Friction multipliers

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... 

Eq. (5.25) with C = 5 are well over the present data. On the other hand, the friction multiplier values calculated with C = 0.66 are slightly higher than the experimental data, while a slightly smaller value of C = 0.24 was found by Kawahara et al. (2002) to best fit the results. 

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

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. ... 

To measure all the parameters pertinent to simulating reactor conditions, Ny-lund and co-workers (1968, 1969) presented data from tests carried out on a simulated full-scale, 36-rod bundle in the 8-MW loop FRIGG at ASEA, Vasteras, Sweden (Malnes and Boen, 1970). Their experimental results indicate that the two-phase friction multiplier in flow through bundles can be correlated by using Becker s correlation (Becker et al., 1962),... 

The equation for the mass flux effect, AF, has been obtained by correlating the measured friction multiplier values by means of regression analyses (Fig. 3.52). It is assumed that the two-phase friction loss in the channel is essentially unchanged by the presence of spacers. However, the increase in total pressure drop is determined by its presence in rod bundles (Janssen, 1962). 

Figure 3.52 Mass flow modified coefficient in the Becker two-phase friction multiplier. (From Malnes and Boen, 1970. Copyright 1970 by Office for Official Publication of the European Community, Luxembourg. Reprinted with permission.)...

Several frictional multiplier correlations have been developed using a separated flow model. These correlations are listed in Table 14.2. Hewitt [151] makes the following tentative recommendations ... 

TABLE 14.2 Two-Phase Flow Frictional Multiplier Correlations... 

Souza et al. [157] measured two-phase pressure drops during turbulent flow of R-12 and R-134a and developed an expression for the two-phase frictional multiplier that successfully predicted their data to within 10 percent ... 

Free Radical Self-Termination. The cage efficiencies and activation parameters for the phenylthiyl collisional cage pair provide the basis for illustrating some of the important features of equations (3)-(5) and for predicting the observed rates of self-termination of phenylthiyl free radicals. Application of the SW procedure to the completely diffusion controlled step of Scheme 1 (kj) ) for phenylthiyl free radicals in cis-decalin can be expressed by the transition state equation with a AH d of 3448 cal/mole and a AS d of -4.3 cal/mole-K. The corresponding activation enthalpy (AH d) from the Stokes-Einstein-Schmoluchowski relationship is 3685 cal/mole for cis-decalin) so that the a of equation (8) is 0.94. The micro-frictional multiplier (mf, equation 8 above), which is incorporated into the SW activation entropy (AS j)), is 2.4. The SW activation entropy for a truly diffusion controlled self-termination of phenylthiyl free radicals (2k obs -2kj), - 1 at... 

Thus, the steps in estimating the pressure drop using Equation 7.36 are (i) estimation of the frictional pressure drop of each individual phase, (ii) calculation of the Lockhart-Martinelli parameter ( P), and (iii) estimation of the friction multiplier for liquid, and... 

Friction multipliers for gas and liquid in Lockhart and Martinelli equation Lockhart—Martinelli parameter Frictional pressure gradients when liquid and gas are assumed to flow alone... 

The separated flow model (for more details, see Collier and Thome [54]) considers that the phases are artificially segregated into two steams one liquid and one vapor, and has been continuously developed since 1949 when Lockhart and Martinelli [56] published their classic paper on two-phase gas-liquid flow. The main goal in this approach is to find an empirical correlation or simplified concept to relate the two-phase friction multiplier, ( ), to the independent variables of the flow. For example, the... 

One of the most commonly used models to characterize the pressure drop in MSR is that proposed by Lockhart and Martinelli [41] for gas-liquid horizontal flow in pipes, which is used for all regimes. It employs two friction multipliers for gas and liquid, and as given by the following equation ... 

However, from experimental measurements, Yue et al. [43] reported for the CO2-water system that the friction multiplier cannot be predicted reliably with a... 

Pressure gradient of single phase fiow fiowing through same microreactor of film fiow Fraction of liquid in the dynamic phase Friction multipliers Volume fraction of liquid phase which fiows in the form of enclosed slug (discrete phase) Interfacial tension Geometric factors Film thickness... 

The Armand model was chosen to calculate the two-phase friction multiplier, through Eq.2. 

Table 1 shows comparisons between pressure drop data for a full-scale channel assembly and the PATRIARCH code predictions. The latter have been based on empirically determined two-phase friction multipliers which seem to have a wide range of validity under SGHW conditions. In general, three two-phase pressure drop friction factors for rod clusters lie between the predictions of the Martlnelli-Nelson and Thom correlations for single round tubes. 

Static slip resistance of footwear sole and heel materials can be measured using a horizontal pull slipmeter. The force required to cause one body in contact with another to begin to move is called static slip resistance. The ratio of the force required to initiate movement and the perpendicular force between surfaces is known as coefficient of friction. Coefficient of friction multiplied by a factor of 10 is known as slip index and this is measured by the horizontal pull slipmeter. Similarly, the result of measurement of slip resistance may not fully predict resistance to slipping while walking. Surface of tested materials is slightly sanded to remove the effect of mold release materials. 

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