Mass flux fraction

Consider the behavior of upstream diffusion as illustrated by the solutions in Fig. 16.8. Despite the fact that the unbumed reagents are only methane and air, it may be observed in the lower left-hand panel that significant levels of H2 are present at the inlet boundary. Had the burner-face boundary condition been specified as a fixed composition of methane and air (instead of the mass-flux fractions as in Eq. 16.100), the solution in the vicinity of the burner would have been different, since the H2 fraction would have vanished at the boundary. The influence of upstream diffusion, and hence the need for the mass-flux-fraction boundary condition, is increasingly important at low flow rates or low pressure. In either case relatively strong diffusive mass transport can cause reaction-product species to diffuse to the inlet boundary. 

In steady one-dimensional flows it is often useful to introduce the mass-flux fraction of chemical species i. 

The radial mass-flux fraction of chemical species k, averaged over all directions for nonspherically symmetrical surface layers, flowing to the gas from the outer edge of the surface layer of a roplet of kind j, will be denoted by j. As will be seen in the subsequent applications, these quantities usually are determined by the overall stoichiometry of the surface-layer reaction and by the composition of the particle. Since — H is... 

Figure 9. A log-log plot of the annual average ( Paxs/ °Thxs) as a function of sediment trap particle composition, and as a function of total mass flux. Note the importance of particle composition on the ( Paxs/ °Thxs) of trapped material, with a high opal fraction leading to higher ratios. Note also the poor relationship between ( Paxs/ °Thxs) and mass flux. This data was compiled by Chase et al. (in press-b) and includes data from that study, as well as from Lao et al. (1993), Scholten et al. (2001), and Yu et al. (2001a).

Using a homogeneous model proposed by Owens (1961) for low void fractions (a < 0.30) and high mass flux, as is usually encountered in a water-cooled reactor, the momentum change (or acceleration) pressure gradient term is obtained from... 

In inverted annular flow dryout, liquid mass flux is low enough and wall heat fluxes are high enough to cause vapor to be generated rapidly near the wall, forming a vapor annulus surrounding a liquid core (Fig. 4.176). The vapor generation near the wall occurs so quickly that the velocities of the two phases are about equal, or S = 1, so the expression for the void fraction at dryout, ado, can be calculated from the known dryout quality, Ydo ... 

The quantity G of the effective mixing mass flux is determined by the turbulent velocity fluctuations at the bubble-layer edge. The distance of the edge of the bubble layer from the wall is taken as the distance at which the size of the turbulent eddies is k times the average bubble diameter. Weisman and Pei have determined empirically that k equals 2.28. Only a fraction of the turbulent velocity fluctuations produced are assumed to be effective in reaching the wall. The effective velocity fluctuations are those in which the velocity exceeds the average velocity away from the wall produced by evaporation heat flux q"b. At the bubble layer-core interface, the effective mass flux to the wall is computed as... 

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. 

Lahey, R. T., Jr., and F. A. Schraub, 1969, Mixing, Flow Regimes and Void Fraction for Two-Phase Flow in Rod Bundles, in Two-Phase Flow and Heat Transfer in Rod Bundles, ASME, New York. (5) Lahey, R. T., Jr., B. S. Shiralkar, and D. W. Radeliffe, 1971, Mass Flux and Enthalpy Distribution in a Rod-Bundle for Single and Two-Phase Flow Conditions, Trans. ASME, J. Heat Transfer, 93 197-209. (5)... 

By replacing the mole fraction of water with the ratio of water vapor pressure (Pw) divided by the total gas pressure (PT), one can solve for the diffusive flux of water vapor. Also, by multiplying Nw by the molecular weight of water, the mass flux of water vapor is arrived at ... 

The derivatives of the mass fluxes to the solid volume fractions can subsequently be obtained from the solid phase momentum equations. From Eq. (85), the discretized x-momentum equation, the derivatives of the mass fluxes in the x-direction can easily be obtained, e.g.,... 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

Figures 3(a) and 3(b) show the computed fraction profiles of component A and B in the liquid film corresponding to, respectively, run 1 and run 6 from Table 1. Figure 3(a) shows that low fractions of A and B produce straight profiles, whereas high fractions of A and B result in curved profiles [see Fig. 3(b)]. The latter is due to the fact that the mass fluxes consist of a diffusive part as well as a convective (i.e. drift) part. This is also the reason why the fraction of B possesses a gradient, although the flux of component B equals zero.

The emission index in general is defined as the mass of pollutant emitted per unit mass of fuel consumed. In quasi-steady diffusion flames, this is the ratio of the mass flux of pollutant out of the flame to the mass rate of consumption of fuel per unit flame area. Depending on the application, it may be more desirable to consider only the flux of pollutant to the air or the sum of the pollutant flux to both air and fuel. The latter definition is selected here, and a pollutant balance for the flame then enables the emission index to be expressed as the ratio of the mass rate of production of pollutant per unit area to the mass rate of consumption of fuel per unit area. In terms of the mass rate of production of species i per unit volume cDj, the mixture fraction, and the magnitude of its gradient VZ, the mass rate of production of species i per unit area is... 

For clarity, use w to denote mass fraction (dimensionless, i.e., the concentration unit is not kg/m or mol/m ) in the melt Wqtz denotes mass fraction in quartz. The mass flux toward the interface (in the interface-fixed reference frame) is... 

In these equations is the partial molal free energy (chemical potential) and Vj the partial molal volume. The Mj are the molecular weights, c is the concentration in moles per liter, p is the mass density, and z, is the mole fraction of species i. The D are the multicomponent diffusion coefficients, and the are the multicomponent thermal diffusion coefficients. The first contribution to the mass flux—that due to the concentration gradients—is seen to depend in a complicated way on the chemical potentials of all the components present. It is shown in the next section how this expression reduces to the usual expressions for the mass flux in two-component systems. The pressure diffusion contribution to the mass flux is quite small and has thus far been studied only slightly it is considered in Sec. IV,A,6. The forced diffusion term is important in ionic systems (C3, Chapter 18 K4) if gravity is the only external force, then this term vanishes identically. The thermal diffusion term is impor-... 

For ideal gas mixtures and for dilute liquid solutions the activity is equal to the mole fraction, and then the various mass fluxes may be written 10... 

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