An SPH Approach for Non-Spherical Particles Immersed in Newtonian Fluids

Abstract

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modeling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid–solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modeling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid and with other solid bodies by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortex formation in the fluid flow in between.

Mastering the rheology of fresh concrete: New knowledge from a DFG priority program SPP 2005

“…The participating research projects have aimed to understand the principal reasons for the shortcomings in the structure of rheological knowledge and experience, working to fill these gaps using advanced analytical [11][12][13][14][15][16][17], experimental [18][19][20][21][22][23][24], and numerical tools [25][26][27][28][29][30]. Special attention has been paid to aspects such as testing fresh cement-based suspensions [9; 31-33] capturing the effects of binder flocculation and early hydration in the…”

An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions

“…The density of a particle i is determined via summation of the respective smoothing kernel contributions of all neighboring particles j within the support radius r c ρ i = m i j W ij (14) with mass m i of particle i. This approach is typically denoted as density summation and results in an exact conservation of mass in the fluid domain, which can be shown in a straightforward manner considering the commonly applied normalization of the smoothing kernel to unity.…”

“…In the latter case, rigid particles r of rigid bodies k are considered, while naturally describing the fluid-solid interface fs . In both cases, a boundary particle b or a rigid particle r contribute to the density summation (14) and to the momentum equation ( 15) evaluated for a fluid particle i considered as neighboring particle j. The respective quantities of boundary Fig.…”

“…The velocities and the positions of rigid particles r are updated, considering the underlying rigid body motion of the corresponding rigid bodies k, in consistency with the applied time integration scheme following of fluid and rigid particles a ∈ {i, r}, the densities ρ n+1 i of fluid particles i are computed via Eq. (14). The densities ρ r of rigid particles r are not evolved and remain constant.…”

“…Most current mesh-or grid-based methods, e.g., the finite element method (FEM), the finite difference method (FDM), or the finite volume method (FVM), require substantial methodological and computational efforts to model the motion of rigid bodies in fluid flow. To overcome those issues, several approaches, e.g., based on the particle finite element method (PFEM) [1][2][3], on the discrete element method (DEM) [4][5][6][7], or on smoothed particle hydrodynamics (SPH) [8][9][10][11][12][13][14], have been proposed. SPH as a mesh-free discretization scheme is, due to its Lagrangian nature, very well suited for flow problems involving multiple phases, dynamic and reversible phase transitions, and complex interface topologies.…”