Turbulence amplification is crucial in shock-wave/turbulent boundary layer interaction (SWTBLI). To examine the impact of interaction intensity on turbulence amplification and inter-component energy transfer, direct numerical simulations of impinging oblique shock reflections at strong ($37^\circ$) and weak ($33.2^\circ$) incident angles are conducted. The results indicate that strong interaction generates a larger permanent separation zone, featuring the unique ‘oblique platform’ in Reynolds stress peaks and ‘secondary turbulence amplification’ downstream. Reynolds stress budget and spanwise spectral analyses reveal that $\widetilde {u^{\prime \prime}u^{\prime \prime}}$ and $-\!\widetilde{\ u^{\prime\prime}v^{\prime\prime}}$ amplify primarily by production terms. $u''$, $v''$ and $w''$ represent the streamwise, wall-normal and spanwise velocity fluctuations. At the investigated Reynolds number, deceleration effect dominates the initial amplification of $\widetilde {u^{\prime \prime}u^{\prime \prime}}$, influencing multi-scale wall-bounded turbulence structures, while shear effect remains active along the shear layer and may primarily affects streaky structures. The initial amplification of $-\!\widetilde{\ u^{\prime\prime}v^{\prime\prime}}$ is driven by the adverse pressure gradient, which reshapes the velocity profile and affects the wall-normal velocity. The primary energy for $\!\widetilde{\ v^{\prime\prime}v^{\prime\prime}}$ and $\widetilde {w^{\prime \prime}w^{\prime \prime}}$ amplification originates from $\widetilde{ u^{\prime \prime}u^{\prime \prime}}$ via the pressure-strain term. The delayed amplification of $\!\widetilde{\ v^{\prime\prime}v^{\prime\prime}}$ is influenced by its production term and energy redistribution, with $\widetilde {w^{\prime \prime}w^{\prime \prime}}$ exhibiting higher spectral consistency with $\widetilde {u^{\prime \prime}u^{\prime \prime}}$ and receiving more energy. In strong interaction, the ‘oblique platform’ serves as a stable dissipation region, formed by increased separation–incident shock distance, characterised by progressively concentrated stress spectra and the transition to large-scale streaks. The downstream ‘secondary amplification’ process resembles the initial amplification near the separation shock foot, driven by intermittent compression waves that strengthen shear instabilities and the deceleration effect. These findings detail the streamwise stress evolution, providing a more comprehensive turbulence amplification mechanism in SWTBLI.

This study examines the reflection of a rightward-moving shock (RMS) over expansion waves, dividing the reflection structure into three components. The first component analyses the pre- and post-interaction parts of the expansion waves, categorising primary flow patterns into four types with defined transition criteria, visualised through Mach contours. The second component investigates the curved perturbed shock. Through numerical simulations, the influence of increasing shock strength on the flow structures is displayed. A triple point forms for an RMS of the first family, and the Mach stem height increases with the increase of shock strength. When the RMS is strong enough, a vortex forms in the near-wall region, which acts like a wedge to distort the near-foot part of the RMS. The third component, the near-foot region, is analysed using a one-dimensional Riemann problem approach. The calculated wave speeds are used to mark waves in Mach contours for eight cases. The position of the waves indicates that the left-going shock for an RMS of the first family or the right-going shock for an RMS of the second family corresponds to the foot of the RMS. This can explain the finding that the right-hand side of an RMS of the first family or the left-hand side of an RMS of the second family is disturbed. The regions to have different wave patterns solved from the one-dimensional Riemann problem are displayed in the original Mach number–shock speed Mach number plane.

A model for galloping detonations is conceived as a sequence of very fast re-ignitions followed by long periods of evolution with quenched reactions. Numerical simulations of the one-dimensional Euler equations are conducted in this limit. While the mean speed and structure is found in reasonable agreement with Chapman–Jouguet theory, very strong pulsations of the lead shock appear, along with a train of rear-facing N-waves. These dynamics are analysed using characteristics. A closed-form solution for the lead shock dynamics is formulated, which is found in excellent agreement with numerics. The model relies on the presence of a single time scale of the process, the pulsation period, which controls the shock dynamics via the shock change equations and establishes a shock decay with a single time constant. These long periods of shock decay with known dynamics are punctuated by energy release events, with ‘kicks’ in the shocked speed controlled by the pressure increase and resulting lead shock amplification. Model predictions are found in excellent agreement with previous numerical results of pulsating detonations far from the stability limit.

The flow instabilities in shock-wave–boundary-layer interactions at Mach 6 are comprehensively investigated through compression corner and incident shock cases. The boundary of global stability and the characteristics of globally unstable modes are determined by global stability analysis. In resolvent analysis, cases are categorized into flat plate, no separation, small separation and large separation flows. The optimal response shifts from the first mode in the flat plate case to streaks after the amplification in the interaction region. The amplification of streaks and the first mode (oblique mode) are both attributed to the Görtler instability. Meanwhile, the second mode exhibits minimal growth and higher Mack’s modes appear within the separation bubble. Rounded corner case and linear stability analysis are utilized to further validate the amplification mechanism of the oblique mode.

Large-scale spanwise motions in shock wave–turbulent boundary-layer interactions over a $ 25^{\circ }$ compression ramp at Mach 2.95 are investigated using large-eddy simulations. Spectral proper orthogonal decomposition (SPOD) identifies coherent structures characterised by low-frequency features and a large-scale spanwise wavelength of $ O(15\delta _{0})$, where $ \delta _{0}$ is the incoming boundary-layer thickness. The dominant frequency is at least one order of magnitude lower than that of the shock motions. These large-scale spanwise structures are excited near the shock foot and are sustained along the separation shock. Global stability analysis (GSA) is then employed to investigate the potential mechanisms driving these structures. The GSA identifies a stationary three-dimensional (3-D) mode at a wavelength of $ 15\delta _{0}$ with a similar perturbation field, particularly near the separation shock. Good agreement is achieved between the leading SPOD mode and the 3-D GSA mode both qualitatively and quantitatively, which indicates that global instability is primarily responsible for the large-scale spanwise structures surrounding the shock. The reconstructed turbulent separation bubble (TSB) using the 3-D global mode manifests as spanwise undulations, which directly induce the spanwise rippling of the separation shock. Furthermore, the coupled TSB motions in the streamwise and spanwise directions are examined. The TSB oscillates in the streamwise direction while simultaneously exhibiting spanwise undulations. The filtered wall-pressure signals indicate the dominant role of the streamwise motions.

The dynamics of self-excited shock train oscillations in a back pressured axisymmetric duct was investigated to deepen the understanding of the isolator/combustor coupling in high-speed propulsion systems. The test article consisted of an internal compression inlet followed by a constant area isolator, both having a circular cross-section. A systematic back pressure variation was implemented by using a combination of aerodynamic and physical blockages at the isolator exit. High bandwidth two-dimensional pressure field imaging was performed at $8\,{\rm kHz}$ repetition rate within the isolator for different back pressure settings. The acquisition rate was considerably higher than the dominant frequency of the shock train oscillations across the different back pressure settings. The power spectral density of the pressure fluctuations beneath the leading shock foot exhibited broadband low frequency oscillations across all back pressures that resembled the motions of canonical shock–boundary layer interaction units. A node in the vicinity of reattachment location that originated the pressure perturbations within the separation shock was also identified, which further ascertained that the leading shock low frequency motions were driven by the separation bubble pulsations. Above a threshold back pressure, additional peaks appeared at distinct higher frequencies that resembled the acoustic modes within the duct. However, none of the earlier expressions of the resonance acoustic frequency within a straight duct agreed with the experimentally observed value. Cross-spectral analyses suggested that these modes were caused by the shock interactions with upstream propagating acoustic waves that emanate from the reattachment location, originally proposed for transonic diffusers by Robinet & Casalis (2001) Phys. Fluids 13, 1047–1059. Feedback interactions described using one-dimensional stability analysis of the shock perturbations by obliquely travelling acoustic waves (Robinet & Casalis 2001 Phys. Fluids 13, 1047–1059) made favourable comparisons on the back pressure threshold that emanated the acoustic modes as well as the acoustic mode frequencies.

This work presents detailed 3D modelling and simulation of the mechanical effects induced by lightning strikes in protected carbon fibre-reinforced polymer laminates. Firstly, physically based models that represent the mechanical overpressure that results from a lightning strike are revisited. In particular, this paper compares the implementation of an analytical strong shock wave approximation with the solutions obtained from computational fluid dynamics (CFD), considering different equations of state, to represent the supersonic expansion of the hot plasma channel when simulating the mechanical damage induced by lightning strikes. The assessment of the pressure profiles, the numerical predictions of the displacement and velocity fields and the analysis of the predicted damage maps show that, for two lightning protection layers, the effects of the supersonic plasma expansion loads obtained from the strong shock wave approximation compare reasonably well with those obtained from CFD, independently of the equation of state solved numerically. Subsequently, the predictions of the 3D modelling strategy of the mechanical response of composite laminates subjected to lightning strike employing the strong shock wave approximation are compared with mechanical deformation measurements obtained from lab-scale lightning test results. Accurate deflection and out-of-plane velocity fields are predicted, validating the 3D modelling strategy. Moreover, the predicted damage maps correlate well with the (bulk) damage identified by C-scan (considering only the damaged area below the second ply).

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.