Dispersed two-phase

General equations of momentum and energy balance for dispersed two-phase flow were derived by Van Deemter and Van Der Laan (V2) by integration over a volume containing a large number of elements of the dispersed phase. A complete system of solutions of linearized Navier-Stokes equations... 

The Euler Lagrangian approach is very common in the field of dilute dispersed two-phase flow. Already in the mid 1980s, a particle tracking routine was available in the commercial CFD-code FLUENT. In the Euler-Lagrangian approach, the dispersed phase is conceived as a collection of individual particles (solid particles, droplets, bubbles) for which the equations of motion can be solved individually. The particles are conceived as point particles which move... 

In the two-fluid formulation, the motion or velocity field of each of the two continuous phases is described by its own momentum balances or NS equations (see, e.g., Rietema and Van den Akker, 1983 or Van den Akker, 1986). In both momentum balances, a phase interaction force between the two continuous phases occurs predominantly, of course with opposite sign. Two-fluid models therefore belong to the class of two-way coupling approaches. The continuum formulation of the phase interaction force should reflect the same effects as experienced by the individual particles and discussed above in the context of the Lagrangian description of dispersed two-phase flow. 

In polymeric materials, the morphology development upon spinodal decomposition proceeds through various stages [92,93]. In the early stage of decomposition a co-continuous structure develops. A dispersed two-phase structure results only in the late stage of phase separation and the shape of the domains is not uniform. The morphology development upon spinodal decomposition is presented in Fig. 6. 

Pozorski, J., and J. P. Minier. 1999. Probability density function modeling of dispersed two-phase turbulent flow. Phys. Rev. E 59 855-63. 

Emulsion A dispersed, two-phase system in which one phase is usually water and the other oil. An emulsion in which oil is dispersed in water is termed an oil-in-water emulsion. An emulsion in which water is dispersed in oil is termed a water-in-oil emulsion. 

A reaction occurring in a bulk phase will show an increase in the rate with the area as shown in Fig. 5.3 for a reaction occurring in the film or at the interface, the rate will be linearly dependent on the interfacial area. The interfacial area in a dispersed two-phase liquid-liquid system can be estimated by measuring the rate of a suitable test reaction in a reactor with the known interfacial area (a flat interface, Section 5.3.2.1), and comparing it with the reaction rate in a dispersed system [6, 15]. A convenient reactive system for this purpose is a formate ester and 1-2 M aqueous NaOH. Formate esters are very reactive to hydroxide ion (fo typically around 25 M 1 s 1), so the reaction is complete inside the diffusion film, and the reaction rate is proportional to the interfacial area. A plot of the interfacial area per unit volume against the agitator speed obtained in this way in the author s laboratory for the equipment shown in Fig. 5.12 is shown in Fig. 5.14 [8]. 

Crowe, C. T. (1991). The State-of-the-Art in the Development of Numerical Models for Dispersed Two-Phase Flows. Proceedings of the First International Conference on Multiphase Flows, Tsukuba. 3,49. 

On the other hand, some mechanically compatible blends as well as some dispersed two-phase systems have made respectable inroads into the commercial scene. Many of these are blends of low-impact resins with high-impact elastomeric polymers examples are polystyrene/rubber, poly (styrene-co-acrylonitrile) /rubber, poly (methyl methacrylate) /rubber, poly (ethylene propylene)/propylene rubber, and bis-A polycarbonate/ ABS as well as blends of polyvinyl chloride with ABS or PMMA or chlorinated polyethylene. 

Boersma, W. H., and Jansen, X. X. Modelling of Dispersed Two-Phase Solid-Fluid Riser Flow, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 454-459. Somerset, Pennsylvania (1993). 

Simonin, O., Modelling turbulent reactive dispersed two-phase flows in industrial equipments. Proc. Third World Conf. Applied Computational Fluid Dynamics, May 19-23, Freiburg, Germany, Workshop E, 17.9,1996. 

Sommerfeld, M. (1993), Reviews in numerical modeling of dispersed two phase flows. Proceedings of 5th Int. Symp. on Refined Flow Modeling and Turbulence Measurements, Paris. 

To illustrate the two possible ways of avoiding non-physical values of phase volume fractions, let us consider a dispersed two-phase flow. The volume fraction of two phases can be obtained by solving the following equations ... 

Johansen, S.T. (1988), On the modeling of dispersed two phase flow, PhD thesis. University of Trondheim, Norway. 

H. Rusche, Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions, Imperial College of Science, Technology and Medicine, Ph.D. thesis, 2002. 

Citrate method The preparation procedure consisted in the dissolution of the metal salts, namely Mn(N03)2 4H20 and Ce(N03)3 6H20, in distilled water, the complexation of the metallic cations with citric acid and the rapid concentration of the liquid by evaporation under vacuum. The viscous liquid was dried at 80°C and the amorphous precursor obtained was decomposed in air prior to calcination. Owing to the complexing property of the citrate anion, this procedure leads to the formation of finely dispersed two-phase systems or favours the formation of mixed oxide phases upon calcination, when these exist. Samples were calcined for 5 hours at 200, 300,400 or 500°C. 

Zhang, D.Z., Prospered , A. (1994) Averaged equation for inviscid disperse two-phase flow, J. Fluid Mech. 267, 185-219. 

In the subsequent sections the averaging procedures most frequently used in multiphase reactor modeling are examined. Hence it follows that the basic principles of averaging are presented with emphasis on disperse two phase systems. 

Ishii M, Chawla TC (1979) Local drag laws in dispersed two-phase flows. Ar-gonne National Laboratory Report NUREG/CR-1230, ANL-79-105, Argonne, Illinois, USA... 

Johansen ST (1990) On the Modelling of Dispersed Two-Phase Flows. Dr Techn thesis. The Norwegian Institute of Technology, Trondheim. 

Prosperetti A, Jones AV (1984) Pressure forces in dispersed two-phase flow. Int Journal of Multiphase Plow 10(4) 425-440... 

Zhang DZ, Prosperetti A (1997) Momentum and Energy Equations for Disperse Two-Phase Flows and Their Closure for Dilute Suspensions. Int J Multiphase Flow 23(3) 425-453... 

Dispersed Two-Phase Flows. IMVU, Meserburg, Germany... 

Viollet PL, Simonin O (1994) ModelMng dispersed two-phase flows Closure, validation ans software development. Appl Mech Rev 47(6) S80-S84, Part 2, June... 

It is mentioned, although not used in the model evaluation by Enwald and Almstedt [40], that a much simpler closure for the binary turbulent diffusion coefficient has been derived by Simonin [123] by an extension of Tchen s theory. This simple closure has been used by Simonin and Viollet [124], Simonin and Flour [125] and Mudde and Simonin [100] simulating several dispersed two-phase flows. 

Simonin O (1995) Two-fluid model approach for turbulent reactive two-phase flows. Summer school on numerical modelling and prediction of dispersed two-phase flows. IMVU, Merseburg, Germany... 

In the particle-based definition of the NDF, we begin at the microscale and write a dynamic equation for the rate of change of the disperse-phase particle properties at the mesoscale. The simplest system, which we consider first, is a collection of interacting particles in a vacuum wherein the particles interact through collisions and short-range forces. Such a system is referred to as a granular system. We then consider a disperse two-phase system, wherein the particles are dispersed in a fluid. 

A. H. Govan, Modelling of Vertical Annular and Dispersed Two-Phase Flow, Ph.D. thesis, University of London, London, UK, 1990. 

J. C. Chen and J. Costigan, Review of Post-Dryout Heat Transfer in Dispersed Two-Phase Flow, in Post-Dryout Heat Transfer, G. F. Hewitt, J.-M. Delhaye, and N. Zuber eds., chap. 1, CRC Press, Boca Raton, FL, 1992. 

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