Secondary instability and subcritical transition of the leading-edge boundary layer

Abstract

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as Re ≈ 175, i.e. far below the linear critical Reynolds number Re crit ≈ 583 of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above Re tr ≈ 250. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number Re tr ≈ 250 at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

“…The temporal amplification rate for the sinuous symmetry exhibits two peaks at x i ≈ 5 and x i ≈ 12 where ω i ≈ 0.48 and ≈ 0.4, respectively. One may remark that the onset of several modes for large streak amplitudes have also recently been observed by John et al [36] for the leading edge boundary layer near the attachment line. For the varicose case, ω i peaks for x i ≈ 12 with a value ≈ 0.5.…”

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“…To this end, we designed a computational model of a BHV in an anatomically correct model of an AR. The governing equations were solved with a FSI solver (Nestola et al, 2019 ) which comprises a finite-element structural solver for soft tissue and a high-order Navier–Stokes solver that has been designed for the study of laminar-turbulent transition (e.g., Obrist et al, 2012 ; John et al, 2016 ). The FSI solver was verified and validated for canonical benchmarks in Nestola et al ( 2019 ).…”

Secondary Instability and Subcritical Transition in the Leading-Edge Boundary Layer

“…This HSS configuration is connected with vortices supported by the cross-flow situation for larger chordwise x positions downstream. It is therefore unstable at much lower Reynolds numbers than an LSS configuration with an inverted sense of rotation of the vortex pair (John, Obrist & Kleiser 2016).…”