(98aa) A New Boundary Treatment for Complex Geometries in Smoothed Particle Hydrodynamics

Smoothed
Particle Hydrodynamics (SPH) is a Lagrangian particle method, which was
originally developed in astrophysics to simulate flows in boundary-less
domains. Nowadays, the method is mostly used to solve the governing equations
of fluid flow, including free surface flows¹.

However,
the treatment of wall boundaries in SPH is not unique and different approaches
exists, mostly based on particles^2,3.
However, engineering applications often require complex shaped geometries,
usually generated by CAD programs, e.g. in the STL format, where an appropriate
use of boundary particles or ghost particles would be highly complicated or
even lead to wrong results (e.g. at corners). Today it is not obvious how to handle
such STL geometries properly in SPH.

In our
work, we developed a new approach to model the interaction between SPH
particles and wall triangles (i.e., the STL geometry), which can easily be
implemented in a SPH code and lead to a proper behavior of fluid particles near
walls.

We use the
open-source particle simulator LIGGGHTS (www.liggghts.com),
originally developed for the simulation of granular flow via the Discrete
Element Method (DEM), also providing an SPH module. Our boundary treatment
together with the viscosity model of Morris et al.²
leads to a close agreement of the velocity profiles with the analytical
solution for a channel flow between two plates, specifically an accurately
fulfilled no-slip condition (see Figure 1).

The main
focus of our research is the application of SPH to the simulation of mixing in
hot melt extrusion processes (HME), which attracted increasing attention in
pharmaceutical manufacturing in recent years. The typically used co-rotating
twin-screw design consists of a complex shaped, rotating geometry, highly
challenging for mesh-based methods due to the deformation of the free volume
caused by the screw rotation. Our new method for boundary handling was used to
simulate the mixing process within the geometry of a co-rotating twin-screw
extruder (snapshots of the distribution of two different particle types in the
cross section of a twin-screw are shown in Figure 2).

The
presented approach provides a robust basis for efficient simulations of fluid
flow in complex, moving geometries in the STL format.

Figure 1: Velocity profiles in a pressure-driven
channel flow: analytical solution, dots: SPH solution using the developed
boundary conditions.

Figure 2: Snapshots of mixing in a cross-section
of a co-rotating twin-screw extruder. Top: initial state, center after 0.05
revolutions, bottom after 1.05 revolutions.

References

1. Monaghan JJ. Smoothed particle hydrodynamics. Reports on Progress in Physics. 2005;68(8):1703-1759.

2. Morris JP, Fox PJ, Zhu Y. Modeling Low Reynolds
Number Incompressible Flows Using SPH. Journal of Computational Physics. 1997;136(1);214-226.

3. Colagrossi A, Landrini M.
Numerical simulation of interfacial flows by smoothed particle hydrodynamics. Journal of Computational Physics.
2003;191(2):448-475