Lockhart-Martinelli two-phase flow

The two-phase correction factor fc is obtained from Figure 12.56 in which the term l/Xtt is the Lockhart-Martinelli two-phase flow parameter with turbulent flow in both phases (See Volume 1, Chapter 5). This parameter is given by ... 

FORMAT (5X, LOCKHART-MARTINELLI TWO PHASE FLOW MODULUS , ... 

Lockhart and Martinelli used pipes of one inch or less in diameter in their test work, achieving an accuracy of about -l-/-50%. Predictions are on the high side for certain two-phase flow regimes and low for others. The same -l-/-50% accuracy will hold up to about four inches in diameter. Other investigators have studied pipes to ten inches in diameter and specific systems however, no better, generalized correlation has been found.The way... 

Chisolm, D., 1967, A Theoretical Bases for the Lockhart/Martinelli Correlation for Two-Phase Flow, Int. J. Heat Mass Transfer 10 1767-1778. (3)... 

Lockhart and Martinelli (1949) used only liquid and only gas reference flows and, having derived equations for the frictional pressure gradient in the two-phase flow in terms of shape factors and equivalent diameters of the portions of the pipe through which the phases are assumed to flow, argued that the two-phase multipliers and 4>g could be uniquely correlated against the ratio X2 of the pressure gradients of the two reference flows ... 

Since 1949 the correlations of Lockhart and Martinelli, and of Martinelli and Nelson, have been used or checked by many investigators of two-phase flow phenomena. The assumptions made in the derivations of these correlations would seem to rule out certain flow patterns, e.g.. 

The basic assumptions implied in the homogeneous model, which is most frequently applied to single-component two-phase flow at high velocities (with annular and mist flow-patterns) are that (a) the velocities of the two phases are equal (b) if vaporization or condensation occurs, physical equilibrium is approached at all points and (c) a single-phase friction factor can be applied to the mixture if the Reynolds number is properly defined. The first assumption is true only if the bulk of the liquid is present as a dispersed spray. The second assumption (which is also implied in the Lockhart-Martinelli and Chenoweth-Martin models) seems to be reasonably justified from the very limited evidence available. 

For sufficiently large heat flux to mass flow ratios, the nucleation mechanism predominates and the heat transfer becomes independent of the two-phase flow characteristics of the system. Thus at large values of the boiling number, the heat transfer coefficients are virtually independent of the Lockhart-Martinelli parameter, Xn. 

Motionless Mixers. Major mixer manufacturers agree that the Lockhart and Martinelli parameters for two-phase flow in pipes (9) can also be applied to motionless mixers. To estimate the pressure drop, the single-phase liquid and gas pressure drops are first calculated. The Lockhart and Martinelli para-meter X is found from... 

There are a number of pressure drop correlations for two-phase flow in packed beds originating from the Lockhart-Martinelli correlation for two-phase flow in pipes. These correlate the two-phase pressure drop to the single-phase pressure drops of the gas and the liquid obtained from the Ergun equation. See, for instance, the Larkins correlation [Larkins, White, and Jeffrey, AIChE J. 7 231 (1967)]... 

Some correlations of multipliers are listed in Table 6.7. Lockhart and Martinelli distinguish between the various combinations of turbulent and laminar (viscous) flows of the individual phases in this work the transition Reynolds number is taken as 1000 instead of the usual 2000 or so because the phases are recognized to disturb each other. Item 1 of Table 6.7 is a guide to the applicability of the Lockhart-Martinelli method, which is the oldest, and two more recent methods. An indication of the attention that has been devoted to experimentation with two phase flow is the fact that Friedel (1979) based his correlation on some 25,000 data points. 

For vapor-liquid mixtures, the pressure drop in horizontal pipes can be found using the correlation of Lockhart and Martinelli (1949), which relates the two-phase pressure drop to the pressure drop that would be calculated if each phase was flowing separately in the pipe. Details of the correlation and methods for two-phase flow in vertical pipes are given in Perry and Green (1997). 

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