Crossflow instability of a three-dimensional boundary layer is a common cause of
transition in swept-wing flows. The boundary-layer flow modified by the presence of
finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities,
which are believed to harbinger the onset of transition. The role of secondary
instability in transition prediction is theoretically examined for the recent swept-wing
experimental data by Reibert et al. (1996). Exploiting the experimental observation
that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the
secondary instability analysis based on a two-dimensional eigenvalue approach. The
predicted evolution of stationary crossflow vortices is in close agreement with the
experimental data. The suppression of naturally dominant crossflow modes by artificial
roughness distribution at a subcritical spacing is also confirmed. The analysis reveals
a number of secondary instability modes belonging to two basic families which, in
some sense, are akin to the ‘horseshoe’ and ‘sinuous’
modes of the Görtler vortex problem. The frequency range of the
secondary instability is consistent with that
measured in earlier experiments by Kohama et al. (1991), as
is the overall growth of the
secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996).
Results indicate that the N-factor correlation based on secondary instability growth
rates may yield a more robust criterion for transition onset prediction in comparison
with an absolute amplitude criterion that is based on primary instability alone.
Improved Turbulence Prediction in Turbomachinery Flows and the Effect on Three-Dimensional Boundary Layer Transition †
