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An improved method for analyzing a fin and tube evaporator containing a zeotropic mixture refrigerant with air mal-distribution
International Journal of Refrigeration 26 (2003) 707–720 www.elsevier.com/locate/ijrefrig
An improved method for analyzing a fin and tube evaporator containing a zeotropic mixture refrigerant with air mal-distribution Jangho Lee, Young-Chul Kwon1, Moo Hwan Kim* Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, 790-784, South Korea Received 13 October 2001; received in revised form 17 October 2002; accepted 12 December 2002
Abstract A new program was developed to analyze the heat transfer characteristics of fin and tube evaporators that use a zeotropic mixture refrigerant, R-407C, as the working fluid. The calculation algorithm is based on EVSIM (NIST), but a tube is segmented into several sections to provide a base unit for the calculations in this study. Therefore, twodimensional air mal-distribution in the tube-length (horizontal) and vertical directions of the evaporator can be considered. The temperature gradient in the flow direction is traced using a discrete pattern to simulate the continuous variation found in actual evaporators. To validate the simulation results, 45 test cases in a real evaporator were performed with two different refrigerant flow path configurations using R-22 and R-407C refrigerants. The deviation between the simulations and test data was a maximum of 5.4%, and the trends were similar. The local heat transfer predictions were verified by comparing the numerical and test wall temperatures along the refrigerant flow path. Local temperature difference and the heat transfer contributions from each row are also analyzed along refrigerant flow path. And more, the impact of air mal-distribution is studied with two-dimensional four different types of velocity profiles and the significant difference in heat transfer is analyzed. The program developed in this study will be a useful tool to know all of information related with heat and mass transfer at any local point and can be used for improving the efficiency of zeotropic mixture refrigerant evaporators. # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Heat transfer; Modelling; Finned tube; Evaporator; Refrigerant; Zeotropic mixture; Air; Distribution
Me´thode ame´liore´e utilise´e afin d’analyser le fonctionnement d’un e´vaporateur a` tubes a` ailettes utilisant un me´lange ze´otrope et caracte´rise´ par une mauvaise distribution d’air Mots cle´s : Transfert de chaleur ; Mode´lisation ; Tube ailete´ ; E´vaporateur ; Frigorige`ne ; Me´lange Ze´otrope ; Air ; Distribution
* Corresponding author. Tel.: +82-54-279-2165; fax: +82-54-279-3199. E-mail address: [email protected] (M.H. Kim). 1 Present address: Division of Mechanical and Control Engineering, Sun Moon University, #100 Kalsanri, Tangjeong Myeon, Asansi, Chung-Nam, 336-840, South Korea. 0140-7007/03/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/S0140-7007(03)00023-9
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Nomenclature A C D h i k Le m P Q t T u U V X W
Area (m2) Constant, heat capacity (W/kg/K) Diameter (m) Heat transfer coefficient (W/m2/K) Enthalpy (w/kg) Thermal conductivity (W/m/K) Lewis number Mass flow rate (kg/h) Pressure (Pa) Heat transfer rate (w) Thickness (m) Temperature Velocity (m/s) Overall heat transfer coefficient (W/m2/ K) Volumetric flow (m3/s) Quality Absolute humidity (kg/kg)
Subscripts a Air avg Average b Boiling point (saturated liquid in zeotropic mixture) c Contact, corresponding contact area d Dew point (saturated liquid in zeotropic mixture) db Dry bulb eq Equivalent f Fin, saturated liquid phase g Gas phase or saturated vapor i Inner in Inlet l Liquid phase m Mean mix Multi-component zeotropic mixture refrigerant n Nozzle o Outer out Outlet p Pipe, tube pure Single component pure refrigerant r Refrigerant w Tube wall, water wb Wet bulb
1. Introduction In recent years, heat exchanger research has focused on alternative refrigerants since the Montreal Protocol banned the use of halogenated refrigerants (CFC’s and
HCFC’s). One of the more promising alternative refrigerants is the ternary mixture R-407C, which is composed of HFC-32/125/134a, 23/25/52 wt. percentage. The use of a zeotropic mixture refrigerant provides an additional degree of freedom in the composition variation that is not present in single component refrigerants. A change in the saturation temperature during the evaporation and condensation processes at a constant pressure is known to have important effects on the heat exchanger design. The three main parameters used to estimate the heat transfer rate from air to a refrigerant in an evaporator are: the heat transfer coefficient, the heat transfer area, and the temperature difference between the air and refrigerant sides. These parameters can be complicated in a multi-pass evaporator with a zeotropic mixture refrigerant. The heat transfer coefficient can vary locally due to mal-distribution of the air velocity and phase change on the refrigerant side. The temperature gliding due to phase changes in the refrigerant mixture components changes the temperature difference between the air and the refrigerant sides. Furthermore, it is difficult to define the heat transfer area because the evaporator has fin slits and micro-fins inside the tubes; many researchers have neglected the area change due to slits in their experimental correlations. In general, two possible approaches can be used to estimate the heat transfer rate of heat exchangers: a lumped analysis scheme, in which the heat exchanger is analyzed as a single unit with two inlets and outlets on both the cold and hot sides; and a local analysis scheme, in which the heat exchanger is divided into segments or multiple control volumes. In the latter approach, the local variation of the heat transfer conditions can be considered more exactly. Fagan [1] studied the effects of a one-dimensional mal-distribution of the air flow. He showed that the mal-distribution of air affected the heat transfer rate. The capacity degradation was as much as 20% in the worst case. Chwalowski et al. [2] predicted the performance of evaporators using four different methods, and compared their results with test data. They showed that simulated or imposed air velocity profiles must follow the actual air distribution across the coil for successful capacity prediction of a coil. In their laboratory tests, the capacity degradation was up to 30% for mal-distributed air velocity profiles. Domanski [3] developed a program, EVSIM, to analyze an evaporator with a multi-pass refrigerant distribution and one-dimensional air distribution. He showed that the program modeled the one-dimensional air mal-distribution due to the installation angle of the evaporator to the flow direction in a duct. One tube was used as a local analysis unit in his work. Since his model only considers one-dimensional air flow distributions, the effects of the distribution in the tube length direction could not be analyzed.
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In addition, if a zeotropic mixture refrigerant is used, a simple "-NTU relation shown in Eq. (1) is not longer valid because of the temperature variations of refrigerant along the tube length by quality change and pressure drop. We developed the section-by-section scheme for the analysis of evaporator as for the analysis of condensers [4]. One tube is segmented into small sections of equal length. One section is adopted as the local analysis unit, and calculations are performed on this section. The calculation in the section is based on EVSIM (NIST) [3]. The temperature of the zeotropic mixture refrigerant is assumed constant over each small section. Different air velocities can be assigned for each section. The temperature of mixture refrigerant in the next section is calculated using the saturation pressure subtracting the pressure drop from the pressure of the present section. Thus, the temperature variation of the zeotropic mixture refrigerant can be traced along the flow path with a step-by-step pattern as shown in Fig. 1. The larger the width to height ratio of the evaporator, the more effective the section-by-section approach will be.
2. Model and correlations 2.1. Section-by-section scheme One section in the tube (segmented along the refrigerant flow direction) is used as the local heat transfer area to account for the two-dimensional mal-distribution of air and the temperature gliding of the zeotropic refrigerant mixture, R-407C. This is illustrated in Fig. 2 for a 2-row, 6-column evaporator, in which 12 tubes make one refrigerant flow path. Each tube is divided into 4 sections, which gives a total of 48 sections along the refrigerant flow path in this illustration. The heat transfer is calculated for each section. The calculation
Fig. 1. Concept diagram of temperature gliding using a section-by-section scheme along the refrigerant path.
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procedure is similar to that of the tube-by-tube model, EVSIM [3]. Several assumptions are employed to simplify the calculations. First, steady state conditions are assumed in the air and refrigerant sides. The heat transfer to adjacent sections in the tube-length direction is neglected because the temperature difference is relatively small. The velocity profile entering the first row of the air side is assumed to be same as that of the last row of the evaporator. The heat transfer in the return bend is neglected; only the pressure drop is considered because there is no air flow through the return bend in test and field applications. For the first iteration, the initial inlet temperature and velocity profile on the air side are assigned to all sections in all rows for convenience. The flow rate, inlet pressure, and quality on the refrigerant side are provided as input conditions. The calculation proceeds from the inlet to the outlet of the refrigerant side along the refrigerant flow path, as shown in Fig. 2. In each section, the heat transfer rate is calculated using the effectiveness and the temperature difference between the air and refrigerant sides. The temperature of the refrigerant in a section is assumed constant because the amount of temperature gliding is small compared to the temperature variation during the phase change of the zeotropic mixture refrigerant. Therefore, a simple "-NTU relation can be applied to a section in the phase change region: " ¼ 1 eNTU
ð1Þ
The pressure drop across a present section is determined and used to calculate the inlet pressure for the next section by subtracting the pressure drop from the pressure of present section. The refrigerant temperature in the next section is calculated using the corrected pressure with quality. This allows the temperature gliding to be traced step-by-step along the refrigerant path. Once the heat transfer calculations for a section are completed, the refrigerant quality leaving the section and the downstream temperature of air passing through the section can be determined. The quality will be used for the refrigerant inlet condition of the next section and the downstream temperature will be the air inlet condition of the next row, respectively. The temperature differences between the initially-assigned and updated values are examined for all sections. The calculations are iterated until the differences are less than a specified criterion. If the criterion is not satisfied after a given number of iterations, the outlet enthalpy of the refrigerant is compared with the value from the previous iteration until the change is small enough to satisfy a second criterion. The logic flow of the simulation program is shown in Fig. 3: the position indices i, j, and k are the section, tube, and path indices, respectively. A direction flag is assigned to simulate the direction of refrigerant flow as the calculation proceeds through the sections. This is used
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Fig. 2. Section-by-section scheme for evaporator analysis.
as a direction vector in Fig. 3: the section index increases from right to left in row 1, and decreases from left to right in row 2 in Fig. 2. 2.2. Heat and mass transfer calculation [5] The "-NTU equation with the inlet temperature difference between the air and refrigerant sides is used to calculate the heat transfer rate for each section. Several types of "-NTU relations may be used to obtain " [6]: once it is determined, the heat transfer rate from the air to the refrigerant can be obtained using Eq. (3). UA " f NTU ¼ ð2Þ Cpa ma Qair ¼ ma Cpa ðTai Tri Þ"
ð3Þ
The overall heat transfer coefficient, U, for a section in a wetted finned tube is calculated from the sum of the individual resistances to heat transfer as follows: 0 1 Ao A o tp 1 Ao þ þ þ B hi Api Apm Kp hl Apo hc C B C C 1 U¼B ð4Þ Bþ C @ A Af ð1 ’ f Þ ho ð1 þ Þ 1 Ao ¼
ilgw ð!a !w Þ Cpa ðTa Tw Þ
ð5Þ
The first and fifth terms of Eq. (4) refer to the inside and outside heat transfer resistances, respectively. The second term represents the conductive heat transfer resistance through the tube wall and the third term accounts for the conduction resistance through the condensed water layer on the fin and tube. The fourth term represents the contact resistance between the outside tube surface and the fin collar. Eq. (4) gives the additional heat transfer due to the condensation of water vapor from the air to the surface of the fins and tubes. The overall heat transfer coefficient, U, for a non-wetted finned tube can be obtained using Eq. (4) with 1/hl 0, a 0. Once the heat transfer rate from air to refrigerant is calculated, the air, tube wall, and fin surface temperatures are calculated directly using the heat transfer resistance. The humidity at saturation on both the wall and fin is calculated from the fin surface and wall temperatures. The mass transfer from the air to the tube and fin is determined from Eq. (6) [5]: ha Apo ! ¼ ð!ai !w Þ 1 exp LeCpa ma ha Af ð6Þ þ ð!ai !fm Þ 1 exp LeCpa ma The first term in Eq. (6) is the mass transfer from the air to the tube wall, and the second term is the mass transfer to the fin surface. Once the mass transfer is known, the outlet humidity and temperature of the air side at a given section are obtained from Eqs. (7) and (8).
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2.3. Correlations and flow distribution The code uses a complete set of correlations for the heat transfer and pressure drop in both the refrigerant and air sides. They are summarized in Table 1. Gray and Webb’s [7] correlation for flat fins is used to calculate the heat transfer coefficient for the outside (or air side). The enhancement factor is multiplied for the louvered fin [8]. Schmidt’s method is used to calculate the fin efficiency [9]. Gungor and Winterton’s [10] correlation is used to determine the refrigerant side heat transfer coefficient in the phase change region of a smooth tube. Their correlation is modified to compensate for the temperature variation of the zeotropic mixture refrigerant as shown in Eqs. (9) and (10) [11]; these give the heat transfer coefficient for a pure refrigerant when the quality is 1. hmix ¼
hpure
; hpure Teq Td 1þ q
Teq ¼ Td ð1 xÞðTd Tb Þ
Fig. 3. Logic flow chart for the section-by-section calculations.
!ao ¼ !ai !
ð7Þ
Qair ifgw ! þ ð8Þ Cpa ma Cpa The humidity and temperature are then used as input for the next section in the next row of the evaporator. Tao ¼ Tai
ð9Þ
ð10Þ
The heat transfer coefficient for the mist flow region is calculated using linear interpolation between the coefficients at quality 0.8 and the single vapor phase at quality 1.0. The heat transfer coefficient for an internally finned (rifled or grooved) tube is calculated by multiplying by the enhancement factor of Schlager et al. [12]. The in-tube pressure drop is due to friction, momentum change, and gravity. The gravity term was neglected. Pierre’s correlation [13] was used to calculate the pressure drop through a smooth tube in the phase-change region, and Petukhov’s Eq. [14] was employed to determine the friction factor for a smooth tube with turbulent single-phase flow. An enhancement factor is used for the internally finned tube [15]. Ito’s correlation [16] for the single-phase region and Geary’s correlation [17] for the phase change region are used for the U-bend pressure drop calculations.
Table 1 List of correlations used in this study Items
Applying zone
Correlations
Heat transfer coefficient
Air-side Single phase region in refrigerant side Phase change region in refrigerant side Enhanced factor for grooved tube Single phase region in refrigerant side Phase change region in refrigerant side Return bend in phase change region Return bend in single phase region Enhanced factor for grooved tube
Gray and Webb [6,7] Dittus-Boelter [5] Gungor & Winterton [9]; Ebisu and Torikoshi [10] Schlager [11] Petukhov [13] Pierre [12] Geary [16] Ito [15] Schlager [14]
Pressure drop
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Fig. 4. Schematic diagram for the refrigerant flow distribution; (a) equal pressure drop across each multi-pass path, (b) equal mass flow in each multi-pass path.
Refrigerant flows in an evaporator with multi-pass circuits [shown in Fig. 4(a)] will have the same pressure drop across each flow circuit [3,5]. However, the same refrigerant flow can be assigned to each pass circuit of an evaporator when a capillary tube is connected directly to the refrigerant flow inlet [see Fig. 4(b)]. In this case, the pressure drop across the capillary tube will be about 20 times greater than the in-tube pressure drop across the flow path from the distributor to the junction tube at the outlet of the evaporator. Therefore, the individual pressure drops across each flow path of the evaporator need not be considered; the pressure drop will be the same across all circuits of the evaporator. The properties of air are based on ASHRAE Handbook data [18]. The refrigerant properties are based on REFPROP [19] from NIST.
3. Model verification 3.1. Refrigerant supply loop The refrigerant loop consists of a compressor, an oil separator, a shell and tube type condenser, a receiver, a flow meter, capillary tubes, an evaporator, and an accumulator, as shown in Fig. 5. Discharged oil and refrigerant from the compressor passes through the oil separator, and only high pressure and temperature refrigerant flows into the shell and tube condenser. The cooling water loops consist of a constant water bath, a pump, a by-pass loop, and a motor driven micro-valve.
These are used to control the sub-cooling of the refrigerant at the inlet of the distributor. A mass flow meter measures the mass flow rate of the refrigerant liquid. A receiver and sight glass are used to reserve and check the liquid refrigerant. The supplementary temperature control loop controls the refrigerant temperature at the distributor inlet. The temperature and pressure are measured at the distributor inlet to determine the amount of sub-cooling and the properties of the refrigerant. The temperature is measured using a Pt 100 RTD inserted through the copper tube wall. The pressure is detected by a digital pressure gauge with a range of 0–5 MPa. The thermodynamic quality at the inlet of test evaporator is calculated, including the amount of sub-cooling and assuming an adiabatic process in the capillary tubes. After the test section, the refrigerant is returned to the compressor through a supplementary heater and an accumulator. The refrigerant temperature and pressure are measured at the outlet of the evaporator in the same manner as at the inlet of distributor, except that the digital pressure gauge has a range of 0–1.5 MPa. 3.2. Air flow measurement system A volumetric flow rate measurement system for humid air based on the ANSI/ASHRAE 41.2-1987 [20] was designed. It was installed in a constant temperature and humidity room, as shown in Fig. 6. The system consists of five nozzles, a fan, a motor, and an air-sampling unit. The air-sampling unit in the system is not
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
shown in Fig. 6, but it is similar to that shown in front of the evaporator. Two Pt 100 RTD sensors are positioned in the air-sampling unit to measure the dry and wet bulb temperatures of the humid air leaving the evaporator,
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which are then used to calculate the outlet air enthalpy. The volumetric flow rate of air, Va, is obtained from pffiffiffiffiffiffiffiffiffiffi ð11Þ Va ¼ C Pn ;
Fig. 5. Schematic diagram of the refrigerant supply system.
Fig. 6. Schematic diagram of the heat exchanger test facility.
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where Pn is the pressure drop across the nozzles. The flow coefficient and area of the nozzles are included in C. Since the test conditions of the air side remain unchanged in all test cases, C is approximately constant. The other air-sampling unit is installed in front of the evaporator as shown in Fig. 6. The inlet air enthalpy is calculated using the dry and wet bulb temperature in the air-sampling unit. The same procedure is used to calculate the inlet air enthalpy. The room temperature and humidity are controlled according to the inlet dry and wet bulb temperatures. 3.3. Test evaporators and data reduction The path configurations of the test evaporator are shown in Fig. 7. They are the same as those found in a 3-hp commercial air-conditioner. The evaporator (508 mm high, 57.15 mm row depth, and 410 mm tube length) is installed in an upright position, perpendicular to the flow direction, and has slit-louvered fins on the air side and micro-fin tubes on the refrigerant side. The geometry consists of 3 rows and 20 columns, with 16 fins per inch. The step pitch is 25.4 mm, the row pitch is 19.05 mm, and the outside diameter of the tube is 9.52 mm. The path of the evaporator is categorized by the flow direction of the refrigerant and air; the parallel-
cross flow path is shown in Fig. 7(a) and the countercross flow path is shown in Fig. 7(b). The evaporator has five paths. The second and fourth paths shown in Fig. 7 each contain 14 tubes. The first path is 17% shorter (10 tubes), and the last path is 17% longer (14 tubes). The heat transfer rate from the air side is calculated using the measured temperatures and velocities:
Qa ¼ a Va ia;in ia;out ;
ð12Þ
where a is the density and ia is the enthalpy of humid air. The volumetric flow rate of air, Va, is kept constant at 18.0 m3/min in all test cases, which corresponds to a front velocity of 1.44 m/s. The dry and wet bulb temperatures are set at 27 and 19.5 C, respectively, in all test cases. The heat transfer rate to the refrigerant side was calculated by multiplying the mass flow rate by the change of enthalpy:
Qr ¼ mr ir;out ir;in ;
ð13Þ
where mr is the mass flow rate of the refrigerant measured by the mass flow meter using the Coriolis force principal. The enthalpy change in the refrigerant side is calculated by measuring the pressure and
Fig. 7. Test evaporators and their path configurations according to the direction of the air and refrigerant flows: totally, five passes are included in each evaporator.
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J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720 Table 2 Conditions and results for the tests and simulations (va=1.44 m/s) No.
Ref. & path
Gr,in (kg/h)
Pr,outlet (kPa)
Xr,in
QTEST (W)
Qsim (W)
Q (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
R-22 parallel-cross flow type path
181.7 182.7 181.8 183.1 179.2 180.1 179.8 180.5 172.3 180.1 187.1 182.5 182.6 183.2 183.3 183.0 181.2 179.7 180.1 180.4 180.2 180.1 165.4 170.0 174.7 185.1 183.6 182.0 182.0 183.8 182.5 182.8 181.6 160.0 164.7 169.4 176.0 178.7 184.4 189.6 180.4 178.6 180.0 179.3 179.4
417.8 423.6 417.8 422.7 400.1 426.6 458.0 481.5 429.5 426.6 426.6 492.3 494.3 496.2 493.3 493.3 489.3 445.2 464.8 494.3 516.8 534.5 490.3 490.3 489.3 490.3 491.3 495.2 498.2 488.4 494.3 493.3 489.3 496.2 495.2 495.2 496.2 495.2 495.2 495.2 444.2 466.8 491.3 512.9 538.4
0.20 0.22 0.24 0.25 0.24 0.23 0.23 0.23 0.23 0.23 0.23 0.22 0.23 0.24 0.26 0.27 0.28 0.26 0.25 0.24 0.24 0.23 0.25 0.25 0.25 0.25 0.20 0.21 0.22 0.24 0.25 0.26 0.27 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.25 0.25 0.24 0.23
8090 7869 7861 7761 7906 7803 7657 7661 7600 7803 8204 8496 8408 8329 8183 8089 7960 7925 7969 7973 7879 7578 7369 7576 7801 8237 8970 8784 8670 8634 8484 8450 8283 7512 7754 7976 8202 8273 8550 8760 8414 8297 8325 8235 8185
8194 8010 7889 7742 7798 7805 7725 7499 7511 7829 8129 8136 8103 7946 7936 7849 7740 8108 8117 7963 7537 7212 7446 7612 7789 8075 9354 9254 9055 8969 8868 8767 8670 7687 7891 8092 8353 8457 8672 8849 8634 8592 8510 8320 8217
1.29 1.79 0.36 0.24 1.37 0.03 0.88 2.11 1.18 0.34 0.91 4.23 3.64 4.61 3.02 2.96 2.77 2.32 1.85 0.12 4.34 4.83 1.03 0.48 0.16 1.97 4.28 5.36 4.44 3.88 4.53 3.75 4.67 2.34 1.76 1.45 1.84 2.23 1.43 1.02 2.61 3.55 2.22 1.03 0.39
R-407C parallel-cross flow type path
R-407C counter-cross flow type path
temperature. The enthalpy calculated at the inlet of the distributor in Fig. 4(b) is used as the inlet enthalpy for the evaporator, assuming an adiabatic process in the capillary tubes. The outlet enthalpy of the evaporator is determined at the outlet of the junction tube in Fig. 4(b). The difference between the heat removal from the air and the heat gain of the
refrigerant is within 3.0%. The refrigerant side heat transfer rate is higher than that on the out (air) side because of the heat gain from the ambient air. The air side heat transfer rate is used as validation data. All test conditions are listed in Table 2. Inlet conditions (temperature, humidity, velocity) for the air side are kept constant; only the inlet conditions for the refrigerant
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4. Results 4.1. Verification of capacity prediction
side (refrigerant flow rate, evaporation pressure, and input quality) are changed in the validation tests. The uncertainties in the heat transfer rate measurements for the air and refrigerant sides are surveyed and the maximum is within about 3.0% as shown in the Appendix.
Simulations and experiments were performed for the 45 cases shown in Table 2. In the simulations, the inlet pressure of the refrigerant side of the evaporator was modified iteratively to match the outlet pressure obtained in the validation tests. The heat transfer differences between the test and simulation results are within 5.4%, as shown in Table 2 and Fig. 8. The deviation between simulations and test results are evenly distributed in the vicinity of zero line except a countercross flow type evaporator with R-407C, as shown in Fig. 9. The simulation overestimates the counter-cross path evaporator with R-407C by 2.8% on average. The simulation results matched the experimental trends (see Figs. 9–12). The heat transfer rate increases with the refrigerant mass flow rate in Fig. 10, but decreases with increasing inlet quality in Fig. 11. The heat transfer rate as a function of the evaporating pressure at the outlet is shown in Fig. 12. The heat transfer rate decreases as the evaporating pressure increases; the temperature differ-
Fig. 9. Deviations of the simulations from the validation tests.
Fig. 11. Simulation and test results for the refrigerant mass flow rate.
Fig. 10. Simulation and test results for evaporator inlet quality.
Fig. 12. Simulated and measured capacity as a function of evaporator outlet pressure.
Fig. 8. Comparison of the heat transfer rates for the simulations and validation tests.
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Fig. 13. Simulation and test results for the wall temperature along the fifth pass of the refrigerant (shown in Fig. 7): R-407C, Ta,db=27 C, Ta,wb=19.5 C, Teq=5.5 C, Xin=0.21, mr=182 kg/h.
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Measured and simulated wall temperatures are shown in Fig. 13. In the test, the wall temperature was measured on the middle of the U-bend in the evaporator. The length ratio in Fig. 13 is defined as the distance from the inlet divided by the total length of the fifth pass. The values and trends of the wall temperatures were well simulated by the numerical calculations as shown in Fig. 13. Other local characteristics are shown in Fig. 14, the local heat transfer rates, and in Fig. 16, the local temperature differences. The aggregated heat transfer rate from the first to the last sections is shown in Fig. 14 by summing the values along the refrigerant flow path for the fifth pass. The heat transfer rate is given at every 4 sections; 4 sections correspond to 1 tube. The ratio of heat transfer rate in each row is shown in Fig. 15. The heat transfers to the third row in the parallel cross flow type evaporator and to the first row in the counter-cross flow type are relatively small compared to other rows in each evaporator. The heat transfer rate in the countercross flow type path with R-407C increased continuously
Fig. 15. Ratio of simulated heat transfer rate at each row. Fig. 14. Simulated heat transfer rate along the refrigerant flow path.
ence between the air and refrigerant sides decreases with increasing evaporating pressure. 4.2. Analysis of local characteristics The local heat transfer characteristics for different path types with R-407C and R-22 refrigerant are shown from Fig. 13–16. The longest pass shown in Fig. 7 (the fifth pass) was selected to validate the simulation using the local heat transfer rate. The tests and simulations conditions are a refrigerant flow of 182 kg/h, an inlet quality of 0.21, and an equivalent evaporating temperature of 5.5 C. The equivalent evaporating temperature is determined using Eq. (14) at a quality of 0.6. Teq ¼ Tf ð1 XÞ þ Tg X
ð14Þ
Fig. 16. Simulation results for the temperature difference between the air and refrigerant sides in the evaporator along the refrigerant path (temperature differences at every 4 sections).
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from the inlet to the outlet (from the right side to the left side in Fig. 14). However, the heat transfer rate to the third row in the parallel-cross flow type path with R-22 is no more high than in the second row even though the third row has larger area about 20% compared to the first row. In that case, there is almost no heat transfer rate at the third row. It shows that the heat transfer rate in each row is different depending on path configuration and the heat transfer rate is not evenly distributed at each row in parallel-cross path type evaporator with R22. The simulated temperature differences along the refrigerant flow path are shown in Fig. 16. The point of zero temperature difference (pinch point) or negative difference is located in the third row of the parallel-cross path configuration using R-22. After this point, the heat transfer area will not contribute to the heat transfer, as shown in Fig. 15.
Fig. 17. Different velocity profiles with same flow rate (uavg=1.2 m/s) on the parallel cross flow type evaporator (shown in Fig. 7); (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
Fig. 18. Heat transfer rate of evaporator [shown in Fig. 7(a)] depending on different velocity profiles; (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
It can be inferred from the analysis that the fifth pass needs more refrigerant flow for all types of path configuration because the refrigerant is fully evaporated too early before the outlet as shown in Fig. 16. And the path of the evaporator needs to be re-designed to assign equal heat transfer rate at each row, which means higher efficient use of the heat transfer area. 4.3. Two-dimensional air mal-distribution Four types of two-dimensional velocity distributions are adopted to study the impact of air mal-distribution: uniform, convex, concave, and inclined type (see Fig. 17). In all cases, the air- flow rate is same with each other, an average velocity of 1.2 m/s, and only its distribution is changed. Calculation conditions are a refrigerant flow of 183 kg/h, an inlet quality of 0.2, and an equivalent evaporating temperature of 4.3 C. And the evaporator (a) in Fig. 7 is used in the calculation; equal refrigerant flow is assigned to each refrigerant flow pass. The simulation results for this analysis are shown in Fig. 18. The heat transfer rate is changed according to the velocity profiles even though it has same air flow rate. In this analysis, the concave profile is the worst case that has the degradation of heat transfer rate about 6% compared to uniform profile type. We think such variation in heat transfer capacity mainly come from the change of local transfer characteristics due to different air velocity on the section in each refrigerant flow path; pressure drop and heat transfer coefficient in the tube is function of heat flux [10,13]. Fig. 19 shows pressure drops in each pass depending on the types of air flow distribution. Because of the analysis condition of same refrigerant flow to each pass, lower pressure drop will be obtained with smaller two-phase area in which relatively larger pressure drop take place than in single phase area [10]. So, it can be seen that the distribution type (d) has the minimum pressure drop in
Fig. 19. Pressure drops in each flow pass of refrigerant side coming from air mal-distributions; (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
the first pass (higher air velocity zone) and the maximum in the fifth pass (lower velocity zone) compared to other distribution types; higher air velocity will decrease two-phase area in the condition of constant refrigerant flow.
Appendix [21]
5. Concluding remarks
UQr ¼ Qr
A new program was developed to analyze the heat transfer characteristics of fin and tube evaporators that use a zeotropic mixture refrigerant, R-407C, as the working fluid. The calculation algorithm is based on EVSIM (NIST), but a tube is segmented into several sections to provide a base unit for the calculations in this study. Therefore, two-dimensional air mal-distribution in the tube-length (horizontal) and vertical directions of the evaporator can be considered, naturally. The simulations and test data from real evaporators with two different refrigerant flow path configurations were compared, using both R-22 and R-407C refrigerants. The deviation of capacity prediction was a maximum of 5.4%. The heat transfer trend depended on several parameters, and was well traced by the numerical simulations. The simulated wall temperature is compared well with the test data, which shows the verified ability of the simulation to predict local heat transfer characteristics. The heat transfer rate and temperature differences along refrigerant flow path express well the local heat transfer characteristics of the evaporator. As a result of analysis, the heat transfer at each row is estimated and the direction for the better efficiency can be inferred. The impact of two-dimensional air mal-distribution is studied with four different types of velocity profiles. And it shows the difference of heat transfer rate in our cases is about 6% in maximum, which is originated from air mal-distribution along tube length direction. It is verified that the program (section-by-section scheme) in this study has the capability of the better understanding for overall and local characteristics of heat transfer of an evaporator. It can be a useful design tool to improve the efficiency of an evaporator when a zeotropic mixture refrigerant and two-dimensional air mal-distribution are used. It is also possible to find out the optimum combination of design parameters or develop key rules for R-407C evaporator design.
719
Detailed descriptions of the overall uncertainties are given below. Based on the error propagation method, the uncertainty of the heat transfer rate in the refrigerant side is calculated using ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2 1 @Qr 1 @Qr Um r þ Uir ; Qr @mr Qr @ir
ðA1Þ
where U is the uncertainty level. In Eq. (A1), Qr is obtained from the refrigerant heat transfer rate calculation
ðA2Þ Qr ¼ mr ir;in ir;out ¼ mr Dir ; where mr is the mass flow rate of the refrigerant measured by a mass flow meter (OVAL Corp.) operating on the Coriolis force principal. Using Eq. (A2), Eq. (A1) can be simplified as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s UQr Umr 2 UDi 2 ¼ þ : ðA3Þ Qr mr Dir This is used to calculate the overall uncertainty of the refrigerant side. Since the enthalpy of the refrigerant is calculated using the measured temperature and pressure, the source of uncertainty of the enthalpy difference is related to the measurement error of temperature and pressure at the inlet and outlet of the evaporator. The uncertainty level of the temperature measurement was 0.1 C during the calibration process of the RTD and the data acquisition system. The RTD is calibrated using a standard RTD made by OMEGA Inc. and a constant temperature water bath. The digital pressure gauges (VALCOM, Japan) have an uncertainty level of 7.5 kPa, which is 0.5% of the full scale of 1500 kPa. At the minimum pressure for the 45 test cases (417.8 kPa), the relative accuracy level is 1.8%. And the mass flow meter has a measurement error of 0.1% of the reading. The relative uncertainty of the enthalpy difference was surveyed by calculating the enthalpies in the range of uncertainty limit of the temperature and pressure. There are negligible differences in the resulting relative uncertainties for all cases. The maximum value of the uncertainty in the refrigerant side, using Eq. (A3), becomes 0.4% for the minimum refrigerant flow and enthalpy difference of 45 test cases. For the air side, the uncertainty of the heat transfer rate is calculated using following equations: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi Ua 2 UVa 2 UDia 2 þ þ ; a Va Dia
Acknowledgements
UQa ¼ Qa
This work was performed with financial support from LG Electronics, Inc., and the National Research Laboratory of the Korean government.
Qa ¼ a Va ia;in ia;out ¼ ma Dia ;
ðA4Þ
ðA5Þ
720
pffiffiffiffiffiffiffiffiffi Va ¼ C DPn ;
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
ðA6Þ
where Va is the volumetric flow of air. The sources of uncertainty are density, volumetric flow, and enthalpy difference. The dominant sources of uncertainty overall are volumetric flow and air enthalpy difference, since the density change of the upstream air at the level of temperature uncertainty, 0.1 C, is negligible. The volumetric flow is a function of the pressure drop, temperature, and velocity; however, it strongly depends on the pressure drop across the nozzle. The gauge reading corresponding to the volumetric flow of 18.0 CMM (equal to a front velocity of 1.44 m/s) is 23.0 mm H2O. Two nozzles with a diameter of 100 mm are used. The uncertainty level of volumetric flow of air, the second term of Eq. (A4), is 0.11%. The enthalpy difference is a function of the dry and wet bulb temperatures, but the impact of the wet bulb temperature is stronger than that of the dry bulb temperature. The wet and dry bulb temperature difference has an uncertainty limit of 0.2 C, which give a maximum uncertainty of 2.86% for the minimum enthalpy difference of the 45 test cases. Therefore, the uncertainty of the heat transfer rate from the air side, using Eq. (A4), is 2.9%. The uncertainty level of the air side is larger than that of the refrigerant side. Therefore, the uncertainty level in this study is a maximum of 2.9% because the test conditions of air do not change and the uncertainty level is larger on the air side than on the refrigerant side.
References [1] Fagan TJ. The effect of air flow mal-distributions on airto-refrigerant heat exchanger performance. ASHRAE Transactions 1980;DV-80-7:699–713. [2] Chwalowski M, Didion DA, Domanski PA. Verification of evaporator computer models and analysis of performance of an evaporator coil. ASHRAE Trans 1989;CH23-1:1229–36. [3] Domanski PA. An evaporator simulation model accounting for refrigerant and one-dimensional air distribution, 1989, NISTIR 89-4133. [4] Lee J, Bae SW, Bang KH, Kim MH. Experimental and
[5]
[6] [7]
[8] [9] [10]
[11]
[12]
[13] [14]
[15]
[16] [17] [18] [19]
[20] [21]
numerical research on condenser performance for R-22 and R-407C refrigerants. International Journal of Refrigeration 2002;May:372–82. Lee J, Domanski PA. Impact of air and refrigerant maldistributions on the performance of finned-tube evaporators with R-22 and R-407C, 1997, ARTI MCLR Project, DOE/CE/23810-81. Incropera FP, Dewitt DP. Introduction to heat transfer. John Wiley & Sons, Inc; 1996. Gray D, Webb R. Heat transfer and friction correlations for plate finned-tube heat exchangers having plain fins. In: Proc. of Eighth Int. Heat Transfer Conference, San Francisco, 1986. Nakata H. Finned tube heat exchanger. Japanese J Refrigeration 1990;65(758):1–14. Schmidt TE. Heat transfer calculations for extended surfaces. J of ASRE 1949:351–7. Gungor KE, Winterton RHS. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transfer 1986;29(3):351–8. Ebisu T, Torikoshi K. Evaporation and condensation heat transfer characteristics of hfc refrigerants in a horizontal tube. Proc 30th National Heat Transfer Symposium of Japan 1993;1:334–6 (in Japanese). Schlager LM, Pate MB, Bergles AE. Performance predictions of refrigerant-oil mixtures in smooth and internally finned tubes—part II: design equations. ASHRAE Trans 1990;3321:170–82. Pierre B. Flow resistance with boiling refrigerants. ASHRAE Journal, September, 1964. Petukhov BS. Heat transfer and friction in turbulent pipe flow with variable physical properties. Advances in Heat Transfer 1970;6:503–64. Schlager LM, Pate MB, Bergles AE. Heat transfer and pressure drop during evaporation and condensation of R22 in horizontal micro-fin tubes. Int J Refrigeration 1989; 12(1):6–14. Ito H. Pressure losses in smooth pipe bends. Basic Engineering Transaction of ASME 1960:135. Geary David F. Return bend pressure drop in refrigeration systems. ASHRAE Transactions 1975;2342:252–65. ASHRAE Handbook (Fundamentals), 1993. Gallagher J, McLinden MO, Morrison G, Huber M. NIST Standard Reference Database 23, Version 5.0 (REFPROP v4.0), 1993. ANSI/ASHRAE 41.2-1987. Standard methods for laboratory air-flow measurement, 1987. Coleman HW, Glenn Steele W Jr. Experimentation and uncertainty analysis for engineers. John Wiley & Sons, Inc.; 1986.
An improved method for analyzing a fin and tube evaporator containing a zeotropic mixture refrigerant with air mal-distribution Jangho Lee, Young-Chul Kwon1, Moo Hwan Kim* Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang, 790-784, South Korea Received 13 October 2001; received in revised form 17 October 2002; accepted 12 December 2002
Abstract A new program was developed to analyze the heat transfer characteristics of fin and tube evaporators that use a zeotropic mixture refrigerant, R-407C, as the working fluid. The calculation algorithm is based on EVSIM (NIST), but a tube is segmented into several sections to provide a base unit for the calculations in this study. Therefore, twodimensional air mal-distribution in the tube-length (horizontal) and vertical directions of the evaporator can be considered. The temperature gradient in the flow direction is traced using a discrete pattern to simulate the continuous variation found in actual evaporators. To validate the simulation results, 45 test cases in a real evaporator were performed with two different refrigerant flow path configurations using R-22 and R-407C refrigerants. The deviation between the simulations and test data was a maximum of 5.4%, and the trends were similar. The local heat transfer predictions were verified by comparing the numerical and test wall temperatures along the refrigerant flow path. Local temperature difference and the heat transfer contributions from each row are also analyzed along refrigerant flow path. And more, the impact of air mal-distribution is studied with two-dimensional four different types of velocity profiles and the significant difference in heat transfer is analyzed. The program developed in this study will be a useful tool to know all of information related with heat and mass transfer at any local point and can be used for improving the efficiency of zeotropic mixture refrigerant evaporators. # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Heat transfer; Modelling; Finned tube; Evaporator; Refrigerant; Zeotropic mixture; Air; Distribution
Me´thode ame´liore´e utilise´e afin d’analyser le fonctionnement d’un e´vaporateur a` tubes a` ailettes utilisant un me´lange ze´otrope et caracte´rise´ par une mauvaise distribution d’air Mots cle´s : Transfert de chaleur ; Mode´lisation ; Tube ailete´ ; E´vaporateur ; Frigorige`ne ; Me´lange Ze´otrope ; Air ; Distribution
* Corresponding author. Tel.: +82-54-279-2165; fax: +82-54-279-3199. E-mail address: [email protected] (M.H. Kim). 1 Present address: Division of Mechanical and Control Engineering, Sun Moon University, #100 Kalsanri, Tangjeong Myeon, Asansi, Chung-Nam, 336-840, South Korea. 0140-7007/03/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/S0140-7007(03)00023-9
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Nomenclature A C D h i k Le m P Q t T u U V X W
Area (m2) Constant, heat capacity (W/kg/K) Diameter (m) Heat transfer coefficient (W/m2/K) Enthalpy (w/kg) Thermal conductivity (W/m/K) Lewis number Mass flow rate (kg/h) Pressure (Pa) Heat transfer rate (w) Thickness (m) Temperature Velocity (m/s) Overall heat transfer coefficient (W/m2/ K) Volumetric flow (m3/s) Quality Absolute humidity (kg/kg)
Subscripts a Air avg Average b Boiling point (saturated liquid in zeotropic mixture) c Contact, corresponding contact area d Dew point (saturated liquid in zeotropic mixture) db Dry bulb eq Equivalent f Fin, saturated liquid phase g Gas phase or saturated vapor i Inner in Inlet l Liquid phase m Mean mix Multi-component zeotropic mixture refrigerant n Nozzle o Outer out Outlet p Pipe, tube pure Single component pure refrigerant r Refrigerant w Tube wall, water wb Wet bulb
1. Introduction In recent years, heat exchanger research has focused on alternative refrigerants since the Montreal Protocol banned the use of halogenated refrigerants (CFC’s and
HCFC’s). One of the more promising alternative refrigerants is the ternary mixture R-407C, which is composed of HFC-32/125/134a, 23/25/52 wt. percentage. The use of a zeotropic mixture refrigerant provides an additional degree of freedom in the composition variation that is not present in single component refrigerants. A change in the saturation temperature during the evaporation and condensation processes at a constant pressure is known to have important effects on the heat exchanger design. The three main parameters used to estimate the heat transfer rate from air to a refrigerant in an evaporator are: the heat transfer coefficient, the heat transfer area, and the temperature difference between the air and refrigerant sides. These parameters can be complicated in a multi-pass evaporator with a zeotropic mixture refrigerant. The heat transfer coefficient can vary locally due to mal-distribution of the air velocity and phase change on the refrigerant side. The temperature gliding due to phase changes in the refrigerant mixture components changes the temperature difference between the air and the refrigerant sides. Furthermore, it is difficult to define the heat transfer area because the evaporator has fin slits and micro-fins inside the tubes; many researchers have neglected the area change due to slits in their experimental correlations. In general, two possible approaches can be used to estimate the heat transfer rate of heat exchangers: a lumped analysis scheme, in which the heat exchanger is analyzed as a single unit with two inlets and outlets on both the cold and hot sides; and a local analysis scheme, in which the heat exchanger is divided into segments or multiple control volumes. In the latter approach, the local variation of the heat transfer conditions can be considered more exactly. Fagan [1] studied the effects of a one-dimensional mal-distribution of the air flow. He showed that the mal-distribution of air affected the heat transfer rate. The capacity degradation was as much as 20% in the worst case. Chwalowski et al. [2] predicted the performance of evaporators using four different methods, and compared their results with test data. They showed that simulated or imposed air velocity profiles must follow the actual air distribution across the coil for successful capacity prediction of a coil. In their laboratory tests, the capacity degradation was up to 30% for mal-distributed air velocity profiles. Domanski [3] developed a program, EVSIM, to analyze an evaporator with a multi-pass refrigerant distribution and one-dimensional air distribution. He showed that the program modeled the one-dimensional air mal-distribution due to the installation angle of the evaporator to the flow direction in a duct. One tube was used as a local analysis unit in his work. Since his model only considers one-dimensional air flow distributions, the effects of the distribution in the tube length direction could not be analyzed.
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
In addition, if a zeotropic mixture refrigerant is used, a simple "-NTU relation shown in Eq. (1) is not longer valid because of the temperature variations of refrigerant along the tube length by quality change and pressure drop. We developed the section-by-section scheme for the analysis of evaporator as for the analysis of condensers [4]. One tube is segmented into small sections of equal length. One section is adopted as the local analysis unit, and calculations are performed on this section. The calculation in the section is based on EVSIM (NIST) [3]. The temperature of the zeotropic mixture refrigerant is assumed constant over each small section. Different air velocities can be assigned for each section. The temperature of mixture refrigerant in the next section is calculated using the saturation pressure subtracting the pressure drop from the pressure of the present section. Thus, the temperature variation of the zeotropic mixture refrigerant can be traced along the flow path with a step-by-step pattern as shown in Fig. 1. The larger the width to height ratio of the evaporator, the more effective the section-by-section approach will be.
2. Model and correlations 2.1. Section-by-section scheme One section in the tube (segmented along the refrigerant flow direction) is used as the local heat transfer area to account for the two-dimensional mal-distribution of air and the temperature gliding of the zeotropic refrigerant mixture, R-407C. This is illustrated in Fig. 2 for a 2-row, 6-column evaporator, in which 12 tubes make one refrigerant flow path. Each tube is divided into 4 sections, which gives a total of 48 sections along the refrigerant flow path in this illustration. The heat transfer is calculated for each section. The calculation
Fig. 1. Concept diagram of temperature gliding using a section-by-section scheme along the refrigerant path.
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procedure is similar to that of the tube-by-tube model, EVSIM [3]. Several assumptions are employed to simplify the calculations. First, steady state conditions are assumed in the air and refrigerant sides. The heat transfer to adjacent sections in the tube-length direction is neglected because the temperature difference is relatively small. The velocity profile entering the first row of the air side is assumed to be same as that of the last row of the evaporator. The heat transfer in the return bend is neglected; only the pressure drop is considered because there is no air flow through the return bend in test and field applications. For the first iteration, the initial inlet temperature and velocity profile on the air side are assigned to all sections in all rows for convenience. The flow rate, inlet pressure, and quality on the refrigerant side are provided as input conditions. The calculation proceeds from the inlet to the outlet of the refrigerant side along the refrigerant flow path, as shown in Fig. 2. In each section, the heat transfer rate is calculated using the effectiveness and the temperature difference between the air and refrigerant sides. The temperature of the refrigerant in a section is assumed constant because the amount of temperature gliding is small compared to the temperature variation during the phase change of the zeotropic mixture refrigerant. Therefore, a simple "-NTU relation can be applied to a section in the phase change region: " ¼ 1 eNTU
ð1Þ
The pressure drop across a present section is determined and used to calculate the inlet pressure for the next section by subtracting the pressure drop from the pressure of present section. The refrigerant temperature in the next section is calculated using the corrected pressure with quality. This allows the temperature gliding to be traced step-by-step along the refrigerant path. Once the heat transfer calculations for a section are completed, the refrigerant quality leaving the section and the downstream temperature of air passing through the section can be determined. The quality will be used for the refrigerant inlet condition of the next section and the downstream temperature will be the air inlet condition of the next row, respectively. The temperature differences between the initially-assigned and updated values are examined for all sections. The calculations are iterated until the differences are less than a specified criterion. If the criterion is not satisfied after a given number of iterations, the outlet enthalpy of the refrigerant is compared with the value from the previous iteration until the change is small enough to satisfy a second criterion. The logic flow of the simulation program is shown in Fig. 3: the position indices i, j, and k are the section, tube, and path indices, respectively. A direction flag is assigned to simulate the direction of refrigerant flow as the calculation proceeds through the sections. This is used
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Fig. 2. Section-by-section scheme for evaporator analysis.
as a direction vector in Fig. 3: the section index increases from right to left in row 1, and decreases from left to right in row 2 in Fig. 2. 2.2. Heat and mass transfer calculation [5] The "-NTU equation with the inlet temperature difference between the air and refrigerant sides is used to calculate the heat transfer rate for each section. Several types of "-NTU relations may be used to obtain " [6]: once it is determined, the heat transfer rate from the air to the refrigerant can be obtained using Eq. (3). UA " f NTU ¼ ð2Þ Cpa ma Qair ¼ ma Cpa ðTai Tri Þ"
ð3Þ
The overall heat transfer coefficient, U, for a section in a wetted finned tube is calculated from the sum of the individual resistances to heat transfer as follows: 0 1 Ao A o tp 1 Ao þ þ þ B hi Api Apm Kp hl Apo hc C B C C 1 U¼B ð4Þ Bþ C @ A Af ð1 ’ f Þ ho ð1 þ Þ 1 Ao ¼
ilgw ð!a !w Þ Cpa ðTa Tw Þ
ð5Þ
The first and fifth terms of Eq. (4) refer to the inside and outside heat transfer resistances, respectively. The second term represents the conductive heat transfer resistance through the tube wall and the third term accounts for the conduction resistance through the condensed water layer on the fin and tube. The fourth term represents the contact resistance between the outside tube surface and the fin collar. Eq. (4) gives the additional heat transfer due to the condensation of water vapor from the air to the surface of the fins and tubes. The overall heat transfer coefficient, U, for a non-wetted finned tube can be obtained using Eq. (4) with 1/hl 0, a 0. Once the heat transfer rate from air to refrigerant is calculated, the air, tube wall, and fin surface temperatures are calculated directly using the heat transfer resistance. The humidity at saturation on both the wall and fin is calculated from the fin surface and wall temperatures. The mass transfer from the air to the tube and fin is determined from Eq. (6) [5]: ha Apo ! ¼ ð!ai !w Þ 1 exp LeCpa ma ha Af ð6Þ þ ð!ai !fm Þ 1 exp LeCpa ma The first term in Eq. (6) is the mass transfer from the air to the tube wall, and the second term is the mass transfer to the fin surface. Once the mass transfer is known, the outlet humidity and temperature of the air side at a given section are obtained from Eqs. (7) and (8).
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2.3. Correlations and flow distribution The code uses a complete set of correlations for the heat transfer and pressure drop in both the refrigerant and air sides. They are summarized in Table 1. Gray and Webb’s [7] correlation for flat fins is used to calculate the heat transfer coefficient for the outside (or air side). The enhancement factor is multiplied for the louvered fin [8]. Schmidt’s method is used to calculate the fin efficiency [9]. Gungor and Winterton’s [10] correlation is used to determine the refrigerant side heat transfer coefficient in the phase change region of a smooth tube. Their correlation is modified to compensate for the temperature variation of the zeotropic mixture refrigerant as shown in Eqs. (9) and (10) [11]; these give the heat transfer coefficient for a pure refrigerant when the quality is 1. hmix ¼
hpure
; hpure Teq Td 1þ q
Teq ¼ Td ð1 xÞðTd Tb Þ
Fig. 3. Logic flow chart for the section-by-section calculations.
!ao ¼ !ai !
ð7Þ
Qair ifgw ! þ ð8Þ Cpa ma Cpa The humidity and temperature are then used as input for the next section in the next row of the evaporator. Tao ¼ Tai
ð9Þ
ð10Þ
The heat transfer coefficient for the mist flow region is calculated using linear interpolation between the coefficients at quality 0.8 and the single vapor phase at quality 1.0. The heat transfer coefficient for an internally finned (rifled or grooved) tube is calculated by multiplying by the enhancement factor of Schlager et al. [12]. The in-tube pressure drop is due to friction, momentum change, and gravity. The gravity term was neglected. Pierre’s correlation [13] was used to calculate the pressure drop through a smooth tube in the phase-change region, and Petukhov’s Eq. [14] was employed to determine the friction factor for a smooth tube with turbulent single-phase flow. An enhancement factor is used for the internally finned tube [15]. Ito’s correlation [16] for the single-phase region and Geary’s correlation [17] for the phase change region are used for the U-bend pressure drop calculations.
Table 1 List of correlations used in this study Items
Applying zone
Correlations
Heat transfer coefficient
Air-side Single phase region in refrigerant side Phase change region in refrigerant side Enhanced factor for grooved tube Single phase region in refrigerant side Phase change region in refrigerant side Return bend in phase change region Return bend in single phase region Enhanced factor for grooved tube
Gray and Webb [6,7] Dittus-Boelter [5] Gungor & Winterton [9]; Ebisu and Torikoshi [10] Schlager [11] Petukhov [13] Pierre [12] Geary [16] Ito [15] Schlager [14]
Pressure drop
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Fig. 4. Schematic diagram for the refrigerant flow distribution; (a) equal pressure drop across each multi-pass path, (b) equal mass flow in each multi-pass path.
Refrigerant flows in an evaporator with multi-pass circuits [shown in Fig. 4(a)] will have the same pressure drop across each flow circuit [3,5]. However, the same refrigerant flow can be assigned to each pass circuit of an evaporator when a capillary tube is connected directly to the refrigerant flow inlet [see Fig. 4(b)]. In this case, the pressure drop across the capillary tube will be about 20 times greater than the in-tube pressure drop across the flow path from the distributor to the junction tube at the outlet of the evaporator. Therefore, the individual pressure drops across each flow path of the evaporator need not be considered; the pressure drop will be the same across all circuits of the evaporator. The properties of air are based on ASHRAE Handbook data [18]. The refrigerant properties are based on REFPROP [19] from NIST.
3. Model verification 3.1. Refrigerant supply loop The refrigerant loop consists of a compressor, an oil separator, a shell and tube type condenser, a receiver, a flow meter, capillary tubes, an evaporator, and an accumulator, as shown in Fig. 5. Discharged oil and refrigerant from the compressor passes through the oil separator, and only high pressure and temperature refrigerant flows into the shell and tube condenser. The cooling water loops consist of a constant water bath, a pump, a by-pass loop, and a motor driven micro-valve.
These are used to control the sub-cooling of the refrigerant at the inlet of the distributor. A mass flow meter measures the mass flow rate of the refrigerant liquid. A receiver and sight glass are used to reserve and check the liquid refrigerant. The supplementary temperature control loop controls the refrigerant temperature at the distributor inlet. The temperature and pressure are measured at the distributor inlet to determine the amount of sub-cooling and the properties of the refrigerant. The temperature is measured using a Pt 100 RTD inserted through the copper tube wall. The pressure is detected by a digital pressure gauge with a range of 0–5 MPa. The thermodynamic quality at the inlet of test evaporator is calculated, including the amount of sub-cooling and assuming an adiabatic process in the capillary tubes. After the test section, the refrigerant is returned to the compressor through a supplementary heater and an accumulator. The refrigerant temperature and pressure are measured at the outlet of the evaporator in the same manner as at the inlet of distributor, except that the digital pressure gauge has a range of 0–1.5 MPa. 3.2. Air flow measurement system A volumetric flow rate measurement system for humid air based on the ANSI/ASHRAE 41.2-1987 [20] was designed. It was installed in a constant temperature and humidity room, as shown in Fig. 6. The system consists of five nozzles, a fan, a motor, and an air-sampling unit. The air-sampling unit in the system is not
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
shown in Fig. 6, but it is similar to that shown in front of the evaporator. Two Pt 100 RTD sensors are positioned in the air-sampling unit to measure the dry and wet bulb temperatures of the humid air leaving the evaporator,
713
which are then used to calculate the outlet air enthalpy. The volumetric flow rate of air, Va, is obtained from pffiffiffiffiffiffiffiffiffiffi ð11Þ Va ¼ C Pn ;
Fig. 5. Schematic diagram of the refrigerant supply system.
Fig. 6. Schematic diagram of the heat exchanger test facility.
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where Pn is the pressure drop across the nozzles. The flow coefficient and area of the nozzles are included in C. Since the test conditions of the air side remain unchanged in all test cases, C is approximately constant. The other air-sampling unit is installed in front of the evaporator as shown in Fig. 6. The inlet air enthalpy is calculated using the dry and wet bulb temperature in the air-sampling unit. The same procedure is used to calculate the inlet air enthalpy. The room temperature and humidity are controlled according to the inlet dry and wet bulb temperatures. 3.3. Test evaporators and data reduction The path configurations of the test evaporator are shown in Fig. 7. They are the same as those found in a 3-hp commercial air-conditioner. The evaporator (508 mm high, 57.15 mm row depth, and 410 mm tube length) is installed in an upright position, perpendicular to the flow direction, and has slit-louvered fins on the air side and micro-fin tubes on the refrigerant side. The geometry consists of 3 rows and 20 columns, with 16 fins per inch. The step pitch is 25.4 mm, the row pitch is 19.05 mm, and the outside diameter of the tube is 9.52 mm. The path of the evaporator is categorized by the flow direction of the refrigerant and air; the parallel-
cross flow path is shown in Fig. 7(a) and the countercross flow path is shown in Fig. 7(b). The evaporator has five paths. The second and fourth paths shown in Fig. 7 each contain 14 tubes. The first path is 17% shorter (10 tubes), and the last path is 17% longer (14 tubes). The heat transfer rate from the air side is calculated using the measured temperatures and velocities:
Qa ¼ a Va ia;in ia;out ;
ð12Þ
where a is the density and ia is the enthalpy of humid air. The volumetric flow rate of air, Va, is kept constant at 18.0 m3/min in all test cases, which corresponds to a front velocity of 1.44 m/s. The dry and wet bulb temperatures are set at 27 and 19.5 C, respectively, in all test cases. The heat transfer rate to the refrigerant side was calculated by multiplying the mass flow rate by the change of enthalpy:
Qr ¼ mr ir;out ir;in ;
ð13Þ
where mr is the mass flow rate of the refrigerant measured by the mass flow meter using the Coriolis force principal. The enthalpy change in the refrigerant side is calculated by measuring the pressure and
Fig. 7. Test evaporators and their path configurations according to the direction of the air and refrigerant flows: totally, five passes are included in each evaporator.
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J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720 Table 2 Conditions and results for the tests and simulations (va=1.44 m/s) No.
Ref. & path
Gr,in (kg/h)
Pr,outlet (kPa)
Xr,in
QTEST (W)
Qsim (W)
Q (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
R-22 parallel-cross flow type path
181.7 182.7 181.8 183.1 179.2 180.1 179.8 180.5 172.3 180.1 187.1 182.5 182.6 183.2 183.3 183.0 181.2 179.7 180.1 180.4 180.2 180.1 165.4 170.0 174.7 185.1 183.6 182.0 182.0 183.8 182.5 182.8 181.6 160.0 164.7 169.4 176.0 178.7 184.4 189.6 180.4 178.6 180.0 179.3 179.4
417.8 423.6 417.8 422.7 400.1 426.6 458.0 481.5 429.5 426.6 426.6 492.3 494.3 496.2 493.3 493.3 489.3 445.2 464.8 494.3 516.8 534.5 490.3 490.3 489.3 490.3 491.3 495.2 498.2 488.4 494.3 493.3 489.3 496.2 495.2 495.2 496.2 495.2 495.2 495.2 444.2 466.8 491.3 512.9 538.4
0.20 0.22 0.24 0.25 0.24 0.23 0.23 0.23 0.23 0.23 0.23 0.22 0.23 0.24 0.26 0.27 0.28 0.26 0.25 0.24 0.24 0.23 0.25 0.25 0.25 0.25 0.20 0.21 0.22 0.24 0.25 0.26 0.27 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.25 0.25 0.24 0.23
8090 7869 7861 7761 7906 7803 7657 7661 7600 7803 8204 8496 8408 8329 8183 8089 7960 7925 7969 7973 7879 7578 7369 7576 7801 8237 8970 8784 8670 8634 8484 8450 8283 7512 7754 7976 8202 8273 8550 8760 8414 8297 8325 8235 8185
8194 8010 7889 7742 7798 7805 7725 7499 7511 7829 8129 8136 8103 7946 7936 7849 7740 8108 8117 7963 7537 7212 7446 7612 7789 8075 9354 9254 9055 8969 8868 8767 8670 7687 7891 8092 8353 8457 8672 8849 8634 8592 8510 8320 8217
1.29 1.79 0.36 0.24 1.37 0.03 0.88 2.11 1.18 0.34 0.91 4.23 3.64 4.61 3.02 2.96 2.77 2.32 1.85 0.12 4.34 4.83 1.03 0.48 0.16 1.97 4.28 5.36 4.44 3.88 4.53 3.75 4.67 2.34 1.76 1.45 1.84 2.23 1.43 1.02 2.61 3.55 2.22 1.03 0.39
R-407C parallel-cross flow type path
R-407C counter-cross flow type path
temperature. The enthalpy calculated at the inlet of the distributor in Fig. 4(b) is used as the inlet enthalpy for the evaporator, assuming an adiabatic process in the capillary tubes. The outlet enthalpy of the evaporator is determined at the outlet of the junction tube in Fig. 4(b). The difference between the heat removal from the air and the heat gain of the
refrigerant is within 3.0%. The refrigerant side heat transfer rate is higher than that on the out (air) side because of the heat gain from the ambient air. The air side heat transfer rate is used as validation data. All test conditions are listed in Table 2. Inlet conditions (temperature, humidity, velocity) for the air side are kept constant; only the inlet conditions for the refrigerant
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4. Results 4.1. Verification of capacity prediction
side (refrigerant flow rate, evaporation pressure, and input quality) are changed in the validation tests. The uncertainties in the heat transfer rate measurements for the air and refrigerant sides are surveyed and the maximum is within about 3.0% as shown in the Appendix.
Simulations and experiments were performed for the 45 cases shown in Table 2. In the simulations, the inlet pressure of the refrigerant side of the evaporator was modified iteratively to match the outlet pressure obtained in the validation tests. The heat transfer differences between the test and simulation results are within 5.4%, as shown in Table 2 and Fig. 8. The deviation between simulations and test results are evenly distributed in the vicinity of zero line except a countercross flow type evaporator with R-407C, as shown in Fig. 9. The simulation overestimates the counter-cross path evaporator with R-407C by 2.8% on average. The simulation results matched the experimental trends (see Figs. 9–12). The heat transfer rate increases with the refrigerant mass flow rate in Fig. 10, but decreases with increasing inlet quality in Fig. 11. The heat transfer rate as a function of the evaporating pressure at the outlet is shown in Fig. 12. The heat transfer rate decreases as the evaporating pressure increases; the temperature differ-
Fig. 9. Deviations of the simulations from the validation tests.
Fig. 11. Simulation and test results for the refrigerant mass flow rate.
Fig. 10. Simulation and test results for evaporator inlet quality.
Fig. 12. Simulated and measured capacity as a function of evaporator outlet pressure.
Fig. 8. Comparison of the heat transfer rates for the simulations and validation tests.
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
Fig. 13. Simulation and test results for the wall temperature along the fifth pass of the refrigerant (shown in Fig. 7): R-407C, Ta,db=27 C, Ta,wb=19.5 C, Teq=5.5 C, Xin=0.21, mr=182 kg/h.
717
Measured and simulated wall temperatures are shown in Fig. 13. In the test, the wall temperature was measured on the middle of the U-bend in the evaporator. The length ratio in Fig. 13 is defined as the distance from the inlet divided by the total length of the fifth pass. The values and trends of the wall temperatures were well simulated by the numerical calculations as shown in Fig. 13. Other local characteristics are shown in Fig. 14, the local heat transfer rates, and in Fig. 16, the local temperature differences. The aggregated heat transfer rate from the first to the last sections is shown in Fig. 14 by summing the values along the refrigerant flow path for the fifth pass. The heat transfer rate is given at every 4 sections; 4 sections correspond to 1 tube. The ratio of heat transfer rate in each row is shown in Fig. 15. The heat transfers to the third row in the parallel cross flow type evaporator and to the first row in the counter-cross flow type are relatively small compared to other rows in each evaporator. The heat transfer rate in the countercross flow type path with R-407C increased continuously
Fig. 15. Ratio of simulated heat transfer rate at each row. Fig. 14. Simulated heat transfer rate along the refrigerant flow path.
ence between the air and refrigerant sides decreases with increasing evaporating pressure. 4.2. Analysis of local characteristics The local heat transfer characteristics for different path types with R-407C and R-22 refrigerant are shown from Fig. 13–16. The longest pass shown in Fig. 7 (the fifth pass) was selected to validate the simulation using the local heat transfer rate. The tests and simulations conditions are a refrigerant flow of 182 kg/h, an inlet quality of 0.21, and an equivalent evaporating temperature of 5.5 C. The equivalent evaporating temperature is determined using Eq. (14) at a quality of 0.6. Teq ¼ Tf ð1 XÞ þ Tg X
ð14Þ
Fig. 16. Simulation results for the temperature difference between the air and refrigerant sides in the evaporator along the refrigerant path (temperature differences at every 4 sections).
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from the inlet to the outlet (from the right side to the left side in Fig. 14). However, the heat transfer rate to the third row in the parallel-cross flow type path with R-22 is no more high than in the second row even though the third row has larger area about 20% compared to the first row. In that case, there is almost no heat transfer rate at the third row. It shows that the heat transfer rate in each row is different depending on path configuration and the heat transfer rate is not evenly distributed at each row in parallel-cross path type evaporator with R22. The simulated temperature differences along the refrigerant flow path are shown in Fig. 16. The point of zero temperature difference (pinch point) or negative difference is located in the third row of the parallel-cross path configuration using R-22. After this point, the heat transfer area will not contribute to the heat transfer, as shown in Fig. 15.
Fig. 17. Different velocity profiles with same flow rate (uavg=1.2 m/s) on the parallel cross flow type evaporator (shown in Fig. 7); (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
Fig. 18. Heat transfer rate of evaporator [shown in Fig. 7(a)] depending on different velocity profiles; (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
It can be inferred from the analysis that the fifth pass needs more refrigerant flow for all types of path configuration because the refrigerant is fully evaporated too early before the outlet as shown in Fig. 16. And the path of the evaporator needs to be re-designed to assign equal heat transfer rate at each row, which means higher efficient use of the heat transfer area. 4.3. Two-dimensional air mal-distribution Four types of two-dimensional velocity distributions are adopted to study the impact of air mal-distribution: uniform, convex, concave, and inclined type (see Fig. 17). In all cases, the air- flow rate is same with each other, an average velocity of 1.2 m/s, and only its distribution is changed. Calculation conditions are a refrigerant flow of 183 kg/h, an inlet quality of 0.2, and an equivalent evaporating temperature of 4.3 C. And the evaporator (a) in Fig. 7 is used in the calculation; equal refrigerant flow is assigned to each refrigerant flow pass. The simulation results for this analysis are shown in Fig. 18. The heat transfer rate is changed according to the velocity profiles even though it has same air flow rate. In this analysis, the concave profile is the worst case that has the degradation of heat transfer rate about 6% compared to uniform profile type. We think such variation in heat transfer capacity mainly come from the change of local transfer characteristics due to different air velocity on the section in each refrigerant flow path; pressure drop and heat transfer coefficient in the tube is function of heat flux [10,13]. Fig. 19 shows pressure drops in each pass depending on the types of air flow distribution. Because of the analysis condition of same refrigerant flow to each pass, lower pressure drop will be obtained with smaller two-phase area in which relatively larger pressure drop take place than in single phase area [10]. So, it can be seen that the distribution type (d) has the minimum pressure drop in
Fig. 19. Pressure drops in each flow pass of refrigerant side coming from air mal-distributions; (a) uniform type, (b) convex type, (c) concave type, (d) inclined type.
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
the first pass (higher air velocity zone) and the maximum in the fifth pass (lower velocity zone) compared to other distribution types; higher air velocity will decrease two-phase area in the condition of constant refrigerant flow.
Appendix [21]
5. Concluding remarks
UQr ¼ Qr
A new program was developed to analyze the heat transfer characteristics of fin and tube evaporators that use a zeotropic mixture refrigerant, R-407C, as the working fluid. The calculation algorithm is based on EVSIM (NIST), but a tube is segmented into several sections to provide a base unit for the calculations in this study. Therefore, two-dimensional air mal-distribution in the tube-length (horizontal) and vertical directions of the evaporator can be considered, naturally. The simulations and test data from real evaporators with two different refrigerant flow path configurations were compared, using both R-22 and R-407C refrigerants. The deviation of capacity prediction was a maximum of 5.4%. The heat transfer trend depended on several parameters, and was well traced by the numerical simulations. The simulated wall temperature is compared well with the test data, which shows the verified ability of the simulation to predict local heat transfer characteristics. The heat transfer rate and temperature differences along refrigerant flow path express well the local heat transfer characteristics of the evaporator. As a result of analysis, the heat transfer at each row is estimated and the direction for the better efficiency can be inferred. The impact of two-dimensional air mal-distribution is studied with four different types of velocity profiles. And it shows the difference of heat transfer rate in our cases is about 6% in maximum, which is originated from air mal-distribution along tube length direction. It is verified that the program (section-by-section scheme) in this study has the capability of the better understanding for overall and local characteristics of heat transfer of an evaporator. It can be a useful design tool to improve the efficiency of an evaporator when a zeotropic mixture refrigerant and two-dimensional air mal-distribution are used. It is also possible to find out the optimum combination of design parameters or develop key rules for R-407C evaporator design.
719
Detailed descriptions of the overall uncertainties are given below. Based on the error propagation method, the uncertainty of the heat transfer rate in the refrigerant side is calculated using ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2 2 1 @Qr 1 @Qr Um r þ Uir ; Qr @mr Qr @ir
ðA1Þ
where U is the uncertainty level. In Eq. (A1), Qr is obtained from the refrigerant heat transfer rate calculation
ðA2Þ Qr ¼ mr ir;in ir;out ¼ mr Dir ; where mr is the mass flow rate of the refrigerant measured by a mass flow meter (OVAL Corp.) operating on the Coriolis force principal. Using Eq. (A2), Eq. (A1) can be simplified as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s UQr Umr 2 UDi 2 ¼ þ : ðA3Þ Qr mr Dir This is used to calculate the overall uncertainty of the refrigerant side. Since the enthalpy of the refrigerant is calculated using the measured temperature and pressure, the source of uncertainty of the enthalpy difference is related to the measurement error of temperature and pressure at the inlet and outlet of the evaporator. The uncertainty level of the temperature measurement was 0.1 C during the calibration process of the RTD and the data acquisition system. The RTD is calibrated using a standard RTD made by OMEGA Inc. and a constant temperature water bath. The digital pressure gauges (VALCOM, Japan) have an uncertainty level of 7.5 kPa, which is 0.5% of the full scale of 1500 kPa. At the minimum pressure for the 45 test cases (417.8 kPa), the relative accuracy level is 1.8%. And the mass flow meter has a measurement error of 0.1% of the reading. The relative uncertainty of the enthalpy difference was surveyed by calculating the enthalpies in the range of uncertainty limit of the temperature and pressure. There are negligible differences in the resulting relative uncertainties for all cases. The maximum value of the uncertainty in the refrigerant side, using Eq. (A3), becomes 0.4% for the minimum refrigerant flow and enthalpy difference of 45 test cases. For the air side, the uncertainty of the heat transfer rate is calculated using following equations: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffi Ua 2 UVa 2 UDia 2 þ þ ; a Va Dia
Acknowledgements
UQa ¼ Qa
This work was performed with financial support from LG Electronics, Inc., and the National Research Laboratory of the Korean government.
Qa ¼ a Va ia;in ia;out ¼ ma Dia ;
ðA4Þ
ðA5Þ
720
pffiffiffiffiffiffiffiffiffi Va ¼ C DPn ;
J. Lee et al. / International Journal of Refrigeration 26 (2003) 707–720
ðA6Þ
where Va is the volumetric flow of air. The sources of uncertainty are density, volumetric flow, and enthalpy difference. The dominant sources of uncertainty overall are volumetric flow and air enthalpy difference, since the density change of the upstream air at the level of temperature uncertainty, 0.1 C, is negligible. The volumetric flow is a function of the pressure drop, temperature, and velocity; however, it strongly depends on the pressure drop across the nozzle. The gauge reading corresponding to the volumetric flow of 18.0 CMM (equal to a front velocity of 1.44 m/s) is 23.0 mm H2O. Two nozzles with a diameter of 100 mm are used. The uncertainty level of volumetric flow of air, the second term of Eq. (A4), is 0.11%. The enthalpy difference is a function of the dry and wet bulb temperatures, but the impact of the wet bulb temperature is stronger than that of the dry bulb temperature. The wet and dry bulb temperature difference has an uncertainty limit of 0.2 C, which give a maximum uncertainty of 2.86% for the minimum enthalpy difference of the 45 test cases. Therefore, the uncertainty of the heat transfer rate from the air side, using Eq. (A4), is 2.9%. The uncertainty level of the air side is larger than that of the refrigerant side. Therefore, the uncertainty level in this study is a maximum of 2.9% because the test conditions of air do not change and the uncertainty level is larger on the air side than on the refrigerant side.
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