Propagation of stationary and traveling waves in a leading-edge boundary layer of a swept wing

A Yakeno,S Obayashi

doi:10.1063/5.0063936

Abstract

The transition characteristics around the leading edge of a swept-back wing shape were numerically investigated. We conducted direct numerical simulations (DNSs) of a swept-wing shape with a high Reynolds number Re=Rec/cos Λ=5.85×106 based on the chord length with a sweep angle Λ=70°. In the study, a randomly distributed impulsive local body force was applied at the wall to encourage a transition. Through impulsive local forcing, two coherent waves formed in both an attachment line and a three-dimensional boundary layer: A stationary elongated streak structure in the external flow direction and a traveling wave in the sweep direction. These characteristics in the attachment line were slightly different from those in the three-dimensional boundary layer. We computed the nonmodal transient energy growth for the present leading-edge boundary layer and compared the coherent waves observed in the DNSs. The stationary and traveling modes in the DNSs are found to be in a transient growth group; these modes temporally grow to the maximum in the short target time (τ&lt;0.02). One of our conclusions is that both waves occurring in the present attachment line are strongly related to the short-term transient energy growth phenomena of the nonorthogonality of the flow field. When the roughness forcing was gradually increased, the traveling wave was not generated, whereas the stationary wave was. This was considered because the present attachment-line boundary layer was receptive to a small disturbance and more likely to generate a stationary wave than a traveling wave.

Highlights

Commercial aircraft often have a swept-back main wing to suppress the shock waves
We investigated the transition characteristics around an attachment line of a swept wing by employing direct numerical simulations (DNSs) at high Reynolds numbers and conducted optimal energy growth analysis in consideration of the nonorthogonality effect of the system
We identified the coexistence of the propagation of stationary and traveling waves in the attachment line and downstream three-dimensional boundary layers

Summary

Introduction

Commercial aircraft often have a swept-back main wing to suppress the shock waves. The boundary layer around a swept wing becomes three dimensional, and the crossflow makes the flow highly unstable, thereby increasing the viscous drag. To delay a transition and reduce the drag, the three-dimensional transition around a swept wing has been investigated experimentally, theoretically, and numerically for decades. Flight tests, wind tunnel visualizations, and linear stability theories have revealed that stationary crossflow instability occurs in the downstream three-dimensional boundary layer and causes streamwise vortices owing to the inflection point instability.[1,2,3,4,5,6] the linear stability theory successfully predicted the expected shapes for a stationary crossflow but not the growth rate.[6] On the other hand, the transition in a leading-edge attachment-line boundary layer has been under discussion for decades, and there have not been many numerical simulations to analyze the transition details

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