The effects of expansion on the turbulence structure of compressible boundary layers

A fully developed Mach 3 turbulent boundary layer subjected to four expansion regions (centred and gradual expansions of 7 degrees and 14 degrees) was investigated with laser Doppler velocimetry. Measurements were acquired in the incoming flat-plate boundary layer and to s/delta similar or equal to 20 downstream of the expansions. While mean velocity profiles exhibit significant progress towards recovery by the most downstream measurements, the turbulence structure remains far from equilibrium. Comparisons of computed (method of characteristics) and measured velocity profiles indicate that the postexpansion flow evolution is largely inviscid for approximately 10 delta. Turbulence levels decrease across the expansion, and the reductions increase in severity as the wall is approached. Downstream of the 14 degrees expansions, the reductions are more severe and reverse transition is indicated by sharp reductions in turbulent kinetic energy levels and a change in sign of the Reynolds shear stress. Dimensionless parameters such as anisotropy and shear stress correlation coefficient highlight the complex evolution of the post-expansion boundary layer. An examination of the compressible vorticity transport equation and estimates of the perturbation impulses attributable to streamline curvature, acceleration, and dilatation both confirm dilatation to be the primary stabilizer. However, the dilatation impulse increases only slightly for the 14 degrees expansions, so the dramatic differences downstream of the 7 degrees and 14 degrees expansions indicate nonlinear boundary layer response. Differences attributable to the varied radii of surface curvature are fleeting for the 7 degrees expansions, but persist through the spatial extent of the measurements for the 14 degrees expansions.