Peixu Guo

This paper proposes a modular parametric framework for axisymmetric high-speed wind tunnel nozzle design, which innovatively introduces the Terminal Characteristic Line (TCL) theory to isolate upstream and downstream flow fields. It divides the wind tunnel nozzle into several modules for design. In the upstream initial expansion section module, this work improves the Method of Characteristics (MOC), which abandons empirical axial Mach number distributions and supports user-controlled length. In the downstream damping section module, it references the minimum-length nozzle (MLN) design method, serving as a case for modular design. The framework is developed in Python code and open-sourced on GitHub, which can design and output inviscid contours and boundary layer correction results based on user needs. Validation using Computational Fluid Dynamics (CFD), which covers multiple design cases from the framework, shows excellent outlet flow uniformity and demonstrates length-to-diameter ratio control capability.

According to the state of incoming boundary layer, shock wave/boundary layer interaction can be classified into three groups: shock wave/laminar boundary layer interaction (SLBLI), shock wave/transitional boundary layer interaction (STrBLI) and shock wave/turbulent boundary layer interaction (STBLI). Although STBLI has been comprehensively studied, the difference between SLBLI and STrBLI is still not fully understood, especially in the framework of laminar–turbulent transition. In this work, a compression-ramp flow at Mach 6.5 is studied using experiment, direct numerical simulations (DNS) and stability analysis. Two distinct transition scenarios are revealed. On the one hand, without introducing external disturbances in the DNS, transition to turbulence is observed downstream of reattachment. This transition process is excited by the global instability in the separation bubble. On the other hand, the experiment captures a much smaller separation bubble under the same flow conditions. When realistic disturbances are superimposed on the freestream of DNS, a good agreement between the DNS and the experiment is achieved. The first mode is shown to be responsible for the transition. It is found that in the first transition scenario, the transition zone is located downstream of the reattachment region, and as a result, the size of the separation bubble is nearly not affected by the transition. This identifies an SLBLI. In the second transition scenario, however, the reattachment region is fully covered by the transition zone, accompanied by the shrinking of the separation bubble. This features an STrBLI. Therefore, the relative position between the reattachment region and the transition zone can be used to identify whether a flow belongs to SLBLI or STrBLI.

This study investigates the Mach-6 compression ramp flows at a unit Reynolds number of [ ] in a Ludwieg tube tunnel, with ramp angles ranging from 4 to 10 deg. Global stability analysis indicates that global instability is absent in all cases. Resolvent analysis identifies three convective instability modes: Mack’s first mode, second mode, and a streak mode, each exhibiting distinct features across different cases. A combination of schlieren visualization, Rayleigh scattering photography, surface pressure measurements, and infrared thermography is employed to reveal the convective instability characteristics and the associated laminar-to-turbulent boundary-layer transition mechanisms. It is found that the transition point significantly shifts upstream when flow separation occurs at the ramp corner for ramp angles exceeding 4 deg. The shear-layer mode and Mack’s second mode are measured by pressure sensors. The spatial evolution of detailed flow structures within the reattached boundary layer, such as staggered wavelike structures, [ ] vortices, and streamwise streaks, is visualized. Analysis of the evolution and breakdown of these structures reveals that the nonlinear evolution of the first mode predominantly drives boundary-layer transition in the 4-deg-ramp case, referred to as the oblique transition. Görtler instability is significantly amplified near the separation and reattachment regions, with its strength increasing with the ramp angle. Consequently, it plays a more critical role in the transition process at higher ramp angles and dominates in the 10-deg-ramp case. For moderate ramp angles, both the first mode and Görtler instability are pronounced in the transition process.

Boundary-layer instability and transition control have drawn extensive attention from the hypersonic community. The acoustic metasurface has become a promising passive control method, owing to its straightforward implementation and lack of requirement for external energy input. Currently, the effects of the acoustic metasurface on the early and late transitional stages remain evidently less understood than the linear instability stage. In this study, the transitional stage of a flat-plate boundary layer at Mach 6 is investigated, with a particular emphasis on the nonlinear mode–mode interaction. The acoustic metasurface is modelled by the well-validated time-domain impedance boundary condition. First, the resolvent analysis is performed to obtain the optimal disturbances, which reports two peaks corresponding to the oblique first mode and the planar Mack second mode. These two most amplified responses are regarded as the dominant primary instabilities that trigger the transition. Subsequently, both optimal forcings are introduced upstream in the direct numerical simulation, which leads to pronounced detuned modes before breakdown. The takeaway is that the location of the acoustic metasurface is significant in minimising skin friction and delaying transition onset simultaneously. The bispectral mode decomposition results reveal the dominant energy-transfer routine along the streamwise direction – from primary modes to low-frequency detuned modes. By employing the acoustic metasurface, the nonlinear triadic interaction between high- and low-frequency primary modes is effectively suppressed, ultimately delaying transition onset, whereas the late interaction related to lower-frequency detuned modes is reinforced, promoting the late skin friction. The placement of the metasurface in the linearly unstable region of the second mode delays the transition, which is due to the suppressed streak in the oblique breakdown scenario. However, in the late stage of the transition, the acoustic metasurface induces an undesirable increment of skin friction overshoot due to the augmented shear-induced dissipation work, which mainly arises from reinforced detuned modes related to the combination resonance. Meanwhile, by restricting the location of the metasurface upstream of the overshoot region, this undesirable augmentation of skin friction can be eliminated. As a result, the reasonable placement of the metasurface is crucial to damping the early instability while causing less negative impacts on the late transitional stage.

Transition onset of high-speed boundary layers can move first downstream and then upstream with increasing nose-tip bluntness, which is called transition reversal. For the first time, our recent research reproduced the experimentally observed transition reversal by direct numerical simulation (DNS, Guo et al. , J. Fluid Mech. vol. 1005, 2025, A5). As a continuation study, this work explores the effect of the form of free-stream disturbances, as the transition in the large-bluntness regime still remains poorly understood. The free-stream Mach number is 5 and the nose-tip radius 3 mm of the blunt plate exceeds the experimental reversal value. Three-dimensional broadband perturbation is carefully constructed through superimposition of planar fundamental waves in the free stream, which initiates the transition in DNS. For each Fourier component, the same perturbation strength is applied for slow/fast acoustic, vortical and entropic waves. All the cases present a ‘streak-turbulent spot’ two-stage transition scenario due to non-modal instabilities. The transition onset locations induced by entropic and slow/fast acoustic waves are close and significantly ahead of that by vortical waves. More evident impact of the disturbance form is manifested in the length of the transitional region, which is the shortest for entropic waves and the longest for vortical waves. Regarding the effect of the angle of incidence that mimics the tunnel environment, it alters the post-shock acoustic-wave structure and reduces the length of the transitional region. In the streaky stage, the form of free-stream disturbances changes the pronounced spanwise wavelengths on the blunt nose and the plate, where the two regions also differ from each other. In the turbulent-spot region, the shortest transitional region induced by the entropic wave is attributed to its largest mean spanwise spreading rate of the turbulent spot. From the perspective of energy budget, shear-induced dissipation dominates the heat transfer escalation in the transitional region. Overall, with significant leading-edge bluntness, the flight environment may tend to result in delayed transition onset compared with the tunnel counterpart.

This study investigates the effect of angle of attack (AOA) on the convective instability of a hypersonic flow over a compression ramp at Mach 7.7, with particular emphasis on high-frequency two-dimensional Mack modes and low-frequency three-dimensional shear-layer instabilities. Combining linear stability theory (LST) and resolvent analysis, we examine how the change in AOA affects the convective instability mechanisms associated with separation bubbles. Results show that as AOA decreases from zero to negative, the separation bubble elongates, leading to increased growth rates and spatial extent of higher-order Mack modes. The negative AOA also promotes the emergence of additional shear-layer instabilities within concave high-curvature regions near the aft portion of the bubble. In contrast, positive AOAs compress the separation bubble, suppress higher-order modes, and reduce both the number and growth rates of shear-layer instability modes. Notably, at large positive AOA, the separation bubble acts as a broadband perturbation amplifier in the vicinity of the separation point for high-frequency Mack modes. For both large positive or negative AOAs, the low-frequency shear layer modes are shown to be unsteady Görtler modes. A comparison between LST and resolvent analysis demonstrated good agreement, confirming that the parallel-flow assumption underlying LST remains largely valid across multiple AOAs. These results indicate that, despite the changing bubble morphology with AOA, LST remains a valid tool for stability studies of the shock wave–boundary layer interaction (laminar flow).

The simulation of transcritical flows remains challenging due to strong thermodynamic nonlinearities that induce spurious pressure oscillations in conventional schemes.While primitive-variable formulations offer improved robustness under such conditions, they are always limited by energy conservation errors and the absence of systematic high-order treatments for numerical fluxes. In this paper, we introduce the Central Differential flux with High-Order Dissipation (CDHD), a novel numerical flux solver designed for primitive-variable discretization. This method combines a central flux for advection with a minimal, upwind-biased dissipation term to stabilize the simulation while maintaining formal accuracy. The dissipation term effectively suppresses oscillations and improves stability in transcritical flows. Compared to traditional primitive-variable approaches, CDHD reduces the energy conservation error in two order of magnitude. When incorporated into a hybrid framework with a conservative shock-capturing scheme, the method robustly handles both smooth transcritical phenomena and shock waves. Numerical tests validate the accuracy, stability, and energy-preserving capabilities of CDHD, demonstrating its potential as a reliable tool for complex real-gas flow simulations.

The hypersonic flow stability over a two-dimensional compression corner is studied using Resolvent analysis, linear stability theory (LST), and parabolized stability equation. The authors find that the interaction between upstream convective-type disturbances and the laminar separation bubble can be divided into two regimes. First, two-dimensional (2D) high-frequency Mack (second, third, etc.) modes neutrally oscillate with the presence of alternating stable and unstable regions inside the separation bubble, which arises from repeated synchronizations between discrete modes with evolving branches. Meanwhile, the second modes upstream and downstream of the separation bubble can differ significantly from each other. Second, the 2D low-frequency shear-layer mode is stable, whereas multiple unstable three-dimensional (3D) eigenmodes are identified by LST. These modes are found to be sensitive to the streamline curvature effect. The locally dominant modes agree with the Resolvent response in terms of the preferential spanwise wave number, the disturbance shape, and the growth rate of energy. Thus, a combination of global and local analyses demonstrates that the separation bubble tends to selectively amplify low-frequency 3D disturbances and freeze high-frequency Mack-mode disturbances in an explainable manner. These findings facilitate the understanding of the early evolution of low- and high-frequency instabilities in hypersonic separated flows.