Lockhart-Martinelli parameter

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 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... 

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... 

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

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

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. 

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,... 

Hughmark and Pressburg (H12) have correlated statistically their void data and others for vertical flow, using a modified Lockhart-Martinelli parameter, X, given as... 

TJse of the Lockhart-Martinelli Parameters for Heat Transfer... 

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. 

Again referring to Fig. 13, the same general trend is apparent in both the pressure-drop and number-of-transfer-unit curves. This suggests that another empirical correlating procedure could be arrived at for example, an approximate relationship exists between the length of a transfer unit (LTU) and the Lockhart-Martinelli parameters, X. 

In Figure 5.2-18, the pressure drop is represented as a function of the simplified Lockhart-Martinelli parameter, Xc, (Xo = (GIL) (pjpaf]i). This figure shows that, at a given mass flow rate of the liquid, the pressure drop is a function of the ratio of G/ fpc, regardless of the nature of the gas. 

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... 

For fully developed incompressible horizontal gas/liquid flow, a quick estimate for RL may be obtained from Fig. 6-27, as a function of the Lockhart-Martinelli parameter X defined by Eq. (6-131). Indications are that liquid volume fractions may be overpredicted for liquids more viscous than water (Alves, Chem. Eng. Prog., 50, 449-456 [1954]), and underpredicted for pipes larger than 25 mm diameter (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). 

A method for predicting pressure drop and volume fraction for non-Newtonian fluids in annular flow has been proposed by Eisen-berg and Weinberger (AlChE J., 25, 240-245 [1979]). Das, Biswas, and Matra (Can. J. Chem. Eng., 70, 431—437 [1993]) studied holdup in both horizontal and vertical gas/liquid flow with non-Newtonian liquids. Farooqi and Richardson Trans. Inst. Chem. Engrs., 60, 292-305, 323-333 [1982]) developed correlations for holdup and pressure drop for gas/non-Newtonian liquid horizontal flow. They used a modified Lockhart-Martinelli parameter for non-Newtonian... 

Basically, two types of correlation for the dynamic or total liquid holdup are reported in the literature. Some investigators have correlated the liquid holdup directly to the liquid velocity nd fluid properties by either dimensional or dimensionless relations. In more recent investigations, the liquid holdup is correlated to the Lockhart-Martinelli parameter APl/APg (or an equivalent of it. as discussed in the earlier section). 

Sato et al.27 correlated liquid holdup to the Lockhart-Martinelli parameter for the pressure drop. Based on their own data, they obtained a relation... 

This can be readily integrated numerically as long as we use the appropriate nonequilibrium equivalent specific volume v, in the integration. A reasonably simple form for o, has been suggested by Chisholm (1983), which makes use of established correlations for the slip velocity K, which depends on the Lockhart-Martinelli parameter X Integrating Eq. (26-118) gives ... 

In general, the quantity X defined by (4.147) is known as the Lockhart-Martinelli parameter. It assumes different values depending on the type of flow for the two phases, whether laminar or turbulent. The following combinations, indicated by indices on X, are possible ... 

The factor F is principally determined by the shear stress exerted by the vapour on the liquid and, as Chen showed, may be expressed by the Lockhart-Martinelli parameter (4.153). With that equation (4.159) becomes... 

The Lockhart-Martinelli parameter should be determined first... 

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... 

---