Delay of Crossflow Transition on a Yawed Cone at Mach 6

A combination of stability analysis methods are used to predict and control transition
in a Mach 6 flow over a 0.5 m long, 7-degree half-angle cone with an angle of attack (or,
equivalently, a yaw angle) of 6 degrees and freestream Reynolds number of 10.8 million per
meter. The boundary layer on the yawed cone supports the amplification of both Mack’s
second mode (MM) and crossflow (CF) instabilities. While MM is moderately amplified on
the windward side, stationary CF (SCF) vortices reach a quiet-flow transition N-factor as early
as 0.33 m from the nose tip and at an azimuthal angle of 148 degrees from the windward
side. A receptivity analysis is used to identify the effective CF initial amplitude as a function
of the spanwise wavelength associated with the natural stochastic surface roughness. The
inferred initial amplitudes are used to predict the nonlinear evolution of SCF vortices and their
secondary instability characteristics, resulting in the identification of the SCF mode that is most
likely to induce CF-driven transition. Control input in the form of subdominant CF vortices
is superimposed on the naturally dominant SCF mode to delay transition by controlling the
amplification of the target mode without causing premature transition due to excessive control
input. Results show that, contrary to previous studies of low-speed swept-wing configurations
that used shorter control mode wavelengths than the dominant CF vortex, the present yawed
circular cone configuration shows potential for significant transition delay when using control
modes with larger wavelengths. A potential transition delay of 41% is predicted for control
modes with twice the wavelength of the dominant CF vortex.