Influence of deep gaps on laminar–turbulent transition in two–dimensional boundary layers at subsonic Mach numbers

Abstract

Systematic experimental investigations on the influence of deep gaps on the location of laminar–turbulent transition are reported. The tests were conducted in the Cryogenic Ludwieg–Tube Göttingen, a blow-down wind tunnel with good flow quality, at eight different unit Reynolds numbers ranging from Re_1 = 17.5 × 10^6 m^−1 to 80 × 10^6 m^−1, three Mach numbers, M = 0.35, 0.50 and 0.65, and various pressure gradients. A flat-plate configuration, the extended two-dimensional wind tunnel model PaLASTra was modified in order to allow the installation of gaps with nominal widths of 30 μm, 100 μm and 200 μm and a depth of d = 9 mm. A maximum Reynolds number based on the gap width Re_w = Re_1 ⋅ w ≈ 16,000 was reached. Transition Reynolds numbers ranging from Re_tr ≈ 1 × 10^6 to 11 × 10^6 were measured, as a function of gap width, pressure gradient and Mach and Reynolds number. This systematic investigation facilitates a linear approximation of Re_tr dependent on the boundary layer shape factor H_12 for various flow conditions and gap widths. It was therefore possible to conduct an investigation of Retr depending on Re_1 and the relative change of the transition location depending on the gap width w. Incompressible linear stability analysis was used to calculate amplification rates of Tollmien–Schlichting waves and determine critical N-factors by correlation with measured transition locations. The change in the critical N-factor DN by installation of the gap is investigated as a function of w and Rew. It was found that a gap width of 30 μm reduces the critical N-factors in the range of DN ≈ 0.5 ± 0.25, while gap widths of 100 μm and 200 μm reduce the critical N-factor in the range of DN ≈ 1.5 ± 1. Interestingly, an increase in gap width from 100 to 200 μm was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.