Interfacial flow modeling

Keywords Finite element Finite volume Finite difference Volume of fluid Level set Interface tracking Free surface flows Fixed mesh Boimdary-fitted coordinates Boundary integral Marker and cell Immersed boxmdary Volume tracking Surface tracking Surface capturing Interfacial flow modeling... 

Interfacial flow modeling Surface capturing Surface tracking Volume tracking... 

Volume tracking Surface tracking Surface capturing Interfacial flow modelling... 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

Annular flow. Modeling the interfacial shear is central to the problem of modeling hydrodynamics and transport during annular flow. The mechanisms are not clear, and the extent of basic modeling that has appeared is still very limited (Dukler and Taitel, 1991b). Only empirical treatments are currently available (see Sec. 3.5.3.3). 

To summarize, to properly model liquid water transport and ensuing flooding effect on cell performance, one must consider four submodels (1) a model of catalytic surface coverage by liquid water inside the catalyst layer, (2) a model of liquid water transport through hydrophobic microporous layer and GDL, (3) an interfacial droplet model at the GDL surface, and last (4) a two-phase flow model in the gas channel. Both experimental and theoretical works, in academia and industry alike, are ongoing to build models for the four key steps of water generation, transport, and removal from a PEFC. 

Calculation of Solute Separation and Product Rate. Once the pore size distribution parameters R, ou R >,2, 02, and h2 are known for a membrane and the interfacial interaction force parameters B and D are known for a given system of membrane material-solute, solute separation f can be calculated by eq 6 for any combination of these parameters. Furthermore, because the PR-to-PWP ratio (PR/PWP) can also be calculated by the surface force-pore flow model (9), PR is obtained by multiplying experimental PWP data by this ratio. 

The interfacial force constants available in the literature for many organic solutes that constitute potential pollutants in water enable one to calculate the separation of such solutes at various operating conditions by a membrane of a given average pore size and pore size distribution on the basis of the surface force-pore flow model. The product rate of the permeate solution can also be calculated. Such data further allow us to calculate the processing capacity of a membrane to achieve a preset ratio of concentration in the concentrate to concentration of the initial feed solution. 

Considering the interfacial pressure model, the flow rates should be between the higher and lower limits. APpiow can be evaluated by considering the pressure loss in the microchannels. Assuming that the pressure at the opened outlet is atmospheric pressure, Patm, then the pressure P of each phase from the pressure loss AP is expressed as follows ... 

Mass-Transfer Models Because the mass-transfer coefficient and interfacial area for mass transfer of solute are complex functions of fluid properties and the operational and geometric variables of a stirred-tank extractor or mixer, the approach to design normally involves scale-up of miniplant data. The mass-transfer coefficient and interfacial area are influenced by numerous factors that are difficult to precisely quantify. These include drop coalescence and breakage rates as well as complex flow patterns that exist within the vessel (a function of impeller type, vessel geometry, and power input). Nevertheless, it is instructive to review available mass-transfer coefficient and interfacial area models for the insights they can offer. 

Stuhmiller JH (1977) The Influence of interfacial pressure forces on the character of two-phase flow model equations. Int J Multiphase Flow 3 551-560 Sussman M, Smereka P, Osher S (1994) A Level-Set Approach for Computing Solutions to Incompressible Two-Phase Flow. J Comput Phys 114 146-159. Sussman M, Smereka P (1997) Axisymmetric free boundary problems. J Fluid Mech 341 269-294. 

The front-tracking method has been developed by Trgyyvason and coworkers and been successfully used for computational modeling of interfacial flows... 

It is a challenging task to model the effects of interfacial flows with soluble surfactants since surfactants are advected and diffused both at the interface and in the bulk fluid by the motion of fluid and by molecular mechanism, respectively. Therefore the evolution equations of the surfactant concentrations at the interface and in the bulk fluid must be solved coupled with the flow equations. The surfactant concentration at the interface alters the interfacial tension and thus alters the flow field in a complicated way. This interaction between the surfactant and the flow field is highly nonlinear and poses a computational challenge. 

After the static test mentioned above, the method is now tested for the impact and spreading of a glycerin droplet on a wax substrate and the computational results are compared with the experimental data of Sikalo et al. [32], The details of the experimental setup, material properties and computational model can be found in Refs. [33, 51]. The computed and experimental spread factor and contact line are plotted in Figs. 19a and b, respectively. These figures show that the present front-tracking method is a viable tool for simulation of interfacial flows involving moving contact lines. 

Equations 12.S.b-l, 2 reduce to a large variety of special cases. As written, they are the standard equations for interfacial mass transfer used in Chapters 6 and 14 (also see Pavlica and Olson [60]. They are also the basis of the cross-flow models for fluidized beds (see Chapter 13) or other multiphase reactors, and have been used for heat transfer studies. 

T2 mass transfer coefficient (including interfacial area) beween regions 1 and 2 of flow model (Chapter 12) mj,, m, hr miVm/s... 

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