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Unsteady steam condensation flow patterns inside a miniature tube
Applied Thermal Engineering 27 (2007) 1225–1235 www.elsevier.com/locate/apthermeng
Review
Unsteady steam condensation flow patterns inside a miniature tube H. Louahlia-Gualous *, B. Mecheri FEMTO ST, LPMO, CNRS-UMR 6174, UTBM, rue Thierry Mieg, 90000 Belfort, France Received 28 April 2006; accepted 17 October 2006 Available online 12 December 2006
Abstract Unsteady steam condensation inside a single miniature tube has been studied. The visualization of different instantaneous and periodically two-phase flow is conducted for different experimental conditions. The two-phase flow characterization is obtained using the image processing. Annular, slug bubbly, spherical bubbly, and wavy flows are observed by varying the steam inlet pressure and cooling heat transfer. The cycle of the periodically flows are compared. It is shown that increasing the cooling heat flow rate reduces the number of the instabilities and the injected bubbles. The axial vapor velocity decreases during the waves growth. The local distribution of the condensate film thickness is analyzed. It is shown that the liquid film becomes thinner near the meniscus-like interface because of the surface tension effect. The reverse annular flow is observed at the end of each periodic flow when the bubbles leave the channel. It can be concluded from experimental results that the stratification effect is not significant during the condensation inside the miniature tube. The capillary pressure evolution is measured. The maximum values are obtained in the waves locations and near the meniscus of the annular flow. 2006 Elsevier Ltd. All rights reserved. Keywords: Miniature tube; Condensation; Film thickness; Two-phase flows pattern; Instability; Waves
Contents 1. 2. 3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Condensate flow patterns . . . . . . . . . . . . . . . . . . . . . 3.2. Analysis of flow patterns – influence of the cooling heat 3.3. Local evolution of the liquid film thickness . . . . . . . . . 3.4. Local evolution of the capillary pressure . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Condensation in the small channels is used in microelectronic, cooling, and automotive air-conditioners. It is *
Corresponding author. Tel.: +33 3 8457 8212; fax: +33 3 8457 0032. E-mail address: [email protected] (H. Louahlia-Gualous).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.10.033
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noted by several experimental analysis that reducing channel diameter for condensation increases the thermal performance of heat exchangers. It is seems to be necessary to analyze the local thermal characteristics of compact heat condensers. The aim of the research in this field is to maximize the heat transfer coefficient and to minimize the pressure drop in the heat exchangers. Several experimental
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Nomenclature A g K L La Lb Nu R P t U z
Hamaker constant (N m) acceleration of gravity (m/s2) interface curvature (m1) condensate length (m) displacement distance for annular flow (m) displacement distance for bubble (m) Nusselt number tube radius (m) absolute pressure (Pa) time (s) axial velocity (m/s) axial coordinate (m)
d r
liquid film thickness (m) surface tension (N/m)
Subscripts c capillary d disjoining f condensate film L liquid v vapor x local
Greek symbols l dynamic viscosity (kg/ms) q mass density (kg/m3)
studies were conducted previously for condensation inside the sub-millimeter-scale diameter channels [1–7]. Numerous experimental results and empirical correlations were reported in the literature for condensation inside a large hydraulic diameter of the channel [8–10]. However, heat transfer coefficient and pressure loss for condensation inside the microchannel cannot be predicted using the correlations for condensation inside the macrochannel. Extrapolating correlations for larger tube to smaller tube introduces errors because of the significant gravity, shear and surface tension magnitudes [11] where the tube diameter is lower than 1 mm. According to the classification of Kandlikar and Grande [12], the conventional channel has a hydraulic diameter higher than 3 mm. The minichannel has a hydraulic diameter range covering 200 lm–3 mm. The hydraulic diameter of microchannels ranges between 10 lm and 200 lm. The flow geometry or flow regime for condensation inside a channel depends on the vapor shear stress, surface tension and gravity forces. The annular flow is associated with high vapor shear but the slug flow appears when the gravity is the controlling force. The thin liquid film in the annular flow appeared on the heat exchange surface while the central core was occupied by the vapor phase. In this case, the heat transfer is controlled by the film thickness, interfacial shear stress, etc. Several theoretical and numerical models have been proposed previously for condensation of annular flow [13–15] in order to predict the local and average heat transfer coefficients. However, each model was limited with the validity domain such as: the scale of hydraulic diameter, pure vapor, pressure, velocity, etc. Little investigations about experimental condensation inside a single minichannel have been found in the literature. It has been indicated by several authors that the capillary forces affected the flow pattern and the heat transfer coefficient for two-phase flow inside a minichannel. Little
information was available in the open literature about the hydrodynamic and thermal characterization of the condensation flow patterns inside the minichannels and the microchannels. Numerous studies for adiabatic two-phase flow inside a minichannel show the predominance of the annular flow over broad regions of the flow map [16,17]. Baird et al. [18] found that the two-phase flow for condensation inside a miniature tube has been in annular flow regime when the vapor quality becomes higher than 20%. Garimella [19] identified the annular, intermittent, wavy, and the dispersed flows for condensation inside the small diameter channel. He reported that the intermittent flow regime becomes larger by decreasing the hydraulic diameter of tube from 0.5 mm to 5 mm because the surface tension force predominates over the gravitational force. In this paper, an experimental study for condensation of steam flowing inside a single miniature tube has been carried out. Condensation flow patterns were visualized and investigated. Experiments were conducted for different operating conditions. The pressure at the channel exit is equal to the atmospheric pressure. Different instantaneous and periodically two-phase flow patterns inside a miniature tube are identified and analyzed. The location of the interfacial instabilities, the distribution of the film thickness, and the capillary pressure are measured. 2. Experimental setup Fig. 1 shows the experimental setup for two-phase flow visualization. The experimental apparatus consists of the electric steam boiler where the steam is generated (1), the valve (2), the experimental mini-condenser (3), the second mini-condenser (4), and the weighing system (5). The temperature and the pressure at the channel inlet are measured using the microthermocouples and a pressure sensor. The vapor enters in the test section at the saturated state and
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235 Camera P
(2)
(3) (4)
(1) Boiler
P
(2) Valve Boiler
(1)
(3) Test section (4) Second mini-condenser
(5)
(5) Weighing system Balance
Fig. 1. Experimental system.
the condensation appears along the surface of the miniature tube. The cooling water flows in counter flow of the two-phase flow inside the minichannel. The inlet and the outlet temperatures of the cooled water are measured through the chromel–alumel microthermocouples. The liquid and the vapor at the channel exit were cooled inside the second condenser in order to condense all the vapor mass flow. The exit liquid temperature of the second condenser was measured by means of microthermocouples in order to be sure that the liquid was subcooled. The second condenser is cooled using water and the cooling heat flow rate is measured. The total mass flow rate was measured by weighing the condensate flow using a microbalance at the outlet of the second condenser. The test section shown in Fig. 2 has an effective length of 690 mm. The miniature glass tube was 0.78 mm inner diameter and 0.8 mm outer diameter. It is cooled using water flowing inside a glass tube of 10 mm diameter. A convergent was placed at the channel inlet and thereby uniform vapor velocity profile has been assumed at the channel inlet. The condensate flow rate inside the miniature tube is determined from the energy balance on the cooling waterside. The cooling water flow rate is measured using the flow meter. A Labview data acquisition system
Fig. 2. Test section.
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has been used to record all temperature measurements for each experimental condition. Experiments were conducted using distilled water vapor as the working fluid. The cooling heat flow rate, the saturated temperature and the vapor pressure at the channel inlet were varied. A high-speed camera with spatial resolution of 512 · 480 pixels was used to capture the two-phases flow images. The flow patterns were recorded using the maximum frame rates of 1000 frames per second. The data acquisition system was used to record the images of the two-phase flow for transient state. The inlet steam pressure and the flow rate of the cooling water were regulated during experiments. The outlet condensate flow was at the atmospheric pressure. Different two-phase flows were observed inside the miniature glass tube by varying the cooling heat flow rate or the steam mass flux. Before each experiment, the boiler was discharged in order to evacuate the incondensable gases. All the results presented in this paper were obtained using the pure vapor of distilled water. 3. Results and discussion Different condensation flow patterns were identified for different experimental conditions. The vapor pressure and temperature, and the total mass flow rate were controlled at the channel inlet. The cooling heat flow rate was imposed during experiments by adjusting the water flow rate and the inlet water temperature. 3.1. Condensate flow patterns For inlet pressure of 73.6 kPa, and inlet vapor temperature of 99.1 C, the annular two-phase flow was observed. The average mass velocity at the channel inlet was deduced from the total mass condensate liquid measured by weighting and it was of 82 g/cm2 s. Fig. 3 shows an example of images that recorded during this experiment. Note that the flow direction is from the right to the left with only vapor entering in the miniature tube. Photographs of the two-phase flow patterns show that the condensate flow is periodic and condensation process is unsteady. The vapor is condensed along the cooling surface and thereby the thin liquid film appears. For this experiment, the annular flow occupies the entire channel. Fig. 3d and e show an example of photographs that illustrate the wave formation at the liquid–vapor interface at the bottom part of the tube. In general, the interfacial waves resulted from the interfacial shear between the liquid and vapor phases moving at difference velocities (Kelvin–Helmotz instability). Therefore, the liquid resulting from vapor condensation accumulates and forms wave at the surface. The wave growths during time and attains the limit value for which the waves on both part of the tube coalesce. Therefore, the vapor flow cuts out (see Fig. 3b and c) and the liquid fills up the space between the inlet annular flow and the injected vapor. The down stream of the annular flow travels the channel because of the
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Fig. 4. Annular/spherical bubbly flow (73.6 kPa, 33 g/cm2 s).
Fig. 3. Annular flow (73.6 kPa, 82 g/cm2 s).
incoming vapor and the process will be repeated. The annular flow appears when the interfacial shear predominates on the capillary and the gravity forces. Therefore, the wavelength becomes very large and liquid–vapor interface becomes stable. However, when the condensate film attains a significant thickness on the heat exchange surface, the vapor travels in channel with difficulty and the difference between the vapor and liquid velocities increases. An accumulation of the condensate vapor occurs and the instability appears on the heat exchange surface. For inlet pressure of 73.6 kPa and inlet vapor temperature of 96.7 C, the annular flow with the continuous injection of the spherical bubbles is observed. Photographs of flow patterns during this experiment are reported in Fig. 4. The average mass velocity is 33 g/cm2 s. In the first photograph, the upstream of the flow is constituted by the annular flow and the down stream of the flow is occupied by the spherical bubbly flow. At the end of the annular flow, the shape of the liquid–vapor interface can be seen and it has a form of spherical cap. The second image shows the strangled vapor flow because of the instability and the injection of the third bubble. The wave formed at the bottom part of the channel is bigger than the wave at the top of the channel. In fact, the draining of the condensate film from the top to the bottom part of the channel under the gravity force increases the liquid film thickness on the bottom part of the channel. This effect was called stratification for condensation in the macrochannel. It is negligible when the channel diameter was reduced below 1 mm [5]. It seems that the instability occurs earlier for low mass velocity
(33 g/cm2 s) (see Fig. 3) because the liquid film thickness increases with decreasing the inlet vapor velocity. After detachment of each bubble, the length of the annular flow is reduced and the reverse vapor flow from the left to the right of the channel is observed. The third photograph illustrates that the diameter of the vapor flow increases at the channel inlet because the liquid fills up the space of each injected bubble. Therefore, the interfacial liquid pressure is probably increased, and the liquid film thickness on the heat exchange surface is reduced (Fig. 4c). For the same experimental conditions (Pv = 73.6 kPa and Tv = 96.7 C), as the inlet average mass vapor velocity increases till 50 g/cm2 s, the length of the annular flow and the number of the interfacial waves on the vapor surface
Fig. 5. Wavy annular and bubbly flow (73.6 kPa, 50 g/cm2 s).
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
increase. Examples of photographs of two-phase flow patterns were reported in Fig. 5. The first photograph shows that the two-phase flow is constituted by the annular flow in the channel inlet and the spherical bubbly flow occurs at the down stream of the flow (Fig. 5a). This photograph presents the zone of the bubble injection and it shows that the stratification effect is less significant compared to the previous experiment (Fig. 4b). In general, an asymmetric of the liquid film around the tube results from the stratification effect. During this experiment, the wavy surface of
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the liquid film was observed (Fig. 5b). The neighboring waves at the top and the bottom of the tube have approximately the same amplitude. Therefore, increasing the inlet vapor velocity reduces the effect of stratification. The bubbles move inside the channel from the injection zone to the channel exit, in contact with the upper portion of the channel because of the capillary force. During this experiment, the two-phase flow changes in the space and with time. Fig. 6 presents the entire sequence of the two-phase flow patterns. This sequence is periodic and it is repeated
Fig. 6. The complete sequence of the wavy annular and bubbly flow (73.6 kPa, 50 g/cm2 s).
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approximately at any second. The number of the injected bubbles is approximately 10 for each sequence. The reverse vapor flow from the left to the right of the channel is observed after the injection of the last bubble. This phase was reported in the photograph recorded at 376 ms. As the annular flow was reversed, the bubbles move the channel from the left to the right during 80 ms. At t = 488 ms, the bubbles travel the channel from the right to the left, but at t = 568 ms the bubbles flow is reversed during 152 ms. At t = 720 ms, the bubbles move from the right to the left and leave the channel at t = 1000 ms. For range of time between 448 ms and 880 ms, Fig. 6 illustrates that the distance between the two neighboring bubbles and the bubbles sizes are variable during the oscillatory bubbly flow.
3.2. Analysis of flow patterns – influence of the cooling heat flow rate For inlet pressure of 73.59 kPa, and inlet vapor temperature of 99 C, the annular/spherical bubbles and slug bubble are produced. The inlet temperature of the cooling water was fixed to 14 C but the cooling heat flow rate was varied. The vapor temperature and pressure at the channel inlet were fixed during experiments. For each cooling heat flow rate, the flow pattern is constituted by the annular flow at the upstream flow and the slug bubbly flow at the downstream flow. Fig. 7 shows an example of the periodic two-phase flow sequence that obtained for inlet mass velocity of 136 g/cm2 s. The first image shows that the two-phase flow is annular and the vapor flow length
Fig. 7. The complete sequence of the smooth annular and slug bubbly flow (73.6 kPa, 136 g/cm2 s).
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
increases during time. The first instability appears and the first bubble was injected. This bubble has an elongated form and it called the Taylor’s bubble. After this phase, the length of the annular flow increases and the second spherical bubble was injected. Others instabilities appeared and two other spherical bubbles were injected resulting from the incoming vapor at the channel inlet. The bubbles flow to the channel exit in proximity of the channel top because of the buoyancy forces. This phenomenon is also observed by Mederic et al. [3,4] for condensation of pentane inside a minichannel. When the Taylor’s bubble attains the channel exit, the reverse flow occurs from the exit to the inlet channel (photograph at t = 718 ms). The hemispherical meniscus is formed (photograph at t = 726 ms) and the bubbles leave the tube (photograph at t = 806 ms). The analysis of the periodically condensate flow and the influence of the cooling heat flow rate on the two-phase flow have been conducted by studying the cycle of the condensate flow. The cycle is defined as the temporal displacement distances of the injected bubbles and the annular flow. Fig. 8a shows an example of a sketch of the twophase flow patterns inside a minichannel at certain instant of time, where the upstream of the injection flow is occupied by the annular flow and the downstream is occupied by the slug bubbly flow. The aim of this figure is to show the displacement distance of the annular flow meniscus,
La Lb
Channel
denoted by La, which was measured from the channel inlet and along the axial direction. The displacement distance of the bubbles meniscus, denoted by Lb, was also measured along the axial direction, from the channel inlet to the meniscus of the bubble. Fig. 8b illustrates the temporal variation of the distances La and Lb for the periodically condensate flow shown in Fig. 7. It is noted that for the annular flow, La increases linearly during time until the first wave appears at approximately 170 ms. After that, it can be seen that La becomes sensibly uniform because the incoming vapor condenses and it is retained in the zone where the wave is formed. Therefore, the interfacial wave amplitude increases along the radial direction during the time until the injection of the first elongated bubble at approximately 240 ms. At this time, La decreases suddenly and induces the reverse condensate flow. Fig. 8b illustrates this phenomenon and it shows that after 240 ms, the distances La and Lb are variable very slowly because of the damping of both the annular and the bubbly flows. During this period of cycle (240 ms < t < 300 ms), the incoming vapor is condensed and it is retained to flow when the second wave appears. Therefore, the interfacial amplitude of the wave increases and the injection of the second bubble is produced at approximately 300 ms. After this moment, the process is repeated for the third and fourth injected bubbles. The sizes of the injected bubbles are reduced along the minichannel because of the condensation of the vapor at the interface of the bubbles. The velocity of the annular flow meniscus is deduced from the profile of the distance La as follows: U¼
Vapor
Vapor
Vapor
Liquid
Injected bubble
1231
dLa dt
ð1Þ
Fig. 9 shows the temporal evolution of the velocity U. It shows that U decreases during time because of the increase
Annular flow
U [mm / s]
L a [mm]
120
16
L [mm]
Velocity
20 14
Lb
18
profile of La
100
12
16
80
10
14
60
La
12
8
Injection of the bubble 1
10 6
40
Injection of the bubble 2
8
Injection of the bubble 3
4
6
Annular flow bubble 1 bubble 2 bubble 3 bubble 4
4 2
0
2
Injection of the bubble 4 0 0
0 0
100
200
300
400
500
600
20
700
Time [ms]
Fig. 8. The distance of the meniscus displacement (73.6 kPa, 136 g/cm2 s).
100
200
300
400
500
600
-20 700
Time t [ [ms] ]
Fig. 9. The temporal evolution of the axial vapor velocity (73.6 kPa, 136 g/cm2 s).
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Therefore, the first wave appears nearly to the channel inlet compared to the case when the mass vapor velocity was 136 g/cm2 s. It can be concluded from Fig. 10a that the instability appears later when the mass velocity decreases, this confirms that the condensation has a stabilizing effect. During 600 ms, the number of the produced instabilities is reduced to 50% when the mass vapor velocity decreases from 136 g/cm2 s to 84 g/cm2 s. Fig. 10b shows the evolution of the meniscus velocity of the annular flow following the axial direction. The damping of the vapor flow is observed when the mass velocity decreases because the quantity of the condensate mass increases and it tends to reduce the shear stress at the liquid–vapor interface. The results presented in this figure confirmed the damping effect of the condensation on the interfacial waves initiation.
L a [mm]
16 14
136 g/cm2s 30W
12 10 8
38W 84 g/cm2s
6 4 2 0 0
100
200
300
400
500
600
700
Time [ms]
3.3. Local evolution of the liquid film thickness
U [mm/s] 120 3884Wg/cm²s
30136 W g/cm²s
100
80
60 Injection of the second bubble for 84 g/cm²s
Injection of the first bubble for 84 g/cm²s
40
20
Injection of the bubble 1
0 Injection of the bubble 2
Injection of the bubble 3
-20 0
100
200
300
400
500
Injection of the bubble 4
600
700
Time [ms]
Fig. 10. Influence of the velocity of the annular flow meniscus (73.6 kPa).
of the condensate film. It is noted that the velocity U decreases quickly from approximately 80 mm/s to 4 mm/s during the growth phases of the first wave. This phenomenon was observed for each wave growth on the heat exchange surface because the condensate vapor was retained at the wave location. During wave growth, the condensate film is reversed and the vapor velocity decreases under the shear stress at the liquid–vapor interface. After the detachment of the first bubble, the vapor velocity decreases and it ranges between 0 and 20 mm/s during the short phases of the bubbles growth and injection. The temporal evolution of La for the periodic condensate flow is shown in Fig. 10a for inlet pressure of 73.59 kPa, and inlet vapor temperature of 99 C, and for two mass velocities (84 g/cm2 s and 136 g/cm2 s). The onset annular length (Lo) is defined as the distance between the channel inlet and the zone where the first bubble is detached. It is shown that decreasing the mass velocity decreases Lo because the liquid film thickness increases.
The heat transfer inside a channel is very dominated by the thermal resistance of the condensate film. The film thickness represents the most important property required to predict the local heat transfer coefficient and to localize the zones where the heat transfer is intensified. The local distribution of the film thickness was determined from the images processing for the annular flow. The essential step is to produce the binary image (image threshold) in which the darker regions produced by vapor flow and the liquid–vapor interface, are separated from the light zones (condensate film). The film interface is smooth and provides a good contrast for detection of the liquid contour. However, when the wave appears on the liquid–vapor interface, the deformation of the interface scatters most the light and the contrast becomes poor in this zone. This disturbance represents a small portion of the total images of each given sequence. In this work, it is found that the tube length affected by the waves represents 10–15% of the total condensate length. In general, several sources of uncertainty exist when extracting quantitative data from images. In this paper, the uncertainty due to the illumination and optics systems is assumed to be negligible. The essential uncertainty in the liquid film thickness was introduced by the image processing and it was estimated to be lower than 10%. The thickness of the liquid film varies during time and along the length of the minichannel. The experimental data presented in Fig. 11a–c were obtained for inlet pressure of 73.59 kPa, inlet vapor temperature of 99 C, and for mass velocity of 136 g/cm2 s. Fig. 11a shows the distribution of the liquid film thickness for annular flow at t = 80 ms. The condensate film is thinner at the channel inlet and increases far from this zone because during condensation of the vapor, the interfacial shear stress decreases along the channel and reduces the interfacial vapor velocity. For this experiment, the total condensate length was approximately 4.2 mm. Fig. 11a shows that the interfacial wave appears at 75% of the total condensate length. The interfacial wave amplitude is not uniform around the chan-
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
400
1233
δ [µm]
At bottom the upperside side The At the bottom The upper side side
350
t = 130 ms 0.9
Condensate length
300
δ/R
1
0.8 250
wave initiation
0.7 0.6
200
0.5 150 0.4
t = 130ms t = 154ms t = 170ms t = 210ms t = 226ms
0.3
100
0.2 50 0.1 0
0 0
1
2
3
4
5
0
2
4
Tube length [mm]
0.2
6
8
10
Tube length [mm]
Nux
t = 226 ms 0.18
t = 218 ms
0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
2
4
6
8
10
Tube length [mm]
Fig. 11. Local characterization of the annular flow (73.6 kPa, 136 g/cm2 s).
nel because of the stratification effect. It is about 100 lm and 150 lm at the upper and the bottom sides of the tube respectively. The liquid film at the bottom part is seen to be thicker than on the top wall over most of the axial length for the annular flow. The condensate film thickness is higher on the bottom side than on the upper side of the channel because the liquid was drained from the upper to the bottom part of the tube under the effect of the gravity. For all experiments, the condensation flow is unsteady. The local film thickness and the complete condensation length were changed during time (Fig. 11b). This figure presents the film thickness distribution only at the bottom part of the channel for more clarity. It is shown that the film thickness ranges between 30% and 60% of the tube radius near
the channel inlet. At t = 176 ms, a significant variation in the film thickness is observed along the channel and the large quantity of the liquid is collected at 3.4 mm far from the channel inlet. The wave formed at this location has achieved the very significant amplitude (0.85R). It tends to form a slug bubble at the end of the vapor flow. For each time, the liquid film thickness decreases in the downstream direction before converging because of the capillary force (Fig. 11b, zone A). In this zone, Zhang et al. [14] are also observed that the liquid thickness decreases for condensation inside a miniature tube. The analysis of the local heat transfer coefficient is studied by using the well-known Nusselt theory [20] defined for laminar film condensation. The Nusselt theory provides the
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H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
local Nusselt number as a function of the local film thickness as follows: 2 1=3 lf 1 ð2Þ Nux ¼ d q2f g
1000
3.4. Local evolution of the capillary pressure
100
ð3Þ
where Pd is the disjoining pressure defined as: Pd ¼
A d3
ð4Þ
where A is the Hamaker constant. Begg et al. [5] defined previously the pressure difference for condensation inside a minichannel as follows: Pv PL 8 9 " 2 #3=2 =
The end of the annular flow
t = 226 ms
800 700
P c ¼ P v P L ¼ rK P d
t = 130 ms
900
According to this theory, the local Nusselt number was deduced from the local distribution of the film thickness measured just before the detachment of the bubble. Fig. 11c shows that the local Nusselt number deteriorates in the zone where the wave is formed because the thermal resistance of the condensate film becomes significant in this location. The Nusselt number near the channel inlet is very high because the liquid film is thinner in this zone.
It is known that for the condensation inside a microchannel the surface tension effect predominates but it was usually neglected in the macro scale channels. From experimental data, it can be concluded that the stratification effect is low except in the zone where the complete condensation occurs and the slug bubbles were produced. In this zone, the significant mass of liquid is collected and the curvature of the liquid–vapor interface results from the interaction between the shear stress and the predominant capillary force. The combined effects of the disjoining pressure, the thermo-capillary effects, and the dynamic flow cause the variation of the condensate film in a capillary tube. As defined by the known Young–Laplace equation, the wetting characteristics and the surface tension result in a pressure difference between the liquid and the vapor, which can be shown to be:
Pc [Pa]
Instability zone 600 500 400 300 200
0 0
1
2
3
4
5
6
7
8
9
Tube length [mm]
Fig. 12. Local capillary pressure profiles (73.6 kPa, 136 g/cm2 s).
of the film (t = 80 ms), the capillary pressure is approximately uniform along the channel length and achieves a significant value near the end of the annular flow where the meniscus-like interface is formed. For the same experimental condition, the capillary pressure distribution at t = 176 ms is also presented in Fig. 12. The maximum values of the capillary pressure are obtained in the zone where the wave was formed. 4. Conclusions The visualization and the experimental measurements for condensation flow patterns inside a single miniature tube has been studied. It is shown that the two-phase flow inside the channel depends on time and the location. Annular, slug bubbly, spherical bubbly, and wavy flows are identified and analyzed experimentally. The vapor flow was decelerated and the number of the instabilities was reduced when the inlet vapor mass velocity decreases. The condensation has a stabilizing effect. The analysis of the local distribution of the condensate film thickness shows that the liquid film is thinner at the channel inlet and increased far from this zone. This paper shows the presence of the periodic two-phase flows represented by the cycles in order to show the zones where the instabilities were produced and the bubbles were injected. The reverse annular flow is observed at the end of each periodic flow. The stratification effect is not significant for condensation inside the miniature tube because when the hydraulic diameter decreases, the effects of surface tension increasingly counteract the effects of gravity and extending the size of the annular flow pattern. The liquid film is wavy and it is unsymmetrical. The maximum values of the capillary pressure are measured in the waves locations and near the end of the annular flow. Measurements
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
show that the velocity of the annular flow meniscus decreases quickly during the waves growth because the thinner liquid flow is probably reversed and decreases the vapor shear stress at the liquid–vapor interface. References [1] Y. Yan, T. Lin, Condensation heat transfer and pressure drop of refrigerant R134a in a small pipe, Int. J. Heat Mass Transfer 42 (1999) 697–708. [2] W.W.W. Wang, T.D. Radcliff, R.N. Christensen, A condensation heat transfer correlation for millimeter-scale tubing with flow regime transition, Exp. Therm. Fluid Sci. 26 (2002) 473–485. [3] B. Mederic, M. Miscevic, V. Platel, P. Lavieille, J.L. Joly, Experimental study of flow characteristics during condensation in narrow channels: the influence of the diameter channel on structure patterns, Superlattices Microstruct. 36 (2004) 573–586. [4] B. Mederic, P. Lavieille, M. Miscevic, Void fraction invariance properties of condensation flow inside a capillary glass tube, Int. J. Multiphase Flow 31 (2005) 1049–1058. [5] E. Begg, D. Khrustalev, A. Faghri, Complete condensation of forced convection two-phase flow in a miniature tube, J. Heat Transfer, ASME 123 (1999) 904–915. [6] H.Y. Wu, P. Cheng, Condensation flow patterns in silicon microchannels, Int. J. Heat Mass Transfer 48 (2005) 2186–2197. [7] Y. Chen, P. Cheng, Condensation of steam in silicon microchannels, Int. Commun. Heat Mass Transfer 32 (2005) 175–183. [8] A. Cavallini, G. Censi, D. Del Col, L. Doretti, G.A. Longo, L. Rosseto, Condensation heat transfer and pressure drop inside channels for AC/HP application, in: 12th International Heat Transfer Conference Grenoble, vol. 1, 2002, pp. 171–186. [9] J.S. Shin, M.H. Kim, An experimental study of condensation heat transfer inside a mini-channel with a new measurement technique, Int. J. Multiphase Flow 30 (2004) 311–325.
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[10] Sh. Koyama, K. Kuwahara, K. Nakashita, Condensation of refrigerant in a multi-port channel, in: First International Conference Microchannels and Minichannels, Rochester, USA, 2003, pp. 193– 205. [11] W.E. TeGrotenhuis, V.S. Stenkampn, Testing of microchannel partial condenser and phase separator in reduced gravity, in: First International Conference Microchannels and Minichannels, Rochester, USA, 2003, pp. 699–705. [12] S.G. Kandlikar, W.J. Grande, Evolution of microchannel flow passages – Thermohydraulic performance and fabrication technology, Proce. IMECE (2002) 1–13. [13] H. Louahlia, P.K. Panday, Condensation en film entre deux plaques planes verticales. Comparaison des performances thermiques du R134a et du R12, Canad. J. Chem. Eng. 75 (1997) 704–711. [14] Y. Zhang, A. Faghri, M.B. Shafii, Capillary blocking in forced convection condensation in horizontal minature channels, J. Heat Transfer, Trans. ASME 123 (2001) 501–511. [15] D.X. Jin, J.T. Kwon, M.H. Kim, Prediction in tube condensation heat transfer characteristics of binary refrigerant mixtures, Int. J. Refrig. 26 (2003) 593–600. [16] A. Kawahara, M. Sadatomi, K. Okayama, M. Kawaja, P.M. Chung, Effects of channel diameter and liquid properties on void fraction in adiabatic two phase flow through microchannels, Heat Transfer Eng. 26 (3) (2005) 13–19. [17] J.W. Coleman, S. Garimella, Characterization of two phase flow patterns in small diameter round and rectangular tubes, Int. J. Heat Mass Transfer 42 (1999) 2869–2891. [18] J.R. Baird, D.F. Fletcher, B.S. Haynes, Local condensation heat transfer rates in fine passages, Int. J. Heat Mass Transfer 46 (2003) 4453–4466. [19] S. Garimella, Condensation flow mechanisms in microchannels: basis for pressure drop and heat transfer models, Heat Transfer Eng. 25 (3) (2004) 104–116. [20] W. Nusselt, Die oberfla¨chenkondensation des wasserdampfes, Z. VDI, vol. 60, 1916, pp. 541–546, 569–575.
Review
Unsteady steam condensation flow patterns inside a miniature tube H. Louahlia-Gualous *, B. Mecheri FEMTO ST, LPMO, CNRS-UMR 6174, UTBM, rue Thierry Mieg, 90000 Belfort, France Received 28 April 2006; accepted 17 October 2006 Available online 12 December 2006
Abstract Unsteady steam condensation inside a single miniature tube has been studied. The visualization of different instantaneous and periodically two-phase flow is conducted for different experimental conditions. The two-phase flow characterization is obtained using the image processing. Annular, slug bubbly, spherical bubbly, and wavy flows are observed by varying the steam inlet pressure and cooling heat transfer. The cycle of the periodically flows are compared. It is shown that increasing the cooling heat flow rate reduces the number of the instabilities and the injected bubbles. The axial vapor velocity decreases during the waves growth. The local distribution of the condensate film thickness is analyzed. It is shown that the liquid film becomes thinner near the meniscus-like interface because of the surface tension effect. The reverse annular flow is observed at the end of each periodic flow when the bubbles leave the channel. It can be concluded from experimental results that the stratification effect is not significant during the condensation inside the miniature tube. The capillary pressure evolution is measured. The maximum values are obtained in the waves locations and near the meniscus of the annular flow. 2006 Elsevier Ltd. All rights reserved. Keywords: Miniature tube; Condensation; Film thickness; Two-phase flows pattern; Instability; Waves
Contents 1. 2. 3.
4.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Condensate flow patterns . . . . . . . . . . . . . . . . . . . . . 3.2. Analysis of flow patterns – influence of the cooling heat 3.3. Local evolution of the liquid film thickness . . . . . . . . . 3.4. Local evolution of the capillary pressure . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction Condensation in the small channels is used in microelectronic, cooling, and automotive air-conditioners. It is *
Corresponding author. Tel.: +33 3 8457 8212; fax: +33 3 8457 0032. E-mail address: [email protected] (H. Louahlia-Gualous).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.10.033
.......... .......... .......... . . . . . . . . . flow rate . . . . . . . . . . . . . . . . . . . . . .......... ..........
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noted by several experimental analysis that reducing channel diameter for condensation increases the thermal performance of heat exchangers. It is seems to be necessary to analyze the local thermal characteristics of compact heat condensers. The aim of the research in this field is to maximize the heat transfer coefficient and to minimize the pressure drop in the heat exchangers. Several experimental
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Nomenclature A g K L La Lb Nu R P t U z
Hamaker constant (N m) acceleration of gravity (m/s2) interface curvature (m1) condensate length (m) displacement distance for annular flow (m) displacement distance for bubble (m) Nusselt number tube radius (m) absolute pressure (Pa) time (s) axial velocity (m/s) axial coordinate (m)
d r
liquid film thickness (m) surface tension (N/m)
Subscripts c capillary d disjoining f condensate film L liquid v vapor x local
Greek symbols l dynamic viscosity (kg/ms) q mass density (kg/m3)
studies were conducted previously for condensation inside the sub-millimeter-scale diameter channels [1–7]. Numerous experimental results and empirical correlations were reported in the literature for condensation inside a large hydraulic diameter of the channel [8–10]. However, heat transfer coefficient and pressure loss for condensation inside the microchannel cannot be predicted using the correlations for condensation inside the macrochannel. Extrapolating correlations for larger tube to smaller tube introduces errors because of the significant gravity, shear and surface tension magnitudes [11] where the tube diameter is lower than 1 mm. According to the classification of Kandlikar and Grande [12], the conventional channel has a hydraulic diameter higher than 3 mm. The minichannel has a hydraulic diameter range covering 200 lm–3 mm. The hydraulic diameter of microchannels ranges between 10 lm and 200 lm. The flow geometry or flow regime for condensation inside a channel depends on the vapor shear stress, surface tension and gravity forces. The annular flow is associated with high vapor shear but the slug flow appears when the gravity is the controlling force. The thin liquid film in the annular flow appeared on the heat exchange surface while the central core was occupied by the vapor phase. In this case, the heat transfer is controlled by the film thickness, interfacial shear stress, etc. Several theoretical and numerical models have been proposed previously for condensation of annular flow [13–15] in order to predict the local and average heat transfer coefficients. However, each model was limited with the validity domain such as: the scale of hydraulic diameter, pure vapor, pressure, velocity, etc. Little investigations about experimental condensation inside a single minichannel have been found in the literature. It has been indicated by several authors that the capillary forces affected the flow pattern and the heat transfer coefficient for two-phase flow inside a minichannel. Little
information was available in the open literature about the hydrodynamic and thermal characterization of the condensation flow patterns inside the minichannels and the microchannels. Numerous studies for adiabatic two-phase flow inside a minichannel show the predominance of the annular flow over broad regions of the flow map [16,17]. Baird et al. [18] found that the two-phase flow for condensation inside a miniature tube has been in annular flow regime when the vapor quality becomes higher than 20%. Garimella [19] identified the annular, intermittent, wavy, and the dispersed flows for condensation inside the small diameter channel. He reported that the intermittent flow regime becomes larger by decreasing the hydraulic diameter of tube from 0.5 mm to 5 mm because the surface tension force predominates over the gravitational force. In this paper, an experimental study for condensation of steam flowing inside a single miniature tube has been carried out. Condensation flow patterns were visualized and investigated. Experiments were conducted for different operating conditions. The pressure at the channel exit is equal to the atmospheric pressure. Different instantaneous and periodically two-phase flow patterns inside a miniature tube are identified and analyzed. The location of the interfacial instabilities, the distribution of the film thickness, and the capillary pressure are measured. 2. Experimental setup Fig. 1 shows the experimental setup for two-phase flow visualization. The experimental apparatus consists of the electric steam boiler where the steam is generated (1), the valve (2), the experimental mini-condenser (3), the second mini-condenser (4), and the weighing system (5). The temperature and the pressure at the channel inlet are measured using the microthermocouples and a pressure sensor. The vapor enters in the test section at the saturated state and
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235 Camera P
(2)
(3) (4)
(1) Boiler
P
(2) Valve Boiler
(1)
(3) Test section (4) Second mini-condenser
(5)
(5) Weighing system Balance
Fig. 1. Experimental system.
the condensation appears along the surface of the miniature tube. The cooling water flows in counter flow of the two-phase flow inside the minichannel. The inlet and the outlet temperatures of the cooled water are measured through the chromel–alumel microthermocouples. The liquid and the vapor at the channel exit were cooled inside the second condenser in order to condense all the vapor mass flow. The exit liquid temperature of the second condenser was measured by means of microthermocouples in order to be sure that the liquid was subcooled. The second condenser is cooled using water and the cooling heat flow rate is measured. The total mass flow rate was measured by weighing the condensate flow using a microbalance at the outlet of the second condenser. The test section shown in Fig. 2 has an effective length of 690 mm. The miniature glass tube was 0.78 mm inner diameter and 0.8 mm outer diameter. It is cooled using water flowing inside a glass tube of 10 mm diameter. A convergent was placed at the channel inlet and thereby uniform vapor velocity profile has been assumed at the channel inlet. The condensate flow rate inside the miniature tube is determined from the energy balance on the cooling waterside. The cooling water flow rate is measured using the flow meter. A Labview data acquisition system
Fig. 2. Test section.
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has been used to record all temperature measurements for each experimental condition. Experiments were conducted using distilled water vapor as the working fluid. The cooling heat flow rate, the saturated temperature and the vapor pressure at the channel inlet were varied. A high-speed camera with spatial resolution of 512 · 480 pixels was used to capture the two-phases flow images. The flow patterns were recorded using the maximum frame rates of 1000 frames per second. The data acquisition system was used to record the images of the two-phase flow for transient state. The inlet steam pressure and the flow rate of the cooling water were regulated during experiments. The outlet condensate flow was at the atmospheric pressure. Different two-phase flows were observed inside the miniature glass tube by varying the cooling heat flow rate or the steam mass flux. Before each experiment, the boiler was discharged in order to evacuate the incondensable gases. All the results presented in this paper were obtained using the pure vapor of distilled water. 3. Results and discussion Different condensation flow patterns were identified for different experimental conditions. The vapor pressure and temperature, and the total mass flow rate were controlled at the channel inlet. The cooling heat flow rate was imposed during experiments by adjusting the water flow rate and the inlet water temperature. 3.1. Condensate flow patterns For inlet pressure of 73.6 kPa, and inlet vapor temperature of 99.1 C, the annular two-phase flow was observed. The average mass velocity at the channel inlet was deduced from the total mass condensate liquid measured by weighting and it was of 82 g/cm2 s. Fig. 3 shows an example of images that recorded during this experiment. Note that the flow direction is from the right to the left with only vapor entering in the miniature tube. Photographs of the two-phase flow patterns show that the condensate flow is periodic and condensation process is unsteady. The vapor is condensed along the cooling surface and thereby the thin liquid film appears. For this experiment, the annular flow occupies the entire channel. Fig. 3d and e show an example of photographs that illustrate the wave formation at the liquid–vapor interface at the bottom part of the tube. In general, the interfacial waves resulted from the interfacial shear between the liquid and vapor phases moving at difference velocities (Kelvin–Helmotz instability). Therefore, the liquid resulting from vapor condensation accumulates and forms wave at the surface. The wave growths during time and attains the limit value for which the waves on both part of the tube coalesce. Therefore, the vapor flow cuts out (see Fig. 3b and c) and the liquid fills up the space between the inlet annular flow and the injected vapor. The down stream of the annular flow travels the channel because of the
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Fig. 4. Annular/spherical bubbly flow (73.6 kPa, 33 g/cm2 s).
Fig. 3. Annular flow (73.6 kPa, 82 g/cm2 s).
incoming vapor and the process will be repeated. The annular flow appears when the interfacial shear predominates on the capillary and the gravity forces. Therefore, the wavelength becomes very large and liquid–vapor interface becomes stable. However, when the condensate film attains a significant thickness on the heat exchange surface, the vapor travels in channel with difficulty and the difference between the vapor and liquid velocities increases. An accumulation of the condensate vapor occurs and the instability appears on the heat exchange surface. For inlet pressure of 73.6 kPa and inlet vapor temperature of 96.7 C, the annular flow with the continuous injection of the spherical bubbles is observed. Photographs of flow patterns during this experiment are reported in Fig. 4. The average mass velocity is 33 g/cm2 s. In the first photograph, the upstream of the flow is constituted by the annular flow and the down stream of the flow is occupied by the spherical bubbly flow. At the end of the annular flow, the shape of the liquid–vapor interface can be seen and it has a form of spherical cap. The second image shows the strangled vapor flow because of the instability and the injection of the third bubble. The wave formed at the bottom part of the channel is bigger than the wave at the top of the channel. In fact, the draining of the condensate film from the top to the bottom part of the channel under the gravity force increases the liquid film thickness on the bottom part of the channel. This effect was called stratification for condensation in the macrochannel. It is negligible when the channel diameter was reduced below 1 mm [5]. It seems that the instability occurs earlier for low mass velocity
(33 g/cm2 s) (see Fig. 3) because the liquid film thickness increases with decreasing the inlet vapor velocity. After detachment of each bubble, the length of the annular flow is reduced and the reverse vapor flow from the left to the right of the channel is observed. The third photograph illustrates that the diameter of the vapor flow increases at the channel inlet because the liquid fills up the space of each injected bubble. Therefore, the interfacial liquid pressure is probably increased, and the liquid film thickness on the heat exchange surface is reduced (Fig. 4c). For the same experimental conditions (Pv = 73.6 kPa and Tv = 96.7 C), as the inlet average mass vapor velocity increases till 50 g/cm2 s, the length of the annular flow and the number of the interfacial waves on the vapor surface
Fig. 5. Wavy annular and bubbly flow (73.6 kPa, 50 g/cm2 s).
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
increase. Examples of photographs of two-phase flow patterns were reported in Fig. 5. The first photograph shows that the two-phase flow is constituted by the annular flow in the channel inlet and the spherical bubbly flow occurs at the down stream of the flow (Fig. 5a). This photograph presents the zone of the bubble injection and it shows that the stratification effect is less significant compared to the previous experiment (Fig. 4b). In general, an asymmetric of the liquid film around the tube results from the stratification effect. During this experiment, the wavy surface of
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the liquid film was observed (Fig. 5b). The neighboring waves at the top and the bottom of the tube have approximately the same amplitude. Therefore, increasing the inlet vapor velocity reduces the effect of stratification. The bubbles move inside the channel from the injection zone to the channel exit, in contact with the upper portion of the channel because of the capillary force. During this experiment, the two-phase flow changes in the space and with time. Fig. 6 presents the entire sequence of the two-phase flow patterns. This sequence is periodic and it is repeated
Fig. 6. The complete sequence of the wavy annular and bubbly flow (73.6 kPa, 50 g/cm2 s).
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approximately at any second. The number of the injected bubbles is approximately 10 for each sequence. The reverse vapor flow from the left to the right of the channel is observed after the injection of the last bubble. This phase was reported in the photograph recorded at 376 ms. As the annular flow was reversed, the bubbles move the channel from the left to the right during 80 ms. At t = 488 ms, the bubbles travel the channel from the right to the left, but at t = 568 ms the bubbles flow is reversed during 152 ms. At t = 720 ms, the bubbles move from the right to the left and leave the channel at t = 1000 ms. For range of time between 448 ms and 880 ms, Fig. 6 illustrates that the distance between the two neighboring bubbles and the bubbles sizes are variable during the oscillatory bubbly flow.
3.2. Analysis of flow patterns – influence of the cooling heat flow rate For inlet pressure of 73.59 kPa, and inlet vapor temperature of 99 C, the annular/spherical bubbles and slug bubble are produced. The inlet temperature of the cooling water was fixed to 14 C but the cooling heat flow rate was varied. The vapor temperature and pressure at the channel inlet were fixed during experiments. For each cooling heat flow rate, the flow pattern is constituted by the annular flow at the upstream flow and the slug bubbly flow at the downstream flow. Fig. 7 shows an example of the periodic two-phase flow sequence that obtained for inlet mass velocity of 136 g/cm2 s. The first image shows that the two-phase flow is annular and the vapor flow length
Fig. 7. The complete sequence of the smooth annular and slug bubbly flow (73.6 kPa, 136 g/cm2 s).
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
increases during time. The first instability appears and the first bubble was injected. This bubble has an elongated form and it called the Taylor’s bubble. After this phase, the length of the annular flow increases and the second spherical bubble was injected. Others instabilities appeared and two other spherical bubbles were injected resulting from the incoming vapor at the channel inlet. The bubbles flow to the channel exit in proximity of the channel top because of the buoyancy forces. This phenomenon is also observed by Mederic et al. [3,4] for condensation of pentane inside a minichannel. When the Taylor’s bubble attains the channel exit, the reverse flow occurs from the exit to the inlet channel (photograph at t = 718 ms). The hemispherical meniscus is formed (photograph at t = 726 ms) and the bubbles leave the tube (photograph at t = 806 ms). The analysis of the periodically condensate flow and the influence of the cooling heat flow rate on the two-phase flow have been conducted by studying the cycle of the condensate flow. The cycle is defined as the temporal displacement distances of the injected bubbles and the annular flow. Fig. 8a shows an example of a sketch of the twophase flow patterns inside a minichannel at certain instant of time, where the upstream of the injection flow is occupied by the annular flow and the downstream is occupied by the slug bubbly flow. The aim of this figure is to show the displacement distance of the annular flow meniscus,
La Lb
Channel
denoted by La, which was measured from the channel inlet and along the axial direction. The displacement distance of the bubbles meniscus, denoted by Lb, was also measured along the axial direction, from the channel inlet to the meniscus of the bubble. Fig. 8b illustrates the temporal variation of the distances La and Lb for the periodically condensate flow shown in Fig. 7. It is noted that for the annular flow, La increases linearly during time until the first wave appears at approximately 170 ms. After that, it can be seen that La becomes sensibly uniform because the incoming vapor condenses and it is retained in the zone where the wave is formed. Therefore, the interfacial wave amplitude increases along the radial direction during the time until the injection of the first elongated bubble at approximately 240 ms. At this time, La decreases suddenly and induces the reverse condensate flow. Fig. 8b illustrates this phenomenon and it shows that after 240 ms, the distances La and Lb are variable very slowly because of the damping of both the annular and the bubbly flows. During this period of cycle (240 ms < t < 300 ms), the incoming vapor is condensed and it is retained to flow when the second wave appears. Therefore, the interfacial amplitude of the wave increases and the injection of the second bubble is produced at approximately 300 ms. After this moment, the process is repeated for the third and fourth injected bubbles. The sizes of the injected bubbles are reduced along the minichannel because of the condensation of the vapor at the interface of the bubbles. The velocity of the annular flow meniscus is deduced from the profile of the distance La as follows: U¼
Vapor
Vapor
Vapor
Liquid
Injected bubble
1231
dLa dt
ð1Þ
Fig. 9 shows the temporal evolution of the velocity U. It shows that U decreases during time because of the increase
Annular flow
U [mm / s]
L a [mm]
120
16
L [mm]
Velocity
20 14
Lb
18
profile of La
100
12
16
80
10
14
60
La
12
8
Injection of the bubble 1
10 6
40
Injection of the bubble 2
8
Injection of the bubble 3
4
6
Annular flow bubble 1 bubble 2 bubble 3 bubble 4
4 2
0
2
Injection of the bubble 4 0 0
0 0
100
200
300
400
500
600
20
700
Time [ms]
Fig. 8. The distance of the meniscus displacement (73.6 kPa, 136 g/cm2 s).
100
200
300
400
500
600
-20 700
Time t [ [ms] ]
Fig. 9. The temporal evolution of the axial vapor velocity (73.6 kPa, 136 g/cm2 s).
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Therefore, the first wave appears nearly to the channel inlet compared to the case when the mass vapor velocity was 136 g/cm2 s. It can be concluded from Fig. 10a that the instability appears later when the mass velocity decreases, this confirms that the condensation has a stabilizing effect. During 600 ms, the number of the produced instabilities is reduced to 50% when the mass vapor velocity decreases from 136 g/cm2 s to 84 g/cm2 s. Fig. 10b shows the evolution of the meniscus velocity of the annular flow following the axial direction. The damping of the vapor flow is observed when the mass velocity decreases because the quantity of the condensate mass increases and it tends to reduce the shear stress at the liquid–vapor interface. The results presented in this figure confirmed the damping effect of the condensation on the interfacial waves initiation.
L a [mm]
16 14
136 g/cm2s 30W
12 10 8
38W 84 g/cm2s
6 4 2 0 0
100
200
300
400
500
600
700
Time [ms]
3.3. Local evolution of the liquid film thickness
U [mm/s] 120 3884Wg/cm²s
30136 W g/cm²s
100
80
60 Injection of the second bubble for 84 g/cm²s
Injection of the first bubble for 84 g/cm²s
40
20
Injection of the bubble 1
0 Injection of the bubble 2
Injection of the bubble 3
-20 0
100
200
300
400
500
Injection of the bubble 4
600
700
Time [ms]
Fig. 10. Influence of the velocity of the annular flow meniscus (73.6 kPa).
of the condensate film. It is noted that the velocity U decreases quickly from approximately 80 mm/s to 4 mm/s during the growth phases of the first wave. This phenomenon was observed for each wave growth on the heat exchange surface because the condensate vapor was retained at the wave location. During wave growth, the condensate film is reversed and the vapor velocity decreases under the shear stress at the liquid–vapor interface. After the detachment of the first bubble, the vapor velocity decreases and it ranges between 0 and 20 mm/s during the short phases of the bubbles growth and injection. The temporal evolution of La for the periodic condensate flow is shown in Fig. 10a for inlet pressure of 73.59 kPa, and inlet vapor temperature of 99 C, and for two mass velocities (84 g/cm2 s and 136 g/cm2 s). The onset annular length (Lo) is defined as the distance between the channel inlet and the zone where the first bubble is detached. It is shown that decreasing the mass velocity decreases Lo because the liquid film thickness increases.
The heat transfer inside a channel is very dominated by the thermal resistance of the condensate film. The film thickness represents the most important property required to predict the local heat transfer coefficient and to localize the zones where the heat transfer is intensified. The local distribution of the film thickness was determined from the images processing for the annular flow. The essential step is to produce the binary image (image threshold) in which the darker regions produced by vapor flow and the liquid–vapor interface, are separated from the light zones (condensate film). The film interface is smooth and provides a good contrast for detection of the liquid contour. However, when the wave appears on the liquid–vapor interface, the deformation of the interface scatters most the light and the contrast becomes poor in this zone. This disturbance represents a small portion of the total images of each given sequence. In this work, it is found that the tube length affected by the waves represents 10–15% of the total condensate length. In general, several sources of uncertainty exist when extracting quantitative data from images. In this paper, the uncertainty due to the illumination and optics systems is assumed to be negligible. The essential uncertainty in the liquid film thickness was introduced by the image processing and it was estimated to be lower than 10%. The thickness of the liquid film varies during time and along the length of the minichannel. The experimental data presented in Fig. 11a–c were obtained for inlet pressure of 73.59 kPa, inlet vapor temperature of 99 C, and for mass velocity of 136 g/cm2 s. Fig. 11a shows the distribution of the liquid film thickness for annular flow at t = 80 ms. The condensate film is thinner at the channel inlet and increases far from this zone because during condensation of the vapor, the interfacial shear stress decreases along the channel and reduces the interfacial vapor velocity. For this experiment, the total condensate length was approximately 4.2 mm. Fig. 11a shows that the interfacial wave appears at 75% of the total condensate length. The interfacial wave amplitude is not uniform around the chan-
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
400
1233
δ [µm]
At bottom the upperside side The At the bottom The upper side side
350
t = 130 ms 0.9
Condensate length
300
δ/R
1
0.8 250
wave initiation
0.7 0.6
200
0.5 150 0.4
t = 130ms t = 154ms t = 170ms t = 210ms t = 226ms
0.3
100
0.2 50 0.1 0
0 0
1
2
3
4
5
0
2
4
Tube length [mm]
0.2
6
8
10
Tube length [mm]
Nux
t = 226 ms 0.18
t = 218 ms
0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
2
4
6
8
10
Tube length [mm]
Fig. 11. Local characterization of the annular flow (73.6 kPa, 136 g/cm2 s).
nel because of the stratification effect. It is about 100 lm and 150 lm at the upper and the bottom sides of the tube respectively. The liquid film at the bottom part is seen to be thicker than on the top wall over most of the axial length for the annular flow. The condensate film thickness is higher on the bottom side than on the upper side of the channel because the liquid was drained from the upper to the bottom part of the tube under the effect of the gravity. For all experiments, the condensation flow is unsteady. The local film thickness and the complete condensation length were changed during time (Fig. 11b). This figure presents the film thickness distribution only at the bottom part of the channel for more clarity. It is shown that the film thickness ranges between 30% and 60% of the tube radius near
the channel inlet. At t = 176 ms, a significant variation in the film thickness is observed along the channel and the large quantity of the liquid is collected at 3.4 mm far from the channel inlet. The wave formed at this location has achieved the very significant amplitude (0.85R). It tends to form a slug bubble at the end of the vapor flow. For each time, the liquid film thickness decreases in the downstream direction before converging because of the capillary force (Fig. 11b, zone A). In this zone, Zhang et al. [14] are also observed that the liquid thickness decreases for condensation inside a miniature tube. The analysis of the local heat transfer coefficient is studied by using the well-known Nusselt theory [20] defined for laminar film condensation. The Nusselt theory provides the
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local Nusselt number as a function of the local film thickness as follows: 2 1=3 lf 1 ð2Þ Nux ¼ d q2f g
1000
3.4. Local evolution of the capillary pressure
100
ð3Þ
where Pd is the disjoining pressure defined as: Pd ¼
A d3
ð4Þ
where A is the Hamaker constant. Begg et al. [5] defined previously the pressure difference for condensation inside a minichannel as follows: Pv PL 8 9 " 2 #3=2 =
The end of the annular flow
t = 226 ms
800 700
P c ¼ P v P L ¼ rK P d
t = 130 ms
900
According to this theory, the local Nusselt number was deduced from the local distribution of the film thickness measured just before the detachment of the bubble. Fig. 11c shows that the local Nusselt number deteriorates in the zone where the wave is formed because the thermal resistance of the condensate film becomes significant in this location. The Nusselt number near the channel inlet is very high because the liquid film is thinner in this zone.
It is known that for the condensation inside a microchannel the surface tension effect predominates but it was usually neglected in the macro scale channels. From experimental data, it can be concluded that the stratification effect is low except in the zone where the complete condensation occurs and the slug bubbles were produced. In this zone, the significant mass of liquid is collected and the curvature of the liquid–vapor interface results from the interaction between the shear stress and the predominant capillary force. The combined effects of the disjoining pressure, the thermo-capillary effects, and the dynamic flow cause the variation of the condensate film in a capillary tube. As defined by the known Young–Laplace equation, the wetting characteristics and the surface tension result in a pressure difference between the liquid and the vapor, which can be shown to be:
Pc [Pa]
Instability zone 600 500 400 300 200
0 0
1
2
3
4
5
6
7
8
9
Tube length [mm]
Fig. 12. Local capillary pressure profiles (73.6 kPa, 136 g/cm2 s).
of the film (t = 80 ms), the capillary pressure is approximately uniform along the channel length and achieves a significant value near the end of the annular flow where the meniscus-like interface is formed. For the same experimental condition, the capillary pressure distribution at t = 176 ms is also presented in Fig. 12. The maximum values of the capillary pressure are obtained in the zone where the wave was formed. 4. Conclusions The visualization and the experimental measurements for condensation flow patterns inside a single miniature tube has been studied. It is shown that the two-phase flow inside the channel depends on time and the location. Annular, slug bubbly, spherical bubbly, and wavy flows are identified and analyzed experimentally. The vapor flow was decelerated and the number of the instabilities was reduced when the inlet vapor mass velocity decreases. The condensation has a stabilizing effect. The analysis of the local distribution of the condensate film thickness shows that the liquid film is thinner at the channel inlet and increased far from this zone. This paper shows the presence of the periodic two-phase flows represented by the cycles in order to show the zones where the instabilities were produced and the bubbles were injected. The reverse annular flow is observed at the end of each periodic flow. The stratification effect is not significant for condensation inside the miniature tube because when the hydraulic diameter decreases, the effects of surface tension increasingly counteract the effects of gravity and extending the size of the annular flow pattern. The liquid film is wavy and it is unsymmetrical. The maximum values of the capillary pressure are measured in the waves locations and near the end of the annular flow. Measurements
H. Louahlia-Gualous, B. Mecheri / Applied Thermal Engineering 27 (2007) 1225–1235
show that the velocity of the annular flow meniscus decreases quickly during the waves growth because the thinner liquid flow is probably reversed and decreases the vapor shear stress at the liquid–vapor interface. References [1] Y. Yan, T. Lin, Condensation heat transfer and pressure drop of refrigerant R134a in a small pipe, Int. J. Heat Mass Transfer 42 (1999) 697–708. [2] W.W.W. Wang, T.D. Radcliff, R.N. Christensen, A condensation heat transfer correlation for millimeter-scale tubing with flow regime transition, Exp. Therm. Fluid Sci. 26 (2002) 473–485. [3] B. Mederic, M. Miscevic, V. Platel, P. Lavieille, J.L. Joly, Experimental study of flow characteristics during condensation in narrow channels: the influence of the diameter channel on structure patterns, Superlattices Microstruct. 36 (2004) 573–586. [4] B. Mederic, P. Lavieille, M. Miscevic, Void fraction invariance properties of condensation flow inside a capillary glass tube, Int. J. Multiphase Flow 31 (2005) 1049–1058. [5] E. Begg, D. Khrustalev, A. Faghri, Complete condensation of forced convection two-phase flow in a miniature tube, J. Heat Transfer, ASME 123 (1999) 904–915. [6] H.Y. Wu, P. Cheng, Condensation flow patterns in silicon microchannels, Int. J. Heat Mass Transfer 48 (2005) 2186–2197. [7] Y. Chen, P. Cheng, Condensation of steam in silicon microchannels, Int. Commun. Heat Mass Transfer 32 (2005) 175–183. [8] A. Cavallini, G. Censi, D. Del Col, L. Doretti, G.A. Longo, L. Rosseto, Condensation heat transfer and pressure drop inside channels for AC/HP application, in: 12th International Heat Transfer Conference Grenoble, vol. 1, 2002, pp. 171–186. [9] J.S. Shin, M.H. Kim, An experimental study of condensation heat transfer inside a mini-channel with a new measurement technique, Int. J. Multiphase Flow 30 (2004) 311–325.
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