The hypersonic flow over 30$^{\circ }$–50$^{\circ }$ double-cone configurations with three nose bluntness levels was experimentally investigated at Mach 6. High-speed schlieren photography, pressure sensors and pressure-sensitive paint were used to examine both global flow patterns and unsteady dynamics at a transitional Reynolds number. The experimental results indicate that the size of the separation region at the cone junction increases with increasing nose bluntness. Type V shock–shock interactions were observed in all three configurations, while the shock wave structures in the region below the triple point exhibited two patterns: Mach shock wave reflection in the sharp and small-blunt-nose cases, and regular shock wave reflection in the large-blunt-nose case. Spectral analysis of high-speed schlieren sequences revealed two types of unsteadiness across all cases: low-frequency shock oscillations and high-frequency unsteady structures along the boundary of supersonic jet on the second cone. For the low-frequency unsteadiness, shock oscillations displayed a broadband nature in the sharp and small-blunt-nose configurations, while a dominant frequency of approximately 2 kHz was observed in the large-blunt-nose case, characterised by shock motion and bubble breathing – an observation not experimentally reported before. Additionally, spectral analysis of wall pressure contours indicated that the low-frequency unsteadiness was primarily characterised by axisymmetric modes for all configurations. Global stability analysis and resolvent analysis further demonstrated noise-amplifier behaviour in all configurations, and the dominant low-frequency unsteadiness in the large-blunt-nose case is attributed to modal resonance induced by environmental noise.

The explosive dispersal of granular media, exemplified by the rapid radial expansion of a dense particle ring driven by internal pressurised gases, serves as a paradigmatic system for investigating multiphase blast dynamics. Despite the ubiquity of jetting and clustering phenomena in explosive dispersal scenarios, their governing mechanisms remain poorly resolved. In this work, we combine compressible computational fluid dynamics–discrete parcel method simulations, and theoretical modelling to elucidate the multiscale physics underlying explosion-induced particle jetting. We reveal a hierarchy of jetting structures, comprising non-jetting, suppressed jetting and prominent jetting, which are governed by the interplay between microscale particle force-chain evolution, mesoscale gas–particle coupling and macroscale ring dynamics. Jetting initiation emerges from the transient competition between shock-induced particle compaction and gas filtration during the early expansion phase, whereas sustained jet development requires subsequent ring implosion driven by adverse pressure gradients. By unifying this multiscale dynamics, we reduce the system’s complexity into two dimensionless parameters: one characterising mesoscale gas–particle interactions and another quantifying macroscale implosion intensity. A phase diagram for jetting morphology under weak-shock conditions is established in this dimensionless parameter space, delineating two necessary criteria for jet formation. Systems failing either criterion exhibit no jetting, resolving long-standing ambiguities in the prediction of explosive dispersal structures.

The interaction between cylindrically converging shock waves (SWs) in a water–gelatine solution and a coaxial cylindrical air bubble is studied experimentally and numerically. Two configurations are considered: (i) an azimuthally symmetric, cylindrically converging SW of Mach 1.35 impinging on a coaxial cylindrical bubble, and (ii) a semicylindrical converging SW of Mach 1.45 (corresponding to half of the cylindrical front), interacting with the same target. Shock waves are generated by exploding wire arrays driven by a high-voltage pulsed power system at beamline ID19 of the European Synchrotron Radiation Facility, delivering currents up to $130\,\text{kA}$ with rise times of $0.35$ and $0.55\,\unicode{x03BC} \text{s}$ to the cylindrical and semicylindrical wire loads, respectively. X-ray radiography is conducted at a pulse repetition rate of 5.68 MHz using two synchronised high-speed cameras. Numerical hydrodynamic simulations are performed using a compressible multiphase Navier–Stokes solver. A Gilmore-type model for compressible cylindrical bubble pulsation provides an independent analytical estimate of the interface evolution. In the cylindrical SW configuration, the bubble collapse in experiments exhibits Richtmyer–Meshkov instability spikes. The cylindrically converging shock is analysed with Guderley’s solution and Whitham’s approximation using a real-gas equation of state, predicting Mach 14.1 near the focus. In the semicylindrical configuration, momentum focuses into a single supersonic jet with a speed of 885 $\pm$ 30 m s−1, producing localised high-pressure regions, coherent vortices and complex internal Mach reflections. Experiments, simulations and theory are consistent in collapse time, interface motion and overall flow dynamics.

An experimental study was conducted to investigate the characteristics of unsteady oblique shock trains in a constant-area rectangular duct under an asymmetric incoming boundary layer. High-speed schlieren techniques and high-frequency pressure measurements were utilised in this study. The results indicate that the oblique shock train mainstream leans significantly towards the thin-boundary-layer side. Under downstream periodic excitation, the shock train moves periodically, and its shape changes during the movement. This phenomenon occurs to match the downstream pressure by altering the relative Mach number in front of the shock train, with the average pressure rise slope along the thick-boundary-layer side changing periodically. Additionally, unlike a normal shock train, the pressure rise distribution along the thick-boundary-layer side is nearly linear, and the correlation coefficients between the transducers on this side and the most downstream transducer are higher than those on the thin-boundary-layer side. Due to differences in flow structure and pressure rise distribution, the existing amplitude prediction model proposed by Xiong et al. (J. Fluid Mech. vol. 846, 2018, pp. 240–262) for the unsteady normal shock train is no longer applicable to the unsteady oblique shock train. Therefore, a new prediction model is derived and verified by experiments. Moreover, it is found that using only the downstream pressure transducer information on the thick-boundary-layer side can effectively predict the amplitude of the shock-train motion. Combined with the prediction model, a novel method is proposed to estimate the amplitude of the shock-train motion conveniently.

Supersonic diamond airfoils operating in ground effect exhibit choking phenomena, where slight variations in free-stream Mach number can induce significant alterations in the ground effect flow structure and consequently affect the aerodynamic loading on the airfoil. However, existing models for predicting the choking limit Mach number demonstrate systematic discrepancies. This study establishes a novel predictive model by analysing the steady inviscid supersonic flow field around a two-dimensional diamond airfoil in ground effect. Benchmarking against numerical simulations demonstrates that the prediction errors for the choking limit Mach number across various diamond airfoil geometries are all below 3.5 %. These results affirm the high accuracy of the proposed predictive model. Under critical choking conditions, the ground effect flow field manifests multiple shock structures, including regular reflection, curved reflection and strong Mach reflection. Crucially, all of these configurations share the characteristic feature of the reflected shock impinging on the lower vertex of the airfoil. Consequently, the problem of predicting the choking limit is reformulated as determining the free-stream Mach number at which the reflected shock strikes the lower vertex of the airfoil. To circumvent complications from the reflected shock curvature inherent to critical choking, the model solves mass and momentum conservation equations for a strategically defined control volume. This approach eliminates curvature-induced errors, enabling precise prediction of the choking limit Mach number for supersonic diamond airfoils in ground effect.

Shock tube experiments are essential in understanding the environment encountered by hypersonic vehicles. Such experiments provide information used to determine rate constants of chemical, relaxation and radiative processes taking place in non-equilibrium plasmas. These constants are significant drivers of uncertainty in surface heat flux predictions. Recent work has shown that flow non-uniformities in real shock tube experiments can be misinterpreted as a need to alter these parameters; however, no comprehensive model exists to decouple the effects. We show that there is a rigorous method to achieve this by using experimental measurements as boundary conditions and including their effects via reverse time integration. This method improves over previous implementations by rigorously enforcing conservation laws, incorporating two-temperature, non-equilibrium thermochemistry and explicitly modelling both forward- and backward-running sound waves in the shock tube test slug through a method of characteristics formulation. This approach allowed the effect of shock speed variation in highly non-equilibrium tests, specifically those relevant to Titan entry, to be studied for the first time. A validation study showed that properties predicted by the method were found to agree with results from a viscous, two-dimensional axisymmetric Navier–Stokes solver within 1.5 %. When applied to shock tube test cases from the EAST and T6 facilities for simulation of lunar return and Titan entry representative conditions, the method offered improved agreement with experimentally measured oxygen 777 nm and 240–440 nm radiance, respectively, when compared with previous implementations, particularly towards the rear of the test slug where forward-running sound waves from the driver become influential.

Richtmyer–Meshkov instability (RMI) at a single-mode interface separating an inert gas (N$_2$) and a reactive gas mixture (H$_2$/O$_2$/Xe) under reshock conditions is numerically investigated using a newly developed compressible reactive Navier–Stokes solver. The solver employs the Kéromnès mechanism (10 species, 21 reactions) for combustion modelling and a dual-flux algorithm to suppress numerical oscillations at material interfaces, demonstrating high accuracy across a wide range of benchmark tests. By systematically varying incident shock Mach numbers, we identify four distinct evolution regimes: an inert regime (${\textit{Ma}} \lt 1.80$), characterised by negligible combustion effects on interface evolution; a deflagration regime ($1.80 \lt Ma \lt 1.86$), marked by strong coupling between interface dynamics and combustion through sustained interactions; a detonation regime ($1.86 \lt Ma \lt 2.50$), where rapid transition to detonation leads to moderate coupling; and an immediate detonation regime (${\textit{Ma}} \gt 2.50$), where detonation occurs directly after incident shock impact, modifying interface evolution from the outset through intense heat release and pressure waves. Mixing width and mixing level are most significantly enhanced in the deflagration regime due to prolonged combustion-flow interactions, while cases with higher Mach numbers show reduced mixing due to rapid combustion completion. Heat release and enstrophy also display clear regime-dependent evolution behaviour: maximum heat release occurs in the detonation regime, while peak enstrophy is observed in the deflagration regime. A clear correlation is observed between the Damköhler number ($Da$), which represents the ratio of hydrodynamic to chemical time scales, and the flow regimes: for ${\textit{Ma}} \lt 1.80$, $Da \lt 1$ indicates negligible coupling; at ${\textit{Ma}} = 1.83$, $Da \approx 1$ reflects sustained coupling; and for ${\textit{Ma}} \gt 2.00$, $Da \gt 1$ denotes strong early coupling. This correlation provides a theoretical basis for interpreting the distinct regimes and guiding the modulation of reactive RMI.

Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modelling of compressible mixtures, with limited connections between different classes of models. On the one hand, existing compressible two-phase flow models accurately describe wave dynamics, but do not incorporate phase separation mechanisms. On the other hand, phase-field technology in fluid dynamics consists of models incorporating spinodal decomposition; however, a general phase-field theory for compressible mixtures remains largely undeveloped. In this paper we take an initial step toward bridging the gap between compressible two-phase flow models and phase-field models by developing a theory for compressible, isothermal N-phase mixtures. Our theory establishes a system of reduced complexity by formulating N mass balance laws alongside a single momentum balance law, thereby naturally extending the Navier–Stokes Korteweg model to N phases and providing the Navier–Stokes Cahn–Hilliard/Allen–Cahn model for compressible mixtures. Key aspects of the framework include its grounding in continuum mixture theory and its preservation of thermodynamic consistency despite its reduced complexity.

The interaction between turbulence and shock waves significantly modulates the frequency and amplitude of hydrodynamic fluctuations experienced by aerospace vehicles during low-altitude hypersonic flight. In these high-speed flows, intrinsic compressibility effects arise alongside high-enthalpy phenomena manifested through internal-energy excitation. The present study compares direct numerical simulation and linear interaction analysis (LIA) to characterise the influence of solenoidal and dilatational fluctuations, as well as endothermic processes, on a Mach 5 canonical shock–turbulence interaction (STI). Whilst the computational approach involves directly resolving all relevant length scales and potential nonlinear interactions, the LIA framework models the upstream compressible turbulence as a superposition of weakly vortical, entropic and acoustic fluctuations, with the thermal non-equilibrium thickness assumed to be much thinner than the turbulence scales. Both the numerical and theoretical methods reveal that increasing upstream compressibility enhances the turbulent kinetic energy (TKE) across the STI for varying turbulent Mach numbers. The effect of vibrational excitation is shown to further amplify the TKE downstream of the shock. The influence of upstream dilatational disturbances on the postshock turbulent spectra is also analysed, and an improved LIA-based estimate of the Kolmogorov length scale across the shock is obtained.

Since the early 1990s, numerous theoretical methods have been proposed to predict Mach stem height in steady supersonic shock reflections by assembling sub-models for local flow structures, including incident/reflected shocks, the triple point, the slipline, and Mach stem curvature. We constructed an updated model and employed it as a benchmark to evaluate the performance of various sub-models corresponding to typical flow regions. The results show that the curved assumption for the free part of the slipline outperforms the straight-line approximation, considering the differences in regions after the reflected shock can improve the predictive accuracy, while using compatibility relations in the interactive part of the slipline is superior to the wave reflection model and better captures the linear slope of Mach stem height with wedge trailing edge height. Nevertheless, prediction errors in the slope and systematic biases in the overall Mach stem height prediction persist. To address these shortcomings, we developed a calibrated scaling law for the coefficient of a linear Mach stem model. Grounded in asymptotic reasoning and high-fidelity numerical simulations, this law yields a compact, easy-to-implement expression that achieves substantially higher accuracy than existing analytical composite models across the full parameter space. It retains well-established limiting cases, clarifies how inadequate sub-modelling degrades prediction accuracy, and provides uncertainty estimates for practical engineering applications.

For regular reflection (RR) and Mach reflection (MR), the critical parameter of the trailing-edge height ($H_{R,min }$), at which the reflected shock grazes the trailing edge, is the critical condition for stable and unstable reflection. A proof of the statement that $H_{R,min }$ for MR is larger than $H_{R,min }$ for RR, within some region in the dual-solution domain, is important for confirming the existence of a dual-solution stability gap, within which RR is stable while MR is unstable. This proof is accomplished here by transitivity, with the intermediate value corresponding to the minimum height of the Mach stem. By establishing a bridge between the evaluation of $H_{R,min }$ for MR and that of the linear coefficients for Mach stem height variation with the trailing-edge height, we overcome the difficulty of quantifying $H_{R,min }$ exactly, and show that the difference between $H_{R,min }$ for MR and $H_{R,min }$ for RR is significant, meaning that there is a large enough dual-solution stability gap. The confirmation of this gap has further impact on shock transition, suggesting a new transition scenario: stable to unstable dynamic transition, i.e., within the dual-solution stability gap, a stable RR can undergo a dynamic transition to an unstable MR state (unstart flow) under suitable disturbance of the flow parameters. This dynamic transition is demonstrated here numerically. The time history of dynamic transitions displays (i) direct transitions from RR to MR to unstart flow, with complex flow structures such as hybrid MR–type VI shock interference and double MR–MR reflections, and (ii) inverted transitions, in which RR first shifts to MR and then returns back to RR.

We present a semi-analytic investigation of the resolvent operator, and its associated forcing and response modes for quasi-one-dimensional shock-laden flows. Using a Green’s function approach, we derive resolvent solutions for isentropic (subsonic and supersonic) and transonic flows with shocks in converging–diverging nozzles of arbitrary geometry. Our analysis demonstrates that shock-induced heightened sensitivity in the resolvent across flow discontinuities leads to significant discrepancies between numerically computed and the analytical input and output modes if shock effects are not properly accounted for. In particular, we find that the resolvent operator exhibits singular behaviour at the shock location. Specifically, the inviscid (where the shock is treated purely as a flow discontinuity) and viscous analytical leading resolvent modes do not converge as the viscosity parameter $\mu \rightarrow 0$, which affects the accuracy of flow control and stability analyses that rely on resolvent-based methods. Furthermore, the derived solutions serve as benchmarks for verifying numerical schemes designed to compute adjoint and resolvent modes in shock-laden flows, ensuring that they capture the correct physical behaviour in the presence of shocks.

This study investigates the reflection of a moving shock on a stationary oblique shock – a prototype for supersonic vehicle encounters. Combining computational fluid dynamics (CFD) with a simplified model with key assumptions checked against CFD, we reveal how triple-point trajectories and pressure peaks evolve with wedge angle, and identify mechanisms governing transitions between interference types. It is shown that: (i) for Type V interference, the triple points move at distinct velocities, so the equations must be set in each triple point’s moving frame rather than in a single nominal intersection point’s frame of the incident and oblique shocks. Reducing the wedge angle weakens confinement, lowering overpressure and slowing triple-point motion. (ii) At the Type VI–V transition, a sudden Mach stem emergence creates a sharp pressure spike. (iii) For Type II and IV interferences, a major difficulty arises in determining the postreflection pressure behind the shock – a key to closing the model. This obstacle is overcome by treating the flow as a normal shock impinging on a wall, an analogy that yields the missing parameter and is checked by CFD. We also find that transitions between interference types are governed by the emergence and disappearance of triple points in their moving frames, accounting for deviations from classical critical conditions. These results uncover fine-scale flow physics previously overlooked in global studies.

This study investigates the aerobreakup mechanisms of a liquid droplet initially at a temperature below its critical point impacted by a shockwave in a supercritical environment, i.e. transcritical conditions, occurring in high-pressure/speed liquid-fuelled propulsion systems. Aerobreakup droplet breakup mechanisms have been extensively studied at atmospheric conditions, not considering the significant changes in fluid properties past the critical point that occur within very short breakup time scales in shock-dominated flows. Furthermore, the effects of decreased surface tension forces due to the weakening of intermolecular forces at supercritical conditions on the droplet breakup behaviour have not been resolved to date. This study aims to address these major gaps by developing a direct numerical simulation method to investigate the governing mechanism of droplet aerobreakup at transcritical conditions considering the changes in surface tension. A diffuse interface method coupled with a real-gas equation of state is developed to capture the fluid behaviour beyond the critical point. The results show that simultaneous changes in surface tension and density ratio unique to transcritical flows dictate the droplet aerobreakup mechanisms and the resultant breakup modes. This study presents the first transcritical droplet breakup regime map as a function of Weber number and density ratio compared with the classical breakup criteria commonly accepted for subcritical conditions, proving that the breakup is facilitated at supercritical conditions. The findings are expected to significantly contribute to the development of transcritical droplet aerobreakup models to enable the simulation of spray-shock interaction needed for designing new high-speed/pressure liquid fuel injection systems.

In the article, the unsteady flow phenomenon of self-excited and forced oscillations in a rectangular diverging isolator is studied by using large eddy simulation, and the shock train region is analysed particularly. Self-excited oscillations are analysed under four pressure ratios, with pressure statistically processed to reveal shock train oscillation characteristics. The interference factors of the external environment on the unsteady flow in the isolator are investigated, and the function of upstream disturbance and downstream disturbance on the shock train oscillation is studied. Both disturbance types show that pressure amplitude increases oscillation amplitude, while frequency variations have opposing effects. Due to mismatched response speeds, low-frequency disturbances intensify oscillations, whereas high-frequency ones suppress them. The difference is that the pressure frequency excitation upstream is transmitted along the flow direction and directly acts on the shock train in the trough period of each unsteady pressure transformation, which intensifies the negative effect on shock train oscillations. The downstream disturbance arrives at the shock train region after passing through the complex flow coupling in the mixing region. The superposition of the external pressure excitation frequency and the mixing region makes the response of the shock train slower leading to a weakening effect of the shock train oscillation. Moreover, the unsteady flow develops in the mixing district and transmits upstream, and the inhibition effect is stronger than that of upstream pressure frequency excitation.

We investigate the control effects of spanwise heterogeneous roughness on shock-wave/turbulent boundary-layer interactions (STBLIs) using wall-resolved large-eddy simulations. The roughness extends over the entire computational domain and consists of streamwise-aligned sinusoidal ridges alternating with flat valleys. The baseline case is a Mach 2.0 impinging STBLI flow with a 40$^\circ$ impinging-shock angle, for which we consider incoming turbulent boundary layers at two friction Reynolds numbers, $Re_\tau \approx$ 350 and 1200. Multiple roughness configurations are analysed, which maintain consistent geometric characteristics under either inner or outer scaling. The results show that the rough-wall configurations introduce a moderate increase in mean drag, while substantially modifying the dynamics of the interaction. The wall-pressure fluctuations near the separation-shock foot consist of two components: low-frequency fluctuations associated with large-scale shock excursions and high-frequency fluctuations linked to amplified turbulence. We find that both spectral components can be significantly attenuated by the investigated wall roughness. At low Reynolds number, the attenuation of low- and high-frequency components contributes comparably to the overall reduction. At high Reynolds number, an overall stronger reduction of the pressure fluctuation peak is observed and is mainly attributed to the effective suppression of the low-frequency component. Cross-correlation analyses support downstream mechanisms for the low-frequency dynamics in the current strong interaction regime, where large-scale shock excursions are mainly driven by the breathing of the reverse-flow bubble. Large-scale Görtler-like vortices are identified around the reattachment location in all cases. They appear largely unaffected by roughness geometry and contribute to the flow dynamics over a wide range of frequencies.

Six types of shock wave interference resulting from the impingement of an incident shock on a bow shock are revisited by examining the sub-types that arise between the canonical types. Several new sub-types are predicted based on the theories of weak shock reflection and double-wedge shock interference, and verified via numerical simulations. Two additional types, Type IIw and Type IIs, are identified between Type II and Type III, whereas a Type Vw emerges between Type IV and Type V. These types originate from the transformation of the Mach reflection at the triple point, which evolves through weak shock reflections (von Neumann reflection, Vasilev reflection, Guderley reflection) before disappearing. The transition from Type III to Type IV is further shown to mirror sequences of double-wedge shock interference. Two additional types (Type IIIb and Type IVt) are found. Meanwhile, it is found that under large incoming flow Mach number ($M_0$ = 5), Types III, IV and their sub-types dominate, whereas Type II is absent; under small incoming flow Mach number ($M_0$ = 2.5), Types III and IV vanish and a modified Type Va emerges. This study adds seven new sub-types to the existing six types of shock interference. These work extend the classical six types of shock interferences into six-plus shock interference, a picture that shed new insight into shock interference.

High-intensity focused ultrasound (HIFU) is a non-invasive alternative to traditional surgery for detection and treatment. When HIFU targets a specific area, ultrasonic cavitation occurs with mechanical stress, causing tissue damage, a process that is significantly influenced by the surroundings. This paper presents a numerical study on the cavitation initiation and evolution mechanisms under focused ultrasonic waves considering the influence of a solid surface. Firstly, the dynamic property of focused ultrasonic waves and the generation of diffraction waves is explained based on the Huygens–Fresnel principle, and the prefocused phenomenon is analysed. Notably, the scenario considering the existence of a solid wall is discussed, with the corresponding cavitation clouds in a ‘tree-like’ pattern that can be generally divided into three or four subregions. The different initiation mechanisms of the near-wall cavitation clouds under a different relative distance between the theoretical focal point and the solid wall are discussed in detail. Finally, by considering the effects of the incident waves, scattered waves and their reflected waves on the solid wall, a wave superposition model is established that can clearly explain the distribution characteristics of the near-wall cavitation clouds with different modes. The understanding of the ultrasonic cavitation mechanism may support precise control in future HIFU applications.

The mixing mechanism within a single vortex has been a theoretical focus for decades, while it remains unclear especially under the variable-density (VD) scenario. This study investigates canonical single-vortex VD mixing in shock–bubble interactions (SBI) through high-resolution numerical simulations. Special attention is paid to examining the stretching dynamics and its impact on VD mixing within a single vortex, and this problem is investigated by quantitatively characterising the scalar dissipation rate (SDR), namely the mixing rate, and its time integral, referred to as mixedness. To study VD mixing, we first examine single-vortex passive-scalar (PS) mixing with the absence of a density difference. Mixing originates from diffusion and is further enhanced by the stretching dynamics. Under the axisymmetry and zero diffusion assumptions, the single-vortex stretching rate illustrates an algebraic growth of the length of scalar strips over time. By incorporating the diffusion process through the solution of the advection–diffusion equation along these stretched scalar strips, a PS mixing model for SDR is proposed based on the single-vortex algebraic stretching characteristic. Within this framework, density-gradient effects from two perspectives of the stretching dynamics and diffusion process are discovered to challenge the extension of the PS mixing model to VD mixing. First, the secondary baroclinic effect increases the VD stretching rate by the additional secondary baroclinic principal strain, while the algebraic stretching characteristic is still retained. Second, the density source effect, originating from the intrinsic nature of the density difference in the multi-component transport equation, suppresses the diffusion process. By accounting for both the secondary baroclinic effect on stretching and the density source effect on diffusion, a VD mixing model for SBI is further modified. This model establishes a quantitative relationship between the stretching dynamics and the evolution of the mixing rate and mixedness for single-vortex VD mixing over a broad range of Mach numbers. Furthermore, the essential role of the stretching dynamics on the mixing rate is demonstrated by the derived dependence of the time-averaged mixing rate $\overline {\langle \chi \rangle }$ on the Péclet number ${\textit{Pe}}$, which scales as $\overline {\langle \chi \rangle } \sim {\textit{Pe}}^{{2}/{3}}$.

An experimental investigation of separation bubble shaped control bumps for oblique shock wave–boundary-layer interactions was performed in two supersonic wind tunnel facilities at Mach 2.5 and 2, with incident shock deflection angles of $8^\circ$ and $12^\circ$, respectively, and momentum thickness Reynolds numbers of approximately $1.5 \times 10^4$. Shock control bumps were designed to replicate the time-averaged separation bubble shape, and were placed onto the floor in the separation location. This resulted in almost complete elimination of flow separation. There was also a marked improvement in the downstream boundary-layer state. A low-frequency bubble breathing oscillation was identified in the baseline interaction using high-speed shadowgraphy and particle image velocimetry measurements. This oscillation was strongly suppressed in the controlled interactions. Velocity fluctuations in the downstream boundary layer were also significantly reduced. We propose that the key mechanism by which flow separation is eliminated is by breaking down the overall pressure rise into smaller steps, each of which is below the separation threshold. A key feature is the bump crest expansion fan, located near to where the incident shock terminates, which negates the shock induced pressure jump. Thus, the precise bump geometry is critical for control efficacy and should be designed to manage these pressure rise steps as well as the expansion fan strength and location with respect to the incident shock wave. The length of the bump faces must also be sufficiently long for the boundary layer to recover between successive adverse pressure jumps.