Pressure drop in two-phase flow

In two-phase flow, the boiling temperature falls in the direction of flow as a result of the pressure drop. This results in a change in the driving temperature drop decisive for heat transfer along the flow path. Calculation of the heat transfer without simultaneous investigation of the pressure drop is therefore impossible. The fundamentals steps for this shall be explained in the following. 

4 Convective heat and mass transfer. Flows with phase change 

In the calculation of the pressure drop, we will consider a channel inclined at an angle 7 to the horizontal, through which a two-phase fluid flows, Fig. 4.50. 

The forces exerted by the pressure, the friction forces at the channel wall and gravity all act on a volume element of length dz, as illustrated in the picture. We are presuming the flow to be steady and one-dimensional and that the cross section of the channel is constant. The pressure, density and momentum flux over a cross section are only dependent on the flow path z. The momentum balance implies that the sum of the pressure, friction and gravitational forces are equal to the change in momentum 

The flow momentum is made up of that of the gas and the liquid, according to 

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Dukler, A. E. Moye Wicks III, and Cleveland, R. G. <4. I. Ch. E. Jl. 10 (1964) 38. Frictional pressure drop in two-phase flow. A comparison of existing correlations for pressure loss and holdup. 

Transient Two-Phase Flow in Rod Bundles Pressure Drop in Two-Phase Flow... 

Since the pressure drop in two-phase flow is closely related to the flow pattern, most investigations have been concerned with local pressure drop in well-characterized two-phase flow patterns. In reality, the desired pressure drop prediction is usually over the entire flow channel length and covers various flow patterns when diabatic condition exist. Thus, a summation of local Ap values is necessary, assuming the phases are in thermodynamic equilibrium. The addition of heat in the case of single-component flow causes a phase change along the channel consequently, the vapor void increases and the phase (also velocity) distribution as well as the momentum of the flow vary accordingly. 

So far the pressure drop in two-phase flow in pipes and rod bundles has often been predicted by empirical correlations, despite the development of analytical models as described in the previous sections. Thus, in the highly subcooled boiling region,... 

Dukler, A. E., M. Wicks, and R. E. Cleveland, 1964, Frictional Pressure Drop in Two Phase Flow, B. 

Duckler AE, M Wicks III, RG Cleveland. Frictional pressure drop in two-phase flow B. An approach through similarity analysis. AIChE J. 10 44—51, 1964b. 

Ferguson MEG, PL Spedding. Measurement and prediction of pressure drop in two-phase flow. J Chem Technol Biotechnol 62 262-278, 1995. 

Pressure drop in two-phase flow is found in terms of pressure drops of the individual phases with empirical multipliers. The basic relation is... 

Another possibility for the investigation of the pressure drop in two-phase flows exists in the determination of the frictional pressure drop of the gas and the liquid, under the assumption that the total mass of the fluid would be flowing through the tube either as liquid or as gas. In this case the factors L0 and 4>G0 are defined... 

The method that is usually adopted for the calculation of pressure drop in two-phase flow systems is based on empirical correlations, and involves putting parameters 4>g and ( f)Lagainst the variable x as defined by the following equations ... 

Lockhart and Martinelli proposed that the pressure drop in two-phase flow can be related to the equivalent pressure drop in single-phase flow using a two-phase parameter [72]. For the gas phase, the single-phase pressure drop is given by... 

This chapter describes the various hydraulic phenomena that occur in a bed of random dumped tower packing shapes. First, those factors that influence only gas-phase flow are considered. Then, the more complex hydraulics that result when liquid is introduced onto the packed bed are examined. Finally, a method for predicting pressure drop in two-phase flow through the packed bed is developed. 

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