Lockhart-Martinelli

Rapid approximate predictions of pressure drop for fully developed, incompressible horizontal gas/fiquid flow may be made using the method of Lockhart and MartineUi (Chem. Eng. Prog., 45, 39 8 [1949]). First, the pressure drops that would be expected for each of the two phases as if flowing alone in single-phase flow are calculated. The LocKhart-Martinelli parameter X is defined in terms of the ratio of these pressure drops ... 

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... 

Empirical void fraction correlations, relating to the Lockhart-Martinelli factor X and from there to volumetric quality x, have been provided by Lockhart and Mar-tinelli (1949), Baroczy (1963), Wallis (1969), and have been discussed by Butter-worth (1975) and Chen and Spedding (1983). Butterworth (1975) showed that Lockhart and Martinelli s correlation (1949) for void fraction, as well as several other void fraction correlations, can be represented in the following generic form ... 

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... 

The Lockhart and Martinelli (1949) correlation also uses a two-phase friction multiplier, defined by Eq. (5.16). The friction multiplier has been correlated in terms of the Lockhart-Martinelli parameter, X, given by... 

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. 

Figure 5.31 shows a comparison of the two-phase friction multiplier data with the values predicted by Eq. (5.25) with C = 5, for both phases being laminar, and with C = 0.66 given by Mishima and Hibiki s (1996) correlation. It is clear that the data correlate well using a Lockhart-Martinelli parameter, but the predictions of... 

Fig. 5.29a-c Two-phase frictional multiplier 0 vs. Lockhart-Martinelli parameter X (Lockhart and Mar-tinelli 1949). Reprinted from Zhao and Bi (2001b) 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-... 

Fig. 5.31 Variation of two-phase friction multiplier data with Lockhart-Martinelli parameter. Reprinted from Kawahara et al. (2002) with permission...

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. ... 

Lockhart-Martinelli parameter Volumetric quality, void fraction Streamwise coordinate... 

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 ... 

Lockhart and Martinelli (1949) suggested an empirical void fraction correlation for annular flow based mostly on horizontal, adiabatic, two-component flow data at low pressures, Martinelli and Nelson (1948) extended the empirical correlation to steam-water mixtures at various pressures as shown in Figure 3.27. The details of the correlation technique are given in Chapter 4. Hewitt et al. (1962) derived the following expression to fit the Lockhart-Martinelli curve ... 

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... 

Here 7 was shown to be essentially independent of the Lockhart-Martinelli parameter, X, for values of (1/30 greater than unity. Further study, however, is necessary to develop a generalized equation for the coefficient 7. 

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

The classic Lockhart- Martinelli (1949) method is based on the two-phase multiplier defined previously for either liquid-only (Lm) or gas-only (Gm) reference flows, i.e.,... 

Lock-and-key type receptor, 16 770, 771 Lockhart-Martinelli method, 16 716 Locking and tagging practices, 21 853-854 Locust bean (carob) gum, 4 724t, 726-727 12 53 13 67 properties of, 13 74t... 

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. 

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