Drift flux, calculation

Calculation methods are given here for cases (a) to (c). In section A3.4 below, references are given to a calculation method for case (d). The level swell calculation methods presented here use the drift flux correlations developed by DIERS[11. The DIERS correlations apply to a vertical cylindrical vessel, which is most often the case for chemical reactors. Modifications for horizontal cylindrical vessels are given by Sheppard[2,3]. 

The method uses the drift-flux level swell calculation models to take into account there being more vapor in the inlet stream to relief device than average for the vessel. 

This form of the mixture model is called the drift flux model. In particular cases the flow calculations is significantly simplified when the problem is described in terms of drift velocities, as for example when ad is constant or time dependent only. However, in reactor technology this model formulation is restricted to multiphase cold flow studies as the drift-flux model cannot be adopted simulating reactive systems in which the densities are not constants and interfacial mass transfer is required. 

Figure 13 The regime transition velocity (a) in a bubble column. Open symbols are obtained by standard deviation of pressure fluctuation and drift flux model closed symbols are calculated by the correlation of Wilkinson et al. (1992). (From Lin et al., 1999.) (b) In a three-phase fluidized bed. (From Luo et al., 1997a.)...

A full-range drift-flux model is available for the calculation of the relative velocity between phases for the five-equation model. The model comprises all flow patterns from homogeneous to separated flow occurring in vertical and horizontal two-phase flow. It also takes into account counter-current flow limitations in different geometry. 

The APROS calculation used 5-equation model. The drift flux model was used to describe the velocity difference between phases. The CMT was modelled with five equal sized nodes. Sensitivity analyses with different number of nodes was not performed. With five nodes, it was not possible to model exactly the thermal stratification in the CMT. In the base case calculation, the top node liquid temperature was initiated to 140°C, which corresponds to the average temperature of the upper part of the CMT. 

The fluid model is a description of the RF discharge in terms of averaged quantities [268, 269]. Balance equations for particle, momentum, and/or energy density are solved consistently with the Poisson equation for the electric field. Fluxes described by drift and diffusion terms may replace the momentum balance. In most cases, for the electrons both the particle density and the energy are incorporated, whereas for the ions only the densities are calculated. If the balance equation for the averaged electron energy is incorporated, the electron transport coefficients and the ionization, attachment, and excitation rates can be handled as functions of the electron temperature instead of the local electric field. 

An equivalent dehnition of the drift velocity E" may be obtained by using the diffusion equation alone to calculate the average flux velocity in a statishcal ensemble characterized by a probability distribution... 

First, the drift current is calculated in the case of a constant electrical field, as one would expect for very thin bulk heterojunction solar cells. If the width W of the active layer is similar to the drift length of the carrier, the device will behave as a MIM junction, where the intrinsic semiconductor is fully depleted. The current is then determined by integrating the generation rate G = —dP/dx over the active layer, where P is the photon flux ... 

The derivation of the basic relation (4.147) reveals the conditions under which the proportionality between drift velocity (or flux) and electric field breaks down. It is essential to the derivation that in a collision, an ion does not preserve any part of its extra velocity component arising from the force field. If it did, then the actual drift velocity would be greater than that calculated by Eq. (4.147) because there would be a cumulative carryover of the extra velocity from collision to collision. In other words, every collision must wipe out all traces of the force-derived extra velocity, and the ion must start afresh to acquire the additional velocity. This condition can be satisfied only if the drift velocity, and therefore the field, is small (see the autocorrelation function. Section 4.2.19). 

As described in Section 19.2.3.8, regional models, such as a Baltic Sea model, can get the boundary values for the calculation of surface fluxes from simulations with atmosphere models, which have been carried out previously. This is possible, because the influence of the Baltic Sea on the Northern Hemisphere weather system is only important for local phenomena, and inaccuracy in the feedback from the Baltic Sea to the atmosphere is of minor importance, Schrumm and Backhaus (1999). Widely used datasets, such as the ERA-40 reanalysis data, are improved by assimilation of observations. If surface variables calculated by the ocean model tend to drift away, this is compensated to a large extent by the calculated surface fluxes. For this reason numerical simulations with standalone ocean-ice models can be successful. 

Table III gives the conditions, data and reactions for the long irradiations of iridium, osmium and ruthenium. Samples and standards were irradiated in the University of London Reactor under a maximum thermal neutron flux of 1.4 x 10 n cm" s". The samples were counted using a lithium drifted germanium detector (Ortec Inc) linked to a computer based gamma ray spectrometer (Nuclear Data Inc. 6620 Multichannel Analyser). A general Neutron Activation Package written in FORTRAN IV was employed to run a peak search and calculate PGM concentrations in the plant samples. The irradiation of platinum is a special case and details are given in Table IV. Various nuclides emit y-rays of similar energy, and in INAA these become a serious interference in the determination of platinum in biological samples.

The simplest and classical treatment of the Kirkendall effect in binary homogeneous systems assumes that the differences between the intrinsic diffusion fluxes of the two substitutional constituents are compensated by the action of local vacancy sinks and sources that maintains the system in local equilibrium, i.e. in states that can be completely defined by the knowledge of appropriate state variables to permit the calculation of pertinent state functions such as, for example, the chemical potential of system constituents. The drift of lattice planes is one important characteristic of the Kirkendall effect in stress-free homogeneous systems and is a consequence of the action of these vacancy sources and/or sinks distributed along the diffusion zone. As the system remains in local equilibrium by the action of vacancy sinks and sources, the vacancy concentration or molar fraction remains constant and equal to its equilibrium value within the entire diffusion couple. Therefore, no effective gradient of vacancy concentration is established in the diffusion zone. However, the local action of vacancy sinks or sources along the diffusion direction is formally equivalent to a vacancy flux Jy related to the required local density of vacancy sources or sinks ps equal to the flux divergence,... 

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