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Heat transfer and pressure drop during condensation of R152a in circular and square microchannels
Experimental Thermal and Fluid Science 47 (2013) 60–67
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Heat transfer and pressure drop during condensation of R152a in circular and square microchannels Na Liu a, Jun Ming Li a,⇑, Jie Sun b, Hua Sheng Wang b a b
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK
a r t i c l e
i n f o
Article history: Received 15 August 2012 Received in revised form 2 November 2012 Accepted 3 January 2013 Available online 16 January 2013 Keywords: Condensation Heat transfer Microchannel R152a Pressure drop
a b s t r a c t The paper reports experimental data for heat transfer and pressure drop during condensation of R152a in circular and square microchannels with hydraulic diameters of 1.152 mm and 0.952 mm, respectively. Saturation temperatures are 40 °C and 50 °C with mass fluxes varying from 200 to 800 kg/m2 s and vapor mass qualities from 0.1 to 0.9. Effects of mass flux, vapor mass quality and channel geometry on heat transfer and pressure drop were investigated. The results show that heat-transfer coefficients and pressure drop both increase with increasing mass flux and vapor mass quality while decrease with increasing saturation temperature. Channel geometry has much effect on heat transfer at low mass fluxes while has little effect on pressure drop. The present data were compared with earlier empirical correlations and a theoretical solution. Heat transfer coefficients agree within experimental error with several correlations and a theoretical solution for both circular and square microchannels. One pressure drop correlation underestimates the data for the two microchannels while another pressure drop correlation overestimates the data for the square microchannel. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Microchannels are increasingly used to improve heat-transfer performance and to enable compact geometries in many applications. For condensation, owing to surface tension effects, methods used to treat larger channels are not suitable when channel dimension is around 1 mm or less. Recently, increasing attention on environmental issues has brought substantial requirements and changes in refrigerants. Though HFCs substitutes have no ozone depletion potential (ODP), many of them have relatively high global warming potential (GWP). Moreover, the European Union’s F-gas regulations specify beginning on January 1, 2011 new models and on January 1, 2017 new vehicles fitted with air conditioning cannot be manufactured with fluorinated greenhouse gases having GWP greater than 150 [1,2]. Su et al. [3] reviewed earlier experimental work during condensation in microchannels. In many of the earlier heat-transfer measurements, most fluids are with similar properties, predominantly R134a. Vapor-side heat-transfer coefficients have generally been inferred from overall measurements by subtraction of thermal resistance or using Wilson plot techniques [4]. Such data have high uncertainty. ⇑ Corresponding author. Tel.: +86 10 62771001; fax: +86 10 62770209. E-mail address: [email protected] (J.M. Li). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.01.002
Recently, heat-transfer coefficients with various refrigerants were obtained from direct measurement of wall temperatures during condensation in circular and non-circular microchannels. Matkovic et al. [5–8] measured heat-transfer coefficients and pressure drop of R134a, R32, R1234yf and R245fa in a circular 0.96 mm microchannel. Del Col et al. [9] measured heat-transfer coefficients of R134a in a 1.18 mm side length square microchannel. Heattransfer coefficients of R134a were obtained by Derby et al. [10] during condensation in 1 mm square, triangular and semicircular multiple parallel minichannels. Mass flux and quality were determined to have significant effects on the condensation process, even at lower mass fluxes, while saturation pressure, heat flux, and channel shape had no significant effects. Kim and Mudawar [11] proposed a theoretical control-volume-based model based on the assumptions of smooth interface between the annular liquid film and vapor core, and uniform liquid film thickness around the channel’s circumference. The new model accurately captures the pressure drop and heat transfer coefficients in both magnitude and trend. Kim et al. [12,13] experimentally investigated flow regimes, pressure drop and heat transfer of FC-72 during condensation along parallel, square micro-channels with a hydraulic diameter of 1 mm. In their study, smooth-annular, wavy-annular, transition, slug, and bubbly flow regimes were identified. A detailed pressure model was presented and assessment of pressure drop correlations was conducted. Comparing the data to predictions of previous annular condensation heat transfer correlations showed correla-
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Nomenclature a a.m. A b Cc d dh G f h hlv I k l m N Nu U p Q r.m.s. Ra Re T
data referring to a or dp/dl, see Eqs. (12) and (13) arithmetic mean error cross sectional area of channel (m2) side length of square channel (m) coefficient of contraction, see Eq. (8) diameter of circular channel (m) hydraulic diameter (m) mass flux (kg/m2 s) friction factor specific enthalpy (J/kg) specific enthalpy of evaporation (J/kg) electric current (A) thermal conductivity (W/m K) length (m) mass flow rate (kg/s) number of data points Nusselt number, adh/kl electric voltage (V) pressure (Pa) heat transfer rate (W) root-mean-square error arithmetical mean deviation of the assessed profile (lm) Reynolds number, Gdh/ll temperature (K)
tions intended for macro-channels generally provided better predictions than correlations intended for mini/micro-channels. Besides, a new condensation heat transfer correlation was proposed for annular condensation heat transfer in mini/micro-channels. Agarwal et al. [14] used thermal amplification technique to measure heat-transfer coefficients of R134a in six non-circular horizontal microchannels. Saturation and environmental properties of R22, R134a and R152a are listed in Table 1. R152a and R134a have zero ozone depletion potentials. Global warming potential of R152a is 120, which is an order of magnitude lower than those of R22 and R134a. It is noted that thermal conductivity, latent heat and surface tension are higher for R152a than for R22 and R134a. Wang et al. [15] theoretically studied heat-transfer coefficients of R22, R134a and R152a during condensation. According to their results, heat-transfer coefficients of R152a are higher than those of R22 and R134a. Therefore, R152a is a potential substitute for R22. However, to the authors’ knowledge, there are no experimental studies on heat transfer and pressure drop during condensation of R152a in microchannels. In the present paper, heat transfer and pressure drop are investigated experimentally during condensation of R152a in a circular and a square microchannels. Experiments are performed at saturation temperatures of 40 °C and 50 °C with mass fluxes from 200 to 800 kg/m2 s and vapor mass qualities from 0.1 to 0.9. Effects of mass flux, vapor mass quality and channel geometry on heat transfer and pressure drop are presented in the paper.
Greek symbols heat-transfer coefficient (W/m2 K) area ratio, Atest-section/Aheader d channel thickness (m) l viscosity (Pa s) n void fraction q density (kg/m3) v vapor mass quality
a c
Subscripts de deceleration exp experimental f frictional i inside in inlet l liquid o outside out outlet pre predicted r refrigerant s saturation v vapor w wall
2. Apparatus and procedure 2.1. Test rig Fig. 1a shows the schematic of the experimental rig designed for heat transfer and pressure drop measurements. The rig consists of one refrigerant loop and two cooling water loops. The sub-cooled refrigerant from the reservoir is pumped to the Coriolis-effect mass flow meter by the magnetic-driven gear pump after filtered. The mass flux is controlled by a bypass loop. In the evaporator, the refrigerant is heated to a desired vapor mass quality by adjusting electric heating power. The two-phase refrigerant enters the test section which is a counter-flow tube-in-tube heat exchanger. The fluid is partly condensed in the test section by the cooling water outside. After the test section, the fluid is sent to the post-condenser, where it is condensed and sub-cooled and finally flows back to the reservoir. A 500 W electric cartridge heater is fixed at the bottom of the refrigerant reservoir to compensate for system energy losses and make the system pressure stable. Two thermostatic water baths are used in the rig. One provides the cooling water for the test section and the other for the post condenser. The electric cartridge heater at the bottom of the reservoir was used to change the system pressure to the test saturation pressure. Meanwhile, the two thermostatic water baths were started to provide constant temperature water for the test section and the postcondenser. The test mass flux was initially set higher than the test value because pressure drop in the test section increased with the vaporization of the fluid causing a decrease of the mass flux. Differ-
Table 1 Properties of R22, R134a and R152a.
R22 R134a R152a
ts (°C)
ps (MPa)
ql (kg/m3)
qv (kg/m3)
hlv (kJ/kg)
ll (lPa s)
kl (W/m K)
r (N/m)
ODP
GWP
50 50 50
1.943 1.318 1.177
1082 1102.3 830.8
86.0 66.3 37.1
154.2 151.8 245.4
123.0 141.8 122.2
0.0719 0.0704 0.0875
0.00474 0.00489 0.00648
0.05 0 0
1700 1300 120
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(a)
(b) Fig. 1. Schematics of the apparatus (a) and the test section (b).
ent desired inlet vapor quality of the test section was obtained by adjusting electric heating power in the evaporator. The saturation state was maintained by the coincidence of measured saturation temperatures with the saturation temperatures derived from the saturation pressures. For different mass velocities and saturation temperatures, the cooling water temperature at the inlet of the test section was held constant while the cooling water flow rate was adjusted to ensure water temperature difference in the test section larger than 1 K. The data were collected by the data acquisition system when all the measured values were steady. 2.2. Test section The test section is a counter flow tube-in-tube condenser. The refrigerant condenses inside the test tube while the cooling water flows in the annulus as shown in Fig. 1b. The test tubes are a stain-
(a) circular
less steel single circular microchannel (dh = 1.152 mm) and a stainless steel single square microchannel (dh = 0.952 mm). Cross sectional dimensions were measured by a KYKY2800 series scanning electron microscope with the accuracy of 4.5 nm. The arithmetical mean deviations of the assessed profile Ra of the circular and square inner surfaces are 2.0 lm and 3.2 lm. Fig. 2 shows cross sectional views of the microchannels. The effective heat transfer lengths of the circular and square microchannels are 0.336 m and 0.352 m. The outer wall temperatures were measured with eight 76 lm diameter type T thermocouples symmetrically attached on the top and bottom outside of the microchannels. The four pairs of thermocouples were uniformly soldered along the microchannel as shown in Fig. 1b and the average data was used as the outer wall temperature. The refrigerant and cooling water temperatures were measured by inserting Pt100 temperature transducers into the measured fluids through tee fittings. All the thermocouples and Pt100 transducers were calibrated using a 6020 Series high precision calibration bath before experiments. Mixers were set before each fluid temperature measurement point to ensure the fluids fully mixed. The pressures of the refrigerant were measured by Trafag type 8251 pressure transducers with the accuracy of ±0.3% and the measuring range of 0–6 MPa. The refrigerant was drawn out through tee fittings which connected to pressure transducers with 3 mm inner diameter copper tubes. The pressure drop in the test section was measured by an EJA110A differential pressure transducer with the full scale accuracy of ±0.08% and the measuring range of 0–100 kPa. Mass fluxes of the refrigerant and the cooling water were measured by two DMF-I Coriolis-effect mass flow meters with the accuracy of ±0.2% and the measuring range of 0.5–5 kg/h. All data were collected using an Agilent 34970A data acquisition system with three 34901A cards in real time. The saturation states at the inlet and outlet of the test section are checked using the measured temperature and pressure. Deviations between the measured saturation temperatures and the saturation temperature derived from the saturation pressure are within ±0.12 °C which can be attributed to the accuracy of the temperature and pressure transducers, the properties and purity supplied by R152a manufacturer. Therefore, the measured saturation temperatures coincide well with the saturation temperatures derived from the saturation pressures. The deviation between measured saturation temperature and saturation temperature derived from saturation pressure was beyond the Pt temperature sensor accuracy, while the deviation between measured saturation pressure and saturation pressure derived from saturation temperature was within the pressure transducer accuracy indicating that the temperature sensor has relatively higher accuracy. Therefore, the average saturation temperature between the inlet and outlet of the test section was used to calculate heat transfer coefficients.
(b) square
Fig. 2. Cross sectional view of the microchannels.6.
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Aheader) and Cc is the coefficient of contraction, which is in turn a function of the area ratio
2.3. Data reduction The vapor mass quality of R152a at the inlet of the test section
Cc ¼
vin is calculated from the energy balance in the evaporator
vin ¼
UI mr ðhl hin Þ mr hfg
ð1Þ
where U and I are the heating voltage and current, mr is the refrigerant mass flux, hl is specific enthalpy of the saturation liquid, hin is specific enthalpy at the inlet of the evaporator and hlv is specific enthalpy of evaporation. As single microchannels were used in the paper, heat transfer rate was small when obtaining local heat transfer coefficients. In order to ensure the cooling water temperature difference larger than 1 K, vapor quality difference Dv in the test section was controlled to be 0.22–0.25 for lowest mass flux G = 200 kg/m2 s and 0.08–0.13 for highest mass flux G = 800 kg/m2 s during the experiments. Dv is calculated
Q Dv ¼ water mr hlv
ð2Þ
2vin Dv 2
ð3Þ
The inner and outer wall temperature differences DTw for circular and square microchannels are expressed as
lnðdo =di Þ 2pkl d DT w ¼ Q water 4blk
DT w ¼ Q water
ð4:aÞ ð4:bÞ
where k is the thermal conductivity of the microchannel, l is the effective heat transfer length, do and di are the outer and inner diameters of the circular microchannel, b is the side length of the square microchannel and d is the channel thickness. The average heat-transfer coefficient a for the condensation of R152a in the test section is determined by
Q water a¼ AðT s T w DT w Þ
ð5Þ
where Tw is the average outer wall temperature of the microchannel, Ts is the refrigerant saturation temperature and A is the cross sectional area of the microchannel. The range of temperature difference between the saturation temperature Ts and the average outer wall temperature Tw is 1.4–3.3 °C. The measured pressure drop Dpmeasured includes the frictional loss Dpf, the expansion loss Dpexpansion, the contraction loss Dpcontraction and the deceleration loss Dpde caused by the vapor fraction variation during condensation. Therefore, Dpmeasured is represented as
Dpmeasured ¼ Dpf þ Dpexpansion þ Dpcontraction þ Dpde
ð6Þ
Pressure drop caused by contraction Dpcontraction is estimated using a homogeneous flow model recommended by Butterworth and Hewitt [16]
Dpcontraction
G2 ¼ 2q l
"
1 1 Cc
2
2
þ1c
#
1þv
ql 1 qv
ð7Þ
where G is the mass flux, ql and qv are the liquid and vapor densities, c is the area ratio of the test section and the header (Atest-section/
ð8Þ
For the expansion loss, the following separated flow model recommended by Butterworth and Hewitt [13] is used
Dpexpansion ¼
G2 cð1 cÞws
ð9Þ
ql
where ws, the separated flow multiplier, is a function of the two phase densities and the vapor mass quality. The pressure drop caused by fluid deceleration Dpde is calculated using the model recommended by Carey [17]
Dpde
" # G2 v2 G2 ð1 vÞ2 ¼ þ qv n ql ð1 nÞ
v¼vout
" # G2 v2 G2 ð1 vÞ2 þ qv n ql ð1 nÞ
ð10Þ v¼vin
where the void fraction n is evaluated using Baroczy correlation [18]
" n¼ 1þ
where Qwater is the heat transfer rate of the cooling water in the test section. Therefore, the average vapor mass quality v in the test section is calculated by
v¼
1 0:639ð1 cÞ0:5 þ 1
0:74 0:65 0:13 #1 1v qv ll
v
ql
ð11Þ
lv
Therefore, the frictional pressure loss Dpf can be obtained by subtracting the expansion loss Dpexpansion, the contraction loss Dpcontraction and the deceleration loss Dpde from the measured pressure drop Dpmeasured. Then the frictional pressure gradient is defined as
dp Dpf ¼ dl l
ð12Þ
According to the data reduction results, the fraction ranges of the contraction loss Dpcontraction, the expansion loss Dpexpansion, the frictional loss Dpf and the deceleration loss divided by measured total pressure loss Dpde are 7.3–15.4%, 105, 89.5–95.2% and 1.7–5.9%. The expansion loss is small enough to neglect. The physical properties of R152a were obtained from REFPROP [19]. 2.4. Uncertainty analysis The uncertainty for the experimental results was determined by a procedure proposed by Kline and McClintock [20]. Experimental uncertainties of the measured parameters are listed in Table 2. 3. Results and discussion 3.1. Heat transfer and pressure drop of single-phase flow Before any two phase measurements, single-phase heat transfer and pressure drop experiments in the circular microchannel were conducted to validate the experimental rig. The arithmetic mean error, a.m., and root-mean-square error, r.m.s. are used to assess Table 2 Experimental uncertainties for measured parameters. Parameter
Uncertainty
Temperature (thermocouple) Temperature (Pt100 transducer) Refrigerant mass flow rate Cooling water mass flow rate Pressure Pressure difference Heat transfer coefficient
±0.1 °C ±0.05 °C ±0.2% (5 kg/h) ±0.2% (5 kg/h) ±0.3% (6 MPa) ±0.08% (100 kPa) ±15.0% W/m2 K
Notes: The percentage uncertainties for refrigerant and cooling water flow rates, pressure and pressure difference are relative to the end of scale values. The end of scale values are reported in the table.
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the reliability of the test rig. The two parameters are defined as follows:
80
1 X apre aexp a:m: ¼ 100% N aexp
ð13Þ
present
circular R152a
70
Gnielinski (1976)
60
ð14Þ
Nu
50
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 X apre aexp r:m:s: ¼ 100% N1 aexp
40 30 20 10 0
0
2000
4000
6000
8000
10000
12000
Re Fig. 4. Comparison of measured Nu with predictions by Gnielinski correlation [19] for single-phase flow.
20 o
18
ts = 40 C
16
Δ t=
o
10 C
14
α / kW/ m2 K
where a refers to heat transfer coefficient a or pressure gradient dp/ dl and N is the number of data points. Single-phase pressure drop experiments were conducted during adiabatic flow of R152a with Reynolds number ranging from 800 to 1.01 104. Fig. 3 shows comparison between measured and predicted friction factors. The present data agree well with predictions of Blasius equation [21] with the a.m. and r.m.s deviations within 1.7% and 8.8%, respectively. Single-phase heat transfer experiments were performed with Reynolds number ranging from 1.3 103 to 1.2 104 and temperature of liquid R152a from 27 °C to 33 °C. Fig. 4 shows comparison between measured and predicted Nusselt numbers. The present data agree well with predictions of Gnielinski correlation [22] with the a.m. and r.m.s deviations within 4.1% and 12.1%, respectively. Deviations of heat transfer rate between the refrigerant and cooling water in the test section are within ±5%. Single-phase experiments show that the heat loss in the test section is rather small and the experimental rig is appropriate for condensation experiments.
12
circular square G / kg/(m2 s) 200 400 600 800
10 8 6
3.2. Heat transfer during condensation
4
3.2.1. Effects of mass flux and vapor mass quality Fig. 5 shows the effects of mass flux and vapor mass quality on heat transfer coefficients with the saturation temperature of 40 °C and the temperature difference between the refrigerant and the cooling water of 10 °C. During the experiments, mass fluxes varied from 200 to 800 kg/m2 s. Heat transfer coefficients increase with increasing mass flux and vapor mass quality both in circular and square microchannels, which agrees with the previous studies [23]. Heat transfer coefficients become more sensitive to mass flux at high vapor mass qualities implying the dominant effect of shear stress. Error bars have been introduced for the heat transfer coefficients in Fig. 5.
2 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-χ Fig. 5. Effects of mass flux, vapor mass quality and channel geometry on heattransfer coefficients.
20 o
circular R152a
18 16
ts / C 40 50
G=400 kg/(m2 s)
α / kW/(m2 K)
14 0.10 present
circular R152a
0.09
f =64/Re
0.08
f =0.3164/Re
0.25
0.07
f
10 8 6
0.06
4
0.05
2
0.04
0 0.0
0.03
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-χ
0.02
Fig. 6. Effect of saturation temperature on heat-transfer coefficients.
0.01 0.00
12
0
2000
4000
6000
8000
10000
12000
Re Fig. 3. Comparison of measured and predicted friction factors.
3.2.2. Effect of saturation temperature Experiments were conducted at two saturation temperatures of 40 °C and 50 °C in the circular microchannel. Fig. 6 shows the effect of the saturation temperature on heat-transfer coefficients of
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3.2.4. Comparison with heat transfer correlations and a theoretical solution Four heat transfer correlations and a theoretical solution are used to predict experimental data in the circular and square microchannels ([24,25,8,26,27]). Except for Wang and Rose [27] a theoretical solution, rest are based on experimental data of refrigerants. The work of Wang and Rose [27] shows that there is a region where heat transfer coefficient is governed only by surface tension and the solution is derived based on the calculated results in the region. Fig. 7 shows comparison between measured and predicted heat-transfer coefficients. Table 3 summarizes evaluation results of heat transfer correlations and the theoretical solution which were assessed in terms of the arithmetic mean error, a.m., and root-mean-square error, r.m.s. The results for the circular microchannel agree within experimental error with Wang et al. [24] and Koyama et al. [25] correlations and the theoretical solution [27], while for the square microchannel the results agree within experimental error with Koyama et al. [25], Cavallini et al. [8] and Bandhauer et al. [26] correlations and the theoretical solution [27]. Fig. 7 shows that deviations between the data and predictions of Wang and Rose [27] depend much on vapor mass quality.
150
(αpre-αexp)/αexp×100%
3.2.3. Effect of channel geometry Fig. 5 also shows effects of channel geometry on heat-transfer coefficients of R152a with various mass fluxes. At G = 200 kg/m2 s heat-transfer coefficients in the square microchannel are all higher than those in the circular microchannel. On one hand, the heat transfer enhancement is caused by effects of the corners in the square microchannel. The condensate is pulled to the corners due to the effect of surface tension, which reduces the average thermal resistance across the cross section in the square microchannel. On the other hand, the hydraulic diameter decrease of the square microchannel (circular: dh = 1.152 mm, square: dh = 0.952 mm) increases heat-transfer coefficients according to the previous studies of Zhang et al. [23]. At G = 400 kg/m2 s heat-transfer coefficients in the square microchannel are still larger than those in the circular microchannel though the enhancement is weaker compared with that at G = 200 kg/m2 s. At G = 600 kg/m2 s heat-transfer coefficients of the two microchannels almost overlap each other. Shear stress plays a much more important role than surface tension with increase of mass flux. Effect of the square microchannel corners becomes weaker at higher mass fluxes.
200
+30%
100 50 0 -50 -30% -100 -150 -200 0.0
Wang et al. (2002) Koyama et al. (2003) Cavallini et al. (2011) Bandhauer et al. (2006) Wang and Rose (2011)
0.2
0.4
0.6
0.8
1.0
1- χ
(a) circular 200 150
(αpre-αexp)/αexp×100%
R152a. Heat-transfer coefficients decrease with increasing saturation temperature, which can be attributed to dependence of thermodynamic properties of the refrigerant on saturation temperature. The saturation pressure and vapor density increase with increasing saturation temperature, which increases the vapor and liquid phase density ratio. The vapor phase velocity decreases and the shear stress between the liquid and vapor phase decreases with increasing saturation temperature leading to thicker condensate and lower heat-transfer coefficients.
100
+30%
50 0 -50 -100 -150 -200 0.0
-30%
Wang et al. (2002) Koyama et al. (2003) Cavallini et al. (2011) Bandhauer et al. (2006) Wang and Rose (2011)
0.2
0.4
0.6
0.8
1.0
1- χ
(b) square Fig. 7. Comparison of measured and predicted heat-transfer coefficients.
Table 3 Performance of heat transfer correlations and a theoretical solution compared with the present data. Circular
Wang et al. [24] (2002) correlation Koyama et al. [25] (2003) correlation Cavallini et al. [8] (2011) correlation Bandhauer et al. [26] (2006) correlation Wang and Rose [27] (2011) theoretical solution
Square
a.m.
r.m.s
a.m.
r.m.s
11.2 12.7 17.9 29.3 14.6
15.4 29.6 27.4 14.1 52.3
26.3 5.4 0.9 7.4 4.3
16.3 5.6 19.8 21.9 30.0
a.m.: Arithmetic mean error (%); r.m.s.: root-mean-square error (%).
3.3. Pressure drop during condensation 3.3.1. Effects of mass flux and vapor mass quality Fig. 8 shows effects of mass flux and vapor mass quality on frictional pressure gradients both in circular and square microchannels. The frictional pressure gradients increase with mass flux and vapor mass quality which is similar to heat-transfer coefficients shown in Fig. 5. Pressure gradient trends become smooth at high vapor mass qualities. The mist flow regime with droplet entrained in the vapor core emerges at high vapor mass qualities according to results of Garimella and Coleman [28] where pressure gradients increase less with vapor mass quality.
3.3.2. Effect of saturation temperature Fig. 9 shows effect of saturation temperature on frictional pressure gradients of R152a in the circular microchannel. The frictional pressure gradient decreases with increasing saturation temperature similar to that for heat-transfer coefficients in Fig. 6. The saturation pressure increases with the saturation temperature leading to higher reduced pressure and larger vapor and liquid phase density ratio. The decrease of the velocity difference between the two phases decreases the frictional pressure gradient.
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N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
300
200
[(dp/dl)pre-(dp/dl)exp]/(dp/dl)exp×100%
dp/dl / kPa/m
200 400 600 800
ts =40 oC
250
240
G / kg/(m2 s)
circular square
R152a
150
100
50
0 0.0
0.2
0.4
0.6
0.8
180 120 60
+30%
0 -60
-30% -120 -180 -240 0.0
1.0
Koyama et al. (2003) Agarwal & Garimella (2009) Cavallini et al. (2009)
0.2
0.4
1.0
o
circular
ts / C 2
G=400 kg/(m s)
240
[(dp/dl)pre-(dp/dl)exp]/(dp/dl)exp×100%
120
40 50
80
dp/dl / kPa/m
0.8
(a) circular
Fig. 8. Effects of mass flux, vapor mass quality and channel geometry on frictional pressure gradients.
100
0.6
1-χ
1- χ
60
40
180 120
+30%
60 0 -60
-30%
-120 -180 -240 0.0
20
Koyama et al. (2003) Agarwal & Garimella (2009) Cavallini et al. (2009)
0.2
0.4
0.8
0.6
1.0
1-χ 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(b) square
1.0
1- χ
Fig. 10. Comparison of measured and predicted frictional pressure gradients.
Fig. 9. Effect of saturation temperature on frictional pressure gradients.
3.3.3. Effect of channel geometry Effect of channel geometry on frictional pressure gradients is shown in Fig. 8. Frictional pressure gradients of the square microchannel are slightly lower than those in the circular microchannel at higher vapor mass qualities for the same operating conditions. However, at lower vapor mass qualities, frictional pressure gradients are almost equivalent in the two microchannels. Therefore, channel geometry has little effect on frictional pressure gradients. 3.3.4. Comparison with pressure drop correlations Three pressure drop correlations [25,29,30] based on experimental data of R134a in microchannels were used to predict experimental data. As 2 Ra/Dh was larger than 0.0027, zero surface roughness Ra was inserted in the Cavallini et al. [30] equations when computing pressure gradients, while the surface roughness was not needed in Koyama et al. [25] and Agarwal and Garimella [29] equations. Comparison results are shown in Fig. 10. Table 4 summarizes the evaluation results of pressure drop correlations. The performance of each correlation was assessed in terms of the arithmetic mean error, a.m., and root-mean-square error, r.m.s. Koyama et al. [25] underestimates the data for both microchannels while Agarwal and Garimella [29] overestimate the data for the square microchannel. Predictions of Cavallini et al. [30] show large
Table 4 Performance of pressure drop correlations compared with the present data. Correlations
Koyama et al. [23] (2003) correlation Agarwal and Garimella [29] (2009) correlation Cavallini et al. [6] (2009) correlation
Circular
Square
a.m.
r.m.s.
a.m.
r.m.s
78.1 4.2
6.9 20.5
64.5 34.2
14.0 20.1
25.5
43.9
11.7
41.0
a.m.: Arithmetic mean error (%); r.m.s.: root-mean-square error (%).
root-mean-square errors for data in both circular and square microchannels.
4. Conclusions Heat transfer and pressure drop during condensation of R152a were investigated experimentally in a circular (d = 1.152 mm) and a square (dh = 0.952 mm) microchannels. Experiments were conducted with mass fluxes from 200 to 800 kg/m2 s, saturation temperatures of 40 °C and 50 °C and vapor mass qualities from 0.1 to 0.9. Experimental data were compared with empirical correlations and a theoretical solution. The following conclusions can be drawn:
N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
1. Heat-transfer coefficients and pressure gradients during condensation increase with mass flux and vapor mass quality while decrease with the saturation temperature both in circular and square microchannels. 2. Heat-transfer coefficients of the square microchannel are higher than those of the circular microchannel at G = 200 kg/m2 s and 400 kg/m2 s due to the effect of surface tension. The heat transfer enhancement decreases with mass flux as the shear stress plays a much more important role at higher mass fluxes. However, channel geometry has little effect on two phase pressure gradients. 3. The heat transfer results for the circular microchannel agree within experimental error with Wang et al. [24] and Koyama et al. [25] correlations and the theoretical solution [27], while for the square microchannel the results agree within experimental error with Koyama et al. [25], Cavallini et al. [8] and Bandhauer et al. [26] correlations and the theoretical solution [27]. For pressure drop results, Koyama et al. [25] underestimates the data for both microchannels while Agarwal and Garimella [29] overestimate the data for the square microchannel.
Acknowledgements The work was financially supported by the National Basic Research Program of China (‘‘973’’ Project, No. 2011CB706904), Guangdong Industry-Academia-Research Project (No. 2011A090200018) and the new energy vehicles industry Project (2011) of Guangdong Special Funds for Strategic Emerging Industries. The work was also supported by EU research Grant FP7-2010IRSES-269205. References [1] Regulation (EG) No 842/2006 of the European Parliament and of the Council of 17 May 2006 on certain fluorinated greenhouse gases, Official Journal of the European Union, 2006. [2] Directive 2006/40/EC of The European Parliament and of the Council of 17 May 2006 relating to emissions from air-conditioning systems in motor vehicles and amending Council Directive 70/156/EC, Official Journal of the European Union, 2006. [3] Q. Su, G.X. Yu, H.S. Wang, J.W. Rose, Microchannel condensation: correlations and theory, International of Refrigeration 32 (2009) 1149–1152. [4] E.E. Wilson, A basis for rational design of heat transfer apparatus, ASME Transactions 37 (1919) 47–70. [5] M. Matkovic, A. Cavallini, D. Del Col, L. Rossetto, Experimental study on condensation heat transfer inside a single circular minichannel, International Journal of Heat and Mass Transfer 52 (2009) 2311–2323. [6] A. Cavallini, D. Del Col, M. Matkovic, L. Rossetto, Pressure drop during twophase flow of R134a and R32 in a single minichannel, Journal of Heat Transfer 131 (2009) 0331071–0331078. [7] D. Del Col, D. Torresin, A. Cavallini, Heat transfer and pressure drop during condensation of the low GWP refrigerant R1234yf, International Journal of Refrigeration 33 (2010) 1307–1318.
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[8] A. Cavallini, S. Bortolin, D. Del Col, M. Matkovic, L. Rossetto, Condensation heat transfer and pressure losses of high and low pressure refrigerants flowing in a single circular minichannel, Heat Transfer Engineering 32 (2) (2011) 90–98. [9] D. Del Col, S. Bortolin, A. Cavallini, M. Matkovic, Effect of cross sectional shape during condensation in a single square minichannel, International Journal of Heat and Mass Transfer 54 (2011) 3909–3920. [10] M. Derby, H.J. Lee, Y. Peles, M.K. Jensen, Condensation heat transfer in square, triangular and semicircular mini-channels, International Journal of Heat and Mass Transfer 55 (2012) 187–197. [11] S.M. Kim, I. Mudawar, Theoretical model for annular flow condensation in rectangular microchannels, International Journal of Heat and Mass Transfer 55 (2012) 958–970. [12] S.M. Kim, J. Kim, I. Mudawar, Flow condensation in parallel micro-channels – Part 1: Experimental results and assessment of pressure drop correlations, International Journal of Heat and Mass Transfer 55 (2012) 971–983. [13] S.M. Kim, I. Mudawar, Flow condensation in parallel micro-channels – Part 2: Heat transfer results and correlation technique, International Journal of Heat and Mass Transfer 55 (2012) 984–994. [14] A. Agarwal, T.M. Bandhauer, S. Garimella, Measurement and modeling of condensation heat transfer in non-circular microchannels, International Journal of Refrigeration 33 (2010) 1169–1179. [15] H.S. Wang, J. Ding, J.W. Rose, Heat transfer during annular film condensation in microchannels: calculations for R152a, R134a, R22, R410A, propane, ammonia and carbon dioxide, Sixth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science, Engineering and Technology 2 (2007) 12–16. [16] G.F. Hewitt, D. Butterworth, Two Phase Flow and Heat Transfer, Oxford Press, 1977. [17] C.J. Carey, Liquid–Vapor Phase Change Phenomena, Taylor & Francis Series in Mechanical Engineering, Hemisphere Publishing, 1992. [18] C.J. Baroczy, Correlation of liquid fraction in two-phase flow with application to liquid metals, Atomics International, 1963. [19] NIST Thermodynamic and Transport Properties of Refrigerants and Refrigerants Mixtures REFPROP, Version 7.0. [20] S.J. Kline, F.A. McClintock, The description of uncertainties in single sample experiments, Mechanical Engineering 75 (1953) 3–9. [21] H. Blasius, Grenzschichten in flussigkeiten mit kleiner reibung, Zeit. Math. Phys. 56 (1908) 1–37. [22] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 16 (2) (1976) 359–368. [23] H.Y. Zhang, J.M. Li, N. Liu, B.X. Wang, Experimental investigation of condensation heat transfer and pressure drop of R22, R410A and R407C in mini-tubes, International Journal of Heat and Mass Transfer 55 (2012) 3522– 3532. [24] W.W. Wang, T.D. Radcliff, R.N. Christensen, A condensation heat transfer correlation for millimeter-scale tubing with flow regime transition, Experimental Thermal and Fluid Science 26 (2002) 473–485. [25] S. Koyama, K. Kuwahara, K. Nakashita, K. Yamamoto, An experimental study on condensation of refrigerant R134a in a multi-port extruded tube, International Journal of Refrigeration 24 (2003) 425–432. [26] T.M. Bandhauer, A. Agawal, S. Garimella, Measurement and modeling of condensation heat transfer coefficients in circular microchannels, Journal of Heat Transfer 128 (2006) 1050–1059. [27] H.S. Wang, J.W. Rose, Theory of heat transfer during condensation in microchannels, International Journal of Heat and Mass Transfer 54 (2011) 2525–2534. [28] J.W. Coleman, S. Garimella, Characterization of two-phase flow patterns in small diameter round and rectangular tubes, International Journal of Heat and Mass Transfer 42 (1999) 2869–2881. [29] A. Agarwal, S. Garimella, Modeling of pressure drop during condensation in circular and noncircular microchannels, Journal of Fluids Engineering 131 (2009) 0113021–0113028. [30] A. Cavallini, D. Del Col, M. Matkovic, L. Rossetto, Frictional pressure drop during vapour–liquid flow in minichannels: modeling and experimental evaluation, International Journal of Heat and Fluid Flow 30 (2009) 131–139.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Heat transfer and pressure drop during condensation of R152a in circular and square microchannels Na Liu a, Jun Ming Li a,⇑, Jie Sun b, Hua Sheng Wang b a b
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, UK
a r t i c l e
i n f o
Article history: Received 15 August 2012 Received in revised form 2 November 2012 Accepted 3 January 2013 Available online 16 January 2013 Keywords: Condensation Heat transfer Microchannel R152a Pressure drop
a b s t r a c t The paper reports experimental data for heat transfer and pressure drop during condensation of R152a in circular and square microchannels with hydraulic diameters of 1.152 mm and 0.952 mm, respectively. Saturation temperatures are 40 °C and 50 °C with mass fluxes varying from 200 to 800 kg/m2 s and vapor mass qualities from 0.1 to 0.9. Effects of mass flux, vapor mass quality and channel geometry on heat transfer and pressure drop were investigated. The results show that heat-transfer coefficients and pressure drop both increase with increasing mass flux and vapor mass quality while decrease with increasing saturation temperature. Channel geometry has much effect on heat transfer at low mass fluxes while has little effect on pressure drop. The present data were compared with earlier empirical correlations and a theoretical solution. Heat transfer coefficients agree within experimental error with several correlations and a theoretical solution for both circular and square microchannels. One pressure drop correlation underestimates the data for the two microchannels while another pressure drop correlation overestimates the data for the square microchannel. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Microchannels are increasingly used to improve heat-transfer performance and to enable compact geometries in many applications. For condensation, owing to surface tension effects, methods used to treat larger channels are not suitable when channel dimension is around 1 mm or less. Recently, increasing attention on environmental issues has brought substantial requirements and changes in refrigerants. Though HFCs substitutes have no ozone depletion potential (ODP), many of them have relatively high global warming potential (GWP). Moreover, the European Union’s F-gas regulations specify beginning on January 1, 2011 new models and on January 1, 2017 new vehicles fitted with air conditioning cannot be manufactured with fluorinated greenhouse gases having GWP greater than 150 [1,2]. Su et al. [3] reviewed earlier experimental work during condensation in microchannels. In many of the earlier heat-transfer measurements, most fluids are with similar properties, predominantly R134a. Vapor-side heat-transfer coefficients have generally been inferred from overall measurements by subtraction of thermal resistance or using Wilson plot techniques [4]. Such data have high uncertainty. ⇑ Corresponding author. Tel.: +86 10 62771001; fax: +86 10 62770209. E-mail address: [email protected] (J.M. Li). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.01.002
Recently, heat-transfer coefficients with various refrigerants were obtained from direct measurement of wall temperatures during condensation in circular and non-circular microchannels. Matkovic et al. [5–8] measured heat-transfer coefficients and pressure drop of R134a, R32, R1234yf and R245fa in a circular 0.96 mm microchannel. Del Col et al. [9] measured heat-transfer coefficients of R134a in a 1.18 mm side length square microchannel. Heattransfer coefficients of R134a were obtained by Derby et al. [10] during condensation in 1 mm square, triangular and semicircular multiple parallel minichannels. Mass flux and quality were determined to have significant effects on the condensation process, even at lower mass fluxes, while saturation pressure, heat flux, and channel shape had no significant effects. Kim and Mudawar [11] proposed a theoretical control-volume-based model based on the assumptions of smooth interface between the annular liquid film and vapor core, and uniform liquid film thickness around the channel’s circumference. The new model accurately captures the pressure drop and heat transfer coefficients in both magnitude and trend. Kim et al. [12,13] experimentally investigated flow regimes, pressure drop and heat transfer of FC-72 during condensation along parallel, square micro-channels with a hydraulic diameter of 1 mm. In their study, smooth-annular, wavy-annular, transition, slug, and bubbly flow regimes were identified. A detailed pressure model was presented and assessment of pressure drop correlations was conducted. Comparing the data to predictions of previous annular condensation heat transfer correlations showed correla-
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N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
Nomenclature a a.m. A b Cc d dh G f h hlv I k l m N Nu U p Q r.m.s. Ra Re T
data referring to a or dp/dl, see Eqs. (12) and (13) arithmetic mean error cross sectional area of channel (m2) side length of square channel (m) coefficient of contraction, see Eq. (8) diameter of circular channel (m) hydraulic diameter (m) mass flux (kg/m2 s) friction factor specific enthalpy (J/kg) specific enthalpy of evaporation (J/kg) electric current (A) thermal conductivity (W/m K) length (m) mass flow rate (kg/s) number of data points Nusselt number, adh/kl electric voltage (V) pressure (Pa) heat transfer rate (W) root-mean-square error arithmetical mean deviation of the assessed profile (lm) Reynolds number, Gdh/ll temperature (K)
tions intended for macro-channels generally provided better predictions than correlations intended for mini/micro-channels. Besides, a new condensation heat transfer correlation was proposed for annular condensation heat transfer in mini/micro-channels. Agarwal et al. [14] used thermal amplification technique to measure heat-transfer coefficients of R134a in six non-circular horizontal microchannels. Saturation and environmental properties of R22, R134a and R152a are listed in Table 1. R152a and R134a have zero ozone depletion potentials. Global warming potential of R152a is 120, which is an order of magnitude lower than those of R22 and R134a. It is noted that thermal conductivity, latent heat and surface tension are higher for R152a than for R22 and R134a. Wang et al. [15] theoretically studied heat-transfer coefficients of R22, R134a and R152a during condensation. According to their results, heat-transfer coefficients of R152a are higher than those of R22 and R134a. Therefore, R152a is a potential substitute for R22. However, to the authors’ knowledge, there are no experimental studies on heat transfer and pressure drop during condensation of R152a in microchannels. In the present paper, heat transfer and pressure drop are investigated experimentally during condensation of R152a in a circular and a square microchannels. Experiments are performed at saturation temperatures of 40 °C and 50 °C with mass fluxes from 200 to 800 kg/m2 s and vapor mass qualities from 0.1 to 0.9. Effects of mass flux, vapor mass quality and channel geometry on heat transfer and pressure drop are presented in the paper.
Greek symbols heat-transfer coefficient (W/m2 K) area ratio, Atest-section/Aheader d channel thickness (m) l viscosity (Pa s) n void fraction q density (kg/m3) v vapor mass quality
a c
Subscripts de deceleration exp experimental f frictional i inside in inlet l liquid o outside out outlet pre predicted r refrigerant s saturation v vapor w wall
2. Apparatus and procedure 2.1. Test rig Fig. 1a shows the schematic of the experimental rig designed for heat transfer and pressure drop measurements. The rig consists of one refrigerant loop and two cooling water loops. The sub-cooled refrigerant from the reservoir is pumped to the Coriolis-effect mass flow meter by the magnetic-driven gear pump after filtered. The mass flux is controlled by a bypass loop. In the evaporator, the refrigerant is heated to a desired vapor mass quality by adjusting electric heating power. The two-phase refrigerant enters the test section which is a counter-flow tube-in-tube heat exchanger. The fluid is partly condensed in the test section by the cooling water outside. After the test section, the fluid is sent to the post-condenser, where it is condensed and sub-cooled and finally flows back to the reservoir. A 500 W electric cartridge heater is fixed at the bottom of the refrigerant reservoir to compensate for system energy losses and make the system pressure stable. Two thermostatic water baths are used in the rig. One provides the cooling water for the test section and the other for the post condenser. The electric cartridge heater at the bottom of the reservoir was used to change the system pressure to the test saturation pressure. Meanwhile, the two thermostatic water baths were started to provide constant temperature water for the test section and the postcondenser. The test mass flux was initially set higher than the test value because pressure drop in the test section increased with the vaporization of the fluid causing a decrease of the mass flux. Differ-
Table 1 Properties of R22, R134a and R152a.
R22 R134a R152a
ts (°C)
ps (MPa)
ql (kg/m3)
qv (kg/m3)
hlv (kJ/kg)
ll (lPa s)
kl (W/m K)
r (N/m)
ODP
GWP
50 50 50
1.943 1.318 1.177
1082 1102.3 830.8
86.0 66.3 37.1
154.2 151.8 245.4
123.0 141.8 122.2
0.0719 0.0704 0.0875
0.00474 0.00489 0.00648
0.05 0 0
1700 1300 120
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N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
(a)
(b) Fig. 1. Schematics of the apparatus (a) and the test section (b).
ent desired inlet vapor quality of the test section was obtained by adjusting electric heating power in the evaporator. The saturation state was maintained by the coincidence of measured saturation temperatures with the saturation temperatures derived from the saturation pressures. For different mass velocities and saturation temperatures, the cooling water temperature at the inlet of the test section was held constant while the cooling water flow rate was adjusted to ensure water temperature difference in the test section larger than 1 K. The data were collected by the data acquisition system when all the measured values were steady. 2.2. Test section The test section is a counter flow tube-in-tube condenser. The refrigerant condenses inside the test tube while the cooling water flows in the annulus as shown in Fig. 1b. The test tubes are a stain-
(a) circular
less steel single circular microchannel (dh = 1.152 mm) and a stainless steel single square microchannel (dh = 0.952 mm). Cross sectional dimensions were measured by a KYKY2800 series scanning electron microscope with the accuracy of 4.5 nm. The arithmetical mean deviations of the assessed profile Ra of the circular and square inner surfaces are 2.0 lm and 3.2 lm. Fig. 2 shows cross sectional views of the microchannels. The effective heat transfer lengths of the circular and square microchannels are 0.336 m and 0.352 m. The outer wall temperatures were measured with eight 76 lm diameter type T thermocouples symmetrically attached on the top and bottom outside of the microchannels. The four pairs of thermocouples were uniformly soldered along the microchannel as shown in Fig. 1b and the average data was used as the outer wall temperature. The refrigerant and cooling water temperatures were measured by inserting Pt100 temperature transducers into the measured fluids through tee fittings. All the thermocouples and Pt100 transducers were calibrated using a 6020 Series high precision calibration bath before experiments. Mixers were set before each fluid temperature measurement point to ensure the fluids fully mixed. The pressures of the refrigerant were measured by Trafag type 8251 pressure transducers with the accuracy of ±0.3% and the measuring range of 0–6 MPa. The refrigerant was drawn out through tee fittings which connected to pressure transducers with 3 mm inner diameter copper tubes. The pressure drop in the test section was measured by an EJA110A differential pressure transducer with the full scale accuracy of ±0.08% and the measuring range of 0–100 kPa. Mass fluxes of the refrigerant and the cooling water were measured by two DMF-I Coriolis-effect mass flow meters with the accuracy of ±0.2% and the measuring range of 0.5–5 kg/h. All data were collected using an Agilent 34970A data acquisition system with three 34901A cards in real time. The saturation states at the inlet and outlet of the test section are checked using the measured temperature and pressure. Deviations between the measured saturation temperatures and the saturation temperature derived from the saturation pressure are within ±0.12 °C which can be attributed to the accuracy of the temperature and pressure transducers, the properties and purity supplied by R152a manufacturer. Therefore, the measured saturation temperatures coincide well with the saturation temperatures derived from the saturation pressures. The deviation between measured saturation temperature and saturation temperature derived from saturation pressure was beyond the Pt temperature sensor accuracy, while the deviation between measured saturation pressure and saturation pressure derived from saturation temperature was within the pressure transducer accuracy indicating that the temperature sensor has relatively higher accuracy. Therefore, the average saturation temperature between the inlet and outlet of the test section was used to calculate heat transfer coefficients.
(b) square
Fig. 2. Cross sectional view of the microchannels.6.
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Aheader) and Cc is the coefficient of contraction, which is in turn a function of the area ratio
2.3. Data reduction The vapor mass quality of R152a at the inlet of the test section
Cc ¼
vin is calculated from the energy balance in the evaporator
vin ¼
UI mr ðhl hin Þ mr hfg
ð1Þ
where U and I are the heating voltage and current, mr is the refrigerant mass flux, hl is specific enthalpy of the saturation liquid, hin is specific enthalpy at the inlet of the evaporator and hlv is specific enthalpy of evaporation. As single microchannels were used in the paper, heat transfer rate was small when obtaining local heat transfer coefficients. In order to ensure the cooling water temperature difference larger than 1 K, vapor quality difference Dv in the test section was controlled to be 0.22–0.25 for lowest mass flux G = 200 kg/m2 s and 0.08–0.13 for highest mass flux G = 800 kg/m2 s during the experiments. Dv is calculated
Q Dv ¼ water mr hlv
ð2Þ
2vin Dv 2
ð3Þ
The inner and outer wall temperature differences DTw for circular and square microchannels are expressed as
lnðdo =di Þ 2pkl d DT w ¼ Q water 4blk
DT w ¼ Q water
ð4:aÞ ð4:bÞ
where k is the thermal conductivity of the microchannel, l is the effective heat transfer length, do and di are the outer and inner diameters of the circular microchannel, b is the side length of the square microchannel and d is the channel thickness. The average heat-transfer coefficient a for the condensation of R152a in the test section is determined by
Q water a¼ AðT s T w DT w Þ
ð5Þ
where Tw is the average outer wall temperature of the microchannel, Ts is the refrigerant saturation temperature and A is the cross sectional area of the microchannel. The range of temperature difference between the saturation temperature Ts and the average outer wall temperature Tw is 1.4–3.3 °C. The measured pressure drop Dpmeasured includes the frictional loss Dpf, the expansion loss Dpexpansion, the contraction loss Dpcontraction and the deceleration loss Dpde caused by the vapor fraction variation during condensation. Therefore, Dpmeasured is represented as
Dpmeasured ¼ Dpf þ Dpexpansion þ Dpcontraction þ Dpde
ð6Þ
Pressure drop caused by contraction Dpcontraction is estimated using a homogeneous flow model recommended by Butterworth and Hewitt [16]
Dpcontraction
G2 ¼ 2q l
"
1 1 Cc
2
2
þ1c
#
1þv
ql 1 qv
ð7Þ
where G is the mass flux, ql and qv are the liquid and vapor densities, c is the area ratio of the test section and the header (Atest-section/
ð8Þ
For the expansion loss, the following separated flow model recommended by Butterworth and Hewitt [13] is used
Dpexpansion ¼
G2 cð1 cÞws
ð9Þ
ql
where ws, the separated flow multiplier, is a function of the two phase densities and the vapor mass quality. The pressure drop caused by fluid deceleration Dpde is calculated using the model recommended by Carey [17]
Dpde
" # G2 v2 G2 ð1 vÞ2 ¼ þ qv n ql ð1 nÞ
v¼vout
" # G2 v2 G2 ð1 vÞ2 þ qv n ql ð1 nÞ
ð10Þ v¼vin
where the void fraction n is evaluated using Baroczy correlation [18]
" n¼ 1þ
where Qwater is the heat transfer rate of the cooling water in the test section. Therefore, the average vapor mass quality v in the test section is calculated by
v¼
1 0:639ð1 cÞ0:5 þ 1
0:74 0:65 0:13 #1 1v qv ll
v
ql
ð11Þ
lv
Therefore, the frictional pressure loss Dpf can be obtained by subtracting the expansion loss Dpexpansion, the contraction loss Dpcontraction and the deceleration loss Dpde from the measured pressure drop Dpmeasured. Then the frictional pressure gradient is defined as
dp Dpf ¼ dl l
ð12Þ
According to the data reduction results, the fraction ranges of the contraction loss Dpcontraction, the expansion loss Dpexpansion, the frictional loss Dpf and the deceleration loss divided by measured total pressure loss Dpde are 7.3–15.4%, 105, 89.5–95.2% and 1.7–5.9%. The expansion loss is small enough to neglect. The physical properties of R152a were obtained from REFPROP [19]. 2.4. Uncertainty analysis The uncertainty for the experimental results was determined by a procedure proposed by Kline and McClintock [20]. Experimental uncertainties of the measured parameters are listed in Table 2. 3. Results and discussion 3.1. Heat transfer and pressure drop of single-phase flow Before any two phase measurements, single-phase heat transfer and pressure drop experiments in the circular microchannel were conducted to validate the experimental rig. The arithmetic mean error, a.m., and root-mean-square error, r.m.s. are used to assess Table 2 Experimental uncertainties for measured parameters. Parameter
Uncertainty
Temperature (thermocouple) Temperature (Pt100 transducer) Refrigerant mass flow rate Cooling water mass flow rate Pressure Pressure difference Heat transfer coefficient
±0.1 °C ±0.05 °C ±0.2% (5 kg/h) ±0.2% (5 kg/h) ±0.3% (6 MPa) ±0.08% (100 kPa) ±15.0% W/m2 K
Notes: The percentage uncertainties for refrigerant and cooling water flow rates, pressure and pressure difference are relative to the end of scale values. The end of scale values are reported in the table.
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the reliability of the test rig. The two parameters are defined as follows:
80
1 X apre aexp a:m: ¼ 100% N aexp
ð13Þ
present
circular R152a
70
Gnielinski (1976)
60
ð14Þ
Nu
50
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 X apre aexp r:m:s: ¼ 100% N1 aexp
40 30 20 10 0
0
2000
4000
6000
8000
10000
12000
Re Fig. 4. Comparison of measured Nu with predictions by Gnielinski correlation [19] for single-phase flow.
20 o
18
ts = 40 C
16
Δ t=
o
10 C
14
α / kW/ m2 K
where a refers to heat transfer coefficient a or pressure gradient dp/ dl and N is the number of data points. Single-phase pressure drop experiments were conducted during adiabatic flow of R152a with Reynolds number ranging from 800 to 1.01 104. Fig. 3 shows comparison between measured and predicted friction factors. The present data agree well with predictions of Blasius equation [21] with the a.m. and r.m.s deviations within 1.7% and 8.8%, respectively. Single-phase heat transfer experiments were performed with Reynolds number ranging from 1.3 103 to 1.2 104 and temperature of liquid R152a from 27 °C to 33 °C. Fig. 4 shows comparison between measured and predicted Nusselt numbers. The present data agree well with predictions of Gnielinski correlation [22] with the a.m. and r.m.s deviations within 4.1% and 12.1%, respectively. Deviations of heat transfer rate between the refrigerant and cooling water in the test section are within ±5%. Single-phase experiments show that the heat loss in the test section is rather small and the experimental rig is appropriate for condensation experiments.
12
circular square G / kg/(m2 s) 200 400 600 800
10 8 6
3.2. Heat transfer during condensation
4
3.2.1. Effects of mass flux and vapor mass quality Fig. 5 shows the effects of mass flux and vapor mass quality on heat transfer coefficients with the saturation temperature of 40 °C and the temperature difference between the refrigerant and the cooling water of 10 °C. During the experiments, mass fluxes varied from 200 to 800 kg/m2 s. Heat transfer coefficients increase with increasing mass flux and vapor mass quality both in circular and square microchannels, which agrees with the previous studies [23]. Heat transfer coefficients become more sensitive to mass flux at high vapor mass qualities implying the dominant effect of shear stress. Error bars have been introduced for the heat transfer coefficients in Fig. 5.
2 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-χ Fig. 5. Effects of mass flux, vapor mass quality and channel geometry on heattransfer coefficients.
20 o
circular R152a
18 16
ts / C 40 50
G=400 kg/(m2 s)
α / kW/(m2 K)
14 0.10 present
circular R152a
0.09
f =64/Re
0.08
f =0.3164/Re
0.25
0.07
f
10 8 6
0.06
4
0.05
2
0.04
0 0.0
0.03
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1-χ
0.02
Fig. 6. Effect of saturation temperature on heat-transfer coefficients.
0.01 0.00
12
0
2000
4000
6000
8000
10000
12000
Re Fig. 3. Comparison of measured and predicted friction factors.
3.2.2. Effect of saturation temperature Experiments were conducted at two saturation temperatures of 40 °C and 50 °C in the circular microchannel. Fig. 6 shows the effect of the saturation temperature on heat-transfer coefficients of
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3.2.4. Comparison with heat transfer correlations and a theoretical solution Four heat transfer correlations and a theoretical solution are used to predict experimental data in the circular and square microchannels ([24,25,8,26,27]). Except for Wang and Rose [27] a theoretical solution, rest are based on experimental data of refrigerants. The work of Wang and Rose [27] shows that there is a region where heat transfer coefficient is governed only by surface tension and the solution is derived based on the calculated results in the region. Fig. 7 shows comparison between measured and predicted heat-transfer coefficients. Table 3 summarizes evaluation results of heat transfer correlations and the theoretical solution which were assessed in terms of the arithmetic mean error, a.m., and root-mean-square error, r.m.s. The results for the circular microchannel agree within experimental error with Wang et al. [24] and Koyama et al. [25] correlations and the theoretical solution [27], while for the square microchannel the results agree within experimental error with Koyama et al. [25], Cavallini et al. [8] and Bandhauer et al. [26] correlations and the theoretical solution [27]. Fig. 7 shows that deviations between the data and predictions of Wang and Rose [27] depend much on vapor mass quality.
150
(αpre-αexp)/αexp×100%
3.2.3. Effect of channel geometry Fig. 5 also shows effects of channel geometry on heat-transfer coefficients of R152a with various mass fluxes. At G = 200 kg/m2 s heat-transfer coefficients in the square microchannel are all higher than those in the circular microchannel. On one hand, the heat transfer enhancement is caused by effects of the corners in the square microchannel. The condensate is pulled to the corners due to the effect of surface tension, which reduces the average thermal resistance across the cross section in the square microchannel. On the other hand, the hydraulic diameter decrease of the square microchannel (circular: dh = 1.152 mm, square: dh = 0.952 mm) increases heat-transfer coefficients according to the previous studies of Zhang et al. [23]. At G = 400 kg/m2 s heat-transfer coefficients in the square microchannel are still larger than those in the circular microchannel though the enhancement is weaker compared with that at G = 200 kg/m2 s. At G = 600 kg/m2 s heat-transfer coefficients of the two microchannels almost overlap each other. Shear stress plays a much more important role than surface tension with increase of mass flux. Effect of the square microchannel corners becomes weaker at higher mass fluxes.
200
+30%
100 50 0 -50 -30% -100 -150 -200 0.0
Wang et al. (2002) Koyama et al. (2003) Cavallini et al. (2011) Bandhauer et al. (2006) Wang and Rose (2011)
0.2
0.4
0.6
0.8
1.0
1- χ
(a) circular 200 150
(αpre-αexp)/αexp×100%
R152a. Heat-transfer coefficients decrease with increasing saturation temperature, which can be attributed to dependence of thermodynamic properties of the refrigerant on saturation temperature. The saturation pressure and vapor density increase with increasing saturation temperature, which increases the vapor and liquid phase density ratio. The vapor phase velocity decreases and the shear stress between the liquid and vapor phase decreases with increasing saturation temperature leading to thicker condensate and lower heat-transfer coefficients.
100
+30%
50 0 -50 -100 -150 -200 0.0
-30%
Wang et al. (2002) Koyama et al. (2003) Cavallini et al. (2011) Bandhauer et al. (2006) Wang and Rose (2011)
0.2
0.4
0.6
0.8
1.0
1- χ
(b) square Fig. 7. Comparison of measured and predicted heat-transfer coefficients.
Table 3 Performance of heat transfer correlations and a theoretical solution compared with the present data. Circular
Wang et al. [24] (2002) correlation Koyama et al. [25] (2003) correlation Cavallini et al. [8] (2011) correlation Bandhauer et al. [26] (2006) correlation Wang and Rose [27] (2011) theoretical solution
Square
a.m.
r.m.s
a.m.
r.m.s
11.2 12.7 17.9 29.3 14.6
15.4 29.6 27.4 14.1 52.3
26.3 5.4 0.9 7.4 4.3
16.3 5.6 19.8 21.9 30.0
a.m.: Arithmetic mean error (%); r.m.s.: root-mean-square error (%).
3.3. Pressure drop during condensation 3.3.1. Effects of mass flux and vapor mass quality Fig. 8 shows effects of mass flux and vapor mass quality on frictional pressure gradients both in circular and square microchannels. The frictional pressure gradients increase with mass flux and vapor mass quality which is similar to heat-transfer coefficients shown in Fig. 5. Pressure gradient trends become smooth at high vapor mass qualities. The mist flow regime with droplet entrained in the vapor core emerges at high vapor mass qualities according to results of Garimella and Coleman [28] where pressure gradients increase less with vapor mass quality.
3.3.2. Effect of saturation temperature Fig. 9 shows effect of saturation temperature on frictional pressure gradients of R152a in the circular microchannel. The frictional pressure gradient decreases with increasing saturation temperature similar to that for heat-transfer coefficients in Fig. 6. The saturation pressure increases with the saturation temperature leading to higher reduced pressure and larger vapor and liquid phase density ratio. The decrease of the velocity difference between the two phases decreases the frictional pressure gradient.
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N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
300
200
[(dp/dl)pre-(dp/dl)exp]/(dp/dl)exp×100%
dp/dl / kPa/m
200 400 600 800
ts =40 oC
250
240
G / kg/(m2 s)
circular square
R152a
150
100
50
0 0.0
0.2
0.4
0.6
0.8
180 120 60
+30%
0 -60
-30% -120 -180 -240 0.0
1.0
Koyama et al. (2003) Agarwal & Garimella (2009) Cavallini et al. (2009)
0.2
0.4
1.0
o
circular
ts / C 2
G=400 kg/(m s)
240
[(dp/dl)pre-(dp/dl)exp]/(dp/dl)exp×100%
120
40 50
80
dp/dl / kPa/m
0.8
(a) circular
Fig. 8. Effects of mass flux, vapor mass quality and channel geometry on frictional pressure gradients.
100
0.6
1-χ
1- χ
60
40
180 120
+30%
60 0 -60
-30%
-120 -180 -240 0.0
20
Koyama et al. (2003) Agarwal & Garimella (2009) Cavallini et al. (2009)
0.2
0.4
0.8
0.6
1.0
1-χ 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
(b) square
1.0
1- χ
Fig. 10. Comparison of measured and predicted frictional pressure gradients.
Fig. 9. Effect of saturation temperature on frictional pressure gradients.
3.3.3. Effect of channel geometry Effect of channel geometry on frictional pressure gradients is shown in Fig. 8. Frictional pressure gradients of the square microchannel are slightly lower than those in the circular microchannel at higher vapor mass qualities for the same operating conditions. However, at lower vapor mass qualities, frictional pressure gradients are almost equivalent in the two microchannels. Therefore, channel geometry has little effect on frictional pressure gradients. 3.3.4. Comparison with pressure drop correlations Three pressure drop correlations [25,29,30] based on experimental data of R134a in microchannels were used to predict experimental data. As 2 Ra/Dh was larger than 0.0027, zero surface roughness Ra was inserted in the Cavallini et al. [30] equations when computing pressure gradients, while the surface roughness was not needed in Koyama et al. [25] and Agarwal and Garimella [29] equations. Comparison results are shown in Fig. 10. Table 4 summarizes the evaluation results of pressure drop correlations. The performance of each correlation was assessed in terms of the arithmetic mean error, a.m., and root-mean-square error, r.m.s. Koyama et al. [25] underestimates the data for both microchannels while Agarwal and Garimella [29] overestimate the data for the square microchannel. Predictions of Cavallini et al. [30] show large
Table 4 Performance of pressure drop correlations compared with the present data. Correlations
Koyama et al. [23] (2003) correlation Agarwal and Garimella [29] (2009) correlation Cavallini et al. [6] (2009) correlation
Circular
Square
a.m.
r.m.s.
a.m.
r.m.s
78.1 4.2
6.9 20.5
64.5 34.2
14.0 20.1
25.5
43.9
11.7
41.0
a.m.: Arithmetic mean error (%); r.m.s.: root-mean-square error (%).
root-mean-square errors for data in both circular and square microchannels.
4. Conclusions Heat transfer and pressure drop during condensation of R152a were investigated experimentally in a circular (d = 1.152 mm) and a square (dh = 0.952 mm) microchannels. Experiments were conducted with mass fluxes from 200 to 800 kg/m2 s, saturation temperatures of 40 °C and 50 °C and vapor mass qualities from 0.1 to 0.9. Experimental data were compared with empirical correlations and a theoretical solution. The following conclusions can be drawn:
N. Liu et al. / Experimental Thermal and Fluid Science 47 (2013) 60–67
1. Heat-transfer coefficients and pressure gradients during condensation increase with mass flux and vapor mass quality while decrease with the saturation temperature both in circular and square microchannels. 2. Heat-transfer coefficients of the square microchannel are higher than those of the circular microchannel at G = 200 kg/m2 s and 400 kg/m2 s due to the effect of surface tension. The heat transfer enhancement decreases with mass flux as the shear stress plays a much more important role at higher mass fluxes. However, channel geometry has little effect on two phase pressure gradients. 3. The heat transfer results for the circular microchannel agree within experimental error with Wang et al. [24] and Koyama et al. [25] correlations and the theoretical solution [27], while for the square microchannel the results agree within experimental error with Koyama et al. [25], Cavallini et al. [8] and Bandhauer et al. [26] correlations and the theoretical solution [27]. For pressure drop results, Koyama et al. [25] underestimates the data for both microchannels while Agarwal and Garimella [29] overestimate the data for the square microchannel.
Acknowledgements The work was financially supported by the National Basic Research Program of China (‘‘973’’ Project, No. 2011CB706904), Guangdong Industry-Academia-Research Project (No. 2011A090200018) and the new energy vehicles industry Project (2011) of Guangdong Special Funds for Strategic Emerging Industries. The work was also supported by EU research Grant FP7-2010IRSES-269205. References [1] Regulation (EG) No 842/2006 of the European Parliament and of the Council of 17 May 2006 on certain fluorinated greenhouse gases, Official Journal of the European Union, 2006. [2] Directive 2006/40/EC of The European Parliament and of the Council of 17 May 2006 relating to emissions from air-conditioning systems in motor vehicles and amending Council Directive 70/156/EC, Official Journal of the European Union, 2006. [3] Q. Su, G.X. Yu, H.S. Wang, J.W. Rose, Microchannel condensation: correlations and theory, International of Refrigeration 32 (2009) 1149–1152. [4] E.E. Wilson, A basis for rational design of heat transfer apparatus, ASME Transactions 37 (1919) 47–70. [5] M. Matkovic, A. Cavallini, D. Del Col, L. Rossetto, Experimental study on condensation heat transfer inside a single circular minichannel, International Journal of Heat and Mass Transfer 52 (2009) 2311–2323. [6] A. Cavallini, D. Del Col, M. Matkovic, L. Rossetto, Pressure drop during twophase flow of R134a and R32 in a single minichannel, Journal of Heat Transfer 131 (2009) 0331071–0331078. [7] D. Del Col, D. Torresin, A. Cavallini, Heat transfer and pressure drop during condensation of the low GWP refrigerant R1234yf, International Journal of Refrigeration 33 (2010) 1307–1318.
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