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

Abstract

A fully developed Mach 3 turbulent boundary layer subjected to four expansion regions (centred and gradual expansions of 7° and 14°) was investigated with laser Doppler velocimetry. Measurements were acquired in the incoming flat-plate boundary layer and to s/δ≃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 post-expansion flow evolution is largely inviscid for approximately 10δ. Turbulence levels decrease across the expansion, and the reductions increase in severity as the wall is approached. Downstream of the 14° 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° expansions, so the dramatic differences downstream of the 7° and 14° expansions indicate nonlinear boundary layer response. Differences attributable to the varied radii of surface curvature are fleeting for the 7° expansions, but persist through the spatial extent of the measurements for the 14° expansions.

Advances in CFD prediction of shock wave turbulent boundary layer interactions

“…The primary experimental observation is the increase of the boundary layer thickness. In the measurements of Dawson et al [108] and Arnette et al [109] for a Mach 3 turbulent boundary layer through centered or gradual expansions of 7 (Fig. 48).…”

“…49) shows that the structures undergo an increase in both scale and angular orientation behind the expansion. Arnette et al [109] suspected that the increase in structure angle is a kinematic effect associated with the acceleration of the bottom of the structure through the inclined expansion region before the top of the structure.…”

Recovery of a supersonic turbulent boundary layer after an expansion corner

“…Therefore the expansion length Le is set to be Le≥10δ0. The experiments of Dawson et al [10] and Arnette et al [9] for 7° and 14° expansion corners at Ma=3 indicated that the boundary layer remains far from recovery even though the downstream length is 20 times the boundary layer thickness. In this study, to simulate the full recovery process, we only consider two small expansion deflection angles at 2° and 4° and set Le=16δ0≈100mm.…”

“…So far the recovery process of supersonic flow over an expansion corner is not fully understood. For a supersonic flow at Ma=3 with 7° and 14° expansions, experiments by Arnette et al [9] and Dawson et al [10] showed that the boundary layer remains far from fully recovered 19.3δ downstream of the expansion corner (δ is the incoming boundary layer thickness). Measurements of Dussauge and Gaviglio [4] even showed that the incoming boundary layer re-laminarized downstream and the subsequent evolution of the outer part of the boundary layer is very slow.…”

“…Arnette et al [8,9] used filtered Rayleigh scattering to investigate the expansion effects on a Mach 3 TBL subjected to four expansion regions (centered and gradual expansions of 7° and 14°).…”