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Heat transfer and flow characteristics of rising Taylor bubbles
International Journal of Heat and Mass Transfer 89 (2015) 379–389
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and flow characteristics of rising Taylor bubbles Alex Scammell a, Jungho Kim b,⇑ a b
Department of Mechanical Engineering, University of Maryland, College Park 20740, USA Department of Mechanical Engineering, 3137 Glenn L. Martin Hall, Building 088, University of Maryland, College Park 20740, USA
a r t i c l e
i n f o
Article history: Received 3 February 2015 Received in revised form 9 May 2015 Accepted 15 May 2015
Keywords: Slug flow Taylor bubble Heat transfer distribution Liquid film thickness Infrared thermography
a b s t r a c t The heat transfer enhancement due to slug flow has been widely studied both experimentally and numerically, yet identification of the main heat transfer mechanisms has been debated and little experimental evidence is available. In this work, an infrared thermography technique, high-speed visualization, and a film thickness sensor were used to characterize vapor Taylor bubbles rising in a vertical, co-current, liquid flow. Measurements of the local heat transfer around each bubble indicated that the largest enhancement resulted from turbulent mixing in the bubble wake due to vortex shedding at the tail. The effect of the vortices on heat transfer was found to decline with increasing liquid velocity as a result of shortened residence time of the bubbles over a particular tube location. Liquid film thickness measurements showed excellent agreement with correlations when the film was fully developed. Bubble velocities and vortex shedding frequencies were experimentally determined for several liquid velocities. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Slug flow, characterized by elongated bubbles separated by liquid slugs, is frequently seen in pulsating heat pipes, microchannels, and in macro-scale channels at low vapor qualities. Vapor/gas slugs rising in a vertical column are called Taylor bubbles, and have been widely studied-a review of the literature prior to 1992 is given in Fabre and Line [1]. A review of some of the more recent work follows. Polonsky et al. [2] analyzed high speed video of rising Taylor bubbles in air–water vertical flow to characterize the bubble velocity and shape. Oscillations in the bubble tail were found to be of higher frequency and amplitude for longer bubbles. Nogueira et al. [3] used non-intrusive particle image velocimetry (PIV) to track the flow field around rising bubbles within stagnant and flowing fluids of varying viscosities in a 32 mm inner diameter (ID) tube. Comparison of the experimental data to theoretical correlations found that both film velocity and thickness were under-predicted for film Reynolds numbers greater than 80. In a similar study, Nogueira et al. [4] observed the velocity patterns in the wake behind rising bubbles and related the wake flow pattern to the dimensionless parameter Nf for stagnant liquid conditions, and a modified Reynolds number for co-current flow. Shemer et al. [5] used PIV to study the velocity profiles in the wake of single bubbles rising in both laminar and turbulent background flows. They found the wake flow field could be effectively turbulent even when the base flow was laminar. Turbulent velocity ⇑ Corresponding author. Tel.: +1 301 405 5437. E-mail addresses: [email protected] (A. Scammell), [email protected] (J. Kim). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.068 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
quantities calculated from the data showed that the initial mixing process occurred in the near wake region and persisted a few diameters downstream of the bubble tail. Thickness measurements of the liquid film surrounding bubbles in 0.3, 0.5, 0.7, 1, and 1.3 mm ID tubes were carried out by Han and Shikazono [6] using a laser focus displacement meter. They proposed correlations to predict the initial bubble film thickness using the collected experimental data. They later expanded their study to include the effect of evaporation and developed relations for calculation of the film thickness [7]. Llewellin et al. [8] calculated the film thickness based on the observed bubble length for experiments conducted with liquids of varying viscosities and tube IDs of 10, 20, and 40 mm. Two correlations were proposed (one theoretical and one empirical) for the fully-developed film thickness of Taylor bubbles rising in stagnant liquid. Accurate prediction of liquid film thickness and other bubble characteristics are crucial in the development of physics-based models for determining the heat transfer in slug flows. One such model by Jacobi and Thome [9] featured a two-zone representation of evaporation for elongated bubble flows where the regime was divided into a liquid slug region and a thin film region. It was suggested that the main mechanism of heat transfer was evaporation of the thin film trapped between the bubble and heated channel wall. This model was modified by Thome et al. [10] to include three zones: a liquid slug, an evaporating elongated bubble, and a vapor slug. As with the two-zone model, evaporation in the thin liquid film provided heat transfer several orders of magnitude higher than the single phase heat transfer due to the liquid slug.
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Nomenclature General C D g G h hlv k L P q00 r R Re T U x z
velocity drift constant tube diameter gravitational acceleration liquid mass flux heat transfer coefficient latent heat thermal conductivity length pressure heat flux radial position tube radius Reynolds number temperature velocity vapor quality axial distance
l m q r
dynamic viscosity kinematic viscosity density surface tension
Subscripts abs absolute act actual B bubble cam IR camera f film L liquid meas measured p polyimide sat saturation Si silicon SP single phase v vortex 0 stagnant conditions
Greek
a d
absorptivity film thickness
Magnini et al. [11] numerically obtained the shape, length, and local heat transfer of Taylor bubbles during boiling of several fluids in a 0.5 mm circular channel. They found that as the bubble entered a heated channel containing a developing thermal boundary layer, evaporation of the liquid film removed heat from the fluid and caused the heat transfer to become larger than for single-phase flow. The heat transfer coefficient rose monotonically from the bubble nose towards the tail, with the highest values occurring in the bubble wake region. Based on these results, they modified the three-zone model by Thome et al. [10] to include unsteady conduction through the liquid, and obtained better agreement with the simulations. The experimental heat transfer work to date has largely focused on measuring the overall heat transfer enhancement of slug trains with respect to single phase flow, rather than on the mechanisms of heat transfer around each bubble. For example, Walsh et al. [12,13] utilized an infrared (IR) measurement technique in which the outer wall temperature of a 1.5 mm diameter stainless steel tube was measured when air–water bubble trains were present. The observed outer wall temperature was used as a boundary condition for a thermal resistance problem to obtain the time-averaged heat transfer coefficient. The maximum heat transfer enhancement over fully developed Poiseuille flow occurred at a liquid slug length to diameter ratio of unity. A correlation to predict the fully developed Nusselt number at other ratios was proposed. Mehta and Khandekar [14] utilized a similar IR technique in bubble train experiments using deionized water and air within a 5 mm 5 mm square mini-channel. The heat transfer coefficient along the channel length was calculated using the experimentally measured channel wall temperature contours. An enhancement in heat transfer coefficient of 1.2–2 times over thermally developing single-phase flow was observed depending on the axial location. Hetsroni and Rozenblit [15] briefly touched upon the mechanisms of heat transfer in slug flow. A thin heated film was installed within a 74 mm ID tube and coated with black paint to allow temperature measurement using an IR camera. Wall temperature profiles were observed to be uniform for passing liquid slugs, while
faint higher temperature streaks occurred on the wall when the bubbles passed. This suggests a higher heat transfer coefficient in the liquid slug than in the liquid film, but no quantitative data was presented. The objective of the current work is to identify the contributions of various heat transfer mechanisms acting on a heated tube in the presence of a single Taylor bubble. Additionally, observations of the bubble shape and dynamics allow for predictions of the flow field which complement the heat transfer measurements. The collected data can be utilized to update current models for slug flow heat transfer or develop new models.
2. Experimental facility To characterize the heat transfer and dynamics of rising Taylor bubbles, a flow boiling experiment was conducted in which measurements of the local wall heat transfer and film thickness along with high speed images were obtained as single bubbles of varying length rose in a vertical column containing upward flowing liquid. The study of single bubbles was chosen in lieu of bubble trains so flow conditions upstream and downstream of the bubbles could be measured, reducing the complexity in approximating the flow patterns and understanding the heat transfer profile around each bubble.
2.1. Flow loop description A schematic of the experiment flow loop is shown in Fig. 1. The working fluid was 3M Novec HFE 7100 (C4F9OCH3), a non-toxic, dielectric fluid with a normal boiling temperature of 57 °C. Properties at saturation conditions for 1 bar of pressure are summarized in Table 1. HFE 7100 was pumped in a subcooled liquid state using a gear pump (Micropump L21755) as the flow rate was measured by a turbine flowmeter (Omega FLR1009). The liquid was heated to saturation at the test section inlet using a stainless steel preheater powered by a modified 1000W computer power unit (Silverstone
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Fig. 1. Functional diagram for experimental test rig.
Table 1 Summary of HFE 7100 properties at saturations conditions for 1 bar. Property
Saturation value
T sat [°C] qL [kg/m3] hlv [MJ/kg] lL [cP] rL [mN/m]
60 1372 112.1 0.375 128
SST-ST1000-P) and controlled using pulse width modulation via a LabVIEW™ interface. The fluid then entered a section of the flow loop designed to create and release single Taylor bubbles. This section consisted of a bubble generation segment and a bypass segment connected at the downstream end by a three-way valve. To generate a bubble, the valve was set to divert the liquid flow through the bypass segment, while a wire heater evaporated liquid in the bubble generation segment. The bubble volume was varied by adjusting the power to the wire and the heating time. Once the desired bubble volume was generated, it was released by rotating the valve such that liquid was redirected through the bubble generation segment, pushing the bubble into the test section. The bubble rose vertically into a 6 mm ID silicon test section positioned 200 mm downstream of the three-way valve where
Table 2 Typical uncertainties for important system parameters and measurements. Parameter
Uncertainty
G [kg/m2 s] Pabs [millibar] d [lm] Tcam [°C] kp [W/m-K] aSi [m1] ap [m1] Tsat [°C]
5.2 1.3 10 0.14 0.01 6.5 192 0.14
heat transfer measurements and flow visualization were made. Pressure taps were located at the inlet and outlet of silicon tube so differential and absolute pressures could be measured. The absolute pressure transducer (Omega PX209-030A5V) was used to determine the saturation temperature of the fluid entering the test section. Immediately after leaving the heated silicon tube, the rising bubble passed through a glass adiabatic section (380 mm downstream of the three-way valve) where high speed video was obtained using a CMOS video camera (Phantom Miro eX4) at frame rates between 900 and 1200 frames per second. The high-speed visualization was used to determine the bubble length, study the dynamics of the tail, and analyze the bubble shape. A laser displacement sensor (Keyence LK-G5000) was used to measure the liquid film thickness around the bubble. The sensor was calibrated by measuring known thicknesses of HFE 7100 with a maximum uncertainty of 10 lm. Further information on the calibration and uncertainty analysis of the film thickness measurement is provided in Appendix A. Bubbles were condensed and the liquid subcooled in a counterflow heat exchanger where the secondary fluid was cold water provided by a Neslab CoolFlow CFT-75 recirculator. A bellows-type accumulator was included after the condenser with the dry side open to the room to maintain the system pressure at nominally 1 bar. Before re-entering the gear pump, the fluid was sent through a de-gassing membrane (Liqui-Cel SuperPhobic). A vacuum pump connected to the membrane for several hours prior to data being collected was used to degas the liquid. Transducer data was collected using a 24-channel data acquisition system (Omega OMB-DAQ-3000) and recorded at a rate of 100 Hz through a LabVIEW™ interface. T-type thermocouples were installed at various locations in the flow loop for data analysis, calibration, and safety purposes. Uncertainty for the thermocouples was calculated to be ±0.12 °C. Heat transfer measurements and flow visualization were made using an IR camera (Electrophysics Silver 660M) at a frame rate of 246 Hz. Typical uncertainties for the major instrumentation and some of the reduced parameters are summarized in Table 2.
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Fig. 2. Mirrors to provide simultaneous heat transfer measurements and flow visualization (left image), and cross-sectional view of silicon tube with coated polyimide tape (right image).
2.2. IR technique Heat transfer measurements and flow visualization were obtained using an IR thermometry technique developed by Kim et al. [16] that takes advantage of the transparency of silicon in the mid-IR range (3–5 lm). HFE 7100 passed through the 6 mm ID (8 mm OD) single crystal silicon tube which was coated on the inner wall with a 57 lm layer of polyimide tape (k = 0.12 W/m-K) as shown in Fig. 2. One half of the inner circumference was then covered with an IR opaque paint containing carbon black (Nazdar GV111), which allowed an effective inner wall temperature to be measured through the silicon and polyimide layer. Two strips of the painted polyimide tape were also attached to the outer wall of the tube so the outer wall temperature could be measured. A coupled conduction/radiation problem was solved which accounted for absorption, emission, and reflection of thermal energy from the layers and the surroundings to determine the temperature profiles within the multilayer. The heat flux and heat transfer coefficient were then calculated for every camera pixel along the axial length of the tube. Details of the data reduction procedure can be obtained in Kim et al. [16]. To complement the heat transfer measurements, the flow was visualized using a set of six gold-plated mirrors (Fig. 2) arranged such that flow visualization and heat transfer measurements could be captured using a single camera.
Fig. 3. Experimental heat transfer coefficient compared to the Dittus Boelter correlation with the Al-Arabi correction for the parameters: HFE 7100, Re = 5545, Tsub = 20 °C, q00 = 11 kW/m2.
Fig. 4. Comparison of two-phase data collected by UMD and IMFT with similar experiments at conditions – UMD: G = 100 kg/m2 s, q00 = 10 kW/m2; IMFT: G = 100 kg/m2 s, q00 = 9.8–36 kW/m2.
Maximum uncertainties for the heat flux and heat transfer coefficient were estimated to be 2.1 kW/m2 and 279 W/m2 K, respectively. The uncertainty bars shown in heat transfer results include possible error associated with the determination of material optical properties, thicknesses, and camera temperature readings. Values for major sources of uncertainty were summarized in Table 2, including the absorptivity of the silicon tube and polyimide tape. Error associated with the determination of these properties can be considered to be a bias error, whose magnitude is not precisely known, but would have resulted in a relatively constant error for the heat transfer data. Therefore, the presence of a relatively large uncertainty for heat transfer comparisons does not detract from the trends observed. The IR thermography technique was validated through single-phase and two-phase testing in a vertical upward flow configuration. For single-phase flow, liquid passed through the heated silicon tube and the heat transfer coefficient along its length was measured. The experimentally measured heat transfer coefficient was compared to the Dittus-Boelter equation corrected for the thermally developing flow at the beginning of the heated silicon tube using the factor proposed by Al-Arabi [17]. The experimental data shown in Fig. 3 is in good agreement with the correlation. Two-phase validations were conducted by comparing data obtained in the churn and annular flow regime to data collected by a group at IMFT in Toulouse, France using a test apparatus of different design but operated under similar conditions [18]. Fig. 4 shows that data collected from both experiments are in agreement
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Fig. 5. Representative bubbles rising in co-current, saturated flow with UL = 72 mm/s and lengths: (a) LB = 33 mm (LB/D = 5.5), (b) LB = 9 mm (LB/D = 1.5).
with each other as well as the correlations by Chen [19] and Cioncolini and Thome [20] at low vapor qualities. 3. Results and discussion
length. Fig. 6 illustrates the tail shape of two bubbles rising in a co-current flow at UL = 37 mm/s. The shorter bubble (LB/D = 2.1) experienced mild oscillations and the tail profile remained relatively perpendicular to the flow direction, while the longer bubble (LB/D = 8.8) oscillated significantly and exhibited irregular tail
3.1. Bubble dynamics The bubble shape, velocity, and heat transfer characteristics were analyzed for a series of Taylor bubbles rising in fluid with co-current flow. Background liquid velocities within the test section were between 31 mm/s < UL < 106 mm/s (44 kg/m2 s < G < 146 kg/m2 s). Once the generated bubbles were released using the three-way valve, heat transfer was measured as the bubble was tracked through the heated silicon test section. Film thickness measurements and high speed video were obtained in the adiabatic glass tube. Two representative bubbles are shown in Fig. 5 to illustrate their general characteristics. The nose shape remained essentially the same for a given liquid velocity regardless of bubble length. Oscillations of the bubble tail increased in amplitude with bubble
Fig. 7. Comparison of experimental bubble velocities to Eq. (1).
Fig. 6. Representative tail profiles for two bubbles rising in co-current flow with UL = 37 mm/s.
Fig. 8. Comparison of experimental and numerical values of C to predictions of Pinto et al. [23].
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shapes. This trend is in agreement with Polonsky et al. [2], who showed that a small increase in oscillation frequency and large increase in amplitude accompanied bubbles with longer lengths. The bubble velocity was determined by identifying the bubble nose location on the IR and high speed video as a function of time. A series of 15–20 bubbles were analyzed and averaged to obtain the bubble velocity at each liquid velocity. The experimental bubble velocities were then compared to the equation proposed by Nicklin et al. [21]:
U B ¼ CU L þ U B;0
ð1Þ
where UB is the bubble velocity, C is a constant that defines the bubble drift velocity depending on the fluid velocity profile, and UB,0 is the bubble rise velocity in a stagnant fluid column determined from a graphical relation in White and Beardmore [22]. Comparison of the bubble velocities to Eq. (1) is shown on Fig. 7. It is evident that the experimental values deviate from those predicted by Eq. (1) where the coefficient C equals 2 and 1.2 in the laminar and turbulent flow regimes, respectively. Two explanations for the discrepancy are: (1) the background flow undergoes a transition to turbulence over the range of liquid velocities tested, or (2) underdevelopment of the background liquid flow causes the measured bubble velocity to be skewed. In support of the first theory, Nicklin et al. [21] found that C was approximately 1.2 at ReL > 8000, but rose to 1.9 when the flow was almost stagnant. Pinto et al. [23] also observed a transition of C from 2 to 1.2 as the flow transitioned to turbulence, but noted that the value of ReL at which this occurred was affected by the Weber number of the fluid. They proposed a correlation to predict C based on their experimental data and the data of Collins et al. [24]. Values of C derived from bubbles in the current study are compared to the typical constants for laminar and turbulent flow (C = 2 and 1.2) in Fig. 8 along with predictions by Pinto et al. [23]. Experimental values deviate from those predicted over the entire data range, but the decreasing trend of Pinto et al. [23] is followed by current the data at liquid velocities above 47 mm/s. The disagreement in C is not necessarily surprising since the properties of HFE 7100 (particularly for viscosity and surface tension) are significantly different from the fluids (water and aqueous glycerol solutions) used in Pinto et al. [23]. It could also be argued that the bubble velocity data, and therefore the calculated values for C, differ from traditional predictions
Fig. 10. Film thickness at the bubble tail vs. bubble length at various liquid velocities.
as a result of underdevelopment of the background flow since our two velocity measurement sections are only 33D and 63D (IR and visual, respectively) downstream of the bubble release valve. If the velocity profile was assumed uniform at the valve, the corresponding development lengths for a laminar flow at the data points tested would range from 34D to 115D (204 mm to 690 mm) according to the classical correlation, LD/D = Re/20. Under these circumstances, the bubble velocities measured at the lower liquid velocities should agree more closely with Eq. (1) with a C value of 2. Increasing the liquid velocity would then lead to more underdeveloped flow in the measurement sections and cause an over-prediction of the bubble velocity, a trend evident in Fig. 7. One might also expect, however, that since the visual measurement section is 30 diameters further downstream of the infrared section, it would be more developed and therefore exhibit a bubble velocity closer to the predictions. Fig. 7 shows that this occurs at some liquid velocities, but all differences in bubble velocities between the two positions fall in the range of uncertainty for the measurements.
Fig. 9. Film thickness vs. axial distance from tail for bubble rising in co-current flow at UL = 46 mm/s.
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In addition to the bubble rise velocity, knowledge of the liquid film thickness is important if the velocity of the film and the film heat transfer are to be predicted. Liquid thickness measurements were made for each bubble as shown in Fig. 9. Due to the film thickness sensor’s operating principle of measuring reflected light from the bubble interface, data could only be collected once the film neared a fully developed state. A comparison of film thickness at the bubble tail as a function of bubble length for various liquid velocities is shown in Fig. 10. The film thickness measured at the tail decreases with bubble length and approaches a constant value as the velocity profile within the film becomes fully developed. Campos and Carvalho [25] proposed a correlation to predict the distance (LB ) from the bubble nose where the wall boundary layer reached the bubble interface:
h 2 i2 ðgd Þ þ UB 2v LB D 2gD
ð2Þ
Calculated values for LB /D range from 13.8 to 16.1 for the current experimental results depending on the bubble velocity. Nogueira et al. [3] found that at film Reynolds numbers (ReUf ¼ ðUB UL ÞD=4v) above approximately 80, the Campos and Carvalho correlation over-predicted their experimental results by as much as 30%. The current data shown in Fig. 10 suggests LB/D 6 is required for the film thickness to stabilize, which is not inconsistent with either of these predictions. Fig. 10 also includes a comparison of the film thickness predicted using a theoretical relation developed by Brown [26] for a stabilized free-falling laminar film around a Taylor bubble rising in a co-current flowing liquid:
d¼
3v ððR dÞ2 U B R2 U L Þ 2gðR dÞ
1=3 ð3Þ
Once the liquid film becomes fully developed beyond approximately LB/D = 6, the agreement between experimental and predicted results is quite good. Very little variation in measured film thickness with liquid velocity is also seen. This is supported by Eq. (3), which suggests the fully developed thicknesses differ by only 10 lm (equal to the uncertainty of the measurements themselves) when bubble velocities for our test conditions are included.
Fig. 11. Heat transfer coefficient vs. time at a single location on the tube for a bubble with L = 21 mm, rising in co-current flow at UL = 72 mm/s and imposed heat flux of q00 = 2.4 kW/m2.
Fig. 12. Normalized heat transfer coefficient as a function of distance ahead of the bubble tail for a series of bubbles at liquid velocities UL = 36 mm/s (q00 = 2.1 kW/m2) and UL = 108 mm/s (q00 = 2.6 kW/m2).
3.2. Heat transfer Wall heat transfer was measured for each bubble as they passed through the test section. Steady-state, thermally developing flow was established within the heated section prior to each test to ensure reproducible boundary conditions. The heat transfer coefficient with time for a typical bubble passing a fixed position within the tube is shown on Fig. 11. Ahead of the bubble nose, the heat transfer coefficient corresponds to single-phase flow. As the bubble passes, the flow is forced into the liquid film where it accelerates, thinning the thermal boundary layer and increasing the heat transfer coefficient slightly. Vortices are generated when the downward moving film passes the bubble tail and interacts with the trailing liquid slug, inducing turbulence and a large spike in heat transfer. Once the turbulent mixing behind the bubble dies out, a thermally developing boundary layer is re-established and the heat transfer coefficient decays to the single-phase flow value. The largest contribution to heat transfer enhancement over single-phase flow occurs in the wake region immediately behind the bubble, a finding in opposition to current slug flow models which assume the
Fig. 13. Normalized heat transfer coefficient as a function of distance ahead of the bubble tail for liquid velocities UL = 36, 61, 72, and 108 mm/s (q00 = 2.1, 2.1, 2.4, and 2.6 kW/m2, respectively).
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highest heat transfer occurs in the evaporating thin liquid film [9,10]. These models, however, were formulated for high wall heat fluxes (q00 = 5–178 MW/m2) and thin liquid films (d < 3 lm) that are present in microchannel applications. The experimental data presented here were collected at very small heat fluxes (q00 = 2.1– 2.6 kW/m2) and the bubbles exhibited fairly thick liquid films (d > 240 lm). The film heat transfer for these experiments is likely a result of both conductive and convective mechanisms, corresponding to the thinning of the film and acceleration of the liquid toward the tail. The film heat transfer at two liquid velocities (UL = 36 mm/s and UL = 108 mm/s) are shown in Fig. 12. In this figure, z/D is the distance ahead of the bubble tail in a reference frame moving with the tail. The wake heat transfer coefficient at each z-location is normalized with the single phase heat transfer coefficient ahead of the bubble. The single phase heat transfer profile is evaluated by selecting a series of frames just prior to the bubble arrival in the test section to ensure the boundary conditions are identical but also that the bubble has no effect. Single phase heat transfer coefficients were in agreement with predictions for thermally developing flow [17] and varied over the tested liquid velocities by amounts smaller than the uncertainty of the measurements (maximum variation of 142 W/m2 K; uncertainty of 279 W/m2 K). As a result, the trends seen are independent of the normalization. Inspection of the film heat transfer in Fig. 12 reveals a slight scatter in the data for each liquid velocity due to the varying lengths of the bubbles. The bubble length determines the distance ahead of the tail where the single phase value (h/hSP = 1) is obtained. Bubbles rising with a slower liquid velocity show a slightly higher maximum heat transfer coefficient at the tail and also a more rapid increase in heat transfer in the wake region. These trends are further supported in Fig. 13, where five to nine film heat transfer profiles for each liquid velocity were averaged. The tail heat transfer coefficients vary marginally over the liquid velocities tested. This is not unexpected as the tail film thickness has been shown to be insensitive to flow velocity, thereby providing similar conduction heat transfer through the film. The liquid film is drawn downward by gravity, plunging into the liquid slug behind the bubble, and generates vortices that induce turbulence as shown in Fig. 14. The image is lighter ahead of the bubble tail due to warmer fluid being present. In the bubble wake, strong mixing is evident and vortices can be seen emanating from the tail. The effect of the vortices can be characterized using a reference frame moving with the bubble tail. A 2-D plot of the temporal and spatial history of the heat transfer in the wake can be created as shown in Fig. 15 for three liquid velocities. Low heat transfer is observed immediately behind the tail as the liquid within the film decelerates and diffuses into the trailing liquid. A large peak in the heat transfer follows due to the impact of a vortex on the wall, which decays as the vortex is separated from the bubble. The streaks generated by each vortex can be utilized to approximate the average frequency at which they are shed. This value was found to be consistently 81 ± 5 Hz over the range of tested liquid velocities, despite an increase of the film velocity by 27% (0.84 m/s < Uf < 1.07 m/s) from the lowest to the highest liquid velocity when calculated from a mass balance on the slug via Eq. (4):
Fig. 15. Contour illustration of vortices being shed from a bubble with a moving reference frame located at the tail (z/D = 0) and rising in co-current flow at: (a) UL = 36 mm/s, q00 = 2.1 kW/m2; (b) UL = 72 mm/s, q00 = 2.4 kW/m2; (c) UL = 108 mm/s, q00 = 2.6 kW/m2.
Uf ¼
ðU L U B ÞR2 ð2Rd d2 Þ
UB
Fig. 14. IR image of passing Taylor bubble showing temperature fluctuations due to vortex induced mixing in the wake region.
ð4Þ
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Fig. 16. Vortex velocities as a function of liquid velocity at the impinging point just behind the bubble tail and downstream when the vortices diffuse.
It should be noted that the frequency at which vortices were observed is approximately seven times greater than the frequency of tail oscillations for the longest bubble tested. Small periodic oscillations in the heat transfer signature within each vortex streak were measured to have an average frequency of 301 ± 8 Hz for the bubbles tested. Limitations of the experiment prevented detailed observation of the flow field and conclusive interpretation of these fluctuations. The slope of the vortex streaks indicate their velocity at each axial location behind the bubble tail. Fig. 15a illustrates two distinct slope regions: the impinging region just behind the bubble tail where the vortex velocity is the highest, and the diffusing region downstream of the bubble where the vortices move at rates near the liquid velocity. Through an analysis of each bubble, average impinging and diffusing region velocities could be found as a function of liquid velocity as shown in Fig. 16. The velocities displayed are with respect to a fixed reference frame attached to the tube wall. A dashed line has been included which signifies the average velocity of single phase liquid in the tube. The impinging velocity (measured at z/D 1) is found to move rearward with respect to the fixed reference frame and increases in magnitude as the liquid velocity increases. The same trend is seen for
Fig. 17. Normalized heat transfer coefficient as a function of distance behind the bubble tail for a series of bubbles at UL = 36 mm/s (q00 = 2.1 kW/m2) and UL = 108 mm/s (q00 = 2.6 kW/m2).
387
Fig. 18. Normalized heat transfer coefficient as a function of distance behind the bubble tail for liquid velocities UL = 36, 61, 72, and 108 mm/s (q00 = 2.1, 2.1, 2.4, and 2.6 kW/m2, respectively).
the diffusing velocity (measured at z/D 2.5), yet the direction is always positive, indicating a deceleration of the vortex as it moves away from the bubble. The diffusing velocity at UL = 36 and 60 mm/s agrees well with the liquid velocity, suggesting that the vortices have slowed entirely and are moving upward with the bulk single phase flow. Above UL = 60 mm/s, the vortices still move rearward at the diffusing measurement location. The effect of the vortices on heat transfer coefficient is best observed by using a moving reference frame attached to the bubble tail and plotting the profiles as a function of non-dimensional distance behind the tail, as shown in Fig. 17, for several bubbles at two liquid velocities (UL = 36 mm/s and UL = 108 mm/s). Moderate scatter exists in the data for UL = 36 mm/s at the heat transfer apex just behind the bubble, while data for UL = 108 mm/s is fairly repeatable. The average wake heat transfer profiles for four liquid velocities are shown in Fig. 18. The enhancement of heat transfer in the wake becomes more pronounced with decreasing liquid velocity. This might be counter intuitive since the bubble velocity and the film velocity increase according to Eq. (4) at higher liquid velocities. It is believed that the mechanism for vortex generation is the difference in velocity
Fig. 19. Schematic of triangulation technique used by film thickness sensor.
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between the liquid film moving toward the bubble tail and the liquid slug behind the bubble moving upward. An increase in the liquid and film velocities would lead to more frequent vortex generation. However, Fig. 15 illustrates that this is not the case. An explanation for the unexpected variation in wake heat transfer is as follows. Since the vortex frequency (and presumably the vortex strength) are similar for all liquid velocities, the residence time of the bubble over any particular axial position in the tube dictates the heat transfer. Specifically, a slower moving bubble generating vortices at the same rate as a faster moving bubble would cause mixing for a longer time at a location on the wall. With greater mixing, it could be expected that the thermal boundary layer is more highly disturbed and the heat transfer coefficient would be larger, as shown in Figs. 17 and 18. It can also be observed from Fig. 18 that the average maximum heat transfer occurs at a distance approximately 1 diameter behind the bubble tail (z/D = 1) for all liquid velocities. An argument could be made that the largest heat transfer should coincide with a large radial velocity near the tube wall as an indication of the largest mixing and disruption of the thermal boundary layer. While no direct velocity measurement is available for this experiment, Shemer et al. [5] found for air bubbles rising in water that the
Fig. 23. Film measurement error as a function of film angle with respect to the tube wall.
highest radial velocity occurred at z/D = 1 under laminar background flow conditions. The effect of the impinging liquid film into the liquid slug died out by approximately z/D = 4 when the axial velocity profile became uniform and the radial velocity approached zero. This trend can also be seen in the heat transfer coefficients in Figs. 17 and 18, where nearly all of the profiles have decayed to a steady state value by z/D = 5. 4. Conclusions Fig. 20. Schematic of parallel calibration setup.
An experimental study on heat transfer and flow dynamics for single vapor Taylor bubbles rising in co-current flow was conducted. Film thickness measurements were found to agree well with predictions for long bubbles where the film is fully developed. Analysis of measured heat transfer profiles around each bubble identified turbulent mixing in the bubble wake due to vortex shedding as the main contributor to heat transfer under the tested conditions. The decline in wake heat transfer enhancement with increasing liquid velocity was attributed to decreasing bubble residence time over a particular tube location. This was supported by showing little variation in the vortex shedding frequency over the range of liquid velocities. Conflict of interest None declared. Acknowledgements
Fig. 21. Calibration curve for Keyence film thickness sensor.
This work was supported by NASA Space Technology Research Fellowship NNX11AN49H and NASA grant NNX09AK39A. The authors would also like to thank Dr. Mirco Magnini (Heat and Mass Transfer Laboratory, EPFL, Switzerland) for many fruitful discussions regarding this work. Appendix A
Fig. 22. Schematic of angled calibration setup.
The film thickness sensor (Keyence LK-G5000) utilizes a triangulation method of measurement as illustrated in Fig. 19. Laser light exits the sensor head at a specified angle and is reflected from the inner and outer walls of the tube and from the bubble liquid/vapor interface. Depending on the indices of refraction and thicknesses of the various layers, the reflected beams will intercept
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the sensor measurement array at different locations. The location at which the light reflects from the liquid/vapor interface is dependent on the film thickness as well as the inclination of the interface. Film Thickness Sensor Calibration Assuming that the liquid film is smooth and the film thickness is not changing (i.e. the liquid/vapor interface is parallel to the tube wall), the multilayer can be approximated using flat plates to simplify the setup for calibration (Fig. 20). A fused silica wafer with a thickness of 1.03 mm and index of refraction of 1.456 was used to simulate the Pyrex tube of 1.00 mm thickness and index of refraction of 1.474. Polyimide strips of known thickness (48 ± 1 lm and 24 ± 1 lm) were used as spacers between the silica wafer and a microscope cover class that simulated the bubble interface. The gap created by the spacers was filled with HFE 7100 to replicate the bubble liquid film. The known film thickness as a function of the sensor readout was obtained over the range of film thicknesses measured in our tests and a linear fit to the data was obtained as shown in Fig. 21. Under these conditions, the thickness could be measured to a minimum accuracy of 9.9 lm. Shorter bubbles possessed developing liquid films which were not parallel to the tube wall. Characterizing the uncertainty associated with this angled film was completed in a similar manner to the original calibration. The polyimide films were unevenly stacked such that the microscope glass was inclined relative to the silica wafer as shown in Fig. 22. Measurements were obtained at various inclination angles up to 0.27° (maximum bubble film angle measured was 0.26°) and the error relative to the actual film height was calculated. The error in measured thickness increased with increasing film angle as shown in Fig. 23 as expected. The maximum uncertainty for film thickness with the added correction required for the non-parallel liquid/vapor interfaces was 10.4 lm. References [1] J. Fabre, A. Line, Modeling of two-phase slug flow, Annu. Rev. Fluid Mech. 24 (1992) 21–46. [2] S. Polonsky, D. Barnea, L. Shemer, Averaged and time-dependent characteristics of the motion of an elongated bubble in a vertical pipe, Int. J. Multiphase Flow 25 (1999) 795–812, http://dx.doi.org/10.1016/S03019322(98)00066-4. [3] S. Nogueira, M.L. Riethmuler, J.B.L.M. Campos, A.M.F.R. Pinto, Flow in the nose region and annular film around a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids, Chem. Eng. Sci. 61 (2006) 845–857, http://dx.doi.org/10.1016/j.ces.2005.07.038. [4] S. Nogueira, M.L. Riethmuller, J.B.L.M. Campos, A.M.F.R. Pinto, Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: an experimental study, Chem. Eng. Sci. 61 (2006) 7199–7212, http://dx.doi.org/10.1016/j.ces.2006.08.002.
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[5] L. Shemer, A. Gulitski, D. Barnea, On the turbulent structure in the wake of Taylor bubbles rising in vertical pipes, Phys. Fluids 19 (2007) 035108, http:// dx.doi.org/10.1063/1.2711478. [6] Y. Han, N. Shikazono, Measurement of the liquid film thickness in micro tube slug flow, Int. J. Heat Fluid Flow 30 (2009) 842–853, http://dx.doi.org/10.1016/ j.ijheatfluidflow.2009.02.019. [7] Y. Han, N. Shikazono, N. Kasagi, The effect of liquid film evaporation on flow boiling heat transfer in a micro tube, Int. J. Heat Mass Transfer 55 (2012) 547– 555, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.11.005. [8] E.W. Llewellin, E. Del Bello, J. Taddeucci, P. Scarlato, S.J. Lane, The thickness of the falling film of liquid around a Taylor bubble, Proc. R. Soc. A Math. Phys. Eng. Sci. 468 (2011) 1041–1064, http://dx.doi.org/10.1098/rspa.2011.0476. [9] A.M. Jacobi, J.R. Thome, Heat transfer model for evaporation of elongated bubble flows in microchannels, J. Heat Transfer 124 (2002) 1131, http:// dx.doi.org/10.1115/1.1517274. [10] J.R. Thome, V. Dupont, A.M. Jacobi, Heat transfer model for evaporation in microchannels. Part I: presentation of the model, Int. J. Heat Mass Transfer 47 (2004) 3375–3385, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2004. 01.006. [11] M. Magnini, B. Pulvirenti, J.R. Thome, Numerical investigation of hydrodynamics and heat transfer of elongated bubbles during flow boiling in a microchannel, Int. J. Heat Mass Transfer 59 (2013) 451–471, http:// dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.010. [12] P.A. Walsh, E.J. Walsh, Y.S. Muzychka, Laminar Slug Flow – Heat Transfer Characteristics with Constant Heat Flux Boundary, in: Proc. ASME 2009 Heat Transf. Summer Conf., 2009, pp. HT2009–88428. [13] P.A. Walsh, E.J. Walsh, Y.S. Muzychka, Heat transfer model for gas–liquid slug flows under constant flux, Int. J. Heat Mass Transfer 53 (2010) 3193–3201, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.03.007. [14] B. Mehta, S. Khandekar, Measurement of local heat transfer coefficient during gas–liquid Taylor bubble train flow by infra-red thermography, Int. J. Heat Fluid Flow 45 (2014) 41–52, http://dx.doi.org/10.1016/j.ijheatfluidflow.2013. 12.001. [15] G. Hetsroni, R. Rozenblit, Thermal patterns on a heated wall in vertical airwater flow, Int. J. Multiphase Flow 26 (2000) 147–167. [16] T.H. Kim, E. Kommer, S. Dessiatoun, J. Kim, Measurement of two-phase flow and heat transfer parameters using infrared thermometry, Int. J. Multiphase Flow 40 (2012) 56–67, http://dx.doi.org/10.1016/j.ijmultiphaseflow.2011. 11.012. [17] M. Al-Arabi, Turbulent heat transfer in the entrance region of a tube, Heat Transfer Eng. 3 (1982) 76–83. [18] M. Narcy, A. Scammell, C. Colin, J. Kim, Flow Boiling under Microgravity Conditions: Comparative Study of Two Experimental Data Sets, in: Proc. 15th Int. Heat Transf. Conf., Kyoto, 2014, pp. IHTC15–9072. [19] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Process Des. Dev. 5 (1966) 322–329. [20] A. Cioncolini, J.R. Thome, Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, Int. J. Heat Fluid Flow 32 (2011) 805– 817, http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.05.006. [21] D.J. Nicklin, J.O. Wilkes, J.F. Davidson, Two phase flow in vertical tubes, Trans. Inst. Chem. Eng. 40 (1962) 61–68. [22] E.T. White, R.H. Beardmore, The velocity of rise of single cylindrical air bubbles through liquids contained in vertical tubes, Chem. Eng. Sci. 17 (1962) 351–361. [23] A.M.F.R. Pinto, M.N. Coelho Pinheiro, S. Nogueira, V.D. Ferreira, J.B.L.M. Campos, Experimental study on the transition in the velocity of individual Taylor bubbles in vertical upward co-current liquid flow, Chem. Eng. Res. Des. 83 (2005) 1103–1110, http://dx.doi.org/10.1205/cherd.03238. [24] R. Collins, F.F. De Moraes, J.F. Davidson, D. Harrison, The motion of a large gas bubble rising through liquid flowing in a tube, J. Fluid Mech. 89 (1978) 497– 514. [25] J.B.L.M. Campos, J.R.F.G. De Carvalho, An experimental study of the wake of gas slugs rising in liquids, J. Fluid Mech. 196 (1988) 27–37, http://dx.doi.org/ 10.1017/S0022112088002599. [26] R.A.S. Brown, The mechanics of large gas bubbles in tubes: I. Bubble velocities in stagnant liquids, Can. J. Chem. Eng. 43 (1965) 217–223.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and flow characteristics of rising Taylor bubbles Alex Scammell a, Jungho Kim b,⇑ a b
Department of Mechanical Engineering, University of Maryland, College Park 20740, USA Department of Mechanical Engineering, 3137 Glenn L. Martin Hall, Building 088, University of Maryland, College Park 20740, USA
a r t i c l e
i n f o
Article history: Received 3 February 2015 Received in revised form 9 May 2015 Accepted 15 May 2015
Keywords: Slug flow Taylor bubble Heat transfer distribution Liquid film thickness Infrared thermography
a b s t r a c t The heat transfer enhancement due to slug flow has been widely studied both experimentally and numerically, yet identification of the main heat transfer mechanisms has been debated and little experimental evidence is available. In this work, an infrared thermography technique, high-speed visualization, and a film thickness sensor were used to characterize vapor Taylor bubbles rising in a vertical, co-current, liquid flow. Measurements of the local heat transfer around each bubble indicated that the largest enhancement resulted from turbulent mixing in the bubble wake due to vortex shedding at the tail. The effect of the vortices on heat transfer was found to decline with increasing liquid velocity as a result of shortened residence time of the bubbles over a particular tube location. Liquid film thickness measurements showed excellent agreement with correlations when the film was fully developed. Bubble velocities and vortex shedding frequencies were experimentally determined for several liquid velocities. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Slug flow, characterized by elongated bubbles separated by liquid slugs, is frequently seen in pulsating heat pipes, microchannels, and in macro-scale channels at low vapor qualities. Vapor/gas slugs rising in a vertical column are called Taylor bubbles, and have been widely studied-a review of the literature prior to 1992 is given in Fabre and Line [1]. A review of some of the more recent work follows. Polonsky et al. [2] analyzed high speed video of rising Taylor bubbles in air–water vertical flow to characterize the bubble velocity and shape. Oscillations in the bubble tail were found to be of higher frequency and amplitude for longer bubbles. Nogueira et al. [3] used non-intrusive particle image velocimetry (PIV) to track the flow field around rising bubbles within stagnant and flowing fluids of varying viscosities in a 32 mm inner diameter (ID) tube. Comparison of the experimental data to theoretical correlations found that both film velocity and thickness were under-predicted for film Reynolds numbers greater than 80. In a similar study, Nogueira et al. [4] observed the velocity patterns in the wake behind rising bubbles and related the wake flow pattern to the dimensionless parameter Nf for stagnant liquid conditions, and a modified Reynolds number for co-current flow. Shemer et al. [5] used PIV to study the velocity profiles in the wake of single bubbles rising in both laminar and turbulent background flows. They found the wake flow field could be effectively turbulent even when the base flow was laminar. Turbulent velocity ⇑ Corresponding author. Tel.: +1 301 405 5437. E-mail addresses: [email protected] (A. Scammell), [email protected] (J. Kim). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.068 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
quantities calculated from the data showed that the initial mixing process occurred in the near wake region and persisted a few diameters downstream of the bubble tail. Thickness measurements of the liquid film surrounding bubbles in 0.3, 0.5, 0.7, 1, and 1.3 mm ID tubes were carried out by Han and Shikazono [6] using a laser focus displacement meter. They proposed correlations to predict the initial bubble film thickness using the collected experimental data. They later expanded their study to include the effect of evaporation and developed relations for calculation of the film thickness [7]. Llewellin et al. [8] calculated the film thickness based on the observed bubble length for experiments conducted with liquids of varying viscosities and tube IDs of 10, 20, and 40 mm. Two correlations were proposed (one theoretical and one empirical) for the fully-developed film thickness of Taylor bubbles rising in stagnant liquid. Accurate prediction of liquid film thickness and other bubble characteristics are crucial in the development of physics-based models for determining the heat transfer in slug flows. One such model by Jacobi and Thome [9] featured a two-zone representation of evaporation for elongated bubble flows where the regime was divided into a liquid slug region and a thin film region. It was suggested that the main mechanism of heat transfer was evaporation of the thin film trapped between the bubble and heated channel wall. This model was modified by Thome et al. [10] to include three zones: a liquid slug, an evaporating elongated bubble, and a vapor slug. As with the two-zone model, evaporation in the thin liquid film provided heat transfer several orders of magnitude higher than the single phase heat transfer due to the liquid slug.
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Nomenclature General C D g G h hlv k L P q00 r R Re T U x z
velocity drift constant tube diameter gravitational acceleration liquid mass flux heat transfer coefficient latent heat thermal conductivity length pressure heat flux radial position tube radius Reynolds number temperature velocity vapor quality axial distance
l m q r
dynamic viscosity kinematic viscosity density surface tension
Subscripts abs absolute act actual B bubble cam IR camera f film L liquid meas measured p polyimide sat saturation Si silicon SP single phase v vortex 0 stagnant conditions
Greek
a d
absorptivity film thickness
Magnini et al. [11] numerically obtained the shape, length, and local heat transfer of Taylor bubbles during boiling of several fluids in a 0.5 mm circular channel. They found that as the bubble entered a heated channel containing a developing thermal boundary layer, evaporation of the liquid film removed heat from the fluid and caused the heat transfer to become larger than for single-phase flow. The heat transfer coefficient rose monotonically from the bubble nose towards the tail, with the highest values occurring in the bubble wake region. Based on these results, they modified the three-zone model by Thome et al. [10] to include unsteady conduction through the liquid, and obtained better agreement with the simulations. The experimental heat transfer work to date has largely focused on measuring the overall heat transfer enhancement of slug trains with respect to single phase flow, rather than on the mechanisms of heat transfer around each bubble. For example, Walsh et al. [12,13] utilized an infrared (IR) measurement technique in which the outer wall temperature of a 1.5 mm diameter stainless steel tube was measured when air–water bubble trains were present. The observed outer wall temperature was used as a boundary condition for a thermal resistance problem to obtain the time-averaged heat transfer coefficient. The maximum heat transfer enhancement over fully developed Poiseuille flow occurred at a liquid slug length to diameter ratio of unity. A correlation to predict the fully developed Nusselt number at other ratios was proposed. Mehta and Khandekar [14] utilized a similar IR technique in bubble train experiments using deionized water and air within a 5 mm 5 mm square mini-channel. The heat transfer coefficient along the channel length was calculated using the experimentally measured channel wall temperature contours. An enhancement in heat transfer coefficient of 1.2–2 times over thermally developing single-phase flow was observed depending on the axial location. Hetsroni and Rozenblit [15] briefly touched upon the mechanisms of heat transfer in slug flow. A thin heated film was installed within a 74 mm ID tube and coated with black paint to allow temperature measurement using an IR camera. Wall temperature profiles were observed to be uniform for passing liquid slugs, while
faint higher temperature streaks occurred on the wall when the bubbles passed. This suggests a higher heat transfer coefficient in the liquid slug than in the liquid film, but no quantitative data was presented. The objective of the current work is to identify the contributions of various heat transfer mechanisms acting on a heated tube in the presence of a single Taylor bubble. Additionally, observations of the bubble shape and dynamics allow for predictions of the flow field which complement the heat transfer measurements. The collected data can be utilized to update current models for slug flow heat transfer or develop new models.
2. Experimental facility To characterize the heat transfer and dynamics of rising Taylor bubbles, a flow boiling experiment was conducted in which measurements of the local wall heat transfer and film thickness along with high speed images were obtained as single bubbles of varying length rose in a vertical column containing upward flowing liquid. The study of single bubbles was chosen in lieu of bubble trains so flow conditions upstream and downstream of the bubbles could be measured, reducing the complexity in approximating the flow patterns and understanding the heat transfer profile around each bubble.
2.1. Flow loop description A schematic of the experiment flow loop is shown in Fig. 1. The working fluid was 3M Novec HFE 7100 (C4F9OCH3), a non-toxic, dielectric fluid with a normal boiling temperature of 57 °C. Properties at saturation conditions for 1 bar of pressure are summarized in Table 1. HFE 7100 was pumped in a subcooled liquid state using a gear pump (Micropump L21755) as the flow rate was measured by a turbine flowmeter (Omega FLR1009). The liquid was heated to saturation at the test section inlet using a stainless steel preheater powered by a modified 1000W computer power unit (Silverstone
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381
Fig. 1. Functional diagram for experimental test rig.
Table 1 Summary of HFE 7100 properties at saturations conditions for 1 bar. Property
Saturation value
T sat [°C] qL [kg/m3] hlv [MJ/kg] lL [cP] rL [mN/m]
60 1372 112.1 0.375 128
SST-ST1000-P) and controlled using pulse width modulation via a LabVIEW™ interface. The fluid then entered a section of the flow loop designed to create and release single Taylor bubbles. This section consisted of a bubble generation segment and a bypass segment connected at the downstream end by a three-way valve. To generate a bubble, the valve was set to divert the liquid flow through the bypass segment, while a wire heater evaporated liquid in the bubble generation segment. The bubble volume was varied by adjusting the power to the wire and the heating time. Once the desired bubble volume was generated, it was released by rotating the valve such that liquid was redirected through the bubble generation segment, pushing the bubble into the test section. The bubble rose vertically into a 6 mm ID silicon test section positioned 200 mm downstream of the three-way valve where
Table 2 Typical uncertainties for important system parameters and measurements. Parameter
Uncertainty
G [kg/m2 s] Pabs [millibar] d [lm] Tcam [°C] kp [W/m-K] aSi [m1] ap [m1] Tsat [°C]
5.2 1.3 10 0.14 0.01 6.5 192 0.14
heat transfer measurements and flow visualization were made. Pressure taps were located at the inlet and outlet of silicon tube so differential and absolute pressures could be measured. The absolute pressure transducer (Omega PX209-030A5V) was used to determine the saturation temperature of the fluid entering the test section. Immediately after leaving the heated silicon tube, the rising bubble passed through a glass adiabatic section (380 mm downstream of the three-way valve) where high speed video was obtained using a CMOS video camera (Phantom Miro eX4) at frame rates between 900 and 1200 frames per second. The high-speed visualization was used to determine the bubble length, study the dynamics of the tail, and analyze the bubble shape. A laser displacement sensor (Keyence LK-G5000) was used to measure the liquid film thickness around the bubble. The sensor was calibrated by measuring known thicknesses of HFE 7100 with a maximum uncertainty of 10 lm. Further information on the calibration and uncertainty analysis of the film thickness measurement is provided in Appendix A. Bubbles were condensed and the liquid subcooled in a counterflow heat exchanger where the secondary fluid was cold water provided by a Neslab CoolFlow CFT-75 recirculator. A bellows-type accumulator was included after the condenser with the dry side open to the room to maintain the system pressure at nominally 1 bar. Before re-entering the gear pump, the fluid was sent through a de-gassing membrane (Liqui-Cel SuperPhobic). A vacuum pump connected to the membrane for several hours prior to data being collected was used to degas the liquid. Transducer data was collected using a 24-channel data acquisition system (Omega OMB-DAQ-3000) and recorded at a rate of 100 Hz through a LabVIEW™ interface. T-type thermocouples were installed at various locations in the flow loop for data analysis, calibration, and safety purposes. Uncertainty for the thermocouples was calculated to be ±0.12 °C. Heat transfer measurements and flow visualization were made using an IR camera (Electrophysics Silver 660M) at a frame rate of 246 Hz. Typical uncertainties for the major instrumentation and some of the reduced parameters are summarized in Table 2.
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Fig. 2. Mirrors to provide simultaneous heat transfer measurements and flow visualization (left image), and cross-sectional view of silicon tube with coated polyimide tape (right image).
2.2. IR technique Heat transfer measurements and flow visualization were obtained using an IR thermometry technique developed by Kim et al. [16] that takes advantage of the transparency of silicon in the mid-IR range (3–5 lm). HFE 7100 passed through the 6 mm ID (8 mm OD) single crystal silicon tube which was coated on the inner wall with a 57 lm layer of polyimide tape (k = 0.12 W/m-K) as shown in Fig. 2. One half of the inner circumference was then covered with an IR opaque paint containing carbon black (Nazdar GV111), which allowed an effective inner wall temperature to be measured through the silicon and polyimide layer. Two strips of the painted polyimide tape were also attached to the outer wall of the tube so the outer wall temperature could be measured. A coupled conduction/radiation problem was solved which accounted for absorption, emission, and reflection of thermal energy from the layers and the surroundings to determine the temperature profiles within the multilayer. The heat flux and heat transfer coefficient were then calculated for every camera pixel along the axial length of the tube. Details of the data reduction procedure can be obtained in Kim et al. [16]. To complement the heat transfer measurements, the flow was visualized using a set of six gold-plated mirrors (Fig. 2) arranged such that flow visualization and heat transfer measurements could be captured using a single camera.
Fig. 3. Experimental heat transfer coefficient compared to the Dittus Boelter correlation with the Al-Arabi correction for the parameters: HFE 7100, Re = 5545, Tsub = 20 °C, q00 = 11 kW/m2.
Fig. 4. Comparison of two-phase data collected by UMD and IMFT with similar experiments at conditions – UMD: G = 100 kg/m2 s, q00 = 10 kW/m2; IMFT: G = 100 kg/m2 s, q00 = 9.8–36 kW/m2.
Maximum uncertainties for the heat flux and heat transfer coefficient were estimated to be 2.1 kW/m2 and 279 W/m2 K, respectively. The uncertainty bars shown in heat transfer results include possible error associated with the determination of material optical properties, thicknesses, and camera temperature readings. Values for major sources of uncertainty were summarized in Table 2, including the absorptivity of the silicon tube and polyimide tape. Error associated with the determination of these properties can be considered to be a bias error, whose magnitude is not precisely known, but would have resulted in a relatively constant error for the heat transfer data. Therefore, the presence of a relatively large uncertainty for heat transfer comparisons does not detract from the trends observed. The IR thermography technique was validated through single-phase and two-phase testing in a vertical upward flow configuration. For single-phase flow, liquid passed through the heated silicon tube and the heat transfer coefficient along its length was measured. The experimentally measured heat transfer coefficient was compared to the Dittus-Boelter equation corrected for the thermally developing flow at the beginning of the heated silicon tube using the factor proposed by Al-Arabi [17]. The experimental data shown in Fig. 3 is in good agreement with the correlation. Two-phase validations were conducted by comparing data obtained in the churn and annular flow regime to data collected by a group at IMFT in Toulouse, France using a test apparatus of different design but operated under similar conditions [18]. Fig. 4 shows that data collected from both experiments are in agreement
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383
Fig. 5. Representative bubbles rising in co-current, saturated flow with UL = 72 mm/s and lengths: (a) LB = 33 mm (LB/D = 5.5), (b) LB = 9 mm (LB/D = 1.5).
with each other as well as the correlations by Chen [19] and Cioncolini and Thome [20] at low vapor qualities. 3. Results and discussion
length. Fig. 6 illustrates the tail shape of two bubbles rising in a co-current flow at UL = 37 mm/s. The shorter bubble (LB/D = 2.1) experienced mild oscillations and the tail profile remained relatively perpendicular to the flow direction, while the longer bubble (LB/D = 8.8) oscillated significantly and exhibited irregular tail
3.1. Bubble dynamics The bubble shape, velocity, and heat transfer characteristics were analyzed for a series of Taylor bubbles rising in fluid with co-current flow. Background liquid velocities within the test section were between 31 mm/s < UL < 106 mm/s (44 kg/m2 s < G < 146 kg/m2 s). Once the generated bubbles were released using the three-way valve, heat transfer was measured as the bubble was tracked through the heated silicon test section. Film thickness measurements and high speed video were obtained in the adiabatic glass tube. Two representative bubbles are shown in Fig. 5 to illustrate their general characteristics. The nose shape remained essentially the same for a given liquid velocity regardless of bubble length. Oscillations of the bubble tail increased in amplitude with bubble
Fig. 7. Comparison of experimental bubble velocities to Eq. (1).
Fig. 6. Representative tail profiles for two bubbles rising in co-current flow with UL = 37 mm/s.
Fig. 8. Comparison of experimental and numerical values of C to predictions of Pinto et al. [23].
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shapes. This trend is in agreement with Polonsky et al. [2], who showed that a small increase in oscillation frequency and large increase in amplitude accompanied bubbles with longer lengths. The bubble velocity was determined by identifying the bubble nose location on the IR and high speed video as a function of time. A series of 15–20 bubbles were analyzed and averaged to obtain the bubble velocity at each liquid velocity. The experimental bubble velocities were then compared to the equation proposed by Nicklin et al. [21]:
U B ¼ CU L þ U B;0
ð1Þ
where UB is the bubble velocity, C is a constant that defines the bubble drift velocity depending on the fluid velocity profile, and UB,0 is the bubble rise velocity in a stagnant fluid column determined from a graphical relation in White and Beardmore [22]. Comparison of the bubble velocities to Eq. (1) is shown on Fig. 7. It is evident that the experimental values deviate from those predicted by Eq. (1) where the coefficient C equals 2 and 1.2 in the laminar and turbulent flow regimes, respectively. Two explanations for the discrepancy are: (1) the background flow undergoes a transition to turbulence over the range of liquid velocities tested, or (2) underdevelopment of the background liquid flow causes the measured bubble velocity to be skewed. In support of the first theory, Nicklin et al. [21] found that C was approximately 1.2 at ReL > 8000, but rose to 1.9 when the flow was almost stagnant. Pinto et al. [23] also observed a transition of C from 2 to 1.2 as the flow transitioned to turbulence, but noted that the value of ReL at which this occurred was affected by the Weber number of the fluid. They proposed a correlation to predict C based on their experimental data and the data of Collins et al. [24]. Values of C derived from bubbles in the current study are compared to the typical constants for laminar and turbulent flow (C = 2 and 1.2) in Fig. 8 along with predictions by Pinto et al. [23]. Experimental values deviate from those predicted over the entire data range, but the decreasing trend of Pinto et al. [23] is followed by current the data at liquid velocities above 47 mm/s. The disagreement in C is not necessarily surprising since the properties of HFE 7100 (particularly for viscosity and surface tension) are significantly different from the fluids (water and aqueous glycerol solutions) used in Pinto et al. [23]. It could also be argued that the bubble velocity data, and therefore the calculated values for C, differ from traditional predictions
Fig. 10. Film thickness at the bubble tail vs. bubble length at various liquid velocities.
as a result of underdevelopment of the background flow since our two velocity measurement sections are only 33D and 63D (IR and visual, respectively) downstream of the bubble release valve. If the velocity profile was assumed uniform at the valve, the corresponding development lengths for a laminar flow at the data points tested would range from 34D to 115D (204 mm to 690 mm) according to the classical correlation, LD/D = Re/20. Under these circumstances, the bubble velocities measured at the lower liquid velocities should agree more closely with Eq. (1) with a C value of 2. Increasing the liquid velocity would then lead to more underdeveloped flow in the measurement sections and cause an over-prediction of the bubble velocity, a trend evident in Fig. 7. One might also expect, however, that since the visual measurement section is 30 diameters further downstream of the infrared section, it would be more developed and therefore exhibit a bubble velocity closer to the predictions. Fig. 7 shows that this occurs at some liquid velocities, but all differences in bubble velocities between the two positions fall in the range of uncertainty for the measurements.
Fig. 9. Film thickness vs. axial distance from tail for bubble rising in co-current flow at UL = 46 mm/s.
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In addition to the bubble rise velocity, knowledge of the liquid film thickness is important if the velocity of the film and the film heat transfer are to be predicted. Liquid thickness measurements were made for each bubble as shown in Fig. 9. Due to the film thickness sensor’s operating principle of measuring reflected light from the bubble interface, data could only be collected once the film neared a fully developed state. A comparison of film thickness at the bubble tail as a function of bubble length for various liquid velocities is shown in Fig. 10. The film thickness measured at the tail decreases with bubble length and approaches a constant value as the velocity profile within the film becomes fully developed. Campos and Carvalho [25] proposed a correlation to predict the distance (LB ) from the bubble nose where the wall boundary layer reached the bubble interface:
h 2 i2 ðgd Þ þ UB 2v LB D 2gD
ð2Þ
Calculated values for LB /D range from 13.8 to 16.1 for the current experimental results depending on the bubble velocity. Nogueira et al. [3] found that at film Reynolds numbers (ReUf ¼ ðUB UL ÞD=4v) above approximately 80, the Campos and Carvalho correlation over-predicted their experimental results by as much as 30%. The current data shown in Fig. 10 suggests LB/D 6 is required for the film thickness to stabilize, which is not inconsistent with either of these predictions. Fig. 10 also includes a comparison of the film thickness predicted using a theoretical relation developed by Brown [26] for a stabilized free-falling laminar film around a Taylor bubble rising in a co-current flowing liquid:
d¼
3v ððR dÞ2 U B R2 U L Þ 2gðR dÞ
1=3 ð3Þ
Once the liquid film becomes fully developed beyond approximately LB/D = 6, the agreement between experimental and predicted results is quite good. Very little variation in measured film thickness with liquid velocity is also seen. This is supported by Eq. (3), which suggests the fully developed thicknesses differ by only 10 lm (equal to the uncertainty of the measurements themselves) when bubble velocities for our test conditions are included.
Fig. 11. Heat transfer coefficient vs. time at a single location on the tube for a bubble with L = 21 mm, rising in co-current flow at UL = 72 mm/s and imposed heat flux of q00 = 2.4 kW/m2.
Fig. 12. Normalized heat transfer coefficient as a function of distance ahead of the bubble tail for a series of bubbles at liquid velocities UL = 36 mm/s (q00 = 2.1 kW/m2) and UL = 108 mm/s (q00 = 2.6 kW/m2).
3.2. Heat transfer Wall heat transfer was measured for each bubble as they passed through the test section. Steady-state, thermally developing flow was established within the heated section prior to each test to ensure reproducible boundary conditions. The heat transfer coefficient with time for a typical bubble passing a fixed position within the tube is shown on Fig. 11. Ahead of the bubble nose, the heat transfer coefficient corresponds to single-phase flow. As the bubble passes, the flow is forced into the liquid film where it accelerates, thinning the thermal boundary layer and increasing the heat transfer coefficient slightly. Vortices are generated when the downward moving film passes the bubble tail and interacts with the trailing liquid slug, inducing turbulence and a large spike in heat transfer. Once the turbulent mixing behind the bubble dies out, a thermally developing boundary layer is re-established and the heat transfer coefficient decays to the single-phase flow value. The largest contribution to heat transfer enhancement over single-phase flow occurs in the wake region immediately behind the bubble, a finding in opposition to current slug flow models which assume the
Fig. 13. Normalized heat transfer coefficient as a function of distance ahead of the bubble tail for liquid velocities UL = 36, 61, 72, and 108 mm/s (q00 = 2.1, 2.1, 2.4, and 2.6 kW/m2, respectively).
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highest heat transfer occurs in the evaporating thin liquid film [9,10]. These models, however, were formulated for high wall heat fluxes (q00 = 5–178 MW/m2) and thin liquid films (d < 3 lm) that are present in microchannel applications. The experimental data presented here were collected at very small heat fluxes (q00 = 2.1– 2.6 kW/m2) and the bubbles exhibited fairly thick liquid films (d > 240 lm). The film heat transfer for these experiments is likely a result of both conductive and convective mechanisms, corresponding to the thinning of the film and acceleration of the liquid toward the tail. The film heat transfer at two liquid velocities (UL = 36 mm/s and UL = 108 mm/s) are shown in Fig. 12. In this figure, z/D is the distance ahead of the bubble tail in a reference frame moving with the tail. The wake heat transfer coefficient at each z-location is normalized with the single phase heat transfer coefficient ahead of the bubble. The single phase heat transfer profile is evaluated by selecting a series of frames just prior to the bubble arrival in the test section to ensure the boundary conditions are identical but also that the bubble has no effect. Single phase heat transfer coefficients were in agreement with predictions for thermally developing flow [17] and varied over the tested liquid velocities by amounts smaller than the uncertainty of the measurements (maximum variation of 142 W/m2 K; uncertainty of 279 W/m2 K). As a result, the trends seen are independent of the normalization. Inspection of the film heat transfer in Fig. 12 reveals a slight scatter in the data for each liquid velocity due to the varying lengths of the bubbles. The bubble length determines the distance ahead of the tail where the single phase value (h/hSP = 1) is obtained. Bubbles rising with a slower liquid velocity show a slightly higher maximum heat transfer coefficient at the tail and also a more rapid increase in heat transfer in the wake region. These trends are further supported in Fig. 13, where five to nine film heat transfer profiles for each liquid velocity were averaged. The tail heat transfer coefficients vary marginally over the liquid velocities tested. This is not unexpected as the tail film thickness has been shown to be insensitive to flow velocity, thereby providing similar conduction heat transfer through the film. The liquid film is drawn downward by gravity, plunging into the liquid slug behind the bubble, and generates vortices that induce turbulence as shown in Fig. 14. The image is lighter ahead of the bubble tail due to warmer fluid being present. In the bubble wake, strong mixing is evident and vortices can be seen emanating from the tail. The effect of the vortices can be characterized using a reference frame moving with the bubble tail. A 2-D plot of the temporal and spatial history of the heat transfer in the wake can be created as shown in Fig. 15 for three liquid velocities. Low heat transfer is observed immediately behind the tail as the liquid within the film decelerates and diffuses into the trailing liquid. A large peak in the heat transfer follows due to the impact of a vortex on the wall, which decays as the vortex is separated from the bubble. The streaks generated by each vortex can be utilized to approximate the average frequency at which they are shed. This value was found to be consistently 81 ± 5 Hz over the range of tested liquid velocities, despite an increase of the film velocity by 27% (0.84 m/s < Uf < 1.07 m/s) from the lowest to the highest liquid velocity when calculated from a mass balance on the slug via Eq. (4):
Fig. 15. Contour illustration of vortices being shed from a bubble with a moving reference frame located at the tail (z/D = 0) and rising in co-current flow at: (a) UL = 36 mm/s, q00 = 2.1 kW/m2; (b) UL = 72 mm/s, q00 = 2.4 kW/m2; (c) UL = 108 mm/s, q00 = 2.6 kW/m2.
Uf ¼
ðU L U B ÞR2 ð2Rd d2 Þ
UB
Fig. 14. IR image of passing Taylor bubble showing temperature fluctuations due to vortex induced mixing in the wake region.
ð4Þ
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Fig. 16. Vortex velocities as a function of liquid velocity at the impinging point just behind the bubble tail and downstream when the vortices diffuse.
It should be noted that the frequency at which vortices were observed is approximately seven times greater than the frequency of tail oscillations for the longest bubble tested. Small periodic oscillations in the heat transfer signature within each vortex streak were measured to have an average frequency of 301 ± 8 Hz for the bubbles tested. Limitations of the experiment prevented detailed observation of the flow field and conclusive interpretation of these fluctuations. The slope of the vortex streaks indicate their velocity at each axial location behind the bubble tail. Fig. 15a illustrates two distinct slope regions: the impinging region just behind the bubble tail where the vortex velocity is the highest, and the diffusing region downstream of the bubble where the vortices move at rates near the liquid velocity. Through an analysis of each bubble, average impinging and diffusing region velocities could be found as a function of liquid velocity as shown in Fig. 16. The velocities displayed are with respect to a fixed reference frame attached to the tube wall. A dashed line has been included which signifies the average velocity of single phase liquid in the tube. The impinging velocity (measured at z/D 1) is found to move rearward with respect to the fixed reference frame and increases in magnitude as the liquid velocity increases. The same trend is seen for
Fig. 17. Normalized heat transfer coefficient as a function of distance behind the bubble tail for a series of bubbles at UL = 36 mm/s (q00 = 2.1 kW/m2) and UL = 108 mm/s (q00 = 2.6 kW/m2).
387
Fig. 18. Normalized heat transfer coefficient as a function of distance behind the bubble tail for liquid velocities UL = 36, 61, 72, and 108 mm/s (q00 = 2.1, 2.1, 2.4, and 2.6 kW/m2, respectively).
the diffusing velocity (measured at z/D 2.5), yet the direction is always positive, indicating a deceleration of the vortex as it moves away from the bubble. The diffusing velocity at UL = 36 and 60 mm/s agrees well with the liquid velocity, suggesting that the vortices have slowed entirely and are moving upward with the bulk single phase flow. Above UL = 60 mm/s, the vortices still move rearward at the diffusing measurement location. The effect of the vortices on heat transfer coefficient is best observed by using a moving reference frame attached to the bubble tail and plotting the profiles as a function of non-dimensional distance behind the tail, as shown in Fig. 17, for several bubbles at two liquid velocities (UL = 36 mm/s and UL = 108 mm/s). Moderate scatter exists in the data for UL = 36 mm/s at the heat transfer apex just behind the bubble, while data for UL = 108 mm/s is fairly repeatable. The average wake heat transfer profiles for four liquid velocities are shown in Fig. 18. The enhancement of heat transfer in the wake becomes more pronounced with decreasing liquid velocity. This might be counter intuitive since the bubble velocity and the film velocity increase according to Eq. (4) at higher liquid velocities. It is believed that the mechanism for vortex generation is the difference in velocity
Fig. 19. Schematic of triangulation technique used by film thickness sensor.
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between the liquid film moving toward the bubble tail and the liquid slug behind the bubble moving upward. An increase in the liquid and film velocities would lead to more frequent vortex generation. However, Fig. 15 illustrates that this is not the case. An explanation for the unexpected variation in wake heat transfer is as follows. Since the vortex frequency (and presumably the vortex strength) are similar for all liquid velocities, the residence time of the bubble over any particular axial position in the tube dictates the heat transfer. Specifically, a slower moving bubble generating vortices at the same rate as a faster moving bubble would cause mixing for a longer time at a location on the wall. With greater mixing, it could be expected that the thermal boundary layer is more highly disturbed and the heat transfer coefficient would be larger, as shown in Figs. 17 and 18. It can also be observed from Fig. 18 that the average maximum heat transfer occurs at a distance approximately 1 diameter behind the bubble tail (z/D = 1) for all liquid velocities. An argument could be made that the largest heat transfer should coincide with a large radial velocity near the tube wall as an indication of the largest mixing and disruption of the thermal boundary layer. While no direct velocity measurement is available for this experiment, Shemer et al. [5] found for air bubbles rising in water that the
Fig. 23. Film measurement error as a function of film angle with respect to the tube wall.
highest radial velocity occurred at z/D = 1 under laminar background flow conditions. The effect of the impinging liquid film into the liquid slug died out by approximately z/D = 4 when the axial velocity profile became uniform and the radial velocity approached zero. This trend can also be seen in the heat transfer coefficients in Figs. 17 and 18, where nearly all of the profiles have decayed to a steady state value by z/D = 5. 4. Conclusions Fig. 20. Schematic of parallel calibration setup.
An experimental study on heat transfer and flow dynamics for single vapor Taylor bubbles rising in co-current flow was conducted. Film thickness measurements were found to agree well with predictions for long bubbles where the film is fully developed. Analysis of measured heat transfer profiles around each bubble identified turbulent mixing in the bubble wake due to vortex shedding as the main contributor to heat transfer under the tested conditions. The decline in wake heat transfer enhancement with increasing liquid velocity was attributed to decreasing bubble residence time over a particular tube location. This was supported by showing little variation in the vortex shedding frequency over the range of liquid velocities. Conflict of interest None declared. Acknowledgements
Fig. 21. Calibration curve for Keyence film thickness sensor.
This work was supported by NASA Space Technology Research Fellowship NNX11AN49H and NASA grant NNX09AK39A. The authors would also like to thank Dr. Mirco Magnini (Heat and Mass Transfer Laboratory, EPFL, Switzerland) for many fruitful discussions regarding this work. Appendix A
Fig. 22. Schematic of angled calibration setup.
The film thickness sensor (Keyence LK-G5000) utilizes a triangulation method of measurement as illustrated in Fig. 19. Laser light exits the sensor head at a specified angle and is reflected from the inner and outer walls of the tube and from the bubble liquid/vapor interface. Depending on the indices of refraction and thicknesses of the various layers, the reflected beams will intercept
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the sensor measurement array at different locations. The location at which the light reflects from the liquid/vapor interface is dependent on the film thickness as well as the inclination of the interface. Film Thickness Sensor Calibration Assuming that the liquid film is smooth and the film thickness is not changing (i.e. the liquid/vapor interface is parallel to the tube wall), the multilayer can be approximated using flat plates to simplify the setup for calibration (Fig. 20). A fused silica wafer with a thickness of 1.03 mm and index of refraction of 1.456 was used to simulate the Pyrex tube of 1.00 mm thickness and index of refraction of 1.474. Polyimide strips of known thickness (48 ± 1 lm and 24 ± 1 lm) were used as spacers between the silica wafer and a microscope cover class that simulated the bubble interface. The gap created by the spacers was filled with HFE 7100 to replicate the bubble liquid film. The known film thickness as a function of the sensor readout was obtained over the range of film thicknesses measured in our tests and a linear fit to the data was obtained as shown in Fig. 21. Under these conditions, the thickness could be measured to a minimum accuracy of 9.9 lm. Shorter bubbles possessed developing liquid films which were not parallel to the tube wall. Characterizing the uncertainty associated with this angled film was completed in a similar manner to the original calibration. The polyimide films were unevenly stacked such that the microscope glass was inclined relative to the silica wafer as shown in Fig. 22. Measurements were obtained at various inclination angles up to 0.27° (maximum bubble film angle measured was 0.26°) and the error relative to the actual film height was calculated. The error in measured thickness increased with increasing film angle as shown in Fig. 23 as expected. The maximum uncertainty for film thickness with the added correction required for the non-parallel liquid/vapor interfaces was 10.4 lm. References [1] J. Fabre, A. Line, Modeling of two-phase slug flow, Annu. Rev. Fluid Mech. 24 (1992) 21–46. [2] S. Polonsky, D. Barnea, L. Shemer, Averaged and time-dependent characteristics of the motion of an elongated bubble in a vertical pipe, Int. J. Multiphase Flow 25 (1999) 795–812, http://dx.doi.org/10.1016/S03019322(98)00066-4. [3] S. Nogueira, M.L. Riethmuler, J.B.L.M. Campos, A.M.F.R. Pinto, Flow in the nose region and annular film around a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids, Chem. Eng. Sci. 61 (2006) 845–857, http://dx.doi.org/10.1016/j.ces.2005.07.038. [4] S. Nogueira, M.L. Riethmuller, J.B.L.M. Campos, A.M.F.R. Pinto, Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: an experimental study, Chem. Eng. Sci. 61 (2006) 7199–7212, http://dx.doi.org/10.1016/j.ces.2006.08.002.
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