Multiphase flows, definition phase

Liquid-vapor phase change Multiphase flows Definition... 

For multiphase flow that is normally encountered in fluidized bed reactors, there are two kinds of definitions of the micro-scale first, it is the scale with respect to the smaller one between Kolmogorov eddies and particles second, it is the scale with respect to the smallest space required for two-phase continuum. If the first definition is adopted, the... 

Usual interpolation rules and definitions of velocity and pressure corrections, similar to single-phase flows (Eq. (6.29)), can be used to derive a pressure correction equation from the discretized form of the overall continuity (normalized) equation. The momentum equation for multiphase flows (Eq. (7.16)) can also be written in the form of Eq. (6.28) for single-phase flows. Again, following the approximation of SIMPLE, one can write an equation for velocity correction in terms of pressure correction,/ ... 

Hirt and Nichols [12] demonstrated the volume of fluid (VOF) method and started a new trend in multiphase flow simulation. It relies on the definition of an indicator function y. This function allows us to know whether one fluid or another occupies the cell, or a mix of both. In the conventional volume of fluid method [12], the transport equation for an indicator function y, representing the volume fraction of one phase, is solved simultaneously with the continuity and momentum equations as follows ... 

The conventional mobility ratio in multiphase flow is defined as the displacing fluid mobility divided by the total mobility of displaced water and oil phases. From the previous section, we can see that the unit mobility ratio based on the conventional definition is not a valid criterion to distinguish favorable and unfavorable mobility control conditions. We have found that a better criterion should be the unit mobility ratio, which is defined as the displacing fluid mobility divided by the oil mobility multiplied by the oil saturation (Eq. 4.9). In this section, we attempt to justify the proposed idea from the stability of displacement front. 

For the purposes of this book, it will be useful to have a clear definition of what is meant by disperse and polydisperse in the context of multiphase flows. By disperse, we mean that one or more of the phases is composed of clearly identifiable discrete entities such as solid particles, drops, or bubbles. By polydisperse, we mean that the properties of the... 

The primary purpose of this chapter is to introduce the key concepts and notation needed to develop models for polydisperse multiphase flows. We thus begin with a general discussion of the number-density function (NDF) in its various forms, followed by example transport equations for the NDF with known (PBE) and computed (GPBE) particle velocity. These transport equations are written in terms of averaged quantities whose precise definitions will be presented in Chapter 4. We then consider the moment-transport equations that are derived from the NDE transport equation by integration over phase space. Einally, we briefly describe how turbulence modeling can be undertaken starting from the moment-transport equations. 

Several interesting observations relate to such thermodynamic measurements. For example, the exothermic effects, associated with phase separation in LCST-type polymer blends, showed a correlation between the exothermic enthalpy and the interactions between the components (Natansohn 1985) however, the specific interaction parameter xn was not calculated. In another example, there are definitive correlations between the thermodynamic and the transport properties (see Chap. 7, Rheology of Polymer Alloys and Blends ). Thermodynamic properties of multiphase polymeric systems affect the flow, and vice versa. As discussed in Chap. 7, Rheology of Polymer Alloys and Blends , the effects of stress can engender significant shift of the spinodal temperature, AT = 16 °C. While at low stresses the effects can vary, i.e., the miscibility can either increase or decrease. 

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