Lockhart-Martinelli correlation

The two-phase pressure drop is obtained by multiplying either the liquid-phase drop by (t) or the gas-phase pressure drop by. Figure 7-23 gives the Lockhart-Martinelli correlation between X and ([t s... 

Zhao and Bi (2001b) measured pressure drop in triangular conventional size channels d = 0.866—2.866 mm). The variations of the measured two-phase frictional multiplier with the Martinelli parameter X for the three miniature triangular channels used in experiments are displayed, respectively, in Fig. 5.29a-c. In Fig. 5.29 also shown are the curves predicted by Eq. (5.25) for C = 5 and C = 20. It is evident from Fig. 5.29 that the experimental data are reasonably predicted by the Lockhart-Martinelli correlation, reflected by the fact that all the data largely fall between the curves for C = 5 and C = 20, except for the case at very low superficial liquid velocities. 

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-... 

Fig. 5.32 Predictions of two-phase friction pressure gradient data by a Lockhart-Martinelli correlation with different C-values. Reprinted from Kawahara et al. (2002) with permission...

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

Equations 7.81 and 7.83 are not easy to evaluate. In the following sections the Lockhart-Martinelli and Martinelli-Nelson correlations will be considered. The Lockhart-Martinelli correlation is valid when there is no change of phase, so dw/dx=0 in equation 7.81 and the second term in the numerator vanishes. In the Martinelli-Nelson correlation, values are given for the quantities in square brackets in equation 7.83. 

This correlation is an extension of the Lockhart-Martinelli correlation. The earlier correlation is limited to low pressures and systems in which no change of phase occurs. Although Lockhart and Martinelli provided for four flow regimes, it is unusual in industrial processes for either phase to be in laminar flow. The Martinelli-Nelson (1948) correlation is specifically for forced circulation boiling of water in which it is assumed that both phases are in turbulent flow. 

When a change of phase occurs, as in boiling, it is necessary to use the wholly liquid reference flow (an only liquid basis would change as the liquid flow rate decreases during boiling). At low pressures, the results of the Lockhart-Martinelli correlation can be used for the frictional component of the pressure gradient but it is necessary to convert the only liquid basis used in the earlier correlation to the wholly liquid basis. It is assumed that the frictional pressure gradients for the two reference flows are related by the expression... 

The Lockhart-Martinelli correlation provides the relationship between 4>j. and the Martinelli parameter X . Therefore, use of equation 7.95 enables the relationship between 4>lo and X at low pressures to be found. 

It should be remembered that these correlations as originally devised by Lockhart and Martinelli were based almost entirely on experimental data obtained for situations in which accelerative effects were minor quantities. The Lockhart-Martinelli correlation thus implies the assumption that the static pressure-drop is equal to the frictional pressure-drop, and that these are equal in each phase. The Martinelli-Nelson approach supposes that the sum of the frictional and accelerational pressure-drops equals the static pressure-drop (hydrostatic head being allowed for) and that the static pressure-drop is the same in both phases. When acceleration pressure losses become important (e.g., as critical flow is approached), they are likely to be significantly different in the gas and liquid phases, and hence the frictional pressure losses will not be the same in each phase. In these circumstances, the correlation must begin to show deviations from experiment. 

Another modification of the Lockhart-Martinelli approach has been proposed by Chisholm and Laird (C4) to account for the effect of pipe roughness. For the turbulent-turbulent region, it is suggested that the Lockhart-Martinelli correlations, which were presented graphically, can be represented by the equation... 

Void-fractions in slug and annular flow can be estimated from the Lockhart-Martinelli correlations. 

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)]... 

Eqs. (Ga) and (Gb) for hokhq), /L had been derived. semi-empirically [6 J, and are given for the sake of completeness. In the range 0.01 predict values of cp that deviate from the values given by the Lockhart-Martinelli curve with an averaged absolute deviation of less than 4% and a maximum absolute deviation of 10%. Since the pressure drop is proportional to (p , the errors for pressure drop are slightly more than double these values. Such deviations are apt to be acceptable since the Lockhart-Martinelli correlations may sometimes give predictions with errors in excess of 50% of experimental data. 

These correlations require both pressure-drop and gas-holdup values which may be predicted by the Lockhart-Martinelli correlation (L22) or the Hughmark correlation (H13). 

Various studies have been conducted in predicting the two-phase frictional pressure losses in pipes. The Lockhart-Martinelli correlations [19] shown in Figure 3-7 are employed. The basis of the correlations is that the two-phase pressure drop is equal to the single-phase pressure drop of either phase multiplied by a factor that is derived from the singlephase pressure drops of the two-phases. The total pressure drop is based on the vapor-phase pressure drop. The pressure drop computation is based on the following assumptions ... 

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