Influence of backward-facing steps on laminar-turbulent transition in two-dimensional boundary layers at subsonic Mach numbers

Abstract

Backward-facing steps (BFS) can have a detrimental impact on laminar flow lengths because of their strong effect on boundary layer transition. BFS with step heights relative to the boundary-layer displacement thickness in the range of 0.1 to 0.6 (corresponding to height-based Reynolds numbers of 230 to 2430) were installed in a two-dimensional wind tunnel model and tested in the Cryogenic Ludwieg-Tube Göttingen, a blow-down wind tunnel with good flow quality. The influence of BFS on the location of laminar-turbulent transition was investigated over a wide range of unit Reynolds numbers from 17.5 to 80 million/m, three Mach numbers, M = 0.35, 0.50 and 0.65, and various streamwise pressure gradients. The measurement of the transition locations was accomplished non-intrusively by means of temperature-sensitive paint. Transition Reynolds numbers, calculated with the flow length up to the location of laminar-turbulent transition, ranged from 1 million to 11 million, and were measured as a function of step height, pressure gradient, Reynolds and Mach numbers. Incompressible linear stability analysis was used to calculate amplification rates of Tollmien–Schlichting waves; transition N-factors were determined by correlation with the measured transition locations. In parallel to earlier investigations with a similar setup, this systematic approach was used to identify functional relations between non-dimensional step parameters (step height relative to the boundary-layer displacement thickness and height-based Reynolds number) and the relative change of the transition location. Furthermore, the change of the transition N-factor (DeltaN) due to the installation of the steps was investigated. It was found that the installation of backward-facing steps with a step height relative to the boundary-layer displacement thickness below 0.15 and a height-based Reynolds number below 300 does not lead to a reduction of transition Reynolds number and to DeltaN > 0. However, increasing the step size results in a decreasing laminar flow length and thus an increasing DeltaN. The reported results are in general agreement with earlier investigations at significantly lower Mach and Reynolds numbers.