A pressure–velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids

Abstract

Summary A methodology for improved robustness in the simulation of high void fraction free surface polydisperse bubbly flows in curvilinear overset grids is presented. The method is fully two‐way coupled in the sense that the bubbly field affects the continuous fluid and vice versa. A hybrid projection approach is used in which staggered contravariant velocities at cell faces are computed for transport and pressure–velocity coupling while the momentum equation is solved on a collocated grid arrangement. Conservation of mass is formulated such that a strong coupling between void fraction, pressure, and velocity is achieved within a partitioned approach, solving each field separately. A pressure–velocity projection solver is iterated together with a predictor stage for the void fraction to achieve a robust coupling. The implementation is described for general curvilinear grids detailing particulars in the neighborhood to overset interfaces or a free surface. A balanced forced method to avoid the generation of spurious currents is extended for curvilinear grids. The overall methodology allows simulation of high void fraction flows and is stable even when strong packing forces accounting for bubble collisions are included. Convergence and stability in one‐dimensional (1D) and two‐dimensional (2D) configurations is evaluated. Finally, a full‐scale simulation of the bubbly flow around a flat‐bottom boat is performed demonstrating the applicability of the methodology to complex problems of engineering interest. Copyright © 2015 John Wiley & Sons, Ltd.

A mechanistic model of bubble entrainment in turbulent free surface flows

“…This section briefly summarizes the two-fluid model used in this work to provide the mathematical framework for which the air entrainment model is developed. Further details can be found in Castro and Carrica (2013a;2013b), Li et al (2015), and references therein.…”

“…The entrainment model was implemented in the dynamic overset CFD code REX, which has polydisperse bubble transport capabilities. A brief summary is discussed next, but full details can be found in Castro and Carrica (2013a;2013b), Martin et al (2015), Li et al (2015), and references therein.…”

“…The void fraction is then defined as the sum of all group void fractions, and use of the proper models for the interfacial forces listed in Eq. (7) (Li et al 2015),…”

“…Discretization and solution algorithms for the two-fluid polydisperse approach are complex due to the multiple non-linear coupling between the equations, and is discussed in detail in Castro et al (2013aCastro et al ( , 2013b and Li et al (2015). General discretization in REX uses multiblock structured curvilinear body-fitted grids with a dynamic overset capability that allows the placement of local refinements where needed and to perform computations with large amplitude motions.…”

“…Suggar is used to dynamically obtain overset interpolation coefficients (Carrica et al 2010). Pressure-velocity coupling is achieved using a hybrid projection approach as discussed in Li et al (2015).…”