Smooth stratified flows

SHEAR STRESSES MODELLING IN STEADY SMOOTH STRATIFIED FLOWS, 323... 

In searching for the necessary conditions under which the smooth-stratified flow configuration is stable, linear stability analysis is carried out on the transient two-fluid continuity and momentum Equations 1, 2, 7. The equations are perturbed around the smooth fully developed stratified flow pattern. Following the route of temporal stability analysis h = heKkx-m). gi(icx-[Pg.327]

Experimental data for the limiting conditions of smooth stratified flow also are included in Figure 2. Inspection of the figure indicates that for relatively thick water layers (above H = 0.5 line), the neutral stability line represents a reasonable prediction for the departure from smooth-stratified configuration. Waves growing over thick layers tend to block the upper gas phase flow area, and the transition to stratified wavy regime coincides with the transition to slug flow. However, with... 

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. 

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)...

Stratified Flow. The liquid phase flows along the bottom of the pipe while the gas flows over a smooth liquid-gas interface. It occurs for liquid velocities less than 0.5 ft/sec (0.15 m/sec) and gas velocities of about 2-10 ft/sec (0.6 to 3 m/s). 

In the case of very low Re (<100), a segregated flow is observed in smooth microchannels and mixing occurs by molecular diffusion. In microchannels with stratified flow and diameters of d = 100 pm, the characteristic time of diffusion is in the order of a second, which is by far too long for fast chemical reactions with characteristic reaction times less than a second. 

The stability analysis is concerned with the stability of the interface between the phases, presumably smooth, under fully developed stratified flow conditions. In this case the LHS of the combined momentum equation for the two-phases. Equation 7 vanishes ... 

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]). 

The general implication of the stability boundary (ZNS or ZNS ) and the well-posedness boundary (ZRC) is in defining three zones the area within the stability boundary is well-understood to be the stable smooth stratified zone. Beyond the ZRC boundary, the complex characteristics indicate that the governing equations of the stratified flow configuration are ill-posed with respect to long wave modes in the wave spectra. In this sense, the ZRC boundary represents an upper bound... 

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. 

Stratified flow In this flow complete separation of the two phases occurs with the gas flow near top and the liquid flow near bottom of the pipe. The gas and liquid are separated by an undisturbed smooth interface. 

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. 

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.)...

---