Ch. Lechner, H.C. Kuhlmann:

"Direct numerical simulation of particles located close to/at a solid wall in a shear flow";

Talk: The 8th Euromech Fluid Mechanics Conference (EFMC8), Bad Reichenhall; 2010-09-13 - 2010-09-16.

We report on our current progress in developing a code to be applied in

the context of the cleaning of wafer surfaces by hydromechanical forces.

Our goal is to study the detachment of (submicron) particles, exposed to a

shear flow, from a wall by means of a direct numerical simulation.

The particles are treated as rigid bodies with a two-way

interaction with the fluid.

Our software is based on

OpenFOAM\footnote{http://www.opencfd.co.uk/openfoam/}.

Following Uhlmann\footnote{Uhlmann,

\emph{J. Comput. Phys.}, \bf{209} 448, (2005).}

and Taira and Colonius\footnote{Taira and Colonius, \emph{J. Comput. Phys.},

\bf{225} 2118, (2007).}

we implement an immersed boundary method with direct forcing.

The interpolation between the fixed Eulerian grid and the Lagrangian

forcing points is performed with the regularized delta function introduced

by Peskin\footnote{Peskin, \emph{Acta Numerica}, \bf{11} 479,

(2002).}. For the time being we implemented this

approach in 2D using OpenFOAM's standard solver {\tt icoFoam} to

solve the incompressible Navier-Stokes equations. The coupling

between the particle and the fluid is explicit. To validate the

implementation we present results on standard benchmark tests of 2D

laminar flow around a cylinder for one-way and full coupling.

As a first step towards the simulation of the detachment of a

particle from a wall we investigate the behaviour of the above

numerical method for a particle that is located close to a wall.

For the simulation of particles that are attached to the wall we

implement a soft contact model allowing

for a small overlap between the particle and the wall, which is

counteracted by an elastic restoring force.

Thereby deformation and a finite contact area

can be included in the model despite of the assumption that the particles

are rigid (see e.g. Tomas\footnote{Tomas, \emph{Chem. Eng. Sci.}, \bf{62}, 1997

(2007)}). We expose the circular particle to a linear

shear flow.

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