. Kays, W.M., London, A.L., 1984. Compact Heat Exchangers, third ed. McGraw-Hill, Inc, New York. Kim, S.-j., Choi, H.-j., Ha, M.-y., Kim, S.-r., Bang, S.-w., 2010. Heat transfer and pressure drop amidst frost layer presence for the full geometry of fin-tube heat exchanger. 24, 961-969. Kondepudi, S.N., O'Neal, D.L., 1989. Effect of frost growth on the performance of louvered finned tube heat exchangers. International Journal of Refrigeration 12, 151-158. Lee, S.H., Lee, M., Yoon, W.J., Kim, Y., 2013. Frost growth characteristics of spirally-coiled circular fin-tube heat exchangers under frosting conditions. International Journal of Heat and Mass Transfer 64, 1-9. Lenic, K., Trp, A., Frankovic, B., 2009. Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger. International Journal of Heat and Mass Transfer 52, 22-32. Padhmanabhan, S.K., Fisher, D.E., Cremaschi, L., Moallem, E., 2011. Modeling non-uniform frost growth on a fin-and-tube heat exchanger. International Journal of Refrigeration 34, 20182030. Seker, D., Karatas, H., Egrican, N., 2004a. Frost formation on fin-and-tube heat exchangers. Part I—Modeling of frost formation on fin-and-tube heat exchangers. International Journal of Refrigeration 27, 367-374. Seker, D., Karatas, H., Egrican, P.D.N., 2004b. Frost formation on fin- and- tube heat exchangers. Part II—Experimental investigation of frost formation on fin- and- tube heat exchangers. International Journal of Refrigeration 27, 375-377. Stocker, W.F., 1960. Frost formation on refrigeration coils. ASHRAE Transactions 66. Thulukkanam, K., 2013. Heat Exchanges Design Handbook, Second Edition. CRC Press. Wang, W., Guo, Q.C., Feng, Y.C., Lu, W.P., Dong, X.G., Zhu, J.H., 2013. Theoretical study on the critical heat and mass transfer characteristics of a frosting tube. Applied Thermal Engineering 54, 153-160.
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Wang, W., Guo, Q.C., Lu, W.P., Feng, Y.C., Na, W., 2012. A generalized simple model for predicting frost growth on cold flat plate. International Journal of Refrigeration-Revue Internationale Du Froid 35, 475-486. Watters, R.J., O’Neal, D.L., Yang, J.X., 2002. Frost/defrost performance of a three-row fin staged heat pump evaporator. ASHRAE Transactions, 318-329. Yan, W.-M., Li, H.-Y., Wu, Y.-J., Lin, J.-Y., Chang, W.-R., 2003. Performance of finned tube heat exchangers operating under frosting conditions. International Journal of Heat and Mass Transfer 46, 871-877. Yang, D.-K., Lee, K.-S., Song, S., 2006a. Fin spacing optimization of a fin-tube heat exchanger under frosting conditions. International Journal of Heat and Mass Transfer 49, 2619-2625. Yang, D.-K., Lee, K.-S., Song, S., 2006b. Modeling for predicting frosting behavior of a fin–tube heat exchanger. International Journal of Heat and Mass Transfer 49, 1472-1479. Ye, H.-y., Lee, K.-s., 2013. Performance prediction of a fin-and-tube heat exchanger considering air-flow reduction due to the frost accumulation. International Journal of Heat and Mass Transfer 67, 225-233.
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Figure 1. Plain fin-and-tube geometry subject to frost formation.
Figure 2. Flowchart for thermohydraulic simulation of plain fin-and-tube heat exchanger under frost condition.
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Figure 3. Comparison of frost thickness between the present study and others in open literature.
Fin spacing
Fan
Channels 1 2 3 4 5
6 7 8 9 10
Centerline
Figure 4. Geometry (a), flowrate variation through channels as frost develops over time.
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Figure 5. Geometry (a), blockage ratio for several segments and channels during 10 minutes of operation.
Figure 6. Geometry (a), heat load and pressure drop vs. time for air flowrates of 170 and 85 m3h-1.
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Fan
Fin spacing
Fan
Channels 1
5
Channels
Fin spacing 10
1
5
10
Centerline
Centerline
(a) Even fin spacing 10 mm
(b) Increasing fin spacing
Fan
Channels
Fin spacing 1
Fin spacing
Channels 1
5
Centerline
Fan
10
5
10
Centerline
(c) Decreasing fin spacing
(d) Even fin spacing 11 mm
Figure 7. Flow distribution in channels 1, 5 and 10 for plain fin-and-tube geometries with different fin spacing.
Figure 8. Blockage ratio in segment two, for plain fin-and tube geometries with different fin spacing. 16 Page 16 of 19
Figure 9. Heat load and Pressure drop for plain fin-and tube geometries with different fin spacing.
(a) 10 fin with a fin spacing 10 mm
(e) 15 fins with an increased fin density
(f) 15 fins with an increased total length
(g) 10 fins with an equivalent surface area as 15 fins
Figure 10. Flow distribution for plain fin-and-tube geometries with increased heat transfer area.
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Figure 11. Blockage ratio at segment 2, for plain fin-and-tube geometries with increased heat transfer area.
Figure 12. Heat load and Pressure drop for geometries with increased surface area.
Figure 13. Geometry (h), airflow distribution using a flow distributor.
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Table 1. Correlations for Physical properties in dry air and water vapor as function of temperature (in Kelvin).
Dry air
Water vapor
Units
Table 2. Development of the blockage ratio [%] in channels 1, 5 and 10 during an operation of 240 min. CHANNEL 1
Time [min]
Segment
CHANNEL 5
CHANNEL 10
1
2
3
4
1
2
3
4
1
2
3
4
48
1.78
23.45
22.21
21.02
3.90
22.27
20.94
19.65
6.53
21.13
19.70
18.34
96
0.16
15.44
15.09
14.74
0.00
14.95
14.57
14.16
0.00
14.45
14.03
13.57
144
0.14
12.86
12.71
12.54
0.00
12.56
12.38
12.18
0.00
12.22
12.04
11.80
192
0.14
11.34
11.28
11.21
0.00
11.13
11.06
10.96
0.00
10.89
10.83
10.71
240
0.15
10.26
10.31
10.34
0.00
10.13
10.15
10.14
0.00
9.95
9.98
9.94
2.38
73.35
71.61
69.85
3.90
71.04
69.10
67.09
6.53
68.64
66.60
64.37
Accumulated
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