Two phase frictional pressure drop

Several models have been proposed to evaluate the two-phase mixture viscosity, and the model selected may affect the predicted two-phase frictional pressure drop ... 

Figure 3.42 Two-phase friction pressure drop correlation for G = 1 x 106 lb/hr ft2. (From Baroczy. 1966. Copyright 1966 by Rockwell International, Canoga Park, CA. Reprinted with permission.)...

Figure 3.48 Comparison of potassium and sodium two-phase friction pressure drop data with Lock-hart-Martinelli correlation, and with a simple correlation [1/(1 - a)]. (From Fauskeand Grolmes, 1970. Copyright 1970 by American Society of Mechanical Engineers. Reprinted with permission.)...

In summary, the calculation of pressure drops by the Lockhart-Marti-nelli method appears to be reasonably useful only for the turbulent-turbulent regions. Although it can be applied to all flow patterns, accuracy of prediction will be poor for other cases. Perhaps it is best considered as a partial correlation which requires modification in individual cases to achieve good accuracy. Certainly there seems to be no clear reason why there should be a simple general relationship between the two-phase frictional pressure-drop and fictitious single-phase drops. As already pointed out, at the same value of X in the same system, it is possible to have two different flow patterns with two-phase pressure-drops which differ by over 100%. The Loekhart-Martinelli correlation is a rather gross smoothing of the actual relationships. 

By analogy to single-phase flow, the two-phase frictional pressure-drop can be expressed by the conventional Fanning equation, and thereby a friction factor is defined. These friction factors may be based on liquid properties, gas properties, or on a fictitious single fluid of mean properties obtained by some averaging procedure. Typical definitions, such as those shown in equation (32), have been given and discussed recently by Govier and Omer (G4) ... 

In the calculation of frictional pressure drop it is advantageous to define a few parameters that are suitable for the representation of two-phase frictional pressure drop and the volumetric quality. The frictional pressure drop is often reduced to the pressure drop for single phase flow, using the definitions from Lockhart and Martinelli [4.84]... 

Accurate knowledge of two-phase frictional pressure drop and liquid holdup is essential for design, scale-up, and performance of TBR. The hydrodynamics is affected differently in each flow regime.Of particular interest in the industry is the extensively used trickle flow encountered at low gas and liquid superficial velocities. 

The two-phase flow pressure drops are the direct sum of three contributions the static pressure drop Ap, the momentum pressure drop Apm and the frictional pressure drop Apf. For a horizontal tube, there is no change in static head so Aps = 0. The momentum pressure drop reflects the change in kinetic energy of the flow. Both may be obtained using an appropriate void fraction relation. Thus, the major goal of microscale studies on pressure drop is to find an empirical correlation or simplified concept to correlate the two-phase frictional pressure drops. 

G. Ribatski, L. Wojtan, J. R. Thome, An analysis of experimental data and prediction methods for two-phase frictional pressure drop and flow boiling heat transfer in microscale chaimds, Exp. Thermal Fluid Sci., 2006, 31,1-19. 

The two-phase friction pressure drop ratio as function of Lockhart and Marlinelli parameter Xfor different flow combinations. (Data from Todreas, N.E. and Kazimi, M.S., Nuclear System. I Thermal Hydraulic Fundamentals, Hemisphere, New York, 1990.)... 

Moreno Quiben, X, Thome, J.R., 2007. Flow pattern based two-phase frictional pressure drop model for horizontal tubes, Fart II New phenomenological model. International Journal of Heat and Fluid Flow. 28 1060-1072. 

Example 7.13. If the length of the transfer line in Example 7.12 is 300 m, determine the two-phase frictional pressure drop in the transfer line for adiabatic flow. 

Determine the two-phase frictional pressure drop for adiabatic flow of nitrogen in a 130-m-long transfer line. The latter is a 200-mm nominal Schedule 5 pipe. The total mass flow rate is 6 kg/s with a fluid quality of 0.25. Average pressure in the transfer line is maintained at 540 kPa. The liquid temperature is 95 K where the liquid and vapor densities are 718.6 and 3.731 kg/m, respectively. The liquid viscosity and surface tension are 0.093 mPa s and 5.08 mN/m, respectively. 

In coil visbreaking, the inlet pressure is about 2.5 MPa, which is maintained at higher values to facilitate the transport of the feed. Due to the two-phase frictional pressure drop, the inlet pressure along the reactor length is reduced in about 1.7 MPa. 

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