  Modern particle detectors crucially depend on efficient cooling systems.
Two-phase carbon dioxide (CO$_2$) is a suitable solution as a cooling agent.
This publication presents the observations and results of investigations of
horizontal and vertical flow of two-phase CO$_2$ at a temperature of
$T=-15\,^\circ$C and a pressure of approximately $23\,$bar. Heat fluxes between
$98.5\,$kW/m$^2$ and $200\,$kW/m$^2$ were applied to the CO$_2$, covering the
range expected to occur in the future ATLAS Pixel detector being built for the
high-luminosity phase of the Large Hadron Collider. Flow speeds ranged from
$11.8\,$m/s to $28.1\,$m/s. Dedicated sensors were used to measure the
temperature and pressure before and after heating the CO$_2$. Two-phase flow
patterns occuring in the pipe after heating the CO$_2$ were recorded with a
high-speed camera. Stratified, wavy and slug flow are found to be the
predominant patterns for horizontal flow, while upward vertical flow is mainly
found to be slug or churn. Based on the recorded images the void fraction of
the CO$_2$ after heating is determined and compared for the different setups.
The results are summarised in a flow-pattern map. A clear distinction between
vertical and horizontal flow is found, with horizontal flow exhibiting a
significantly higher void fraction than vertical flow. Based on the pressure
measurements, the pressure drop after heating the CO$_2$ is measured and the
corresponding Euler number is computed. While the pressure drop increases with
the heat flux for horizontal flow due to frictional losses, the pressure drop
reduces with the heat flux in case of upward vertical flow, since static
pressure is important in this case.
