Reynolds effects on transition to turbulence for hypersonic expansion and compression corner flows

TL;DR

The paper investigates Reynolds-number–dependent transition in a hypersonic Cone-Cylinder-Flare geometry at $\mathit{M}_\infty=7$, combining wind-tunnel experiments in the R2Ch facility with global stability (Resolvent) analyses and data-driven tools. It demonstrates two distinct transition pathways: at high $\Rey_\infty$, the cone experiences second Mack mode growth that saturates non-linearly and interacts with expansion-induced effects, while at lower $\Rey_\infty$ a coupled regime emerges with coexisting low- and high-frequency modes and trapped acoustic waves in the separated bubble; these acoustic waves account for low-frequency pressure signatures and mediate energy transfer to higher frequencies, eventually driving transition on the flare. The study uses SPOD and Bispectral Modal Decomposition to reveal coherent structures and triadic interactions, and validates resolvent predictions against wall-pressure and schlieren measurements, including the first experimental identification of trapped acoustic waves in such a separated hypersonic flow. Overall, the work advances understanding of hypersonic boundary-layer transition, highlighting the critical roles of Reynolds number and flow separation in shaping transition routes and their implications for aerothermal loads and vehicle design.

Abstract

This experimental and numerical study examines transition to turbulence for a Cone-Cylinder-Flare geometry at Mach 7 and across a broad Reynolds number range. The focus is set on both attached boundary layers and separated shock-boundary layer interactions. The campaign is conducted in the R2Ch facility. Unsteady wall pressure fluctuations and high-speed schlieren images are analysed using data-driven techniques and compared with base flow computations and global linear stability analysis. The results distinguish two transition regimes. At high Reynolds numbers, transition is dominated by the second Mack mode and its non-linear interactions on the cone. High-frequency wall pressure measurements and schlieren imaging permit the capture of both fundamental waves and their non-linear harmonics. Non-linear interaction regions are resolved with unprecedented detail, clarifying the boundary-layer state before rapid breakdown at reattachment. At lower Reynolds numbers, the transition scenario is more intricate, marked by the coexistence of low- and high-frequency modes. A complex coupling between separated flow and convective instabilities is revealed, with trapped acoustic waves inside the recirculation region measured experimentally for the first time. Their linear origin is demonstrated through global stability analysis, and a simple acoustic duct model is provided to predict their frequencies. These waves offer a new interpretation of low-frequency pressure signatures and suggest a mechanism for energy transfer from high to low frequencies, ultimately driving transition on the flare. The findings advance understanding of hypersonic boundary-layer transition and its dependence on Reynolds number and flow separation.

Figures (24)

• Figure 1: Summary of the Cone-Cylinder-Flare hypersonic-flow features
• Figure 2: Overview of the possible routes to turbulence for a CCF-like geometry
• Figure 3: Overview of the wind-tunnel and the CCF12 model used for the campaign.
• Figure 4: Summary of all the $M_\infty=7.0$ flow conditions considered in the experimental campaign and the corresponding flow conditions used in this paper.
• Figure 5: Mean strioscopy of the flow around CCF12 at increasing Reynolds number