Non-boiling two phase flows are categorized into three types: gas-liquid, liquid-liquid, and solid-liquid two phase flows. The gas-liquid two phase flow has a potential to enhance heat transfer while it could be easily generated (compared with liquid-liquid and solid-liquid flows), so many researchers have focused on the fundamentals of this kind of two phase flows including slug formation, flow pattern, pressure drop, and heat
transfer. The gas-liquid two phase flow in small scales have different modes which are bubbly, slug, churn, slug-annular, and annular flows. Figure 1.4 and Fig. 1.5 show the different types of gas-liquid two phase flows in horizontal and vertical (upward) capillaries.
a)
b)
c)
d)
e)
Figure 1.4: Two phase flow regimes in horizontal small tubes, D=1.097 mm, Triplett [22], a) bubble flow, b) slug flow, c) churn flow, d) slug-annular flow, e) annular flow.
Different flow maps have been published for large and small tube diameters which show the type of two phase flow based on the velocities or superficial velocities of two phases. Since there are some differences between the two phase flows in macroscales and microscales, the flow maps generated for macroscales can not accurately predict the flow regime at the microscale. For example, the two phase flow in microchannels is mainly laminar due to small characteristic length but turbulent in large pipes. Furthermore, the liquid slugs in large scale slug flows usually contain small bubbles but this is not the case in slug flow in microchannels. While flow maps are useful
1 TWO PHASE FLOW AT SMALL SCALES 5
Non-Boiling Two Phase Flow in Micro-channels 16
at different superficial gas and liquid velocities for upward gas- liquid flow in the vertical capillaries. To determine flow patterns clearly and eliminate confusion of terminologies used by various researchers, the specific definitions for different flow patterns are given as follows:
Bubbly flow: Bubbly flow often occurs when superficial gas
velocities are low while superficial liquid velocities are high.
It is characterized by distinct or distorted sphere bubbles; generally, the diameters of the bubbles are less than or equal to the capillary inner diameters.
Taylor flow: Taylor flow (which is also called slug flow,
bubble train flow or segmented flow) is characterized by long bubbles separated by liquid slugs. The lengths of the bubbles are greater than the capillary inner diameters. Thin liquid films exist between the bubbles and the capillary walls.
Slug-bubbly flow: This flow pattern simultaneously has the
characteristics of Taylor flow and bubbly flow. The flow pattern
Figure 1. Schematic diagram of the experimental setup.
Figure 2. Detailed structure of the T-mixer.
Table 1. Specifications of the Capillaries Used in the Experiment inner diameter (mm) length (m) capillary number 1.47 0.761 1 2.37 0.917 2 3.04 0.834 3
Figure 3. Representative flow patterns in the 1.47-mm capillary at a low superficial liquid velocity: (a) UG) 0.0113 m/s, UL) 0.0786 m/s, bubbly flow; (b) UG) 0.3048 m/s, UL) 0.0786 m/s, Taylor flow; (c) UG) 1.2203 m/s, UL) 0.0786 m/s, bubble-train slug flow; (d) UG) 4.4745 m/s, UL) 0.0786 m/s, churn flow; and (e) UG) 11.0351 m/s, UL) 0.0786 m/s, annular flow.
Fig. 2 - Flow Patterns typically arising in micro-channel and mini-channel two phase gas/liquid flows for low superficial liquid velocities, Liu and Wang (2008).
is more disordered and is often considered to be a transition flow pattern.
Bubble-train slug flow: This flow pattern typically consists
of series of bubbles, similar to trains, with a clear interface between the connecting bubbles.12The number of bubbles in a
“train” seems to appear in a random manner. In addition, the shape and size of bubbles are not always uniform, under certain circumstances.
Churn flow: This flow occurs when superficial gas velocities
are large enough for the successive several bubbles to coalesce to one bubble after breaking through the liquid slugs between them. A wave or ripple motion is often observed at the bubble tail with tiny gas bubbles entrained in the liquid slug because of the high superficial gas velocity. To some extent, churn flow is similar to Taylor flow, but the former is more chaotic and disordered.
Annular flow: Annular flow is observed at excessively high
superficial gas velocities and very low superficial liquid velocities. This flow is comprised of a continuous gas phase in the central core and a continuous liquid phase that is deposited on the circumference of the capillary walls.
One noteworthy feature is that the major flow patterns, classified as given previously, can be further subdivided into more-specific flow patterns. In other words, some slight difference in appearance can be observed for the flow pattern with the same name. For example, Figure 4a-c showed the diversity of appearance of bubbly flow due to different superficial gas velocities.
Figures 3 and 4 show typical images of the two-phase flow observed in the 1.47-mm capillary at low and high superficial liquid velocities, respectively. With increasing superficial gas velocities, five distinct flow patternssincluding bubbly flow, Taylor flow, bubble-train slug flow, churn flow, and annular flowsappeared one after another at a constant low superficial liquid velocity in Figure 3. Moreover, these flow patterns were comparative ordered or regular. In contrast, at a high superficial liquid velocity in Figure 4, every flow pattern appeared much more disordered and chaotic. In addition, bubbly flow, slug- bubbly flow, bubble-train flow, and churn flow were recorded in a sequence with increasing superficial gas velocities. Fur- thermore, the comparison of the flow patterns between the low and high liquid velocities were performed. Bubbles of the bubbly
flow in Figure 3 were spherical or spheroidal, and the distances between the bubbles were uniform. Bubbles confined in the capillary rose straight regularly. Figures 4a-c show that the number of bubbles in the bubbly flow increased as the gas velocities were enhanced. Also, the bubbles moving up along the capillary oscillated from one side of the wall to another side, which was similar to the phenomenon noticed by Krishna et al.25In addition, slug-bubbly flow was not observed at the
low superficial liquid velocity, and Taylor flow and annular flow were not noticed at the high superficial liquid velocity.
3.1.2. Flow Pattern Map. Figures 5a, 5b, and 5c show the overall flow pattern maps for the three circular capillaries (with diameters of 1.47, 2.37, and 3.04 mm), where the superficial liquid and gas velocities were used as the ordinate and abscissa, respectively. The solid lines represented the boundaries at which flow pattern transitions occurred. Four major flow patternss including bubbly flow, Taylor flow, churn flow, and annular flowsdivided the flow pattern maps into four regions, where the flow patterns possessed definite characteristics that were easily observed. The two transition flow patterns, slug-bubbly flow and bubble-train slug flow, were situated in the small central transition regions of the flow pattern maps. To predict the pressure drop of Taylor flow exactly, which will be described in section 3.2, quasi-Taylor flow was presented as an indepen- dent flow pattern only in Figure 5. Here, quasi-Taylor flow was defined as the Taylor flow of which the lengths of liquid slugs were smaller than or equal to capillary diameters. The flow patterns in the transition regions represented ambiguity char- acteristics and were judged more subjectively. Because these measurements were on the same order of size for the capillary diameters in this study (millimeters), the effects of diameter on flow patterns were not remarkable. Moreover, the three flow pattern maps in Figure 5 were similar (overall). It is well-known that flow patterns are dependent on not only liquid velocities but also gas velocities. In other words, if the gas (or liquid) velocity is not appropriate, some specific flow patterns will not appear at any liquid (or gas) velocity in Figure 5. Therefore, the flow pattern maps are helpful in determining the operational conditions in industry.
3.1.2.1. Comparison with Existing Transition Correlations. The present experimental data were compared with two famous models that have been developed to predict flow pattern transitions during steady gas-liquid flow in vertical circular tubes: one by Taitel et al.6and another by Mishima et al.8To
predict the operational conditions under which the transitions will occur, it is very important to understand the physical mechanisms of flow transitions. However, considerable dis- agreements among various transition mechanisms still exist. Therefore, the theories with different physical mechanisms sometimes predicted different flow patterns under the same operational conditions.
In 1980, Taitel et al.6 presented a physical model and
developed theoretically based transition equations as follows. For the transition from bubbly flow to Taylor flow, Taitel et al.6gave an expression for the flow at which dispersed bubbles
were observed:
This function was plotted in Figure 6 as curve A; above this curve, bubbly flow existed. However, regardless of the amount of liquid turbulent energy for breaking and dispersing the gas phase, bubbly flow could not exist at a gas void fraction
Figure 4. Representative flow patterns in the 1.47-mm capillary at a high superficial liquid velocity: (a) UG) 0.0113 m/s, UL) 1.6365 m/s, bubbly flow; (b) UG) 0.0727 m/s, UL) 1.6365 m/s, bubbly flow; (c) UG) 1.2203 m/s, UL) 1.6365 m/s, bubbly flow; (d) UG) 2.3259 m/s, UL) 1.6365 m/s, slug-bubbly flow; (e) UG) 4.4745 m/s, UL) 1.6365 m/s, bubble- train slug flow; and (f) UG) 11.0351 m/s, UL)1.6365 m/s, churn flow.
UL) -UG+ 4.0
{
d0.429(σ/FL)0.089 νL0.072[
g(FL- FG) F L]
0.446}
(1)246 Ind. Eng. Chem. Res., Vol. 47, No. 1, 2008
Fig. 3 - Flow Patterns typically arising in micro-channel and mini-channel two phase gas/liquid flows for high superficial liquid velocities, Liu and Wang (2008).
Figure 1.5: Two phase flow regimes in vertical small tubes, Liu and Wang [23]. tool to predict the flow pattern, care must be taken when using them since they are not universal. A sample is shown in Fig. 1.6 for a tube diameter of 1.097 (mm) by Triplett [22]. Recently, some researchers [24, 25] compared the existing flow maps for different microchannel sizes in order to unify flow transition boundaries in the flow maps. For example, Sur and Liu [25] developed a new flow map using the modified Weber numbers as the coordinates. Figure 1.7 shows this flow map.
Typically, microchannels are the channels (or capillaries) with a characteristic length of less than 1 (mm). However different extensions exist in the literature, the following criterion, i.e. the Laplace constant, is one of the mostly used criteria (Gal- biati and Andreini [26] and Triplett et al. [22]):
Dh ≤
r σ
g(ρL− ρG)
Figure 1.6: Flow map, D=1.097 mm, Triplett [22].
where σ and ρ are the surface tension between the two phases and density, respectively. The indexes L and G denote liquid and gas, respectively. A rough estimation of the Laplace constant for air and water at room temperature is around 2.7 (mm).
Gas-liquid slug flows are of interest in the present research as it could lead to a great enhancement in heat transfer and consequently help to design smaller heat sinks/exchangers. A slug flow contains elongated gas bubbles, usually with a length more than the hydraulic diameter of the microchannel, which separate liquid phase into plugs of liquids. These gas bubbles are often, but not always, surrounded by a thin liquid film which acts like a lubrication layer and let the bubbles move faster
Figure 1.7: Two phase flow map reconstructed with the proposed dimensionless pa- rameters as the coordinates, Sur and Liu [25].
than the average velocity of the liquid phase. Slug flows are sometimes called as Taylor flow (Taylor [27]), Plug flow, Bolus flow (Prothero and Burton [28]), or segmented flow (Horvath et al. [29]). Figure 1.8 shows gas-liquid slug flows with different slug lengths.