Modeling Volumetric Coupling of the Dispersed Phase using the Eulerian-Lagrangian Approach


Ehsan Shams, Oregon State University , Sourabh V. Apte, Oregon State University


The Eulerian-Lagrangian approach is commonly used in modeling two-phase flows wherein liquid droplets, solid particles, or bubbles are dispersed in a continuum fluid of different phase. Typically, the motion of the dispersed phase is modeled by assuming spherical, point-particles with models for added mass effects, drag, and lift forces. The effect of the dispersed phase on the fluid flow is modeled using reaction forces in the fluid momentum equation. Such an approach is valid for dilute regions of the dispersed phase. For dense regions, however, the point-particle approach does not capture the interactions between the fluid and the dispersed phase accurately. In this work, the fluid volume displaced by the dispersed phase is taken into account to model the dense regions and is termed as volumetric coupling. The size of the dispersed phase is assumed smaller than the grid resolution and the continuum phase is modeled by Eulerian equations based on the mixture theory. The variable--density, low--Mach number equations are solved using a co--located, finite volume scheme. The interphase momentum exchange due to drag forces is treated implicitly to provide robustness in the dense regions. The volumetric coupling approach first validated with analytical studies for flow induced by oscillating bubbles, gravitational settling of particles, and fluidization in granular flows. It is shown that the motion of the dispersed phase results in local, spatio-temporal variations of the volume fraction fields. The resultant divergence in the fluid velocity acts as a source or sink displacing the flow due to dispersed phase. The effectiveness of this approach as applied to dense spray systems is being investigated.



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Ehsan Shams, Oregon State University


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