Convective Condensation Inside Horizontal Smooth

Zan Wu Department of Energy Sciences, Lund University, Box 118, Lund SE-22100, Sweden; Department of Energy Engineering, Zhejiang University, Hangzhou 310027, China

Bengt Sund en1 Department of Energy Sciences, Lund University, Box 118, Lund SE-22100, Sweden e-mail: [email protected]

Lei Wang Department of Energy Sciences, Lund University, Box 118 Lund SE-22100, Sweden

Wei Li Department of Energy Engineering, Zhejiang University, Hangzhou 310027, China

1

Convective Condensation Inside Horizontal Smooth and Microfin Tubes An experimental investigation was performed for convective condensation of R410A inside one smooth tube (3.78 mm, inner diameter) and six microfin tubes (4.54, 4.6 and 8.98 mm, fin root diameter) of different geometries for mass fluxes ranging from 99 to 603 kg m2s1. The experimental data were analyzed with updated flow pattern maps and evaluated with existing correlations. The heat transfer coefficient in the microfin tubes decreases at first and then increases or flattens out gradually as mass flux decreases. This obvious nonmonotonic heat transfer coefficient-mass flux relation may be explained by the complex interactions between the microfins and the fluid, mainly by surface tension effects. The heat transfer enhancement mechanism in microfin tubes is mainly due to the surface area increase at large mass fluxes, while liquid drainage by surface tension and interfacial turbulence enhance heat transfer greatly at low mass fluxes. [DOI: 10.1115/1.4026370] Keywords: Microfin tube, convective condensation, flow pattern, pressure drop, heat transfer

Introduction

Heat transfer enhancement has been an important factor in obtaining energy efficiency improvements in refrigeration and airconditioning applications. Currently, microfin tubes, i.e., tubes with numerous, very small integral fins on the inner surface, are routinely used because they can substantially enhance heat transfer coefficients with a small pressure drop penalty. The dimensions that define a single-groove microfin geometry are shown in Fig. 1(a). The fin layout parameters are defined by the fin pitch normal to the fins (pf) and the helix angle (b). The number of fins is given by ns ¼ pdicosb/pf. The fin shape parameters are defined by the fin height (e), the fin base thickness (tb), and the apex angle of the fin (a). The axial pitch is defined geometrically by p ¼ pdi/(nstanb). The total surface heat exchange area of the microfin tube (A) relative to its nominal inner area (Ani) based on the fin root diameter (di), is given by Webb and Kim [1] A=Ani ¼ 1 þ 2½secða=2Þ tanða=2Þ e=pf

(1)

For a constant tube diameter, a decrease of the fin pitch normal to the fins (pf) will increase the number of fins (ns), which provides increased A/Ani. The cross-sectional profile of the tested microfin tube is presented in Fig. 1(b). Heat transfer characteristics of microfin tubes with outside diameters larger than 6.0 mm have been studied extensively. Webb and Kim [1], Thome [2], Chamra et al. [3,4], Dalkilic and Wongwises [5], and Liebenberg and Meyer [6] have given comprehensive reviews of relevant literature about experimental investigations and semi-empirical or theoretical correlations. Nozu and Honda [7] numerically investigated heat transfer characteristics in annular flow regime for condensation inside horizontal microfin tubes. Jung et al. [8] conducted investigations of condensation of R22, R134a, R407C, and R410A inside smooth and microfin tubes, and found that the heat transfer coefficients of a microfin tube were 1 Corresponding author. Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 26, 2012; final manuscript received December 19, 2013; published online March 6, 2014. Assoc. Editor: W. Q. Tao.

Journal of Heat Transfer

2–3 times higher than those of a smooth tube. Olivier et al. [9] presented a study of flow regime, pressure drop, and heat transfer coefficient during condensation of R22, R407C, and R134a inside a microfin tube of 9.55 mm outer diameter with mass fluxes ranging from 400 to 800 kg m2 s1. Sapali and Patil [10] experimentally investigated the heat transfer coefficient during condensation of R134a and R404A in a smooth tube of 8.56 mm inner diameter and a microfin tube of 8.96 mm fin root diameter, and proposed a predictive correlation based on their own data. Mohseni and Akhavan-Behabadi [11] visually studied the flow patterns during condensation inside a microfin tube with different tube inclinations. Annular flow, semi annular flow and stratified wavy flow exist in sequence for a horizontal microfin tube. Son and Oh [12] investigated the heat transfer characteristics of CO2 in horizontal smooth and microfin tubes at high saturation temperatures, and showed that the Cavallini et al. correlation [13] gave relatively good agreement with experimental data for the microfin tube. More recently, attention has been paid to tubes having smaller diameters to develop more compact heat exchangers. Therefore, microfin tubes with outer diameters below 5.0 mm are primarily in the research and development stage. However, test data for such tubes are very limited. Huang et al. [14] performed a condensation heat transfer study of R410A-oil mixture in 5 mm and 4 mm outer diameter microfin tubes. Kim et al. [15] performed CO2 condensation experiments inside a horizontal microfin tube with an outer diameter of 4.34 mm at low temperatures. Han and Lee [16] examined heat transfer and pressure drop characteristics of four microfin tubes with 8.92, 6.46, 5.1, and 4 mm maximum inner diameter. Based on their own experimental data, correlations for heat transfer, and frictional pressure drop for the four tested microfin tubes were proposed based on the heat momentum relation. The purpose of this study is to perform an experimental investigation on convective condensation of refrigerant R410A inside one smooth tube (3.78 mm, inner diameter) and six microfin tubes (4.54, 4.6, and 8.98 mm, fin root diameter) of different geometries. Geometric parameters of the smooth and six microfin tubes are presented in Table 1. Flow patterns in the tested tubes were analyzed by existing flow pattern maps, and experimental frictional pressure drop and heat transfer data were presented specifically and compared with existing correlations.

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Fig. 1 Microfin surface geometry and cross-sectional profile of the microfin tube: (a) geometric parameters of the microfin surface and (b) cross-sectional profile of the microfin tube

2

Experimental Apparatus and Data Reduction

2.1 Test Apparatus. A schematic diagram of the test apparatus used for in-tube condensation is shown in Fig. 2(a). It consists of 2 closed loops: a refrigerant loop which contains the test section and a water circuit which cools the test section. The refrigerant flow loop consists of a 50 l reservoir tank, a digital gear pump, a pressure regulating valve, a mass flow meter, a preheater, a test section, a condenser, and sight glasses. A bypass line from the pump to the reservoir and the regulating valve are used to control the mass flow rate through the refrigerant loop. A mass flow meter with an accuracy of 60.2% of reading is located between the

pump and the preheater to measure refrigerant flow rates. The subcooled liquid is electrically heated in the preheater to two-phase flow with a certain inlet quality at the preheater outlet, and then goes into the test section to condense. Finally, the two-phase refrigerant is totally condensed and subcooled in a 9 kW alcoholwater mixture low-temperature bath. A Platinum 100 RTD thermometer, calibrated carefully with an accuracy of 60.07 K, and a pressure transducer with an accuracy of 60.2% are located at the preheater inlet to indicate the thermodynamic state of fluid to obtain enthalpy. The horizontal test section is a straight, tube-in-tube heat exchanger with a length of 2 m, as shown in Fig. 2(b). The inner tubes are the seven test tubes described in Table 1. Among the six microfin tubes, five of them (Tubes 1–5) have the same outer diameter (OD) of 5 mm, while Tube 6 has an outer diameter of 9.52 mm. The six microfin tubes have the same helix angle of 18 deg. Tube 4 has the largest area enhancement ratio A/Ani, while Tube 3 has the lowest A/Ani except for the smooth tube. The outer tubes are hard-drawn copper tubes with inner diameters of 9 mm and 13 mm, for 5 mm OD and 9.52 mm OD test tubes, respectively. Inside the heat exchanger, the refrigerant is condensed inside the test tube, while water flows counter-currently in the annulus. A differential pressure transducer with an accuracy of 60.05% of set span is used to measure the pressure drop across the test section. The refrigerant temperatures at the inlet and outlet of the test tube, and the water temperatures at the inlet and outlet of the annulus, are all measured by Platinum 100 RTDs, calibrated with an accuracy of 60.07 K. In addition, two absolute pressure transducers with an accuracy of 60.2% are installed at the inlet and outlet of the test section. The measured saturation temperatures are in good agreement with the temperature calculated from the saturation pressure within 60.4 K. Because of the horizontal, annular design of the test section with measuring positions only at the inlet and outlet of the test section, heat transfer measurements are limited to average values, rather than local values and the pressure drop measurements are limited to overall pressure drop for the entire test section. The water circuit includes the annulus, a water thermostat, a centrifugal pump, a control valve, and a magnetic flow meter. The magnetic flow meter with an accuracy of 60.35% of reading is used to record the flow rates of water in the annulus of the test section. A 40 mm thick foam insulation and a 6 mm thick rubber insulation are fitted well for the entire test facility, especially for the preheater and the test section, to minimize heat losses. 2.2 Experimental Procedure and Conditions. Degassing was performed before all tests. The reservoir tank in the R410A circuit can be heated by an electrically-heated element to evaporate the refrigerant liquid in it. The noncondensable gases and a small amount of refrigerant vapor can be removed by the release valve (not shown in Fig. 2(a)) on the top of the tank. After degassing, noncondensable gases eventually existing in the loops can be removed by using a vacuum pump. For all tests, the room temperature was maintained at 300 K. All the measurements were recorded by a data logger, monitored and analyzed in real time with a PC. Data were recorded every 20 s. Test conditions were considered stable when deviations

Table 1 Test tube geometries Tube No.

do (mm)

Smooth tube Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 Tube 6

5.0 5.0 5.0 5.0 5.0 5.0 9.52

di (mm)

ns (—)

a (deg)

b (deg)

e (mm)

A/Ani (—)

e/pf (mm)

3.78 4.6 4.6 4.54 4.54 4.6 8.98

— 40 38 35 58 50 70

— 40 25 25 25 20 30

— 18 18 18 18 18 18

— 0.15 0.15 0.12 0.12 0.10 0.16

1.0 1.61 1.67 1.50 1.82 1.61 1.64

— 0.44 0.41 0.31 0.51 0.36 0.42

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Transactions of the ASME

Fig. 2 Schematic drawings of (a): test rig and (b): test section

in temperature, mass flux, and pressure for 5 min were below 0.1 K, 2 kg/m2s, and 2.0 kPa, respectively. Average values of twenty consecutive data points were used in analyses for each stable test condition. In order to verify the test facility, preliminary tests were performed. Firstly, we checked the heat balances of single-phase flow at different flow rates. For the test section, the maximum difference between the heat flow rate in the annulus and the heat flow rate in the tube was less than 3%. For the preheater, the maximum difference between the heat rate provided by the electric heater and the heat rate in the tube was also less than 3%. In addition, for the test section, single-phase heat transfer coefficients in both the smooth tube side and the annulus side were calculated and compared with the Gnielinski correlation [17]. The comparison showed that all data points are located within a 610% error band. For single-phase flow in microfin tubes, the Ravigururajan and Bergles correlation [18] can predict the heat transfer coefficient within a 610% error band by replacing the fin root diameter by the hydraulic diameter in the calculation, as presented specifically in Li et al. [19]. During condensation experiments, sufficient sub-cooling (not less than 10 C) was maintained by controlling the alcohol-water mixture low temperature bath to prevent flashing in the downstream flow restrictions, and to ensure single-phase flow at the pre-heater inlet. The minimum coolant (water) temperature rise in the annulus of the test section at all flow rates is larger than 1.8 K. The minimum Reynolds numbers of the water flow in the annulus of the test section are 4000, 6100, and 7500, for the smooth tube, Journal of Heat Transfer

the 5 mm OD microfin tube (Tubes 1–5) and the 9.52 mm OD microfin tube (Tube 6), respectively. Condensation tests of R410A were conducted at 320 K saturation temperature, 99–603 kg m2 s1 mass flux, 5.9–33.3 kW m2 heat flux, 0.8 inlet quality, and 0.1 outlet quality (an average vapor quality of 0.45 for all condensation tests). The mass fluxes were calculated using the actual cross-sectional flow area Ac. The heat fluxes were determined using the total inner surface heat-transfer area A. 2.3 Data Reduction. The data taken by the data acquisition system were reduced to calculate the in-tube heat transfer coefficient. The total heat transferred in the test section was determined by an energy balance for water flowing through the annulus Qt;ts ¼ cpl;w;ts qw;ts vv ðTw;ts;out Tw;ts;in Þ

(2)

where cpl,w,ts, qw,ts, vv and are the specific heat and density of water taken at the average temperature of the annulus inlet and outlet temperature, and the volume water flow rate inside the annulus. The inlet vapor quality (xin) was calculated from an energy balance in the preheater. The total heat transferred in the preheater, Qt,ph, to the refrigerant has two forms, sensible Qsens and latent Qlat Qt;ph ¼ kðV I Þ ¼ Qsens þ Qlat

(3)

Qsens ¼ cpl;ref mref ðTsat Tref;ph;in Þ

(4)

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Qlat ¼ mref hlv xin

(5) e¼

where k, cpl,ref, hlv are the experimentally determined factor to account for heat loss of the preheater through the insulation, the specific heat of refrigerant taken at the average pressure of the preheater inlet pressure and saturation pressure, and the latent heat of vaporization of the refrigerant taken at the saturation temperature in the preheater, respectively. The value of k is between 0.97 and 1.0, which was calculated from preliminary single-phase tests at different heat flow rates and mass flow rates. An approximate calibration line of k versus VI was obtained, which was used for correction of Qt,ph. The outlet quality xout was obtained by the equation below: xout ¼ xin Qt;ts =ðmref hlv Þ

(6)

The log-mean temperature difference (LMTD) was determined by the following equation [20]: LMTD ¼

ðTref;ts;out Tw;ts;in Þ ðTref;ts;in Tw;ts;out Þ ln ðTref;ts;out Tw;ts;in Þ=ðTref;ts;in Tw;ts;out Þ

(7)

where Tref,ts,in and Tref,ts,out are the inlet refrigerant temperature and outlet refrigerant temperature of the test section, respectively. They are not equal because of the pressure drop along the test section. Tref,ts,in and Tref,ts,out can be obtained from the Platinum 100 RTDs installed at the inlet and outlet plenums. Assuming no fouling resistance, the tube-side refrigerant heat transfer coefficient for in-tube condensation was determined by

h¼ Ani

1 LMTD 1 lnðdo =di Þ Qt;ts ho Ao 2pL k

(8)

Previous experimental results showed that the Gnielinski equation [17] can predict the annulus-side heat transfer coefficients accurately. This is valid for 0.5 < Pr < 2000 and 3000 < Re < 5 106. The water Reynolds number in the annulus is located in this range, as given in section 2.2. Thus, the Gnielinski equation [17] was adopted to determine the annulus-side heat transfer coefficient ho ho ¼

ðf =2ÞðRe 1000Þ Pr

lbulk 1 þ 12:7ðf =2Þ1=2 ðPr2=3 1Þ lw

0:14

kl da

(9)

The Fanning friction factor was determined by the Petukhov equation [21], which is valid for 3000 < Re < 5 106 f ¼ ð1:58 ln Re 3:28Þ2

(10)

The property ratio (lbulk/lw)0.14 corrects for the viscosity variations at bulk temperature and wall temperature, but it amounts to less than 1.0% in our experiments. kl is the thermal conductivity of water taken at the average water temperature. The measured two-phase pressure drop in the test tubes can be expressed as the sum of momentum and frictional components. DP ¼ DPm þ DPf

(11)

The momentum component due to density change was calculated by the following equation: (" # " # ) x2 ð1 xÞ2 x2 ð1 xÞ2 2 þ þ (12) DPm ¼ G qv e ql ð1 eÞ qv e ql ð1 eÞ out

in

where e is the void fraction which was calculated by the Rouhani and Axelsson [22] drift flux model, applicable for different flow regimes,

" #1 x x 1x 1:18ð1xÞ½grðql qv Þ0:25 þ ð1þ0:12ð1xÞÞ þ qv qv ql Gq0:5 l (13)

The momentum component can be up to 9.0% of the total pressure drop. All thermal and transport properties in the equations of this study are obtained from REFPROP 8.0 developed by NIST (National Institute of Standards and Technology) [23]. The measurement devices used in this study include Platinum 100 RTDs, absolute pressure transducers, differential pressure transducers, mass flow meters and magnetic flow meters, which are calibrated to NIST traceable standards. The propagation of accuracies through data reduction was estimated by the root-sumsquare method, which was detailed in Wu et al. [24]. The given accuracies of primary measurements and the calculated accuracies of dependent parameters are listed in Table 2.

3

Results and Discussion

3.1 Flow Pattern. Liebenberg and Meyer [25] adopted the power spectral density distribution of the fluctuating pressure signal to predict the prevailing flow regime during condensation inside microfin tubes and proposed an annular to intermittent flow regime transition, which is given below: (" xIA ¼

1=0:875

0:695

)1 1=1:75 1=7 # qv ll þ1 ql lv

(14)

This transitional vapor quality was used to update the El Hajal et al. flow pattern map [26]. The updated El Hajal et al. flow pattern map for condensation inside horizontal tubes with different inner diameters is illustrated in Fig. 3(a) for R410A at Tsat ¼ 320 K. The transition from annular flow to intermittent flow is not dependent on inner diameters. It was found that microfin tubes caused a decrease of 0.2 in the transition vapor quality from annular to intermittent flow, 0.58 and 0.38 for smooth tube and microfin tube, respectively. The transition from intermittent and annular flow to stratified wavy flow was not updated in the El Hajal et al. flow pattern map [26]. For the tested smooth tube with di ¼ 3.78 mm, stratified-wavy flow dominates the entire region at low mass flux of 100 kg m2 s1. At G 200 kg m2 s1, intermittent and annular flow regimes are predicted in the whole vapor quality range. Figure 3(b) gives a flow pattern map reported as a function of nondimensional modified Froude number JG and Martinelli parameter Xtt at Tsat ¼ 320 K and di ¼ 4.6 mm. The empty dots and black dots indicate the flow patterns at mass fluxes of 200 kg m2 s1 and 400 kg m2 s1, respectively, when vapor quality changes from Table 2 Relative accuracy for primary measurements and dependent quantities Primary measurements Diameter Length Temperature Electric current Electric voltage Pressure, range: 0–40 bar Differential Pressure, range: 0–100 kPa Water flow rate, range: 0–12 L min1 Refrigerant flow rate, range: 0–60 kg h1

60.05 mm 60.2 mm 60.07 K 60.01 A 61.0 V 60.2% of full scale 60.05% of reading 60.35% of reading 60.2% of reading

Dependent quantities Mass flux G, kg m2 s1 Heat flux q, W m2 Vapor quality, x Frictional pressure drop, DPf Heat transfer coefficient h, W m2 K1

62.2% 64.3% 65.2% 63.9% 615.4%

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The data for 200 kg m2 s1 are very close to the microfin tube transition, and fall in the DT independent region (annular region). From the above discussion and flow pattern maps, it is safe to infer the following statements according to Fig. 3(a), (1) Stratified wavy flow dominates the flow for the smooth tube with an inner diameter of 3.78 mm at mass flux of 100 kg m2 s1, and intermittent and annular flow when G 200 kg m2 s1; (2) For R410A condensing inside Tube 6 with an inner diameter of 8.98 mm, the major flow pattern is stratified wavy flow when G 200 kg m2 s1, and intermittent and annular flow when G > 200 kg m2 s1; (3) Microfins decrease the transitional vapor quality from annular to intermittent flow by about 0.2 compared to the smooth tube. According to the updated Cavallini et al. map in Fig. 3(b), the transition from annular flow to stratified wavy flow in microfin tubes is expected to occur at lower mass fluxes and vapor qualities; all R410A data lie in the annular region when G 200 kg m2 s1 for the entire experimental vapor quality range in Tubes 1–5. 3.2 Condensation Characteristics Inside a Smooth Tube. Figure 4(a) demonstrates the relationship between the frictional pressure drop and mass flux for R410A condensation inside a smooth tube with an inner diameter of 3.78 mm at 320 K saturation temperature, 190–600 kg m2 s1 mass flux, 0.8 inlet quality,

Fig. 3 Flow pattern maps for R410A in horizontal smooth tubes and updated for use in microfin tubes at Tsat 5 320 K: (a) the updated El Hajal et al. map [26] at di 5 3.78, 4.60, and 8.98 mm and (b) the updated Cavallini et al. map [27] at di 5 4.60 mm

0.8 to 0.1. The smooth tube transition line in Fig. 3(b) conveys the “flow pattern criterion” proposed by Cavallini et al. [27] for the separation of DT dependent/independent regions. In the DT dependent region gravity is the leading force, while in annular flow the DT effect can be considered negligible. Compared to a smooth tube, the transition from annular flow to stratified wavy flow in microfin tubes is expected to occur at lower mass fluxes and vapor qualities. The early transition is related to the spiral groove on the inner surface, which can move the liquid refrigerant to the top part of the tube and distribute the liquid film evenly. Thus, at a low mass flux, the flow pattern in the microfin tube is still annular while the pattern in the smooth tube could already become stratified-wavy under the same conditions. Doretti et al. [28] experimentally observed the flow patterns during condensation of R410A, R134a, and R236ea inside a horizontal microfin tube and found that the annularstratified wavy transition was shifted to lower values of JG. The microfin transition line drawn in Fig. 3(b), was described by the following equation: JGT ¼ 0:6

(

7:5 4:3Xtt1:111 þ 1


3

)0:3333 þ2:53

(15)

Fig. 4 Condensation (a) frictional pressure drop and evaluated by the Gronnerud correlation [29] and (b) heat transfer coefficient and evaluated by the Cavallini et al. correlation [27] in the smooth tube with 3.78 mm ID, at Tsat 5 320 K, with inlet and outlet vapor qualities of 0.8 and 0.1, respectively

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and 0.1 outlet quality. The frictional pressure drop increases when mass flux increases. The experimental data can be accurately predicted by the Gronnerud correlation [29], which is applicable for the three flow regimes (stratified wavy, intermittent, and annular) with a mean absolute deviation (MAD) of 8.2%. The MAD values were calculated by N Uexp Upre 1X 100% (16) MAD ¼ N 1 Uexp where U represents the value of an experimental or a predicted data point. The experimental heat transfer coefficient increases with mass flux, as indicated in Fig. 4(b). The predicted values by the Cavallini et al. correlation [27] for smooth tubes are compared with the experimental values. All possible flow regimes during the experimental condensation process are included into the model: intermittent flow and annular flow (G 200 kg m2 s1) and the stratified wavy flow (G < 200 kg m2 s1). The Cavallini et al. correlation [27] can predict all data points within a 610% error band, with a mean absolute deviation of 3.8%. For every mass flux, experiments are repeated for three times. Good repeatability can be observed from Fig. 4. The low deviations between the experimental frictional pressure drop and heat transfer coefficient and the predicted values from the Gronnerud correlation [29] and the Cavallini et al. correlation [27], respectively, also verified the accuracy of the test facility.

3.3 Condensation Characteristics Inside Microfin Tubes. For the five microfin tubes with the same outer diameter of 5 mm, similar frictional pressure drop characteristics are found for R410A, as presented in Fig. 5(a). The frictional pressure drop of the five microfin tubes: Tubes 1–5 is about 1.1 to 1.2 times of the smooth tube. Tube 6 has the lowest frictional pressure drop due to its largest fin root diameter di. The experimental data have been compared with the predicted values of the Choi et al. correlation [30], the Haraguchi et al. correlation [31] and the modified Gronnerud correlation, as presented in Table 3. The Gronnerud correlation [29] has been verified to be capable of predicting our smooth tube data accurately as discussed above in Sec. 3.2. For microfin tubes, the Fanning friction factor in predicting the liquid-only frictional pressure drop term in the Gronnerud correlation [29] was calculated by the Churchill model [32] in which the roughness effects in the turbulent regime were considered. " fLO ¼ 2

8 ReLO

" a ¼ 2:457 ln

12 þ

1

#1=12

1 ða þ bÞ #16

ð7=ReLO Þ0:9 þ ð0:27Rxf Þ

(17)

3=2

;b ¼

37530 ReLO

16

(18) Rxf is an empirically-fitted relative roughness used to model microfin tubes for condensation, which can be expressed as Rxf ¼

0:18 ðe=di Þ ð0:1 þ cos bÞ

(19)

The predictive ability of the three correlations is shown in Fig. 5(b). The Choi et al. correlation [30] is prone to underestimate the experimental data. All data points in six tested microfin tubes are approximately predicted within the error band between 20% and þ30% by the Haraguchi et al. correlation and the modified Gronnerud correlation. The mean absolute deviation of the modified Gronnerud correlation is 8.7%. It is reasonable to point out that the smooth-tube Gronnerud correlation [29] can be applicable

Fig. 5 Condensation frictional pressure drop in microfin tubes: (a) experimental data and (b) comparison of experimental data and predicted values by existing correlations

for microfin tubes by adopting the Churchill model [32] to include the microfin roughness effects. Figure 6(a) presents the relationship between condensation heat transfer coefficient and mass flux G. For R410A condensation inside the five microfin tubes with the same outer diameter of 5 mm, Tube 4 has the best heat transfer performance covering almost all mass fluxes due to its largest area enhancement ratio A/Ani, while Tube 3 performs worst when G < 600 kg m2 s1 due to its lowest area enhancement ratio A/Ani. The heat transfer coefficient of the five microfin tubes, Tubes 1–5, is about 1.6–2.5 times of the smooth tube. Tube 6 has the lowest heat transfer coefficient due to its relatively larger inner diameter compared to the other five microfin tubes. The six microfin tubes have similar thermal performance when G 400 kg m2 s1. Heat transfer coefficient increases with increasing mass flux. However, when G < 400 kg m2 s1, heat transfer coefficient decreases at first and then increases or flattens out gradually as mass flux decreases. In other words, mass flux has a nonmonotonic relation with heat transfer coefficient in microfin tubes. A transitional mass flux exists for Tube 2, Tube 4, Tube 5, and Tube 6. Heat transfer coefficient of Tube 2, Tube 4, and Tube 5 decreases as G increases, when G < 300 kg m2 s1, and increases with G when G > 300 kg m2 s1, while h of Tube 6 decreases as G increases when

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Table 3

Description of existing correlations for condensation pressure drop and heat transfer coefficient

Authors (1) Frictional pressure drop Gronnerud [29] (smooth tube)

Equations Applicable range: 0 < x < 1.0, pure fluids and "near azeotropic mixtures. # dP dP dP ql =qv 2 ¼ U , ðUÞLO ¼ 1 þ 1 dz dz LO LO dz Fr ðll =lv Þ0:25 f dP G2 0:5 ¼ fFr x þ 4ðx1:8 x10 fFr Þ , FrLO ¼ dz Fr gdi q2l 1 2 0:3 If FrLO 1:0, fFr ¼ 1:0; Or if FrLO < 1:0, fFr ¼ FrLO þ 0:0055 ln FrLO

Choi et al. [30] (microfin tube)

Applicable range: ReLO > Kf, 7.9 < di < 15.9 mm, purerefrigerants and refrigerant/lubricant mixtures fc Lðout þ vin Þ þ ðout vin Þ DP ¼ DPf þ DPm ¼ G2 dh Gdh Kf0:1554 , Reh;LO ¼ , Kf ¼ Dx hlv =ðg LÞ fc ¼ 0:00506 Re0:0951 h;LO ll

Haraguchi et al. [31] (microfin tube)

Applicable range: 100 < G < 300 kg m2 s1, di ¼ 8.37 mm, pure refrigerants. ðdP=dzÞf ¼ U2v ðdP=dzÞv ¼ U2v 2fv ðGxÞ2 =ðqv di Þ Uv ¼ 1:1 þ 1:3fGXtt =½gdm qv ðql qv Þ0:5 g0:35

(2) Heat transfer coefficient Cavallini et al. [27] (smooth tube)

Applicable range: Pred < 0.8, 3.1 < di < 17.0 mm, pure fluids and near azeotropic mixtures, except ammonia. JG > JGT: h i hA;S ¼ hLO 1 þ 1:128x0:817 ðql =qv Þ0:3685 ðll =lv Þ0:2363 ð1 lv =ll Þ2:144 Pr0:1 l

0:8 0:4 0:4 hLO ¼ 0:023 Re0:8 LOhPrl kl =di ¼ 0:023ðGdi =l i l Þ Pr l kl =di T

0:8 T JG JG : hD;S ¼ hA;S JG =JG hSTRAT JG =JGT þ hSTRAT 3 0:25

0:725 kl ql ðql qv Þg hlv hSTRAT ¼ þ 1 x0:087 hLO 0:3321 ll di DT 1x 1 þ 0:741 x

Cavallini et al. [13] (microfin tube)

Applicable range: 0.1 < Pred < 0.67, 6.0 < di < 14.2 mm, halogenated refrigerants and carbon dioxide, except water and ammonia. 0:333 hMF ¼ h3A þ h3D , hA ¼ hA;S EF C !0:3821 G2 ðRx 1Þ0:3586 EF ¼ 1 þ 1:119 gdi ðql qv Þ2 Rx ¼ f½2ens ð1 sinða=2ÞÞ=½pdi cosða=2Þ þ 1g=cos b; C ¼ 1 if (nopt/ns) 0.8, C ¼ (nopt/ns)1.904 if (nopt/ns) < 0.8; nopt ¼ 4064:4d i þ 23:257 h

0:6875 i þ1 hST þ Cð1 xÞ0:087 Rx hLO hD ¼ C 2:4x0:1206 ðRx 1Þ1:466 JG =JGT 3 0:25 0:725 kl ql ðql qv Þg hlv hST ¼ 0:3321 ll di DT 1x 1 þ 0:741 x

Kedzierski and Goncalves [35] (microfin tube)

Applicable range: 57 < G < 552 kg m2 s1, di ¼ 9.5 mm, pure refrigerants and near azeotropic mixtures. 2 2 Pr0:308 ðPred Þ1:16x ð log10 Pred Þ0:887x Sv2:708x kl =dh , Reh ¼ Gdh =ll , hMF ¼ 4:94 Re0:235 h l Sv ¼ ðv l Þ=v, v ¼ xv þ ð1 xÞl , Prl ¼ cpl ll =kl

Chamra et al. [3] (microfin tube)

Applicable range: 40 < G < 850 kg m2 s1, 6.35 < do < 15.88 mm, pure refrigerants. q cpl ðsw =qÞ0:5 dP di hMF ¼ , s ¼ w dz f 4 Tþ T þ ¼ dþ Prl for dþ 5

T þ ¼ 5 Prl þ ln 1 þ Prl dþ =5 1 for 5 < dþ 30 þ d 2:5 for 30 dþ T þ ¼ 5 Prl þ lnð1 þ 5 Prl Þ þ 0:5 ln 27:5 þ 0:87 dþ ¼ 0:866 Re0:5 for 1600 < Rel l for Rel 1600, d ¼ 0:051 Rel

Yu and Koyama [36] (microfin tube)

Applicable range: 100 < G < 300 kg m2 s1, 6.35 < di < 8.78 mm, pure refrigerants and near azeotropic mixtures. 0:5 0:68 hMF ¼ h2F þ h2B , hF ¼ 0:152 0:3 þ 0:1 Pr1:1 L ðUv =Xtt ÞRel 1=4

p ffiffi p ffiffi 0:725 Ga Prl hB ¼ e þ C2 e 1 e , C2 ¼ 10ð1 eÞ0:1 8:0 Phl ðA=Ani Þ1=4 Ga ¼ gq2l di3 =l2l , Phl ¼ cpl ðTsat Tw Þ=hlv

G < 200 kg m2 s1, and increases with G when G > 200 kg m2 s1. This phenomenon, to the authors’ knowledge, has not been reported by previous literature except the similar flatten-out trend observed by Eckels and Tesene [33]. The good accuracy of the Journal of Heat Transfer

test facility has been verified above in Sec. 2.2 by energy balances and in Sec. 3.2 by condensation in smooth tubes, respectively. Repeatability tests for R410A condensation in Tube 2, Tube 4, Tube 5, and Tube 6 have also been conducted. The maximum MAY 2014, Vol. 136 / 051504-7


Fig. 6 Condensation heat transfer coefficient versus mass flux in microfin tubes: (a) experimental heat transfer data and (b) comparison of experimental data and predicted values by existing correlations, with inlet and outlet vapor qualities of 0.8 and 0.1, respectively

difference of heat transfer coefficient values is less than 3% at similar mass fluxes for the same tube. Thus, there must be other reasons for this nonmonotonic h-G relation. The complex interactions between the microfins and the fluid could contribute to this mass-flux effect. The centrifugal force by the microfins spreads the liquid to the upper part, and surface tension pulls the condensate from the fin tips into the drainage channel at the base of the fins, forming a very thin liquid layer on the surface of microfins. Thus, heat transfer is enhanced greatly. Yang and Webb [34] showed that the enhancement by liquid drainage decreases as the mass flux increases. In addition, the enhancement by interfacial turbulence is more significant at low mass fluxes and tends to be lower at larger mass flux. This is perhaps due to the enhanced turbulence already existing at large mass fluxes. Also Kedzierski and Goncalves [35] presented that low Reynolds number flows may be enhanced more readily than high Reynolds number flows due to the reduction in the size of the turbulent eddies at the wall by the interaction of the flow with the fins because smaller eddies transfer momentum more efficiently than larger ones. In short, microfins enhance the heat transfer coefficient mainly by the following three contributions: surface area increase, liquid drainage due to surface tension and interfacial turbulence. As discussed above, the enhancement contributions from liquid drainage and interfacial turbulence are more significant at

lower mass fluxes than at higher mass fluxes. This is why the heat transfer coefficient at lower mass fluxes in microfin tubes can be larger than or equal to that at higher mass fluxes, i.e., the nonmonotonic or flatten-out h-G phenomenon as shown in Fig. 6(a). The nonmonotonic h-G trend is strongly influenced by the liquid drainage mechanism due to surface tension effect. The parameters which can affect the surface tension effect are the fin tip radius, fin height, apex angle, and the ratio of the core area-toactual cross section area. The most important parameter that affects the surface tension force is the fin tip radius, as presented by Yang and Webb [34]. A smaller fin tip radius provides a higher surface tension drainage force. Therefore, it is reasonable to guess that the fin tip radius affects the h-G phenomenon and the differences among the h-G trends is at least partly attributed to the differences in the fin tip radius. This result is very interesting as it sheds insight on the importance of fin tip profiles (fin tip radius) in enhancing heat transfer, besides the mostly investigated microfin parameters such as fin root diameter, fin height, number of fins, helix angle, apex angle, and fin pitch. The obvious nonmonotonic h-G relation and the appearance of the transitional mass flux for Tube 2, Tube 4, Tube 5, and Tube 6 for R410A are probably due to the fact that the fin tip radii in the four microfin tubes are smaller than that of the other microfin tubes. The fin tip profiles were not measured in this study. A metallographic microscope will be used to measure the fin tip profiles accurately and more experimental investigations on a large variety of fin tip profiles will be conducted to develop a robust model to predict the observed nonmonotonic h-G phenomenon in the future. We believe that optimization of fin tip profiles such as fin tip radius will further enhance the heat transfer in microfin tubes at low mass fluxes. The flow regime has significant effects on the heat transfer mechanism, and thus will affect the nonmonotonic h-G relation. For R410A condensation in Tubes 1–5, intermittent and annular flow regimes dominate the entire experimental range, as can be seen from Figs. 3(a) and 3(b). For Tube 6 with a fin root diameter of 8.98 mm, the flow regime is dominated by stratified wavy flow at mass fluxes less than 200 kg m2 s1 (Fig. 3(a)), where a relatively thick liquid film is presented at the lower part of the tube. The effective heat transfer enhancement due to surface tension drainage at low mass fluxes is degraded in the stratified wavy flow regime. In the same stratified wavy regime, the principal reason for the larger heat transfer coefficient at 100 kg m2 s1 compared to that at 200 kg m2 s1 is probably the same as that in the intermittent and annular regimes, as explained specifically above. Four existing correlations, given in Table 3, were evaluated by the present experimental data, including the Cavallini et al. correlation [13], the Kedzierski and Goncalves correlation [35], the Chamra et al. correlation [3], and the Yu and Koyama correlation [36], as shown in Fig. 6(b). For the Chamra et al. correlation [3], the experimental frictional pressure drop were used to calculate the frictional pressure drop gradient (dP/dz)f, rather than existing pressure-drop correlations. All the correlations can approximately predict the experimental data within 630% error band, while all the correlations tend to underestimate the experimental data, especially at low mass fluxes. Figure 7 compares experimental data of Tube 1, Tube 4, and Tube 6 with literature data [8,14,37,38] for R410A condensation in different microfin tubes. The condensation temperature in our experiments and in Refs. [8,14,37,38] ranges from 312 K to 320 K. The quasi-local heat transfer coefficient values at a vapor quality of about 0.45 were adopted for comparison. All heat transfer coefficient values and the corresponding mass fluxes from the literature were recalculated based on the fin root diameter and the actual cross-sectional area, respectively. Generally, the heat transfer coefficient in microfin tubes with smaller fin root diameters (4.6 mm), including Tube 1, Tube 4 and the tested tube in Huang et al. [14], is higher than that of microfin tubes with larger fin root diameters, i.e., Tube 6 and the tubes in Jung et al. [8], Cavallini et al. [37] and Kim and Shin [38]. For microfin tubes with almost the same fin root diameter, the deviations in heat transfer

051504-8 / Vol. 136, MAY 2014



Fig. 7 Heat transfer comparisons of Tube 1, Tube 4, Tube 6 with Huang et al. [14] (di 5 4.6 mm, ns 5 40, a 5 40 deg, b 5 18 deg, e 5 0.14 mm), Jung et al. [8] (di 5 8.92 mm, ns 5 60, a 5 53 deg, b 5 18 deg, e 5 0.2 mm), Cavallini et al. [37] (di 5 8.15 mm, ns 5 60, a 5 43 deg, b 5 13 deg, e 5 0.23 mm) and Kim and Shin [38] (di 5 8.9 mm, ns 5 60, a 5 53 deg, b 5 18 deg, e 5 0.2 mm)

coefficient are mainly due to the differences in microfin geometries (e.g., fin pitch, fin height, fin tip profile, and number of fins) and experimental uncertainties provided in the literature. Tube 4 performs much better than other tubes at low mass fluxes. The reasons for the high heat transfer enhancement at low mass fluxes were stated above specifically. Figure 8 demonstrates the ratio hMF/(hS*A/Ani) versus G for both R22 and R410A in the six microfin tubes. hMF indicates the experimental heat transfer coefficient of the microfin tubes and hS is the predicted heat transfer coefficient by the Cavallini et al. correlation [27] for smooth tubes at the same working conditions. Data of R22 condensation inside the same five microfin tubes with 5 mm OD were extracted from Li et al. [19]. When G > 300 kg m2 s1, the values of hMF/(hS*A/Ani) are equal to unit

Fig. 8 The ratio hMF/(hS*A/Ani) versus mass flux for both R22 [19] and R410A condensation inside the tested microfin tubes


within 610%. However, when G 300 kg m2 s1, the values of hMF/(hS*A/Ani) are larger than unit. The value of hMF/(hS*A/Ani) is 2.8 for Tube 6 at G ¼ 99 kg m2 s1. When G ¼ 200 kg m2 s1 for both R22 and R410A, the values of hMF/(hS*A/Ani) range from 1.5 to 2.2 for the six microfin tubes, 2.2 for R410A condensation inside Tube 2 and Tube 5 and 1.5 for R410A condensation inside Tube 6, respectively. The ratio hMF/(hS*A/Ani) can be used as an measure of the heat transfer enhancement. At large mass fluxes, the condensation heat transfer enhancement is due to the increase of the effective heat exchange area. Therefore, the ratio hMF/(hS*A/Ani) is nearly equal to unity. This means, the heat transfer coefficients in microfin tubes at relatively large mass fluxes can be predicted by a smooth-tube correlation multiplied by the area enhancement ratio A/Ani. For example, the Cavallini et al. correlation [27] for smooth tubes can also predict our heat transfer data accurately for mass fluxes larger than 300 kg m2 s1 if it is multiplied by the area enhancement ratio A/Ani. At low mass fluxes where an obvious nonmonotonic h-G or flatten-out phenomenon happens, besides the surface area enhancement, the surface tension effect on the liquid drainage enhances the heat transfer greatly. Thus, the ratio hMF/(hS*A/Ani) is larger than unity and can be as large as 2.8 at 99 kg m2 s1.

4

Conclusions (1) Condensation frictional pressure drop and heat transfer data for R410A are presented for one smooth tube and six single-grooved microfin tubes of different geometries with small inner diameters at 320 K saturation temperature, 99–603 kg m2 s1 mass flux, 5.9–33.3 kW m2 heat flux, 0.8 inlet quality and 0.1 outlet quality. The convective condensation flow patterns are analyzed by the El Hajal et al. map [26] and the Cavallini et al. map [27]. The flow pattern maps are updated for microfin tubes by Eqs. (14) and (15). The microfins decrease the transition from annular to intermittent flow by approximately 0.2 in vapor quality, and the transition from annular flow to stratified wavy flow in microfin tubes is expected to occur at lower mass fluxes and vapor qualities compared to smooth tubes. (2) The Gronnerud correlation [29] and the smooth-tube Cavallini et al. correlation [27] can predict the experimental frictional pressure drop and heat transfer data of a smooth tube with an inner diameter of 3.78 mm very accurately, with mean absolute deviations of 8.2% and 3.8%, respectively, which also verified the accuracy of the test facility further. (3) The six microfin tubes have similar thermal performance when G 400 kg m2 s1, h increases when G increases. However, when G < 400 kg m2 s1, h decreases at first and then increases or flattens out gradually as G decreases. In other words, the mass flux has a nonmonotonic relation with heat transfer coefficient in microfin tubes. A transitional mass flux exists for Tube 2, Tube 4, Tube 5, and Tube 6. The complex mass-flux effect may be explained by the “complex interactions” between microfins and fluid, including liquid drainage by surface tension and interfacial turbulence, etc. More experimental investigations on a large variety of fin geometries, especially with focus on the fin tip radius, are needed to develop a robust model to predict the observed nonmonotonic h-G phenomenon. (4) By using a suitable friction factor f calculated by the Churchill model [32] and an empirical-fitted relative roughness defined in Eq. (19), the modified Gronnerud correlation can be adopted to predict microfin tube data. Four existing heat-transfer correlations for microfin tubes, including the Cavallini et al. correlation [13], the Kedzierski and Goncalves correlation [35], the Chamra et al. correlation [3], and the Yu and Koyama correlation [36], can approximately predict the experimental data within 630% MAY 2014, Vol. 136 / 051504-9


error band, while all of them are prone to underestimate the experimental data, especially at low mass fluxes. (5) At relatively large mass fluxes, the condensation heat transfer enhancement is due to the increase of the effective heat exchange area. At low mass fluxes where the obvious nonmonotonic h-G or flatten-out phenomenon occurs, besides the surface area enhancement, the surface tension effect on the liquid drainage and the interfacial turbulence enhance heat transfer greatly.

Acknowledgment The authors would like to acknowledge the financial support from Swedish Energy Agency, the National Natural Science Foundation of China (50976096), and the National Basic Research Program of China (973 Program) (2011CB710703).

Nomenclature A¼ Ac ¼ Ao ¼ Ani ¼ cpl ¼ da ¼ di ¼ do ¼ e¼ f¼ g¼ G¼ h¼ hlv ¼ I¼ JG ¼ k¼ L¼ LMTD ¼ m¼ ns ¼ p¼ pf ¼ Pred ¼ Pr ¼ Q¼ Q¼ Re ¼ Rx ¼ Rxf ¼ tb ¼ T¼ v¼ V¼ x¼ Xtt ¼

otal inner surface heat transfer area, m2 actual cross-sectional area, m2 outer surface heat transfer area of tube, m2 nominal surface area based on fin root diameter, m2 constant-pressure specific heat of liquid, J kg1 K1 hydraulic diameter of the annulus, m fin root diameter, m outside diameter of the tube, m fin height, m friction factor gravitational acceleration, m s2 mass flux based on the actual cross-sectional area, kg m2 s1 heat transfer coefficient, W m2 K1 latent heat of vaporization, J kg1 electric current, A nondimensional modified Froude number, xG/(gdiqv(ql qv))0.5 hermal conductivity, W m1 K1 ube length, m logarithmic mean temperature difference, K mass flow rate, kg s1 number of fins axial pitch, m fin pitch normal to the fins, m reduced pressure Prandtl number, cpll/k heat flow rate, W heat flux based on the total inner surface area, W m2 Reynolds number, Gd/l geometry enhancement factor empirically-fitted relative roughness in Eq. (19) fin base thickness, m emperature, K volume flow rate, m3 s1; specific volume m3 kg1 electric voltage, V vapor quality turbulent-turbulent Martinelli parameter, (ll/lv)0.1 (qv/ql)0.5[(1 x)/x]0.9

Greek Symbols a¼ b¼ e¼ l¼ q¼ r¼ DP ¼ DT ¼

apex angle of the fin, deg helix angle, deg void fraction dynamic viscosity, Pas density, kg m3 surface tension, N m1 pressure drop, Pa emperature difference between saturation temperature and internal wall temperature, K

Subscripts A¼ D¼ exp ¼ f¼ in ¼ l¼ LO ¼ m¼ MF ¼ out ¼ ph ¼ pre ¼ ref ¼ S¼ sat ¼ ts ¼ v¼ w¼

DT independent flow regime DT dependent flow regime experimental frictional component inlet liquid liquid phase only with total flow rate momentum component microfin tube outlet pre-heater predicted refrigerant smooth tube saturated test section vapor water; wall

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