Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

Experimental Thermal and Fluid Science 33 (2009) 1087–1099

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Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes Shyy Woei Chang a,*, Tsun Lirng Yang b a b

Thermal Fluids Laboratory, National Kaohsiung Marine University, No. 142, Haijhuan Road, Nanzih District, Kaohsiung City 81143, Taiwan, ROC Department of Marine Engineering, National Kaohsiung Marine University, No. 142, Haijhuan Road, Nanzih District, Kaohsiung City 81143, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 23 April 2009 Received in revised form 8 June 2009 Accepted 15 June 2009

Keywords: Swirl tube Air–water slug flow Forced heat convection

a b s t r a c t This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (ReL) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent ReL and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived. Ó 2009 Published by Elsevier Inc.

1. Introduction Many industrial applications such as the transportation of crude oil–gas mixtures through pipes often encounter the gas–liquid slug flow with heat transfer involved. For the gas–liquid slug flow, most of the gas is coalesced into elongated bubbles (Taylor bubbles) that convect intermittently in the tube with a thin annual liquid film between Taylor bubble and tube wall. A liquid slug fills between two consecutive Taylor bubbles and is sometimes aerated with small dispersed gas bubbles. These dispersed bubbles in the liquid slug are most consumed by Taylor bubbles; while some of them penetrate into the liquid film. Between the gas and liquid slugs, complex interfacial mechanisms are triggered by the drift of Taylor bubbles and varied with the channel inclination and the countercurrent/cocurrent flow conditions. The shapes of Taylor bubbles change constantly with their leading and trailing edges exhibiting strong oscillations [1]. When the slug flow is developing with relatively short separations between two consecutive Taylor bubbles, the trailing Taylor bubbles accelerate and merge with the leading ones. Such merging process increases the lengths of liquid slug and Taylor bubble. Once the liquid velocity profiles behind the Taylor bubble, which are often characterized by vortex pairs [1–3], become fully developed, the merging process is terminated and all * Corresponding author. Tel.: +886 7 8100888 5216. E-mail address: [email protected] (S.W. Chang). 0894-1777/$ - see front matter Ó 2009 Published by Elsevier Inc. doi:10.1016/j.expthermflusci.2009.06.005

the Taylor bubbles propagate at the similar translational velocity. When these Taylor bubbles are drifting in a tube filled with liquid pool, several vortexes in various sizes with vibrant mixing are developed downstream each Taylor bubble. The liquid film flows over the tube wall in the opposite direction of the drifting Taylor bubble and subsequently plunges into the downstream liquid slug in the form of trailing wakes attached to the drifting Taylor bubble. Such process was reported as an annular liquid jet plunging into the liquid slug, which tripped a pressure wave that induced the secondary vortexes near the tube wall immediately following the primary vortexes [3]. The shapes of bubble-nose and bubble-trail as well as the wakes behind each drifting Taylor bubble are affected by the viscosities of fluids, the surface tension forces and the Froude number for Taylor bubble [3]. For the cocurrent slug flow, the gas and liquid slugs convect in the same direction. Several studies have investigated the hydrodynamic characteristics of such slug flow e.g. [4–8]. In this regard, the probability density function of void fraction (a) converted from the dynamic a measurement has proved as an effective method to distinguish the slug flow from the bubbly, churn and annular flows [5]. The propagation velocities of Taylor bubbles in vertical upward tube were generally correlated as functions of the drift velocity of Taylor bubble and the liquid or gas–liquid mixture velocity [6,7]. When the annular liquid film mixes with the liquid slug, the strong turbulence is stimulated and becomes dominant in the near wake region behind each Taylor bubble, resulting in asymmetric instantaneous velocity profiles

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Nomenclature English symbols A, B AW

functional coefficients in heat transfer correlations _ L = v/(1v) _ G =m air-to-water mass flow ratio = m

Cp Cf D G kf L _G m _L m Nu NuP NuS P

specific heat of liquid (water) (J kg1 K1) pressure drop coefficient = (DPP or DPS)/qLgL inner diameter of test tube (m) gravitational acceleration (m s2) thermal conductivity of liquid (water) (W m1 K1) length of test tube (m) mass flow rate of gas-phase (air) (kg s1) mass flow rate of liquid phase (water) (kg s1) local Nusselt number = qfD/[(TwTb)kf] mean Nusselt number for developed flow (plain tube) mean Nusselt number for developed flow (swirl tube) axial distance of twist pitch with 180° rotation of tape (m) Prandtl number of liquid (water) (lCp/kf) pressure difference between plain tube entry and exit (mm-H2O)

Pr DPP

characterized by small-scale vortices with high local velocities [7]. Such mixing process proceeds and evolves in the downstream direction. At locations about 25 tube diameters downstream the flow entrance, only vortices with the scale of the tube diameter survive [7] and the motion of the Taylor bubble is affected by the trailing wakes of its leading Taylor bubble [2]. When the slug flow travels through the vertically curved or serpentine channel, the centrifugal force arises in the bend and drives the liquid with higher inertia as compared to gas that can break the elongated gas bubbles [8]. The twist of the gas–liquid interface through the bend can augment phase interaction in the manner to enhance gas bubble or liquid slug break-up thus altering the flow boundaries between the dispersed bubble and plug/slug flow regimes as well as the boundaries between the annular and plug/slug flow regimes [8]. While previous studies have extensively examined the hydrodynamic characteristics of gas–liquid slug flows, the thermal performance of the slug flow was rarely reported. Clearly, the different two-phase flow patterns such as the bubbly, slug, churn and annular flows generate different near-wall flow structures and result in various wall-to-fluid heat transfer properties even if the channel geometries keep identical. In this respect, a set of heat transfer correlations that correlate the heat transfer ratio between the two-phase and single-phase liquid flows using the superficial gas-to-liquid velocity ratio as the determining variable was collected in Ref. [9]. In general, due to the high velocities of liquid film and the enhanced fluid mixing in the trailing wakes of Taylor bubble, heat transfer performances at slug flow conditions are augmented from the likewise single-phase conditions [9–12]. In a vertical tube with cocurrent upward air–water slug flow, the tube wall thermal pattern exhibits dual character [9]. When the liquid slug, which is aerated by small bubbles, convects through the heated tube wall, the uniform wall-to-fluid heat transfer distribution is obtained. With a Taylor bubble passing though the heated area, the thermal distribution is immediately changed to a streaky structure due to the moving liquid annular film that encompasses the drifting Taylor bubble. With the Taylor bubble intermittently convected through the tube which incurs strong pressure fluctuations at the tube wall, the near-wall turbulent structure is disrupted and the flow becomes intermittent. The wall-to-fluid heat transfer coefficient for slug flow could be accordingly correlated by Peclet and Froude numbers [9].

DPS qf ReL Tb Tw UGS ULS UT x X y

pressure difference between swirl tube entry and exit (mm-H2O) convective heat flux (W m2) superficial liquid (water) Reynolds number = qLULSD/lL fluid bulk temperature (K) wall temperature (K) _ G /(A qG) (m s1) gas (air) superficial velocity = m _ L /(A qL) (m s1) liquid (water) superficial velocity = m translational Taylor bubble velocity (m s1) axial location referred to flow entry as origin (m) dimensionless axial location (x/D) twist ratio (P/D) = 2

Greek symbols a averaged void fraction across test tube _ G /(m _L+m _ G) v dryness fraction = m qG gas (air) density (kg m3) qL liquid (water) density (kg m3) lL liquid (water) dynamic viscosity (kg m1 s1) g thermal performance index = (NuS /NuP )/(DPS/DPP)

When occasions require further heat transfer enhancements from the gas–liquid two-phase flow, the twisted tape insert was a suitable heat transfer enhancement (HTE) measure for bubbly and slug flows. The twisted tape insert in the swirl tube formulates two twisted helical pathways within which the centrifugal force arises when the single- or two-phase flow convects through such swirl tube. Comprehensive studies for single-phase flow in such swirl tube were reported that revealed the flow physics relevant to the HTE impact attributed to the twisted tape insert. The HTE impacts are generated by partitioning and blockage of the ducted flow, the fin effect of twisted tape, the elongated twisted flow path and the centrifugal force influences through the secondary flows in the form of vortexes [13]. With turbulent flows, the pair of vortexes on the sectional plane of a swirl duct is characterized by rather uniform axial velocity [14] that results in large velocity and temperature gradients across the thin boundary layer and leads to augmentations of the wall-to-fluid heat convection and the shearing drag. With a twisted tape insert in circular tube [15,16] or square duct [17,18], the sharp transitions of laminarto-turbulent pressure drop and heat transfer coefficients were not observed. By inferring that the laminar-to-turbulent transitional jump was inhibited due to the presence of twisted tape insert, a set of generalized heat transfer and pressure drop correlations for single-phase flow was derived using the reported data collected from the open literature [19]. With two-phase flows, the centrifugal forces induced by the twisted tape prevail over the entire swirl tube and are radially directed toward the tube wall. This type of body-force influence segregates liquid and gas-phases and drives the liquid with higher radial inertia as compared to gas toward the tube wall. This centrifuge-driven mechanism in the swirl tube with two-phase flow assists the liquid film to attach on the heated wall so that the critical heat flux (CHF) for boiling applications can be elevated. For the dispersed bubbly boiling flow in a tube with a twisted tape insert, the point (wall superheat) of nucleate boiling incipience could be increased by a factor of two with the heat transfer rates improved up to a factor of three in post-dryout regimes [20]. Nevertheless, as the swirls induced by a twisted tape insert were more effective for increasing CHF than its HTE impacts, the previous studies for nucleate boiling in a swirl tube with subcooled liquid were mostly concerned with the CHF increase [21] rather than the pressure drop and HTE performances.

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Along the line of research development for the swirl channel with twisted tape(s) insert, this research group has devised the spiky twisted tape insert with the heat transfer and pressure drop performances at the single-phase [22] and bubbly flow conditions examined [23]. By fitting the spiky twisted tape in the swirl tube, the centrifugal forces and the flow separations tripped by the helically arranged spikes considerably modify the flow and heat transfer performances [22,23] and disturb the phase transition and the void distribution for the cocurrent air–water bubbly flow [23]. As a typical centrifugal force effect in such a swirl tube with the cocurrent upward air–water bubbly flow, the coherent bubble clusters are drifting within the swirls and concentrated in the tube-core to enhance bubble collisions and coalescences with the void fraction prone to the core-peaking profile. Heat transfer correlations for the tube fitted with a spiky twisted tape were derived for the single-phase flow and the cocurrent upward air–water bubbly flow [22,23]. This study is a follow-up work of Ref. [23] that investigates the impact of the spiky twisted tape insert on the heat transfer and pressure drop performances for the cocurrent upward air–water slug flow. The two-phase flow structures, tube-averaged void fractions, pressure drops and wall-to-fluid heat transfer performances detected from the plain and swirl tubes at the slug flow conditions are presented. Previous results obtained with the bubbly flow in the likewise plain and swirl tubes are comparatively examined to reveal the different impacts of the spiky twisted tape insert on the thermal fluid performances between the bubbly and slug flows.

2. Experimental program and test facility This study used high frame-rate videography to visualize the two-phase flow patterns in the plain and swirl tubes and to measure the translational velocity of Taylor bubble. Experimental conditions were controlled by adjusting air-to-water mass flow ratio (AW) and liquid Reynolds number (ReL) at the pre-defined values with the averaged void fractions, pressure drops and local Nusselt numbers individually detected for the plain and swirl tubes. Test ranges of ReL and AW were initially determined from the flow visualization results detected from the plain tube in order to ensure the slug flow pattern. The tested ReL and its corresponding AW range, namely ReL = 4000, 5000, 6000, 8000, 0.003 6 AW 6 0.02, ReL = 10000, 0.003 6 AW 6 0.01, were controlled at the test pressures about 1.19–1.8 bars. Superficial gas (UGS) and liquid (ULS) velocities for the present test conditions were between 0.38–3.8 and 0.18–0.5 m s1, respectively. All the flow and heat transfer measurements detected from the plain tube were treated as the reference results against which the swirl tube results obtained with the identical sets of AW and ReL were compared. With the same slug flow entry conditions for the plain and swirl tubes, the comparative differences in flow structures, pressure drops and heat transfer rates between the plain and swirl tubes were analyzed with the impacts of the spiky twisted tape insert revealed. At each set of ReL and AW tested, the tube-averaged void fractions and pressure drops across the plain (DPP) and swirl (DPS) tubes were measured with the corresponding air–water flow images recorded under isothermal conditions. Local Nusselt numbers along the plain (NuP) and swirl (NuS) tubes were subsequently measured at the identical test conditions selected for the flow measurements. Heat fluxes were constantly adjusted to maintain the wall temperature at the hottest spot along the plain or swirl tube at about 80 °C. The on-line monitor of the time-averaged wall temperature measurements over a period of 3 s was performed using the present data acquisition system. When several successive wall temperature scans showed that these temporal wall temperature variations were less than 0.3 °C, all the measurements for this set of heat transfer test were recorded for subsequent data processing.

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In general, such quasi-steady flow condition took about 45 min after the flow or heater-power was adjusted. A set of heat transfer correlations using ReL and AW as the controlling variables was derived for the plain and swirl tubes with slug flows. Having acquired the heat transfer and pressure drop data for the present vertical cocurrent air–water slug flows in the plain and swirl tubes, the thermal performance index (g) defined as (NuS/NuP)/(DPS/DPP) was accordingly evaluated to index the relative HTE gains under the increased pressure drop penalties due to the spiky twisted tape insert. Fig. 1a depicts (a) experimental test facility (b) heat transfer test module (c) and spiky twisted tape. The experimental test facility consists of an air–water mixer (1), a 800 mm long developing section (2), a 420 mm long test tube (3) and two quick-closing solenoid valves (4), (5) at the entry and exit of the test section for measuring the tube-averaged void fraction. For direct flow visualization, the test tube, flow settling section and air–water mixer are made from a transparent acrylic resin with the inner diameter of 20 mm. The two electrical solenoid quick valves (4), (5) are normally open and can be closed simultaneously when the electrical signal is supplied. As the length of the settling tube (2) is 40 tube diameters, the same developed slug flow conditions, controlled by ReL and AW, prior to entering the plain or swirl test section can be repeatedly generated. For heat transfer tests, the acrylic test tube (3) is replaced by the heat transfer test module showed in Fig. 2b. Local Nusselt numbers along the plain or swirl tube are measured at the locations indicated in Fig. 2c where the wall temperatures are detected. The inner diameter of the quick-closing valves (4) is 22 mm. Therefore the hydraulic boundary layers of each test tube will be tripped and re-developed at the entry edge of the test section. Heat transfer measurements over the developing flow region for the present turbulent slug flows with and without the spiky twisted tape insert are obtained. Prior to entering the air–water mixer (1), the water flow rate of is adjusted and measured by a needle valve (6) and the digital volume flow meter (7), respectively. The dehumidified dry airflow enters the air–water mixer via four radial inner bores that connect with four cylindrical porous ceramics (8). Fine air-bubbles with diameters between 0.5 and 1 mm are generated after the airflow passing through these cylindrical porous ceramics (8). Each porous ceramic rod is 7 mm long, 10 mm in diameter with the average pore diameter of 5 lm. The two-phase flow patterns in the plain or swirl tube at each ReL and AW condition are visualized from the snapshot of the Computerized Camera Digital (CCD) system (9) which is capable of taking 300 images in 1 s. The CCD camera is mounted on a tripod and aimed the angle normal to the test tube. The camera lens is fixed at a constant focal length so that the viewing area is fixed for each test condition. The locations and strengths of light sources are individually adjusted for each flow visualization test. All flow images are post processed manually to measure the translational velocity of the Taylor bubble. For each tested set of ReL and AW ratio, 30 measurements for the translational velocity of Taylor bubble are performed with the averaged values determined. The airflow is channeled trough a section consisting of pressure regulator and filtering unit (10), needle valve (11) and digital air mass flow meter (12) through which the airflow rate is adjusted and metered. Two pressure taps of 0.5 mm diameter locate at the entrance and exit of the test section (3) to measure the pressure drops across the plain and swirl tubes as indicated in Fig. 1a. These pressure taps connect with a digital micromanometer (13) having the precision of 0.01 mm-H2O to detect the pressure drops across each test tube. With the air–water slug flows, the spatial variations of interfacial pressures are temporal function that results in fluctuations in pressure drops across each test tube. This digital micromanometer (13) cannot detect the detailed oscillatory behaviors for the

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Fig. 1. (a) Test facility (b) heat transfer test module and (c) spiky twisted tape.

pressure drop so that the detailed spectrum analysis for the temporal pressure waves inside the test tube is not permissible by using the present instrumentation. The time-averaged pressure drops over the entire test tube are calculated by averaging the measurements detected from the micromanometer over the scanning period about 45 s after the slug flow reached the developed condition. A digital pressure transducer (14) was installed at the flow entrance of each test section to measure the inlet pressure of air– water flow. Signals detected from the micromanometer (13), the pressure transducer (14) and the thermocouples embedded in the heat transfer test module were fed to the computer through the multi-channel Fluke data logger. For wall temperature measurements during each heat transfer test, the integrated average temperatures over a period of 10 s were acquired with the timeaveraged temperature data stored after the flow condition was satisfactory for the pre-defined condition. A thermocouple probed into the entry core of the test tube to detect the flow entry temperature. At the exit of the test tube, five equally spaced thermocouples were installed to detect the fluid exit temperatures which were averaged as the representative fluid exit temperature at each test condition. Due to the basically uniform heat flux provided for each test tube, the local fluid bulk temperatures were accordingly evaluated by assuming the linear streamwise increase of fluid bulk temperature based on the detected fluid entry and exit temperatures. The volume flow rate of airflow was determined based on

the detected mass flow rate, flow entry pressure and temperature. Having acquired the volume flow rates for air and water flows, the superficial gas and liquid velocities were accordingly determined. Fig. 2b depicts the heat transfer test module. The test tube (I), with or without the spiky twisted tape insert (II), was made from a seamless stainless steel tube with an inner diameter (D) of 20 mm, a wall thickness of 5 mm and a nominal length of 420 mm. The Teflon insulating bushes (III), (IV), the entry cap (V) and the test tube (I) were tightened by four draw bolts (VI) that gave the heating length of 420 mm. A pair of twin start threads using the same pitch of 3 mm but different depths of 4 and 1.5 mm was machined on the outer surface of the test tube (I) to respectively install the wall thermocouples (VII) and the Ni/Ch alloy resistance heating wire (VIII) for supplying the electrical heating power. The cross sectional view of the test section at a wall thermocouple location is indicated in Fig. 1. The deep groove for wall thermocouple installation was covered by a 0.5 mm thick electrical insulating tape to prevent the thermocouple lead electrically shorting. To secure the thermocouple lead, the groove was coated by a layer of cement above which the epoxy was filled into the entire groove. Ten equally spaced K type wall thermocouples (VII) were embedded along the test tube at locations indicated in Fig. 1c. These wall thermocouples were radially positioned with a fixed distance of 1 mm away from the inner bore of each test tube. The locations of these wall thermocouples (VII) corresponded to

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Fig. 2. Snapshots of air–water slug flow at AW = 0.003 and 0.008 with ReL = (a) 4000 (b) 6000 (c) 8000 (d) 10000.

the mid-pitch locations for the present spiky twisted tape with the twist ratio (y) of 2. Thermocouples were probed into the tube-core for fluid temperature measurements at the entry (IX) and exit (X) locations. A Teflon stiffened tube (XI) shielded the complete heat transfer test assemblies. In order to reduce the external heat loss, the outer surface of the stiffening tube was wrapped by thermal insulation material. As shown in Fig. 1c, the widths of this spiky twisted tape and each spike were 20 and 5 mm, respectively. These 7.5 mm long spikes were joined with a 5 mm wide central twisted strip which formulated the spirally arranged spikes. With 180°

rotation of the twisted tape, there were eight spikes over the axial span of a twist pitch. The local heat transfer rate for this study was experimentally determined as NuS,P = qfD/[(TwTb)kf] where qf, Tw, Tb and kf are the convective heat flux, wall temperature at the inner bore of each test tube, local fluid bulk temperature and the thermal conductivity of water evaluated at local Tb. Local convective heat flux was determined by subtracting the external heat loss flux from the total heat flux supplied with the axial wall conductive flux considered. The characteristic of external heat loss was determined via the

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pre-calibration heat loss tests which correlated the local heat loss flux as the function of wall-to-ambient temperature difference. For each heat loss calibration test, the flow was blocked off and the test channel was fitted with thermal insulation material. Under such test condition for the heat loss calibration test, the heater-power supplied to the test tube was entirely lost into the surrounding atmosphere through paths of conduction via test assemble and natural convection via the exposed external surface. When the heat transfer test module reached a thermodynamic equilibrium state, the supplied heating power was balanced with the heat loss power at the corresponding steady state wall-to-ambient temperature difference. By plotting the heat loss flux against its corresponding steady wall-to-ambient temperature difference, it showed that the heat loss flux increased linearly as the wall-to-ambient temperature difference increased. This set of data trend also satisfied the limiting condition of zero heat loss flux when the wall and ambient temperatures were equal. The curve fitting routine revealed the proportionality between the heat loss flux and the prevailing wall-to-ambient temperature difference, which was incorporated into the data processing program to evaluate the local heat loss flux. The estimation of axial wall conductive heat flux was based on the Fourier conduction law using the finite difference scheme for any set of axial wall temperature distributions measured. As the axial wall-to-ambience temperature differences varied along each test tube due to the streamwise variations in local convective performances of the two-phase flow, the axial variations in heat loss and conductive heat fluxes were inevitable. The perfect uniformity of convective heat flux distribution for each test tube was thus impractical. However, by way of reducing the external heat loss, the non-uniformity in qf distribution could be decreased. The external heat loss for this study was controlled to be less than 9.1% of the total heat flux supplied so that the basically uniform heat flux heating condition was simulated. Experimental uncertainties for each non-dimensional parameter determined by this study were performed [24]. The wall and fluid temperature measurements were the major sources for the uncertainties of Nu. With the heater-power in the ranges of 2240–2280 W and the wall-to-fluid temperature differences between 23 and 60 °C, the maximum uncertainties for Nu and ReL were about 9.8% and 3.7%, respectively.

3. Results and discussion 3.1. Flow visualization results Fig. 2 compares two sets of instantaneous stereoscopic views of air–water slug flows between the plain and swirl tubes with AW = 0.003 and 0.008 at ReL = (a) 4000 (b) 6000 (c) 8000 (d) 10000. The snapshots in each plot of Fig. 2 depict the flow images for the leading and trailing edges of the Taylor bubble as well as their corresponding superficial gas (UGS) and liquid (ULS) velocities, translational Taylor bubble velocity (UT) and void fraction (a). With the blockage effect provided by the twisted tape insert, the sectional area for fluid flows in the swirl tube is reduced from the plain tube condition. As a result, UGS and ULS obtained in the swirl tube at the same ReL and AW condition are higher than the plain tube counterparts. As shown in Fig. 2 for the plain tube, the leading edge of Taylor bubble always retains a permanent shape of asymmetric convex. But the continuous display of the snapshots detected from the plain tube at each ReL–AW condition shows that the Taylor bubble sways and the shape of the Taylor bubble-nose is constantly changing. Clearly, the liquid slug aerated by the dispersed bubbles in front of each Taylor bubble is unsteady, which stimulate the oscillating pressure waves to trigger the temporal variations in the shape and motion of the Taylor bubble-nose.

The continuous display of the flow images in the plain tube also reveals the vortical motion of the dispersed bubbles in the liquid slug behind each Taylor bubble where the trailing wakes are the dominant flow structures. Unlike the Taylor bubble-nose in the plain tube that always retains as a permanent convex arc, the trailing edge of each Taylor bubble undergoes considerable oscillations with temporal variations in its characteristic shape; showing the sloshing anti-symmetric nature as described in Ref. [1]. This is exemplified by the snapshots collected in Fig. 2 which reveals a variety of instantaneous Taylor bubble bottom shapes for the plain tube images. As ReL and/or AW increases, the interfacial profile of Taylor bubble in the plain or swirl tube gradually evolves into the undulant plenum indicating the penetrations of air-bubbles and oscillating pressure waves into the liquid film between the Taylor bubble and the tube wall. This is demonstrated in Fig. 2 with the plots for AW = 0.008 which show the undulant interfacial profile of each Taylor bubble. The aforementioned unsteady features are temporally periodic and reach the ReL and AW controlled quasi-steady state in the test section where the slug flow is considered as developed based on the criteria defined in Ref. [1]. As compared in Fig. 2, the two-phase flow structures of Taylor bubble and the dispersed bubbles in the swirl tube are considerably modified from the plain tube scenarios. Surprisingly, the Taylor bubble is not disrupted into small bubbles after traversing the helically arranged spikes at each ReL–AW test condition. The gas– liquid interfacial tension that holds each Taylor bubble overcomes the interfacial shearing and turbulent forces when the Taylor bubble flows through the spiky twisted tape. But the Taylor bubblenose has to squeeze through the gap between two spiral spikes so that the Taylor bubble in the swirl tube is guided to spiral around the central axis of the twisted tape. As a result, the Taylor bubble is twisted and encapsulates the spiky twisted tape. After the Taylor bubble squeezes through the spiral gaps between two neighboring spikes, the shape of Taylor bubble-nose turns into the skewed acute sharp arc. Particularly, as seen in each swirl tube flow image in Fig. 2, the Taylor bubbles undergo considerable deformations when they squeeze through the twisted gaps between two neighboring spikes where water is trapped. Such Taylor bubble deformations are highly unstable and trigger local pressure oscillating waves to intensify the interfacial oscillations along the stratified water–air layers between the Taylor bubble and tube wall. The sectional secondary flows induced by the centrifugal force are likely to be simultaneously present in each Taylor bubble as well as in the liquid slug. At the trailing edge of each Taylor bubble, the upward bulk movements of the dispersed bubbles are yielded from the vortical pattern observed in the plain tube to the swirling pattern in the swirl tube. All the small bubbles aerated in the liquid slugs that surround the leading and trailing edges of each Taylor bubble in the swirl tube are radially segregated toward the tube-core from the more-dense liquid phase by the centrifugal force. While the spiral motion of the Taylor bubble-nose has twisted the downstream Taylor bubble, the phase segregation driven by the twisted tape induced centrifugal force contracts the Taylor bubble and the aerated bubbles toward the tube-core. As a result, the void fraction in the swirl tube with slug flow is prone to the core-peaking distribution and becomes consistently lower than its plain tube counterpart as demonstrated in Fig. 3. Fig. 3a compares a variations against UGS at all test conditions for both plain and swirl tubes. As seen in Fig. 3a for each ReL controlled a trend, the averaged void fractions in the plain and swirl tubes follow the typical increasing pattern as UGS increases. At any selected UGS, the increase of ReL reduces AW and causes the systematic a reduction for both plain and swirl tubes. With the same ReL and UGS, the void fraction in the swirl tube is consistently lower than the plain tube counterpart, as compared in Fig. 3a, due to the phase segregation effect driven by the twisted tape induced

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and ULS controlled data trend is an interesting result. Although the interfacial structures in the swirl tube undergo considerable modifications from the plain tube scenarios due to the presence of the twisted tape induced centrifugal force, the consistently lower a values in the swirl tube from the plain tube levels at each fixed ReL and AW condition seem to be well taken into account by evaluating UGS and ULS based on the actual sectional area with the tapeblockage effect considered. The accountancy of UGS and ULS based on the actual sectional area also leads to good convergence of all UT measurements from the plain and swirl tubes as demonstrated in Fig. 4. As well as the re-confirmation, all the translational velocities of Taylor bubble in both plain and the present swirl tubes pffiffiffiffiffiffi agree with the correlation of UT = 0:35 gD + 1.29(UGS + ULS) [25,26] for turbulent flow conditions. The consequential variations in the interfacial flow structures as a result of varying ReL and/or AW described in this section incur consider modifications in pressure drop and heat transfer performances from the single-phase conditions for both plain and swirl tubes, which will be comparatively examined in details in the following sections. 3.2. Pressure drop measurements

Fig. 3. (a) Variation of void fraction (a) against superficial gas-phase velocity (UGS) (b) normalized void fraction (UGS/a) against superficial gas-to-liquid slip velocity (UGSULS).

centrifugal force. The lower void fractions in the swirl tube are indicative of the higher degrees of bubble coalescence toward the tube-core and have modified the stratified interfacial water films from the plain tube conditions. As observed in Fig. 2, the drastic deformation of Taylor bubble through the gaps between spikes stimulates the interfacial oscillations over the water film in the swirl tube. Such oscillating water film as well as the swirls developed in Taylor bubbles and liquid slugs in the swirl tube have profound impacts on the two-phase interfacial structures that differentiate the HTE and pressure drop performances from the plain tube conditions. To derive the empirical a correlation, the drift flux model with the gas drift flux corresponding to Taylor bubble rising velocity (Ud) in a stationary liquid has been previously attempted for the bubbly flows in the likewise swirl tube [23] and for the countercurrent air–water flow in a vertical tube with wire–coil inserts [25]. In these attempts, UGS/a varies linearly with the gas-to-liquid slip velocity (UGSULS) in the form of UGS/a = Ud + C(UGSULS) where Ud and C are determined from the equation proposed for the propagation velocity of Taylor pffiffiffiffiffiffibubble (UT) in a vertical upward continuous slug flow as 0:35 gD and 1.2 for turbulent flow [7]. However, with slug flows, the previous studies [26,27] reported that UT was underestimated with C = 1.2 in the drift flux model. Instead, C = 1.29 correlated all the experimental data well for the propagation velocities of Taylor bubbles in vertical upward, continuous slug flow. This result [26,27] is reconfirmed by the present study for UT measurements. Therefore the C factor in the drift flux model adapted to the a correlation for the present plain and swirl tubes with slug flows is replaced by 1.29 from 1.2. As demonstrated in Fig. 3b, all the void fractions obtained from the present plain and swirl tubes with slug flows are well correlated by the pffiffiffiffiffiffi equation of UGS/a = 0:35 gD + 1.29(UGSULS). The convergence of all a data obtained from the plain and swirl tubes into the UGS

The variations of pressure drop in plain (DPP) and swirl (DPS) tubes and the ratio of pressure drop (DPS/DPP) against AW for all test conditions are respectively shown in Fig. 5a–c. Pressure drops in the plain and swirl tubes with the single-phase water flow [22] and the bubbly flow [23] are also included in each plot of Fig. 5 to depict the impacts of interfacial structure on the pressure drop performance. It is worth noting that the range of ReL tested for our previous study at bubbly flow conditions is 5000–15000 [23]. Justified by the flow images detected from our previous study with the likewise test tubes [23], the AW ratio at the bubbly flow condition can be extended to 0.001 as indicated in Fig. 5. As shown in Fig. 5a and b for both plain and swirl tubes, DPP and DPS increase dramatically in a discontinuous manner from the AW = 0 levels after the singlephase water flow transits into the two-phase bubbly flow. With the presence of dispersed bubbles at bubbly flow conditions, the additional frictional, accelerational and form drags over the interfacial areas of these dispersed bubbles considerably elevate the pressure drops across the plain and swirl tubes. The two sets of DPP,S data detected from the bubbly [23] and slug flow regimes in Fig. 5a and b are individually measured. But the two sets of DPP,S data obtained at the bubbly and slug flow conditions as depicted in Fig. 5a and b follow a continuous data trend without discontinuity when the interfacial structures transit from bubbly to slug flows. Although the detailed variations of DPP and DPS are controlled by

Fig. 4. Variation of Taylor bubble velocity (UT) against ULS + UGS for plain and swirl tube.

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Fig. 5. Variations of (a) DPP (b) DPS (c) DPS/DPP against AW ratio at ReL = 4000, 5000, 6000, 8000 and 10000.

AW and ReL at the bubbly flow condition to reflect the competitive influences between the friction and pressure drags due to the variations in bubble density and bubble size [23], the pressure drops for bubbly flows generally decrease with the increase of AW as seen in Fig. 5a and b. But the degrees of AW impact on DPP and DPS for slug flows are considerably suppressed from those experienced by the bubbly flows. With bubbly flows in the plain and swirl tubes, the AW variation considerably varies the density and size of the dispersed bubbles [23] which therefore have profound influences on DPP and DPS. But with slug flows as typified in Fig. 2, the interfacial two-phase flow structures in both plain and swirl tubes are characterized by the elongated Taylor bubbles which are followed by liquid slugs with aerated bubbles within. The AW increase at each ReL tested mainly increases the length of Taylor bubble while the characteristic interfacial structure still remains unchanged. As the form drag induced by drifting the Taylor bubble in the flowing liquid plays the dominant role in characterizing the pressure drop for both plain and swirl tubes at the slug flow condition, DPP and DPS are moderately increased by increasing AW throughout the slug flow regime. The form drag of Taylor bubble in the plain tube seems to be less affected by the drifting velocity so that the DPP data obtained in the ReL range of 4000–10000 collapse into a tight data band at each AW tested as seen in Fig. 5a. But with the presence of the spiky twisted tape insert, the enhanced dominance of turbulent and frictional drags leads to the emergence of ReL impacts on DPS for slug flows. At a fixed AW ratio, an increase in ReL requires

the attendant increase in UGS. In general, the strengths of the vortical flows developed in Taylor bubbles and liquid slugs for the present swirl tube are accordingly enhanced as ULS and UGS increase. As a result, the fluid mixing and the pressure drop across the swirl tube with slug flow are augmented by increasing ReL at each tested AW ratio. This is clearly seen in Fig. 5b which shows the sensible ReL driven upward data spread at each AW tested at the slug flow condition for the swirl tube. The increased pressure drop penalty due to the spiky twisted tape insert is indexed by DPS/DPP which exhibits three distinct ranges in Fig. 5c when the flow transits from single-phase water flow ? bubbly flow ? slug flow. At the single-phase water flow condition (AW = 0), the DPS/DPP ratios are raised to 18–22 because the turbulent augmentations stimulated by the separated shear layers behind each spike and the friction drags over the surfaces of the spiky twisted tape play the dominant role in determining DPP and DPS. At the bubbly flow condition, the pressure drop is dominant by the movements of the dispersed bubbles rather than the flow phenomena generated by the spiky twisted tape [23]. It has also been previously reported that the pressure drops for upward gas–liquid bubbly flows were mainly an indication of liquid holdup and were weekly dependent on wall drags [28]. As a result, the DPS/DPP ratio at the bubbly flow condition falls dramatically from the single-phase level to the range about 1.2–1.6. The 20– 60% increases of DPS from DPP at the bubbly flow condition are mainly caused by the different interfacial structures caused by the twisted tape induced centrifugal force. At the slug flow condition, the centrifugal force induced by the twisted tape still produces the similar impacts on the aerated bubbles in the liquid slugs as those at the bubbly flow condition by way of generating the coherent bubble streams that swirl about the central axis of the twisted tape. But the impacts of the spiky twisted tape on the pressure drops at the single-phase airflow condition [23] are likely to re-emerge in each Taylor bubble. The dominance of the additional drags produced by the spiky twisted tape at the slug flow condition is therefore enhanced from the bubbly flow condition; but still remains less than that at the single-phase flow condition. As a result, the DPS/DPP ratios in the slug flow regime fall in the range of 1.2–2.6 as seen in Fig. 5c. Due to the emerging dominance of the augmented friction and form drags triggered by the spiky twisted tape at the slug flow condition, the ReL impact on DPS/DPP emerges. At the slug flow condition, DPS/DPP increases as ReL increases for each AW tested as depicted in Fig. 5c. To define the dimensionless pressure drop coefficient (Cf) for deriving the empirical correlations, the pressure drops measured from the plain and swirl tubes (DPP and DPS) are normalized by qLgL as Cf = (DPP or DPS)/qLgL. A set of Cf correlations for the plain and swirl tubes is generated as Eqs. (1) and (2).

   ð0:109þ1:79e900AW Þ C f P ¼ 0:314 1  e43:1AW  ReL

ðPlain tubeÞ ð1Þ

Cf S

   ð0:652þ1:44e1195AW Þ ¼ 0:00154 1  e348AW  ReL

ðSwirl tubeÞ ð2Þ

The maximum discrepancy between the experimental CfP,S data and the correlative predictions is ±25% discrepancies for the entire set of data generated. Justified by the accuracy achieved by Eqs. (1) and (2), these Cf correlations can be applied to evaluate the pressure drops in the plain and swirl tubes at the slug flow condition using ReL and AW as the determining variables. 3.3. Heat transfer results The heat transfer measurements obtained from the plain and swirl tubes here are evaluated in the dimensionless forms as NuP

S.W. Chang, T.L. Yang / Experimental Thermal and Fluid Science 33 (2009) 1087–1099

and NuS, respectively. The NuP and NuS correlations can therefore be expressed as functions of the dimensionless parameters, namely AW and ReL. In our previous work that examined the thermal fluid performances of the likewise plain and swirl tubes at the bubbly flow condition [23], NuP in the developed flow region at AW = 0 for single-phase water flow was verified to be well agreed with Dittus–Boelter correlation [29]. The NuS data detected from the developed flow region in the swirl tube at AW = 0 condition was well correlated by 0.28ReL0.65Pr1/3 which agreed with the results reported in [22] for the likewise swirl tube with airflow. Pr impacts on NuS obtained with the single-phase air [22] and water flows [23] are well accounted by Pr1/3 in the NuS correlation. With the presence of the spiky twisted tape insert at the single-phase water flow condition, the developing length is extended from the plain tube condition of 5 tube diameters to about 10 tube diameters due to the longer settling length required for the development of swirls. Fig. 6 compares the axial NuP and NuS variations obtained with various AW and ReL between plain and swirl tubes at the slug flow conditions. The NuP and NuS results obtained at AW = 0 in each plot of Fig. 6 feature the single-phase water flow heat transfer levels. As demonstrated by each plot of Fig. 6, the axial NuP and NuS variations at the slug flow condition follow the general pattern of exponential decay which reaches the developed flow region after about 15 tube diameters for both plain and swirl tubes. The similar developing length required for both plain and swirl tubes at the slug flow condition, despite the different developing lengths between the plain and swirl tubes at the AW = 0 (single-phase) condition,

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indicates that the streamwise development of interfacial twophase structures play the predominate role in determining the axial NuP and NuS distributions. Due to the high velocities of liquid film and the enhanced fluid mixing in the trailing wakes of Taylor bubbles [9–12], NuP and NuS obtained at the slug flow conditions are consistently elevated from the single-phase water flow levels as seen in Fig. 6a–e. An increase in AW at each ReL tested increases both UGS and ULS and modifies the two-phase structures of the slug flows. As illustrated by Fig. 2, the increase of AW (ReL) at fixed ReL (AW) causes the cylindrical profile of each Taylor bubble in both plain and swirl tubes to oscillate and deform into the undulant plenum due to the penetrations of air-bubbles and oscillating pressure waves into the liquid film between the Taylor bubble and the tube wall. The aeration of dispersed air-bubbles in the liquid regions is also intensified as AW and/or ReL increases. As a result, local NuP and NuS increase consistently as AW increases for each ReL tested as seen in each plot of Fig. 6. The cross examination of NuP and NuS results compared in Fig. 6 for each AW and ReL tested indicates the similar distributing pattern of axial heat transfer variations but different heat transfer levels between the plain and swirl tubes at the slug flow conditions. Although the characteristic feature of coherent Taylor bubble and aerated liquid slug is shared by plain and swirl tubes, the centrifugal force induced by the spiky twisted tape as well as the separated shear layers tripped behind the spikes create different two-phase flow structures between the plain and swirl tubes. In the swirl tube at the slug flow condition, the elongated air plenum (Taylor bubble) traverses through the spiky twisted tape in a periodic manner.

Fig. 6. Axial NuP and NuS distributions with various AW ratios at ReL = 4000, 5000, 6000, 8000, 10000.

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The flow mechanisms taking place at the single-phase airflow condition [22], namely the swirls with separated shear layers behind the helically arranged spikes, are likely to re-emerge in each elongated Taylor bubble. In the liquid slug, the vortical wakes behind each Taylor bubble in the plain tube yielded into the swirling pattern in the swirl tube as a result of the centrifugal body-force effect. The aerated dispersed air-bubbles are driven to spiral around the central axis of the twisted tape with the core-peaking void distributions in each liquid slug. These flow complexities induced by the spiky twisted tape in the swirl tube at the slug flow condition are in favor of further HTE impacts that elevate NuS from NuP as compared in Fig. 6. In order to enhance the generality of the heat transfer correlations devised by this study for air–water slug flow, the local NuP and NuS obtained from the developed flow region in the plain and swirl tubes at each set of AW and ReL tested are averaged into NuP and NuS . In light of the ReL and AW impacts on NuP and NuS as depicted in Fig. 6, the correlations of NuP and NuS can be derived as functions of ReL and AW at the pre-defined slug flow condition. Fig. 7 compares the variations of (a) NuP and (b) NuS against ReL at three different interfacial flow conditions, namely the singlephase water flow (AW = 0), the bubby flow and the slug flow conditions. As compared in Fig. 7, NuP;S obtained at the slug and bubbly flow conditions are elevated from the single-phase water flow levels; but the NuP;S obtained at the bubbly flow condition [23] are higher than those obtained at the slug flow conditions. As ReL increases at a fixed AW or as AW increases at a fixed ReL, NuP;S are consistently increased. Justified by all the ReL driven data trends displayed in Fig. 7 for the data obtained at the slug flow condition, NuP;S are correlated into the equation of NuP;S = A{AW}ReLB{AW} in which the coefficient A and exponent B are functions of AW. Clearly, due to the different interfacial phase structures between the single-phase, bubbly and slug flows and between the plain and swirl tubes, B exponents vary with the phase condition and are different between the plain and swirl tube. As exponents B obtained with slug flows in both plain and swirl tubes are generally less than their counterparts obtained with bubbly flows as com-

Fig. 7. Variations of (a) NuP (b) NuS against ReL at various AW ratios.

pared by the data trends depicted in Fig. 7, the heat transfer differences in both plain and swirl tubes between the bubbly and slug flows increase as ReL increases. Based on the results obtained from the regression-type analysis using the data trends depicted in Fig. 7, the functional structures of A{AW} and B{AW} in NuP;S correlations can be revealed by plotting the A coefficients and B exponents against AW for both plain and swirl tubes as seen in Fig. 8a and b, respectively. To recover the heat transfer scenarios for the single-phase water flow at AW = 0 condition, NuP and NuS correlations are respectively reverted to 0.023ReL0.8Pr1/3 [29] and 0.28ReL0.65Pr1/3 [22]. These two sets of limiting NuP and NuS correlations predefine the A coefficients and B exponents at the single-phase water flow condition as plotted at AW = 0 in Fig. 8a and b. As revealed in Fig. 8a and b, the exponential like increase of A coefficient is accompanied by the exponential like decrease of B exponent for both plain and swirl tubes when AW increases. The physical implications of such particular AW-driven varying trends for A coefficient and B exponent are the weakened ReL (inertial force) effect and the enhanced fluid mixing effect on NuP;S when AW increases. It is worth noting that at the single-phase flow condition, the B exponents in Nusselt number correlations often decrease from 0.8 (smooth-walled duct level) to about 0.5–0.65 for the channels with ribs, dimples or twisted tape insert by way of inducing local and/or large-scale secondary flows that modify the near-wall flow structures from the smooth-walled conditions. With the present slug flow, the ReL (inertial force) effects indexed by B exponents as seen in Fig. 8b are considerably reduced from 0.8 and 0.65 at the AW = 0 conditions to 0.12 and 0.22 for the plain and swirl tubes, respectively. Therefore, the near-wall flow structures at the slug flow conditions in both plain and swirl tubes are considerably modified from the typical boundary layer type flow in the smooth-walled tube. The aerated liquid slug and the accelerated annular water film between the Taylor bubble and the tube wall seem to be the dominant flow physics that determine the wall-to-fluid heat transfer performance at the slug flow condition. Relative to the plain tube scenarios, the enhanced air-bubble coalescence due to the centrifugal force effect weakens the degree of bubbly disturbances on the near-wall flow structures for the liquid

Fig. 8. Variations of (a) A coefficient (b) B exponents in NuP and NuS correlations against AW ratio.

S.W. Chang, T.L. Yang / Experimental Thermal and Fluid Science 33 (2009) 1087–1099

slug in the swirl tube. As a result, B exponents in NuS correlation are consistently higher than the plain tube counterparts at the slug flow conditions as shown in Fig. 8b. In this regard, our previous work performed at the bubbly flow conditions also follow the same result with the higher B exponents for swirl tube [23]. But unlike the bubbly flow condition with the impact of air-bubble coalescence on the near-wall flow structure throughout the entire two-phase flow domain, the phase segregation effects driven by centrifugal force are mainly developed in the liquid slug rather than in the Taylor bubble. Therefore the B exponents of about 0.2 in the swirl tube at the slug flow conditions are considerably fallen from 0.75 to 0.79 obtained at the bubbly flow conditions [23]. Having selected the exponential function to correlate A coefficients and B exponents depicted in Fig. 8, the NuP and NuS correlations are, respectively derived as:

  902AW NuP ¼ 41:64  41:6  e242AW  Re0:12þ0:68e L   488AW NuS ¼ 40:638  40:177  e152AW  Re0:22þ0:43e L

ð3Þ ð4Þ

Eqs. (3) and (4) permit the accountancy of the interdependent and individual ReL and AW impacts on NuP;S for the tubular air– water slug flows without and with the spiky twisted tape insert. The correlative coefficients for Eqs. (3) and (4) are 0.92 and 0.95, respectively. However, as the Prandtl number effect is not examined by this study, Eqs. (3) and (4) are limited for the air–water slug flow. To visualize the overall accuracies of NuP;S correlations, the calculated and experimental NuP;S are compared as shown in Figs. 9. The maximum discrepancy of ±20% between the correlation and experimental results is achieved for the entire NuP;S data. The higher NuS over the NuP cluster is also clearly seen in Fig. 9; which reveals the HTE impacts generated by the spiky twisted tape insert at the air–water slug flow conditions. The subsequent data analysis examines the ratio between NuS and NuP obtained at the same ReL and AW so that the HTE impacts generated by the spiky twisted tape at the slug flow condition can be examined in more details. Fig. 10 plots NuS /NuP against AW at each ReL tested by this study. The NuS /NuP obtained at the bubbly flow conditions [23] are also included in Fig. 10 to compare the HTE impacts offered by the spiky twisted tape at the bubbly and slug flow conditions. It is interesting to note that the data clusters obtained at different phase conditions tend to merge into a continuous data trend in Fig. 10 when the phase condition transits from the single-phase water flow ? bubbly flow ? slug flow. As seen in Fig. 10, the NuS /NuP ratios about 3 at the single-phase water flow (AW = 0) conditions decay toward the asymptotic values featured by the slug flows as AW increases. While the NuS /NuP ratios vary considerably by adjusting AW at the bubbly flow conditions, the NuS /NuP ratios over the slug flow regime as seen in Fig. 10 remain relatively stable at about 2. At the single-phase water flow conditions, NuS / NuP decreases consistently from 3.25 to 2.75 as ReL increases from

Fig. 9. Comparisons of correlated NuP and NuS results with experimental measurements.

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Fig. 10. Variations of NuP /NuS against AW ratio at ReL = 4000, 5000, 6000, 8000, 10000.

5000 to 15000 [23]. This is caused by the different B exponents in NuS and NuP correlations at AW = 0 conditions, which are 0.65 and 0.8, respectively. A physical implication of this result is the weakened HTE impact by the twisted tape as ReL increases for singlephase flows. But at the bubbly and slug two-phase conditions, the additional HTE mechanisms in association with the two-phase phenomena develop in both plain and swirl tubes and weaken the dominant role of swirling flows for HTE impacts at the single-phase flow conditions. The degrees of heat transfer variations caused by the twisted tape insert in terms of NuS /NuP are reduced when the flow transits from the single-phase to two-phase conditions. The impacts of varying ReL and AW on the two-phase flow structures in the plain and swirl tubes with bubbly flows incur the considerable HTE enhancements as ReL and/or AW increase [23]. Such ReL and AW impacts on NuS /NuP observed at the bubbly flow conditions are similarly followed by the slug flows as seen in Fig. 10 but the degrees of ReL and AW impacts of NuS /NuP are considerably suppressed from the bubbly flow conditions as the characteristic Taylor bubbles and liquid slugs are basically shared by the plain and swirl tubes. The results demonstrated in Fig. 10 confirm that the spiky twisted tape insert can still offer HTE impacts at the slug flow condition but with less HTE effectiveness than the singlephase and bubbly flows. The different phase conditions in the plain and swirl tubes have led to three distinct DPS/DPP and NuS /NuP regimes at the singlephase, bubbly and slug flow conditions as compared in Figs. 5 and 10. As an attempt to assess the relative HTE impacts on the expense of the increased pressure drops due to the spiky twisted tape insert, the performance index (g) at each ReL and AW condition examined is evaluated as (NuS /NuP )/(DPS/DPP). At the bubbly [23] and slug flow conditions, the two-phase flow structures in the plain and swirl tubes are in the dominant roles to determine the pressure drop and heat transfer performances. As a result, the dominant role of the spiky twisted tape in determining the augmentations of DPS/ DPP and NuS /NuP are weakened by the two-phase flow features. In Fig. 10, NuS /NuP obtained with the bubbly and slug flows decrease from the AW = 0 conditions. But the local NuP and NuS with bubbly [23] and slug flows are elevated from the single-phase water flow levels by the two-phase flow phenomena. Although the DPS/DPP obtained at the slug flow conditions are raised from the bubbly flow counterparts as depicted in Fig. 5, these DPS/DPP ratios are considerably decreased from the single-phase levels. Due to the significant reductions in DPS/DPP for the bubbly and slug flows which offset the reductions in NuS /NuP from the single-phase levels, the g indices compared in Fig. 11 follow the order of g Bubbly flow > g Slug flow > g Single-phase flow. Similar to the g results observed at the bubbly flow conditions [23], each ReL controlled g data-series collected in Fig. 11 at the present slug flow conditions follows the general varying pattern with the initial increase to a maximum value, after which g is moderately declined as AW increases. The optimal g indices for all the ReL tested respectively occur at about

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Fig. 11. Variations of g index against AW ratio at ReL = 4000, 5000, 6000, 8000, 10000.

AW = 0.002 and 0.01 for the bubbly and slug flows. Because NuS /NuP increases consistently with the increase of ReL for both bubbly and slug flows, the g index consistently increases as ReL increases at each selected AW as shown in Fig. 11. Although the NuS /NuP ratios at the slug flow conditions are less than the bubbly flow counterparts, the considerable increases of NuS from NuP as well as the increased g indices from the single-phase flow conditions has assured that the spiky twisted tape insert is also an effective HTE measure for augmenting the thermal performances of the upward cocurrent air–water slug flows. 4. Conclusions This experimental study discloses the two-phase flow characteristics, pressure drops and heat transfer performances in the vertically upward plain and swirl tubes with air–water slug flows. Several salient points are emerged from this study and summarized as follows: 1. The two-phase slug flow structures in swirl tube are considerably modified from the plain tube conditions. As the slug flow traverses through the spirally arranged spikes, the Taylor bubble and liquid slug in the swirl tube are guided to spiral. The Taylor bubble is accordingly twisted with swirls developed in Taylor bubble and liquid slug. Such unstable Taylor bubble deformation triggers pressure waves to intensify the interfacial oscillations along the cylindrical edge of each Taylor bubble that generates the undulant Taylor bubble plenum. The phase segregation driven by the twisted tape induced centrifugal force leads to the slug of the swirl tube. core-peaking a distribution in the pliquid ffiffiffiffiffiffi By way of correlating UT as 0:35 gD + 1.29(UGS + ULS) at the present slug flow conditions for both plain and swirl tubes, the averaged void fractions across the plain and swirl tubes can be well correlated using the drift flux model. 2. Due to the two-phase flow complexities at the slug flow condition, DPP and DPS increase considerably from the single-phase levels for both plain and swirl tubes. Augmentation of DPS from DPP at the slug flow condition are significantly reduced from the single-phase flow condition as the additional drag from the two-phase flow structures has neutralized the dominant role of the drag induced by the spiky twisted tape at the singlephase flow condition. But the dominance of the drags produced by the spiky twisted tape at the slug flow condition is enhanced from the bubbly flow condition and still less than that at the single-phase flow condition. The DPS/DPP ratios in the slug flow regime are in the rage of 1.2–2.6 which range falls between 1.2– 1.6 and 18–22 for the bubbly and single-phase flows, respectively. Correlations of pressure drop coefficient for the plain and swirl tubes using ReL and AW as the controlling parameters are derived as Eqs. (1) and (2).

3. Axial NuP and NuS variations at the slug flow condition follow the general pattern of exponential decay which reaches the developed flow region after about 15 tube diameters. The similar developing length required for both plain and swirl tubes at the slug flow condition, despite the different developing lengths between the plain and swirl tubes at the single-phase flow condition, suggests the dominant role of interfacial two-phase structures for determining the heat transfer performance. Local NuP and NuS are consistently increased from the single-phase water flow levels as AW and/or ReL increase. Correlations for NuP and NuS at the slug flow condition are derived as Eqs. (3) and (4) using ReL and AW as the determining variables. 4. The additional two-phase related HTE mechanisms emerging at the bubbly and slug flows weaken the dominant role of flow mechanics tripped by the spiky twisted tape at the single-phase flow condition. The degrees of heat transfer variations caused by the twisted tape insert in terms of NuS /NuP are therefore reduced when the flow transits into two-phase conditions. As the phase condition transits from the single-phase water flow ? bubbly flow ? slug flow, the data clusters of NuS /NuP follow a continuous AW-driven trend that decays from the single-phase flow levels of 2.75–3.25 toward the asymptotic values about 2 at the slug flow conditions. The NuS /NuP decay from about 3 to 2 takes place over the bubbly flow regime as AW increases. The NuS /NuP results demonstrate that the spiky twisted tape can still offer HTE impacts at the slug flow condition but with less HTE effectiveness than the single-phase and bubbly flows. 5. As the dominant role of the spiky twisted tape in determining the augmentations of DPS/DPP and NuS /NuP are weakened by the two-phase flow phenomena, the significant reductions in DPS/ DPP for the bubbly and slug flows have offset the NuS /NuP reductions from the single-phase conditions. As a result, the g indices follow the order of g Bubbly flow > g Slug flow > g Single-phase flow. At both bubbly and slug flow conditions, the variation of g against AW at each ReL tested follows the general pattern with an initial increase to a maximum value, after which g is moderately declined. The optimal g for all the ReL tested occur at about AW = 0.002 and 0.01 for the bubbly and slug flows, respectively.

Acknowledgement This research facilities were supported by National Science Council, Taiwan, under the grants NSC 96-2221-E-022-015MY3 and NSC 97-2221-E-022-013-MY3. The assistances provided by the research students G.F. Hong and J.Y. Lin are acknowledged. References [1] L. Shemer, Hydrodynamic and statistical parameters of slug flow, International Journal of Heat and Fluid Flow 24 (2003) 334–344. [2] T.C. Aladjem, L. Shemer, D. Barnea, On the interaction between two consecutive elongated bubbles in a vertical tube, International Journal of Multiphase Flow 26 (2000) 1905–1923. [3] D. Zheng, X. He, D. Che, CFD simulations of hydrodynamic characteristics in a gas–liquid vertical upward slug flow, International Journal of Heat and Mass Transfer 50 (2007) 4151–4165. [4] D. Barnea, O. Shoham, Y. Taital, Flow pattern characterization in two phase flow by electrical conductance probe, International Journal of Multiphase Flow 6 (1980) 387–397. [5] G. Costigan, P.B. Whalley, Slug flow regime identification from dynamic void fraction measurements in vertical air–water flows, International Journal of Multiphase Flow 23 (1997) 263–282. [6] H.J.W.M. Legius, H.E.A. van den Akker, T. Narumo, Measurements on wave propagation and bubble and slug velocities in cocurrent upward two-phase flow, International Journal of Experimental Thermal and Fluid Sciences 15 (1997) 267–278. [7] R. van Hout, D. Barnea, L. Shemer, Translational velocities of elongated bubbles in continuous slug flow, International Journal of Multiphase Flow 28 (2002) 1333–1350.

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