Two-phase pressure gradient

Nelson RA, Pasamehmetoglu KO (1992) Quenching phenomena. In Hewitt GF, Delhaye JM, Zu-ber N (eds) Post-dryout Heat transfer. CRC, Boca Raton, pp 39-184 Owens WL (1961) Two-phase pressure gradient. In ASME International Developments in Heat Transfer, Part II. ASME, New York... 

Making the approximation that the value of the friction factor for the two-phase flow is equal to fLO> the frictional component of the two-phase pressure gradient is given by... 

Two-phase pressure gradient is defined as the variation of the internal pressure per unit reactor length. The pressure gradient is related to the mechanical energy dissipation owing to the two-phase flow... 

During in-tube condensation, the local two-phase pressure gradient, when gravity is neglected, may be written in terms of frictional and acceleration components... 

The two-phase pressure gradient is estimated using equation (4.19) in terms of Xmod and streamline flow and the gas is in turbulent regime, C = 12 and... 

Two-phase pressure gradient Pressure gradient due to film region... 

Ratio of local two-phase pressure gradient to pressure gradient for liquid flow only as a function of quality and pressure. (Data from Todreas, N.E. and Kazimi, M.S., Nuclear System. I Thermal Hydraulic Fundamentals, Hemisphere, New York, 1990.)... 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

Figure 6.9. Pressure drop gradient and liquid holdup in liquid-gas concurrent flow in granular beds. [Sato, Hirose, Takahashi, and Toda, J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (a) Correlation of the two phase pressure drop gradient A P/L, = 1.30 + 1.85Y-0 85. (b) Correlation of frictional holdup hL of liquid in the bed a, is the specific surface, 1/mm, d is particle diameter, and D is tube diameter, h, - 0.4a]/3Y 22.

More recently, based on the notion of the fractional pipe surface in contact with the liquid, Kaminsky [1998] has developed a new method for the prediction of the two-phase pressure drop for the flow of a mixture of gas and a power-law fluid. This method is implieit in pressure gradient (and therefore requires an interative solution) and also neeessitates additional information about the fraction of the pipe surface in contact with liquid which is not always available. 

From the first assumption they proposed that the two-phase pressure drop could be determined from the pressure gradient of either the liquid or vapor phase flowing independently. For the case of adiabatic flow (no heat input to the transfer line) this results in the following relationship ... 

Consideration will now be given to the various flow regimes which may exist and how they may be represented on a Flow Pattern Map to the calculation and prediction of hold-up of the two phases during flow and to the calculation of pressure gradients for gas-liquid flow in pipes. In addition, when gas-liquid mixtures flow at high velocities serious erosion problems can arise and it is necessary for the designer to restrict flow velocities to avoid serious damage to equipment. 

There are two types of gradient programmer. In the first type, the solvent mixing occurs at high pressure and in the second the solvents are premixed at low pressure and then passed to the pump. The high pressure programmer is the simplest but most expensive as it requires a pump for each solvent supply. There can be any number of solvents involved in a mobile phase program, however, the majority of LC analyses usually require only two solvents but up to four solvents can... 

The two-phase frictional pressure gradient is obtained from ... 

Fig. 5.30 Comparison of the two-phase frictional pressure gradient between micro-channel data and homogeneous flow model predictions using different viscosity formulations. Reprinted from Kawahara et al. (2002) with permission...

Finally, a comparison of the two-phase frictional pressure gradient data with the predictions of the Lockhart-Martinelli correlation using different C-values is shown in Fig. 5.32, including C = 5, C = 0.66, C calculated from the Lee and Lee model (2001), and C = 0.24. The conventional value of C = 5 again significantly over-... 

The Martinelli correlations for void fraction and pressure drop are used because of their simplicity and wide range of applicability. France and Stein (6 ) discuss the method by which the Martinelli gradient for two-phase flow can be incorporated into a choked flow model. Because the Martinelli equation balances frictional shear stresses cuid pressure drop, it is important to provide a good viscosity model, especially for high viscosity and non-Newtonian fluids. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

Venkateswararao et al. (1982), in evaluating the flow pattern transition for two-phase flow in a vertical rod bundle, suggested the calculation of pressure gradient for annular flow by... 

Chisolm, D., and L. A. Sutherland, 1969, Prediction of Pressure Gradients in Pipeline Systems during Two-Phase Flow, Symp. on Fluid Mechanics and Measurements in Two-Phase Flow Systems, Leeds, pp. 24-25. (3)... 

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