Void fraction correlation,

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 ... 

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 ... 

Smith (1970) developed a saturated void fraction correlation by equating the... 

In a later publication (14) Isbin et al. show the effect of using different void-fraction correlations for the calculation of acceleration effects in horizontal steam-water flow when critical velocities are approached. In this work, additional void-fraction correlations are given The Fauske model (for annular flow when velocities are very high) results in... 

Many of the void-fraction correlations which have been prepared for both vertical and horizontal flow of steam-water mixtures have recently been tested by Haywood et al. (H4) against their extensive experimental data for 1-in. and IJ-in. tubes. Additional valuable evaluation is given by others in the published discussion of this paper. 

G. E. Mueller, Radial void fraction correlation for annular packed beds, AICHE Journal 45(1 l)pp. 2458-2460,1999. 

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

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... 

In Fig. 5.25 the void fraction a is plotted versus a homogeneous void fraction jS with different symbols used for different ranges of liquid superficial velocity [/ls-The void fraction can be correlated with the homogeneous void fraction ... 

On the other hand, in the study by Serizawa et al. (2002) the cross-sectional averaged void fraction was correlated with the Armand (1946) correlation as shown in Fig. 5.26. This trend does not contradict the data reported for conventional size channels, but it is different from results obtained by Kawahara et al. (2002). Disagreement between results of void fraction in micro-channels obtained by different investigators was shown by Ide et al. (2006) and will be discussed in the next section. 

In eontrast, the conventional size channel void fraction data conform to the Ar-mand correlation (1946). To our knowledge, no unusually low void fraction data have been reported for conventional size channels, so the two-phase flow in conven-... 

Thus, similar void fraction data can be obtained in micro-channels and conventional size channels, but the micro-channel void fraction can be sensitive to the inlet geometry and deviate significantly from the Armand correlation. 

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 Martinelli correlations for void fraction and pressure drop are used because of their simplicity and wide range of applicability. France and Stein (6 ) discuss the method by which the Martinelli gradient for two-phase flow can be incorporated into a choked flow model. Because the Martinelli equation balances frictional shear stresses cuid pressure drop, it is important to provide a good viscosity model, especially for high viscosity and non-Newtonian fluids. 

The void fraction should be the total void fraction including the pore volume. We now distinguish Stotai from the superficial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter 9. The pore volume is accessible to gas molecules and can constitute a substantial fraction of the gas-phase volume. It is included in reaction rate calculations through the use of the total void fraction. The superficial void fraction ignores the pore volume. It is the appropriate parameter for the hydrodynamic calculations because fluid velocities go to zero at the external surface of the catalyst particles. The pore volume is accessible by diffusion, not bulk flow. 

W-3 CHF correlation. The insight into CHF mechanism obtained from visual observations and from macroscopic analyses of the individual effect of p, G, and X revealed that the local p-G-X effects are coupled in affecting the flow pattern and thence the CHF. The system pressure determines the saturation temperature and its associated thermal properties. Coupled with local enthalpy, it provides the local subcooling for bubble condensation or the latent heat (Hfg) for bubble formation. The saturation properties (viscosity and surface tension) affect the bubble size, bubble buoyancy, and the local void fraction distribution in a flow pattern. The local enthalpy couples with mass flux at a certain pressure determines the void slip ratio and coolant mixing. They, in turn, affect the bubble-layer thickness in a low-enthalpy bubbly flow or the liquid droplet entrainment in a high-enthalpy annular flow. 

The uncertainty in the predicted CHF of rod bundles depends on the combined performance of the subchannel code and the CHF correlation. Their sensitivities to various physical parameters or models, such as void fraction, turbulent mixing, etc., are complementary to each other. Therefore, in a comparison of the accuracy of the predictions from various rod bundle CHF correlations, they should be calculated by using their respective, accompanied computer codes.The word accompanied here means the particular code used in developing the particular CHF correlation of the rod bundle. To determine the individual uncertainties of the code or the correlation, both the subchannel code and the CHF correlation should be validated separately by experiments. For example, the subchannel code THINC II was validated in rod bundles (Weismanet al., 1968), while the W-3 CHF correlation was validated in round tubes (Tong, 1967a). 

Smith, S. L., 1970, Void Fraction in Two-Phase Flow A Correlation Based upon an Equal Velocity Head Model, Proc. Inst. Mech. Engrs., JS4(Part I), (36) 657. (3)... 

The modified Reynolds number therefore is based on the velocity in the void fraction v/s, the kinematic viscosity v, and an equivalent diameter s/a, where s is total area per unit volume and a is the dimensional coefficient derived from a correlation of pressure drop data ... 

The desire to save energy calls for low pressure drop over the catalyst layers because they account for a significant part of the total pressure drop through the sulphuric acid plant. According to simple correlations such as the Ergun equation [12], the pressure drop over a catalyst bed per bed length at a given flow rate and properties of the gas only depends on the bed void fraction e and a characteristic pellet diameter... 

Authors efforts in this part of the work have been concentrated on developing turbulence closures for the statistical description of two-phase turbulent flows. The primary emphasis is on development of models which are more rigorous, but can be more easily employed. The main subjects of the modeling are the Reynolds stresses (in both phases), the cross-correlation between the velocities of the two phases, and the turbulent fluxes of the void fraction. Transport of an incompressible fluid (the carrier gas) laden with monosize particles (the dispersed phase) is considered. The Stokes drag relation is used for phase interactions and there is no mass transfer between the two phases. The particle-particle interactions are neglected the dispersed phase viscosity and pressure do not appear in the particle momentum equation. 

The length parameter used in this correlation to represent the different types of packing may also contribute to the scatter. The use of the effective diameter may not be the best way to bring the data together, and several of the investigators found that they could correlate their own data quite well by using certain arbitrary functions of the void fraction, c. However, it was found by Bishchoff (B13) that the effective diameter was the most satisfactory size parameter when all of the data were considered. 

IV. Correlating Methods for Two-Phase Pressure Drops and Void Fractions 220... 

---