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Ch. Lechner, M. Koch, W. Lauterborn, R. Mettin:
"Collapse of laser-generated cavitation bubbles close to a solid boundary - results from a numerical model";
Talk: The 12th European Fluid Mechanics Conference, Wien; 2018-09-09 - 2018-09-13.

Cavitation bubbles collapsing close to solid boundaries have been subject to
intense investigations for several decades.
They show a rich variety of phenomena that qualitatively and quantitatively
depend on the normalized distance $D^*$ from the boundary.
Due to their potential role in eroding the solid surface
the most prominent of these phenomena are the formation of a high-speed
axial liquid jet that pierces the bubble and the emission of shock waves
possibly forming very complex patterns. During collapse and subsequent
rebound the bubble moves towards the solid boundary such that the second
collapse happens directly at the wall for a certain range of initial $D^*$.

The experimental method to generate cavitation bubbles by focusing a short
laser pulse into a transparent liquid, while being minimal invasive,
allows to produce bubbles at well defined positions that expand to
some maximum volume in a very reproducible way. Amongst others, this method
has been used to study cavitation bubbles close to a solid boundary
in a systematic way\footnote{Philipp, Lauterborn, \emph{J.~Fluid Mech.}
\textbf{361} (1998)}${}^{,}$\footnote{Lindau, Lauterborn,
\emph{J.~Fluid Mech.} \textbf{479}, 327 (2003)}.

Numerical simulations can reveal details on the collapse
that are not, or not easily, accessible in the experiment. Recent
numerical investigations showed the formation of a secondary sheet-like
annular jet\footnote{Lechner, Koch et al.,
\emph{J.~Acoust.~Soc.~Am.~}\textbf{142},
3649 (2017)}${}^{,}$\footnote{Lauterborn, Lechner et al.~\emph{IMA J.~Appl.~Math.},
accepted} and demonstrated the propagation of a
strong tension wave in the funnel of the torus bubble
after jet impact$^4$, the latter supporting the view of the counter-jet
observed in experiments as secondary cavitation.

In this talk we present results from numerical simulations modeling the
collapse and rebound of laser-generated cavitation bubbles with an initial
normalized distance $D^* \in [1.02,2.6]$ from a rigid wall.
The numerical model consists of a bubble filled with a small amount of
non-condensable gas in a compressible liquid obeying the Tait equation of
state. We use the volume of fluid method to capture the interface
between liquid and gas. The Navier Stokes equations are discretized with the
finite volume method. We have adapted a compressible two-phase solver from
the open source software package OpenFOAM\footnote{The OpenFOAM(R) Extend
Project. http://sourceforge.net/projects/openfoam-extend} for
our purpose\footnote{Koch, Lechner et al.,
\emph{Comput.~Fluids} \textbf{126}, 71 (2016)}.

We describe the dynamics of the bubble (jet formation and impact,
splitting of the torus bubble, first collapse, rebound, second collapse),
the pattern of shock waves as well as
the pressure signal at the solid boundary as a function of $D^*$.
The numerical results concerning bubble shape parameters, jet velocities
and pressure signals are compared to experimental data.