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,,times 10^{6},mathrm{{m}^{-1}}} to 80,times,10^{6},mathrm{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 upmu m, 100 upmu m and 200 upmu m and a depth of d = {9,mathrm{mm}}. A maximum Reynolds number based on the gap width Re_{w} = Re_1 cdot w approx {16{,}000} was reached. Transition Reynolds numbers ranging from Re_{tr}approx 1 × 106 to 11 × 106 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 Re_{tr} 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 varDelta N by installation of the gap is investigated as a function of w and Re_w. It was found that a gap width of 30 upmu m reduces the critical N-factors in the range of varDelta N approx 0.5 pm 0.25, while gap widths of 100 upmu m and 200 upmu m reduce the critical N-factor in the range of varDelta N approx 1.5 pm 1. Interestingly, an increase in gap width from 100 to 200 upmu m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.