The interaction between planar incident shocks and cylindrical boundary layers is prevalent in missiles equipped with inverted inlets, which typically leads to substantial three-dimensional flow separation and the formation of vortical flow. This study utilizes wind-tunnel experiments and theoretical analysis to elucidate the shock structure, surface topology and pressure distributions induced by a planar shock with finite width impinging on a cylinder wall at Mach 2.0. In the central region, a refraction phenomenon occurs as the transmitted shock bends within the boundary layer, generating a series of compression waves that coalesce into a shock, forming a ‘shock triangle’ structure. As the incident shock propagates backward along both sides, it gradually evolves into a Mach stem, where the transmitted shock refracts the expansion wave. The incident shock interacts with the boundary layer, resulting in the formation of a highly swept separation region that yields a pair of counter-rotating horseshoe-like vortices above the separation lines. These vortices facilitate the accumulation of low-energy fluid on both sides. Although the interaction of the symmetry plane aligns with free-interaction-theory, the separation shock angle away from the centre significantly deviates from the predicted value owing to the accumulation of low-energy fluids. The primary separation line and pressure distribution jointly exhibit an elliptical similarity on the cylindrical surface. Furthermore, the potential unsteady behaviour is assessed, and the Strouhal number of the low-frequency oscillation is found to be 0.0094, which is insufficient to trigger significant alterations in the flow field structure.

This study identifies two previously unrecognised screech modes in non-axisymmetric jets. Spectral proper orthogonal decomposition (SPOD) of ultra-high-speed schlieren images reveals a bi-axial flapping mode in a rectangular jet and a quasi-helical mode in an elliptical jet. To educe the complex three-dimensional structure of these new modes, SPOD is performed on datasets from different viewing perspectives, produced by rotating the nozzle with respect to the schlieren path to an azimuthal angle $\theta$. The bi-axial flapping mode is strongly antisymmetric from any perspective. However, the SPOD eigenvalue at the screech frequency ($\lambda _s$) varies with $\theta$ and the axial distance of the SPOD domain from the nozzle lip. This mode most closely resembles a flapping mode in the minor-axis plane close to the nozzle lip and a wagging mode in the major-axis plane further downstream. This transition from flapping to wagging at the same frequency correlates with the axis switching defined by the shock-cell structure in the mean flow. The quasi-helical mode in the elliptical jet is characterised by an antisymmetric structure present in the SPOD spatial modes whose eigenvalue $\lambda _s$ is insensitive to both $\theta$ and the axial domain. These findings indicate that the spatial evolution of the mean flow in non-axisymmetric jets may allow them to support a range of additional screech modes that differ significantly from those supported by the original three-dimensional shape of the jet.

In this paper, we study the rapid transition in Richtmyer–Meshkov instability (RMI) with reshock through three-dimensional double-layer swirling vortex rings. The rapid transition in RMI with reshock has an essential influence on the evolution of supernovas and the ignition of inertial confinement fusion, which has been confirmed in numerical simulations and experiments in shock-tube and high-energy-density facilities over the past few years. Vortex evolution has been confirmed to dominate the late-time nonlinear development of the perturbed interface. However, few studies have investigated the three-dimensional characteristics and nonlinear interactions among vortex structures during the transition to turbulent flows. The coexistence of co-rotating and counter-rotating vortices is hypothesized to induce successive large-scale strain fields, which are the main driving sources for rapid development. The three-dimensional effect is reflected in the presence of local swirling motion in the azimuthal direction, and it decreases the translation velocity of a vortex ring. Large-, middle- and small-scale strain fields are employed to describe the development process of RMI with reshock, e.g. vorticity deposited by the reshock, formation of the coexistence of the co-rotating and counter-rotating vortices, iterative cascade under the amplification of the strain fields and viscous dissipation to internal energy. This provides theoretical suggestions for designing practical applications, such as the estimation of the hydrodynamic instability and mixing during the late-time acceleration phase of the inertial confinement fusion.

The manipulation of the Richtmyer–Meshkov instability growth at a heavy–light interface via successive shocks is theoretically analysed and experimentally realized in a specific shock-tube facility. An analytical model is developed to forecast the interface evolution before and after the second shock impact, and the possibilities for the amplitude evolution pattern are systematically discussed. Based on the model, the parameter conditions for each scenario are designed, and all possibilities are experimentally realized by altering the time interval between two shock impacts. These findings may enhance the understanding of how successive shocks influence hydrodynamic instabilities in practical applications.

Fluid dynamics systems driven by dominant, near-periodic dynamics are common across wakes, jets, rotating machinery and high-speed flows. Traditional modal decomposition techniques have been used to gain insight into these flows, but can require many modes to represent key physical processes. With the aim of generating modes that intuitively convey the underlying physical mechanisms, we propose an intrinsic phase-based proper orthogonal decomposition (IPhaB POD) method, which creates energetically ranked modes that evolve along a characteristic cycle of the dominant near-periodic dynamics. Our proposed formulation is set in the time domain, which is particularly useful in cases where the cyclical content is imperfectly periodic. We formally derive IPhaB POD within a POD framework that therefore inherits the energetically ranked decomposition and optimal low-rank representation inherent to POD. As part of this derivation, a dynamical systems representation is utilized, facilitating a definition of phase within the system's near-periodic cycle in the time domain. An expectation operator and inner product are also constructed relative to this definition of phase in a manner that allows for the various cycles within the data to demonstrate imperfect periodicity. The formulation is tested on two sample problems: a simple, low Reynolds number aerofoil wake, and a complex, high-speed pulsating shock wave problem. The method is compared to space-only POD, spectral POD (SPOD) and cyclostationary SPOD. The method is shown to better isolate the dominant, near-periodic global dynamics in a time-varying IPhaB mean, and isolate the tethered, local-in-phase dynamics in a series of time-varying modes.

This study investigates the heating issue associated with a V-shaped blunt leading edge (VBLE) in a hypersonic flow. The heat flux generation on the VBLE is highly correlated with the shock interaction configurations in the crotch region, determined by the relative position of the triple point T and the curved shock (CS). The primary Mach reflection (MR), accompanied by a series of secondary shock–shock interactions and shock wave–boundary layer interactions, can produce extremely high heating peaks on the crotch. To configure the shock wave structures and reduce the heat flux, a shock-controllable design approach is developed based on the simplified continuity method. The strategy involves the inverse design of the crotch sweep path, according to the location of the triple point and the contour of the CS. The comparisons between the pre-designed shock configurations and the numerical results demonstrate the reliability of the design approach across various free stream Mach numbers ranging from 6 to 10. A VBLE model designed with the shock configuration of regular reflection from the same family (sRR) at a free stream Mach number of 8 is examined. Under the design conditions, the outermost heat flux peak is reduced by 80 % compared with the baseline case. The heating reduction capabilities of the model under varying free stream Mach numbers and sideslip angles are also evaluated, confirming its robustness under undesigned operating scenarios.

An asymptotic matching modal model is established based on the singular perturbation method for predicting mode evolution in single- and dual-mode interfaces accelerated by a shock wave. The startup process is incorporated into the model to provide a complete description of the mode evolution after the shock impact. Through considering the feedback from high-order harmonic to the third-order harmonic, the model accuracy is improved and the model divergence is prevented. In addition, the model can evaluate the mutual-coupling effect on the amplitude variations of high-order harmonics besides the ‘beat modes’. To validate the model, experiments on both light–heavy and heavy–light interfaces subject to a shock wave are conducted, and both single- and dual-mode interfaces formed by the soap-film technique are involved. The interface profiles extracted from mode decomposition and predicted by the model show high consistency with the experimental counterparts. Good agreement of the mode amplitude growths between the experiments and theoretical predictions shows the superiority of the model, especially for the heavy–light interface.

In this study, direct numerical simulation of the particle dispersion and turbulence modulation in a sonic transverse jet injected into a supersonic cross-flow with a Mach number of 2 was carried out with the Eulerian–Lagrangian point-particle method. One single-phase case and two particle-laden cases with different particle diameters were simulated. The jet and particle trajectories, the dispersion characteristics of particles, and the modulation effect of particles on the flow were investigated systematically. It was found that large particles primarily accumulate around shear layer structures situated on the windward side of the jet trajectory. In contrast, small particles exhibit radial transport, accessing both upstream and downstream recirculation zones. Moreover, small particles disperse extensively within the boundary layer and large-scale shear layers, evidently influenced by the streamwise vortices. The particles increase the mean wall-normal velocity near the wall in the wake region of the transverse jet, while reducing the mean streamwise and wall-normal velocities in outer regions. Particles significantly alter the flow velocity adjacent to shock fronts. In particular, the turbulent fluctuations near the windward barrel shock and bow shock are reduced, while those around the leeward barrel shock are increased. An upward displacement of the bow shock in the wall-normal direction is also observed due to particles. In the regions away from the shocks, small particles tend to amplify the Reynolds stress, while large particles attenuate the turbulent kinetic energy.

The fingers known as bubbles (spikes) resulting from the penetration of light (heavy) fluids into heavy (light) fluids are significant large-scale features of Richtmyer–Meshkov instability (RMI). Through shock-tube experiments, we study finger collisions in light fluid layers under reshock conditions. Four unperturbed fluid layers with varying thicknesses are created to analyse the motion of waves and interfaces during finger collisions. The wave dynamics, sensitive to initial layer thicknesses, are characterized by a one-dimensional theory. Eight perturbed fluid layers, with four thicknesses and two interface phase combinations, are generated to explore the finger collision mechanism. It is shown that after reshock, the initial in-phase and anti-phase cases undergo spike–bubble rear-end collisions (SBCs) and spike–spike head-on collisions (SSCs), respectively. Compared with SBCs, SSCs significantly suppress spike growth, leading to the attenuation of perturbation growth, especially for larger thicknesses. As the initial thickness decreases, an SSC impedes the downstream interface from reversing its phase, resulting in abnormal RMI, thereby reducing the SSC's effectiveness in attenuating growth. The effects of rarefaction waves enhance both interfaces’ amplitudes and the whole layer's thickness, diminishing the intensity of finger collisions, while the second reshock exerts an opposing influence. Linear and nonlinear models, incorporating the influence of reshocks and rarefaction waves, are developed to predict the interface perturbation growth before and after finger collisions.

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$, due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.

Experiments of transitional shock wave–boundary layer interactions (SBLIs) over 6$^\circ$ and 10$^\circ$ compression ramps were performed at Mach number 1.65. The unit Reynolds number was varied by a factor of two between 5.6 million per metre and 11 million per metre. Schlieren flow visualization was performed, and mean flow measurements were made using Pitot probes. Free interaction theory was verified from pressure measurements for all operating conditions. A new non-dimensional parameter was developed for scaling the strength of the imposed shock, which was based on the pressure required to separate a boundary layer. The validity of this new scaling was supported by the reconciliation of large discrepancies in a diverse collection of experimental results on the length scales of transitional interactions. This non-dimensional scaling was also applied to turbulent interactions, where different models were used to determine the pressure required to separate a turbulent boundary layer. Finally, a direct comparison between transitional and turbulent SBLIs was made, which revealed new insights into the evolution of length scales based on the state of the boundary layer.

We have experimentally investigated the collisionless shock acceleration of ions via the interaction of a relativistic intensity (3 × 1019 W/cm2), 1.053 µm wavelength laser pulse with an underdense plasma. This plasma is formed through the use of a novel cluster jet design that allows for control of the plasma peak density and front scale length without the use of additional plasma-forming laser pulses. When the front density scale length of the target plasma is less than 60 µm, the laser pulse (1 J, 400 fs) is capable of launching an electrostatic shock wave that accelerates a proton beam. This beam is shown to have a narrow divergence angle of 0.8°, a peak flux of 14 × 106 protons/sr with an ion energy exceeding 440 keV. Particle-in-cell simulations indicate this narrow ion beam is produced by converging shocks generated via filamentation of the laser pulse in high-density (near critical) plasma.

The gas dynamics of shock-induced gas filtration through densely packed granular columns with vastly varying shock intensity and the structural parameters are numerically investigated using a coupled Eulerian–Lagrangian approach. The results shed fundamental light on the thermal effects of the shock-induced gas filtration manifested by a distinctive self-heating hot gas layer traversing the medium. The characteristics of the thermal effects in terms of the thermal intensity and uniformity are found to vary with the shock Mach number, Ms, and the filtration coefficient of the granular media, Π. As the incident shock transitions from weak to strong, and (or) the filtration coefficient increases from O(10−5) to O(104), the heating mechanisms transition between three distinct heating modes. A phase diagram of heating modes is established on the parameter space (Ms, Π), which enables us to predict the characteristics of the thermal effect in different shock-induced gas filtrations. The thermal effects markedly accelerate the pressure diffusion due to the additional heat influx when the time scale of the former is smaller than or comparable to the latter. Based on the contour map displaying the coupling degree of the thermal effects and the pressure diffusion, we identify a decoupling criterion whereby the isothermal assumption holds if only the pressure diffusion is concerned. The thermal effects may well bring about considerable thermal shocks which pose a great threat to the integrity of the solid skeleton and further reduce the overall shock resistance performance of the porous media.

In this paper, curved detonation equations with gradients for the pre-wave and post-wave are constructed followed by analysis, verification and applications. The study focuses on shock induced chemical reaction such as detonation, with the energy effect for the main attention. Equations consider both planar and transverse curvature to accommodate both planar and axisymmetric flow problems. Influence coefficients are derived and used to analyse the effect of energy and curvature on the post-wave gradient. Good agreement with the simulation results demonstrates that the equations presented in this paper can calculate various post-wave gradients accurately. After verification, the equations can be applied to applications, including not only solution and analysis but also in the inverse design. First, the method can be applied with polar analysis to provide a new perspective and higher order parameters for the study of detonation. Second, the equations can be used for the capture of detonation waves, where both planar and axisymmetric examples show better performance. Furthermore, the equations can be used in the inverse design of detonation waves in combination with the method of characteristics, which is one of the unique benefits of the present equations.

Experiments on the Richtmyer–Meshkov instability (RMI) in a dual driver vertical shock tube (DDVST) are described. An initially planar, stably stratified membraneless interface is formed by flowing air from above and sulfur hexafluoride from below the interface location using the method of Jones & Jacobs (Phys. Fluids, vol. 9, issue 1997, 1997, pp. 3078–3085). A random three-dimensional, multi-modal initial perturbation is imposed by vertically oscillating the gas column to produce Faraday waves. The DDVST design generates two shock waves, one originating above and one below the interface, with these shocks having independently controllable strengths and interface arrival times. The shock waves have nominal strengths of $M_L=1.17$ and $M_H=1.18$ for the shock wave originating in the light and heavy gas, respectively, with these strengths chosen to result in arrested bulk interface motion following reshock. The influence of the length of the shock-to-reshock time, as well as the order of shock arrival, on the post-reshock RMI is examined. The mixing layer width grows according to $h\propto t^\theta$, where $\theta _H=0.36\pm 0.018$ (95 %) and $\theta _L=0.38\pm 0.02$ (95 %) for heavy and light shock first experiments, respectively, indicating no strong dependence on the order of shock wave arrival. Volume integrated specific turbulent kinetic energy (TKE) in the mixing layer versus time is found to decay according to $E_{tot}/\bar {\rho }\propto t^p$ with $p_H=-0.823\pm 0.06$ (95 %) and $p_L=-1.061\pm 0.032$ (95 %) for heavy and light shock first experiments, respectively. Notably, the 95 % confidence intervals do not overlap. Analysis on the influence of the shock-to-reshock time on turbulent length scales, transition criteria, spectra and mixing layer anisotropy are also presented.

In hypersonic flight the shock wave and turbulent boundary layer interaction (STBLI) sharply increases wall heat transfer that intensifies the aerodynamic heating problems. In this work the STBLI is modelled by compression ramp flow with a Mach number of 5, a Reynolds number based on momentum thickness of 4652 and a wall to recovery temperature ratio of 0.5. The aerodynamic heat generation and transport mechanisms are investigated in the interaction based on theoretical analysis and direct numerical simulation (DNS) that agrees with previous studies. A prediction correlation of wall heat flux in STBLI is deduced theoretically and validated by some representative data including the present DNS, which improves the prediction accuracy and can be applied to a wider $Ma$ range compared with the canonical Q-P theory. The correlation indicates that the sharp increase of wall heat transfer in the STBLI can be explained by the boundary layer compression and the convection transport enhancement. Based on the DNS results, the aerodynamic heat generation and transport mechanisms are revealed in the separation, recirculation and reattachment zones in the STBLI. From this perspective, the peak heat flux can be further explained by the enhancement of near-wall turbulent energy dissipation, compression aerodynamic heat generation and the near-wall turbulent transport. The generation and transport of compression aerodynamic heat reveal the underlying mechanism of the strong correlation between the peak heat flux ratios and the pressure ratios in STBLIs.

The Taylor–Maccoll (T–M) equations are the governing equations for steady inviscid irrotational axisymmetric conical flow, and have been widely applied to the design of waveriders and intakes. However, only four classic solutions have been reported: external conical flow (ECF), Busemann flow and internal conical flow of types A and B (ICFA and ICFB). In this work, the analysis of the T–M equations clarifies all possible solutions and reveals their relations. The domain where elementary solutions exist is divided into four domains. The classic Busemann and ICFB solutions share the same elementary solution as the template in a domain called the pre-shock domain, while the classic ECF and ICFA solutions belong to a domain named the ECF domain. Two new solutions, the inner flow of ECF (IECF) and degenerate conical flow (DCF), are found in the domains named after the corresponding solutions, namely the IECF and DCF domains. The IECF behaves as the mass injection supporting the classic ECF on an imaginary cone surface, while the DCF behaves as the conical expansion of a uniform flow. Furthermore, possible combinations of pre-shock solutions and supersonic post-shock solutions are clarified. The classic solutions are special cases where the pre-/post-shock solutions are combined with uniform flows. In general, the Busemann and ICFB solutions can be combined with any post-shock solutions in accord with the shock relations, including the ECF, ICFA, IECF and DCF solutions. In addition, numerical analyses are conducted to verify the validity of the two new solutions, DCF, IECF and one combined solution Busemann–ECF.

Explosive dispersal of granular media widely occurs in nature across various length scales, enabling engineering applications ranging from commercial or military explosive systems to the loss prevention industry. However, the correlation between the explosive dispersal behaviour and the structure of dispersal system is far from completely understood, thereby compromising the prediction of the explosive dispersal outcome resulting from a specific dispersal system. Here, we investigate the dispersal behaviours of densely packed particle rings driven by the enclosed pressurized gases using coarse-grained computational fluid dynamics–discrete parcel method. Distinct dispersal modes emerge from the dispersal systems with vastly varying sets of the macro- and micro-scale structural parameters in terms of the dispersal completeness and the spatial uniformity of the dispersed mass. Further investigation reveals the variation in the dispersal modes arises from the collective effects of multiscale gas–particle coupling relationships. Specifically, the macroscale coupling dictates the cyclic momentum/energy transfer between gases and particle ring as an entirety. The mesoscale coupling relates to the inter-pore gas filtration through the thickness of the particle ring, leading to the mass/energy reduction of the explosive source. The microscale coupling involves the individual particle dynamics influenced by the local flow parameters. A persistent macroscale coupling results in an incomplete dispersal which takes the form of an aggregated annular band, whereas the meso- and micro-scale couplings alter the macroscale coupling to a different extent. By incorporating the effects of the variety of structural parameters on the multiscale gas–particle coupling relationships, a non-dimensional parameter referred to as the modified mass ratio is constructed, which shows an explicit correlation with the dispersal mode. We proceed to establish a dispersal ring model in the continuum frame which accounts for the macro and meso-scale coupling effects. This model proves to be capable of successfully predicting the ideal and validated failed dispersal modes.

The effects of reshock conditions, including the interface evolution state before reshock and the second shock intensity, on interface instability induced by two successive shocks propagating in the same direction are investigated via shock-tube experiments. It is observed that the reshock promotes the interface instability, and the post-reshock perturbation evolution relates to both the pre-reshock interface evolution state and second shock intensity. For the linear evolution of the twice-shocked interface, existing models perform poorly when either the pre-reshock interface shape effect or the secondary compression effect is pronounced, as current reduction factors fail to accurately describe these effects. Besides, the reshock-induced linear amplitude growth rate shows a non-monotonic dependence on the scaled pre-reshock amplitude, primarily due to the shape effect of the pre-reshock interface. For the post-reshock nonlinear evolution, the model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) offers reasonable predictions when the second shock is weak. However, when the second shock is moderately strong, the model overestimates the bubble growth and underestimates the spike evolution under the influence of the significant secondary compression effect. Furthermore, empirical linear and nonlinear models capable of describing the dependence of the post-reshock evolution on reshock conditions are proposed based on the present experimental results and existing models.