Form for two-phase flow

Unlike previous calculations, the two-phase calculation is extremely complex, and no single correlation can cover the entire range of calculations. The major problem with two-phase calculation is in regard to the correct prediction of liquid holdup in some cases, the calculated liquid holdup is 

COMPRESSIBLE FLUID PRESSURE DROP [ Cllc iaiel CanoM Cleai  

H )c 3 san [gamit+va) kW Maximum Mach minber Maximum veiodty m/a 

Heel Ices/ gein (gaei is evej Coloulele kW -23SS 

Gate/ Ball/ Plug valve hill bore 

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A momentum balance for the flow of a two-phase fluid through a horizontal pipe and an energy balance may be written in an expanded form of that applicable to single-phase fluid flow. These equations for two-phase flow cannot be used in practice since the individual phase velocities and local densities are not known. Some simplification is possible if it... 

These methods can be used to make a crude estimate of the likely pressure drop. A reliable prediction can be obtained by treating the problem as one of two-phase flow. For tube-side condensation the general methods for two-phase flow in pipes can be used see Collier and Thome (1994) and Volume 1, Chapter 5. As the flow pattern will be changing throughout condensation, some form of step-wise procedure will need to be used. Two-phase flow on the shell-side is discussed by Grant (1973), who gives a method for predicting the pressure drop based on Tinker s shell-side flow model. 

At typical waste-water injection temperatures the oxidant (air or oxygen) will form a two-phase mixture with the wastewater. The injector must, therefore, be designed for two-phase flow. WHB-Injectors are... 

To proceed the limiting forms of the Leibnitz and the Gauss theorems , appropriate for two phase flow, are applied. These theorems are considered direct extensions of the single phase theorems examined in sect 1.2.6 so no further derivation is given here. In most reactor model formulations the pipe walls are supposed to be fixed and impermeable. In the limit z —> 0, the limiting form of the Leibnitz theorem for volume reduces to the following relation for area [43, 47] ... 

For two phase flows we need to consider the interface, and a modified form of the theorem is applied (e.g., [8, 9]). Now we may consider a geometric volume, Vk t), bounded by a closed surface, Ak t) + Ai t), which may either be material or not, moving or not. At a given point belonging to this surface Ak t) + Ai t), the unit normal vector n is outwardly directed. 

Forced convective boiling in channels. Here, evaporation of a liquid occurs in flow in a channel (for instance, a round tube). The vapor generated and the remaining liquid form a two-phase flow within the tube, and there are strong interactions between this two-phase flow (which can occur in a number of different forms) and the boiling process. 

Due to the pressure relief vaporization occurs and vapour bubbles are formed inside the hquid column. As a consequence the level rises. The surface of the liquid column then becomes a surface of a mixture of hquid and vapour. Leaks below this surface are treated according to the methods for two-phase flow. 

The equation is valid throughout the entire operating range up to the flooding point. The resistance coefficient for two phase flow tvL> acc. to Eqs. (5-6), (5-7) and (5-8), is a function of the Reynolds number of the Hquid and the form factor x of packings, vlrvL = f(M ReL). 

The archetypal, stagewise extraction device is the mixer-settler. This consists essentially of a well-mixed agitated vessel, in which the two liquid phases are mixed and brought into intimate contact to form a two phase dispersion, which then flows into the settler for the mechanical separation of the two liquid phases by continuous decantation. The settler, in its most basic form, consists of a large empty tank, provided with weirs to allow the separated phases to discharge. The dispersion entering the settler from the mixer forms an emulsion band, from which the dispersed phase droplets coalesce into the two separate liquid phases. The mixer must adequately disperse the two phases, and the hydrodynamic conditions within the mixer are usually such that a close approach to equilibrium is obtained within the mixer. The settler therefore contributes little mass transfer function to the overall extraction device. 

No and Kazimi (1982) derived the wall heat transfer coefficient for the forced-convective two-phase flow of sodium by using the momentum-heat transfer analogy and a logarithmic velocity distribution in the liquid film. The final form of their correlation is expressed in terms of the Nusselt number based on the bulk liquid temperature, Nuft ... 

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