Channel aspect ratio effect on thermal performance of air–water slug flow through U-bend channels

International Journal of Thermal Sciences 76 (2014) 11e29

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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

Channel aspect ratio effect on thermal performance of airewater slug flow through U-bend channels Shyy Woei Chang a, *, Kuei Feng Chiang b, Ching Yuan Lin c a

Thermal Fluids Laboratory, National Kaohsiung Marine University, No. 142, Hai-Chuan Road, Nan-Tzu District, Kaohsiung 811, Taiwan, ROC CEO Office, Asia Vital Components Co. Ltd, 7F-3, No. 24, Wu-Chuan 2 Rd., Hsin-Chuang City, Taipei 24892, Taiwan, ROC c Department of Marine Engineering, National Kaohsiung Marine University, No. 142, Hai-Chuan Road, Nan-Tzu District, Kaohsiung 811, Taiwan, ROC b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 March 2013 Received in revised form 17 August 2013 Accepted 19 August 2013 Available online

This study investigates the effect of channel height-to-width ratio (Aspect Ratio, AR) on heat-transfer rates, pressure-drop coefficients (f) and thermal performances of airewater flows through horizontal and vertical U-bend rectangular channels at intermittent slug and slug-annular flow conditions. Interfacial two-phase flow structures, local and area-averaged Nusselt numbers (Nu), f coefficients, channelwise averaged void fractions (a) and thermal performance factors (TPF) for three sets of horizontal and vertical U-bend channels of AR ¼ 1, 0.83 and 0.33 are measured with liquid Reynolds numbers (ReL) and air-to-water mass flow ratios (AW) in the range of 1500  Re  10000 and 0  AW0.024. Early transitions from slug flow to slug-annual flow along with the shortened air slug and the extended period of the trailing-edge bubbly flow over each intermittent cycle are promoted by decreasing AR to elevate both heat transfer rates and pressure drops for the U-bend channels with small AR. A set of selective Nu, f and TPF data illustrates the interdependency between Nu, f, TPF and the airewater flow structures in present test channels with different AR. The area averaged endwall Nu for each U-bend test channel ðNuÞ and the corresponding f and TPF are cross-examined to generate a set of heat-transfer and pressure-drop correlations, which permit the evaluations of isolated and interdependent ReL, AW and AR effects on Nu and f, to assist various design applications. Ó 2013 Elsevier Masson SAS. All rights reserved.

Keywords: Airewater flow Thermal performance of slug flow U-bend channel Aspect ratio

1. Introduction Two-phase flows have found various applications for processing, thermal and energy industries, demanding detailed knowledge for heat transfer and pressure drop properties in conjunction with the interfacial flow mechanisms. The adiabatic two-phase (gase liquid) flows also involve a wide range of applications such as the transportation and production systems of oil and natural gas. As a result of the miniaturizations for fluid/thermal systems [1] and the development of sustainable energy sources, gaseliquid flows in thin/small channels have become increasingly important, such as the transport phenomena through the serpentine passages of fuel cells. Due to these industrial applications, several previous studies investigated the gas/vaporeliquid two-phase flows extensively [2e 22] with the various flow patterns; including bubbly, plug, slug, churn, wavy, stratified and annular flows, defined in the flow pattern maps. By way of introducing gas phase into liquid stream,

* Corresponding author. E-mail address: [email protected] (S.W. Chang). 1290-0729/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2013.08.009

the mechanisms for heat transfer enhancements (HTE), namely the increase of liquid and gaseliquid mixture velocities, turbulence augmentations with enhanced mixing via interfacial actions by gas bubble agitations and the thinner viscous sub-layer as a result of eddy penetration from the wakes of rising bubbles [2,3], were utilized [4e6]. As the attempts to develop the gaseliquid flow patterns/maps and devise the general heat transfer correlations, the reviews of heat transfer results by Ghajar group [2,3] identified the functional structure of a general heat transfer correlation formulated by void fraction, flow quality and the liquid-to-gas viscosity and Prandtl number ratios; but the correlative coefficients vary with the two-phase flow pattern, acknowledging no single correlation capable of predicting heat transfer rates for all two-phase flow patterns. For small diameter tubes (<12.5 mm) in which the surface tension effect becomes noticeable, the wettability of gaseliquid flow channel [7] and the capillary forces affect the bubble shape and the two-phase flow regime [8]; while the void fraction and the rising velocities of slug bubbles in vertical tubes were well correlated by drift flux model [8]. The variations of two-phase flow patterns by varying channel shape and size reflect the impacts of

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Nomenclature

English symbols A cross-sectional area of test channel (m2) as,bs,C,M,N correlative coefficients AR channel height-to-width aspect ratio _ G =m _L AW air  to  water mass flow ratio ¼ m Cp specific heat of liquid (water) (J kg1 K1) D diameter of U-bend curvature ¼ 2R (m) DnL superficial liquid Dean number ¼ ReL(dh/D)0.5 dh hydraulic diameter of test channel (m) f dimensionless pressure drop ¼ DP/(0.5rLU2LS)(dh/4L) f0 dimensionless pressure drop at single-phase water flow condition fN reference of dimensionless pressure drop for plain duct H channel height (m) h heat transfer coefficient (W m2 K1) g gravitational acceleration (m s2) kf thermal conductivity of liquid (water) (W m1 K1) L channel length (m) _G m mass flow rate of gas phase (air) (kg s1) _L m mass flow rate of liquid phase (water) (kg s1) Nu local endwall Nusselt number ¼ qfd/[(Tw  Tf)kf] Nu centerline averaged endwall Nusselt number NuN plain duct Nusselt number reference Pr Prandtl number of liquid (water) (mCp/kf) DP pressure drop across test channel (N m2)

surface tension on interfacial mechanisms and shearing actions. While most of the researches on two-phase flows used circular tubes, the early studies on two-phase flows in small rectangular channels [9e12] reported that the smaller channel height-to-width ratio (Aspect Ratio, AR) suppressed the stratified and wavy flow regimes but promoted the onset of elongated bubble and slug flows as the liquid rises more readily to the top of the vertical channel [10]. Two-phase flow pattern maps for horizontal and vertical rectangular channels [11,12] were proposed, reporting an insignificant liquid viscosity effect on flow pattern transition [12]. In general, the transition of two-phase flow patterns featured by the theoretical model for circular tubes [13] was not valid for narrow rectangular channels [9e14]. In Ref. [14], the channel shape effect on gaseliquid flows was highlighted by comparing the airewater flow structures and the flow regime maps obtained from circular and square channels. With sharp corners in rectangular channels, the liquid flow was drawn up and held more readily along the channel walls, leading to the extension of the intermittent flow regime by sustaining the plug, slug and annular flows at higher superficial gas and liquid velocities; but delaying stratified, wavy and dispersed flow regimes for vertical gaseliquid flows. As the channel hydraulic diameter (dh) decreased, the transitions of twophase flow regimes were accordingly changed, requiring a higher superficial liquid velocity for flow transitions to dispersed flows. As well as a reconfirmation, the regimes of stratified and intermittent flows are respectively suppressed and extended as dh decreases [14]. With the differences in relative magnitudes of shear, inertia and surface tension forces between circular (large) and rectangular (small) channels, which affect the phase distributions, the differential transport phenomena/properties due to the differences in relative magnitudes of these forces are constantly reported [14e 16]. When the surface forces and local strain rates play dominant roles for momentum transportations in curved micro-channels, the

qf R ReL St T t Tf Tp Tw TB TPF USG USL W X

convective heat flux (W m2) radius of U-bend curvature (m) Superficial liquid (water) Reynolds number ¼ rLULSd/mL Stanton number ¼ Nu/(ReLPr) dimensionless time ¼ t/Tp time (s) fluid bulk temperature (K) period of intermittent slug or slug-annular flow (s) wall temperature (K) period of bubbly flow region in each intermittent cycle (s) thermal performance factor ¼ ðNu=NuN Þ=ðf =fN Þ1=3 _ G =ðArG Þ ðms1 Þ gas ðairÞ superficial velocity ¼ m _ L =ðArL Þ ðms1 Þ liquid ðwaterÞ superficial velocity ¼ m channel width (m) dimensionless streamwise coordinate (x/L)

Greek symbols a averaged void fraction across test channel rG gas (air) density (kg m3) rL liquid (water) density (kg m3) mL liquid (water) dynamic viscosity (kg m1 s1) Subscripts single-phase water-flow condition 0 G gas L liquid

combined effects of curvature and initial conditions trigger the rich modes of dynamic responses to finite random disturbances, leading to the complicate bifurcation of the flow structures which involve the steady 2-cell flow, the intermittent flow oscillation among 2cell structures, and the chaotic flow with oscillations between 4cell and 2-cell flow structures [17]. In this respect, there has been less works on gaseliquid flows in curved rectangular narrow channels; but the works investigating the effects of centrifugal forces on two-phase flow phenomena in curved tubes are closely relevant. While the centrifugal forces induced by the curved square micro-channels affect the single-phase flow structures to large extents [17], the heterogeneous effects by the differential centrifuge actions upon liquid and gaseous phases through a U-bend channel considerably modify the interfacial mechanisms [18e22] and the corresponding heat-transfer and pressure-drop properties [22]. Based on a series of flow visualization results obtained from the 6.9, 4.95 and 3 mm U-bend tubes [18e20], the flow regime map for a number of two-phase flow patterns was constructed and discovered the temporal annular flow in the straight tube downstream the U-bend. As an attempt to investigate the two-phase flow morphology and the flow regime maps for airewater flows through the curved and serpentine tubes of 1 and 3 mm diameters, Kirpalani et al. [21] reported that the transition from intermittent (or slug) flow regime to annular and dispersed bubble flow regimes occurs at significantly lower superficial liquid velocities in serpentine channels due to increased pressure gradients as previously reported in Ref. [14].Such curvature induced centrifugal force drives the liquid fluid with the higher inertia as compared to gaseous fluid, leading to the heterogeneous effects which break gas bubbles, reduce the dispersed phase velocities and increase the contacts between bubbles to enhance bubble coalesce or breakup. The heterogeneous effects on bubble dynamics generally raised the bubble growth rates in U-bends to 2e4 times faster than those in

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the downstream horizontal straight tube [22]. With bubbly or intermittent flows, the flow phenomena associated with the turning motion of gaseliquid flow through a U-bend affect the trajectories, growths and interfacial mechanisms of the flowing bubbles; whereas the heterogeneous effects triggered in the Ubend can be extended into the downstream straight channel to raise both heat-transfer and pressure-drop coefficients [22]. For gaseliquid flows through rectangular channels, the intermittent flow regime is generally extended from the tubular gaseliquid flow conditions [10e12]; while the knowledge for the impacts of channel aspect ratio on the interfacial mechanisms and the associated transport phenomena in the rectangular small channel (dh < 12.5 mm) [7] with U-bend is lacking. This experimental work investigates the AR impacts on heattransfer and pressure-drop properties of intermittent airewater flows by comparatively examining the flow structures, channelaveraged void fractions (a), local and area averaged Nusselt numbers, pressure drop coefficients and thermal performance factors detected from three sets of horizontal and vertical rectangular U-bend channels of AR ¼ 1, 0.83 and 0.33. Air-water flow structures through the U-bend at the controlled air-to-water mass flow ratios (AW) and superficial liquid Reynolds numbers (ReL) with slug and slug-annular flows as the entry conditions are visualized from the snapshots of the charged-coupled device (CCD) camera which is capable of taking 300 images in 1 s. Initially, the airewater flow structures and the channel-wise averaged void fraction are analyzed to identify the two-phase flow patterns by visualizing the interfacial flow transitions through the U-bend. The responsive heat-transfer and pressure-drop properties to the interfacial flow transitions through the U-bend are subsequently examined. To disclose the differential efficiencies for heat transmissions, the thermal performance factors (TPF) evaluated at the criteria of constant pumping power consumptions at various ReL and AW are comparatively examined for the horizontal and vertical rectangular U-bend channels with different AR. Empirical correlations of endwall averaged Nusselt number ðNuÞ and mean Fanning pressure drop coefficient (f) using ReL and AW as the controlling parameters for the horizontal and vertical U-bend test channels with AR ¼ 1, 0.83 and 0.33 are generated. This work is aimed at disclosing the AR effects on the heat transfer rates, the pressure drop coefficients and the thermal performance factors for the horizontal and vertical rectangular U-bend channels with single-phase (water) and aire water two-phase flows at the slug and slug-annular entry flow conditions. 2. Experimental details 2.1. Experimental facilities Fig. 1 depicts (a) experimental test facilities and (b) rectangular U-bend test channel. The experimental test facilities consist of (1) airewater mixer, (2) divergent entry plenum chamber within which steel meshes and honeycomb are installed, (3) 300 mm flow entry tube in which the slug flow entry conditions as depicted in Fig. 1(a) are ensured, (4) convergent exit plenum chamber and (5)(6) two quick closing solenoid valves at the entry and exit of the U-bend test channel (7) for measuring the channel-averaged void fraction. With flow visualization tests, the two pairs of channel sidewalls and endwalls are made of transparent acrylic resin. With heat transfer tests, these transparent channel walls are replaced by Teflon walls. To generate the airewater flows, the dehumidified dry airflow enters the airewater mixer (8) via four radial inner bores that connect with four cylindrical porous ceramic rods. The average pore diameter for each 7 mm long, 10 mm diameter porous ceramic rod is 5 mm. The four cylindrical porous ceramic rods are immersed

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in water by feeding the water flow in both horizontal and vertical directions through the airewater mixer (8). Air bubbles with diameters between 0.5 and 1 mm are generated by passing the airflow through these immersed cylindrical porous ceramics rods. A spiral passage is installed downstream the airewater mixer (8) to enhance bubble coalesce for generating slug flows. A 300 mm long airewater flow calming section is fitted upstream the entrance of the test U-bend channel. Prior to entering the heated test channel, the pre-mixed airewater flow through the airewater mixer and the flow calming section, which is about 25 dh (300 mm) for present test U-bend channels, is generally at saturated condition with the relative humidity of the air-bubble approaching unity. When the heating commences, the increase of fluid temperature reduces the relative humidity of each air-bubble by increasing the saturation pressure of vapor. As a result, the evaporation of water within each air bubble is initiated until the vapor within the air-bubble reaches the saturated state at the elevated fluid temperature. The absorption of latent heat due to such evaporation within each air-bubble attributes to the additional convective heat transfer capacity. However, with the fluid temperature rise through each of present U-bend test channels less than 6.5  C, such evaporation process triggered by the reduced relatively humidity due to the increased fluid temperature is unlikely to be the dominant mechanism for the HTE properties generated by the airewater flows through present U-bend test channels. The mass flow rates of air and water flows are individually adjusted and measured by needle valves (9)(10) and the digital mass flow meters (11)(12) prior to entering the airewater mixer (8) in order to acquire the targeting superficial liquid ReL and AW. The CCD camera (13) is aimed at the angle normal to the test U-bend with a constant focal length. Locations of the light sources are individually adjusted at each test condition. This imaging system recorded the flow image at 300 fps with 172 pixels per channel width. The airewater flow structures in the inlet leg, U-bend and outlet leg at tested ReL and AW are visualized from the snapshots collected by the CCD system (13). The Fluke data logger (14) collects the signals transmitted from the calibrated K type thermocouples for wall (Tw) and fluid (Tf) temperature measurements. To detect the fluid entry temperature, a thermocouple is probed into the entry core of the inlet leg. On the exit plane of the outlet leg of each U-bend test channel, three equally spaced thermocouples are installed to measure the fluid temperatures which are averaged as the representative fluid exit temperature. Based on the mass fractions of air and water flows, the variations of specific heat by different AW in the range of 4012e4103 are less than 2.2%. With the basically uniform heat fluxes issued from the bottom endwall of the U-bend channel, the local fluid bulk temperature (Tb) is evaluated from the measured fluid entry temperature using the enthalpy balance method. Having all the thermocouple signals transmitted from the data logger (14) to the PC for condition monitoring, the fluid exit Tb is constantly calculated from the enthalpy rise through the test U-bend channel. As the criterion for collecting the data batch from the heat transfer test at each controlled ReL and AW condition, the measured and calculated fluid exit temperatures are compared to ensure that the discrepancies between the calculated and measured fluid exit Tb are less than 10% for each collected data batch. The constructional details of the U-bend test channel with rectangular section are illustrated by Fig. 1(b). The entry and exit Teflon flanges (1)(2) transit the sectional shapes of each rectangular U-bend test channel (3) from the circular calming tubes which connect with the two quick closing solenoid valves. For the three Ubend test sections, the channel width is fixed at 12 mm with different channel heights of 12, 10 and 4 mm, giving rise the channel aspect ratios of 1, 0.83 and 0.33 and the channel hydraulic

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Fig. 1. (a) Experimental test facilities (b) U-bend test channel (c) slug and slug-annular flow entry conditions.

diameters (dh) of 12, 11 and 6 mm respectively. The channel hydraulic diameter (dh) is selected as the characteristic length to evaluate Nu, f and ReL. As indicated by Fig. 1(b), the diameter of curvature (D) along the streamwise middle plane of each tested Ubend with different AR is fixed at 96 mm. The abrupt area ratios at the flow entrance are 2.18, 2.62 and 6.54 for present U-bend channels of AR ¼ 1, 0.83 and 0.33, respectively. Superficial liquid Dean number (DnL) is evaluated as ReL(dh/D)0.5. Acting by the combined effect of the abrupt flow entrance and the change of channel shape from circular to rectangular, the transition of aire water flow pattern takes place at the immediate flow entrance. The second transition of the airewater flow structure is triggered at the entry plane of the U-bend by the centrifugal force. The detailed geometries of the test channel, including the locations of pressure taps in Fig. 1(a) and the exact locations of thermocouples along the U-bend centerline, the heater plate, the present streamwise coordinate (x) system and the channel shapes in Fig. 1(b) are indicated.

To detect the pressure drops across the test U-bend channel, the pressure taps of 0.5 mm diameter penetrate into the core of the circular conduits from the endwall, Fig. 1(a). It is noticed that the length of the straight inlet leg for present U-bend test channel is longer than its outlet leg. The length of the inlet leg is pre-defined to enable the acquisition of developed flow heat transfer data for validating the present heat transfer results, which will be later illustrated. Also such shape change with abrupt flow entry condition is practical, which is beneficial for heat transfer performances due to the re-developments of boundary layers but requiring the additional pumping power to compensate the additional pressure drops due to the changes of flow momentum through the entry and exit manifolds. Therefore the locations of the pressure taps are selected at the core of the sectional planes adjoining the U-bend test section and the entry/exit chambers (2)(4), Fig. 1(a). As a result, the measured pressure drop (DP) across the U-bend test channel includes the effects of the flow pattern transition by changing the

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sectional shapes of flow passages through the abrupt entry and exit. The additional HTE benefit from the abrupt entry effect is justified by the additional pumping power increase when the thermal performance factor is evaluated. All the pressure drop measurements are individually performed at isothermal conditions with the identical ReL and AW selected for the heat transfer tests. These pressure taps connect with a digital micro-manometer with the precision of 0.01 mm-H2O to measure the pressure drop at each test condition. With the airewater flows, the agitating air bubbles stimulate considerable fluctuations in pressure drops across the Ubend channel. Time averaged pressure drops (DP) are calculated by averaging the instant measurements from the digital micromanometer over the scanning period about 45 s. Each U-bend test channel is constructed by two sidewalls (4), a 20 mm thick Teflon back wall (5) and its opposite endwall (6). The test channel which composes the U-bend and the inlet and outlet straight legs with equal length of 55 mm are milling machined from the Teflon back-wall (5). Three 1.5 mm thick and 12 mm wide heating foils (7) are connected in series to fit the endwalls of the Ubend and the inlet and outlet legs. Joule heating powers in the range of 1200e3200 W are fed through these heating foils (7) for generating the basically uniform heat fluxes over the endwall of the entire U-bend test channel. A continuous copper plate (8) of 0.3 mm thick is fitted over the heater foil. A 1 mm wide groove of 0.2 mm depth is machined along the centerline of the copped plate (8), along which fifteen K type thermocouples with equal intervals are embedded to measure the centerline wall temperature distributions along the inlet leg, U-bend and outlet leg. The entire test module assembly is tightened by four rows of axial bolts along the periphery of the two endwalls of the U-bend test channel. As indicated in Fig. 1(b), the origin of the present streamwise (X) coordinate system along the centerline of the U-bend channel is positioned at the entry of the inlet leg. Due to the different channel hydraulic diameters (dh), the dimensionless diameters of the Ubend curvatures in terms of D/dh for the test channels of AR ¼ 1, 0.83 and 0.33 are 8.3, 9.1 and 16.7 respectively. 2.2. Program and data processing The experimental conditions were controlled by specifying ReL and AW at the airewater flow pressures in the range of 1.05e 1.16 bars. At each tested ReL of 1500, 2100, 3000, 5000, 7000, 10,000, and 12,500 at the entry of each test U-bend channel, five different AW ratios in the range of 0e0.024 are selected to ensure the slug flow entry conditions. The corresponding superficial gas (UGS) and liquid (ULS) velocities were in the respective ranges of 1.05e24.73 and 0.12e1.77 m s1. At each set of ReL and AW test conditions, the channel-averaged void fraction and the pressure drop (DP) were measured with the corresponding airewater flow images recorded under isothermal conditions. The snapshots of the airewater flows visualized by high frame-rate videography are analyzed to examine the interfacial mechanics through the Ubends with different AR and to establish the associate flow maps with slug flow as the entry conditions. Depending on ReL and AW, two types of airewater flow entry conditions, namely the slug flow and the slug-annual flow as typified by Fig. 1(c), are generated prior to entering the U-bend test channel through which the interfacial structures are subject to modifications by the centrifugal forces in the U-bend and the shape change of the flow passage. Prior to carrying out the detailed Nu and f measurements for present Ubend test channels at vertical and horizontal orientations, the perturbation lengths are individual measured for at all the targeting ReL and AW conditions. By viewing the airewater flow structures detected from the present imaging system as typified by the selective snapshots shown in Fig. 1(c), the required flow entry

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length upstream the quick close solenoid valve (6) is about 15e 20 dh in order to ensure the periodical entry conditions with intermittent slug and slug-annular flows. As a result, the length of the flow entry tube (3) is selected as 300 mm, equivalent to 25 dh for the test channel of AR ¼ 1. In Fig. 1(c), the symbol T represents the dimensionless time defined as t/Tp where t is time in second. With present study, the increase of ReL at fixed AW is achieved by increasing both water and air mass flow rates for each U-bend test channel. Heat transfer tests were subsequently performed to detect the Nusselt number (Nu) distributions along the centerline on the endwall of each test U-bend channel at the identical test conditions for flow measurements. The hot spot wall temperatures were maintained at about 60  C by adjusting the heater powers. Having completed the flow and heat transfer tests at horizontal conditions, the experimental procedures were repeated for all the three test channels at vertical conditions. While the targeting ReL and AW at both horizontal and vertical test conditions are identical, the subtle differences in the air/water flow rates and the heater powers are necessary due to the different airewater flow structures developed in the horizontal and vertical U-bend channels. The continuous scans of the time-averaged wall temperature measurements at several locations along the centerline of each test Ubend channel over a period of 3 s were constantly performed during each heat transfer test run. The flow condition was assumed as the quasi-steady state when several successive scans of such time-averaged wall temperatures showed the temporal variations less than 0.3  C, which generally took about 30e45 min after ReL, AW or heater power was adjusted. The experimental heat transfer data were collected at the quasi-steady states. The local heat transfer property along the U-bend test channel was experimentally determined as Nu ¼ hdh/kf ¼ qfdh/[(Tw  Tf)kf] where h, qf, Tw, Tb and kf are the convective heat transfer coefficient, local convective heat flux, wall temperature at the inner wall of each test channel, local fluid bulk temperature and the thermal conductivity of water evaluated at local Tf. At each steady state, the enthalpy increase over a streamwise segment (Dx) is equal to the net heater power convected by the working fluid over this streamwise segment expressing as qf  dA in which dA is the corresponding segmental heating area. With the present airewater flow subject to the basically constant pressure heating process, the enthalpy increase of the working fluid over the streamwise _ G  CpG þ m _ L  CpL Þ  DTb in which DTb segment is evaluated as ðm is the increase of the working fluid temperature over the streamwise segment (Dx). Accordingly, the segmental Tf increase in the streamwise direction at each test condition is determined after _ G and m _ L into the equation of DTb ¼ substituting the measured qf, m _ G  CpG þ m _ L  CpL Þ: The downstream fluid temperaðqf  dAÞ=ðm ture (Tb,iþ1) over a streamwise segment (Dx) can be determined from it upstream fluid temperature (Tb,i) as Tb,iþ1 ¼ Tb,I þ DTb. This sequential calculating process proceeds from the streamwise location immediately upstream the flow entrance at which the heating is not commenced yet and the fluid entry temperature (Tf,in) is measured. Having completed such sequential calculating process along the entire test channel, the local fluid temperatures corresponding to all the x locations at which the Tw are measured can be determined. At the same Nu level for the three test U-bend channels with different dh, the convective heat transfer coefficients (h) for the test channels of AR ¼ 0.83 and 0.33 are respective 1.14 and 2.36 times of those obtained from the test channel of AR ¼ 1. The local convective heat flux was determined by subtracting the external heat loss flux from the total heat flux supplied with the axial wall conduction considered. To estimate the net conductive heat flux at each axial location where the thermocouple for wall temperature measurements is embedded, the finite difference presentation for the second derivative of wall temperature at each

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thermocouple location is performed using the measured axial wall temperature profile at each test condition. The net convective heat flux at each axial location where the wall temperature is detected can be accordingly determined by subtracting the external heat loss flux and the conductive heat flux from the supplied heat flux. Having acquired the net convective heat flux at each axial location where the thermocouple is embedded, the wall temperature measurement by each thermocouple is corrected to the channel inner wall using the one-dimensional Fourier conduction equation to determine the wall temperature at the wallefluid interface (Tw). As the streamwise Tw distributions varied with the local heat transfer properties of the airewater flows, local heat-loss and conductive heat fluxes were accordingly varied with the test conditions. While the perfect uniform heat flux heating condition was impractical, the basically uniform heat flux heating condition was simulated by controlling the external heat loss flux less than 7.8% of the total heat flux supplied using adequate thermal insulation to reduce external heat loss from each test section. The review of the entire conductive heat fluxes estimated for all the test conditions indicates that the maximum conductive heat flux takes place at the mid-turn due to the large Tw gradients, which is about 2.12% by using the highly conductive copper plate to construct the heated channel wall. The pressure drop coefficient (f) was calculated from the timeaveraged pressure drop (DP) across the entire length (L) of each U-bend test channel with the liquid (water) superficial velocity (ULS) as the reference velocity using the equation of f ¼ DP/ (0.5rLU2SL)(dh/4L) in which rL stands for the liquid (water) density. Unlike the horizontal test channels, the differential hydrostatic pressure (water) heads between the inlet and outlet legs of present vertical U-bend test channels are considered to correct the raw pressure drop measurements for determining DP. While the laminar-to-turbulent transitional Reynolds numbers for airewater flows with U-bend are expected to be varied from the reference conditions for single-phase developed flow through the smooth straight tube, the typical laminar-to-turbulent transition at ReL < 2200 and ReL > 3000 for fN and NuN at the reference conditions is still followed to evaluate the fN and NuN at ReL < 2200 and ReL > 3000 for normalizing the present f and Nu data to disclose the degrees of HTE impacts and pressure drop augmentations by feeding the airewater flows through present U-bend at the similar ReL. The reference Nusselt number (NuN) and pressure drop coefficient (fN) at laminar (ReL  2200) and turbulent (ReL  3000) conditions for the single-phase developed flow through the smooth straight tube are respectively selected as NuN ¼ 48/11, fN ¼ 16/Re and NuN ¼ 0.023Re0.8Pr1/3, fN ¼ 0.079/ Re0.25. The thermal performance factor (TPF) which evaluates the relative heat transfer elevations at the expense of increased pressure drop losses is defined as ðNu=NuN Þ=ðf =fN Þ1=3 at the constant pumping power consumptions for each ReL and AW tested. The cross examination of the Nu, f and TPF results obtained from present test U-bend channels of different AR with horizontal and vertical orientations reveal the impacts of AR and channel orientation on the thermal performances of the intermittent airewater flows through the U-bend channels. Empirical correlations for channelaveraged Nusselt number ðNuÞ and f are subsequently developed along with a detailed examination of the thermal fluid properties for the airewater flows through present U-bend channels. The estimation of experimental uncertainties for the nondimensional parameters determined by this study was performed [23]. The Tw and Tf measurements were the major sources for the uncertainties of Nu; while the DP measurement is the predominant factor attributing to f uncertainties. With the wall-to-fluid temperature differences, the pressure drops across test channel and the heater powers in the respective ranges 17e38 K, 48.91e5264 mm-

H2O and 1200e3200 W, the maximum uncertainties for Nu, ReL and f are approximated as 9.6% and 5.2% and 7.2% respectively. 3. Results and discussion 3.1. Airewater flow characteristics As a general abrupt contraction entry effect for each rectangular U-bend test channel, the intermittent Taylor bubbles fed from the upstream straight calming pipe are elongated. At such two-phase flow entry conditions, two types of airewater flow patterns, namely the slug and the slug-annual flows, are accordingly developed in the test channels as typified by Fig. 2(a) and (b) respectively. As the flow in the wake of the Taylor bubble is strongly unsteady, the shape of the leading nose is also affected by the downstream drift of the trailing bubbles and the resulting fluctuations of velocity and pressure. The bubble nose is no longer in spherical shape but exhibits quasi-periodic oscillations. The distances between two successive Taylor bubbles vary with the test conditions in the range of 0.4e90 dh, which are not sufficient to damp out the fluctuations of velocity and pressure in the wake region via the viscous dissipation. As a result, the shape transition of the leading nose for the Taylor bubble through the U-bend reflects the combined impacts of the centrifugal forces and the fluctuations of velocity and pressure triggered by the trailing wake of the Taylor bubble. Through the U-bend section, the centrifugal forces arise to generate the regional heterogeneous effects on bubble dynamics and induce the Dean-type swirls within the turning Taylor bubble. As depicted by Fig. 2(a) and (b), the leading nose of each elongated air bubble in the U-bend section is stretched further along the inner bend due to the heterogeneous effect triggered by the centrifugal force. Recalling the study of single phase flow through the curved channel [24], the shearing drags acting upon the turning air-slug along the outer edge of each U-bend, which is the unstable side of the curved channel, are higher than the inner-edge counterparts. Accordingly, the spherical leading nose for each elongated air bubble in the inlet leg is skewed into the sharpened shape along the U-bend, Fig. 2(a) and (b). At the locations immediate downstream the turning section, the skewed leading nose of the Taylor bubble in the U-bend tends to revert into the axially symmetrical shape in the straight outlet leg by breaking the sharpened leading edge into several separate but coherently joined air bubbles in front of the reformed bubble nose through the outlet leg, Fig. 2(a). The flow images collected at the occasions when the Taylor bubble fully occupies the U-bend still show the traces of centrifugal force effects. In this regard, the review of the entire airewater flow snapshots confirms that the water films over the U-bend outer wall and at the entry region of the outlet leg take the intermittent waveforms during which the elongated air bubble fully occupies the Ubend, Fig. 2(a) and (b). The formation of such wavy liquid film over the outer wall is relevant to the regional flow instabilities [25] and the Dean-type vortical cellar flows developed within the air slug. Clearly, the Dean-type vortical flows in the turning air slug stir the turning liquid film, while the downstream swirls in the U-bend burst the regional flows at the entry region of the outlet leg, generating several traces of skewed shadow fringes to reflect the stirred water films as indicated by several flow snapshots collected in Fig. 2(a) and (b). At the occasions that the small air bubbles downstream the Taylor bubble enter the U-bend section; the prevailing centrifugal forces affect both the liquid and air flows. Due to the phase segregation effect by centrifugal forces, the small trailing bubbles behind each air slug drift toward the inner wall of the Ubend. Acting by the combined effects of the Dean-type swirls, the trailing vortices of Taylor bubble and the centrifugal forces in the U-

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17

Fig. 2. Typical airewater (a) slug (b) slug-annual flows developed in horizontal or vertical U-bend test channels.

bend, the drifting small trailing bubbles are wafting; whereas the trailing edge of each turning Taylor bubble is skewed as depicted by Fig. 2. Further increases of the superficial gas or liquid velocities, the slug flow pattern as exemplified by Fig. 2(a) transits to the slugannual flow as typified by Fig. 2(b). With the enhanced flow momentum at the slug-annual flow condition, the water film rolls and surges along the two channel sidewalls to encapsulate the air slugs even within the horizontal test channel. However, such agitated annual liquid film develops intermittently; while the variations of the airewater flow structures through each U-bend test channel basically follow the results developed at the slug flow conditions. But the oscillations of wavy films along the outer wall of each Ubend and over the entry region of the outlet leg at the slug-annular

flow conditions are amplified from the slug flow scenarios. In addition, the review of the entire flow images detected by this study also reveals that the cycle time (period, Tp) of the intermittent slug or slug-annual flows is systematically reduced as AR decreases. After a lapse of elongated air slug, the period of bubbly flow region (TB) in each cycle time (Tp) is also subject to AR impacts, which will be later examined as the TB/Tp ratio affects the time-mean transport properties due to the differential heat transfer rates and pressure/ friction drags between the bubbly and slug flows. For acquiring the phase distribution in a single plane of present U-bend test channels of AR ¼ 1, 0.83, 0.33, the flow visualization tests using light sheet illumination are performed. The phase distributions over the middle cross-section of the horizontal and vertical U-bends of AR ¼ 1. 0.83 and 0.33 are respectively typified by

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Fig. 3(a) and (b) at ReL ¼ 3000, AW ¼ 0.01. The interfacial boundary between the gaseous zone and liquid film is indicated by the dashed line in each snapshot of Fig. 3. As indicated by Fig. 3(a) and (b), while the centrifugal force is always directed toward the outer wall of the U-bend, the gravity acts toward the bottom wall for the horizontal U-bend but toward the inner wall over the middle crosssection of the vertical U-bend. Due to the different orientations between the centrifugal and gravitational forces over the middle cross-sections of the horizontal and vertical U-bend channels, the differential phase distributions at horizontal and vertical orientations are readily seen by comparing the flow images detected from the horizontal and vertical U-bends. In this respect, the most different phase distributions over the middle cross-sections between the horizontal and vertical U-bend develop in the square channels of AR ¼ 1. However, as AR decreases from 1 to 0.33, which enhances the relative significance of surface tension on the phase distribution over the middle cross-section of the U-bend, the differences in phase distributions between the horizontal and vertical

U-bends are correspondingly moderated. As shown by Fig. 3(a) for the horizontal U-bends, the liquid phase at most of the instants over an intermittent cycle is driven toward the bottom wall by gravity and toward the outer wall by centrifugal force. With T ¼ 1 at which the laser light sheet intercepts the agitating tiny air-bubbles behind the trailing edge of each Taylor bubble, the scattering of laser light by the wafting air-bubbles illuminates the entire middle cross-section of both horizontal and vertical U-bends, Fig. 3(b)(a) and (b). It is interesting to find the wafting tiny bubbles in the liquid film that accumulates over the bottom wall of the horizontal Ubend of AR ¼ 1, Fig. 3(a). Such wafting tiny air-bubbles in the liquid film could promote both heat transfer rates and frictional drags for the horizontal channels from their vertical counterparts. With vertical U-bends, the centrifugal force counteracts the gravity over the middle cross-sections of these vertical U-bends. As a result, the thickness of liquid film over the bottom heated wall in the vertical U-bend of AR ¼ 1 is considerably reduced from the horizontal counterpart, Fig. 3. As depicted by the sequential snapshots shown

Fig. 3. Phase distributions over middle cross-section of (a) horizontal (b) vertical U-bends of AR ¼ 1. 0.83 and 0.33 at ReL ¼ 3000, AW ¼ 0.01.

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by Fig. 3(a) for the horizontal U-bend of AR ¼ 1, the liquid films are respectively driven by the gravitational and centrifugal forces to accumulate over the inner and outer walls of the U-bend. The traces of agitated tiny air bubbles in the liquid films over the vertical Ubend of AR ¼ 1 are considerably reduced from the horizontal counterparts by cross-examining Fig. 3(a) and (b). Unlike the horizontal U-bends with no sign of dry-out over the bottom heated wall due to the gravitational effect, the partial dry-out along the bottom heated edge of the middle cross-section in the vertical Ubend emerges at several instants as exemplified by T ¼ 0.15 (AR ¼ 1), T ¼ 0.13 (AR ¼ 0.83) and T ¼ 0.67 (AR ¼ 0.33) in Fig. 3(b). The various phase distributions caused by different orientations between the centrifugal and gravitational forces as exemplified by the comparative flow images detected from the horizontal and vertical U-bends of AR ¼ 1, 0.83 and 0.33 in Fig. 3 incur the corresponding differences in heat-transfer and pressure-drop properties, which will be later illustrated. Fig. 4 depicts the temporal variations of airewater flow structures through (a) horizontal (b) vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33 at ReL ¼ 3000, AW ¼ 0.01. With fixed ReL and AW, both superficial liquid (USL) and gas (USG) velocities are decreased as AR decreases. As a result, while the slug-annular flow patterns are developed in the horizontal or vertical U-bend test

19

channels of AR ¼ 1 and 0.83, the airewater flow structures in the horizontal and vertical test channels of AR ¼ 0.33 remain as slug flows, Fig. 4. Cross examining the sequential snapshots obtained from the horizontal and vertical U-bend test channels with the same AR, the sequential transitions of airewater flow structures through these U-bend channels are similar but the subtle differences between the horizontal and vertical U-bend test channels are systematically reduced as AR decreases. In this respect, the cycle time (Tp) for the intermittent flow through the horizontal U-bend channel of AR ¼ 1 is noticeably longer than the Tp in the vertical channel. As AR decreases from 1 to 0.33, Tp decreases systematically and the differential cycle time (Tp) between the horizontal and vertical U-bend test channels tends to be diminished. Although the transition sequences of the airewater flow structures through the horizontal and vertical U-bend test channels are generally similar for the three sets of U-bend test channels with different AR, the transitional boundaries from slug to slug-annual flows are affected considerably by AR and marginally by channel orientation. This is demonstrated by Fig. 5 in which the transitional boundary for the flow patterns in each of the horizontal or vertical U-bend test channel is mapped out. Also indicated in Fig. 5 are the entry conditions with which the slug-annular flows are generated prior to entering each U-bend test channel.

Fig. 4. Airewater flow structures for (a) horizontal (b) vertical U-bend channels of AR ¼ 1, 0.83 and 0.33 at ReL ¼ 3000, AW ¼ 0.01.

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Fig. 5. Transitional boundary of flow patterns in (a) horizontal (b) vertical U-bend test channels.

For comparisons with the straight duct-flow conditions, the dotted demarcation lines in Fig. 5 envelope the slug and slugannular flow regimes for the straight tube [26] and the intermittent flow regime for the rectangular straight channel with dh ¼ 5.36 mm and AR ¼ 0.725 [14]. With reduced dh and AR for present rectangular test channels, which in turn raises the frictional drags by increasing the near-wall flow velocity gradients, the demarcation lines separating the slug and slug-annual flows for present U-bend test channels systematically shift toward the higher superficial gas velocities (USG) as AR decreases for both sets of horizontal and vertical channels. While the late transitions from slug flow to slug-annual flow for present U-bend test channels are caused by decreasing AR; the U-bend effect on the transitional boundary of the flow patterns for the intermittent flows is revealed by comparing the present test results with those obtained from the straight rectangular [14] and circular [26] channels. In comparison with the straight tube result [26], both the slug and slug-annular flows in present U-bend test channel of AR ¼ 1 transit at the lower USG, indicating the early developments of slug and slugannular flows in the U-bend channel, Fig. 5(a). In this regard, the USG and USL for generating the slug-annular flows in the flow calming section upstream the entrance of each U-bend test channel are also reduced for present U-bend test channels, Fig. 5. For the Ubend test channel of AR ¼ 0.83, the intermittent flow regime covering both slug flows and slug-annular flows is extended from the USG range reported for the straight rectangular channel of AR ¼ 0.75 [14], Fig. 4(a). While the previous results for flow regime transitions in the small channels (dh ¼ 1.3e5.5 mm) concluded that the compound effects of surface tension and the reduced dh for the horizontal rectangular straight channels suppressed the stratified flow regime but extended the intermittent flow regime [14], the centrifugal force effects over each U-bend tend to extend the intermittent flow regime further and promote the early transition from slug to slug-annual flows. With the prevailing centrifugal force effects generated by the twisted tape inserts in vertical tube of upward airewater flows, our previous works reported that the heat transfer levels and pressure drop coefficients for bubbly flow regime are both raised from the slug flow counterparts [27,28]. As a result, the TB/Tp ratio can affect the time-mean heat transfer rates and pressure drop coefficients of present slug and slug-annular flows. Fig. 6 compares the varying

manners of TB/Tp against AW at all the ReL tested for (a) horizontal (b) vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33. The numbers of recorded periods on which Figs. 6 and 7 are based for present intermittent airewater flows are not less than 20. Justify by the data convergence obtained at all the tested ReL, the TB/Tp ratios appear as the weak function of ReL; but decrease as AW increases for all the U-bend test channels, Fig. 6. Although these AW controlled TB/Tp variations follow a general trend of exponential decay as depicted by Fig. 6, the AR impacts gradually emerge as AW increases for both sets of horizontal and vertical test channels. While the TB/ Tp ratios at small AW share the similar values for each of the three horizontal or vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33, the rate of AW driven TB/Tp decay is moderated by decreasing AR from 1 to 0.33, leading to the higher TB/Tp ratios at high AW for the test channels of AR ¼ 0.33. Accompanying with the reduced Tp by decreasing AR, the higher TB/Tp ratios for the channels of AR ¼ 0.33 at high AW also enhance the contributions of bubbly flow regime to the transport properties over an interfacial varying cycle for present slug and slug-annular flows through these U-bend channels. The consequential AR impacts on the heat transfer and pressure drop properties for present U-bend test channels will be later examined. As an important interfacial parameter for vaporeliquid flows, the void fractions (a) detected at all the test conditions for the Ubend test channels of AR ¼ 1, 0.83 and 0.33 are examined with the empirical a correlation developed. In this regard, the drift flux model with the gas drift flux corresponding to Taylor bubble rising velocity in a stationary liquid (UT) has been previously attempted to correlate the a data measured from the vertical swirl tubes with counter-current airewater bubbly [27] and slug [28] flows. In these attempts [27,28], USG/a varies linearly with the gas-to-liquid slip velocity (USG  USL) in the form of USG/a ¼ UT þ C  (USG  USL) where UT is p determined for the vertical upward continuous slug ffiffiffiffiffiffiffiffi flow as 0:35 gdh [29], while the coefficient C for slug flows was correlated as 1.29 [28]. For all the U-bend test channels, the a data can also be favorably correlated by the drift flux model taking the pffiffiffiffiffiffiffiffi general form of USG =a ¼ 0:35 gdh þ C  ðUSG  USL Þ: This is demonstrated by Fig. 7 in which all the USG/a data for each U-bend test channel at horizontal and vertical orientations converge into a tight data trend, indicating the negligible impact of channel orientation on a for present set of U-bend channels. While the drift flux model correlates well all the present a data, the C coefficient

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21

Fig. 6. Variations of TB/Tp against AW at all the tested ReL for (a) horizontal (b) vertical U-bend channels of AR ¼ 1, 0.83 and 0.33.

decreases systematically from 1.43 / 1.33 / 1.23 as AR decreases from 1 / 0.83 / 0.33, Fig. 7. As these C coefficients obtained from present U-bend test channels are raised from the plain tube value of 1.2 [28,29], the void fractions in these U-bend test channels are reduced from the plain-tube levels at the similar USG and (USG  USL) conditions or at the fixed ReL and AW conditions. The systematic C reduction by decreasing AR implies the increased void fraction for the narrow channel of low AR. This particular AR-driven a reduction reflects the raised TB/Tp ratios as AW decreases, which enhances the contributions of bubbly flow regime over each intermittent cycle of interfacial variations. The aforementioned variations of interfacial flow structures by varying ReL and/or AW for present U-bend test channels generate the consequential impacts on pressure-drop and heat-transfer performances from the single-phase flow conditions, which are comparatively examined in the following sections. 3.2. Heat transfer properties Initially, the streamwise profiles of Nusselt numbers (Nu0) at AW ¼ 0 conditions along the endwall centerline of the three U-bend test channels of AR ¼ 1, 0.83 and 0.33 at horizontal and vertical orientations are examined to generate the base-line heat transfer

Fig. 7. Variations of USG/a against gas-to-liquid slip velocity (USG  USL) for U-bend test channels.

results at single-phase water flow conditions. The typical heat transfer results at AW ¼ 0 are exemplified by Fig. 8 in which the streamwise centerline Nu0 and h0 distributions along three U-bend test channels of AR ¼ 1, 0.83 and 0.33 at horizontal and vertical orientations with ReL ¼ 1500 (laminar) and 7000 (turbulent) are respectively compared in Fig. 8(a) and (b). As well as for validation, the Nusselt number levels at developed flow conditions in a plain straight duct obtained from the theoretical result for Re ¼ 1500 and from the DittuseBoelter correlation for Re ¼ 7000 are also indicated in the Nu0 plots depicted by Fig. 8(a) and (b), respectively. In this regard, the Nu0 data in present straight inlet leg over the axial region of 0.2e0.3 x/L agree favorably with the Nusselt number results evaluated from the typical laminar level of 48/11 and the DittuseBoelter level for the developed duct flows subject to uniform heat flux. The depiction of centerline Nu0 distribution by each plot of Fig. 8 indicates the similar pattern, regardless the channel orientation and AR ratio for single-phase water flows at AW ¼ 0. Along the inlet straight leg, the centerline Nu0 distribution follows the typical boundary layer flow pattern with initial high Nu0 in the developing flow regime. Due to the present abrupt entry effect, the heat transfer levels along the inlet leg of each U-bend test channel decay axially toward the developed flow level with limited Nu0 differences between the three test channels of different AR, Fig. 8. Upon entering the U-bend section through which the Dean vortices are induced by the centrifugal forces, the centerline endwall Nu0 are considerably raised from the inlet-leg levels and reached the peak values at the turning angle about 1200 along the planar bend of each test channel, Fig. 8. Downstream the Nu0 peak along the turning pathway in each U-bend is the subsequent Nu0 decay which proceeds toward the exit of the outlet leg at which the Nu0 values re-approach the straight plain duct levels for the developed flows, Fig. 8. Along with the developments of Dean-type vortices in the U-bend, the noticeable AR impacts on the endwall heat transfer performances gradually emerge with the consistent Nu0 elevations by reducing AR, Fig. 8. The collective research results from the curved rectangular channels with different AR [17,30,31] suggested the developments of multi-cellar vortical flow structures in the curved channels with the smaller AR. Due to the multi-cellar vortical flows in present U-bend channels of AR ¼ 0.33, the endwall centerline Nu0 values along present U-bends with the smaller AR are consistently raised from those in the square (AR ¼ 1) Ubends; while the centrifugal force effects indexed by the heat transfer elevations over the unstable outer wall of the curved

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Fig. 8. Streamwise centerline Nu0 and h0 distributions in horizontal and vertical U-bend test channels of AR ¼ 1, 0.83, 0.33 with AW ¼ 0 at ReL ¼ (a) 1500 (b) 7000.

channel with small AR were alleviated as previously reported in Ref. [30]. Over the channel region immediate downstream the U-bend in the straight outlet leg, the AR driven Nu0 differences still remain visible in each plot of Fig. 8 due to the downstream effects of the various vortical flows generated in these U-bends. Such AR driven Nu0 differences are correspondingly faded at further downstream locations in the outlet leg as the swirls downstream the U-bends are gradually diminished via viscous dissipations. Cross examining the streamwise h0 and the corresponding Nu0 distributions collected in Fig. 8, the dh effect on the conversion of Nusselt number to h is disclosed. With the similar Nu0 levels for the test channels of AR ¼ 1, 0.83 and 0.33 shown by the Nu0 plots over the straight inlet leg, the corresponding h levels follow the order of AR ¼ 0.33 > AR ¼ 0.83 > AR ¼ 1 due to the smaller dh for the channel with the smaller AR. Nevertheless, as featured by the DittuseBoelter correlation and the standard Nu0 level for the laminar developed pipe flow; for which the Nusselt number for singlephase straight duct flow is independent of dh, the present Nu0

data along the straight inlet leg obtained from the three test channels of AR ¼ 1, 0.83 and 0.33 converge tightly to reflect the typical Nusselt number results for duct flows. In the attempt to devise the single phase water-flow Nu0 references against which the heat transfer results obtained with airewater flows are compared, the centerline Nusselt numbers measured at AW ¼ 0 are averaged as Nu0 at all the tested ReL for each U-bend test channel. The ReL driven Nu0 variations for each of present horizontal and vertical U-bend test channels with the same AR converge into a tight data trend as depicted by Fig. 9(a). Due to the inclusion of U-bend section through which the Dean number (Dn) is accordingly raised to enrich the centrifugal force effects by increasing ReL, Nu0 remains no longer constant but increases with the increase of ReL even at ReL  2200, Fig. 9(a). In this regard, as the reduction of channel height at fixed channel width simultaneously reduces AR and dh, the Dean numbers are systematically decreased by reducing the channel height at fixed ReL in the ratio of 1: 0.9: 0.5 for present test

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23

Nu0 ¼ 0:274  Re0:676 horizontal=vertical channels of AR L ¼ 0:33at AW ¼ 0ð3000  ReL  10; 000Þ

Fig. 9. Nu0 variations against ReL (a) experimental data (b) comparisons of experimental and correlation results for laminar and turbulent flows.

channels of AR ¼ 1, 0.83 and 0.33. However, although the Nu0 values for each U-bend test channel are elevated from the straight channel levels by including the ReL and thus Dn effects over the bend region, the clear laminar-to-turbulent Nu0 transitions still remain evident for present U-bend test channels, Fig. 9(a). The Nu0 correlations are thus individually developed at ReL  2200 (laminar) and ReL  3000 (turbulent) conditions for the U-bend test channels of different AR. As demonstrated by Figs. 8 and 9(a), the Nu0 values at horizontal and vertical channels with the same AR for single-phase water flows (AW ¼ 0) are similar, which can be well correlated by the same Nu0 correlation. Two pairs of three-set Nu0 correlations for present U-bend test channels of AR ¼ 1, 0.83 and 0.33, irrespective of the channel orientation at AW ¼ 0 conditions, are developed as equations (1)e(3) and (4)e(6) for laminar (ReL  2200) and turbulent (3000  ReL  10,000) reference conditions respectively.

Nu0 ¼ 0:023  Re0:771 L

horizontal=vertical channels of AR

¼ 1at AW ¼ 0ðReL  2200Þ (1) Nu0 ¼ 0:033  Re0:735 horizontal=vertical channels of AR L ¼ 0:83at AW ¼ 0ðReL  2200Þ

(2)

Nu0 ¼ 0:065  Re0:659 horizontal=vertical channels of AR L ¼ 0:33at AW ¼ 0ðReL  2200Þ

(3)

Nu0 ¼ 0:233  Re0:669 horizontal=vertical channels of AR L ¼ 1at AW ¼ 0ð3000  ReL  10; 000Þ

(4)

Nu0 ¼ 0:256  Re0:671 horizontal=vertical channels of AR L ¼ 0:83at AW ¼ 0ð3000  ReL  10; 000Þ

(5)

(6)

As compared by Fig. 9(b), all the experimental Nu0 data are favorably correlated by equations (1)e(3) and (4)e(6) with the maximum discrepancies less than 15%. The noticeable Nu0 elevations from the plain straight-duct developed flow levels [32,33] for each of present U-bend test channels are mainly attributed to the favorable centrifugal force effects on the endwall heat transfer properties over the U-bend section, Fig. 9(b). Having established the single-phase water flow heat transfer references, the endwall heat transfer properties of the airewater flows through the U-bend test channels of different AR are examined as typified by Fig. 10 in which the streamwise centerline Nu distributions along the horizontal and vertical U-bend test channels of AR ¼ (a) 1 (b) 0.83 (c) 0.33 with AW ¼ 0, 0.004, 0.013, 0.018 at ReL ¼ 5000 are compared. For highlighting the differential heat transfer performances between single-phase (water) and twophase (airewater) flows through present U-bend test channels, the dashed line in each plot of Fig. 10 corresponds to the centerline Nu0 distribution obtained at the same ReL and AR with single-phase water flow at AW ¼ 0. With present parametric conditions tested, the centerline Nu levels along each horizontal or vertical U-bend test channel are consistently raised by increasing AW at fixed ReL, Fig. 10. While the similar centerline Nu0 profiles at AW ¼ 0 conditions are detected from the horizontal and vertical channels with the same AR, the Nu differences caused by different vertical and horizontal channel orientations are noticeable for the airewater flows as compared by the two plots collected in Fig. 10(a), (b) or (c). The degrees of AW-driven Nu elevations from the AW ¼ 0 references in the horizontal U-bend test channel are generally higher than the vertical counterparts, Fig. 10. Such AW-driven heat transfer elevations also exhibit the different degrees of AW impacts between the inlet leg, U-bend and outlet leg. In this respect, the AW impacts on the centerline heat transfer performances are most evident in the straight inlet leg within which the Dean-type vortices are not yet triggered; whereas the least AW impacts emerge in the U-bend through which the centrifugal-force effects are most dominant. Due to the various degrees of AW impacts on the heat transfer properties between the inlet leg, U-bend and outlet leg, the patterns of centerline Nu distributions for the airewater flows are yielded from the Nu0 profiles with AW ¼ 0. As demonstrated by Fig. 8, the decreased dh as AR decreases from 1 / 0.83 / 0.33 incurs the corresponding increase of heat transfer coefficients (h) when the Nu levels for the three U-bend test channels of different AR are similar. While the local endwall Nu values depicted by Fig. 10 fall into the similar range for the three horizontal or vertical U-bend test channels with different AR, the convective heat transfer coefficients (h) of the airewater flows through the test channels with the smaller AR are generally higher than those obtained with the larger AR due to the various phase distributions and different dh to reflect the AR influences on the airewater flow structures depicted by Fig. 6 in which the higher TB/Tp ratios generally develop in the Ubend test channel of AR ¼ 0.33 at high AW. Accompanying with the decreased Tp by reducing AR as exemplified by Fig. 6, the contributions of bubbly flow regime to the heat transfer properties over an interfacial varying cycle for the U-bend test channel with the smaller AR are enhanced. As the h values and the pressure drop coefficients (f) with bubbly flows are generally higher than the slug-flow counterparts [27,28], the increased TB/Tp incurs the corresponding h increase as AR decreases from 1 / 0.83 / 0.33. Similarly, the decrease of AR also raises the f coefficient, which will be later demonstrated. To assess the heat transfer impacts by the airewater flows via the modifications of flow structures from the AW ¼ 0 scenarios, the

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Fig. 10. Streamwise centerline Nu distributions in horizontal and vertical U-bend test channels of AR ¼ (a) 1 (b) 0.83 (c) 0.33 with AW ¼ 0, 0.004, 0.013, 0.018 at ReL ¼ 5000.

ratios of centerline averaged Nusselt numbers between airewater (AW > 0) and water (AW ¼ 0) flows at the same ReL for each U-bend test channel are evaluated as Nu=Nu0 : Variations of Nu=Nu0 against AW for all the tested ReL in the U-bend test channels with horizontal and vertical orientations of AR ¼ (a) 1 (b) 0.83 (c) 0.33 are collected in Fig. 11. In each plot of Fig. 11, two distinct converged data trends for the horizontal and vertical channels suggest the weak dependency of Nu=Nu0 on ReL. The higher slopes for the horizontal channel than the vertical counterparts demonstrate the larger AW impact on Nu=Nu0 for the horizontal channel. As AR decreases, the slope for each AW-driven Nu=Nu0 varying trend is decreased for both horizontal and vertical channels, indicating the weakened AW impacts on Nu=Nu0 as AR decreases, Fig. 11. Above all, the linear increasing data trend shown by each plot of Fig. 11(a)/c enables the Nu=Nu0 correlation taking the general form of:

Nu=Nu0 ¼ 1 þ NfARg  AW

(7)

in which the slope (N value) of each data trend depicted by Fig. 11 is function of AR and the channel orientation. The varying manners of N values against AR with horizontal and vertical orientations, which follow a general trend of exponential increase, are depicted by Fig. 11(d). The N correlations for the horizontal and vertical test channels with the present test conditions are generated as equations (8) and (9) respectively.

N ¼ 41:9 þ 1:49E  4  e13AR N ¼ 18:3 þ 2:16E  4  e12:4AR

ðhorizontal orientationÞ

(8)

ðvertical orientationÞ

(9)

The Nu levels for the airewater flows through the present Ubend test channels at horizontal and vertical orientations can be determined using equations (1)e(9). A comparison of the Nu results determined by equations (1)e(9) and 87% of the entire experimental data shows the maximum discrepancies of 20% for the entire set of heat transfer data generated by this study. Consider the complex interfacial flow structures in present U-bend test channels with horizontal and vertical orientations, this set of heat transfer correlations permits the evaluations of individual ReL, AW and AR impacts on Nu for various engineering applications. As an attempt to disclose the relative importance of centrifugal forces and gravity for different AW ratios, flow rates and geometries, the dimensionless parameter featuring the different degrees of heterogeneous effects by centrifugal forces through the bend is defined. With single-phase water flow through the U-bend with the curvature radius of R, the centrifugal acceleration can be approximated as U2SL/R. As present investigation focused on the heterogeneous effects initiated from the differential densities between air and water through the U-bend where the centrifugal forces arise, the dimensionless parameter to feature the relative strength of such phase-differentials driven by the centrifugal and

S.W. Chang et al. / International Journal of Thermal Sciences 76 (2014) 11e29

25

Fig. 11. Variations of Nu=Nu0 against AW for horizontal and vertical test channels of AR ¼ (a) 1 (b) 0.83 (c) 0.33 with the entire ReL tested (d) variations of N values against AR for horizontal and vertical test channels; variations of Nu and Nu=Nu0 against a[U2SL/(Rg)] for horizontal and vertical channels of AR ¼ (e)1 (f)0.83 (g)0.33.

gravitational forces is formulated as a[U2SL/(Rg)] in which a is the channel averaged void fraction controlled by channel configurations and AW ratio. The variations of Nu and Nu=Nu0 against a[U2SL/ (Rg)] for present test channels of AR ¼ 1, 0.83 and 0.33 are respectively depicted by Fig. 11(e)/(g). As a[U2SL/(Rg)] increases at each fixed ReL, which is typified by the data series at ReL ¼ 10,000 indicating in each plot of Fig. 11(e)/(g), both Nu and Nu=Nu0 for all the horizontal and vertical test channels increase with the increase of a[U2SL/(Rg)]. The increase of relative strength of the centrifugedriven heterogeneous effects by raising a and/or U2SL/(Rg) not only improves the endwall heat transfer levels (Nu) but also amplifies the centrifugal force effects by raising Nu=Nu0 ratios at fixed ReL. While such a[U2SL/(Rg)] driven Nu and Nu=Nu0 data trends are remained for all the test channels and ReL, the Nu=Nu0 ratios are systematically decreased as ReL increases, indicating the weakened centrifugal force effects when the inertial force effects are enhanced, Fig. 11(e)/(g). As expected, the Nu levels are raised by increasing ReL at each fixed a[U2SL/(Rg)], Fig. 11(e)/(g). However, the differential centrifuge-driven heterogeneous effects due to different channel orientations are also consistently depicted by Fig. 11(e)/(g). With the vertical channel orientation, the gravitational force acts on the same plane with the centrifugal forces developed through the U-bend; while the gravitational and centrifugal forces are orthogonal in the horizontal U-bend. As compared in each plot of Fig. 11(e)/(g), both Nu and Nu=Nu0 for the horizontal channel are higher than the vertical counterparts at the similar a[U2SL/(Rg)], indicating the higher HTE benefits by the centrifugal force effects when the centrifugal and gravitational forces act on the same plane, Fig. 11(e)/(g). As the larger ranges of

Nu and Nu=Nu0 variations are driven by varying a[U2SL/(Rg)] or ReL for the channel of AR ¼ 1 as shown by Fig. 11(e)/(g), the larger extents of centrifugal and inertial forces effects tend to develop in present test channel of AR ¼ 1. 3.3. Pressure drop and thermal performance The f factor determined by this experimental work is the dimensionless pressured drop evaluated as the Fanning pressure drop coefficient (f) rather than the typical skin friction coefficient developed for two-phase airewater flows. The main focus to detect the pressure drops through the test channel at single-phase and two-phase conditions is to comparatively examine the additional pumping power required in order to gain the additional HTE benefits by the complex airewater interfacial mechanisms. The measuring locations selected for evaluating the pressure drops as indicated in Fig. 1(a) only provide the channel-averaged pressure drop measurements in respect to the specific locations where the pressure taps are installed. The corresponding changes for these dimensionless pressure drops to AR and AW are examined to study their general effect on the pressure drops for present test channels. The depiction of f variations by adjusting AW and ReL to accordingly alter the interfacial airewater flow structures through each U-bend test channel, as an attempt to develop the empirical correlation for the dimensionless pressure drop (f), is shown by Fig. 12. The more details of pressure drop and f measurements, including the validations, test facilities and method of data reduction, for the straight tube at single phase (water) and two-phase (airewater) flow conditions without and with spiky twisted tape insert can be referred

26

S.W. Chang et al. / International Journal of Thermal Sciences 76 (2014) 11e29

to our previous works reported in Refs. [27,28]. In Fig. 12, the f variations against AW at fixed ReL for each horizontal or vertical Ubend test channel with AR ¼ (a)(d) 1 (b)(e) 0.83 (c)(f) 0.33 and (g) single-phase water-flow f0 variations against ReL for horizontal and vertical channels of AR ¼ 1, 0.83, 0.33 are collectively compared in these plots. While all the f values obtained at fixed ReL increase linearly as AW increases for each U-bend test channel, the f scale constructing Fig. 12(a)e(f) is selected as log scale for acquiring the

clear vision of ReL impacts on f, which depicts the consistent f decrease by increasing ReL at fixed AW. The linear f increase against AW enables the general form of f correlations as

f ¼ f0 þ MfReL g  AW

(10)

where the slope of each f correlation, namely the M value in equation (10), is function of ReL, AR and channel orientation.

Fig. 12. Variations of f against AW at fixed ReL for horizontal and vertical U-bend test channels with AR ¼ (a)(d) 1 (b)(e) 0.83 (c)(f) 0.33 (g); f0 variations against ReL for horizontal and vertical channels of AR ¼ 1, 0.83, 0.33; variations of M against ReL for (h) horizontal (i) vertical channels of AR ¼ 1, 0.83, 0.33.

S.W. Chang et al. / International Journal of Thermal Sciences 76 (2014) 11e29

Comparing Fig. 12(h) and (i), it is interesting to note the different trends of ReL-driven M variations between the horizontal and vertical channels. The different airewater flow structures developed in the horizontal and vertical U-bend test channels result in the respective increase and decrease of M values as ReL increases, Fig. 12(h) and (i). While the increase of ReL weakens the AW impacts on f by reducing the M values for the horizontal U-bend test channels of AR ¼ 1, 0.83 and 0.33, the AW impacts on f are amplified by increasing ReL at vertical orientation. However at single-phase water-flow conditions, similar to the heat transfer results at AW ¼ 0 with the negligible Nu0 differences between the horizontal and vertical U-bend test channels of the same AR, the f0 differences between horizontal and vertical test channels with the same AR at AW ¼ 0 are not noticeable. This is demonstrated by Fig. 12(g) which depicts the converged f0 data obtained at horizontal and vertical orientations for each U-bend test channel. These f0 data trends consistently decrease as ReL increases. The typical functional structure of pressure drop correlations for the boundary-layer type flows is also followed by the present f0 data for these U-bend test channels, Fig. 12(g). Irrespective of laminar or turbulent conditions, equations 11e13 favorably correlate the entire f0 data for each Ubend test channel with horizontal and vertical orientations.

f0 ¼ 11; 574=Re1:395 L

horizontal=vertical channels of AR

¼ 1at AW ¼ 0 (11) f0 ¼ 10; 087=Re1:386 L

horizontal=vertical channels of AR

¼ 0:83at AW ¼ 0 (12) f0 ¼ 93:37=Re0:99 L

horizontal=vertical channels of AR

¼ 0:33at AW ¼ 0

(13)

Having acquired the f0 correlations, the development of f correlations requires the determination of M coefficients as the functions of ReL for each horizontal and vertical U-bend test channel. Justified by the data trends depicted by Fig. 12(h) and (i), the M values for the horizontal and vertical U-bend test channels are respectively correlated as

M ¼ a0 þ a1  expða2  ReL Þ M ¼ b0 þ b1  ReL

ðhorizontal channelÞ

ðvertical channelÞ

(14) (15)

Table 1 summarizes the coefficients a0  a2 and b0  b1 for the horizontal and vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33. The f correlations for the airewater flows through the horizontal and vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33 are generated as equations 10e15. The maximum discrepancy between the correlated f values and the experimental data is less than 30% for 90% of the entire f data generated. It is worth noting the AR impacts on the pressure drops (DP), which indicates the systematic increase of DP by decreasing AR from 1 to 0.33 at each set of AW and ReL. Nevertheless, due to the reduced dh by decreasing AR for the present set of U-bend test channels, the f coefficients still decrease with the decrease of AR even though the DP value is increased by reducing AR. Having devised the Nu and f correlations, the thermal performances of present airewater flows through the horizontal and vertical U-bend test channels of AR ¼ 1, 0.83 and 0.33 are subsequently analyzed. The correlative relationships between the heat-

27

Table 1 Coefficients a0  a2 and b0  b1 for horizontal and vertical U-bend test channels. AR

1 0.83 0.33

Horizontal channel

Vertical channel

a0

a1

a2

b0

b1

50.82 41.75 6.832

182.12 171.95 44.82

3.724E-4 3.55E-4 7E-4

18.21 17.56 3.41

6.5E-4 6E-4 3E-4

transfer and pressure-drop properties for the airewater flows through present U-bend test channels are examined by plotting Stanton numbers (St) against f coefficients obtained at the same ReL and AW for each U-bend test channel. Even with the complex aire water flows by varying ReL and AW, the St data detected from all the tested ReL and AW converge into a tight f-driven linear data trend for each U-bend test channel as depicted by Fig. 13(a) and (b) for laminar (ReL  2200) and turbulent (ReL  3000) reference conditions respectively. The centerline averaged St for the present aire water flows are closely correlative with f coefficients irrespective of the various interfacial flow structures generated at different ReL and AW. Following the recent trend to revise the qualitative form of validity for Reynolds’ analogy, the linear St increase against f for present U-bend test channels at laminar and turbulent reference conditions re-ensures the general consideration that the Reynolds’ analogy is valid for flows that the changes in the gradients of field variables, such as velocity and temperature, along the flow direction are small [34]. With the complex airewater interfacial mechanisms, the converged St versus f data shown by Fig. 13(a) and (b) give evidences on pursuing the validity of Reynolds’ analogy for airewater two-phase flows. However, comparing each pair of the converged f-driven St data trends between the horizontal and vertical U-bend test channels of the same AR in Fig. 13(a) and (b), the slope of the St versus f data-trend for the horizontal channel is generally less than its vertical counterpart due to the higher f for the horizontal channel with the similar St between horizontal and vertical channels. As the f levels in the U-bend test channels of AR ¼ 0.33 are considerably less than those detected from the channels of AR ¼ 1 and 0.83, despite the systematic increases of pressure drops (DP) by reducing AR, the most steep f-driven St datatrends develop in the horizontal/vertical U-bend test channels of AR ¼ 0.33, Fig. 13(a),(b). Cross-examining Fig. 12(a),(d) and (b),(e), the f values for the horizontal/vertical U-bend test channels of AR ¼ 1 and AR ¼ 0.83 are similar even though the dh are different. However, although present set of heat transfer data consistently show the higher heat transfer coefficients (h) at the smaller AR, the larger dh for the square channel of AR ¼ 1 results in the higher Nu and thus St than the AR ¼ 0.83 counterparts. Comparing the channels of AR ¼ 1 and 0.83, due to the higher Nu and thus St for the channel of AR ¼ 1; whereas the similar f are shared by the test channels of AR ¼ 1 and 0.83, the slopes of St number for the channel of AR ¼ 1 are slightly higher than the AR ¼ 0.83 counterparts. Above all, the St slopes collected in Fig. 13 thus follow the sequence of AR ¼ 0.33 > AR ¼ 1 > AR ¼ 0.83. The relative heat transfer improvements at the expense of the increased pressure drops for present airewater flows through the U-bend test channels with horizontal and vertical orientations are evaluated as the thermal performance factors (TPF) evaluated as ðNu=NuN Þ=ðf =fN Þ1=3 at constant pumping power consumptions. The variations of TPF against ReL for the U-bend test channels of AR ¼ 1, 0.83 and 0.33 at horizontal and vertical orientations are depicted by Fig. 13(a) and (b) respectively. As an overall assessment, the TPF variations against ReL or AW for all the three U-bend test channels at either horizontal or vertical orientation follow the similar trends as depicted by Fig. 12(c) and (d). As AR decreases

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S.W. Chang et al. / International Journal of Thermal Sciences 76 (2014) 11e29

Fig. 13. Variations of St against f with (a) ReL  2200 (b) ReL  3000 for horizontal and vertical channels of AR ¼ 1, 0.83, 0.33; variations of TPF against ReL for (c) horizontal (d) vertical channels of AR ¼ 1, 0.83, 0.33.

from 1 to 0.33, TPF accordingly increases at each set of ReL and AW. Such elevated TPF by reducing AR from 1 to 0.33 is mainly driven by the reduced f as AR decreases. For the three U-bend test channels at all the test conditions, the TPF peaks generally emerge in the ReL range of 3000e5000; whereas the increase of AW, which simultaneously elevates Nu and f, consistently raise TPF, Fig. 12(c) and (d). In general, the overall heat transfer enhancements attributing to the two-phase flow mechanisms through these U-bend channels cannot counterbalance with the raised pumping powers to compensate the increased pressure drops due to the 1800 turning motion of the bulk stream and the aiding interfacial drags among the airewater flows for the test channels of AR ¼ 1 and 0.83. The TPF values for these two U-bend test channels of AR ¼ 1 and 0.83 are generally less than unity at both laminar and turbulent conditions, Fig. 13(c) and (d). However, as the f coefficients for the test channels of AR ¼ 0.33 are noticeably less than those detected from the test channels of AR ¼ 1 and 0.83 as compared by Fig. 12(a)e(f), the TPF values for present horizontal and vertical U-bend test channels remain above than unity for all the test conditions performed by this study. TPF values for the horizontal and vertical U-bend test channel of AR ¼ 0.33 are in the respective ranges of 0.98e1.24 and 1.26e1.44 at the laminar and turbulent reference conditions, Fig. 13(c) and (d). The present U-bend geometry of AR ¼ 0.33 with slug and slug-annular airewater flows appears as an efficient HTE measure for various engineering applications.

4. Conclusions This experimental study examines the endwall heat-transfer and pressure-drop properties along with their associated airewater interfacial structures for three U-bend test channels of AR ¼ 1, 0.83, 0.33 in the attempt to disclose the AR impacts on the thermal performances of slug and slug-annular flows. The following concluding remarks emerge from this work. 1. With slug and slug-annual flows through the U-bends, the regional heterogeneous effects on bubble dynamics and the Dean-type swirls respectively skew the leading nose toward the inner bend and twist the air slug. As AR decreases from 1 to 0.33, the period (Tp) of the intermittent slug or the slug-annual flow is reduced. The ratio between the period of bubbly flow region (TB) in each cycle time (Tp) appears as the weak function

of ReL but decreases as AW increases. Demarcation lines separating the slug and slug-annual flows for present U-bend test channels in flow maps systematically shift toward the higher superficial gas velocities (USG) as AR decreases. Relative to the straight duct-flow conditions, the slug and slug-annular flows in these U-bend test channels transit at the lower USG and cover the wider ranges than the straight-duct scenarios. The channelwise averaged void fraction (a) for each U-bend test channel with horizontal or vertical orientation is favorably correlated by the drift flux model, but is reduced from the straight-duct levels and increased with the decrease of AR to echo the increased TB/Tp as AW decreases. 2. At single-phase water-flow (AW ¼ 0) conditions, the noticeable AR impacts on endwall heat transfer properties emerge in the U-bend section with the consistent Nu0 elevations by reducing AR. By adding the airewater interfacial mechanisms for present U-bend channels, the endwall heat transfer levels are consistently raised by increasing AW at fixed ReL with noticeable channel orientation effects to offer the higher degrees of HTE impacts at horizontal orientation. The ratios of Nu=Nu0 show weak dependency on ReL with the higher degrees of AW impacts for horizontal U-bend channels. A set of Nu=Nu0 and Nu0 correlations are generated to permit the evaluation of individual and interdependent ReL and AW impacts on Nu for present U-bend channels of AR ¼ 1, 0.83, 0.33 at horizontal and vertical orientations. 3. With present single-phase water flows, f0 consistently decrease as ReL increases with negligible channel orientation effect at the same AR. The f values for airewater flows increase linearly as AW increases at fixed ReL; whereas the slope of each AWdriven linear f increase is respectively reduced and elevated by increasing ReL at horizontal and vertical orientations. Empirical correlations of f/f0 and f0 are individually devised to evaluate the channel-wised averaged pressure drop coefficients at various ReL and AW conditions for each U-bend channel of AR ¼ 1, 0.83 or 0.33 at horizontal or vertical orientation. 4. The strong correlative relationships between St and f for all the U-bend test channels, which consistently depict the linear St increase by increasing f, are individually followed by present airewater flows obtained at laminar (ReL  2200) and turbulent (ReL  3000) reference conditions. The TPF values evaluated as constant pumping power consumptions increase as AR decreases from 1 to 0.33 at fixed ReL and AW. For each of

S.W. Chang et al. / International Journal of Thermal Sciences 76 (2014) 11e29

present U-bend test channels, the TPF peaks emerge in the ReL range of 3000e5000; whereas the increase of AW consistently raises TPF. With AR ¼ 1 and 0.83, the TPF at present test conditions are generally less than unity; but the TPF values for the U-bend test channel of AR ¼ 0.33 remain above unity for all the test conditions at laminar and turbulent reference conditions. Acknowledgment The research work is financially supported by National Science Council, Taiwan, under NSC 100-2628-E-022-001MY3 project and the research fund from AVC company. References [1] R. Shekarriz, Challenges in thermal systems miniaturization, Heat Transf. Eng. 21 (2000) 1e2. [2] D. Kim, A.J. Ghajar, R.L. Dougherty, V.K. Ryali, Comparison of twenty twophase heat transfer correlations with seven sets of experimental data, including flow pattern and tube orientation effects, Heat Transf. Eng. 20 (1999) 15e40. [3] D. Kim, A.J. Ghajar, Heat transfer measurements and correlations for aire water flow of different flow patterns in a horizontal pipe, J. Exp. Thermal Fluid Sci. 25 (2002) 659e676. [4] G.P. Celata, A. Chiaradia, M. Cumo, F. D’Annibale, Heat transfer enhancement by air injection in upward heated mixed-convection flow of water, Int. J. Multiphase Flow 25 (1999) 1033e1052. [5] P. Vlasogiannis, G. Karagiannis, P. Argyropoulos, V. Bontozoglou, Airewater two-phase flow and heat transfer in a plate heat exchanger, Int. J. Multiphase Flow 28 (2002) 757e772. [6] S.W. Chang, B.-J. Huang, Thermal performance improvement by injecting air into water flow, Int. J. Heat Mass Transf. 57 (2013) 439e456. [7] D. Barnea, Y. Luninski, Y. Taitel, Flow pattern in horizontal and vertical two phase flow in small diameter pipes, Can. J. Chem. Eng. 61 (1983) 617e620. [8] K. Mishima, T. Hibiki, Some characteristics of airewater flow in small diameter vertical tubes, Int. J. Multiphase Flow 22 (1996) 703e712. [9] O.C. Jones, N. Zuber, The interrelation between void fraction fluctuations and flow patterns in two-phase flow, Int. J. Multiphase Flow 2 (1975) 273e306. [10] L. Troniewski, R. Ulbrich, Two-phase gaseliquid flow in rectangular channels, Chem. Eng. Sci. 39 (1984) 751e765. [11] M.W. Wambsganss, J.A. Jendrzejczyk, D.M. France, Two-phase flow patterns and transitions in a small, horizontal, rectangular channel, Int. J. Multiphase Flow 17 (1991) 327e342. [12] T. Wilmarth, M. Ishii, Two-phase flow regimes in narrow rectangular vertical and horizontal channels, Int. J. Heat Mass Transf. 37 (1994) 1749e1758. [13] Y. Taitel, A.E. Dukler, A model for predicting flow regime transitions in horizontal and near horizontal gaseliquid flow, AIChE J. 22 (1976) 47e55. [14] J.W. Coleman, S. Garimella, Characterization of two-phase flow patterns in small diameter round and rectangular tubes, Int. J. Heat Mass Transf. 42 (1999) 2869e2881.

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