Local flow boiling heat transfer characteristics in three

International Journal of Heat and Mass Transfer 121 (2018) 1021–1032

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Local flow boiling heat transfer characteristics in three-dimensional enhanced tubes J. Chen a,b, Wei Li a,⇑ a b

Department of Energy Engineering, Zhejiang University, Hangzhou 310027, China Co-Innovation Center for Advanced Aero-Engine, Department of Energy Engineering, Zhejiang University, 310027, China

a r t i c l e

i n f o

Article history: Received 5 October 2017 Received in revised form 27 November 2017 Accepted 14 January 2018 Available online 7 March 2018 Keywords: Flow boiling Local heat transfer Heat flux Enhanced tube Three dimensional surface

a b s t r a c t Experimental study on local flow boiling heat transfer characteristics in two three-dimensional dimplegrooved tubes (2EHT) and an equivalent smooth tube was performed. All the three test copper tubes have the same inner diameter of 11.07 mm and outer diameter of 12.7 mm. The working fluid was the nearazeotropic mixture, R410A. All test runs were conducted in a 2 m long horizontal tube-in-tube heat exchanger. Constant evaporation temperature was maintained at 10 °C when heat flux ranged from 32.6 kW/m2 to 37 kW/m2. Refrigerant quality varied from inlet 0.1 to outlet 0.9 and mass flux was controlled from 70 kg/(m2 s) to 150 kg/(m2 s). The enhanced surface areas of two 2EHT tubes are 1.02 and 1.03 times of the smooth tube, respectively. The local HTC results of saturate flow boiling were presented and compared with the existing correlations. Wall temperature was measured and critical heat flux effect on the tube-side evaporation was discussed. Local wall temperature results showed that the 2EHT tubes produce a better saturate evaporation at a relatively lower wall superheat. HTC increases with increasing heat flux when heat flux is smaller than CHF and decreases when heat flux is larger than CHF. Based on the local thermal properties, a new flow boiling heat transfer correlation for these 2EHT tubes is derived. The new correlation can predict all the experimental heat transfer coefficients within an error band of ±30% and 96.89% of test data within an error band of ±20%. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Enhanced flow boiling systems are commonly used in aerospace application, refrigeration, air conditioning, micro and macro electronic devices and other thermal control systems to cool the heat source. Enhanced tubes such as dimple tubes, micro-fin tubes, surface coating tubes and other modified surface tubes are used to improve the heat transfer performance [1]. Li and Wu [1], Kim [2] and Jiang et al. [3] studied the flow boiling heat transfer characteristics in micro-fin tubes using different refrigerants. Li and Wu [1] proposed a semi-empirical heat transfer model which has predicted their experimental data within an error band of ±20%. Kim [2] and Jiang et al. [3] proposed a performance factor to evaluate the heat transfer enhancement for enhanced tubes. Li and Chen et al. [4] and Shafaee et al. [5] studied the modified surface tubes (dimpled, helically dimpled tubes) using mixture refrigerants. They found that dimpled tubes have a much larger evaporation heat transfer coefficient than smooth tubes. Yang et al. [6] studied the flow boiling heat transfer performance of nanowire⇑ Corresponding author. E-mail address: [email protected] (W. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.065 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

coated micro-channel and found that this device is more energy saving and more effective at low mass fluxes. Zhang et al. [7,8] studied the flow boiling heat transfer in internally grooved tubes and a new heat transfer model was proposed to predict the evaporation HTC. Goto et al. [9] experimentally studied the R410A and HCFC22 evaporation in two conventional spiral grooved tubes and they concluded that the groove structure has an important effect on liquid redistribution around the circumference to reduce the occurrence of local wall superheat. Earlier studies suggested that the dimpled and grooved structures are good choices to develop new types of enhanced tubes. However, recent researches related to flow boiling in dimple-grooved tubes are very limited because these new types of tubes (2EHT tubes) are newly developed. A smooth tube with the same inner and outer diameter was used as a reference tube to evaluate the heat transfer performance of 2EHT tubes. Flow pattern map was used to predict the liquid and vapor phase distribution at a specified cross-section for smooth tube. Wojtan et al. [10] proposed a modified flow boiling map from the Kattan-Thome-Favrat flow pattern map [11]. They divided the stratified-wavy region in the Kattan-Thome-Favrat flow pattern map into slug, slug/stratified-wavy and stratified-wavy regions

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J. Chen, W. Li / International Journal of Heat and Mass Transfer 121 (2018) 1021–1032

Nomenclature Ai ALD AVD A cp D di do E Fr G g h hlv L q Rel Q S Spar Sdar Sa Sq Sp Sv Sz Ssk T x

inner surface area of test tube, m2 dimensionless parameter, ALD = A(1 e)/di2 dimensionless parameter, ALD = Ae/di2 cross-sectional area, m2 specific heat, J kg1 K1 hydraulic diameter, m inner diameter, m outer diameter, m enhanced factor Froude number, Fr = G2/(q2gD) mass flux, kg m2 s1 gravity acceleration, m s2 heat transfer coefficient, W/m2 K1 latent heat of vaporization, J kg1 tube length, m heat flux, W/m2 Reynolds number of liquid phase Rel=G(1 x)D/ll heat transfer rate, W suppress factor projected surface area, mm2 developed surface area, mm2 RR arithmetical mean height, Sa ¼ A1 A jzðx; yÞjdxdy qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi RR root mean square height, Sq ¼ A1 A z2 ðx; yÞdxdy maximum peak height from mean plane, lm maximum pit height from mean plane, lm maximum height, Sz ¼ Sp þ Sv Skewness of the height distribution temperature, K vapor quality

and added annular-to-dryout, dryout-to-mist boundary curves into that map. Thome and Hajal [12] also redefined the Kattan-ThomeFavrat flow pattern map according to their experimental observations and test data. The Wojtan map [10] was used to predict flow patterns in the smooth tube (shown in Fig. 3), and then the same mass flux was tested with 2EHT tubes. Fundamental issues of flow boiling heat transfer also have been widely investigated by many researchers. Kandlikar [13] studied the flow boiling heat transfer characteristics of mini-/microchannels, and they concluded that isolated bubble and confined bubble or slug flow and annular flow would appear in these channels at low mass flux. Moreover, the surface tension plays a significant role in liquid distribution. Cheng [14] reviewed a large variety of data on critical heat flux effect on flow boiling in micro channel and confined space. They found that the existing critical heat flux (CHF) results show a great discrepancy, and no generalized correlations can correctly predict CHF in micro-channels and confined spaces. Thus, more CHF studies on flow boiling should be conducted, especially for enhanced tubes. Barraza et al. [15] experimentally studied the flow boiling of azeotropic mixtures in small channels so as to supplement the lack of data, and indicated that models suitable for pure refrigerant cannot predict the HTC of azeotropic mixtures boiling. Cheng and Xia [16] reported that the channel size effect on flow boiling was not completely understood and suggested that the flow pattern map was a promising method to understand the heat transfer behavior. The critical heat flux phenomenon is a crisis signal of heat transfer deterioration when the mist flow or dry-out flow occurs as explained by Wu and Li [17]. They proposed a new correlation to predict the saturated CHF which can predict almost 97% of their data within an error band of ±30%. Cheng [18] reviewed and summarized the CHF studies on flow boiling in micro-channels and confined spaces, which

V I W We

voltage, V electric current, A mass flow rate, kg s1 Weber number, We = G2D/(qr)

Greek symbols k thermal conductivity of copper, W m1 K1 r surface tension, N m1 q density, kg m3 e void fraction l viscosity, Pa s h dry-out angle Subscripts CHF critical eat flux eV evaporation in inlet IA Transition of intermittent to annular out outlet l liquid phase v vapor phase ref refrigerant lv liquid to vapor phase change sat saturation pre preheating section o outer wall of test tube i inner wall of test tube water water local local parameters

helped to understand the CHF effect on heat transfer coefficient as presented in Figs. 7 and 8. The literature review shows that most of the previous studies focused on smooth tubes and micro-fin tubes, and the heat transfer characteristics of these new 2EHT tubes are not available. The objective of this paper is to study the flow boiling heat transfer characteristics of two types of three-dimensional dimple-grooved tubes. The heat transfer mechanisms related to the mass flux, local wall temperature superheat, critical heat flux and flow pattern maps are located. The HTC is calculated from the direct measurement parameters. The HTC results are then compared with an equivalent smooth tube. The experimental data has provided a comprehensive understanding on local flow boiling heat transfer near the nominal critical heat flux for two tested 2EHT tubes and the smooth tube. Another purpose is to develop a heat transfer model for the 2EHT tubes to reduce the large error band predicted by existing flow boiling heat transfer models [19–21]. 2. Experimental facilities Fig. 1 shows the cycle diagram of this experimental system and the detailed distribution of all T-type thermocouples that are used to measure the temperatures of tube wall and water. As is presented in Fig. 1(a), the test system includes three loops: the refrigerant circulation loop, the water circuit which is used to control the outlet quality of the test section by changing the water inlet temperature, and the condensation section which is used to subcool the refrigerant coming from the outlet of the test section, and is simplified as a condenser in Fig. 1(a). The inlet quality is adjusted by changing the voltage and current supply of the preheating section. The refrigerant driven by a digital gear pump enters the


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Fig. 1. Schematic of (a) the experimental set up and test section details, (b) measurement points of water and outer wall temperatures of each cross section, (c) thermocouple distribution and local HTC measuring method.

preheating section where it is heated to a designed vapor quality. Subsequently, the refrigerant is evaporated to the specified outlet vapor quality in the test section. Finally, the high vapor quality flow is condensed to subcooled liquid at the condenser, and then goes back to the liquid reservoir. A detailed illustration about test section (a mounted tube-in-tube heat exchanger in the dashed box) is presented in Fig. 1(b) and (c). To measure the outer wall temperature, four T-type thermocouples with a wire diameter of 0.114 mm are equally distributed over the circumference. Top and bottom water temperatures are measured directly in the annulus by two T-type thermocouples. The 2 m long test tube installed in the outer tube (with I.D. 17 mm) is divided into eight sections. The local heat transfer coefficient is obtained at each sub-section, as is shown in Fig. 1(c). The interval between each sub-section near the inlet is designed larger than that near the outlet so as to eliminate the non-linear effects and inlet effects of the vapor quality along the tube. Fig. 2 shows the 3-D and 2-D surface structures of two enhanced tubes with a 15 mm square sample. Fig. 2(a) displays the magnified 3-D view of the composite surface of two enhanced tubes. The enhanced surface is obtained by using two different molds rolling across the smooth copper plate. Then, the enhanced surface is fabricated into the enhanced tubes. All three tested tubes are made from copper and have the same outer diameter of 12.7 mm and inner diameter of 11.07 mm. The only difference is that the dimple interval of 2EHT-1 tube is three times of that of 2EHT-2 tube, d1=3d2, as Fig. 2(b) shows. 2EHT -1 tube and 2EHT2 tube share the same pitch of fins, L1 = L2 = 3.4 mm, and the same sample surface before fabricated. Such surface structure of 2EHT-2 tubes can produce a better evaporation due to the combined action

of liquid redistribution and more nucleate cores produced by longitudinal grooves and dimples. Liquid redistribution reduces the local dry out regions and more nucleate cores ensure a smaller degree of wall superheat that initiates bubble product and departure from the tube surface. Fig. 2(b) presents the 2-D profile analysis of the test enhanced tube. Results show that the surface areas of 2EHT-1 and 2EHT-2 tubes are increased by 2% and 3.3% compared to the equivalent smooth tube, respectively. The parameters Sp and Sv shown in Table 1, indicate deeper dimples in the 2EHT-2 tube surface while Sz illustrates a thinner nominal wall thickness for 2EHT-2 tube than 2EHT-1 tube. The Ssk parameter describes the height distribution of surface roughness, and a larger positive Ssk indicates more peaks on tube surface. The height parameters of grooves and dimples that are measured by the Nanovea 3D Non-Contact Profilometer are listed in Table 1. All thermocouples used in the present experimental setup are calibrated with a standard platinum resistance thermometer and are calibrated to an accuracy of ±0.1 K. The inlet and outlet temperature (water side and refrigerant side) are measured by RTD-100 (with a calibrated accuracy of ±0.1 K) which are installed at the inlet and outlet of the test section. The water mass flow rates are measured by an electromagnetic flow meter (with an accuracy of ±0.2% of reading) and the refrigerant mass flow rate is measured by a Coriolis Effect mass flow meter (with an accuracy of ±0.2% of reading). 3. Data reduction All temperatures and mass flow rates are measured directly when a steady-state condition is achieved. The calculation of heat

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(a)

L2=3.4 mmL2=3.4 mmL 2=3.4 mm δ2=2.2 mm δ2=2.2 mm δ2=2.2 mm

δ1=6.6 mm

δ1=6.6 mm

L1=3.4 mmL 1=3.4 mmL 1=3.4 mm

(b) 2EHT-2

2EHT-1

(c) Fig. 2. Inner surface parameters of the 2EHT tubes, (a) 3-D surface structure, left for 2EHT-1 tube, right for 2EHT-2 tube, (b) 2-D surface parameters report for 2EHT tubes, (c) samples of 2EHT-1 tube and 2EHT-2 tube.

transfer coefficient is based on local thermal equilibrium between water side and refrigerant side. The local heat transfer coefficient, h, is defined by

Q ¼ hAi ðT w;i T ref ;ev Þ ¼ cp W water ðT water;in T water;out Þ h¼

cp W water ðT water;in T water;out Þ Ai ðT w;i T ref ;ev Þ

ð1-aÞ ð1-bÞ

where Q is the heat transfer from water side to refrigerant side, h is the local heat transfer coefficient, Ai is the actual inner heat transfer area, W water is the water side mass flow rate. T w;i , T ref ;ev T water;in ; T water;out are the local inner wall temperature, the evaporating temperature, the directly measured inlet and outlet water temperature, respectively.

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where VI is the power product supplied to pre-heating section,

g is the efficiency of the electric power that is obtained by the fluid, cp;l;ref ; W ref , T ref ;pre;in , hlv , are the corresponding parameters of refrigerant side. All refrigerant temperatures are obtained by platinum RTD-100s. The outlet vapor quality of each cross section is then derived from the local heat equilibrium between water side and refrigerant side, and is given by Eq. (5).

xout ¼ xin þ

cp;water W water ðT water;in T water;out Þ W ref hlv

ð5Þ

Then the local vapor quality of each sub-section is given by,

x¼

Fig. 3. Experimental data in the developed flow pattern map by Wojtan et al. [11] for R410A evaporation in the horizontal smooth tube, di = 11.07 mm, Tsat = 10 °C.

Heat loss from the outer tube wall to environment and heat conduction along the axial direction can be neglected due to good insulation treatment before experiment, as is verified in Li and Chen [22]. Local wall temperature is determined by onedimensional steady heat conduction equation, and is given by,

T w;i ¼ T w;o

Q do ln 2 p k DL d i

ð2Þ

where k, DL are the copper thermal conductivity and the length of each sub-section, T w;o is the calculated mean temperature of outer tube wall, and it is defined by

T w;o ¼

T w;u þ T w;l þ T w;r þ T w;d 4

ð3Þ

where T w;u , T w;l , T w;r , T w;d are the temperatures measured by four thermocouples, represented by up, left, right and down positions of inner tube. The determination of T ref ;ev can vary in three ways. The first is that a linear temperature decrease is expected [23]. The second and widely used method is to treat the evaporation temperature as a constant temperature which is measured at the inlet of the test section, such as used in Refs. [9,15]. The third method assumes a linear pressure drop, and the evaporation temperature is referred to local pressure at each sub-section. In this work, the third method is used to measure Tref,ev because it is closer to the real fact. Due to the good isolation treatment to preheating section and pipeline, the heat loss of this test device is less than 4%, which is validated by the author’s previous work [5]. Thus, the heat energy wasted to the surroundings might be neglected. The inlet vapor quality, xin ; is calculated by heat balance of pre-heating section.

VI g ¼ cp;l;ref W ref ðT sat T ref ;pre;in Þ þ W ref hlv xin or

xout þ xin 2

ð6Þ

where W water , W ref are the water mass flow rate and refrigerant mass flow rate, respectively; T water;in , T water;out are the water temperature of inlet and outlet, respectively. The uncertainty analysis is based on Eq. (7). The calculated uncertainty of heat transfer coefficient is ±10.6%. All the measurement uncertainties and dependent uncertainties are listed in Table 2, and the experimental parameters are summarized in Table 3.

1 rðyÞ ¼ y

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn @y 2 r2 ðxi Þ i¼1 @x i

4. Results and discussions 4.1. Flow boiling pattern map The particular flow pattern map for saturated flow boiling depends on many parameters such as the evaporation pressure, fluid, mass flux, heat flux, channel geometry and so on. Besides, the recognition of a specified local flow pattern is more of subjective element, and there are still many undefined variables, such as the amount of bubbles departing from local hydrodynamic equilibrium, the cause of formation of two-phase flow and the structural factor of different boiling surfaces, that affect the formation of local flow pattern. Thus, most of the present flow pattern maps are based on smooth surface channels. Fig. 3 shows the flow patterns what may occur in the current flow boiling experiment predicted by using the well-accepted Wojtan flow pattern map [10]. In the lower quality region, x < xIA, calculated by Eq. (8-a), stratified flow in the tube side cannot develop into stratified-wavy flow due to lower surface superheat which cannot produce enough heat to maintain the thermodynamic and hydrodynamic equilibrium. The continuous mass flow from upstream makes the bubbles submerged and collapsed in the non-equilibrium fluid which results in unsteady liquid-vapor distribution along the tube. Thus, the slug flow occurs in the low vapor quality region. In the higher quality region (x > xIA), the stratified to stratified-wavy flow transition is calculated by Kattan-Thome boundary, GS-SW using Eq. (8-b) [9].

("

VI g cp;l;ref W ref ðT sat T ref ;pre;in Þ xin ¼ W ref hlv

ð4Þ

ð7Þ

xIA ¼

0:34

1=0:875

qv ql

1=1:75

ll lv

1=7 #

)1 ð8-aÞ

þ1

Table 1 Analysis report of dimple-grooved tube surface. Tube

Spar/mm2

Sdar/mm2

Sa/um

Sq/um

Sp/um

Sv/um

Sz/um

Ssk

2EHT-1 2EHT-2

225 225

229.5 232.5

69.82 76.19

83.42 74.54

141.8 197.3

100.9 137.7

242.7 335.0

0.3055 0.0973

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Table 2 Relative accuracy of measurement and dependent values. Primary measurements

Uncertainty

Diameter Electricity Voltage Length Temperature Water flow rate, range: 0–1000 kg/h Refrigerant flow rate, range: 0–130 kg/h

±0.05 mm ±0.1 A ±0.1 V ±0.5 mm ±0.1 K ±0.2% of reading ±0.2% of reading

Dependent quantities Mass flux G, kg/(m2 s) Heat flow rate of water side, kW Vapor quality, x Heat transfer coefficient h, W/(m2 K)

±0.89% ±6.2% ±8.7% ±10.6%

4.3. Local boiling heat transfer coefficient result vs. mass flux

Table 3 Experimental parameters.

GSSW ¼

Parameters

Values

Refrigerant Mass flux (kg/m2 s) Saturation temperature (°C) Heat flux (kW/m2) Vapor quality (–)

R410A 70–150 10 15.7–37 0.1–0.9

226:32 ALD A2VD qv ðql qv ÞlL g x2 ð1 xÞp3

!1=3 ð8-bÞ

The stratified-wavy flow to annular/intermittent flow transition is calculated from Eq. (9) [10],

( GSWI=A ¼

16A3VD gDh ql qv

" 2 0:5

x2 p2 ð1 ð2hLD 1Þ Þ

1þ

p2 2

25hLD

the Liu and Winterton correlation [20], the Mahmoud correlation [21] and Fang correlation [26]. The Gungor and Winterton correlation [19] and the Fang correlation [26] predicted more than 97% of evaporation data within an error band of ±15% for smooth tube. By contrast, the Liu and Winterton correlation [20] and Mahmoud correlation[21] only predict 70.84% of the data set within an error band of ±20% but 100% of the data set within an error band of ±30%. This indicates that the test data has a good consistency with existing correlations for the tested smooth tube.

#)0:5 Fr þ 50 We L

ð9Þ where hLD, ALD, AVD are the dimensionless liquid height from the bottom of tube, cross-sectional areas of liquid and vapor phase, respectively. The void fraction, e of local cross section is calculated from the Steiner version [24] of the Rouhani-Axelsson drift flux model for the horizontal tube, " #1 x x 1x 1:18ð1 xÞ½g rðql qv Þ0:25 e¼ ð1 þ 0:12ð1 xÞÞ þ þ qv qv ql Gref q0:5 l

ð10Þ

Fig. 5 illustrates the local heat transfer coefficient as a function of local vapor quality at different mass fluxes of the three tested tubes. It is observed that local evaporation HTC of R410A decreases along the refrigerant flow direction (opposite to the water flow direction) in the counter flow heat exchanger (as Fig. 1 presented) at a fixed mass flux. Moreover, the local HTC increases with increasing mass flux for both smooth tube and two 2EHT tubes. According to Fig. 3, the calculated xI/A by Eq. (8-a) is 0.422. A heat transfer trend is observed in Fig. 5(a)–(c) that the local HTC is relatively high in the region x < xI/A while the local HTC tends to be smaller and steady in the region x > xI/. This heat transfer performance validates the accuracy of Wojtan flow pattern map [10] that there is flow transition from stratified-wavy flow to slug/stratified flow near xI/A. It is also validated by the wall temperature measurement, as Fig. 6 indicates that there is a sharp increase of wall temperature near xI/A. Moreover, xI/A for the two 2EHT tubes seems a little higher. As Fig. 3 implies that stratified-wavy flow dominates the flow pattern at high vapor quality while slug flow or plug flow occurs at low vapor quality. It can be explained that the gravity force drags the liquid phase to the bottom while the vapor phase occupies the upper part of the horizontal tube. At low mass flux, the gravity force and the resistance of grooves and embossments dominate the distribution of liquid phase. The interfacial shear force at the phase interface is very limited, and surface tension can be neglected compared to the gravity force. Hasan et al. [27,28] and O’Neill et al. [27,28] found that effect of gravity force decreases and the effect of shear force increases with increasing mass flux, and the gravity effect can be neglected when a moderate vapor velocity appears. Hence, the slug/stratified-wavy flow results in a higher heat transfer performance in two ways: (1) A better washing acted on the inner tube wall and less intermittent dry-out parts along the channel than the stratified-wavy flow; (2)

The determination of cross-sectional area occupied by the vapor/liquid phase is calculated by the dry angle, hstrat at a specified cross-section, and hstrat is calculated from an approximate evaluation of Biberg [25] as Eq. (11),

8 9 3p1=3 ½1 2ð1 eÞ þ ð1 eÞ1=3 e1=3 > > < pð1 eÞ þ 2 = hstrat ¼ 2p 2 1 ð1 eÞe½1 2ð1 eÞ½1 þ 4ð1 eÞ2 þ 4e2 > 200 > : ; ð11Þ Other transition curves are indicated in Wojtan flow pattern map [10], and all the tested mass flux values are located in the stratified-wavy flow region. This flow pattern map is used to provide a better understanding of the local flow boiling heat transfer performance at low mass fluxes. 4.2. Validation of experimental works Fig. 4 compares the experimental results of smooth tube with predicted results by the Gungor and Winterton correlation [19],

Fig. 4. Comparison of experimental HTCs of smooth tube with predicted HTCs by the Gungor and Winterton correlation [19], the Liu and Winterton correlation [20], the Mahmoud et al. correlation [21] and the Fang et al. correlation [26].


Fig. 5. Local flow boiling heat transfer coefficient vs. local vapor quality at different mass flux, (a) smooth tube, (b) 2EHT-1 tube, (c) 2EHT-2 tube.

The continuous and effective generation of waves by vapor phase produce a higher heat transfer rate than the stratified-wavy flow (relatively high vapor quality region, x > xI/A) at low mass flux. The local heat transfer coefficient tends to be steady in the region x > xI/A, as shown in Fig. 5(a)–(c). At high vapor quality, stratified-wavy flow dominates the flow pattern except several

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Fig. 6. The inner wall temperature measurement result, (a) smooth tube, (b) 2EHT1 tube, (c) 2EHT-2 tube.

dry-out or mist flow conditions. The heat transfer process is suppressed by the vapor phase when no continuous waves cool the super-heated tube wall. At a fixed mass flux, higher vapor quality means a thinner liquid film at the bottom part of the tube which results in a higher proportion of tube surface remains superheated. As mass flux increases, the amplitude of waves (evoked by shear force due to the unequal velocity of vapor and liquid phase at

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Fig. 7. Critical superheated temperature difference of each cross section, (a) smooth tube, (b) 2EHT-1 tube, (c) 2EHT-2 tube.

the interface) increases and the liquid film becomes thicker, which can efficiently wash and cool the super-heated wall. The two-phase flow exchanger works well when local vapor quality is smaller than xI/A, and the heat transfer performance is deteriorated when vapor quality is larger than xI/A at low mass flow rate. The HTC decreases as local vapor quality increases when mass flux is fixed.

Fig. 8. Local heat transfer coefficient vs. local vapor quality of R410A evaporation at different heat fluxes and fixed mass flux G = 150 kg/(m2 s) (a) smooth tube, (b) 2EHT-1 tube, (c) 2EHT-2 tube.

4.4. Local wall temperature Fig. 6 presents the inner wall temperatures of three test tubes for each test condition. One-dimensional cylindrical thermal conductivity is assumed to derive the inner wall temperature. Results show that the inner wall temperature increases with increasing

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heat flux. The wall temperatures of two 2EHT tubes increase sharply which is mainly resulted from the thinner liquid film and the resistance of embossment and grooves. The embossments and grooves prevent the liquid film go up and tear it, which leads to more superheated surfaces exposed in vapor phase. Furthermore, the gravity force also prevents the liquid film going up at low mass flux. The liquid film becomes thinner with increasing vapor quality, until the vapor phase takes up the whole space where the wall temperature reaches to the peak temperature. Compared to 2EHT tubes, the smooth tube is not affected by the surface roughness. Fig. 7 presents the critical surface super-heated temperature difference derived from the inlet temperature at each cross section. The Wojtan correlation [29] (Eq. (12-1)), was used to calculate the critical heat flux at different experimental conditions for the smooth tube. Considering the surface enhancement, the critical heat fluxes for 2EHT tubes are calculated by multiplying a surface factor A2EHT/ ASM. The Twi,CHF (Eqs. (12)–(14) in Ref. [29]) is calculated from the measured local HTC and the predicted critical heat flux of each sub-section. The critical super-heated temperature is defined as the surface temperature when the heat flux reaches to the critical heat flux.

0:073 0:72 q L qCHF;SM ¼ 0:437 v We0:24 Ghl;v L Dh ql

ð12-1Þ

0:073 0:72 q L A2EHT We0:24 Ghl;v qCHF;2EHT ¼ 0:437 v L Dh ql ASM

ð12-2Þ

WeL ¼

G2 LH

rql

T wi;CHF ¼

qCHF þ T sat hlocal

ð13Þ ð14Þ

For all tested tubes, no superheat is controlled when studying the mass flux effect on HTC (mass flux less than 150 kg/(m2 s)) and the super-heated phenomenon occurs when studying the heat flux effect on HTC at a fixed mass flux, 150 kg/(m2 s). For the increase of mass flux, the heat flux (determined by inlet water temperature) should be adjusted to maintain the designed inlet and outlet quality as shown in Figs. 6 and 7. 4.5. Heat flux effect on HTC Fig. 8 demonstrates the local heat transfer coefficients of three test tubes at three heat fluxes. The three heat flux values are selected such that one is lower, second is higher and third is close to the critical heat flux. To determine the critical heat flux in confined channels, a correlation proposed by Wojtan et al. [29] is used which predicts 34.7 kW/m2 for smooth tube, 35.4 kW/m2 for two 2EHT-1 tube and 35.85 kW/m2 for 2EHT-2 tube by using the Eqs. (12-1) and (12-2). It can be seen from Fig. 8 that the heat transfer coefficient is at a higher state for all three tubes when the heat flux is lower than the CHF. A sharp decrease in HTC is found as compared to the normal saturated flow boiling. This decrease implies the fact that inner tube surface is no longer as efficiently wetted as normal condition (heat flux lower than CHF). Vapor phase in this state occupies the inner tube surface more frequently which increases the thermal resistance during the heat transfer process. At higher vapor quality, even the smooth tube provides a better heat transfer performance due to the absent resistance of grooves and embossments. It is shown in Fig. 7 that the larger critical surface super-heated temperature difference can lead to a lower heat transfer performance when heat flux is higher than CHF. In the high vapor quality region, the wall temperature remains at a relatively higher state because

that the liquid film is much thinner and high vapor velocity could cuts off the liquid film or wavy on the tube wall more easily than the low vapor quality region. Under this condition, the heat transfer performance is deteriorated. 4.6. Average heat transfer coefficient Figs. 9 and 10 present the average heat transfer coefficient and pressure drop in the three test tubes. The HTC and pressure drop increases with increasing mass flux. The 2EHT tubes provide a very close pressure characteristics because that they have a exactly similar surface structures except different dimple interval. The average HTC is calculated by Eq. (15). At low mass flux, three tubes tend to have the same heat transfer characteristics; even the smooth tube seems to have a higher HTC than 2EHT-2 tube, as Fig. 9 shows. This is mainly result from the geometric effect on heat transfer and flow conditions. The 2EHT tubes have more surface roughness than the smooth tube, and 2EHT-2 tube has more embossments than 2EHT1 tube. At low mass flux, kinetic energy of the liquid film cannot overcome the resistance (from gravity and surface roughness) to climb to upper part of the tube. Thus, the lower the mass flux is, the more superheated parts of 2EHT-2 tube than that of the 2EHT-1 tube. Note that, the lower the mass flux is, the thinner the liquid film is, which will help the embossment and grooves to tear the liquid film and result in more dry-out surfaces exposed to the vapor phase. But this phenomenon will not happen if the channel is round and smooth. However, if the mass flux is enough high (the kinetic energy of the liquid film is enough) to overcome these resistances, the advantages of 2EHT tubes over smooth tube begin to make a difference. Compared to the smooth tube, the 2EHT tubes present a higher heat transfer performance at high mass flux mainly due to the enhanced surface structure. Based on the above results, the surface roughness also suppresses the heat transfer at low mass flux.

HTC av erage

, 8 8 X X ¼ ðHTC local;i DLi Þ Li 1

ð15Þ

1

4.7. Assessment of predicting correlations The measured heat transfer coefficients are compared with four predictive correlations, as shown in Fig. 11. The Gungor and Winterton correlation and its revised version predict approximate 80% of our data within a deviation of ±50%. The results show a large

Fig. 9. Average evaporation HTC vs. mass flux with the inlet vapor quality 0.1 ± 0.05 and outlet vapor quality 0.9 ± 0.05.

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discrepancy between smooth tube and 2EHT tube. The flow boiling model proposed and advanced by Mikielewicz et al. [30] was based on the energy dissipation theory, and their data bank only include the pure refrigerants (R141b, R134a, R12, R11 and R22). This may be the main reason that their correlation over predicted our experimental HTC with near-azeotropic mixture, R410A. Predictability of these correlations is listed in Table 4. The Gungor and Winterton correlation [19], Liu and Winterton correlation [20] and Mahmoud et al. correlation [21] have similar formulation in the flow boiling model equation, n

n 1=n

hTP ¼ ½ðS hNCB Þ þ ðE hlo Þ

Fig. 10. Pressure drop vs. mass flux with the inlet vapor quality 0.1 ± 0.05 and outlet vapor quality 0.9 ± 0.05.

ð16Þ

This flow boiling model cannot directly predict the saturated flow boiling heat transfer coefficient because an assumption was made for the flow boiling in tubes which was treated as a mixing effect of convective flow and nucleate pool boiling. Even though an enhanced factor and a suppression factor were proposed. Actually, there are three prime reasons for inaccuracy of this model to predict the heat transfer coefficient of tube side flow boiling. Firstly, nucleate pool boiling heat transfer coefficient multiplied by a suppression factor, S, still cannot accurately predict the flow boiling heat transfer coefficient at a confined space such as tubes. Secondly,

Fig. 11. Comparison of experimental heat transfer coefficient with existing correlations, (a) the Gungor and Winterton correlation [19], (b) the Liu and Winterton correlation [20], (c) the Mahmoud et al. correlation[21], (d) the Mikielewicz et al. [30] correlation.

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J. Chen, W. Li / International Journal of Heat and Mass Transfer 121 (2018) 1021–1032 Table 4 Prediction accuracies of the presented correlations (%). Correlation

MAD

MRD

n1

n2

Gungor and Winterton [19] Liu and Winterton [20] Mahmoud et al. [21] Mikielewicz et al. [30]

0.328 0.269 0.340 0.439

0.314 0.187 0.227 0.408

78.47 83.33 74.31 54.86

30.56 43.75 39.58 40.28

n1 percentile of the data points having a relative deviation within ±50%. n2 percentile of the data points having a relative deviation within ±30%.

by the local thermal dynamics and the thermal properties, thus the HTC is a function of thermal based parameters. Dimensionless analysis suggested in Fang et al. [26] is referenced in this paper. As Eq. (17) defines,

Nu ¼ f

lf ql ; Bo; Bd; Rel ; Fr; qv lw

ð17Þ

where the density ratio reflects the fluid effect on HTC; Boiling number, Bo, considers the heat flux and mass flux effects on evaporation heat transfer process; Bond number, Bd, measures the importance of gravity force compared to the surface tension forces; liquid Reynolds number, Rel, is taken into accounts for the effect of inertia force of the liquid film and the viscous forces; the Froude number, Fr, considers the effect of mass flux effect, and the last term is the viscosity correction of liquid phase referred to the local fluid and wall temperatures, respectively. The proposed correlation can be expressed as Eq. (18),

x1 x6 lf q x Nu ¼ x l Box2 Bd 3 Rexl 4 Frx5

ð18Þ

lw

qv

where x, x1 . . . x6 are the unknown parameters that are determined directly by local measurements. Apply the natural logarithm to both side of Eq. (18) and obtain 144 linear equations based on the 144 sets of local HTC measurements as,

lnðNui Þ ¼ x0 þ x1 ln

ql qv

þ x2 ln Boi þ x3 ln Bdi þ x4 ln Rel;i i

þ x5 ln Fr i þ x6 ln

lf lw i

ð19Þ

where i = 1, 2, 3 . . . 144. The above expression can be simplified to a matrix form as,

A1447 X 71 ¼ Nu

ð20Þ

Eq. (19) is an over determined equation. Thus, boundary conditions should be satisfied to find the optimal solution. The least square method is used to find the optimal solution and is given by Eqs. (21) and (21). The optimal solution must meet the minimum variance principle of the test Nu sample data. Thus, the F must reach the minimum value and the extreme conditions are expressed as Eq. (22).

F ¼ ðAX NuÞT ðAX NuÞ

ð21Þ

@F ¼ 0 ði ¼ 0; 1; 2: . . . 6Þ @xi

ð22Þ

The final term of this model is shown as Eq. (23). Fig. 12. (a) Comparison of experimental HTC vs. predicted HTC of new heat transfer model, (b) relative deviation of measurement data points.

Nu ¼ 5:332 109

the shear force and the gravity force have different influence on liquid film distribution in the tube side flow boiling. Third reason is that the confined space in tube makes the heat transfer more complex than pool boiling, such as bubble generation and departure from the tube wall. Thus, new models are required based on the local heat transfer process and new correlation should be summarized from the experimental data.

4.8. Local thermal-properties based heat transfer model Based on the above local heat transfer characteristics and predicting methods, a new heat transfer correlation for these 2EHT tubes is established. At low mass flux, the HTC is mainly affected

ql qv

1:3812

5:3070

Bo0:7987 Bd

Re0:0461 Fr 0:4712 l

lf 8:194 lw ð23Þ

The optimal model can predict 96.89% of our test data within an error band of ±20%, and 100% of test data within an error band of ±30%. Fig. 12(a) shows comparison of the experimental HTC with predicted HTC of the new heat transfer model. The new model shows a good performance to predict the heat transfer coefficient of these two enhanced tubes. The deviation between the predicted HTC and the experimental HTC is shown in Fig. 12(b). Although, the new model has accurate predictability but the entire data sample obtained in this paper are limited to the stratified/stratified-wavy flow regions (due to the pump power). More data base is needed to examine the accuracy of this model in other flow patterns and different enhanced tubes.

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5. Conclusions An experimental study on local flow boiling heat transfer performance in two 2EHT tubes and an equivalent smooth tube was performed using the near-azeotropic mixture R410A. A local thermal properties based heat transfer correlation is proposed for the 2EHT tubes. Local wall temperature and local HTC are reported and a detailed analysis on the effects of mass flux, heat flux were discussed, and flow pattern based heat transfer performance on HTC also was presented. The following conclusions are obtained: (1) Mass flux has significant effect on the heat transfer performance even though all experimental runs are operated in a relatively low mass flux region (stratified-wavy flow and slug flow/confined flow). The HTC decreases with increasing vapor quality in the confined flow region. Increasing vapor quality means a larger vapor core in the tube and the gravity force cannot be ignored at low mass flux. It ultimately results in a thinner liquid film washing the tube wall. Even the partial and unstable dry out region occurs at the upper space of the tube surface. (2) 2EHT tubes provide a higher HTC at relatively higher mass flux, but the 2EHT-2 tube suppresses the heat transfer at lower mass flux mainly due to the resistance of embossments and grooves and gravity force. (3) The local measurement of wall surface superheat gives a clear understanding of the local heat transfer performance of saturated flow boiling at temperature of 10 °C. The 2EHT tubes reduce the surface superheat when heat flux exceeds the CHF, and maintain a better saturate flow boiling at a relatively lower surface superheat compared to the smooth tube. (4) Heat flux has a significant and complex effect on the local saturate flow boiling. At the test mass fluxes, the HTC increases as the heat flux increases. But when heat flux exceeds the CHF, the HTC decreases with increasing heat flux for 2EHT tubes and smooth tube. (5) The conventional flow boiling model cannot precisely predict the heat transfer coefficient, and the predictability gets worse when the length of heated tube increases. The new proposed correlation can predict all the experimental data within an error band of ±30%, and 96.89% of test data within an error band of ±20% for both smooth and 2EHT tubes. (6) This experimental work reports a worthy set of flow boiling data which can be used in the future work. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgments This work is supported by the National Science Foundation of China (NSFC51210011). References [1] Z. Wu, Y. Wu, B. Sundén, W. Li, Convective vaporization in micro-fin tubes of different geometries, Exp. Therm Fluid Sci. 44 (2013) 398–408. [2] N.H. Kim, Evaporation heat transfer and pressure drop of R-410A in three 7.0 mm O.D. microfin tubes having different inside geometries, J. Mech. Sci. Technol. 29 (2015) 3519–3530.

[3] G.B. Jiang, J.T. Tan, Q.X. Nian, S.C. Tang, W.Q. Tao, Experimental study of boiling heat transfer in smooth/micro-fin tubes of four refrigerants, Int. J. Heat Mass Transf. 98 (2016) 631–642. [4] S.-P. Guo, Z. Wu, W. Li, D. Kukulka, B. Sundén, X.-P. Zhou, J.-J. Wei, T. Simon, Condensation and evaporation heat transfer characteristics in horizontal smooth, herringbone and enhanced surface EHT tubes, Int. J. Heat Mass Transf. 85 (2015) 281–291. [5] M. Shafaee, H. Mashouf, A. Sarmadian, S.G. Mohseni, Evaporation heat transfer and pressure drop characteristics of R-600a in horizontal smooth and helically dimpled tubes, Appl. Therm. Eng. 107 (2016) 28–36. [6] F. Yang, W. Li, X. Dai, C. Li, Flow boiling heat transfer of HFE-7000 in nanowirecoated microchannels, Appl. Therm. Eng. 93 (2015) 260–268. [7] X. Zhang, X. Zhang, Y. Chen, X. Yuan, Heat transfer characteristics for evaporation of R417a flowing inside horizontal smooth and internally grooved tubes, Energy Convers. Manage. 49 (2008) 1731–1739. [8] X. Zhang, C. Ji, X. Yuan, Prediction method for evaporation heat transfer of nonazeotropic refrigerant mixtures flowing inside internally grooved tubes, Appl. Therm. Eng. 28 (2008) 1974–1983. [9] M. Goto, N. Inoue, N. Ishiwatari, Condensation and evaporation heat transfer of R410A inside internally grooved horizontal tubes, Int. J. Refrig. 24 (2001) 628– 638. [10] L. Wojtan, T. Ursenbacher, J.R. Thome, Investigation of flow boiling in horizontal tubes: Part I—A new diabatic two-phase flow pattern map, Int. J. Heat Mass Transf. 48 (2005) 2955–2969. [11] N. Kattan, D. Favrat, J.R. Thome, Flow boiling in horizontal tubes. Part 1; Development of a diabatic two-phase flow pattern map, J. Heat Transfer 120 (1998) 140–147. [12] J.R. Thome, J.E. Hajal, Two-phase flow pattern map for evaporation in horizontal tubes: latest version, Heat Transfer Eng. 24 (2010) 3–10. [13] S.G. Kandlikar, Fundamental issues related to flow boiling in minichannels and microchannels, Exp. Therm Fluid Sci. 26 (2002) 389–407. [14] L. Cheng, Fundamental issues of critical heat flux phenomena during flow boiling in microscale-channels and nucleate pool boiling in confined spaces, Heat Transf. Eng. 34 (2013) 1016–1043. [15] R. Barraza, G. Nellis, S. Klein, D. Reindl, Measured and predicted heat transfer coefficients for boiling zeotropic mixed refrigerants in horizontal tubes, Int. J. Heat Mass Transf. 97 (2016) 683–695. [16] L. Cheng, G. Xia, Fundamental issues, mechanisms and models of flow boiling heat transfer in microscale channels, Int. J. Heat Mass Transf. 108 (2017) 97– 127. [17] Z. Wu, W. Li, S. Ye, Correlations for saturated critical heat flux in microchannels, Int. J. Heat Mass Transf. 54 (2011) 379–389. [18] L. Cheng, Critical heat flux in microscale channels and confined spaces: a review on experimental studies and prediction methods, Russ. J. Gen. Chem. 82 (2012) 2116–2131. [19] K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transf. 29 (1986) 351–358. [20] Z. Liu, R.H.S. Winterton, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, Int. J. Heat Mass Transf. 34 (1991) 2759–2766. [21] M.M. Mahmoud, T.G. Karayiannis, Heat transfer correlation for flow boiling in small to micro tubes, Int. J. Heat Mass Transf. 66 (2013) 553–574. [22] W. Li, J.X. Chen, H. Zhu, D.J. Kukulka, W.J. Minkowycz, Experimental study on condensation and evaporation flow inside horizontal three dimensional enhanced tubes, Int. Commun. Heat Mass Transfer 80 (2017) 30–40. [23] X. Han, P. Li, Z. Wang, X. Wang, X. Zhang, G. Chen, Evaporation heat transfer and pressure drop of R161 in a 7 mm micro-fin tube, Int. J. Heat Mass Transf. 62 (2013) 638–646. [24] M. Niederkrüger, D. Steiner, Flow boiling heat transfer to saturated pure components and non-azeotropic mixtures in a horizontal tube, Chem. Eng. 33 (1994) 261–275. [25] D. Biberg, An explicit approximation for the wetted angle in two-phase stratified pipe flow, Can. J. Chem. Eng. 77 (1999) 1221–1224. [26] X. Fang, Q. Wu, Y. Yuan, A general correlation for saturated flow boiling heat transfer in channels of various sizes and flow directions, Int. J. Heat Mass Transf. (2016). [27] M.M. Hasan, A Method for Assessing the Importance of Body Force on Flow Boiling CHF, J. Heat Transf. 126 (2004) 161–168. [28] L.E. O’Neill, I. Park, C.R. Kharangate, V.S. Devahdhanush, V. Ganesan, I. Mudawar, Assessment of body force effects in flow condensation, part II: Criteria for negating influence of gravity, Int. J. Heat Mass Transf. (2016). [29] L. Wojtan, R. Revellin, J.R. Thome, Investigation of Critical Heat Flux in Single, Uniformly Heated Microchannels, ECI International Conference on Heat Transfer and Fluid Flow in Microscale, 2005. [30] D. Mikielewicz, J. Mikielewicz, J. Tesmar, Improved semi-empirical method for determination of heat transfer coefficient in flow boiling in conventional and small diameter tubes, Int. J. Heat Mass Transf. 50 (2007) 3949–3956.