Immersed boundary method (IBM) based direct numerical simulation of open‐cell solid foams: Hydrodynamics

Abstract

A sharp interface implicit immersed boundary method is developed and used for direct numerical simulations of the flow through open-cell solid foams with a cellular structure. The complex solid structure of the foam is resolved on a non-boundary fitted Cartesian computational-grid. A single representative unit cell of the foam is considered in a periodic domain, and its geometry is approximated based on the structural packing of a tetrakaidecahedron. Simulations are performed for a wide range of porosities (0.638-0.962) and Reynolds numbers (0-500). Flow is enforced by applying a constant body force (momentum source) for three different flow directions along the {100}, {110}, and {111} latticevectors. The drag force on the foam is calculated and a non-dimensional drag/pressure drop correlation is proposed that fits the entire data set with an average deviation of 5.6%. Moreover, the accurate numerical simulations have helped to elucidate the detailed fluid-solid interaction in complex porous media.

Multiscale modeling of fixed-bed reactors with porous (open-cell foam) non-spherical particles: Hydrodynamics

“…The flow at a length scale inside the particles i.e. d μ is not fully resolved, and represented using closure terms, derived separately from fully resolved computations [18]. However, the inter-particle flow (at the length scale of d P ) is fully resolved.…”

“…In the present modeling approach, the flow around the particle will be fully resolved, however, the flow inside the particle will be modeled by closure terms developed separately from fully-resolved simulations. a ( ) Packed bed filled with porous non-spherical particles and a Representative Elementary Volume (REV) of a typical foam sample that is fully resolved in a DNS domain [18,38]. b ( ) Macroscopic modeling of the full bed where flow inside the particles is not resolved and instead modeled using volume averaging theory (VAT).…”

“…Although some details of the flow field are lost due to averaging, the hierarchical modeling technique is essential when two substantially different length scales are persist in the problem. The drag closure (flow resistance) for the fluid-foam interaction at the micro-scale has been obtained separately by performing fully resolved direct numerical simulations using idealized geometry of a single unit-cell of open-cell solid foams [18]. The cylindrical wall effect is important for slender packed beds and in the adopted Cartesian computational domain it is resolved by an implicit, sharp interface immersed boundary method (IBM) [19].…”

Simple immersed boundary matrix‐cut‐method for cartesian grids using FV and FD discretizations

“…To explain the simplicity of the method, we consider two cases shown in Figure 1. One case corresponds to the two-dimensional rectangular plate subjected to Dirichlet boundary conditions on the [6] Khadra et al [7] Discrete forcing (FD, FV) unsteady iterative Mohd-Yosuf, [11] Faldun et al, [12] Balaras [13] Cut-cell method (FV) steady or unsteady iterative Udaykumar et al, [15] Ye et al, [16] Udaykumar et al [17] Flag-matrix concept (FD, FV) steady or unsteady iterative Kuipers et al, [18] Deen et al, [19] Das et al [21][22][23] Implicit fictitious boundary (FEM) steady or unsteady iterative…”

“…This method was extended to include a 3D finite‐volume formulation applied to the DNS of flow and heat transfer in dense fluid‐particle systems and the DNS of a dispersed gas‐liquid two‐phase flow using a volume‐of‐fluid (VOF) approach. Recently, Das et al developed a new second‐order implicit IB method for a structured grid, enabling the incorporation of the Dirichlet, Neumann, and Robin boundary condition types. This method requires a matrix iterative solver.…”