Stratified-wavy flow

Stratified-Wavy. At high vapor velocities, the flow deviates from the idealized situation just described. First of all, heat transfer in the stratified liquid pool at the bottom of the tube may not be negligible. Secondly, axial interfacial vapor shear may influence the motion and heat transfer in the thin film region around the top part of the tube. Dobson [144] studied this more complex situation and reported that stratified-wavy flow exists when G < 500 kg/m2s and Frm < 20, where Frm is a modified Froude number given by ... 

In this mode of flow, the gravitational forces dominate and the gas phase flows in the upper part of the pipe. At relatively low flowrates, the gas-liquid interface is smooth, but becomes ripply or wavy at higher gas rates thereby giving rise to the so-called wavy flow . As the distinction between the smooth and wavy interface is often ill-defined, it is usual to refer to both flow patterns as stratified-wavy flow. 

In two-phase microscale flows, the liquid phase is laminar for almost all the test conditions, which is rare in macroscale studies. In addition, it is expected in small diameter tubes that the effect of surface tension will become more pronounced while the influence of gravity will become less important and consequently stratified types of flows are rarely observed, i.e. no more fully stratified or stratified-wavy flow... 

It is commonly believed that a correct mathematical presentation of physical situations ought to result in properly posed problems. In two-phase flow problems, however, the existence of an assumed physical situation, e.g., stratified wavy flow configuration, is not certain under all operational conditions. Therefore, ill-posedness in some domains of the parameters space does not necessarily imply that the formulation is globally incorrect. Moreover, the boundary of the well-posed domain may have physical significance since it signals the existence of additional physical features which the original model neglects. When these features become consequential, one expects a different physical behavior, such as transition to a different flow pattern, and a different model is required to simulate this transition. 

The well-posedness boundary (ZRC) (included in Figures 10, 11, 13) represents the limit of operational conditions (U, U, ) for which the governing set of continuity and momentum equations is still well-posed with respect to all wave modes. Hence, it is considered as an upper bound for the stratified-wavy flow pattern. Indeed, the data of stratified-wavy/annular transition follows the ZRC curve in the region of H < 0.5. 

Stratified-wavy flow Increasing the gas velocity in a stratified flow creates waves on the interface which travel in the direction of flow. The wave crests do not reach the top of the pipe. 

The plot of K versus X shows the transitions between stratified and stratified-wavy flow regimes. 

Lockhart and Martinelh (ibid.) correlated pressure drop data from pipes 25 mm (1 in) in diameter or less within about 50 percent. In general, the predictions are high for stratified, wavy, ana slug flows and low for annular flow The correlation can be applied to pipe diameters up to about 0.1 m (4 in) with about the same accuracy. 

Stratified (S) - Liquid flows at the bottom of the pipe with gas at the top. The stratified pattern is subdivided into stratified smooth (SS) where the liquid surface is smooth, and stratified wavy (SW) where the interface is wavy. 

Wavy flow As stratified but with a wavy interlace due to ... 

Figure 3.3 Horizontal flow regime map curves A, B, (Fr) versus Xn curve C, K versus Y curve D, T versus X . (AD, annular dispersed DB, dispersed bubble SW, stratified wavy I, intermittent SS, stratified smooth.) (From Taitel and Dukler, 1976b. Copyright 1976 by American Institution of Chemical Engineers, New York. Reprinted with permission.)...

L Stratified wavy annular Minimum inclination angle to show bubble flow Trajectory of drops tom from liquid film Lift versus buoyant forces... 

At a constant low liquid-flow rate with steadily increasing gas flow, the patterns observed will tend to be stratified, wavy, annular and mist flow. At a somewhat higher liquid rate, stratified, plug, slug, annular, and mist flow occur while at high liquid flows the patterns follow the order bubble, plug, slug, annular, and mist, as gas flow increases. 

Fig. 5. Types of two-phase How in a horizontal pipeline (a) Stratified smooth flow where gas velocity is low. Liquid flows along bottom portion of pipelines with essentially a smooth surface, (b) Stratified flow with a wavy. surface, the waviness caused by increased gas flow velocity, (c) Liquid bridges the pipeline cross section, thus causing slugs or plugs of liquid, which move at a velocity approximately that of ihe flowing gas, (d) Annular flow, in which the liquid essentially flows as an annular film on the pipe wall while gas flows as in a centra) core of the pipe, (e) Dispersed bubble flow usually results when liquid flow rates are high and gas rates are low. Because of comparative density differences, most bubbles are found above the pipe center line. Conditions vary somewhat when the pipeline is in a vertical orientation. After Cindric, Gandhi, and Williams)...

Fig. 4.45 Flow patterns in a horizontal, unheated tube a bubble flow b plug flow c stratified flow d wavy flow e slug flow f annular flow g spray or drop flow...

Wavy flow With increased velocity in stratified flow, waves appear on the surface of the liquid layer. It is possible for droplets to be torn from the tops of the waves to be carried forward in the gas phase. Some droplets may coalesce and fall back into the liquid layer. 

Except for the transition from wavy to stratified-slug flow, the agreement is good. 

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