Lockhart-Martinelli two-phase flow parameter

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 ... 

Thus, both flows are turbulent and the Lockhart-Martinelli correlation parameters for Re > 5 X lO from Table 7.14 are the appropriate ones to use, namely, m = n —0.2 and C = C(- = 0.184. The two-phase flow parameter X in Eq. (7.77) for turbulent-turbulent flow after substitution of the correlation parameter reduces to... 

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... 

The Lockhart-Martinelli method is especially simple and clear. In certain parameter regions its accuracy is surpassed by other methods, but it delivers satisfactory values for the pressure drop, irrespective of the application, within a range of uncertainty of around 50%. Larger deviations are to be expected for tube diameters d > 0.1 m. Furthermore, it should also be taken into account, that the two-phase multipliers L and G were determined from measurements at low pressures. Other equations have been developed for higher pressure and greater demands on the accuracy of the result. They are normally only valid for certain substances and in a narrow range of parameters. The extensive literature on two-phase flow, in particular the summary in [4.83], is suggested for further information on this subject. 

Lockhart and Martinelli proposed that the pressure drop in two-phase flow can be related to the equivalent pressure drop in single-phase flow using a two-phase parameter [72]. For the gas phase, the single-phase pressure drop is given by... 

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 ... 

Lockhart and Martinelli divided gas-liquid flows into four cases (1) laminar gas-laminar liquid (2) turbulent gas-laminar liquid (3) laminar gas-turbulent liquid and (4) turbulent gas-turbulent liquid. They measured two-phase pressure drops and correlated the value of 0g with parameter % for each case. The authors presented a plot of acceleration effects, incompressible flow (3) no interaction at the interface and (4) the pressure drop in the gas phase equals the pressure drop in the liquid phase. 

Dengler and Addoms 8 measured heat transfer to water boiling in a 6 m tube and found that the heat flux increased steadily up the tube as the percentage of vapour increased, as shown in Figure 14.4. Where convection was predominant, the data were correlated using the ratio of the observed two-phase heat transfer coefficient (htp) to that which would be obtained had the same total mass flow been all liquid (hi) as the ordinate. As discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt, the parameter for two-phase turbulent flow developed by Lockhart and Martinelli(9). The liquid coefficient hL is given by ... 

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 37 [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 liquid holdup. They found that two-phase pressure drop may actually be less than the single-phase liquid pressure drop with shear thinning liquids in laminar flow. 

In the calculation of frictional pressure drop it is advantageous to define a few parameters that are suitable for the representation of two-phase frictional pressure drop and the volumetric quality. The frictional pressure drop is often reduced to the pressure drop for single phase flow, using the definitions from Lockhart and Martinelli [4.84]... 

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 discussion so far has related to the drag reduction occurring when a gas is introduced into a shear-thinning fluid initially in streamline flow. A more general method is required for the estimation of the two phase pressure drop for mixtures of gas and non-Newtonian liquids. The well-known Lockhart-Martinelli [1949] method will now be extended to encompass shear-thinning liquids, first by using the modified Lockhart-Martinelli parameter, Xmod (equation 4.8). Figure 4.14 shows a comparison between... 

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