81 research outputs found
Optimal two-dimensional roughness for transition delay in high-speed boundary layer
The influence of surface roughness on transition to turbulence in a Mach 4.5
boundary layer is studied using direct numerical simulations. Transition is
initiated by the nonlinearly most dangerous inflow disturbance, which causes
the earliest possible breakdown on a flat plate for the prescribed inflow
energy and Mach number. This disturbance is primarily comprised of two normal
second-mode instability waves and an oblique first mode. When localized
roughness is introduced, its shape and location relative to the synchronization
points of the inflow waves are confirmed to have a clear impact on the
amplification of the second-mode instabilities. The change in modal
amplification coincides with the change in the height of the near-wall region
where the instability wave-speed is supersonic relative to the mean flow; the
net effect of a protruding roughness is destabilizing when placed upstream of
the synchronization point and stabilizing when placed downstream. Assessment of
the effect of the roughness location is followed by an optimization of the
roughness height, abruptness and width with the objective of achieving maximum
transition delay. The optimization is performed using an ensemble-variational
(EnVar) approach, while the location of the roughness is fixed upstream of the
synchronization points of the two second-mode waves. The optimal roughness
disrupts the phase of the near-wall pressure waves, suppresses the
amplification of the primary instability waves, and mitigates the nonlinear
interactions that lead to breakdown to turbulence. The outcome is a sustained
non-turbulent flow throughout the computational domain
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