Lockhart-Martinelli model

For a micro-channel connected to a 100 pm T-junction the Lockhart-Martinelli model correlated well with the data, however, different C-values were needed to correlate well with all the data for the conventional size channels. In contrast, when the 100 pm micro-channel was connected to a reducing inlet section, the data could be fit by a single value of C = 0.24, and no mass velocity effect could be observed. When the T-junction diameter was increased to 500 pm, the best-fit C-value for the 100 pm micro-channel again dropped to a value of 0.24. Thus, as in the void fraction data, the friction pressure drop data in micro-channels and conventional size channels are similar, but for micro-channels, significantly different data can be obtained depending on the inlet geometry. 

The Lockhart-Martinelli model can correlate the data obtained from pressure drop measurements in gas-liquid flow in channels with hydraulic diameter of 0.100-1.67 mm. The friction multiplier is 0l = 1 + C/X - -1 /X. ... 

Example 6.14 compares the homogeneous and Lockhart-Martinelli models for the flow of a mixture of oil and hydrogen. 

Pinna, D. Tronconi, E. Tagliabue, L. High interaction regime Lockhart-Martinelli model for pressure drop in trickle-bed reactors. Am. Inst. Chem. Eng. J. 2001, 47, 19. 

Salim et al. (2008) investigated oil-water two-phase flows in quartz and glass microchannels. Their pressure drop measurements were interpreted by using the homogeneous and Lockhart-Martinelli models, where the two-phase pressure drop is correlated to the pressure drop of each single phase ... 

The main uncertainty related with the Lockhart-Martinelli model is the determination of the C-fector. Different C-factor... 

The Uquid fihn thickness surrounding the Taylor bubble in a microchannel can be precisely predicted with a number of correlations derived from Bretherton s theory. In the closed micro-channels, the pressure drop in Taylor flow can be correctly estimated by the Wamier model and in the annular regime by the Lockhart-Martinelli model. A number of correlations for the C-factor are available for the Lockhart-MartinelU model... 

In Figure 6, the pressure drop calculated by means of the Lockhart-Martinelli model is reported against the experimental measures. Again, a classification of the data, based on the inlet vapor quality X is also reported. 

Figure 6. Pressure drop in straight pipes. Comparison between the Lockhart-Martinelli model s predictions and experimental data.

As already done for the Friedel model, the possible influence of the specific flow pattern has been checked also for the Lockhart-Martinelli model. However, since the influence of the vapor quality has been already found negligible from the previous results, the ratio of the predicted pressure drop over the experimental one, has been plotted as a function of the inlet pressure (Fig. 7). It can be seen that, apart from the expected marked dispersion of the data (based on the RMS value already reported in Fig. 6), a general increase of the ratio is observed at increasing inlet pressures. Again, an apparent dependency of the predictions with the flow pattern is found, with the intermittent flow regime always characterized by larger ratios of the pressure drop, compared with the dispersed bubble. 

In the present section, the pressure drops calculated by means of the Friedel and the Lockhart-Martinelli models, for the first of the two elbows of the experimental rig, are compared with the measured values. 

In Figure 11, the predictions obtained with the Lockhart-Martinelli model, using both the allliquid equivalent length and that derived from two-phase flow measurements, are compared with the... 

Fig. 5.22a,b Comparison of measured void fractions by Triplett et al. (1999b) for circular test section with predictions of various correlations (a) homogeneous flow model (b) Lockhart-Martinelli-Butterworth (Butterworth 1975). Reprinted from Triplett et al. (1999b) 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-... 

A separated flow model for stratified flow was presented by Taitel and Dukler (1976a). They indicated analytically that the liquid holdup, R, and the dimensionless pressure drop, 4>G, can be calculated as unique f unctions of the Lockhart-Martinelli parameter, X (Lockhart and Martinelli, 1949). Considering equilibrium stratified flow (Fig. 3.37), the momentum balance equations for each phase are... 

The definition of friction factor using mean fluid properties has been most widely used because it reduces to the correct single-phase value for both pure liquid and pure gas flow. This technique is very similar to the so-called homogeneous model, because it has a clear physical significance only if the gas and liquid have equal velocities, i.e., without slip. Variations of this approach have also been used, particularly the plotting of a ratio of a two-phase friction factor to a single-phase factor against other variables. This approach is then very similar to the Lockhart-Martinelli method, since it can be seen that (G4)... 

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. 

Davis (Dl) has suggested that the introduction of the Froude number into the Lockhart-Martinelli parameter. A, gives a description of gravitational and inertial forces so that this model can be applied to vertical flow. The revised parameter, X, is defined empirically for turbulent-turbulent flow as,... 

Concurrent flow of liquid and gas can be simulated by the homogeneous model of Section 6.8.1 and Eqs. 6.109 or 6.112, but several adequate correlations of separated flows in terms of Lockhart-Martinelli parameters of pipeline flow type are available. A number of them is cited by Shah (Gas-Liquid-Solid Reactor Design, McGraw-Hill, New York, 1979, p. 184). The correlation of Sato (1973) is shown on Figure 6.9 and is represented by either... 

TEMA classification, 200 tube count table, 203 Turbine pumps, 134, 139, 140, 142, 143 Turner equation, leaching, 466 Turbogrid trays, 426 Two-phase fluid flow. 111, 113-117 correlations, 115 granular beds, 118 homogeneous model, 113 Lockhart-Martinelli method, 115, 116... 

The existing hydrodynamic models can be broadly classified into two different categories on the basis of empirical approach and theoretical approach. The empirical approach is based on dimensional analysis to produce explicit correlations for pressure drop and liquid holdup using flow variables and packing characteristics or using the Lockhart-Martinelli parameter, which was proposed for open horizontal The theoretical... 

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