10

(xlxx ydf

DiluteXuspension2

Denseïuspension2

FIGURE 4.2 Coupling between phases in dispersed multiphase flows (from Elghobashi, 1991).

(xlxx ydf

DiluteXuspension2

Denseïuspension2

FIGURE 4.2 Coupling between phases in dispersed multiphase flows (from Elghobashi, 1991).

turbulent flows. The extent of coupling can be analyzed by examining relevant length and time scales. Elghobashi (1991) proposed a regime map for this purpose. His classification map is shown in Fig. 4.2. (x1 — x2)/dP denote the relative distance between the particles, which is approximately related to the volume fraction of the dispersed phase, a2. rX2 is a particle relaxation time, which represents entrainment of the particles by the continuous phase (expressions for various relevant time scales for dispersed multiphase flows are listed in Appendix 4.1). When particle relaxation time is much smaller than the eddy lifetime experienced by the particle (r*2 ^ r(2), particle motion is governed by continuous phase turbulence. In the other extreme, when (tjx2 > r(2), particle motion is only slightly affected by gas phase turbulence. When the collision time scale is much smaller than the particle relaxation time scale (t2c ^ tjx2), particle motion is governed by particle collisions. This is valid for dense dispersed multiphase flows. Similar analysis can also be carried out by comparing various characteristic length scales of motion with dispersed phase particle diameter (Gore and Crowe, 1989). Governing equations and boundary conditions for three modeling approaches are discussed below.

4.2.1. Volume of Fluid (VOF) Approach

Using the VOF approach, flow processes around individual dispersed phase particles are resolved unlike with EL or EE approaches. In this approach, the participating fluids share a single set of conservation equations. The governing equations can, therefore, be written:

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