Patterns stratified wavy flow

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. 

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 (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. 

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. 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...

The stability conditions derived from linear analysis represent the necessary conditions for maintaining a smooth interface configuration. Therefore, Equations 18 and 19 should predict the stratified-smooth to stratified-wavy transitional boundary. The SS/SW transition is one of the flow pattern transitions reported in experimental studies of horizontal and inclined two-phase flows, (e.g., Mandhane et al. [77], Taitel and Dukler [19], Shoham [78], Lin and Hanratty [37,75], Andritsos and Hanratty [39,81], Simpson et al. [79], Luninski [80], Nakamura et al. [82]).The various flow patterns boundaries are conventionally mapped in the two-phases flow rates coordinates, U. vs. U. ... 

Thus, in the extreme of large or small diameter conduits, the stratified-smooth/ stratified-wavy boundary is predicted by Equations 33.1 or 33.2, respectively, while there exists an intermediate range of pipe diameters in between, where neither of these equations predict the locus of flow pattern transition. In these systems, transition from stratified smooth pattern coincides with the L-T transition of the gas phase and is predicted by the locus of operational conditions where Re = Re, (Brauner and Moalem Maron [105]). 

Thus, while the neutral stability boundary may represent preliminary transition from smooth-stratified flow to a wavy interfacial structure, the well-posedness boundary, which is within the wavy unstable region, represents an upper bound for the existence of a stratified wavy configuration. Beyond the well-posedness boundary transition to a different flow pattern takes place. In the ill-posed region, the model is no longer capable of describing the physical phenomena involved therefore, amplification rates predicted for ill-posed modes or numerical simulation of their growth is actually meaningless. 

For the sake of clarity, the focus in Figure 18 is on the interplay and practical relevance of the stability boundaries (ZNS or ZNS) and the L-T laminar/turbulent flow regime transitional line in predicting the stratified-smooth/wavy flow pattern transition. Other transitional boundaries, which confine the stratified-smooth and stratified-wavy zones, are shown in Figure 19. For relatively low gas rates, the stratified-smooth zone is bounded by the slug or bubbly patterns while the stratified-wavy zone, at high gas rates, is bounded by the transition to annular pattern. 

The two phase flow patterns in horizontal line are bubble, plug, stratified, wavy, slug, annular, and spmy (dispersed), in the order of increase vapor flow. These flow regions will be affected by fluid pressure, line size, liquid surface tension, and line inclination (see [4J p. 7-14 for more details). 

Flow Regimes in Multiphase Reactors. Reactant contacting, product separations, rates of mass and heat transport, and ultimately reaction conversion and product yields are strong functions of the gas and Hquid flow patterns within the reactors. The nomenclature of commonly observed flow patterns or flow regimes reflects observed flow characteristics, ie, armular, bubbly, plug, slug, spray, stratified, and wavy. 

Additional research on the prediction of flow patterns is a necessity, for until detailed stability criteria are developed for the transition from one flow pattern to another, there is no alternative to the empirical flow pattern charts. Some progress in theoretically defining the transition from stratified to wavy or slug flow has been made by Russell and Etchells (R3). Inaccuracy and uncertainty in flow pattern prediction makes estimation of the in situ hydrodynamic quantities and the rate of heat transfer a difficult task. 

In two-phase systems of > 1, surface tension contributes a dominant stabilizing term in the well-posedness criterion. Hence, the region of stable wavy stratified pattern extends and the transition to annular flow is delayed to higher gas rates, compared to those predicted by (infinite) long wave analysis (k —> 0). For instance, for air-water flow in a 1 inch pipe, < 0.01, while for D = 0.4cm, = 20. 

Although many flow patterns are possible, including flows described as (1) bubble, (2) plug, (3) stratified, (4) wavy, (5) slug, (6) annular, and (7) spray or dispersed, it is felt that these merge smoothly into one another so that the single relationship of Fig. 13-3 can be used. 

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