  The assumption of axial symmetry for hypersonic flows over conically shaped
geometries is ubiquitous in both experiments and numerical simulations. Yet
depending on the free stream conditions, many of these flows are unsteady and
their transition from laminar to turbulent is a three-dimensional phenomena.
Combining triple deck theory/linear stability analysis with the kinetic direct
simulation Monte Carlo method we analyze the azimuthal eigenmodes of flows over
single and double-cone configurations. For Mach 16 flows we find that the
strongest amplification rate occurs for the non-axisymmetric azimuthal
wavenumber of n = 1. This occurs in regions quite close to the tip of the cone
due to the proximity of the conical shock to the viscous shear layer where
non-axisymmetric modes are amplified through linear mechanisms. Comparison of
triple deck linear stability predictions shows that in addition to the
azimuthal wavenumber, both the temporal content and amplification rate of these
non-axisymmetric disturbances agree well with the time accurate DSMC flowfield.
In addition to the loss of axial symmetry observed at the conical shock, the
effect of axial symmetry assumptions on the more complex shock-shock and
shock-boundary layer interactions of a flow over a double cone are considered.
The results for the separation region show that axisymmetric and three
dimensional simulations differ in almost all of the main flow structures. Three
dimensional flowfields result in a smaller separation bubble with weaker shocks
and three dimensional effects were manifest in the variation in surface
parameters in the azimuthal direction as well. Interestingly, the DSMC
simulations show that the loss of axial symmetry in the separation region,
begins near the cone tip.
