Density mixtures

The corresponding acoustic velocity /(dp/dp, ), is normally much less than the acoustic velocity for gas flow. The mixture density is given in terms of the individual phase densities and the quality (mass flow fraction vapor) x by... 

Ds = particle diameter (such that 85 percent by weight of particles are smaller than Ds = the slurry mixture density [L = hquid viscosity... 

Steady-state operation (i.e., accumulation in the reactor is zero) Constant fluid mixture density Stirrer input energy is neglected Wj,... 

H = visible flame height S = 2.3 X = flame speed = wind speed d = cloud depth g = gravitational acceleration po = fuel-air mixture density pj = density of air r = stoichiometric air-fuel mass ratio a = expansion ratio for stoichiometric combustion under constant pressure (typically 8 for hydrocarbons)... 

Mixture densities of Uie binary mixtures require a knowledge of volume fraction for each component. The component molar volume is ... 

This is based on a frothed mixture density of 0.4 that of the clear liquid on the tray, and has been found to be a reasonable average for several mixtures. 

In the homogeneous flow model, pa is the homogenous mixture density defined... 

Figure 2.1 Hexane and C02 at 25 °C as predicted by the PR-EOS (a) volumeexpansionofthe liquid phase with pressurization of C02 and (b) solvent mixture density and molar volume with pressurization of C02.

Note that both the local mixture density and the holdup increase as the slip ratio (S) increases. The no slip (S = 1) density or volume fraction is identical to the equilibrium value entering (or leaving) the pipe. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

Since we are mainly interested in combustion in the gas phase, we must be able to describe reacting gas mixtures. For a thermodynamic mixture, each species fills the complete volume (V) of the mixture. For a mixture of N species, the mixture density (p) is related to the individual species densities (pi) by... 

In the LHF models, it is assumed that droplets are in dynamic and thermodynamic equilibrium with gas in a spray. This means that the droplets have the same velocity and temperature as those of the gas everywhere in the spray, so that slip between the phases can be neglected. The assumptions in this class of models correspond to the conditions in very thin (dilute) sprays. Under such conditions, the spray equation is not needed and the source terms in the gas equations for the coupling of the two phases can be neglected. The gas equations, however, need to be modified by introducing a mixture density that includes the partial density of species in the liquid and gas phases based on their mass fractions. Details of the LHF models have been discussed by Faeth.l589]... 

Although a laminar flame speed. S L is a physicochemical and chemical kinetic property of the unbumed gas mixture that can be assigned, a turbulent flame speed. S T is, in reality, a mass consumption rate per unit area divided by the unbumed gas mixture density. Thus,. S r must depend on the properties of the turbulent field in which it exists and the method by which the flame is stabilized. Of course, difficulty arises with this definition of. S T because the time-averaged turbulent flame is bushy (thick) and there is a large difference between the area on the unbumed gas side of the flame and that on the burned gas side. Nevertheless, many experimental data points are reported as. S T. 

The effect of hills is interesting, in that no credit can be taken for the downhill side of the pipeline. The sum of all the uphill elevations appears as a pressure loss in actual operating practice. Baker includes an elevation correction factor which attempts to allow for the fact that the fluid-mixture density in the inclined uphill portion of the line is not accurately known. The gas mass-velocity seems to be the major variable affecting this correction factor, although liquid mass-velocity, phase properties. 

The application of ideal-solution principles to the calculation of the density of a liquid is very easy. One simply calculates the mass and volume of each of the components of the mixture. Then these quantities are added to determine the mass and volume of the mixture. Density is simply mass divided by volume. 

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