Over-expansion flow can generate asymmetric shock wave interactions, which lead to significant lateral forces on a nozzle. However, there is still a lack of a suitable theory to explain the phenomenon of asymmetry. The current work carefully investigates the configurations of shock wave interactions in a planar nozzle, and proposes a theoretical method to analyse the asymmetry of over-expansion flows. First, various possible flow patterns of over-expansion flows are discussed, including regular and Mach reflections. Second, the free interaction theory and the minimum entropy production principle are used to analyse the boundary layer flow and main shock wave interactions, establish the relationship between the separation shock strength and separation position, and predict asymmetric configurations. Finally, experiments are conducted to validate the theoretical method, and similar experiments from other studies are discussed to demonstrate the effectiveness of the proposed method. Results demonstrate that the direction of asymmetric over-expansion flow is random, and the separated flow strives to adopt a pattern with minimal total pressure loss. Asymmetric interaction is a mechanism through which the flow can achieve a more efficient thermodynamic balance by minimising entropy production.

Shock interactions on a V-shaped blunt leading edge (VBLE) that are commonly encountered at the cowl lip of an inward-turning inlet are investigated at freestream Mach numbers ($ M_\infty$) 3–6. The swept blunt leading edges of the VBLE generate a pair of detached shocks with varying shapes due to the changes in $ M_\infty$ and $L/r$ (i.e. the ratio of the leading-edge length $L$ to the leading-edge blunt radius $r$), which causes intriguing shock interactions at the crotch of the VBLE. Three subtypes of regular reflection (RR) and a Mach reflection (MR) are produced successively with increasing $ M_\infty$ for a given $L/r$, which appear in the opposite order to those with increasing $L/r$ for a given $ M_\infty$. These shock interactions identified in numerical simulations are verified in supersonic and hypersonic wind tunnel experiments. It is demonstrated that the relative position of the shocks is crucial in determining the transitions of shock interactions by varying either $L/r$ or $ M_\infty$. Transition criteria between subtypes of RR and from RR to MR are theoretically established in the parameter space $(M_\infty,L/r)$ by analysing the shock structures, showing good agreement with the numerical and experimental results. Interactions between either immature or fully developed detached shocks are embedded in these criteria. Specifically, the transition criteria asymptotically approach the corresponding critical $ M_\infty$ when $L/r$ is sufficiently large. These transition criteria provide guidelines for improving the design of the cowl lip of an inward-turning inlet in supersonic and hypersonic regimes.

Compressible jets impinging on a perpendicular surface can produce high-intensity, discrete-frequency tones. The character of these tones is a function of nozzle shape, jet Mach number, impingement-plate geometry, and the distance between nozzle and plate. Though it has long been recognised that these tones are associated with a resonance cycle, the exact mechanism by which they are generated has remained a topic of some debate. In this work, we present evidence for a number of distinct tone-generation mechanisms, reconciling some of the different findings of prior authors. We demonstrate that the upstream-propagating waves that close resonance can be confined within the jet, or external to it. These waves can be either weak and relatively linear, or strong and nonlinear from their inception. The waves can undergo coalescence or merging, and in some configurations, pairs of waves rather than singletons appear. We discuss both historical and new evidence for multiple distinct processes by which upstream-propagating waves are produced: direct vortex sound, shock leakage, wall-jet-boundary fluctuations, and wall-jet shocklets. We link these various mechanisms to the disparate collection of upstream-propagating waves observed in the data. We also demonstrate that multiple mechanisms can be provoked by a single vortex, providing an explanation as to why sometimes pairs of waves or merging waves are observed. Through this body of work, we demonstrate that rather than being in opposition, the various pieces of past research on this topic were simply identifying different mechanisms that can support resonance.

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF$_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.

A new model is presented for the decay of plane shock waves in equilibrium flows with an arbitrary equation of state. A fundamental challenge for the accurate prediction of shock propagation using analytical modelling is to account for the coupling between a shock’s motion and the post-shock flow. Our model accomplishes this by neglecting only higher-order perturbations to the second velocity gradient, $u_{xx}$, in the incident simple wave. The second velocity gradient is generally small and exactly zero for centred expansion waves in a perfect gas, so neglecting its effect on the shock motion provides an accurate closure criterion for a shock-change equation. This second-order shock-change equation is derived for a general equation of state. The model is tested by comparison with numerical simulations for three problems: decay by centred waves in a perfect gas, decay by centred waves in equilibrium air and decay by the simple wave generated from the constant deceleration of piston in a perfect gas. The model is shown to be exceptionally accurate for a wide range of conditions, including small $\gamma$ and large shock Mach numbers. For a Mach 15 shock in equilibrium air, model errors are less than 2 % in the first 60 % of the shock’s decay. The analytical results possess a simple formulation but are applicable to fluids with a general equation of state, enabling new insight into this fundamental problem in shock wave physics.

Rayleigh–Taylor (RT) stability occurs when a single-mode light/heavy interface is accelerated by rarefaction waves, exhibiting a sustained oscillation in perturbation amplitude. If the perturbation is accelerated again by a shock propagating in the same direction as the rarefaction waves, the interface evolution will shift from RT stability to Richtmyer–Meshkov (RM) instability. Depending upon the interface state when the shock arrives, the perturbation growth can be actively manipulated through controlling the magnitudes of vorticity deposited by rarefaction and shock waves. The present work first theoretically analyses the 12 different growth possibilities of a light/heavy interface accelerated by co-directional rarefaction and shock waves. A theoretical model is established by combining the RT growth rate with the RM growth rate, providing the conditions for the different possibilities of the perturbation growth. Based on the model, extensive experiments are designed and conducted in the specially designed rarefaction-shock tube. By precisely controlling the shock arrival time at the interface, the different growth possibilities, including promotion, reduction and freeze-out, are realised in experiments. This work verifies the feasibility of manipulating the light/heavy perturbation via co-directional rarefaction and shock waves, which sheds light on control of hydrodynamic instabilities in practical applications.

Non-spherical bubble collapses near solid boundaries, generating water hammer pressures and shock waves, were recognized as key mechanisms for cavitation erosion. However, there is no agreement on local erosion patterns, and cavitation erosion damage lacks quantitative analysis. In our experiments, five distinct local erosion patterns were identified on aluminium sample surfaces, resulting from the collapse of laser-induced cavitation bubbles at moderate stand-off distances of $0.4\leqslant \gamma \leqslant 2.2$, namely bipolar, monopolar, annular, solar-halo and central. Among them, the bipolar and monopolar patterns exhibit the most severe cavitation erosion when the toroidal bubbles undergo asymmetrical collapse along the circumferential direction during the second cycle. Shadowgraphy visualization revealed that asymmetrical collapse caused shockwave focusing through head-on collision and oblique superposition of wavefronts. This led to the variations in toroidal bubble radii and the positions of maximum erosion depth not matching at certain stand-off distances. Both initial plasma asymmetry and bubble–wall stand-off distance were critical in determining circumferential asymmetrical collapse behaviours. At large initial aspect ratios, the elliptical jet tips form during the contraction process, resulting in the toroidal bubble collapsing from regions with smaller curvature radii, ultimately converging to the colliding point along the circumferential direction. Our three-dimensional simulations using OpenFOAM successfully reproduce the key features of circumferentially asymmetrical bubble collapse. This study provides new insights into the non-spherical near-wall bubble collapse dynamics and provides a foundation for developing predictive models for cavitation erosion.

Supersonic free jets are extensively employed across a range of applications, especially in high-tech industries such as semiconductor processing and aerospace propulsion. Due to the difficulties involved in flow measurement, previous research on supersonic free jets has primarily focused on investigating near-field shockwave structures, with quantitative experimental analysis of the far-field zone being relatively scarce. However, physical understanding of the far-field flow, particularly post-shockwave energy dissipation, holds significant importance for the application and utilisation of these jets in vacuum environments. Therefore, this study aims to provide a robust experimental foundation for a rarefied supersonic free jet through the analysis of the flow field in both the near- and far-field zones. Nanometre-sized tracer particles and molecules were utilised to measure the rarefied supersonic jet flow field using particle image velocimetry and acetone molecular tagging velocimetry, respectively. The experiments revealed that in rarefied conditions, the supersonic jet exhibits a one-barrel shockwave structure in the near field, and after passing the Mach disk, a long annular viscous layer develops downstream. Experimental data on the jet velocity profile and width demonstrated a transition to a laminar flow regime in the far-field zone. This transition aligns with the theoretically inferred flow regimes based on the complex Reynolds number. The velocity profile and potential core length of the laminar flow regime could be modelled using a bi-modal distribution, which represents the summation of symmetric Gaussian distributions.

We present a theoretical framework and validation for manipulating instability growth in shock-accelerated dual-layer material systems, which feature a light–heavy interface followed by two sequential heavy–light interfaces. An analytical model is first developed to predict perturbation evolution at the two heavy–light interfaces, explicitly incorporating the effects of reverberating waves within the dual-layer structure. The model identifies five distinct control regimes for instability modulation. Shock-tube experiments and numerical simulations are designed to validate these regimes, successfully realising all five predicted states. Notably, the selective growth stagnation of a perturbation at either the upstream or downstream heavy–light interface is realised numerically by tuning the initial separation distances of the three interfaces. This work elucidates the critical role of the wave dynamics in governing interface evolution of a shocked dual layer, offering insights for mitigating hydrodynamic instabilities in practical scenarios such as inertial confinement fusion.

The work investigates the response dynamics of non-premixed jet flames to blast waves that are incident along the jet axis. In the present study, blast waves, generated using the wire-explosion technique, are forced to sweep across a non-premixed jet flame that is stabilised over a nozzle rim positioned at a distance of 264 mm from the source of the blast waves. The work spans a wide range of fuel-jet Reynolds numbers ($Re$; ranging from 267 to 800) and incident blast-wave Mach numbers ($M_{s,r}$; ranging from 1.025 to 1.075). The interaction imposes a characteristic flow field over the jet flame marked by a sharp discontinuity followed by a decaying profile and a delayed second spike. The second spike in the flow field profile corresponds to the induced flow that follows the blast front. While the response of the flame to the blast front was minimal, it was found to detach from the nozzle rim and lift off following the interaction with the induced flow. Subsequently, the lifted flame was found to reattach back at the nozzle or extinguish, contingent on the operating $Re$ and $M_{s,r}$. Alongside flame lift-off, flame-tip flickering was aggravated under the influence of the induced flow. A simplified theoretical model extending the vorticity transport equation was developed to estimate the change in flickering time scales and length scales owing to the interaction with the induced flow. The observed experimental trends were further compared against theoretical predictions from the model.

The investigation of shock/blast wave diffraction over various objects has garnered significant attention in recent decades on account of the catastrophic changes that these waves inflict on the environment. Equally important flow phenomena can occur when the moving expansion waves diffract over bodies, which has been hardly investigated. To investigate the effect of expansion wave diffraction over different bodies, we conducted shock tube experiments and numerical simulations to visualise the intricate wave interactions that occur during this process. The current investigation focuses on the phenomenon of expansion wave diffraction across three distinct diffracting configurations, namely the bluff, wedge and ogive bodies. The diffraction phenomenon is subsequently investigated under varying expansion wave strengths through the control of the initial diaphragm rupture pressure ratios. The shock waves generated by the expansion wave diffraction in the driver side of the shock tube, which was initially identified in numerical simulations by Mahomed & Skews (2014 J. Fluid Mech., vol. 757, pp. 649–664), have been visualised in the experiments. Interesting flow features, such as unsteady shock generation, transition, and symmetric/asymmetric vortex breakdown, have been observed in these expansion flows. An in-depth analysis of such intricate flow features resulting from expansion wave diffraction is performed and characterised in the current study.

Turbulent mixing driven by the reshocked Richtmyer–Meshkov (RM) instability plays a critical role in numerous natural phenomena and engineering applications. As the most fundamental physical quantity characterizing the mixing process, the mixing width transitions from linear to power-law growth following the initial shock. However, there is a notable absence of quantitative models for predicting the pronounced compression of initial interface perturbations or mixing regions at the moment of shock impact. This gap has restricted the development of integrated algebraic models to only the pre- and post-shock evolution stages. To address this limitation, the present study develops a predictive model for the compression of the mixing width induced by shocks. Based on the general principle of growth rate decomposition proposed by Li et al. (Phy. Rev. E, vol. 103, issue 5, 2021, 053109), two distinct types of shock-induced compression processes are identified, differentiated by the dominant mechanism governing their evolution: light–heavy and heavy–light shock-induced compression. For light–heavy interactions, both stretching (compression) and penetration mechanisms are influential, whereas heavy–light interactions are governed predominantly by the stretching (compression) mechanism. To characterize these mechanisms, the average velocity difference between the extremities of the mixing zone is quantified, and a physical model of RM mixing is utilized. A quantitative theoretical model is subsequently formulated through the independent algebraic modelling of these two mechanisms. The proposed model demonstrates excellent agreement with numerical simulations of reshocked RM mixing, offering valuable insights for the development of integrated algebraic models for mixing width evolution.

The quasi-steady shock refraction at a diffusive air–SF$_6$ interface (fast–slow type) is investigated numerically and theoretically. A new refraction pattern where both shock and expansion waves are simultaneously present in the reflected waves (named RRR-E) is first observed at the diffusive interface. The new refraction pattern is a regular pattern that is not expected to occur in classical shock refraction at a sharp fast–slow interface. Through the shock polar method, continuous refraction processes occur within the diffusion layer to satisfy the kinematic relationship between the reflected wave and the transmitted shock, which results in the RRR-E formation. Subsequently, the conditions for the RRR-E occurrence are obtained theoretically and verified numerically. In the phase diagram of the refraction patterns, the presence of RRR-E results in the transition boundaries of different refraction patterns at the sharp fast–slow interface no longer being valid. Specifically, the appearance of RRR-E delays the Mach reflection refraction (MRR) process, which is of great significance for the design of scramjet engines.

This work is a numerical study of a transitional shock wave boundary layer interaction (SWBLI). The main goal is to improve our understanding of the well-known low-frequency SWBLI unsteadiness and especially the suspected role of triadic interactions in the underlying physical mechanism. To this end, a direct numerical simulation is performed using a high-order finite-volume scheme equipped with a suitable shock capturing procedure. The resulting database is then extensively post-processed in order to extract the main dynamical features of the interaction zone dynamics (involved characteristic frequencies, characteristics of the vortical structures, etc.). The dynamical organisation and space–time evolution of the flow at dominant frequencies are then further characterised by mean of an spectral proper orthogonal decomposition analysis. In order to study the role of triadic interactions occurring in the interaction region, a bispectral mode decomposition analysis is applied to the database. It allows us to extract the significant triadic interactions, their location and the resulting physical spatial modes. Strong triadic interactions are detected in the downstream part of the separation bubble whose role on the low-frequency unsteadiness is characterised. All the results of the various analyses are then discussed and integrated to formulate a possible mechanism fuelling low-frequency SWBLI unsteadiness.

Attenuation of shock waves through dense granular media with varying macro-scale and micro-scale parameters has been numerically studied in this work by a coupled Eulerian–Lagrangian approach. The results elucidate the correlation between the attenuation mechanism and the nature of shock-induced unsteady flows inside the granular media. As the shock transmission becomes trivial relative to the establishment of unsteady interpore flows, giving way to the gas filtration, the shock attenuation mechanism transitions from the shock dynamics and deduction of propagation area associated with the shock transmission, to the drag-related friction dissipation alongside the gas filtration. The ratio between the maximum shock transmission length and the thickness of the particle layer is found to be a proper indicator of the nature of shock-induced flows. More importantly, it is this ratio that successfully collapses the upstream and downstream pressures of shock impacted particle layers with widely ranging thickness and volume fraction, leading to a universal scaling law for the shock attenuation effect. We further propose a correlation between the structure of particle layer and the corresponding maximum shock transmission length, guaranteeing adequate theoretical predictions of the upstream and downstream pressures. These predictions are also necessary for an accurate estimation of the spread rate of shock dispersed particle bed through a pressure-gradient-based scaling method.

The reflection of multiple incident shock waves that converge to a single point on the reflecting surface is studied in this paper. The number of the incident shocks, denoted $K$, is arbitrary. The interaction between the reflected shock of one incident shock and the other incident shocks may produce various possible configurations, such as type-I, type-II and type-IV shock interferences. The number of possible reflection configurations is shown to be an exponential function of ($K-1$) with base 2. The possibility of pre-, middle- and post-Mach reflections, which means Mach reflection occurs for the first, middle and last incident shock, is revealed through numerical simulation for $K=3$. For the particular case where the incident shocks are produced by equal variation of wedge surface deflection, the conventional von Neumann condition and detachment condition for the $k\mathrm{th}$ incident shock to have Mach reflection are derived. It is shown that the von Neumann condition for regular reflection is lowered and the detachment condition for Mach reflection is elevated as $k$ increases. The shock reflection patterns for $ K=1,2,\ldots ,10$ are obtained by numerical simulations. We observe a shock interaction train structure, where we have pre-Mach reflection followed by ($K-1$) type-I or type-II shock interferences. We also observe that the Mach stem height decreases with $K$ well above the von Neumann condition and becomes non-monotonic near the von Neumann condition.

Reflection of a rightward-moving shock over a steady oblique shock, equivalent to a shock-on-shock interaction, is typically studied with post-formed shock waves. Law, Felthun and Skews (Shock Waves, vol. 13, 2003, pp. 381–394) reported post-formed expansion fan (PFEF) reflection for second-family incident shock. Here, we show that PFEF reflection also exists for first-family incident shock. We derive the critical condition for PFEF reflection in the shock speed Mach number and incident shock angle plane. Our findings indicate PFEF emergence near type post-I region. Numerical simulations reveal that PFEF with rising incident angle can intersect the incident shock, triple point or Mach stem, echoing the Hillier (J. Fluid Mech., vol. 575, 2007, pp. 399–424) three-type classification of shock–expansion fan interactions. The complex shock reflection pattern is essentially composed of an upstream structure linked to the moving shock wave, and a downstream structure linked to the unperturbed oblique shock wave. Under the conditions investigated, the upstream structure is characterized by a Mach reflection of the incident shock over the wall, potentially featuring a triple point formed within the Mach stem. Below this triple point, there is a curved segment of the Mach stem that is close to the wall. As the inclined angle increases, the curved shock may expand and interact with the incident shock, leading to an asymmetric regular reflection, which is a phenomenon that has not been observed previously. The downstream structure is a double $\lambda$ shock structure, with the lower shock resulting from the generation of recompression shock waves.

This work reports high-fidelity shock-tube experiments on the convergent Richtmyer–Meshkov (RM) instability at a heavy gas layer. The convergent shock tube is designed based on shock dynamics theory, significantly mitigating interface deceleration and reflected shock. As a result, long-term observation of instability growth up to nonlinear stage, free of interface deceleration and reshock, is achieved. Various types of SF$_6$ layers surrounded by air with controllable thicknesses and shapes, created using a soap film technique, are examined. For thick layers, the evolutions of the outer and inner interfaces are nearly decoupled regardless of the layer shape. The weakly nonlinear model of Wang (Phys. Plasmas,vol. 22, 2015, p. 082702), designed for cylindrical RM instability at a single interface, provides a reasonable prediction of perturbation growth at the inner interface, while slightly underestimating instability growth at the outer interface, as it neglects the effects of rarefaction wave. For thin layers, perturbation growth is fastest at either interface when both interfaces initially possess in-phase perturbations, moderate when only one interface is initially perturbed and slowest when the two interfaces have anti-phase perturbations. This variation in growth rates is due to the fact that the evolution of a thin layer is influenced by both reverberating waves and interface coupling, with each factor being highly sensitive to the layer shape. The original vortex method is extended to address the convergent RM instability by incorporating the influences of unsteady background flow, interface coupling and reverberating waves into the transport of a vortex sheet. This extended vortex method enables accurate prediction of convergent RM instability at a gas layer, covering the full range from early linear to late nonlinear stages.

The dependence of the Richtmyer–Meshkov instability (RMI) on post-shock Atwood number ($A_1$) is experimentally investigated for a heavy–light single-mode interface. We create initial interfaces with density ratios of heavy to light gases ranging from 1.73 to 34.07, and achieve the highest $|A_1|$ value reported to date for gaseous-interface experiments (0.95). For the first time, spike acceleration is observed in experiments with a heavy–light configuration. The models for the start-up, linear and weakly nonlinear evolution stages are evaluated over a wide range of $A_1$ conditions. Specifically, the models proposed by Li et al. (Phys. Fluids, vol. 36, 2024, 056104) and Wouchuk & Nishihara (Phys. Plasmas, vol. 4, 1997, 1028–1038) effectively describe the start-up and linear stages, respectively, across all cases. None of the considered nonlinear models is valid under all $A_1$ conditions. Based on the dependence of spike and bubble evolutions on $A_1$ provided by the present work and previous study (Chen et al., J. Fluid Mech., vol. 975, 2023, A29), the SEA model (Sadot et al., Phys. Rev. Lett., vol. 80, 1998, pp. 1654–1657), whose expression has clear physical meanings, is modified by revising the coefficient that governs its prediction for early-time evolution. The modified model applies to prediction of the weakly nonlinear evolution of RMI with $A_1$ ranging from −0.95 to −0.35 and from 0.30 to 0.86. Based on this model, an approximation of the critical $A_1$ for the occurrence of spike acceleration is obtained.

The aerodynamic deformation and breakup of wall-attached droplets in axisymmetric stagnation flow are investigated experimentally. A vertical shock tube is used to generate the shock wave accompanying the post-wave airflow, and the axisymmetric stagnation flow is formed through the impingement of an air stream on a solid wall. For the wall-attached droplets with initially hemispherical profile, four typical droplet deformation and breakup modes can be identified with the continuous increase of the droplet local Weber number, which are the vibrating mode, the compressing mode, the sheet thinning mode and the shear-induced entrainment mode. Quantitative analyses of droplet evolution dynamics are also conducted for the compressing mode and the sheet thinning mode, and the significant differences of air flow separation at the droplet lateral surface between these two modes are revealed. The potential flow model and the energy conservation model are further developed to predict the entire droplet deformation processes. The vibrating frequency and amplitude of droplets under the vibrating mode are predicted by a spring-mass model, and the surface perturbation wavelengths of droplets under the shear-induced entrainment mode are estimated based on the dispersion relation of Kelvin–Helmholtz instability. This work is proposed to give potential guidance for regulating the aerodynamic fragmentation of wall-attached droplets in practical engineering applications.