  We investigate flows interacting with a square and a fractal shape
multi-scale structures in the compressible regime for Mach numbers at subsonic
and supersonic upstream conditions using large-eddy-simulations (LES). We also
aim at identifying similarities and differences that these interactions have
with corresponding interactions in the canonical incompressible flow problem.
To account for the geometrical complexity associated with the fractal
structures, we apply an immersed boundary method to model the no-slip boundary
condition at the solid surfaces, with adequate mesh resolution in the vicinity
of the small fractal features. We validate the numerical results through
extensive comparisons with experimental wind tunnel measurements at a low Mach
number. Similar to the incompressible flow case results, we find a break-up of
the flow structures by the fractal plate and an increase in turbulent mixing in
the downstream direction. As the Mach number increases, we observe noticeable
wake meandering and higher spread rate of the wake in the lateral direction
perpendicular to the streamwise-spanwise plane. Although not significant, we
quantify the difference between the square and the fractal plates using
two-point velocity correlations across the Mach number range. The wakes
generated by the fractal plate in the compressible regime showed lower
turbulent kinetic energy (TKE) and energy spectra levels compared to those of
the square case. Moreover, results in terms of the near-field pressure spectra
seem to indicate that the fractal plate has the potential to reduce the
aerodynamic noise.
