Modeling single-phase simulations

Single-phase simulations in relatively small boxes (20 -30 sites) were performed after the determination of the surfactant/silica liquid crystal composition to generate model materials for adsorption simulation. The advantage of generating such materials is that they have truly periodic boundary conditions in the three directions. In contrast, extracted model materials obtained directly from the interfacial simulation will have periodic boundary conditions in two directions, but in the third direction (z-direction) there are two liquid-crystal/dilute phase interfaces. 

A qualified question is then whether or not the multicomponent models are really worthwhile in reactor simulations, considering the accuracy reflected by the flow, kinetics and equilibrium model parts involved. For the present multiphase flow simulations, the accuracy reflected by the flow part of the model is still limited so an extended binary approach like the Wilke model sufEce in many practical cases. This is most likely the case for most single phase simulations as well. However, for diffusion dominated problems multicomponent diffusion of concentrated ideal gases, i.e., for the cases where we cannot confidently designate one of the species as a solvent, the accuracy of the diffusive fluxes may be significantly improved using the Maxwell-Stefan approach compared to the approximate binary Fickian fluxes. The Wilke model might still be an option and is frequently used for catalyst pellet analysis. 

It can be seen from the figures that, the diffusion overpotentials predicted in multi-phase model is quantitatively higher than that predicted in single-phase simulations, due to the presence of liquid water inside GDL. This water reduces the limiting current density in the cell by increasing the acciunulation of liquid water at the GDL, which decreases its permeability to reactant gas flow and lead to the onset of pore plugging by liquid water. 

Guichardon etal. (1994) studied the energy dissipation in liquid-solid suspensions and did not observe any effect of the particles on micromixing for solids concentrations up to 5 per cent. Precipitation experiments in research are often carried out at solids concentrations in the range from 0.1 to 5 per cent. Therefore, the stirred tank can then be modelled as a single-phase isothermal system, i.e. only the hydrodynamics of the reactor are simulated. At higher slurry densities, however, the interaction of the solids with the flow must be taken into account. 

The number of equations to be solved is, among other things, related to the turbulence model chosen (in comparison with the k-e model, the RSM involves five more differential equations). The number of equations further depends on the character of the simulation whether it is 3-D, 21/2-D, or just 2-D (see below, under The domain and the grid ). In the case of two-phase flow simulations, the use of two-fluid models implies doubling the number of NS equations required for single-phase flow. All this may urge the development of more efficient solution algorithms. Recent developments in computer hardware (faster processors, parallel platforms) make this possible indeed. 

The CFD models considered up to this point are, as far as the momentum equation is concerned, designed for single-phase flows. In practice, many of the chemical reactors used in industry are truly multiphase, and must be described in the context of CFD by multiple momentum equations. There are, in fact, several levels of description that might be attempted. At the most detailed level, direct numerical simulation of the transport equations for all phases with fully resolved interfaces between phases is possible for only the simplest systems. For... 

The "correlative" multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a "multilevel" approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

These models consider the mechanisms of formation of oscillations a mechanism involving the phase transition of planes Pt(100) (hex) (lxl) and a mechanism with the formation of surface oxides Pd(l 10). The models demonstrate the oscillations of the rate of C02 formation and the concentrations of adsorbed reactants. These oscillations are accompanied by various wave processes on the lattice that models single crystalline surfaces. The effects of the size of the model lattice and the intensity of COads diffusion on the synchronization and the form of oscillations and surface waves are studied. It was shown that it is possible to obtain a wide spectrum of chemical waves (cellular and turbulent structures and spiral and ellipsoid waves) using the lattice models developed [283], Also, the influence of the internal parameters on the shapes of surface concentration waves obtained in simulations under the limited surface diffusion intensity conditions has been studied [284], The hysteresis in oscillatory behavior has been found under step-by-step variation of oxygen partial pressure. Two different oscillatory regimes could exist at one and the same parameters of the reaction. The parameters of oscillations (amplitude, period, and the... 

Counter-current gas/vapor-liquid film flows in SP above the load conditions are extremely complicated. For this reason, it appears improbable that the CFD-based virtual experiments replace real experiments entirely in the near future. However, even single-phase CFD simulations can improve predictivity of pressure drop models, since all correlations pressure drop - gas load used in practice contain some dry pressure drop correlation as a basic element. Replacing this correlation by the rigorous CFD analysis helps to avoid heuristic assumptions on possible correlation structure, which are inevitable both in conventional mechanistic models (Rocha et ah, 1993) and in more sophisticated considerations (Olujic, 1997). 

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