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Boiling heat-transfer coefficient variation for R407C inside horizontal tubes of a refrigerating vapour-compression plant’s shell-and-tube evaporator
APPLIED ENERGY
Applied Energy 83 (2006) 239–252
www.elsevier.com/locate/apenergy
Boiling heat-transfer coefficient variation for R407C inside horizontal tubes of a refrigerating vapour-compression plantÕs shell-and-tube evaporator Enrique Torrella a, Joaquı´n Navarro-Esbrı´ a
b,*
, Ramo´n Cabello
b
Department of Applied Thermodynamics, Camino de Vera, 14, Polytechnic University of Valencia, E-46022 Valencia, Spain b Department of Technology, Campus de Riu Sec,University Jaume I, E-12071 Castello´n, Spain Received 7 December 2004; revised 28 January 2005; accepted 29 January 2005 Available online 13 June 2005
Abstract The present paper presents experimental results obtained from a refrigerating vapourcompression plantÕs shell-and-tube (1–2) evaporator working with R407C. Several tests have been carried out to study the influence of the evaporating pressure and the refrigerantÕs mass flow rate on the refrigerantÕs boiling heat-transfer coefficient inside horizontal tubes. This work has been performed by analyzing the variations of the evaporatorÕs overall thermal-resistance, computed using the effectiveness-NTU method, considering the influence of pressure drops and glide at the evaporator, and finally transferring the results and conclusions to the boiling heattransfer coefficient. It has been observed that the variations of the boiling heat-transfer coefficient show a dependence on the evaporating temperature and the refrigerantÕs mass-flow rate, which has been analyzed in the test range. 2005 Elsevier Ltd. All rights reserved. Keywords: Shell-and-tube heat-exchanger; R407C; Boiling heat-transfer coefficient; Overall heat-transfer coefficient; Refrigeration vapour-compression plant
*
Corresponding author. Tel.: +34 964728199; fax: +34 964728106. E-mail address: [email protected] (J. Navarro-Esbrı´).
0306-2619/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2005.01.010
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E. Torrella et al. / Applied Energy 83 (2006) 239–252
Nomenclature A C cp CR G h m N NTU p Q0 R T U
heat-transfer area (m2) heat-capacity rate (kW/kg) specific heat-capacity at constant pressure (kJ/kg K) minimum/maximum capacity rate ratio volumetric flow-rate (m3/s) specific enthalpy (kJ/kg) mass flow-rate (kg/s) compressorÕs rotation speed (r.p.m.) number of transfer units pressure (kPa) cooling capacity, heat-transfer rate (kW) thermal resistance (K/kW) temperature (C) overall heat-transfer coefficient (kW/m2 K)
Greek symbols a heat transfer coefficient (kW/m2 K) /i inside diameter /e outside diameter D change, difference e effectiveness k0 latent heat of evaporation gv compressor volumetric efficiency Subscripts h hot fluid in inlet k condenser out outlet c cold fluid cc counter flow max maximum min minimum 0 evaporator r refrigerant sc secondary coolant
1. Introduction The heat-transfer rate between two fluids in an evaporator is determined by the overall heat-transfer coefficient (U). In order to compute U, it is necessary to estimate
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the heat-transfer coefficient for each fluid, the thermal resistance through the tubeÕs wall and the fouling resistance. Considering on a shell-and-tube evaporator, where the refrigerant flows inside tubes, we can find in the literature several estimations of the boiling heat-transfer coefficient for different refrigerants. For single pure-fluid refrigerants, Chen [1] considers two main mechanisms in the process, nucleate boiling (microscopic) and convective boiling (macroscopic). At the evaporator inlet, the vapour quality is relatively low and nucleate boiling is the dominant heat-transfer mechanism. As the fluid advances inside the evaporator, the vapour quality increases, and also the velocity and convective transport, and this fact causes a major influence of the convective boiling. The correlation presented by Chen was initially developed for vertical tubes, however, it was also proposed for horizontal tubes introducing the Froude number, to take into account the gravitational forces. From the basic mechanisms proposed by Chen, Shah [2] establishes a new correlation distinguishing three stages: one dominated by the nucleate-boiling regime, a second stage of bubble suppression and a third stage dominated by convective boiling. Other works based on the consideration of the two mentioned mechanisms are those presented by Kandlikar [3], Gungor–Winterton [4], and Yoshida et al. [5]. In the case of the boiling heat-transfer coefficient for R407C (R32/125/134 difluoromethane/1,1,1,2-tetrafluoroethane/pentafluoroethane 23/25/52% by mass), the comparison between experimental results and those obtained from correlations presents strong deviations. Aprea et al. [6] have detected a range of deviations of about 30/+20% in 80% of the experimental tests in comparison with Gungor– Winterton correlations and greater deviations comparing the results predicted using the correlations proposed by Chen and Yoshida. In the same way, Boisseux et al. [7] have also detected significant deviations in the correlations proposed for pure fluids. These deviations seem to be caused, for zeotropic blends, by the differences in the boiling process in comparison with pure (single) fluids. For instance, during the evaporation of R407C, the R32 (difluoromethane) proportion diminishes in the liquid near the vapour interface, due to its greater volatility. This fact slows the phase-change process, since this more volatile fluid has to diffuse through the less volatile R134a (1,1,1,2-tetrafluoroethane) before it can vaporize, and this causes the heat-transfer coefficient drops during evaporation [8], and so, the heat-transfer coefficient becomes a function of the blend composition during the boiling process at the evaporator. So, the boiling heat-transfer coefficient evaluation for zeotropic blends presents a greater difficulty. Some authors, like Kaul et al. [9], propose boiling heat-transfer coefficient correlations for R407C inside microfinned tubes, taking into account the molar composition of R32 in each phase. Furthermore, we note that variations in the boiling heat-transfer coefficient due to changes in operating conditions of the facility must also be taken into consideration. Here, the study of the R407C boiling heat-transfer coefficient variations in a refrigerating vapour-compression plant shell-and-tube evaporator with the operating conditions is addressed. Due to the lack of correlations and reliability, these variations are evaluated by means of the evaporator overall heat-transfer coefficient
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behaviour, obtained using the evaporator inlet and outlet temperatures, the refrigerant and secondary fluid mass flow rates and the heat-exchanger configuration.
2. Experimental plant and test procedure Fig. 1 shows a picture of the experimental refrigerating vapour-compression plant. It consists of three loops: the refrigerant loop, the condenser-water loop and the secondary coolant loop. The refrigerant loop is a single-stage vapour-compression cycle working with R407C, including a reciprocating open-type compressor, an oil separator, a condensing section, a liquid-suction heat-exchanger, a thermostatic expansion valve and an evaporating section. The evaporating section consists of an evaporator and a secondary coolant loop, which circulates a water/propylene glycol mixture (50/50% by mass). The evaporator is a shell-and-tube (1–2) heat-exchanger, with the refrigerant R407C inside tubes. The main geometric characteristics of the evaporator are summarized in Table 1. It has to be noted that the evaporator is isolated, a fact that allows one to neglect the heat losses to the ambient environment (maximum error introduced is evaluated as 1.9% of the cooling capacity). The use of microfinned tubes in the evaporator compensates for the necessary increase of heat-exchange surface area due to the low heat-transfer coefficients associated with R407C [10].
Fig. 1. Refrigerating test facility.
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Table 1 EvaporatorÕs main geometric characteristics Tube Number /i//e Thickness of inner microfins Total length External exchange surface Tube-side volume Shell-side volume
76 8.22 · 103/9.52 · 103 m 0.2 · 103 m 0.92 m 1.81 m2 3.3 · 103 m3 8 · 103 m3
The liquid-suction heat-exchanger has been installed in order to minimize the risk of liquid refrigerant presence at the compressor inlet, since in the experimental test a minimum superheating degree at the evaporator outlet was intended in order to consider only refrigerant phase-change and to have a low refrigerant vapour quality at the evaporator inlet. The test apparatus is equipped with the following instrumentation. An inverter is used to control the compressor driven motor, controlling the rotation speed that is measured by a capacitive sensor, with a maximum error after calibration of ±1%. The electrical-power consumption of the compressor is evaluated using a digital Wattmeter (maximum error of ±0.5%). The refrigerantÕs mass-flow rate is measured by a Coriolis-effect mass-flow meter with a certified precision of ±0.22%, while the secondary fluid (water/propylene glycol) mass-flow rate is measured with an electromagnetic flow-meter, with a maximum error of ±0.25%. The sensors used to measure temperature are ‘‘K’’-type thermocouples. They are located on the pipeÕs surface, for refrigerant temperature measurements, or submerged in fluid to measure the secondary coolantÕs temperature. A total of fourteen thermocouples and eight piezoelectric sensors, used to measure pressure, are distributed throughout the plant. In the secondary-fluid side, only the evaporatorÕs inlet and outlet temperatures are registered. The pressure and temperature sensors are calibrated in our own laboratory using certified references, so achieving a degree of uncertainty of 0.3 K in the thermocouples and a precision of 10 kPa in the pressure sensors. With all these measurements, gathered by a data-acquisition system, the thermodynamic states of the refrigerant at each point are provided with the help of our own software based on REFPROP 7.0 subroutines [11]. A more detailed explanation about the refrigeration facility is reported in a previous work [12]. Concerning the test procedure, two types of global tests have been done: Test 1. Evaporating-pressure variation test. The evaporating pressure has been modified, maintaining the constant condensing pressure and the secondary fluid mass-flow rate. Test 2. Compressor rotation speed variation test, keeping constant the compression ratio and the secondary fluid mass flow rate. For each global test, a set of three experiments has been performed. Each experiment consists of three stationary periods of 40 min working at different operating
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variable stages, the sample time interval being fixed to 2 min. The average values of the main operating conditions are summarized in Table 2; the maximum deviation evaluated for each one, during the experimental tests, being of ±5%. When it has been necessary, the condensing pressure has been controlled using a water-regulating valve. The evaporating pressure has been maintained by controlling the evaporator load, modifying the temperature increase of the secondary fluid and maintaining its mass-flow rate. 3. Methodology In this work, the boiling heat-transfer coefficient for R407C inside horizontal tubes is analyzed through the evaporatorÕs overall heat-transfer coefficient, which is obtained using the effectiveness-NTU thermal-design method. This method constitutes an approximation that can be used in the evaporatorÕs thermal-design in spite of breaking some of the initial assumption established in the heat-exchanger thermaldesign method development. Following the evaporating process in a pure fluid, without pressure drops, the heat-exchanger configuration becomes irrelevant, that is, the problem could be treated as a counter-flow configuration. Nevertheless, in the real process with R407C, two considerations have to be taken into account: In the case of zeotropic blends, the phase change leads to a temperature shift (i.e. glide) between bubble and dew point, even if the pressure is maintained perfectly constant. In the presence of pressure drops (actual process), the evaporatorÕs outlet-pressure is lower than the inlet pressure, and then the saturating temperatures corresponding to those pressures are different. Table 2 Average values of the main operating conditions Global test
Experiment
Stage
pK (kPa)
p0 (kPa)
N (r.p.m.)
Gsc (m3/s)
Evaporating-pressure variation
1
1 2 3 1 2 3 1 2 3
1776.96 1778.26 1779.12 1938.21 1935.22 1939.55 2088.57 2079.73 2074.01
364.06 304.27 234.17 390.34 328.30 242.98 412.25 338.18 239.36
578 580 580 578 578 582 578 578 580
0.000706 0.000692 0.000685 0.000635 0.000648 0.000663 0.000664 0.000675 0.000687
1 2 3 1 2 3 1 2 3
1636.91 1639.39 1643.55 1845.08 1845.83 1847.16 1597.66 1592.00 1585.60
380.85 379.14 375.19 412.85 409.21 405.89 366.61 363.40 360.17
578 497 419 577 496 413 582 501 420
0.000177 0.000179 0.000178 0.000215 0.000214 0.000215 0.000241 0.000242 0.000242
2
3
CompressorÕs rotational speed variation
1
2
3
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The heat-exchangerÕs effectiveness can be interpreted as the ratio of the actual heat transferred to the maximum heat that could possibly be exchanged from one stream to the other, that is, assuming that the maximum temperature-difference is given at the minimum heat capacity flow, e¼
Q0 C min ðT h
in
T c in Þ
ð1Þ
.
In a pure fluid, without taking into account the pressure drops given at the evaporator, it can be assumed that the chilled water has the minimum heat capacity, since the heat capacity associated with the refrigerant during the phase change is evaluated as infinite. With this assumption, the evaporator effectiveness can be expressed as e ¼ 1 eNTU ;
ð2Þ
and from (2), the number of transfer units (NTU) can be obtained, once the heat exchanger effectiveness is known, as NTU ¼ lnð1 eÞ.
ð3Þ
However, in the case of having different temperatures at the evaporator inlet and outlet, due to refrigerant temperature glide or pressure drops, the heatexchanger configuration should be considered. So, for shell-and-tube (1–2) heat-exchangers, the effectiveness expression is given by Incropera and DeWitt [13] as 2 3 0. 5 NTUð1þC 2R Þ 1 þ e 0 . 5 5; C R ¼ C min ; e ¼ 241 þ C R þ 1 þ C 2R ð4Þ 0. 5 2 C max 1 eNTUð1þCR Þ being the NTU expression:
NTU ¼ 1 þ
0.5 C 2R
E1 ln ; Eþ1
2 ð1 þ C R Þ E ¼ e 0.5 . 1 þ C 2R
ð5Þ
In this way, once the NTU is obtained, the product of the global heat-transfer coefficient by the heat-transfer area (UA) can be determined using the expression: NTU ¼
UA . C min
ð6Þ
Either the glide or the pressure drops result in a difference between the evaporatorÕs inlet and outlet conditions, a fact that breaks the assumption of constant evaporating temperature and infinite specific heat-capacity. To avoid this problem, the specific heat-capacity of R407C is computed using the following expression [14]: cp0 ¼
h0;out h0;in . T 0;out T 0;in
ð7Þ
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Assuming that the fouling and tubeÕs wall thermal-resistances are constant during the experimental tests, and since the secondary fluid (brine) mass-flow rate has also been maintained constant, we can assume a constant brine convective heattransfer coefficient and, finally, the evaporatorÕs overall thermal resistance, 1/ (UA), can be expressed as a function of the refrigerantÕs boiling heat-transfer coefficient, as follows: R0 ¼
1 1 ¼ þ ðRF þ Rw þ RG Þ. UA a0 A
ð8Þ
So, the variations of the boiling heat-transfer coefficient, a0, can be deduced from the analysis of the overall thermal resistance, since the heat-transfer area is also a constant in the tests.
4. Results and discussion During normal operation, refrigerating and air conditioning facilities operating conditions are modified to follow the load variations. For consideration of this operation, two experimental tests have been carried out to adapt the cooling capacity to the load; one modifying the evaporating pressure and the other adapting the compressorÕs rotation speed. Both tests lead to a refrigerant mass-flow rate variation due to the variation of the compressorÕs volumetric efficiency and suction conditions or the variation of the compressorÕs rotation-speed [12], as it can be deduced from the following expression: mr ¼
NV G gv ; vsuction
ð9Þ
VG being the compressorÕs swept volume and v the compressorÕs suction specific volume. 4.1. Test 1. Evaporating-pressure variation test The objective of this test is to analyze the evolution of the boiling heat-transfer coefficient for R407C inside horizontal tubes when the evaporating pressure (or temperature) is modified. This evaporating pressure-variation involves a compressor ratio variation and then the compressorÕs volumetric efficiency changes, as is shown in Fig. 2, so leading jointly with the compressorÕs suction condition modification to a refrigerant mass-flow rate variation, Fig. 3. In reference to the secondary fluid, its mass-flow rate has been maintained constant during these tests, as can be observed in Fig. 4. Using the effectiveness-NTU thermal-design method, the evaporatorÕs overall thermal-resistance is obtained from the experimental measurements, using the values of the product ‘‘UA’’ observed in Fig. 5. The results show a significant increase of the
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247
1.00
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.90
ηV
0.80
0.70
0.60
0.50 220
240
260
280
300
320 p0 [kPa]
340
360
380
400
420
Fig. 2. Dependence of the R407C compressorÕs volumetric efficiency on the evaporating pressure (Test 1).
0.08 pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
mr [kg/s]
0.07
0.06
0.05
0.04
0.03 220
240
260
280
300
320 340 p0 [kPa]
360
380
400
420
Fig. 3. R407C mass-flow rate variation with the evaporating pressure.
overall thermal resistance (i.e. a decrease of the product UA) and, consequently, a diminution of the boiling heat-transfer coefficient with the evaporating pressure reduction. This fact is a joint consequence of the evaporating-temperatureÕs decrease and the refrigerantÕs mass-flow rate drop. The UA evolution can be included in a logarithmic correlation as a function of the evaporating pressure, fitting adequately as can be seen in Fig. 5.
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0.25 0.24
msc [kg/s]
0.23
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.22 0.21 0.20 0.19 0.18 0.17 220
240
260
280
300
320 p0 [kPa]
340
360
380
400
420
Fig. 4. Dependence of the secondary fluidÕs mass-flow rate on the evaporating pressure.
0.70 UA = 0.6533·ln(p0) - 3.3398
0.60
R2 = 0.9921
UA [kW/K]
0.50 0.40 0.30
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.20 0.10 220
270
320 p0 [kPa]
370
420
Fig. 5. Dependence of the UA value during the evaporating-pressure variation test.
4.2. Test 2. Compressor rotation speed variation test Refrigerating and air-conditioning systems are designed to satisfy maximum loads, however, they mostly operate at partial load. One efficient technique to adapt the system to the load requirements is to vary the compressorÕs rotation-speed. The consideration of this regulating technique leads us to study the variation of the R407C boiling heat-transfer coefficient when the compressor rotation speed is modified.
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249
When the compressorÕs rotation-speed is modified, two effects can be observed, first the evident variation of the refrigerant mass flow rate due to the new rotation speed, and secondly a little mass-flow rate modification due to the compressorÕs volumetric efficiency change with the rotation speed, Fig. 6. Finally, the refrigerantÕs mass-flow rate variation during each test is shown in Fig. 7. Again the secondary fluid mass-flow rates are maintained constant for each test, as can be seen in Fig. 8. So, the R407C boiling heat-transfer evolution can be deduced from the evaporatorÕs overall thermal-resistance obtained from experimental 0.9 0.85
ηV
0.8 0.75 0.7
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa;p0 = 369.06 kPa
0.65 0.6 350
pk = 1809.52 kPa; p0 = 400.01 kPa
400
450 N [r.p.m.]
500
550
600
Fig. 6. CompressorÕs volumetric efficiency with the compressorÕs rotation-speed N.
0.10 0.09
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06 kPa
mr [kg/s]
0.08
pk = 1809.52 kPa; p0 = 400.01 kPa
0.07 0.06 0.05 0.04 0.03 350
400
450
500
550
600
N [r.p.m.] Fig. 7. Variation of the R407C mass-flow rate with the compressorÕs rotation-speed.
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E. Torrella et al. / Applied Energy 83 (2006) 239–252 0.30
msc [kg/s]
0.25
0.20
0.15
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06kPa pk = 1809.52 kPa; p0 = 400.01 kPa
0.10 350
400
450
500
550
600
N [r.p.m.]
Fig. 8. Dependence of the secondary fluidÕs mass-flow rates on the compressorÕs rotation-speed.
measurements using the methodology described before, and based on the effectiveness-NTU thermal-design method. The values of the inverse of the evaporatorÕs overall thermal-resistance, that is the product UA for R407C at different compressor rotation-speeds, are presented in Fig. 9 as a function of the refrigerantÕs mass-flow rate for the three values of the evaporating pressure. Evidently, the higher the value of the brineÕs mass-flow rate, the higher the value of UA, since the brineÕs convective thermal-resistance is reduced.
0.60
UA [kW/K]
0.50
0.40 pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06 kPa pk = 1809.52 kPa; p0 = 400.01 kPa 0.30 0.045
0.05
0.055
0.06 0.065 mr [kg/s]
0.07
Fig. 9. UA vs refrigerantÕs mass-flow rate.
0.075
0.08
E. Torrella et al. / Applied Energy 83 (2006) 239–252
251
Table 3 Comparison of tests results for similar fluids mass-flow rates
mr (kg/s) msc (kg/s) p0 (kPa) UA (kW/K)
Test 1 (Dp0)
Test 2 (DN)
0.054–0.077 0.21 298.35–405.59 0.397–0.563
0.054–0.077 0.22 400.01 0.451–0.514
For a constant value of the evaporating pressure, a logarithmic variation of the inverse of the overall thermal-resistance is observed, and so a UA reduction takes place when decreasing the refrigerant mass-flow rate. Now, comparing the results obtained from Test 1 and Test 2 for the same range of refrigerant mass-flow rates and similar brine mass-flow rates (Table 3), we can find a difference of 0.166 K/kW in the evaporatorÕs UA during the evaporating pressure variation test, while the drop of the evaporatorÕs UA observed for the compressor rotation-speed variation test, at a evaporating pressure of 400 kPa, is about 0.0632 K/kW. Since the refrigerantÕs mass-flow rate variation is the same in the two tests, the difference found for the overall thermal-resistance increment is caused by the different evaporating temperatures. So, in the operating range tested, it can be concluded from the experimental tests that the increase of the evaporatorÕs UA is caused by the increment in the refrigerantÕs mass-flow rate (about 38%) and by the variation of the evaporating temperature (62%), being then more significant than the influence of the evaporating temperature on the boiling heat-transfer coefficient for R407C.
5. Conclusions The influence of the refrigerantÕs mass-flow rate (compressor rotation speed) and evaporating temperature (pressure) on the boiling heat-transfer coefficient for R407C inside horizontal tubes in a shell-and-tube (1–2) evaporator has been analyzed by means of the evaporatorÕs overall thermal-resistance, obtained from experimental results using a corrected finite refrigerant specific-heat-capacity in the effectiveness-NTU method. The experimental tests, evaporating pressure variation test and compressor rotation speed variation test, maintaining the secondary fluidÕs mass-flow rate, allow us to associate the variations of the evaporatorÕs overall thermal-resistance with the variations of the R407C boiling heat-transfer coefficient, which shows a clear dependence upon the evaporating temperature and refrigerantÕs mass-flow rate. Finally, comparing two experiments with the same refrigerant mass-flow rate variation, and with similar brine mass-flow rate, it is concluded that the evaporating temperature has a more significant influence on the boiling heat-transfer coefficient than the refrigerantÕs mass-flow rate in the test range.
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Acknowledgement The authors are indebted to the Generalitat Valenciana for partial support under project GVA01-100.
References [1] Chen JC. Correlation for boiling heat-transfer to saturated fluids in convective flow. Indust Eng Process Design Develop 1966;5-3:322–9. [2] Shah MM. Chart correlation for saturated boiling heat-transfer: equations and further study. ASHRAE Trans 1982;88-1:185–96. [3] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat-transfer inside horizontal and vertical tubes. J Heat Transfer 1989;112:219–28. [4] Gungor KE, Winterton RHS. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Transfer 1986;29:351–8. [5] Yoshida S, Mari H, Hong H, Matsunaga T. Prediction of heat-transfer coefficients for refrigerants flowing in horizontal evaporation tubes. Trans JAR 1994;11:67–78. [6] Aprea C, de Rossi F, Greco A. Experimental evaluation of R22 and R407C evaporative heat-transfer coefficients in a vapour-compression plant. Int J Refrigerat 2000;23:366–77. [7] Boissieux X, Heikal MR, Johns RA. Two-phase heat-transfer coefficients of three HFC refrigerants inside a horizontal smooth tube, part I: evaporation: Coefficient dÕe´change diphasiques de trois fluides frigorifiques HFC a` lÕinte´rieur dÕun tube lisse horizontal, premie`re partie: e´vaporation. Int J Refrigerat 2000;23-4:269–83. [8] Didion DA. The influence of the thermophysical fluid properties of the new ozone-safe refrigerants on performance. Int J Appl Thermodyn 1999;2-1:19–35. [9] Kaul MP, Kedzierski MA, Didion DA. Process enhanced and multiphase heat-transfer. In: Manglik RM, Kraus AD (Eds.), Proceedings of a symposium in honor of Professor Arthur E. Bergles, Georgia Institute of Technology, Begell House, Inc., New York, USA, 1996. p. 167–73. [10] Lallemand M, Branescu C, Haberschill P. Coeffcients dÕe´change locaux au cours de lÕe´bullition du R22 et du R407C dans des tubes horizontaux, lisse ou micro-ailete´. Int J Refrigerat 2001;24:57–72. [11] Lemmon EW, McLinden MO, Huber ML. REFPROP, version 7.0, NIST properties of refrigerants and refrigerant mixtures, NIST standard reference data-base 23 Standard Reference Data Program. Gaithersburg, MD: US Department of Commerce; 2002. [12] Cabello R, Torrella E, Navarro-Esbrı´ J. Experimental evaluation of a vapour-compression plant performance using R134a, R407C and R22 as working fluids. Appl Thermal Eng 2004;24-13:1905–17. [13] Incropera FP, DeWitt DP. Fundamentals of heat and mass transfer. New York: John Wiley; 2001. [14] Torrella E, Cabello R, Navarro-Esbrı´ J. Considerations about an evaporatorÕs thermal-design in a vapour-compression liquid chiller. Experimental analysis with HFC fluids (R134a and R407C). Int J Energy Res 2004;28-15.
Applied Energy 83 (2006) 239–252
www.elsevier.com/locate/apenergy
Boiling heat-transfer coefficient variation for R407C inside horizontal tubes of a refrigerating vapour-compression plantÕs shell-and-tube evaporator Enrique Torrella a, Joaquı´n Navarro-Esbrı´ a
b,*
, Ramo´n Cabello
b
Department of Applied Thermodynamics, Camino de Vera, 14, Polytechnic University of Valencia, E-46022 Valencia, Spain b Department of Technology, Campus de Riu Sec,University Jaume I, E-12071 Castello´n, Spain Received 7 December 2004; revised 28 January 2005; accepted 29 January 2005 Available online 13 June 2005
Abstract The present paper presents experimental results obtained from a refrigerating vapourcompression plantÕs shell-and-tube (1–2) evaporator working with R407C. Several tests have been carried out to study the influence of the evaporating pressure and the refrigerantÕs mass flow rate on the refrigerantÕs boiling heat-transfer coefficient inside horizontal tubes. This work has been performed by analyzing the variations of the evaporatorÕs overall thermal-resistance, computed using the effectiveness-NTU method, considering the influence of pressure drops and glide at the evaporator, and finally transferring the results and conclusions to the boiling heattransfer coefficient. It has been observed that the variations of the boiling heat-transfer coefficient show a dependence on the evaporating temperature and the refrigerantÕs mass-flow rate, which has been analyzed in the test range. 2005 Elsevier Ltd. All rights reserved. Keywords: Shell-and-tube heat-exchanger; R407C; Boiling heat-transfer coefficient; Overall heat-transfer coefficient; Refrigeration vapour-compression plant
*
Corresponding author. Tel.: +34 964728199; fax: +34 964728106. E-mail address: [email protected] (J. Navarro-Esbrı´).
0306-2619/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2005.01.010
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E. Torrella et al. / Applied Energy 83 (2006) 239–252
Nomenclature A C cp CR G h m N NTU p Q0 R T U
heat-transfer area (m2) heat-capacity rate (kW/kg) specific heat-capacity at constant pressure (kJ/kg K) minimum/maximum capacity rate ratio volumetric flow-rate (m3/s) specific enthalpy (kJ/kg) mass flow-rate (kg/s) compressorÕs rotation speed (r.p.m.) number of transfer units pressure (kPa) cooling capacity, heat-transfer rate (kW) thermal resistance (K/kW) temperature (C) overall heat-transfer coefficient (kW/m2 K)
Greek symbols a heat transfer coefficient (kW/m2 K) /i inside diameter /e outside diameter D change, difference e effectiveness k0 latent heat of evaporation gv compressor volumetric efficiency Subscripts h hot fluid in inlet k condenser out outlet c cold fluid cc counter flow max maximum min minimum 0 evaporator r refrigerant sc secondary coolant
1. Introduction The heat-transfer rate between two fluids in an evaporator is determined by the overall heat-transfer coefficient (U). In order to compute U, it is necessary to estimate
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the heat-transfer coefficient for each fluid, the thermal resistance through the tubeÕs wall and the fouling resistance. Considering on a shell-and-tube evaporator, where the refrigerant flows inside tubes, we can find in the literature several estimations of the boiling heat-transfer coefficient for different refrigerants. For single pure-fluid refrigerants, Chen [1] considers two main mechanisms in the process, nucleate boiling (microscopic) and convective boiling (macroscopic). At the evaporator inlet, the vapour quality is relatively low and nucleate boiling is the dominant heat-transfer mechanism. As the fluid advances inside the evaporator, the vapour quality increases, and also the velocity and convective transport, and this fact causes a major influence of the convective boiling. The correlation presented by Chen was initially developed for vertical tubes, however, it was also proposed for horizontal tubes introducing the Froude number, to take into account the gravitational forces. From the basic mechanisms proposed by Chen, Shah [2] establishes a new correlation distinguishing three stages: one dominated by the nucleate-boiling regime, a second stage of bubble suppression and a third stage dominated by convective boiling. Other works based on the consideration of the two mentioned mechanisms are those presented by Kandlikar [3], Gungor–Winterton [4], and Yoshida et al. [5]. In the case of the boiling heat-transfer coefficient for R407C (R32/125/134 difluoromethane/1,1,1,2-tetrafluoroethane/pentafluoroethane 23/25/52% by mass), the comparison between experimental results and those obtained from correlations presents strong deviations. Aprea et al. [6] have detected a range of deviations of about 30/+20% in 80% of the experimental tests in comparison with Gungor– Winterton correlations and greater deviations comparing the results predicted using the correlations proposed by Chen and Yoshida. In the same way, Boisseux et al. [7] have also detected significant deviations in the correlations proposed for pure fluids. These deviations seem to be caused, for zeotropic blends, by the differences in the boiling process in comparison with pure (single) fluids. For instance, during the evaporation of R407C, the R32 (difluoromethane) proportion diminishes in the liquid near the vapour interface, due to its greater volatility. This fact slows the phase-change process, since this more volatile fluid has to diffuse through the less volatile R134a (1,1,1,2-tetrafluoroethane) before it can vaporize, and this causes the heat-transfer coefficient drops during evaporation [8], and so, the heat-transfer coefficient becomes a function of the blend composition during the boiling process at the evaporator. So, the boiling heat-transfer coefficient evaluation for zeotropic blends presents a greater difficulty. Some authors, like Kaul et al. [9], propose boiling heat-transfer coefficient correlations for R407C inside microfinned tubes, taking into account the molar composition of R32 in each phase. Furthermore, we note that variations in the boiling heat-transfer coefficient due to changes in operating conditions of the facility must also be taken into consideration. Here, the study of the R407C boiling heat-transfer coefficient variations in a refrigerating vapour-compression plant shell-and-tube evaporator with the operating conditions is addressed. Due to the lack of correlations and reliability, these variations are evaluated by means of the evaporator overall heat-transfer coefficient
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behaviour, obtained using the evaporator inlet and outlet temperatures, the refrigerant and secondary fluid mass flow rates and the heat-exchanger configuration.
2. Experimental plant and test procedure Fig. 1 shows a picture of the experimental refrigerating vapour-compression plant. It consists of three loops: the refrigerant loop, the condenser-water loop and the secondary coolant loop. The refrigerant loop is a single-stage vapour-compression cycle working with R407C, including a reciprocating open-type compressor, an oil separator, a condensing section, a liquid-suction heat-exchanger, a thermostatic expansion valve and an evaporating section. The evaporating section consists of an evaporator and a secondary coolant loop, which circulates a water/propylene glycol mixture (50/50% by mass). The evaporator is a shell-and-tube (1–2) heat-exchanger, with the refrigerant R407C inside tubes. The main geometric characteristics of the evaporator are summarized in Table 1. It has to be noted that the evaporator is isolated, a fact that allows one to neglect the heat losses to the ambient environment (maximum error introduced is evaluated as 1.9% of the cooling capacity). The use of microfinned tubes in the evaporator compensates for the necessary increase of heat-exchange surface area due to the low heat-transfer coefficients associated with R407C [10].
Fig. 1. Refrigerating test facility.
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Table 1 EvaporatorÕs main geometric characteristics Tube Number /i//e Thickness of inner microfins Total length External exchange surface Tube-side volume Shell-side volume
76 8.22 · 103/9.52 · 103 m 0.2 · 103 m 0.92 m 1.81 m2 3.3 · 103 m3 8 · 103 m3
The liquid-suction heat-exchanger has been installed in order to minimize the risk of liquid refrigerant presence at the compressor inlet, since in the experimental test a minimum superheating degree at the evaporator outlet was intended in order to consider only refrigerant phase-change and to have a low refrigerant vapour quality at the evaporator inlet. The test apparatus is equipped with the following instrumentation. An inverter is used to control the compressor driven motor, controlling the rotation speed that is measured by a capacitive sensor, with a maximum error after calibration of ±1%. The electrical-power consumption of the compressor is evaluated using a digital Wattmeter (maximum error of ±0.5%). The refrigerantÕs mass-flow rate is measured by a Coriolis-effect mass-flow meter with a certified precision of ±0.22%, while the secondary fluid (water/propylene glycol) mass-flow rate is measured with an electromagnetic flow-meter, with a maximum error of ±0.25%. The sensors used to measure temperature are ‘‘K’’-type thermocouples. They are located on the pipeÕs surface, for refrigerant temperature measurements, or submerged in fluid to measure the secondary coolantÕs temperature. A total of fourteen thermocouples and eight piezoelectric sensors, used to measure pressure, are distributed throughout the plant. In the secondary-fluid side, only the evaporatorÕs inlet and outlet temperatures are registered. The pressure and temperature sensors are calibrated in our own laboratory using certified references, so achieving a degree of uncertainty of 0.3 K in the thermocouples and a precision of 10 kPa in the pressure sensors. With all these measurements, gathered by a data-acquisition system, the thermodynamic states of the refrigerant at each point are provided with the help of our own software based on REFPROP 7.0 subroutines [11]. A more detailed explanation about the refrigeration facility is reported in a previous work [12]. Concerning the test procedure, two types of global tests have been done: Test 1. Evaporating-pressure variation test. The evaporating pressure has been modified, maintaining the constant condensing pressure and the secondary fluid mass-flow rate. Test 2. Compressor rotation speed variation test, keeping constant the compression ratio and the secondary fluid mass flow rate. For each global test, a set of three experiments has been performed. Each experiment consists of three stationary periods of 40 min working at different operating
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variable stages, the sample time interval being fixed to 2 min. The average values of the main operating conditions are summarized in Table 2; the maximum deviation evaluated for each one, during the experimental tests, being of ±5%. When it has been necessary, the condensing pressure has been controlled using a water-regulating valve. The evaporating pressure has been maintained by controlling the evaporator load, modifying the temperature increase of the secondary fluid and maintaining its mass-flow rate. 3. Methodology In this work, the boiling heat-transfer coefficient for R407C inside horizontal tubes is analyzed through the evaporatorÕs overall heat-transfer coefficient, which is obtained using the effectiveness-NTU thermal-design method. This method constitutes an approximation that can be used in the evaporatorÕs thermal-design in spite of breaking some of the initial assumption established in the heat-exchanger thermaldesign method development. Following the evaporating process in a pure fluid, without pressure drops, the heat-exchanger configuration becomes irrelevant, that is, the problem could be treated as a counter-flow configuration. Nevertheless, in the real process with R407C, two considerations have to be taken into account: In the case of zeotropic blends, the phase change leads to a temperature shift (i.e. glide) between bubble and dew point, even if the pressure is maintained perfectly constant. In the presence of pressure drops (actual process), the evaporatorÕs outlet-pressure is lower than the inlet pressure, and then the saturating temperatures corresponding to those pressures are different. Table 2 Average values of the main operating conditions Global test
Experiment
Stage
pK (kPa)
p0 (kPa)
N (r.p.m.)
Gsc (m3/s)
Evaporating-pressure variation
1
1 2 3 1 2 3 1 2 3
1776.96 1778.26 1779.12 1938.21 1935.22 1939.55 2088.57 2079.73 2074.01
364.06 304.27 234.17 390.34 328.30 242.98 412.25 338.18 239.36
578 580 580 578 578 582 578 578 580
0.000706 0.000692 0.000685 0.000635 0.000648 0.000663 0.000664 0.000675 0.000687
1 2 3 1 2 3 1 2 3
1636.91 1639.39 1643.55 1845.08 1845.83 1847.16 1597.66 1592.00 1585.60
380.85 379.14 375.19 412.85 409.21 405.89 366.61 363.40 360.17
578 497 419 577 496 413 582 501 420
0.000177 0.000179 0.000178 0.000215 0.000214 0.000215 0.000241 0.000242 0.000242
2
3
CompressorÕs rotational speed variation
1
2
3
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The heat-exchangerÕs effectiveness can be interpreted as the ratio of the actual heat transferred to the maximum heat that could possibly be exchanged from one stream to the other, that is, assuming that the maximum temperature-difference is given at the minimum heat capacity flow, e¼
Q0 C min ðT h
in
T c in Þ
ð1Þ
.
In a pure fluid, without taking into account the pressure drops given at the evaporator, it can be assumed that the chilled water has the minimum heat capacity, since the heat capacity associated with the refrigerant during the phase change is evaluated as infinite. With this assumption, the evaporator effectiveness can be expressed as e ¼ 1 eNTU ;
ð2Þ
and from (2), the number of transfer units (NTU) can be obtained, once the heat exchanger effectiveness is known, as NTU ¼ lnð1 eÞ.
ð3Þ
However, in the case of having different temperatures at the evaporator inlet and outlet, due to refrigerant temperature glide or pressure drops, the heatexchanger configuration should be considered. So, for shell-and-tube (1–2) heat-exchangers, the effectiveness expression is given by Incropera and DeWitt [13] as 2 3 0. 5 NTUð1þC 2R Þ 1 þ e 0 . 5 5; C R ¼ C min ; e ¼ 241 þ C R þ 1 þ C 2R ð4Þ 0. 5 2 C max 1 eNTUð1þCR Þ being the NTU expression:
NTU ¼ 1 þ
0.5 C 2R
E1 ln ; Eþ1
2 ð1 þ C R Þ E ¼ e 0.5 . 1 þ C 2R
ð5Þ
In this way, once the NTU is obtained, the product of the global heat-transfer coefficient by the heat-transfer area (UA) can be determined using the expression: NTU ¼
UA . C min
ð6Þ
Either the glide or the pressure drops result in a difference between the evaporatorÕs inlet and outlet conditions, a fact that breaks the assumption of constant evaporating temperature and infinite specific heat-capacity. To avoid this problem, the specific heat-capacity of R407C is computed using the following expression [14]: cp0 ¼
h0;out h0;in . T 0;out T 0;in
ð7Þ
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Assuming that the fouling and tubeÕs wall thermal-resistances are constant during the experimental tests, and since the secondary fluid (brine) mass-flow rate has also been maintained constant, we can assume a constant brine convective heattransfer coefficient and, finally, the evaporatorÕs overall thermal resistance, 1/ (UA), can be expressed as a function of the refrigerantÕs boiling heat-transfer coefficient, as follows: R0 ¼
1 1 ¼ þ ðRF þ Rw þ RG Þ. UA a0 A
ð8Þ
So, the variations of the boiling heat-transfer coefficient, a0, can be deduced from the analysis of the overall thermal resistance, since the heat-transfer area is also a constant in the tests.
4. Results and discussion During normal operation, refrigerating and air conditioning facilities operating conditions are modified to follow the load variations. For consideration of this operation, two experimental tests have been carried out to adapt the cooling capacity to the load; one modifying the evaporating pressure and the other adapting the compressorÕs rotation speed. Both tests lead to a refrigerant mass-flow rate variation due to the variation of the compressorÕs volumetric efficiency and suction conditions or the variation of the compressorÕs rotation-speed [12], as it can be deduced from the following expression: mr ¼
NV G gv ; vsuction
ð9Þ
VG being the compressorÕs swept volume and v the compressorÕs suction specific volume. 4.1. Test 1. Evaporating-pressure variation test The objective of this test is to analyze the evolution of the boiling heat-transfer coefficient for R407C inside horizontal tubes when the evaporating pressure (or temperature) is modified. This evaporating pressure-variation involves a compressor ratio variation and then the compressorÕs volumetric efficiency changes, as is shown in Fig. 2, so leading jointly with the compressorÕs suction condition modification to a refrigerant mass-flow rate variation, Fig. 3. In reference to the secondary fluid, its mass-flow rate has been maintained constant during these tests, as can be observed in Fig. 4. Using the effectiveness-NTU thermal-design method, the evaporatorÕs overall thermal-resistance is obtained from the experimental measurements, using the values of the product ‘‘UA’’ observed in Fig. 5. The results show a significant increase of the
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1.00
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.90
ηV
0.80
0.70
0.60
0.50 220
240
260
280
300
320 p0 [kPa]
340
360
380
400
420
Fig. 2. Dependence of the R407C compressorÕs volumetric efficiency on the evaporating pressure (Test 1).
0.08 pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
mr [kg/s]
0.07
0.06
0.05
0.04
0.03 220
240
260
280
300
320 340 p0 [kPa]
360
380
400
420
Fig. 3. R407C mass-flow rate variation with the evaporating pressure.
overall thermal resistance (i.e. a decrease of the product UA) and, consequently, a diminution of the boiling heat-transfer coefficient with the evaporating pressure reduction. This fact is a joint consequence of the evaporating-temperatureÕs decrease and the refrigerantÕs mass-flow rate drop. The UA evolution can be included in a logarithmic correlation as a function of the evaporating pressure, fitting adequately as can be seen in Fig. 5.
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0.25 0.24
msc [kg/s]
0.23
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.22 0.21 0.20 0.19 0.18 0.17 220
240
260
280
300
320 p0 [kPa]
340
360
380
400
420
Fig. 4. Dependence of the secondary fluidÕs mass-flow rate on the evaporating pressure.
0.70 UA = 0.6533·ln(p0) - 3.3398
0.60
R2 = 0.9921
UA [kW/K]
0.50 0.40 0.30
pk = 1529.04 kPa pk = 1684.25 kPa pk = 1822.16 kPa
0.20 0.10 220
270
320 p0 [kPa]
370
420
Fig. 5. Dependence of the UA value during the evaporating-pressure variation test.
4.2. Test 2. Compressor rotation speed variation test Refrigerating and air-conditioning systems are designed to satisfy maximum loads, however, they mostly operate at partial load. One efficient technique to adapt the system to the load requirements is to vary the compressorÕs rotation-speed. The consideration of this regulating technique leads us to study the variation of the R407C boiling heat-transfer coefficient when the compressor rotation speed is modified.
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When the compressorÕs rotation-speed is modified, two effects can be observed, first the evident variation of the refrigerant mass flow rate due to the new rotation speed, and secondly a little mass-flow rate modification due to the compressorÕs volumetric efficiency change with the rotation speed, Fig. 6. Finally, the refrigerantÕs mass-flow rate variation during each test is shown in Fig. 7. Again the secondary fluid mass-flow rates are maintained constant for each test, as can be seen in Fig. 8. So, the R407C boiling heat-transfer evolution can be deduced from the evaporatorÕs overall thermal-resistance obtained from experimental 0.9 0.85
ηV
0.8 0.75 0.7
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa;p0 = 369.06 kPa
0.65 0.6 350
pk = 1809.52 kPa; p0 = 400.01 kPa
400
450 N [r.p.m.]
500
550
600
Fig. 6. CompressorÕs volumetric efficiency with the compressorÕs rotation-speed N.
0.10 0.09
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06 kPa
mr [kg/s]
0.08
pk = 1809.52 kPa; p0 = 400.01 kPa
0.07 0.06 0.05 0.04 0.03 350
400
450
500
550
600
N [r.p.m.] Fig. 7. Variation of the R407C mass-flow rate with the compressorÕs rotation-speed.
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msc [kg/s]
0.25
0.20
0.15
pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06kPa pk = 1809.52 kPa; p0 = 400.01 kPa
0.10 350
400
450
500
550
600
N [r.p.m.]
Fig. 8. Dependence of the secondary fluidÕs mass-flow rates on the compressorÕs rotation-speed.
measurements using the methodology described before, and based on the effectiveness-NTU thermal-design method. The values of the inverse of the evaporatorÕs overall thermal-resistance, that is the product UA for R407C at different compressor rotation-speeds, are presented in Fig. 9 as a function of the refrigerantÕs mass-flow rate for the three values of the evaporating pressure. Evidently, the higher the value of the brineÕs mass-flow rate, the higher the value of UA, since the brineÕs convective thermal-resistance is reduced.
0.60
UA [kW/K]
0.50
0.40 pk = 1555.74 kPa; p0 = 354.92 kPa pk = 1602.18 kPa; p0 = 369.06 kPa pk = 1809.52 kPa; p0 = 400.01 kPa 0.30 0.045
0.05
0.055
0.06 0.065 mr [kg/s]
0.07
Fig. 9. UA vs refrigerantÕs mass-flow rate.
0.075
0.08
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Table 3 Comparison of tests results for similar fluids mass-flow rates
mr (kg/s) msc (kg/s) p0 (kPa) UA (kW/K)
Test 1 (Dp0)
Test 2 (DN)
0.054–0.077 0.21 298.35–405.59 0.397–0.563
0.054–0.077 0.22 400.01 0.451–0.514
For a constant value of the evaporating pressure, a logarithmic variation of the inverse of the overall thermal-resistance is observed, and so a UA reduction takes place when decreasing the refrigerant mass-flow rate. Now, comparing the results obtained from Test 1 and Test 2 for the same range of refrigerant mass-flow rates and similar brine mass-flow rates (Table 3), we can find a difference of 0.166 K/kW in the evaporatorÕs UA during the evaporating pressure variation test, while the drop of the evaporatorÕs UA observed for the compressor rotation-speed variation test, at a evaporating pressure of 400 kPa, is about 0.0632 K/kW. Since the refrigerantÕs mass-flow rate variation is the same in the two tests, the difference found for the overall thermal-resistance increment is caused by the different evaporating temperatures. So, in the operating range tested, it can be concluded from the experimental tests that the increase of the evaporatorÕs UA is caused by the increment in the refrigerantÕs mass-flow rate (about 38%) and by the variation of the evaporating temperature (62%), being then more significant than the influence of the evaporating temperature on the boiling heat-transfer coefficient for R407C.
5. Conclusions The influence of the refrigerantÕs mass-flow rate (compressor rotation speed) and evaporating temperature (pressure) on the boiling heat-transfer coefficient for R407C inside horizontal tubes in a shell-and-tube (1–2) evaporator has been analyzed by means of the evaporatorÕs overall thermal-resistance, obtained from experimental results using a corrected finite refrigerant specific-heat-capacity in the effectiveness-NTU method. The experimental tests, evaporating pressure variation test and compressor rotation speed variation test, maintaining the secondary fluidÕs mass-flow rate, allow us to associate the variations of the evaporatorÕs overall thermal-resistance with the variations of the R407C boiling heat-transfer coefficient, which shows a clear dependence upon the evaporating temperature and refrigerantÕs mass-flow rate. Finally, comparing two experiments with the same refrigerant mass-flow rate variation, and with similar brine mass-flow rate, it is concluded that the evaporating temperature has a more significant influence on the boiling heat-transfer coefficient than the refrigerantÕs mass-flow rate in the test range.
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Acknowledgement The authors are indebted to the Generalitat Valenciana for partial support under project GVA01-100.
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