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Hot gas defrost model development and validation
International Journal of Refrigeration 28 (2005) 605–615 www.elsevier.com/locate/ijrefrig
Hot gas defrost model development and validation N. Hoffenbecker, S.A. Klein*, D.T. Reindl University of Wisconsin—Madison, 1500 Engineering Drive, Madison, WI 53706, USA Received 20 May 2004; received in revised form 25 July 2004; accepted 30 August 2004 Available online 26 January 2005
Abstract This paper describes the development, validation, and application of a transient model for predicting the heat and mass transfer effects associated with an industrial air-cooling evaporator during a hot gas defrost cycle. The inputs to the model include the space dry bulb temperature, space humidity, coil geometry, frost thickness, frost density, and hot gas inlet temperature. The model predicts the time required for a complete frost melt as well as the sensible and latent loads transferred back to the conditioned space during the defrost period. The model is validated by comparing predicted results to actual defrost cycle field measurements and to results presented in previously published studies. A unique contribution of the present model is its ability to estimate parasitic space loads generated during a defrost cycle. The parasitic energy associated with the defrost process includes thermal convection, moisture re-evaporation, and extraction of the stored energy in the coil mass following a defrost cycle. Each of these factors contribute to the parasitic load on compressors connected to the defrost return. The results from the model provide quantitative information on evaporator operation during a defrost cycle which forms the basis to improve the energy efficiency of the defrost process. q 2004 Elsevier Ltd and IIR. All rights reserved. Keywords: Air conditioning; Evaporator; Modelling; Heat transfer; Mass transfer; Cycle; Defrosting; Hot gas
De´veloppement et validation d’un mode`le pour le de´givrage a` gaz chaud Mots cle´s : Conditionnement d’air ; E´vaporateur ; Mode´lisation ; Transfert de chaleur ; Transfert de masse ; Cycle ; De´givrage ; Gaz chaud
1. Introduction Plate-finned heat exchangers are widely utilized as aircooling evaporators in industrial refrigeration systems for space conditioning and product cooling. All refrigerant-toair evaporators operating with coil surface temperatures
* Corresponding author. Tel.: C1 608 263 5626; fax: C1 608 262 8469. E-mail address: [email protected] (S.A. Klein). 0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2004.08.016
both below the freezing point of water and dew point temperature of the air within the conditioned space will lead to the formation of frost on the evaporator surface. Frost accumulation on the evaporator has several consequences. First, the accumulation of large amounts of frost will degrade heat transfer performance of the evaporator by fouling the outside surface since, the frost itself has low thermal conductivity (Stoecker [1], Machielsen and Kerschbaumer [2]). With degraded heat transfer performance, evaporator capacity decreases. To meet a specified load with degraded heat transfer performance, the evaporator
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Nomenclature mass transfer coefficient (kg/m2 s, lbm/ft2 s) Grashof number specific enthalpy (kJ/kg, Btu/lbm) convection coefficient (W/m2 K, Btu/h ft2 R) enthalpy of fusion (kJ/kg, Btu/lbm) thermal conductivity of air (W/m K, Btu/h ft R) kf frost thermal conductivity (W/m K, Btu/h ft R) ki,j thermal conductivity for node i,j (W/m K, Btu/h ft R) Lfin length of the fin (m, ft) mH2 O;s mass fraction of water vapor at the surface of the frost or liquid mH2 O;N mass fraction of water vapor in the conditioned spaces NuL Nusselt number with L as the characteristic length Q_ evap rate of heat transfer by evaporation (W, Btu/h) Qconv the sensible energy convected back to the space during a defrost cycle (kJ, Btu) Qevap the latent energy that transferred to the surroundings during a defrost cycle by reevaporation of water from the coil surfaces (kJ, Btu) Qfin and Qtube the total thermal energy stored within the fins and tubes, respectively after a defrost cycle is complete (kJ, Btu)
gm Gr h hC hig kair
temperature must decrease which decreases system efficiency. Second, the frost impedes airflow through the coil leading to increased fan energy consumption and reduced air flow through the evaporator (Stoecker [1], Barrow [3], Seker et al. [4], and Yao et al. [5]). To counter these effects, the accumulated frost must be removed from the evaporator surface on either a continuous or intermittent basis. Although defrosting can be accomplished using electric resistance heating, warm water, off-cycle (for coolers), or by the use of a liquid desiccant, hot gaseous refrigerant is the most widely used method for removing frost from evaporators in industrial refrigeration systems. During a hot gas defrost, the normal supply of cold refrigerant is stopped while a portion of the hot refrigerant vapor discharged from compressors is re-directed to the evaporator. Fig. 1 shows a direct expansion evaporator undergoing a hot gas defrost. The defrost sequence begins by closing the solenoid valve that normally admits high-pressure liquid (HPL) refrigerant to the evaporator through the thermostatic expansion valve (TXV). After a time delay that allows the remaining refrigerant in the coil to boil off, the hot gas solenoid valve is opened. High-pressure high temperature gas is supplied to the evaporator flowing first through the
Qin Qmelt
rj,in rj,out Ra Sc ShL t Ti,j TN V Dr Dx hdefrost
v rf rN
energy supplied to the coil during a defrost cycle (kJ, Btu) the amount of energy it takes for the mass of frost to reach melting temperature and change phase from ice to water (kJ, Btu) inner radius of node j (m, ft) outer radius of node j (m, ft) Rayleigh number Schmidt number Sherwood number time (s) temperature of node i,j (K, R) temperature of air in the conditioned space (K, R) volume of the ice or fin material in a node (m3, ft3) node spacing in the radial direction (m, ft) node spacing in the axial direction (m, ft) defrost efficiency defined as the ratio of the energy required to melt the accumulated frost to the total energy supplied to the evaporator coil for a defrost cycle kinematic viscosity (m2/s, ft2/s) frost density (kg/m3, lbm/ft3) density of air in the freezer (kg/m3, lbm/ft3)
drain pan to preheat it for draining the frost melt from the coil. The hot gas then leaves the drain pan heater through tubing that connects to the top of the coil through the pan check valve. As the hot gaseous refrigerant flows through the coil, it condenses thereby releasing its latent heat and warming the coil surface. As the pressure of refrigerant in the coil builds, it eventually reaches the set-point of the defrost relief regulator after which, the valve modulates the refrigerant in the evaporator back to the defrost return. The hot gas defrost is continuously supplied to the coil until a time–clock or other controls terminate the defrost sequence. The hot gas supplied to evaporators for defrost is commonly superheated with a saturation temperature well above 0 8C (32 F). In contrast, Nussbaum [7] proposed the use of a vapor-only defrost process. A vapor-only defrost utilizes a superheated vapor refrigerant but with a saturation temperature lower than the temperature of frost on the accumulated coil. The advantage being sought by Nussbaum was the avoidance of condensed liquid refrigerant management associated with a typical condensing hot gas defrost process. With
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Fig. 1. An evaporator in a hot gas defrost process, Reindl et al. [6].
ammonia, a vapor-only defrost is impractical due to the excessively high gas flow rate requirements since, in this case its extremely high heat of condensation cannot be harnessed for frost melting. The energy impacts associated with defrosting an evaporator coil depend on the temperature of the refrigerant supplied for the hot gas defrost process and the hot gas dwell time. The lower the refrigerant gas temperature supplied to the coil for defrosting, the lower the rate of sensible and latent parasitic gains to the space but the longer the time period required to achieve a complete melt of the accumulated frost. Higher refrigerant temperatures result in shorter defrost periods but higher rates of sensible and latent gains to the space. Higher refrigerant temperatures also raise the mass of the coil to higher temperatures leading to a greater parasitic cooling load on the refrigeration system following the hot gas defrost process. In either case, longer than necessary defrost dwell times will increase the parasitic load to the space. Understanding the defrost process is a pre-requisite to making the changes necessary to improve the overall efficiency of the defrost process. The principle contribution of this paper is the development of a mathematical model of the defrost process. The model provides a foundation to understand the energy impacts of the defrost process by quantifying the energy and mass flows involved in the defrost process. The model of the defrost process developed here is compared with available experimental data to validate its performance. The model is then used to investigate the effects of hot gas supply pressure and temperature, hot gas defrost dwell time period, and frost accumulation on evaporators with a goal developing process insights to improve both defrost and refrigeration system efficiency.
2. Modeling the defrost process Air-cooling evaporators used in industrial refrigeration
systems are comprised of a series of multi-row tubes with hundreds of fins pressed over the tubes to enhance heat transfer through the extended surface area. Modeling the defrost process requires consideration of both energy flows and geometry. Due to symmetry, the fin surrounding each tube resembles a hexagon which can be further approximated as a disc, or more appropriately, an annular fin as shown in Fig. 2. Since, the bulk of frost on an air-cooling evaporator adheres to the finned surfaces, heat needs to be efficiently delivered to the finned surfaces of the coil to melt the frost. During the hot gas defrost process, condensing high pressure refrigerant inside the evaporator tubes warms the tube surfaces which in turn warms the base of each individual fin in contact with the tubes. The fin conducts thermal energy from its base (the tubes) to warm the adhered frost, eventually changing its phase from a solid to a liquid. The bulk of the frost condensate then drains, by gravity, down the coil to the drain pan. Some of the frost evaporates and returns to the conditioned space. A number of important heat and mass transfer mechanisms arise during the course of a hot gas defrost process: condensation of high-pressure high temperature gaseous refrigerant inside the tubes of the coil; conduction of heat through the coil tubes and fins; sensible heating of accumulated frost; latent melting of accumulated frost; and re-evaporation of moisture from the coil surface to the surrounding space. The following description indicates how the present model incorporates these heat and mass transfer mechanisms. Fig. 3 illustrates the assumed geometric arrangement for a frosted fin and the associated two-dimensional grid for solving the energy flows during the defrost process. An annular segment of fin forms the basis of the computational domain with a line of symmetry halfway through the fin’s thickness. An adiabatic boundary condition is applied at the two lines of symmetry: outer radius of fin/frost and the centerline (right-hand side) of the fin. During the defrost
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Fig. 2. Typical tube-fin segment for a plate-fin heat exchanger (left) and simplifying circular geometry assumed to approximate the tube-fin segment (right).
process, the fin base is assumed to be at constant temperature due to condensing refrigerant inside the tubes. The boundary condition applied to the left-hand side of the computational domain is convective (heat and mass) transfer to a surrounding environment. The governing two-dimensional axi-symmetric partial differential energy equation is solved numerically using a finite difference approach implemented in the EES equation
solving program [8]. Based on the letter designations shown in Fig. 3 (A–L), there are 12 different types of nodal energy balances that can be formulated. Each nodal balance represents a typical node that has, potentially, different boundary conditions. The nodes labeled ‘J’, ‘K’, and ‘L’ all represent the finned surface and, as such, will not undergo a phase change. The remaining nodes ‘A’ through ‘I’ are nodes within the frost layer and undergo a phase change. Eq. (1)
Fig. 3. Illustration of discretization strategy for annular fin segment (left) and grid arrangement for two-dimensional finite difference solution (right).
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shows the nodal energy balance for a surface node type ‘D’. k1;jK1 C k1;j dh Dx T1;jK1 K T1;j 2p Z rV dt 1;j 2 ln ri C Dr =ri 2 |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} E_ st
boundary a
2 2 2 2 TN K T1;j C gm;D p rj;out mH2 O;s K mH2 O;e hig C hC p rj;out K rj;in K rj;in |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} boundary b
2 2 K rj;in T2;j K T1;j k1;jC1 C k1;j k C k1;j p rj;out Dx T1;jC1 K T1;j C 2;j 2p 2 ln ri C Dr =ri 2 2 Dx |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
C
boundary d
boundary c
The first term represents the energy stored in the node. Since, each frost control volume experiences a phase change (e.g. from ice to water), the stored energy within the control volume cannot be calculated by using temperature alone. As a result, the energy storage for a frost node is expressed in terms of enthalpy to accommodate the change in phase associated with melting the frost upon sufficient accumulation of thermal energy in the node. The terms identified as ‘boundary a’ and ‘boundary c’ correspond to the thermal conduction from the adjacent nodes at smaller and larger radii, respectively. The term identified as ‘boundary b’ represents the convective heat (first term) and mass transfer (second term) associated with the surrounding environment. The convective heat and mass transfer coefficients are estimated using correlations published by Jaluria [9] and Mills [10], respectively. Lastly, the term identified as ‘boundary d’ represents the thermal conduction between adjacent nodes at the same radial location. Energy balances for other nodes are developed in a similar fashion. The thermal conductivity of the frost is assumed to be a function of the frost density, as indicated in Eq. (2) from Tao et al. [11] where kf and rf have units of W/m K and kg/m3, respectively. kf Z 0:02422 C 7:214 !10K4 rf C 1:01797 !10K6 r2f
(2)
During the defrost process, the evaporator fans are cycled off and the thermal energy exchange from the evaporator to the surrounding environment is dominated by natural convection. A free convection relationship is used for estimating the Nusselt number and the corresponding natural convection heat transfer coefficient as indicated in Eq. (3) (Jaluria [9]). Nu L Z
hC Lfin Z 0:13ðRaÞ1=3 kair
for 109 ! Ra! 1013
(1)
(3)
In addition to the sensible energy exchange between the coil and the surrounding by natural convection, latent energy transfers occur due to mass transport from vapor pressure differences between the ice (or water) on the coil surface and the surrounding environment. The latent energy transfer rate
is proportional to the difference in vapor pressure between the exposed ice (water) surface and the surrounding environment as described by Mills [10]. This driving force for mass transfer can be expressed in terms of mass fractions of water in the air defined as the ratios of the densities of the water vapor in the air at each location divided by the total density of the humid air in each location. The densities are found by using partial pressures related to the saturated pressure at each location. The latent energy transfer rate due to evaporation is given by the following equation. 2 2 Q_ evap Z gm p rout mH2 O;s K mH2 O;N hig K rin (4) |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} boundary b
The correlation for the mass transfer coefficient, gm , expressed in terms of the Sherwood number (Eq. (5)), is given by Jaluria [9] and is shown in Eq. (6) assuming the Lewis Number is unity. Sh L Z 0:13ðGrScÞ1=3 g m Z
rNn Sh ScLfin L
for 109 ! GrSc! 1013
(5) (6)
The system of discretized equations is then solved in space while using an implicit time integration scheme to establish estimates of the nodal temperatures and heat flows as a function of time during a defrost cycle. One difficulty that arises during a simulated defrost is the effect that the phase change of frost has on the continuity of the computational domain. Rather than attempting to incorporate a methodology to accommodate the solution of a moving boundary domain, the current model approximates the effects of frost melting by assuming that the mass and volume (and thus the density) of each node is constant. When ice melts in the actual evaporator, water drains and the volume formerly occupied by water is replaced by air that has a much smaller mass. The temperature of the air in this nodal space remains relatively constant because of free convection, i.e. air in the freezer space continuously replaces the air in the nodal space. The model assumes
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that the density of the node is constant which greatly overestimates the mass-specific heat product when the node should be air. However, this overestimate of the massspecific heat product results in a relatively constant temperature for the node, similar to the effect of increased convection. This assumption greatly simplifies the model. The validity of this simplification is supported by comparisons with experimental results and with the results of other studies.
3. Frost model validation The facility that provided experimental information on defrost times was a K21 8C (K5 F) fruit product storage freezer. Additional data on the field measurements can be found in Hoffenbecker [12]. Data were collected during a period of the year when harvested fruit (cranberries) were delivered in bulk and placed in the warehouse for freezing and long-term storage. In this facility, the evaporators were defrosted after an 8 h period of accumulated liquid feed solenoid run time. Details of the field-installed evaporator are provided in Table 1. Physical observations of the coil and the warehouse conditions resulted in coil conditions as shown in Table 2 just prior to the start of a hot gas defrost sequence. The frost density was determined by estimating the volume of frost on the coil from physical measurements and photographs along with collecting the total mass of liquid water drained from the condensate drain pan during a defrost cycle. These conditions are required inputs for the model to simulate the comparative hot gas defrost process. Fig. 4 shows a series of time-lapse photographs of the coil face observed during the defrost process. The coil begins with the initial conditions noted in Table 2. After Table 1 Field-monitored evaporator specifications Imeco air-cooling evaporator specifications model: FCLS 96103.4.3 serial: 7191.1 RHI Coil volume, ft3 (m3) Coil mass, lbm (kg) Coil metal Fin metal Fin pitch, fins/in (fins/cm) No. of fins No. of rows No. tubes on face Tube wall thickness, in (mm) Tube outside diameter Total coil surface area, ft2 (m2) No. of fans Installed fan power (each), HP (kW) Total air flow rate, ft3/min (l/s) Air face velocity, ft/min (m/s)
21.4 (0.61) 9479 (4300) Galvanized steel Aluminum 3 (1.2) 800 10 18 0.060 (1.52) 1.05 (26.7) 11,119 (1033) 4 3 (2.2) 72,416 (34,177) 741 (3.76)
Table 2 Frost properties and freezer conditions used for defrost process simulation Frost properties and freezer conditions Frost density, kg/m3 (lbm/ft3) Frost blockage, % Freezer temperature, 8C (F) Coil temperature, 8C (F) Refrigerant temperature, 8C (F)
300 (18.7) 23 K15 (5) K29 (K20) 10 (50)
2 min into the defrost process, portions of the frost on the coil are beginning to melt. The highest rate of frost melt occurs in the period between 4 and 8 min into the defrost cycle. By 10 min, the coil is completely free of any accumulated frost with some residual water continuing to drain from the finned surfaces. As the hot gas dwell period continues, moisture from the coil surface completely evaporates followed by evaporation of moisture in the coil drain pan. Results from the defrost model given the conditions noted in Table 2 are shown below in Table 3. The model predicted a defrost time of 10 min and 45 s which is in good agreement with the 10 min qualitative observation of the defrosting evaporator in the field. The model predicts that a total of 271.1 MJ (257 mBtu) of energy is supplied to the coil during the 645 s defrost. Only 43.7% of the total energy input is used for melting the accumulated frost. The remaining energy results in an increased load on the refrigeration equipment. Niederer [13] predicted that only 15–25% of the total energy supplied during a typical defrost process is actually carried out by the frost condensate leaving the drain pan. Niederer evaluated a defrost process that removed 11.6 kg (25.5 lbm) of frost from a coil over a 35 min cycle. For this coil, Niederer estimated that a minimum of 4330 kJ (4105 Btu) were required to remove the condensate whereas 28,043 kJ (26,580 Btu) of heat was actually input to accomplish the 35 min defrost. The results of Niederer were compared with the results from the current model using a comparable energy input rate as reported by Niederer (a refrigerant temperature of 4 8C (39 F) and a refrigerant mass flow rate of 0.665 kg/s (88 lbm/min). After 35 min of hot gas dwell time, the present model predicted an Table 3 Coil defrost model results Imeco FCLS evaporator, frost densityZ300 kg/m3, frost blockageZ23% Variable
Value
Qin [MJ] Qconv [%] Qevap [%] Qfin [%] Qtube [%] Qmelt [%] Time, [s]
271.1 29.4 13.7 4.9 8.3 43.7 645
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Fig. 4. Visual observation of defrost sequence (Hoffenbecker [12]).
energy input of 28,640 kJ (27,145 Btu). The predicted quantity of energy needed to melt the frost from the coils was 3995 kJ (3786 Btu). Both results compare well with figures reported by Niederer [13]. Stoecker et al. [14] conducted both laboratory measurements of a defrosting evaporator (copper tubes with aluminum fins) using R-22 as well as a field assessment of an evaporator (steel coil with aluminum fins). A thrust of this work was to evaluate whether or not evaporators could
be defrosted with low-pressure hot gas with the intent of achieving refrigeration system efficiency improvements. In the laboratory, defrost tests were conducted using a range of hot gas pressures. The evaporator was a six row coil with 14 tubes in each row and fins spaced 0.6 cm (1⁄4 in.) apart across a 71 cm (28 in.) wide span. Table 4 shows an energy budget reported by Stoecker et al. [14] to melt 9.1 kg (20.1 lbm) of frost from the coil assuming that the condensate is heated to 7 8C (45 F) and the coil is heated to 13 8C (55 F).
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Table 4 Summary of distributed energy for a copper tube/aluminum fin coil (Stoecker et al. [14]) Item
Aluminum fins Copper tubes Warming the frost Thawing the frost Warming the water Total
Mass
Energy
[lbm]
[kg]
[Btu]
[kJ]
54.5 93.0 20.1 20.1 20.1 –
24.7 42.2 9.1 9.1 9.1 –
629 471 294 2880 260 4534
664 497 310 3038 274 4783
Stoecker et al. [14] found that the energy required to melt 9.1 kg (20.1 lbm) of frost on a coil weighing 66.9 kg (147.5 lbm) was 4783 kJ (4534 Btu). Energy was supplied to the evaporator from hot gaseous R-22 refrigerant passing though the coils at 0.136 kg/s (18 lbm/min). Stocker’s analysis uses only the heating of the coils and the warming and melting of the frost as the factors affecting the defrost efficiency. Convective and evaporative energy losses were not included. To compare the present model with the Stoecker et al. data, the present model was run using frost properties that would yield the same total mass of frost reported by Stoecker et al. [14]. By assuming a mass flow rate of R-22 consistent with that reported by Stoecker et al. the model predicted the amount of energy input during defrost and the resulting energy distribution as shown in Table 5. The results predicted by the present model show good agreement with the energy distribution reported by Stoecker et al. and reasonable agreement with the total energy input during defrost recognizing that the total energy budget estimate of Stoecker et al. did not include convective losses from the coil.
4. Results With confidence that the defrost model is providing reasonable results in predicting the behavior of an evaporator during a defrost sequence, we now are able to use the model to investigate factors that influence the defrost performance and efficiency. The rate of energy supplied to the evaporator during a defrost cycle, Q_ in , is the rate of heat input to the coil resulting from condensation of refrigerant
Ratio [%]
13.9% 10.4% 6.5% 63.5% 5.7% –
vapor during the defrost process. Q_ in , varies with time as shown in Fig. 5. The energy rate is calculated in the model as the rate at which energy is conducted into the base of the fin from the hot refrigerant through the refrigerant pipe. As one would expect, the initial rate of energy input to the coil is high and the rate decreases as the coil, fins, and frost absorb heat and warm in temperature reducing the driving force for heat transfer. As the defrosting process progresses, the fin and frost surfaces increase in temperature thereby, increasing the rate of energy convection to the surrounding freezer environment. Fig. 6 shows the integrated amount of energy convected back to the space for a coil with an initial frost density of 150 kg/m3 (9.36 lbm/ft3) and varying initial frost blockages as a function of the entering hot gas temperature. Interestingly, the total convected heat to the space increases with increasing frost mass, expressed as % blockage. This increase is attributable to the fact that the defrost dwell time increases with increasing frost. Increased defrost dwell time leads to increased space convective loads. Fig. 7 shows the latent energy losses to the surrounding controlled temperature space due to the re-evaporation of water from the coil surface during a defrost cycle. The rate of evaporation depends of the vapor pressure difference between the surface of the ice and the freezer space. The vapor pressure of the ice is a strong function of its temperature. Although the rate of latent energy loss due to evaporation is greater with increased refrigerant temperatures, the integrated latent energy loss from evaporation is less due to the shorter defrosting times experienced at elevated temperatures for a fixed frost mass (expressed as the % blockage).
Table 5 Frosted fin model using a mass flow rate of refrigerant Item
Aluminum fins Copper tubes Frost Frost Frost Frost/Metal
Variable
Qfin Qtube Qmelt Qevap Qconv Qin
Mass
Energy
[lbm]
[kg]
[Btu]
[kJ]
54.5 93.0 20.1 20.1 20.1 167.6
24.7 42.2 9.1 9.1 9.1 76
825.7 540.6 3376.2 398.3 1061.3 6203.0
871.7 570.3 3561.9 420.2 1119.7 6544.2
Ratio [%]
13.4% 8.8% 54.8% 6.5% 17.2% –
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Fig. 5. Rate of supplied energy to the coil during defrost.
613
Fig. 7. Integrated latent energy loss during a hot gas defrost cycle as a function of entering hot gas temperature.
Fig. 8 shows the quantity of stored energy in the coil mass (fins and tubes) just after a defrost process terminates. The model assumes that the tubes are entirely heated to the hot gas inlet temperature; however, the fins will have a temperature distribution as determined by the finite difference model. For reference, the defrost times are shown with dotted lines in the figure. The total quantity of energy supplied during a defrost cycle Qin, represents the integral of the energy supply rate, Q_ in , over the entire defrosting period. This energy quantity represents the total amount of energy supplied for defrost, including the losses associated with the stored and released energy. Fig. 9 shows the total energy supplied during defrost along with the time required to fully melt accumulated frost fin are plotted over a range of entering hot gas refrigerant temperatures with frost densities ranging between 150 and 450 kg/m3 (9.36–28.1 lbm/ft3) as a parameter and an initial frost blockage of 20%. As expected, the time to defrost decreases as the hot gas supply temperature increases. However, higher hot gas supply temperatures lead to a higher rate of sensible and latent heat transfer to the surrounding freezer. In addition,
the higher hot gas temperatures lead to a greater elevation in coil mass temperature above the melting point of water resulting in a larger energy penalty when the defrost cycle is terminated. The parasitic effects of increasing the hot gas temperature along with the decreasing hot gas dwell time lead to competing factors that result in an optimum (from an energy viewpoint) hot gas inlet temperature. The optimum (minimum) integrated defrost energy input is a function of frost density as shown in Fig. 9. The optimum hot gas temperature for a frost density of 150 kg/m3 (9.26 lbm ft3) is 18 8C (65 F) or just over 689 kPa (100 psig) with ammonia. Previous studies have focused on achieving defrost with lower hot gas temperatures with the goal of reducing the parasitic load on the space during defrost (Stoecker et al. [14], Cole [15], and Briley [16]). The assumption is that with lower hot gas temperatures, the difference in temperature between the coil and surrounding space will be lower thereby, decreasing the rate of convective heat loss from the coil. In addition, lower hot gas pressures result when systems are run at lower head pressures to improve
Fig. 6. Total convected energy released during defrost as a function of entering hot gas temperature.
Fig. 8. Stored energy in total evaporator fin surface after the defrost cycle terminates and defrost time as a function of entering hot gas temperature.
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Fig. 9. Total supplied energy and defrost time for a defrost cycle at 20% frost blockage as a function of entering hot gas temperature for a freezer temperature of K23 8C (K10 F).
compressor efficiency. The current results seem to contradict the former premise of defrost efficiency improvement. Consider the defrost data reported by Stoecker et al. [14] shown in Table 6 below. For a given hot gas saturation temperature, the reported data includes the defrost condensate mass, defrost time, and average gas mass flow rate at a point in time where 80% of the condensate has melted. Although not reported by Stoecker et al., we calculated the total hot gas load (the last column) using data presented in the paper. The total hot gas load is simply the product of the average hot gas mass flow rate, defrost time, and the enthalpy of vaporization for R-22 at the given hot gas saturation temperature. This additional result illustrates a key point related to the present study. That is, although lower hot gas saturation temperatures can feasibly melt accumulated frost, the longer defrost dwell time required to melt the frost results in a greater integrated load. Unfortunately, the hot gas defrost results given by Stoecker et al. [14], were not run at higher temperatures to determine whether or not a minimum hot gas load exists. The defrost efficiency is defined as the amount of energy required to melt the accumulated frost with respect to the total energy supplied to the evaporator coil for a defrost cycle. The defrost efficiency definition is consistent with that used by Cole [15]. A plot of the defrost efficiency for a frost density of 150 kg/m3 (9.26 lbm ft3) and frost blockages ranging from 10 to 30% is shown in Fig. 10. At lower refrigerant temperatures, the defrost efficiency
Fig. 10. Defrost efficiency and defrost time as a function of entering hot gas temperature.
is heavily dependent on the time required to melt accumulated frost. Referring to the refrigerant of 10 8C (50 F), at 10% frost blockage the defrost efficiency is approximately 0.3 because, with such little accumulated frost, most of the supplied energy goes into heating the evaporator coils. At 20% frost blockage the efficiency increases to 0.38 because the amount of energy needed to melt the frost is higher than the energy stored in the coils. Also, the frost melts in a timely manner making the convective and evaporative losses less of an issue. As frost blockage increases to 30%, the efficiency for defrost decreases once again to 0.32 because the long period of time to complete the defrost cycle allows for greater convective and evaporative losses. The penalty for operating a defrost cycle on fixed dwell time can be significant. A model of the coil with completely dry finned surfaces is used as a basis for comparison to estimate the energy penalties associated with excess hot gas defrost. The excess time for a specified clock-driven defrost dwell time is found by subtracting the specified clock-driven defrost dwell period from the defrost dwell time estimated by the model. Table 7 shows the defrost efficiency for defrost cycles of differing lengths at different refrigerant inlet temperatures. The time required for frost to completely melt is shown in the first row of the table. Continued supply of hot gas beyond this required melting period necessarily lowers the defrost efficiency. As expected, the defrost efficiency decreases as the hot gas temperature increases and as the defrost dwell time increases.
Table 6 Excerpt of hot gas defrost results reported by Stoecker et al. [14] as well as calculated hot gas load Hot gas saturation temperature, F [8C]
Defrost mass, lbm, [kg]
Defrost timea, min
Average gas flow rate, lbm/s [kg/s]
Hot gas load, Btu [kJ]
36 [2] 43 [6] 52 [11]
21.8 [9.9] 13.6 [6.2] 23.2 (10.5)
6.0 5.9 7.0
0.36 [0.163] 0.35 [0.159] 0.24 [0.109]
11,320 [11,944] 10,650 [11,236] 8,478 [8,944]
a
Condensate collected when the defrost process was 80% complete.
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Table 7 Defrost efficiency for a set hot gas supply of 45 min for a frost density of 150 [kg/m3] and frost blockage of 20% Time Melt time 5 min 10 min 15 min 20 min 25 min 30 min 35 min 40 min 45 min
Frost densityZ150 [kg/m3], Frost blockageZ20% 37.7 8C 100 F
32.2 8C 90 F
26.7 8C 80 F
21.1 8C 70 F
15.6 8C 60 F
10 8C 50 F
48.5 s 18.4% 12.9% 9.9% 8.0% 6.8% 5.8% 5.1% 4.6% 4.1%
56.2 s 20.2% 14.3% 11.0% 9.0% 7.6% 6.6% 5.8% 5.2% 4.7%
1 min 8.2 s 22.3% 15.9% 12.4% 10.2% 8.6% 7.5% 6.6% 5.9% 5.3%
1 min 27.3 s 24.8% 18.0% 14.1% 43.4% 9.9% 8.6% 7.6% 6.8% 6.2%
2 min 5.9 s 27.7% 20.5% 16.3% 13.5% 11.5% 10.1% 8.9% 8.0% 7.3%
4 min 8.6 s 30.8% 23.4% 18.9% 15.8% 13.6% 12.0% 10.7% 9.6% 8.8%
5. Conclusions A mathematical model for a frosted coil was developed to determine the energy requires for defrosting an evaporator. The frosted coil model is scaled-up based on simulation of the defrost process for a single fin surface. When supplied with the specific geometry and operating conditions, the frosted fin model provided defrost time estimates that compared quite well with the time to melt the accumulated frost that observed at a local cold storage warehouse facility. The model developed also compared well with defrost energy use reported in the literature. Results from a parametric analysis using the present model showed an optimum hot gas temperature that is a function of both the accumulated mass and density of frost on an evaporator. An interesting result was that the model predicted the mass of moisture re-evaporated back to the space increases with decreasing hot gas temperature. This behavior is due to the prolonged defrost dwell time to achieve a full melt of accumulated frost. The results of this model suggest that parasitic energy impacts associated with the defrost process can be minimized by limiting defrost dwell times.
Acknowledgements The financial support from the Energy Center Wisconsin is gratefully acknowledged.
References [1] W.F. Stoecker, How frost formation on coils affects refrigeration systems, Refrig Eng 1957; 42–46. [2] C.H. Machielsen, H.G. Kerschbaumer, Influence of frost formation and defrosting on the performance of air coolers: standards and dimensionless coefficients for the system designer, Int J Refrig 12 (3) (1989) 283–290.
[3] H. Barrow, A note on frosting of heat pump evaporator surfaces, Heat Recovery Syst 5 (3) (1985) 195–201. [4] D. Seker, H. Karatas, N. Egrican, Frost formation on fin-andtube heat exchangers. Part I-modeling of frost formation on fin-and-tube heat exchangers, Int J Refrig 27 (2004) 367–374. [5] Y. Yao, Y. Jiang, S. Deng, Z. Ma, A study on the performance of the airside heat exchanger under frosting in an air source heat pump water heater/chiller unit, Int J Heat Mass Transfer 47 (2004) 3745–3756. [6] D.T. Reindl, T.B. Jekel, J.S. Elleson, Industrial refrigeration energy efficiency guidebook, Industrial Refrigeration Consortium, University of Wisconsin—Madison, Madison, WI, 2004. [7] O.J. Nussbaum, Hot gas defrost without condensing refrigerant, Progress in refrigeration science and technology Proceedings of the XIIth International Congress of Refrigeration, vol. II 1969. p. 1265–1271. [8] S.A. Klein, F.L. Alvarado, Engineering equation solver. www.fchart.com, F-Chart Software; 2003. [9] Y. Jaluria, Natural convection, HMT, the science and applications of heat and mass transfer, vol. 5, Pergamon Press, New York, 1980. [10] A.F. Mills, Heat and mass transfer, Richard D. Irwin Inc, Homewood, IL, 1995. [11] Y.-X. Tao, R.W. Besant, K.S. Rezkallah, A mathematical model for predicting the densification and growth of frost on a flat plate, Int J Heat Mass Transfer 36 (2) (1993) 353–363. [12] N. Hoffenbecker. Investigation of alternative defrost strategies. MS Thesis. University of Wisconsin—Madison; 2004. [13] D.H. Niederer, Frosting and defrosting effects on coil heat transfer, ASHRAE Trans 82 (1) (1976) 467–473. [14] W.F. Stoecker, J.J. Lux Jr, R.J. Kooy, Energy considerations in hot-gas defrosting of industrial refrigeration coils, ASHRAE Trans 89 (2) (1983) 549–573. [15] R.A. Cole, Refrigeration loads in a freezer due to hot gas defrost and their associated costs, ASHRAE Trans 95 (2) (1989) 1149–1154. [16] G.C. Briley. Optimizing defrost systems. Process cooling and equipment; 2003.
Hot gas defrost model development and validation N. Hoffenbecker, S.A. Klein*, D.T. Reindl University of Wisconsin—Madison, 1500 Engineering Drive, Madison, WI 53706, USA Received 20 May 2004; received in revised form 25 July 2004; accepted 30 August 2004 Available online 26 January 2005
Abstract This paper describes the development, validation, and application of a transient model for predicting the heat and mass transfer effects associated with an industrial air-cooling evaporator during a hot gas defrost cycle. The inputs to the model include the space dry bulb temperature, space humidity, coil geometry, frost thickness, frost density, and hot gas inlet temperature. The model predicts the time required for a complete frost melt as well as the sensible and latent loads transferred back to the conditioned space during the defrost period. The model is validated by comparing predicted results to actual defrost cycle field measurements and to results presented in previously published studies. A unique contribution of the present model is its ability to estimate parasitic space loads generated during a defrost cycle. The parasitic energy associated with the defrost process includes thermal convection, moisture re-evaporation, and extraction of the stored energy in the coil mass following a defrost cycle. Each of these factors contribute to the parasitic load on compressors connected to the defrost return. The results from the model provide quantitative information on evaporator operation during a defrost cycle which forms the basis to improve the energy efficiency of the defrost process. q 2004 Elsevier Ltd and IIR. All rights reserved. Keywords: Air conditioning; Evaporator; Modelling; Heat transfer; Mass transfer; Cycle; Defrosting; Hot gas
De´veloppement et validation d’un mode`le pour le de´givrage a` gaz chaud Mots cle´s : Conditionnement d’air ; E´vaporateur ; Mode´lisation ; Transfert de chaleur ; Transfert de masse ; Cycle ; De´givrage ; Gaz chaud
1. Introduction Plate-finned heat exchangers are widely utilized as aircooling evaporators in industrial refrigeration systems for space conditioning and product cooling. All refrigerant-toair evaporators operating with coil surface temperatures
* Corresponding author. Tel.: C1 608 263 5626; fax: C1 608 262 8469. E-mail address: [email protected] (S.A. Klein). 0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2004.08.016
both below the freezing point of water and dew point temperature of the air within the conditioned space will lead to the formation of frost on the evaporator surface. Frost accumulation on the evaporator has several consequences. First, the accumulation of large amounts of frost will degrade heat transfer performance of the evaporator by fouling the outside surface since, the frost itself has low thermal conductivity (Stoecker [1], Machielsen and Kerschbaumer [2]). With degraded heat transfer performance, evaporator capacity decreases. To meet a specified load with degraded heat transfer performance, the evaporator
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Nomenclature mass transfer coefficient (kg/m2 s, lbm/ft2 s) Grashof number specific enthalpy (kJ/kg, Btu/lbm) convection coefficient (W/m2 K, Btu/h ft2 R) enthalpy of fusion (kJ/kg, Btu/lbm) thermal conductivity of air (W/m K, Btu/h ft R) kf frost thermal conductivity (W/m K, Btu/h ft R) ki,j thermal conductivity for node i,j (W/m K, Btu/h ft R) Lfin length of the fin (m, ft) mH2 O;s mass fraction of water vapor at the surface of the frost or liquid mH2 O;N mass fraction of water vapor in the conditioned spaces NuL Nusselt number with L as the characteristic length Q_ evap rate of heat transfer by evaporation (W, Btu/h) Qconv the sensible energy convected back to the space during a defrost cycle (kJ, Btu) Qevap the latent energy that transferred to the surroundings during a defrost cycle by reevaporation of water from the coil surfaces (kJ, Btu) Qfin and Qtube the total thermal energy stored within the fins and tubes, respectively after a defrost cycle is complete (kJ, Btu)
gm Gr h hC hig kair
temperature must decrease which decreases system efficiency. Second, the frost impedes airflow through the coil leading to increased fan energy consumption and reduced air flow through the evaporator (Stoecker [1], Barrow [3], Seker et al. [4], and Yao et al. [5]). To counter these effects, the accumulated frost must be removed from the evaporator surface on either a continuous or intermittent basis. Although defrosting can be accomplished using electric resistance heating, warm water, off-cycle (for coolers), or by the use of a liquid desiccant, hot gaseous refrigerant is the most widely used method for removing frost from evaporators in industrial refrigeration systems. During a hot gas defrost, the normal supply of cold refrigerant is stopped while a portion of the hot refrigerant vapor discharged from compressors is re-directed to the evaporator. Fig. 1 shows a direct expansion evaporator undergoing a hot gas defrost. The defrost sequence begins by closing the solenoid valve that normally admits high-pressure liquid (HPL) refrigerant to the evaporator through the thermostatic expansion valve (TXV). After a time delay that allows the remaining refrigerant in the coil to boil off, the hot gas solenoid valve is opened. High-pressure high temperature gas is supplied to the evaporator flowing first through the
Qin Qmelt
rj,in rj,out Ra Sc ShL t Ti,j TN V Dr Dx hdefrost
v rf rN
energy supplied to the coil during a defrost cycle (kJ, Btu) the amount of energy it takes for the mass of frost to reach melting temperature and change phase from ice to water (kJ, Btu) inner radius of node j (m, ft) outer radius of node j (m, ft) Rayleigh number Schmidt number Sherwood number time (s) temperature of node i,j (K, R) temperature of air in the conditioned space (K, R) volume of the ice or fin material in a node (m3, ft3) node spacing in the radial direction (m, ft) node spacing in the axial direction (m, ft) defrost efficiency defined as the ratio of the energy required to melt the accumulated frost to the total energy supplied to the evaporator coil for a defrost cycle kinematic viscosity (m2/s, ft2/s) frost density (kg/m3, lbm/ft3) density of air in the freezer (kg/m3, lbm/ft3)
drain pan to preheat it for draining the frost melt from the coil. The hot gas then leaves the drain pan heater through tubing that connects to the top of the coil through the pan check valve. As the hot gaseous refrigerant flows through the coil, it condenses thereby releasing its latent heat and warming the coil surface. As the pressure of refrigerant in the coil builds, it eventually reaches the set-point of the defrost relief regulator after which, the valve modulates the refrigerant in the evaporator back to the defrost return. The hot gas defrost is continuously supplied to the coil until a time–clock or other controls terminate the defrost sequence. The hot gas supplied to evaporators for defrost is commonly superheated with a saturation temperature well above 0 8C (32 F). In contrast, Nussbaum [7] proposed the use of a vapor-only defrost process. A vapor-only defrost utilizes a superheated vapor refrigerant but with a saturation temperature lower than the temperature of frost on the accumulated coil. The advantage being sought by Nussbaum was the avoidance of condensed liquid refrigerant management associated with a typical condensing hot gas defrost process. With
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Fig. 1. An evaporator in a hot gas defrost process, Reindl et al. [6].
ammonia, a vapor-only defrost is impractical due to the excessively high gas flow rate requirements since, in this case its extremely high heat of condensation cannot be harnessed for frost melting. The energy impacts associated with defrosting an evaporator coil depend on the temperature of the refrigerant supplied for the hot gas defrost process and the hot gas dwell time. The lower the refrigerant gas temperature supplied to the coil for defrosting, the lower the rate of sensible and latent parasitic gains to the space but the longer the time period required to achieve a complete melt of the accumulated frost. Higher refrigerant temperatures result in shorter defrost periods but higher rates of sensible and latent gains to the space. Higher refrigerant temperatures also raise the mass of the coil to higher temperatures leading to a greater parasitic cooling load on the refrigeration system following the hot gas defrost process. In either case, longer than necessary defrost dwell times will increase the parasitic load to the space. Understanding the defrost process is a pre-requisite to making the changes necessary to improve the overall efficiency of the defrost process. The principle contribution of this paper is the development of a mathematical model of the defrost process. The model provides a foundation to understand the energy impacts of the defrost process by quantifying the energy and mass flows involved in the defrost process. The model of the defrost process developed here is compared with available experimental data to validate its performance. The model is then used to investigate the effects of hot gas supply pressure and temperature, hot gas defrost dwell time period, and frost accumulation on evaporators with a goal developing process insights to improve both defrost and refrigeration system efficiency.
2. Modeling the defrost process Air-cooling evaporators used in industrial refrigeration
systems are comprised of a series of multi-row tubes with hundreds of fins pressed over the tubes to enhance heat transfer through the extended surface area. Modeling the defrost process requires consideration of both energy flows and geometry. Due to symmetry, the fin surrounding each tube resembles a hexagon which can be further approximated as a disc, or more appropriately, an annular fin as shown in Fig. 2. Since, the bulk of frost on an air-cooling evaporator adheres to the finned surfaces, heat needs to be efficiently delivered to the finned surfaces of the coil to melt the frost. During the hot gas defrost process, condensing high pressure refrigerant inside the evaporator tubes warms the tube surfaces which in turn warms the base of each individual fin in contact with the tubes. The fin conducts thermal energy from its base (the tubes) to warm the adhered frost, eventually changing its phase from a solid to a liquid. The bulk of the frost condensate then drains, by gravity, down the coil to the drain pan. Some of the frost evaporates and returns to the conditioned space. A number of important heat and mass transfer mechanisms arise during the course of a hot gas defrost process: condensation of high-pressure high temperature gaseous refrigerant inside the tubes of the coil; conduction of heat through the coil tubes and fins; sensible heating of accumulated frost; latent melting of accumulated frost; and re-evaporation of moisture from the coil surface to the surrounding space. The following description indicates how the present model incorporates these heat and mass transfer mechanisms. Fig. 3 illustrates the assumed geometric arrangement for a frosted fin and the associated two-dimensional grid for solving the energy flows during the defrost process. An annular segment of fin forms the basis of the computational domain with a line of symmetry halfway through the fin’s thickness. An adiabatic boundary condition is applied at the two lines of symmetry: outer radius of fin/frost and the centerline (right-hand side) of the fin. During the defrost
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Fig. 2. Typical tube-fin segment for a plate-fin heat exchanger (left) and simplifying circular geometry assumed to approximate the tube-fin segment (right).
process, the fin base is assumed to be at constant temperature due to condensing refrigerant inside the tubes. The boundary condition applied to the left-hand side of the computational domain is convective (heat and mass) transfer to a surrounding environment. The governing two-dimensional axi-symmetric partial differential energy equation is solved numerically using a finite difference approach implemented in the EES equation
solving program [8]. Based on the letter designations shown in Fig. 3 (A–L), there are 12 different types of nodal energy balances that can be formulated. Each nodal balance represents a typical node that has, potentially, different boundary conditions. The nodes labeled ‘J’, ‘K’, and ‘L’ all represent the finned surface and, as such, will not undergo a phase change. The remaining nodes ‘A’ through ‘I’ are nodes within the frost layer and undergo a phase change. Eq. (1)
Fig. 3. Illustration of discretization strategy for annular fin segment (left) and grid arrangement for two-dimensional finite difference solution (right).
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609
shows the nodal energy balance for a surface node type ‘D’. k1;jK1 C k1;j dh Dx T1;jK1 K T1;j 2p Z rV dt 1;j 2 ln ri C Dr =ri 2 |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} E_ st
boundary a
2 2 2 2 TN K T1;j C gm;D p rj;out mH2 O;s K mH2 O;e hig C hC p rj;out K rj;in K rj;in |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} boundary b
2 2 K rj;in T2;j K T1;j k1;jC1 C k1;j k C k1;j p rj;out Dx T1;jC1 K T1;j C 2;j 2p 2 ln ri C Dr =ri 2 2 Dx |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
C
boundary d
boundary c
The first term represents the energy stored in the node. Since, each frost control volume experiences a phase change (e.g. from ice to water), the stored energy within the control volume cannot be calculated by using temperature alone. As a result, the energy storage for a frost node is expressed in terms of enthalpy to accommodate the change in phase associated with melting the frost upon sufficient accumulation of thermal energy in the node. The terms identified as ‘boundary a’ and ‘boundary c’ correspond to the thermal conduction from the adjacent nodes at smaller and larger radii, respectively. The term identified as ‘boundary b’ represents the convective heat (first term) and mass transfer (second term) associated with the surrounding environment. The convective heat and mass transfer coefficients are estimated using correlations published by Jaluria [9] and Mills [10], respectively. Lastly, the term identified as ‘boundary d’ represents the thermal conduction between adjacent nodes at the same radial location. Energy balances for other nodes are developed in a similar fashion. The thermal conductivity of the frost is assumed to be a function of the frost density, as indicated in Eq. (2) from Tao et al. [11] where kf and rf have units of W/m K and kg/m3, respectively. kf Z 0:02422 C 7:214 !10K4 rf C 1:01797 !10K6 r2f
(2)
During the defrost process, the evaporator fans are cycled off and the thermal energy exchange from the evaporator to the surrounding environment is dominated by natural convection. A free convection relationship is used for estimating the Nusselt number and the corresponding natural convection heat transfer coefficient as indicated in Eq. (3) (Jaluria [9]). Nu L Z
hC Lfin Z 0:13ðRaÞ1=3 kair
for 109 ! Ra! 1013
(1)
(3)
In addition to the sensible energy exchange between the coil and the surrounding by natural convection, latent energy transfers occur due to mass transport from vapor pressure differences between the ice (or water) on the coil surface and the surrounding environment. The latent energy transfer rate
is proportional to the difference in vapor pressure between the exposed ice (water) surface and the surrounding environment as described by Mills [10]. This driving force for mass transfer can be expressed in terms of mass fractions of water in the air defined as the ratios of the densities of the water vapor in the air at each location divided by the total density of the humid air in each location. The densities are found by using partial pressures related to the saturated pressure at each location. The latent energy transfer rate due to evaporation is given by the following equation. 2 2 Q_ evap Z gm p rout mH2 O;s K mH2 O;N hig K rin (4) |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} boundary b
The correlation for the mass transfer coefficient, gm , expressed in terms of the Sherwood number (Eq. (5)), is given by Jaluria [9] and is shown in Eq. (6) assuming the Lewis Number is unity. Sh L Z 0:13ðGrScÞ1=3 g m Z
rNn Sh ScLfin L
for 109 ! GrSc! 1013
(5) (6)
The system of discretized equations is then solved in space while using an implicit time integration scheme to establish estimates of the nodal temperatures and heat flows as a function of time during a defrost cycle. One difficulty that arises during a simulated defrost is the effect that the phase change of frost has on the continuity of the computational domain. Rather than attempting to incorporate a methodology to accommodate the solution of a moving boundary domain, the current model approximates the effects of frost melting by assuming that the mass and volume (and thus the density) of each node is constant. When ice melts in the actual evaporator, water drains and the volume formerly occupied by water is replaced by air that has a much smaller mass. The temperature of the air in this nodal space remains relatively constant because of free convection, i.e. air in the freezer space continuously replaces the air in the nodal space. The model assumes
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that the density of the node is constant which greatly overestimates the mass-specific heat product when the node should be air. However, this overestimate of the massspecific heat product results in a relatively constant temperature for the node, similar to the effect of increased convection. This assumption greatly simplifies the model. The validity of this simplification is supported by comparisons with experimental results and with the results of other studies.
3. Frost model validation The facility that provided experimental information on defrost times was a K21 8C (K5 F) fruit product storage freezer. Additional data on the field measurements can be found in Hoffenbecker [12]. Data were collected during a period of the year when harvested fruit (cranberries) were delivered in bulk and placed in the warehouse for freezing and long-term storage. In this facility, the evaporators were defrosted after an 8 h period of accumulated liquid feed solenoid run time. Details of the field-installed evaporator are provided in Table 1. Physical observations of the coil and the warehouse conditions resulted in coil conditions as shown in Table 2 just prior to the start of a hot gas defrost sequence. The frost density was determined by estimating the volume of frost on the coil from physical measurements and photographs along with collecting the total mass of liquid water drained from the condensate drain pan during a defrost cycle. These conditions are required inputs for the model to simulate the comparative hot gas defrost process. Fig. 4 shows a series of time-lapse photographs of the coil face observed during the defrost process. The coil begins with the initial conditions noted in Table 2. After Table 1 Field-monitored evaporator specifications Imeco air-cooling evaporator specifications model: FCLS 96103.4.3 serial: 7191.1 RHI Coil volume, ft3 (m3) Coil mass, lbm (kg) Coil metal Fin metal Fin pitch, fins/in (fins/cm) No. of fins No. of rows No. tubes on face Tube wall thickness, in (mm) Tube outside diameter Total coil surface area, ft2 (m2) No. of fans Installed fan power (each), HP (kW) Total air flow rate, ft3/min (l/s) Air face velocity, ft/min (m/s)
21.4 (0.61) 9479 (4300) Galvanized steel Aluminum 3 (1.2) 800 10 18 0.060 (1.52) 1.05 (26.7) 11,119 (1033) 4 3 (2.2) 72,416 (34,177) 741 (3.76)
Table 2 Frost properties and freezer conditions used for defrost process simulation Frost properties and freezer conditions Frost density, kg/m3 (lbm/ft3) Frost blockage, % Freezer temperature, 8C (F) Coil temperature, 8C (F) Refrigerant temperature, 8C (F)
300 (18.7) 23 K15 (5) K29 (K20) 10 (50)
2 min into the defrost process, portions of the frost on the coil are beginning to melt. The highest rate of frost melt occurs in the period between 4 and 8 min into the defrost cycle. By 10 min, the coil is completely free of any accumulated frost with some residual water continuing to drain from the finned surfaces. As the hot gas dwell period continues, moisture from the coil surface completely evaporates followed by evaporation of moisture in the coil drain pan. Results from the defrost model given the conditions noted in Table 2 are shown below in Table 3. The model predicted a defrost time of 10 min and 45 s which is in good agreement with the 10 min qualitative observation of the defrosting evaporator in the field. The model predicts that a total of 271.1 MJ (257 mBtu) of energy is supplied to the coil during the 645 s defrost. Only 43.7% of the total energy input is used for melting the accumulated frost. The remaining energy results in an increased load on the refrigeration equipment. Niederer [13] predicted that only 15–25% of the total energy supplied during a typical defrost process is actually carried out by the frost condensate leaving the drain pan. Niederer evaluated a defrost process that removed 11.6 kg (25.5 lbm) of frost from a coil over a 35 min cycle. For this coil, Niederer estimated that a minimum of 4330 kJ (4105 Btu) were required to remove the condensate whereas 28,043 kJ (26,580 Btu) of heat was actually input to accomplish the 35 min defrost. The results of Niederer were compared with the results from the current model using a comparable energy input rate as reported by Niederer (a refrigerant temperature of 4 8C (39 F) and a refrigerant mass flow rate of 0.665 kg/s (88 lbm/min). After 35 min of hot gas dwell time, the present model predicted an Table 3 Coil defrost model results Imeco FCLS evaporator, frost densityZ300 kg/m3, frost blockageZ23% Variable
Value
Qin [MJ] Qconv [%] Qevap [%] Qfin [%] Qtube [%] Qmelt [%] Time, [s]
271.1 29.4 13.7 4.9 8.3 43.7 645
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611
Fig. 4. Visual observation of defrost sequence (Hoffenbecker [12]).
energy input of 28,640 kJ (27,145 Btu). The predicted quantity of energy needed to melt the frost from the coils was 3995 kJ (3786 Btu). Both results compare well with figures reported by Niederer [13]. Stoecker et al. [14] conducted both laboratory measurements of a defrosting evaporator (copper tubes with aluminum fins) using R-22 as well as a field assessment of an evaporator (steel coil with aluminum fins). A thrust of this work was to evaluate whether or not evaporators could
be defrosted with low-pressure hot gas with the intent of achieving refrigeration system efficiency improvements. In the laboratory, defrost tests were conducted using a range of hot gas pressures. The evaporator was a six row coil with 14 tubes in each row and fins spaced 0.6 cm (1⁄4 in.) apart across a 71 cm (28 in.) wide span. Table 4 shows an energy budget reported by Stoecker et al. [14] to melt 9.1 kg (20.1 lbm) of frost from the coil assuming that the condensate is heated to 7 8C (45 F) and the coil is heated to 13 8C (55 F).
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Table 4 Summary of distributed energy for a copper tube/aluminum fin coil (Stoecker et al. [14]) Item
Aluminum fins Copper tubes Warming the frost Thawing the frost Warming the water Total
Mass
Energy
[lbm]
[kg]
[Btu]
[kJ]
54.5 93.0 20.1 20.1 20.1 –
24.7 42.2 9.1 9.1 9.1 –
629 471 294 2880 260 4534
664 497 310 3038 274 4783
Stoecker et al. [14] found that the energy required to melt 9.1 kg (20.1 lbm) of frost on a coil weighing 66.9 kg (147.5 lbm) was 4783 kJ (4534 Btu). Energy was supplied to the evaporator from hot gaseous R-22 refrigerant passing though the coils at 0.136 kg/s (18 lbm/min). Stocker’s analysis uses only the heating of the coils and the warming and melting of the frost as the factors affecting the defrost efficiency. Convective and evaporative energy losses were not included. To compare the present model with the Stoecker et al. data, the present model was run using frost properties that would yield the same total mass of frost reported by Stoecker et al. [14]. By assuming a mass flow rate of R-22 consistent with that reported by Stoecker et al. the model predicted the amount of energy input during defrost and the resulting energy distribution as shown in Table 5. The results predicted by the present model show good agreement with the energy distribution reported by Stoecker et al. and reasonable agreement with the total energy input during defrost recognizing that the total energy budget estimate of Stoecker et al. did not include convective losses from the coil.
4. Results With confidence that the defrost model is providing reasonable results in predicting the behavior of an evaporator during a defrost sequence, we now are able to use the model to investigate factors that influence the defrost performance and efficiency. The rate of energy supplied to the evaporator during a defrost cycle, Q_ in , is the rate of heat input to the coil resulting from condensation of refrigerant
Ratio [%]
13.9% 10.4% 6.5% 63.5% 5.7% –
vapor during the defrost process. Q_ in , varies with time as shown in Fig. 5. The energy rate is calculated in the model as the rate at which energy is conducted into the base of the fin from the hot refrigerant through the refrigerant pipe. As one would expect, the initial rate of energy input to the coil is high and the rate decreases as the coil, fins, and frost absorb heat and warm in temperature reducing the driving force for heat transfer. As the defrosting process progresses, the fin and frost surfaces increase in temperature thereby, increasing the rate of energy convection to the surrounding freezer environment. Fig. 6 shows the integrated amount of energy convected back to the space for a coil with an initial frost density of 150 kg/m3 (9.36 lbm/ft3) and varying initial frost blockages as a function of the entering hot gas temperature. Interestingly, the total convected heat to the space increases with increasing frost mass, expressed as % blockage. This increase is attributable to the fact that the defrost dwell time increases with increasing frost. Increased defrost dwell time leads to increased space convective loads. Fig. 7 shows the latent energy losses to the surrounding controlled temperature space due to the re-evaporation of water from the coil surface during a defrost cycle. The rate of evaporation depends of the vapor pressure difference between the surface of the ice and the freezer space. The vapor pressure of the ice is a strong function of its temperature. Although the rate of latent energy loss due to evaporation is greater with increased refrigerant temperatures, the integrated latent energy loss from evaporation is less due to the shorter defrosting times experienced at elevated temperatures for a fixed frost mass (expressed as the % blockage).
Table 5 Frosted fin model using a mass flow rate of refrigerant Item
Aluminum fins Copper tubes Frost Frost Frost Frost/Metal
Variable
Qfin Qtube Qmelt Qevap Qconv Qin
Mass
Energy
[lbm]
[kg]
[Btu]
[kJ]
54.5 93.0 20.1 20.1 20.1 167.6
24.7 42.2 9.1 9.1 9.1 76
825.7 540.6 3376.2 398.3 1061.3 6203.0
871.7 570.3 3561.9 420.2 1119.7 6544.2
Ratio [%]
13.4% 8.8% 54.8% 6.5% 17.2% –
N. Hoffenbecker et al. / International Journal of Refrigeration 28 (2005) 605–615
Fig. 5. Rate of supplied energy to the coil during defrost.
613
Fig. 7. Integrated latent energy loss during a hot gas defrost cycle as a function of entering hot gas temperature.
Fig. 8 shows the quantity of stored energy in the coil mass (fins and tubes) just after a defrost process terminates. The model assumes that the tubes are entirely heated to the hot gas inlet temperature; however, the fins will have a temperature distribution as determined by the finite difference model. For reference, the defrost times are shown with dotted lines in the figure. The total quantity of energy supplied during a defrost cycle Qin, represents the integral of the energy supply rate, Q_ in , over the entire defrosting period. This energy quantity represents the total amount of energy supplied for defrost, including the losses associated with the stored and released energy. Fig. 9 shows the total energy supplied during defrost along with the time required to fully melt accumulated frost fin are plotted over a range of entering hot gas refrigerant temperatures with frost densities ranging between 150 and 450 kg/m3 (9.36–28.1 lbm/ft3) as a parameter and an initial frost blockage of 20%. As expected, the time to defrost decreases as the hot gas supply temperature increases. However, higher hot gas supply temperatures lead to a higher rate of sensible and latent heat transfer to the surrounding freezer. In addition,
the higher hot gas temperatures lead to a greater elevation in coil mass temperature above the melting point of water resulting in a larger energy penalty when the defrost cycle is terminated. The parasitic effects of increasing the hot gas temperature along with the decreasing hot gas dwell time lead to competing factors that result in an optimum (from an energy viewpoint) hot gas inlet temperature. The optimum (minimum) integrated defrost energy input is a function of frost density as shown in Fig. 9. The optimum hot gas temperature for a frost density of 150 kg/m3 (9.26 lbm ft3) is 18 8C (65 F) or just over 689 kPa (100 psig) with ammonia. Previous studies have focused on achieving defrost with lower hot gas temperatures with the goal of reducing the parasitic load on the space during defrost (Stoecker et al. [14], Cole [15], and Briley [16]). The assumption is that with lower hot gas temperatures, the difference in temperature between the coil and surrounding space will be lower thereby, decreasing the rate of convective heat loss from the coil. In addition, lower hot gas pressures result when systems are run at lower head pressures to improve
Fig. 6. Total convected energy released during defrost as a function of entering hot gas temperature.
Fig. 8. Stored energy in total evaporator fin surface after the defrost cycle terminates and defrost time as a function of entering hot gas temperature.
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Fig. 9. Total supplied energy and defrost time for a defrost cycle at 20% frost blockage as a function of entering hot gas temperature for a freezer temperature of K23 8C (K10 F).
compressor efficiency. The current results seem to contradict the former premise of defrost efficiency improvement. Consider the defrost data reported by Stoecker et al. [14] shown in Table 6 below. For a given hot gas saturation temperature, the reported data includes the defrost condensate mass, defrost time, and average gas mass flow rate at a point in time where 80% of the condensate has melted. Although not reported by Stoecker et al., we calculated the total hot gas load (the last column) using data presented in the paper. The total hot gas load is simply the product of the average hot gas mass flow rate, defrost time, and the enthalpy of vaporization for R-22 at the given hot gas saturation temperature. This additional result illustrates a key point related to the present study. That is, although lower hot gas saturation temperatures can feasibly melt accumulated frost, the longer defrost dwell time required to melt the frost results in a greater integrated load. Unfortunately, the hot gas defrost results given by Stoecker et al. [14], were not run at higher temperatures to determine whether or not a minimum hot gas load exists. The defrost efficiency is defined as the amount of energy required to melt the accumulated frost with respect to the total energy supplied to the evaporator coil for a defrost cycle. The defrost efficiency definition is consistent with that used by Cole [15]. A plot of the defrost efficiency for a frost density of 150 kg/m3 (9.26 lbm ft3) and frost blockages ranging from 10 to 30% is shown in Fig. 10. At lower refrigerant temperatures, the defrost efficiency
Fig. 10. Defrost efficiency and defrost time as a function of entering hot gas temperature.
is heavily dependent on the time required to melt accumulated frost. Referring to the refrigerant of 10 8C (50 F), at 10% frost blockage the defrost efficiency is approximately 0.3 because, with such little accumulated frost, most of the supplied energy goes into heating the evaporator coils. At 20% frost blockage the efficiency increases to 0.38 because the amount of energy needed to melt the frost is higher than the energy stored in the coils. Also, the frost melts in a timely manner making the convective and evaporative losses less of an issue. As frost blockage increases to 30%, the efficiency for defrost decreases once again to 0.32 because the long period of time to complete the defrost cycle allows for greater convective and evaporative losses. The penalty for operating a defrost cycle on fixed dwell time can be significant. A model of the coil with completely dry finned surfaces is used as a basis for comparison to estimate the energy penalties associated with excess hot gas defrost. The excess time for a specified clock-driven defrost dwell time is found by subtracting the specified clock-driven defrost dwell period from the defrost dwell time estimated by the model. Table 7 shows the defrost efficiency for defrost cycles of differing lengths at different refrigerant inlet temperatures. The time required for frost to completely melt is shown in the first row of the table. Continued supply of hot gas beyond this required melting period necessarily lowers the defrost efficiency. As expected, the defrost efficiency decreases as the hot gas temperature increases and as the defrost dwell time increases.
Table 6 Excerpt of hot gas defrost results reported by Stoecker et al. [14] as well as calculated hot gas load Hot gas saturation temperature, F [8C]
Defrost mass, lbm, [kg]
Defrost timea, min
Average gas flow rate, lbm/s [kg/s]
Hot gas load, Btu [kJ]
36 [2] 43 [6] 52 [11]
21.8 [9.9] 13.6 [6.2] 23.2 (10.5)
6.0 5.9 7.0
0.36 [0.163] 0.35 [0.159] 0.24 [0.109]
11,320 [11,944] 10,650 [11,236] 8,478 [8,944]
a
Condensate collected when the defrost process was 80% complete.
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Table 7 Defrost efficiency for a set hot gas supply of 45 min for a frost density of 150 [kg/m3] and frost blockage of 20% Time Melt time 5 min 10 min 15 min 20 min 25 min 30 min 35 min 40 min 45 min
Frost densityZ150 [kg/m3], Frost blockageZ20% 37.7 8C 100 F
32.2 8C 90 F
26.7 8C 80 F
21.1 8C 70 F
15.6 8C 60 F
10 8C 50 F
48.5 s 18.4% 12.9% 9.9% 8.0% 6.8% 5.8% 5.1% 4.6% 4.1%
56.2 s 20.2% 14.3% 11.0% 9.0% 7.6% 6.6% 5.8% 5.2% 4.7%
1 min 8.2 s 22.3% 15.9% 12.4% 10.2% 8.6% 7.5% 6.6% 5.9% 5.3%
1 min 27.3 s 24.8% 18.0% 14.1% 43.4% 9.9% 8.6% 7.6% 6.8% 6.2%
2 min 5.9 s 27.7% 20.5% 16.3% 13.5% 11.5% 10.1% 8.9% 8.0% 7.3%
4 min 8.6 s 30.8% 23.4% 18.9% 15.8% 13.6% 12.0% 10.7% 9.6% 8.8%
5. Conclusions A mathematical model for a frosted coil was developed to determine the energy requires for defrosting an evaporator. The frosted coil model is scaled-up based on simulation of the defrost process for a single fin surface. When supplied with the specific geometry and operating conditions, the frosted fin model provided defrost time estimates that compared quite well with the time to melt the accumulated frost that observed at a local cold storage warehouse facility. The model developed also compared well with defrost energy use reported in the literature. Results from a parametric analysis using the present model showed an optimum hot gas temperature that is a function of both the accumulated mass and density of frost on an evaporator. An interesting result was that the model predicted the mass of moisture re-evaporated back to the space increases with decreasing hot gas temperature. This behavior is due to the prolonged defrost dwell time to achieve a full melt of accumulated frost. The results of this model suggest that parasitic energy impacts associated with the defrost process can be minimized by limiting defrost dwell times.
Acknowledgements The financial support from the Energy Center Wisconsin is gratefully acknowledged.
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