Influence of Surface Irregularities on the Expected Boundary-Layer Transition Location on Hybrid Laminar Flow Control Wings
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Influence of deep gaps on laminar–turbulent transition in two-dimensional boundary layers at subsonic Mach numbers
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 $$Re_1 = {17.5\,\,\times 10^{6}\,\mathrm{{m}^{-1}}}$$ R e 1 = 17.5 × 10 6 m - 1 to $$ 80\,\times\,10^{6}\,\mathrm{m}^{-1}$$ 80 × 10 6 m - 1 , three Mach numbers, $$M= 0.35$$ 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 $$30$$ 30 $$\upmu $$ μ m, $$100$$ 100 $$\upmu $$ μ m and $$200$$ 200 $$\upmu $$ μ m and a depth of $$d = {9\,\mathrm{mm}}$$ d = 9 mm . A maximum Reynolds number based on the gap width $$Re_{w} = Re_1 \cdot w \approx {16{,}000}$$ R e w = R e 1 · w ≈ 16 , 000 was reached. Transition Reynolds numbers ranging from $$Re_{tr}\approx $$ R e tr ≈ 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 $$Re_{tr}$$ R e tr dependent on the boundary layer shape factor $$H_{12}$$ H 12 for various flow conditions and gap widths. It was therefore possible to conduct an investigation of $$Re_{tr}$$ R e tr depending on $$Re_{1}$$ R e 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 $$\varDelta N$$ Δ N by installation of the gap is investigated as a function of w and $$Re_w$$ R e w . It was found that a gap width of 30 $$\upmu $$ μ m reduces the critical N-factors in the range of $$\varDelta N \approx 0.5 \pm 0.25$$ Δ N ≈ 0.5 ± 0.25 , while gap widths of 100 $$\upmu $$ μ m and 200 $$\upmu $$ μ m reduce the critical N-factor in the range of $$\varDelta N \approx 1.5 \pm 1$$ Δ N ≈ 1.5 ± 1 . Interestingly, an increase in gap width from 100 to 200 $$\upmu $$ μ m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.
Influence of deep gaps on laminar–turbulent transition in two-dimensional boundary layers at subsonic Mach numbers
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 $$Re_1 = {17.5\,\,\times 10^{6}\,\mathrm{{m}^{-1}}}$$ R e 1 = 17.5 × 10 6 m - 1 to $$ 80\,\times\,10^{6}\,\mathrm{m}^{-1}$$ 80 × 10 6 m - 1 , three Mach numbers, $$M= 0.35$$ 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 $$30$$ 30 $$\upmu $$ μ m, $$100$$ 100 $$\upmu $$ μ m and $$200$$ 200 $$\upmu $$ μ m and a depth of $$d = {9\,\mathrm{mm}}$$ d = 9 mm . A maximum Reynolds number based on the gap width $$Re_{w} = Re_1 \cdot w \approx {16{,}000}$$ R e w = R e 1 · w ≈ 16 , 000 was reached. Transition Reynolds numbers ranging from $$Re_{tr}\approx $$ R e tr ≈ 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 $$Re_{tr}$$ R e tr dependent on the boundary layer shape factor $$H_{12}$$ H 12 for various flow conditions and gap widths. It was therefore possible to conduct an investigation of $$Re_{tr}$$ R e tr depending on $$Re_{1}$$ R e 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 $$\varDelta N$$ Δ N by installation of the gap is investigated as a function of w and $$Re_w$$ R e w . It was found that a gap width of 30 $$\upmu $$ μ m reduces the critical N-factors in the range of $$\varDelta N \approx 0.5 \pm 0.25$$ Δ N ≈ 0.5 ± 0.25 , while gap widths of 100 $$\upmu $$ μ m and 200 $$\upmu $$ μ m reduce the critical N-factor in the range of $$\varDelta N \approx 1.5 \pm 1$$ Δ N ≈ 1.5 ± 1 . Interestingly, an increase in gap width from 100 to 200 $$\upmu $$ μ m was not found to induce smaller transition Reynolds numbers or reduced N-factors, which might be due to resonance effects.
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