Stratified wavy/annular 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. 

O stratified-smooth/slug, stratified-smooth/wavy, A stratified wavy/annular, turbulent/laminar transition of upper phase. 

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 transition to annular flow either from the stratified wavy or slug flow is determined by the entrainment process. Thus if the gas (or relative) velocity exceeds the onset of entrainment velocity, the entrainment of wave crests or liquid slugs occurs. In case of slug flow, this leads to the elimination of liquid slugs. Since the part of entrained droplets are deposited on the wall surface, the onset of entrainment leads to the formation of annular flow with liquid wetting the whole surface. However, due to the gravity effect it is expected that the liquid film thickness at... 

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. 

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