Two-Phase Flow Pressure Drop Characteristics in Trapezoidal Silicon Microchannels

IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGY, VOL. 32, NO. 4, DECEMBER 2009

887

Two-Phase Flow Pressure Drop Characteristics in Trapezoidal Silicon Microchannels S. G. Singh, R. R. Bhide, S. P. Duttagupta, B. P. Puranik, and Amit Agrawal

Abstract— This paper focuses on experimentally studying the pressure drop characteristics for two-phase flow in microchannels of hydraulic diameter 109 μm, over a relatively large range of heat flux of (0–30 W/cm2 ) and mass flow rate values (44–1114 kg/m2 -s). Three fluid flow regimes (single-phase, twophase, and dryout) have been covered in this paper, with deionized water as the working fluid. For a given heat flux, the variation of average pressure drop with flow rate can be classified into three distinct regimes. In the first regime (higher flow rate), the pressure drop decreases linearly with decrease in flow rate. In the second regime (lower flow rate), pressure drop increases with decreasing flow rate and reaches a maximum (with a minimum on either side). Finally, in the very low flow rate regime, pressure drop increases rapidly with decreasing flow rate. The average pressure drop in the two-phase regime is predicted well by the annular flow model. In addition to absolute pressure drop values, we also report pressure fluctuations. The magnitude of pressure fluctuations appears to be correlated to the underlying flow regime, such as bubbly, slug, and annular regimes, which have been identified through the flow visualization. An important outcome of this study is the identification of as many as four operating points with similar pressure drop penalty. This may help to choose the right operating conditions for a microchannelbased heat sink for use in cooling electronics. These detailed experimental results are also expected to be useful for modeling two-phase flow in microchannels. Index Terms— Annular flow, critical heat flux (CHF), flow visualization, heat transfer coefficient, onset of boiling, pressure instability.

N OMENCLATURE A ACh Cp C dh f ff G L

Heating area [m2 ]. Area of cross-section of microchannel [m2 ]. Specific heat [J/kg-K]. Martinelli–Chisholm constant. Hydraulic diameter (= 4 ACh /Pch ) [m]. Friction factor. Friction factor based on local liquid flow rate. Mass velocity in microchannel [kg/m2-s]. Length of the microchannel [m].

Manuscript received August 8, 2008; revised January 4, 2009. First version published September 15, 2009; current version published November 20, 2009. Recommend by Associate Editor T. Lee upon evaluation of the reviewers’ comments. S. G. Singh and S. P. Duttagupta are with the Department of Electrical Engineering at the Indian Institute of Technology (IIT) Bombay, Mumbai 400076, India (e-mail: [email protected]; [email protected]). R. R. Bhide, B. P. Puranik, and A. Agrawal are with the Department of Mechanical Engineering at the Indian Institute of Technology (IIT) Bombay, Mumbai 400076, India (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCAPT.2009.2019634

m mF f Pch P Pt p,a

ρ ρH τi τ

Mass flow rate [kg/s]. Mass flow rate in liquid core [kg/s]. Microchannel perimeter [m]. Average pressure drop across the channel [N/m2 ]. Acceleration component of two-phase pressure drop [N/m2 ]. Frictional component of two-phase pressure drop [N/m2 ]. Reynolds number based on local liquid flow. Reynolds number based on total flow as liquid. Mean velocity fluid (= m/ρ A) [m/s]. Mean vapor core velocity [m/s]. Interfacial velocity [m/s]. Martinelli parameter based on laminar liquid turbulent vapor flow. Martinelli parameter based on laminar liquid laminar vapor flow. Thermodynamic equilibrium quality. Distance perpendicular to channel wall [m]. Streamwise distance [m]. Void fraction. Liquid film thickness [m]. Deposition mass transfer per unit channel length [kg/m]. Evaporation mass transfer per unit channel length [kg/m]. Viscosity of fluid [Pa-s]. Specific volume [m3 /kg]. Two-phase frictional multiplier based on local liquid flow rate. Density of fluid [kg/m3]. Homogeneous density of vapor core [kg/m3]. Interfacial shear stress [N/m2 ]. Local shear stress [N/m2 ].

a avg f g out rms

Acceleration. Average. Liquid; frictional. Vapor. Test module outlet. Root mean square.

Pt p, f Ref Refo U uc ui X vt X vv xe y z α δ d  fg μ υ φ 2f

S UBSCRIPTS

I. I NTRODUCTION

T

HE DESIGN of next-generation nanoscale integrated circuits requires effective cooling for reliable operation. As the device operating frequency increases, heat dissipation will

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increase to greater than 250 W/cm2 , primarily concentrated at one or more hot spots and accompanied by large heat flux transients. The very large heat flux transients will cause degradation in device reliability and may eventually lead to device failure [1]. Due to poor thermal transport properties of air, the traditional heat sinks will not suffice at largescale integration levels. Microchannel heat sinks have emerged as a promising cooling technique, where higher efficiency results from a large surface area to volume ratio. Tuckerman and Pease [2] first studied heat transfer characteristics in microchannels. Subsequent research has focused on modeling and optimization of single-phase liquid microchannel heat exchanger [3], [4]. Compared to single-phase flow, a larger amount of heat can be removed by employing two-phase flow in microchannels. Therefore, numerous studies have been carried out to understand the complicated physics of boiling in micrometer-sized channels. Qu and Mudawar [5], [6] have presented experimental results that provide physical insight into the distinctive nature of saturated-flow boiling heat transfer in a water-cooled microchannel heat sink. The microchannel heat sink contained 21 parallel copper channels with 231 × 713 μm2 cross section. The inlet Reynolds number ranged from 60 to 300. Contrary to the behavior observed in macrochannels, the heat transfer coefficient showed an initial decrease with increasing vapor quality. This unexpected trend was attributed to appreciable droplet deposition leading to an increase in the liquid film thickness [5]. Similar dependence of heat transfer coefficient on vapor quality has been reported by Hetsroni [7] for a heat sink that had 21 parallel triangular silicon microchannels each of 129 μm hydraulic diameter. Vertrel XF with a saturation temperature of 52 °C was used as the working fluid in their study. Steinke and Kandlikar [8] and Yen et al. [9] studied the flow boiling of water and refrigerants (HCFC123, FC72) respectively. They also reported that the heat transfer coefficient decreases monotonically with an increase in vapor quality, in agreement with the earlier studies. Yen et al. [10] reported that for a square microchannel crosssection, bubbly, slug, and annular flow patterns were typically observed, and capillary flow pattern was rarely observed. Here, the dryout of the liquid film was initiated at the center of the inner walls in an annular flow pattern. Jiang et al. [11] performed visualization and measurements of flow-boiling in triangular silicon microchannels for two different hydraulic diameters of 26 and 53 μm. They did not observe bubbly flow in either instance, unlike in macro-channels. Hetsroni et al. [7] have reported fluctuations in pressure drop and outlet fluid temperature with a period of 1–2 s, due to bubble inception and subsequent bubble growth. Hetsroni et al. [12] have also reported alternating occurrence of single-phase and twophase flow, leading to high-frequency fluctuations with an increase in the vapor quality. Li et al. [13] reported two-phase flow instability of flow boiling in two parallel triangular and trapezoidal microchannels, with a hydraulic diameter around 50 μm for both the channels. They reported large-magnitude periodic oscillations with alternative presence of two-phase flow and single-phase vapor flow at high heat fluxes. Wu and Cheng [14] measured long-period fluctuations in fluid

Si (100) wafer (a)

Thermal oxide (b)

Selectively pattern oxide (c) Wl

Sputter Cr-Au (e)

H Wh Etched channel (d)

Selectively pattern etch Cr-Au and bonded channel (f)

Fig. 1. Fabrication process of integrated microchannel and microheater. An oxide layer is grown on double side-polished (100) silicon wafer. The oxide layer is patterned using soft-lighography, and, after etching, fabrication of open microchannel is completed (a)–(d). On the backside of the wafer, chrome-gold is sputter-deposited and patterned, to form the microheater (a, b, e, f). Bonding between silicon etched microchannel and quartz is done after the end of the process (f).

pressure, temperature, and mass flux flow boiling of water, in parallel silicon microchannels having trapezoidal crosssectional area with hydraulic diameters of 158.8 and 82.8 μm. Qu and Mudawar [6] investigated hydrodynamic instability and pressure drop in a water-cooled two-phase microchannel heat sink containing 21 parallel 231×713 μm2 microchannels. They identified two types of two-phase flow instability, namely, severe pressure drop oscillations and mild parallel channel instability. Kandlikar et al. [15] attempted to remove such instabilities by constricting the flow cross section by introducing pressure drop elements upstream of the heated microchannels and addition of nucleation sites on the walls of the microchannel. It was found that the introduction of nucleation sites in conjunction with a 51% area restriction located upstream of the microchannels partially could reduce the instabilities, while 96% area restriction eliminated instabilities completely, but at the cost of a prohibitively large pressure drop. Zhang et al. [16] reported flow-boiling studies in rectangular silicon microchannels of two different hydraulic diameters (31 and 58 μm), and a single mass flow rate of 0.1 ml/min. The pressure drop and wall temperature were measured. The pressure drop was found between 8 and 26 kPa, and up to 5 °C of wall superheat was observed with boiling. The pressure drop was compared with their homogeneous and annular flow model; the comparison was found to be particularly good for the homogeneous model. Zhang et al. [17] report pressure drop of 6–25 kPa in a 113 μm hydraulic diameter rectangular microchannel for heating rate of 1.8–3.3 W, and 37–42 kPa in a 44 μm microchannel for heating rate of 2.15–2.6 W. Qu and Mudawar [6] performed measurements at an inlet temperature of 60 °C and a mass flux of 255 kg/m2-s. The pressure drop was found to increase monotonically from 10 to

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SINGH et al.: TWO-PHASE FLOW PRESSURE DROP CHARACTERISTICS IN TRAPEZOIDAL SILICON MICROCHANNELS

889

TABLE I R ANGE OF H EAT F LUX AND F LOW R ATE OVER W HICH E XPERIMENTS H AVE B EEN P ERFORMED Heat flux (W/cm2 )

Mass flow rate (ml/min)

Mass flux (kg/m2 -s)

Exit quality

1

8.72

0.10–2.5

44.5–1114

0–0.38

2

10.92

0.10–2.5

44.5–1114

0–0.47

3

13.97

0.15–2.5

66.7–1114

0–0.37

4

18.31

0.22–2.5

97.9–1114

0–0.34

5

22.27

0.38–2.5

169–1114

0–0.20

6

29.41

0.82–2.5

364–1114

0–0.07

7

47.2–59.9

0.30

324

0.14–0.182

8

47.8–83.7

0.40

433

0.07–0.20

S. No.

TABLE II Data Logger

Pressure Gauge

To Computer

Pump To Sink Damper Front View

Water Reservoir

Microchannel

Water Circuit Electrical Circuit

Rear View Microheater

(a)

E STIMATION OF E RROR IN VARIOUS PARAMETERS M EASURED AND D ERIVED IN THE E XPERIMENTS Parameter

Maximum error

Volume flow rate

0.01 ml/min

L

100 μm

Wl , Wh

1 μm

H

1 μm

T

0.5 °C

P

2 mbar

Electrical power

0.02 W

PCh

1.2%

ACh

1.7%

Dh

3.2%

M

0.62%

U

2.3%

Re

4.0%

f*Re

8.4%

(b) Fig. 2. (a) Schematic of the experimental setup and (b) photograph of the fabricated microheater.

110 mbar on increasing the heat flux from 40 to 130 W/cm2. Wu et al. [18] worked in the range of 0–25.72 W/cm2 and 65.1–2620 kg/m2-s for heat and mass flux, respectively. They observed a pressure drop between 0.27 and 5.84 bar with water flowing in eight trapezoidal microchannels, each of hydraulic diameter of 72.7 μm and 6 cm length. Lee and Pan [19] employed a 99.8 × 20.3 μm2 microchannel, three mass fluxes (625, 417, 209 kg/m2-s), heat flux in the range of 0.4–30 W/cm2 and found the pressure drop between 90 and 260 kPa. The frictional pressure drop was found to be the most dominant component accounting for about 75% of the overall pressure drop. On the other hand, Bowers and Mudawar [20] report that the acceleration pressure drop is approximately 75% of the total pressure drop in their microchannel (dh = 510 μm) with R-113 as the working fluid. Our long-term goal is to determine the operational characteristics of flow in a microchannel which will be optimum for cooling in electronic application. Recently, we have reported a strong dependence of pressure drop on the

aspect ratio of microchannels [21]. The specific aim of the present paper is to study the pressure drop characteristics (mean value as well as fluctuations) of microchannels in the two-phase flow regime over a relatively large range of parameters. The literature survey shows that not many studies have reported the average pressure drop with water boiling in microchannels. Such data is nonetheless important for validating new models and developing better correlations. The experimental data is compared against existing correlations for microchannels and annular flow model. Flow visualization images showing different flow regimes are also presented, and existence of certain regimes is clarified. II. FABRICATION OF I NTEGRATED M ICROCHANNEL AND M ICROHEATER D EVICE Fig. 1 shows the fabrication process of microchannels on silicon. The microchannels are fabricated on a 2-in. 275 ± 25 μm-thick p-type 100 double-side-polished silicon wafer. Four trapezoidal parallel microchannels each of dimension 78 μm (H) × 273 μm (W L ) (and Wh = 159 μm) ×

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1.60 T = 25 T = 35 T = 60 T = 75 T = 90

Pressure drop, bar

1.20

(a)

0.80

0.40 (b) 0.00 0.80

0.40

2.00

1.20 1.60 Flow rate, ml/min. (a)

(c)

70 60 f*Re

Theoretical Line 50 25ºC 35ºC 60ºC 75ºC 90ºC

40 30

III. E XPERIMENTAL S ETUP AND P ROCEDURE

20 0

20

40

60

80 Re

Fig. 4. Flow visualization in the two-phase regime showing (a) bubbly, (b) slug, and (c) annular flow regimes. The heat fluxes for (a), (b), and (c) are 8.72, 10.9, and 13.97 W/cm2 , respectively, at a constant mass flow rate of 0.20 ml/min. (Single microchannel of hydraulic diameter 140 μm.)

100

120

140

(b) Fig. 3. (a) Pressure drop versus mass flow rate in single-phase flow at different temperatures and (b) f*Re versus Reynolds number at different temperatures in the single-phase regime. The theoretical value as determined by Morini [23] is also plotted for comparison. (Four parallel microchannels of hydraulic diameter 58.8 μm.)

20 mm (L) (yielding a hydraulic diameter of 108.8 μm) are fabricated by a sequence of process steps [Fig. 1(d) shows the cross-section of a microchannel]. The size of reservoir at the two ends of the microchannel is 6 mm × 6 mm. Note that other hydraulic diameter microchannels such as 58.8 μm and 140 μm have also been employed in this paper. The surface roughness is less than 0.1 μm for all the microchannels fabricated. The sealing of the microchannels with a quartz plate is a crucial step in fabrication and special care was taken to avoid leakage. Further details about fabrication can be found in [22]. A microheater fabricated on the top silicon surface and microchannels on the bottom surface is used to supply a controlled heat flux to the working fluid (deionized water with a saturation temperature of 100 °C). A chrome–gold thin-film stack is used as the microheater material, which has good linearity with respect to temperature and has high chemical and thermal stability. The thickness of the chrome–gold stack is 50 nm as measured by profilometer. The linewidth and resistance of fabricated microheater are 400 μm and 356 at room temperature, respectively. Further details on microheater characterization are provided in [22]. The entire fabrication and characterization was done inhouse.

This section discusses the setup used in our experiments, the experimental procedure, and uncertainties in the measurements. Fig. 2 shows the experimental setup for pressure drop measurement across the microchannels. The experimental setup comprises a deionized water reservoir, pump, and damper (to reduce disturbance from the pump), a probe (to provide contact between the dc power supply and microheater), a differential pressure measurement system, K-type thermocouple, data logger, and water collecting container. A precalibrated peristaltic pump (Master Flex, L/S 2) is used for metering and pumping the desired mass flux. It gives a constant mass flow rate at a maximum gauge pressure of 1.7 bar and it was ensured that there was no drift in the calibration of the pump. A precalibrated digital pressure gauge (Keller, Leo 1) with a range of 1–3 bar, resolution of 0.05% of full scale, and response time of 1 s is used to measure the pressure drop across the microchannels. The images are captured by a digital camera (Cannon, Power Shot A560, 7.1 mega pixels) along with a microscope for magnification. The heat flux is determined by dividing the power supplied by the microheater to the fluid by the surface area of the three heated sides of the microchannel. (Due to the presence of quartz plate, the fourth side is nearly insulated.) The value of the parameters used in these experiments are wall heat flux in the range of 0–30 W/cm2, water flow rate from 0.1 ml/min (44.5 kg/m2-s) to 2.5 ml/min (1114 kg/m2 -s), and outlet channel pressure of atmospheric (Table I). The inlet Reynolds number covered in the experiments is 3–140. Note that the pressure drop across the entire microchannel is measured, which includes the entry and exit loses. The pressure drop due to expansion and contraction (at the entry and exit) is, however, estimated to be small (less than 2.5%) as compared to the overall pressure drop, and hence neglected. The heat loss was calculated using the standard technique of supplying power to

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SINGH et al.: TWO-PHASE FLOW PRESSURE DROP CHARACTERISTICS IN TRAPEZOIDAL SILICON MICROCHANNELS

891

105 0.00 W/cm2 2

150

8.72 W/cm

10.90 W/cm

100

2

13.97 W/cm2 18.31 W/cm2

50

22.27 W/cm

2

29.41 W/cm2

0 0.8 0.4 1.2 Mass flow rate (ml/min)

Two-phase region Single-phase region

8.72 W/cm2

75

10.90 W/cm2

60

13.97 W/cm2 18.31 W/cm2

45

22.27 W/cm2

30

29.41 W/cm2

0.0

1.6

0.1

0.2 0.3 Quality

0.4

0.5

Fig. 6. Variation in pressure drop with exit thermodynamic quality for different heat inputs. (Four parallel channels with hydraulic diameter 108.8 μm.) The data points have been connected by straight lines to aid the eye.

(i)

150

90

15

(i)

0.0

Pressure drop (mbar)

Pressure drop (mbar)

Pressure drop (mbar)

200

a

125

dc power supply is set to a predetermined heat flux value and the above experiment is repeated for different sequentially decreasing flow rates.

100 75 50

4

3 d

25 0.25

IV. E XPERIMENTAL R ESULTS

c

e

2 b

Some results on the single-phase flow are first presented with the aim of establishing confidence in our measurements. This is followed by a detailed discussion on two-phase flow.

1 Onset of boiling

0.50 0.75 1.00 1.25 Mass flow rate ml/min

(ii)

1.50

(ii) Fig. 5. Variation in pressure drop with mass flow rate. A single case (corresponding to a heat flux 13.97 W/cm2 ) has been shown separately in (ii) for clarity. The data points in (i) have been connected by straight lines to aid the eye. (Four parallel channels of hydraulic diameter 108.8 μm. Note that mass flow rate of 0.1 ml/min corresponds to a mass flux of 44.5 kg/m2 -s.)

the test section without any flow of water. All the heat supplied in this case would be lost to the atmosphere. The surface temperature is monitored at the steady-state condition using four thermocouples, which probe the different locations of the chip. Knowing the average surface temperature and the heat flux supplied, the average heat transfer coefficient for heat loss is obtained. This heat transfer coefficient in combination with the measured surface temperature for a given experimental run is used for estimating the heat loss. It should be noted that the fluid entering the microchannels is subcooled—the amount of subcooling is in the range of 15–46 °C in the present experiments, while the exit pressure is atmospheric (1 bar). As apparent from the results presented in the following section, the maximum pressure drop is 105 mbar implying that the maximum inlet pressure is 1.10 mbar. The variation in saturation temperature over this pressure range is 2.3%. Table II presents an estimate of the error in quantities measured in the experiments. The following procedure is adopted while performing the experiments. The water reservoir is filled with degassed (boiled vigorously for at least 10 min and cooled to 25 °C) deionized water; the micro pump is then set for the desired flow rate. The pressure drop across the channel, the inlet and outlet temperatures, and the flow rate are measured after reaching steady state for all the desired flow rates. Further, the microheater

A. Pressure Drop in Single-Phase Flow Fig. 3(a) shows that as the flow rate increases, the pressure drop across the microchannel increases linearly. Further, as the temperature of the fluid increases, the pressure drop decreases. Note that the pressure drop reduces to less than half as the temperature increases from 25 to 90 °C. The reason for this behavior is a decrease in the fluid viscosity with an increase in temperature. The significant lowering of pressure drop at higher temperatures has practical implication since pressure drop penalty is regarded as an impediment for application of microchannels for cooling electronics. Upon non-dimensionalizing the pressure drop and mass flow rate to the friction factor ( f ) and Reynolds number (Re), the conventional behavior is however obtained. Fig. 3(b) show that f.Re is independent of both the Reynolds number and the temperature of the fluid. Here f and Re are calculated as f = 2pdh /(LρU 2 ) Re = ρU dh /μ(T ) μ(T ) = μ(Tre f )(T /Tre f )n exp[B(1/T − 1/Tre f )]

(1) (2) (3)

where n = 8.9 B = 4700/K,

(3a) (3b)

μ(Tre f ) = 1.005 × 10−3 kg/m-s

(3c)

Tre f = 293 K.

(3d)

Morini [23] showed that for laminar single-phase flow in trapezoidal microchannels with an aspect ratio of (W L /H = 2.18), f.Re is a constant at 62.53. The experimentally determined values are within experimental uncertainties of this theoretical value. This result is important because several contradicting

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80

75

Pressure drop (mbar)

150 Heat Flux 10 W/cm2

h (KW/m2k)

70

65

47.0 W/cm2 52.6 W/cm2 56.2 W/cm2 58.6 W/cm2 59.9 W/cm2

135 120 105 90 75

60

0

55

100

300

400

(a)

50 0.18

0.21 0.24 0.27 Mass flow rate (ml/min)

0.30

60 55

18

210 Pressure drop (mbar)

(a)

h (KW/cm2k)

200 Time (s)

W/cm2

50

47.8 W/cm2 59.8 W/cm2 64.6 W/cm2 66.5 W/cm2 83.7 W/cm2

180 150 120 90

45

60 40

0

35

60

120 180 Time (s)

240

300

(b)

30 0.30

0.35

0.40 0.45 0.50 0.55 Mass flow rate (ml/min)

0.60

Fig. 8. Variation in pressure drop with time at a flow rate of (a) 0.3 ml/min and (b) 0.4 ml/min for different heat fluxes. (Single microchannel of hydraulic diameter 140 μm.)

(b) Fig. 7. Variation in heat transfer coefficient versus mass flow rate for fixed heat fluxes 10 W/cm2 and 18 W/cm2 .

results on the value of the friction factor for flow in a microchannel have been reported in the literature [24]–[27]. The reason for the dip in f.Re values at low Re is not clear— however, it is reassuring that this dip is within the experimental uncertainty. These results help to validate the experimental setup and procedure employed in this paper. Subsequent results are for two-phase flow. B. Flow Visualization Fig. 4 presents some representative images of two-phase flow in the microchannel. We have observed that for small flow rates and heat fluxes, bubbles are observed along the length of the microchannel. These bubbles appear to be generated from certain preferred sites along the walls of the microchannel. The initial growth of the bubbles could be clearly seen in the experiments and, once in a while, the collapse of the bubbles was also observed. The shape of the bubble as it grows is qualitatively in accordance with the observations reported in the literature. As the heat flux is increased, the bubbles coalesce and the flow transitions to the slug regime. The length of the slug is usually several times the lateral dimensions of

the microchannel. With further increase in heat flux, the flow regime changes to annular—first close to the channel outlet, and subsequently along the entire length. The above visual observations confirm that bubbly, slug, and annular flow regimes exist in microchannels [28]. The annular flow dominates at large values of heat flux and mass flow rate. The impact of mass flow rate on flow regimes is significant. At low flow rates, the flow regimes discussed above exist individually. On the other hand, at high flow rates (and at specific heat flux values), all the three flow regimes are observed to coexist. Further, at higher mass flow rates, annular flow starts right after the bubbly regime, i.e., there is direct transition from bubbly to annular flow with no intermediate slug regime. It is worth mentioning that although the exit quality is sufficiently small (