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The deformation and breakup characteristics of liquid rocket propellant 2 (RP-2) droplets are experimentally investigated in a shock tube. The RP-2 droplets are subjected to a weak shock wave, a strong shock, and a detonation wave to deduce the impacts of high-speed and supersonic reacting flows on droplet deformation and breakup. High-speed shadowgraph and schlieren imaging techniques are employed to characterize droplet morphologies, deformation rates, and displacement of the droplet centroid. The results reveal that the transition from a shock wave to a detonation suppresses the deformation of the droplet and augments small-scale breakup. A shift in dominant breakup mechanisms is linked to a significant increase in the Weber number due to an increase in flow velocities and temperatures when transitioning to the detonation case. The experimental data are combined with a droplet stability analysis to predict the "child" (or fragments of the initial "parent" droplet) droplet sizes of each test condition. The child droplet size is shown to decrease as the flow regime transitions toward a detonation. An analytical mass stripping model was also used to determine that the total mass stripped from the parent droplet increased when approaching supersonic reacting conditions. The child droplet sizes and mass stripping rate will ultimately influence evaporation timescales and ignition in supersonic reacting flows, which is important for the development of detonation-based propulsion and power systems. [ABSTRACT FROM AUTHOR]

Compressible flow varies from ideal-gas behaviour at high pressures where molecular interactions become important. It is widely accepted that density is well described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, $A$ and $B$, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behaviour, a closed-form approximate solution is obtained that is valid over a wide range of conditions. An expansion in these molecular interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behaviour. Real-gas modifications in density, enthalpy and sound speed for a given pressure and temperature lead to variations in many basic compressible-flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear wave propagation and flow across a shock wave, all for a real gas. Modifications are obtained for allowable mass flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl’s shock relation and the Rankine–Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and can be applied to multicomponent flows or to more complex flow configurations.

Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve Riemann problems encountered in compressible flows for extreme pressure jumps (up to 1 0 10 pressure ratio). In particular, we first consider the DeepONet that we train in a two-stage process, following the recent work of Lee and Shin (2023), wherein the first stage, a basis is extracted from the trunk net, which is orthonormalized and subsequently is used in the second stage in training the branch net. This simple modification of DeepONet has a profound effect on its accuracy, efficiency, and robustness and leads to very accurate solutions to Riemann problems compared to the vanilla version. It also enables us to interpret the results physically as the hierarchical data-driven produced basis reflects all the flow features that would otherwise be introduced using ad hoc feature expansion layers. We also compare the results with another neural operator based on the U-Net for low, intermediate, and very high-pressure ratios that are very accurate for Riemann problems, especially for large pressure ratios, due to their multiscale nature but computationally more expensive. Overall, our study demonstrates that simple neural network architectures, if properly pre-trained, can achieve very accurate solutions of Riemann problems for real-time forecasting. The source code, along with its corresponding data, can be found at the following URL: https://github.com/apey236/RiemannONet/tree/main. • Develop surrogate models tailored for handling discontinuous solutions. • Develop and analyze data-driven bases for discontinuous solutions. • Compare two different neural operators for high-speed flows. • Obtain state-of-the-art results for extreme pressure ratios (up to 1 0 10 ). [ABSTRACT FROM AUTHOR]

Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-fitting), adaptive grid refinement, and flow visualization. This study aims to effectively identify and localize multiple shock waves and their interaction points in two-dimensional inviscid steady and unsteady flows. A novel shock wave pattern recognition method based on cluster analysis is proposed, including three processes. First, a series of grid-cells located at the transition zones of captured shock waves are extracted using a shock wave detection approach based on local flow variation. Subsequently, these grid-cells are grouped into numerous clusters using the classical K -means clustering algorithm, with categorization based on nearest neighbor features. Finally, a strategy is introduced to merge relevant adjacent clusters and further localize the points where shock waves interact. The Bézier curve fitting technique is then employed to obtain the high-quality shock-lines. Several numerical cases demonstrate that this method achieves high localization accuracy for shock-lines while being minimally affected by grid type and scale variations. Moreover, it enables clear and effective identification of the shock interaction patterns in both steady and unsteady flows, providing an effective visualization means for analyzing the motion and evolution of shock wave configurations. [ABSTRACT FROM AUTHOR]

Recently, the application of a deep-learning technique to fluid analysis has been suggested. Additionally, a deep-learning-based method called the Deep Galerkin Method (DGM) has been suggested for solving a partial differential equaion. In DGM, a loss function for training a deep neural network is formulated so that differential operators, boundary conditions, and initial conditions of the targeted partial differential equation are satisfied. This study aims to extend and apply DGM to solving compressible Navier-Stokes equations and examine the feasibility of using DGM for fluid analysis. In this paper, DGM is applied to two-dimensional Burgers equations with periodic boundary conditions, one-dimensional Navier-Stokes equations for a shock tube problem, and two-dimensional Navier-Stokes equations for the supersonic flow around a blunt body. The approximate solutions obtained using DGM show generally good agreement with that obtained using a finite difference method. [ABSTRACT FROM AUTHOR]

The effect of magnetic field, the ratio of the density of solid particles to the initial density of the gas, non-idealness of the gas, mass concentration of micro size solid particles, adiabatic exponent, and the heat transfer parameters effect on one-dimensional shock wave propagation in a dusty gas with conductive and radiative heat fluxes in the presence of azimuthal or axial magnetic field in rotating medium have been investigated for cylindrical geometry. By using the similarity method a system of ordinary differential equations are derived from the system of governing equations of motion. The dusty gas is taken to be perfectly conducting mixture of non-ideal gas and small inert solid particles of micro size, in which solid particles are continuously distributed. It is understood that variable energy input is constantly supplied by the moving piston and the equilibrium flow conditions are maintained in the whole flow-field region. The results of numerical integration for the system of ordinary differential equations show that the magnetic field, mass concentration of solid particles, the ratio of the solid particles density to the gas initial density, non-idealness of the gas, adiabatic exponent and the heat transfer parameters have strong influence on the shock wave and on the flow variables. It is found that the presence of magnetic field, an increase in conductive and radiative heat transfer parameters and non-idealness of the gas have decaying effect on the shock wave; whereas the ratio of the solid particles density to the gas initial density or the adiabatic exponent have effect to increase the shock strength. • MHD shock in rotating dusty gas with conductive and radiative heat fluxes is modelled. • Shock strength decreases with non-idealness of the gas and magnetic field. • Density and pressure vanish at the piston i.e. a vacuum is formed at axis of symmetry. • Shock strength increases with adiabatic exponent, and the density ratio of solid particles and that of gas. • Radiative and conductive heat transfer parameters both increase the shock strength. [ABSTRACT FROM AUTHOR]

Shock-wave reflection over concave surfaces poses a difficulty in its analysis due to the unsteady nature of the reflection process and the occurrence of various types of Mach reflections caused by it. In a pseudo-steady flow, the reflection's configuration is self-similar since the shock wave reflects over a surface with constant inclination. The unsteady Mach reflection introduces an additional complexity as it is affected by the changing inclination of the surface, forcing the reflection to continuously adjust itself to the varying boundary condition. In this study, validated simulations of Mach reflection (MR) over cylindrical concave surfaces with different radii were performed for three inviscid perfect gases with moderate incident shock Mach numbers (Ms) ranging from 1.3 to 1.5. The reflection was investigated up to the point of transition from MR to transitioned regular reflection. A similar behaviour of the configuration and evolution of the Mach stem was observed, one that is independent of the surface radius and type of gas. With regards to different gases, the speed of sound a0 is a dominant factor since it dictates the propagation of wall disturbances. A universal condition of the rate of surface change was found, accounting for different radii, different gases and Ms variation. Analysis based on shock dynamics is employed to explain how disturbances caused by surface variations play a significant role in the behaviour of the reflection. This method successfully supports the similarity that was demonstrated and facilitates a more informed perception of the MR process. [ABSTRACT FROM AUTHOR]

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• The evolution of gas-dynamic flow affects the ignition process in the shock tube. • The non-steady flow dynamics determines the origins of ignition kernels. • The reaction wave is forming at the background of non-uniform flow field. • The detonation arises as a result of transient behavior of reaction wave. The paper analyses in details and describes the process of ignition kernel formation and subsequent detonation onset behind the shock wave propagating in the shock tube. To get the overall pattern of the process a series of one- and two-dimensional calculations are carried out with the use of a dissipation-free numerical technique. It is shown that one of the leading roles in the process of ignition kernel formation belongs to the non-steady flow dynamics establishing behind the shock wave. The development of the boundary layer determines both the temperature re-distribution in the near-wall region and the conditions for gas-dynamic acceleration of the flow. With an account of thermal runaway, the most intensively heated region corresponds to the area between the inner margin of the boundary layer and the contact surface separating driver gas and the test mixture. After localized ignition takes place the forming reaction wave propagates out from the ignition epicenter. Reaction wave propagates behind the outrunning compression wave through the already reacting mixture. Shock-induced compression of the test mixture provides conditions for the self-sustained acceleration of the combustion wave, and finally, the detonation onset takes place. [ABSTRACT FROM AUTHOR]

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region. [ABSTRACT FROM AUTHOR]

The development of a non-periodic $\text{air}\text{/}\text{SF}_{6}$ gaseous interface subjected to a planar shock wave is investigated experimentally and theoretically to evaluate the effects of the non-periodic portions of the interface on the Richtmyer–Meshkov instability. Experimentally, five kinds of discontinuous chevron-shaped interfaces with or without non-periodic portions are created by the extended soap film technique. The post-shock flows and the interface morphologies are captured by schlieren photography combined with a high-speed video camera. A periodic chevron-shaped interface, which is multi-modal (81 % fundamental mode and 19 % high-order modes), is first considered to evaluate the impulsive linear model and several typical nonlinear models. Then, the non-periodic chevron-shaped interfaces are investigated and the results show that the existence of non-periodic portions significantly changes the balanced position of the initial interface, and subsequently disables the nonlinear model which is applicable to the periodic chevron-shaped interface. A modified nonlinear model is proposed to consider the effects of the non-periodic portions. It turns out that the new model can predict the growth of the shocked non-periodic interface well. Finally, a method is established using spectrum analysis on the initial shape of the interface to separate its bubble structure and spike structure such that the new model can apply to any random perturbed interface. These findings can facilitate the understanding of the evolution of non-periodic interfaces which are more common in reality. [ABSTRACT FROM AUTHOR]

The deformation of the Mach stem in pseudo-steady shock wave reflections is investigated numerically and theoretically. The numerical simulation provides the typical flow patterns of Mach stem deformation and reveals the differences caused by high-temperature gas effects. The results also show that the wall jet, which causes Mach stem deformation, can be regarded as a branch of the mainstream from the first reflected shock. A new theoretical model for predicting the Mach stem deformation is developed by considering volume conservation. The theoretical predictions agree well with the numerical results in a wide range of test conditions. With this model, the wall-jet velocity and the inflow velocity from the Mach stem are identified as the two dominating factors that convey the influence of high-temperature thermodynamics. The mechanism of high-temperature gas effects on the Mach stem deformation phenomenon are then discussed. [ABSTRACT FROM AUTHOR]

Three-dimensional shock wave reflection comprises flow physics that is significantly different from the well-documented two-dimensional cases in a number of aspects. The most important differentiating factor is the sweep of the shock system. In particular, this work examines the nature of flow fields in which there is a transition of shock reflection configuration in three-dimensional space. The flow fields investigated have been made to exist in the absence of edge effects influencing the shock interaction and transition, as found previously to exist in conventional double-wedge studies. In general, the shock configurations are those with central regular and peripheral Mach reflection portions. It is shown that the sweep angle of the portions on either side of the transition point is subject to a cusp, as per an analytical model that is developed. This is confirmed with the use of numerical models with additional evidence provided by experimental results using oblique shadow photography. Further application of the principles of three-dimensional shock analysis and those pertaining to the sweep cusp model yield important insights regarding the overall shock geometry and that at transition. [ABSTRACT FROM AUTHOR]

In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions. [ABSTRACT FROM AUTHOR]

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle. [ABSTRACT FROM AUTHOR]

Experimental evidence is provided to demonstrate that the upstream-travelling waves in two jets screeching in the A1 and A2 modes are not free-stream acoustic waves, but rather waves with support within the jet. Proper orthogonal decomposition is used to educe the coherent fluctuations associated with jet screech from a set of randomly sampled velocity fields. A streamwise Fourier transform is then used to isolate components with positive and negative phase speeds. The component with negative phase speed is shown, by comparison with a vortex-sheet model, to resemble the upstream-travelling jet wave first studied by Tam & Hu (J. Fluid Mech., vol. 201, 1989, pp. 447-483). It is further demonstrated that screech tones are only observed over the frequency range where this upstream-travelling wave is propagative. [ABSTRACT FROM AUTHOR]

A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics. [ABSTRACT FROM AUTHOR]

Steady self-similar solutions to the supersonic flow of Bethe--Zel'dovich--Thompson fluids past compressive and rarefactive ramps are derived. Inviscid, non-heatconducting, non-reacting and single-phase vapour flow is assumed. For convex isentropes and shock adiabats in the pressure--specific volume plane (classical gas dynamic regime), the well-known oblique shock and centred Prandtl--Meyer fan occur at a compressive and rarefactive ramp, respectively. For non-convex isentropes and shock adiabats (non-classical gas dynamic regime), four additional wave configurations may possibly occur; these are composite waves in which a Prandtl--Meyer fan is adjacent up to two oblique shock waves. The steady two-dimensional counterparts of the wave curves defined for the one-dimensional Riemann problem are constructed. In the present context, such curves consist of all the possible states connected to a given initial state (namely, the uniform state upstream of the ramp/wedge) by means of a steady self-similar solution. In addition to the classical case, as many as six non-classical wave-curve configurations are singled out. Moreover, the necessary conditions leading to each type of wave curves are analysed and a map of the upstream states leading to each configuration is determined. [ABSTRACT FROM AUTHOR]

In this study, we establish a hybrid high-order smoothed particle hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with discontinuities, which is able to achieve genuine high-order convergence in smooth regions and also capture discontinuities well in non-smooth regions. The framework can be either fully Lagrangian, Eulerian or realizing arbitary-Lagrangian-Eulerian (ALE) feature enforcing the isotropic particle distribution in specific cases. In the proposed framework, the computational domain is divided into smooth regions and non-smooth regions, and these two regions are determined by a strong scale separation strategy in the targeted essentially non-oscillatory (TENO) scheme. In smooth regions, the moving-least-square (MLS) approximation is used for evaluating high-order derivative operator, which is able to realize genuine high-order construction; in non-smooth regions, the new TENO scheme based on Vila's framework with several new improvements will be deployed to capture discontinuities and high-wavenumber flow scales with low numerical dissipation. The present MLS-TENO-SPH method is validated with a set of challenging cases based on the Eulerian, Lagrangian or ALE framework. Numerical results demonstrate that the MLS-TENO-SPH method features lower numerical dissipation and higher efficiency than the conventional method, and can restore genuine high-order accuracy in smooth regions. Overall, the proposed framework serves as a new exploration in high-order SPH methods, which are potential for compressible flow simulations with shockwaves. • A hybrid high-order SPH framework for compressible flows is established based on the MLS approximation and the TENO scheme. • The computational domain is divided into smooth and non-smooth regions by a strong scale separation strategy in TENO scheme. • The present method restores genuine high-order accuracy in smooth regions and captures discontinuities in non-smooth regions. • A set of challenging cases is simulated with the present method, showing less numerical dissipation and higher efficiency. [ABSTRACT FROM AUTHOR]

In this work, we use numerical simulation and linear inviscid theory to study the thermodynamic field generated by the interaction of a shock wave with homogeneous isotropic turbulence. Fluctuations in density, pressure, temperature and entropy can play an important role in shock-induced mixing, combustion and energy transfer processes. Data from shock-captured direct numerical simulations (scDNS) are used to investigate the variation of thermodynamic fluctuations for varying shock strengths, and the results are compared with linear interaction analysis (LIA). The density, pressure and temperature variances attain large values at the shock, followed by, in general, a rapid decay in the downstream flow. The rapid variation behind the shock makes it difficult to compare numerical results with theoretical predictions. A threshold method based on instantaneous shock dilatation is used to overcome this problem, and it gives excellent match between scDNS and LIA. We find cases with non-monotonic variation with Mach number as well as local peaks in density fluctuations behind the shock. These are explained in terms of the contribution of the post-shock acoustic and entropy modes in the LIA solution and their cross-correlation. Budget of the transport equations reveals interesting insight into the physics governing the thermodynamic field behind the shock wave. It is found that the variances are primarily determined by the competing effects of dilatational and dissipation mechanisms. The dominant mechanisms are identified for a range of conditions, and their implication for developing predictive models is highlighted. [ABSTRACT FROM AUTHOR]

The unstable evolution of an elongated elliptically shaped inhomogeneity that is embedded in ambient air and aligned both normal and at an angle to an incident plane blast wave of impact Mach number 2.15 is investigated both experimentally and numerically. The elliptic inhomogeneities and the blast waves are generated using gas heating and exploding wire technique and their interaction is captured optically using shadowgraph method. While two symmetric counter-rotating vortices due to Richtmyer-Meshkov instability are observed for the straight interaction, the formation of a train of vortices similar to Kelvin-Helmholtz instability, introducing asymmetry into the flow field, are observed for an inclined interaction. During the early phase of the interaction process in the straight case, the growth of the counter-rotating vortices (based on the sequence of images obtained from the high-speed camera) and circulation (calculated with the aid of numerical data) are found to be linear in both space and time. Moreover, the normalized circulation is independent of the inhomogeneity density and the ellipse thickness, enabling the formulation of a unique linear fit equation. Conversely, the circulation for an inclined case follows a quadratic function, with each vortex in the train estimated to move with a different velocity directly related to its size at that instant. Two factors influencing the quadratic nature are identified: the reduction in strength of the transmitted shock thereby generating vortices with reduced vorticity, along with the gradual loss of vorticity of the earlier-generated vortices. [ABSTRACT FROM AUTHOR]

A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number M = 0.735, an angle of attack α = D 4°, a Reynolds number Rec = 3 × 106 has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies (St = f ּּ· c/U∞ ≃ 0.06–0.07, where St is the Strouhal number, f the shock oscillation frequency, c the chord length and U∞ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency (St = 1.2). The shock oscillation amplitude is also lower: 6% of chord and limited to the shock foot area in the laminar case instead of 20% with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at Uc/U∞ ≃ 0.4 (where Uc is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot. [ABSTRACT FROM AUTHOR]

The three-dimensional single-fin configuration finds application in an intake geometry where the cowl-shock wave interacts with the side-wall boundary layer. Accurate numerical simulation of such three-dimensional shock/turbulent boundary-layer interaction flows, which are characterized by the appearance of strong crossflow separation, is a challenging task. Reynolds-averaged Navier-Stokes computations using the shock-unsteadiness modified Spalart-Allmaras model is carried out at Mach of 5 at large fin angle of 23∘. The computed results using the modified model are compared to the standard Spalart-Allmaras model and validated against the experimental data. The focus of the work is to implement the modified model and to study the flow physics in detail in the complex region of swept-shock-wave turbulent boundary-layer interaction in terms of the shock structure, expansion fan, shear layer and the surface streamlines. The flow structure is correlated with the wall pressure and skin friction in detail. It is observed that the standard model predicts an initial pressure location downstream of the experiments. The modified model reduces the eddy viscosity at the shock and predicts close to the experiments. Overall, the surface pressure using modified model has predicted accurately at all the locations. The skin friction is under-predicted by both the models in the reattachment region and is attributed to the poor performance of turbulence models due to flow laminarization. [ABSTRACT FROM AUTHOR]

The Richtmyer-Meshkov instability on a three-dimensional single-mode light/heavy interface is experimentally studied in a converging shock tube. The converging shock tube has a slender test section so that the non-uniform feature of the shocked flow is amply exhibited in a long testing time. A deceleration phenomenon is evident in the unperturbed interface subjected to a converging shock. The single-mode interface presents three-dimensional characteristics because of its minimum surface feature, which leads to the stratified evolution of the shocked interface. For the symmetry interface, it is quantitatively found that the perturbation amplitude experiences a rapid growth to a maximum value after shock compression and finally drops quickly before the reshock. This quick reduction of the interface amplitude is ascribed to a significant Rayleigh-Taylor stabilization effect caused by the deceleration of the light/heavy interface. The long-term effect of the Rayleigh-Taylor stabilization even leads to a phase inversion on the interface before the reshock when the initial interface has sufficiently small perturbations. It is also found that the amplitude growth is strongly suppressed by the three-dimensional effect, which facilitates the occurrence of the phase inversion. [ABSTRACT FROM AUTHOR]

A pressure-based algorithm for the simulation of compressible interfacial flows is presented. The algorithm is based on a fully-coupled finite-volume framework for unstructured meshes with collocated variable arrangement, in which the governing conservation laws are discretised in conservative form and solved in a single linear system of equations for velocity, pressure and specific total enthalpy, with the density evaluated by an equation of state. The bulk phases are distinguished using the Volume-of-Fluid (VOF) method and the motion of the fluid interface is captured by a state-of-the-art compressive VOF method. A new interface discretisation method is proposed, derived from an analogy with a contact discontinuity, that performs local changes to the discrete values of density and total enthalpy based on the assumption of thermodynamic equilibrium, and does not require a Riemann solver. This interface discretisation method yields a consistent definition of the fluid properties in the interface region, including a unique definition of the speed of sound and the Rankine–Hugoniot relations, and conserves the acoustic features of the flow, i.e. compression and expansion waves. A variety of representative test cases of gas–gas and gas–liquid flows, ranging from acoustic waves and shock tubes to shock-interface interactions in one-, two- and three-dimensional domains, is used to demonstrate the capabilities and versatility of the presented algorithm in all Mach number regimes. The propagation, reflection and transmission of acoustic waves, shock waves and rarefaction fans in interfacial flows are predicted accurately, even for difficult cases that feature fluids with shock impedance matching, transonic shock tubes or strong shocks in gas–liquid flows, as well as on unstructured meshes. [ABSTRACT FROM AUTHOR]

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics (Λ) and its derivative with respect to the density at constant entropy (Γ) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps. [ABSTRACT FROM AUTHOR]

We use continuum conservation equations in conjunction with the entropy inequality to obtain a theoretical model that is accurate for hypersonic flows. This is accomplished by extending the constitutive equations to second order in strain rate and gradients of density and temperature. The accuracy of the extended theory is demonstrated by computing the shock structure in argon and nitrogen gases over a large range of Mach numbers. The solutions indicate that our constitutive equations are more accurate than the classical linear ones and are also more robust and accurate than equations obtained through expansions of the Boltzmann equation or equations arising from diffusion of volume arguments. [ABSTRACT FROM AUTHOR]

High-resolution particle image velocimetry measurements were performed on laminar and transitional oblique shock wave reflections for a range of Mach numbers (M = 1.6-2.3), Reynolds numbers (Rexsh = 1.4 × 106-3.5 × 106) and flow deflection angles (θ = 1°-5° or p3/p1 = 1.11-1.64). The laminar interactions revealed a long, flat and triangular shaped separation bubble. For relatively strong interactions (p3/p1 > 1.2), the bubble grows linearly in the upstream direction with increasing shock strength. Under these conditions, the boundary layer keeps an on average laminar velocity profile up to the shock impingement location, followed by a quick transition and subsequent reattachment of the boundary layer. For weaker interactions (p3/p1 < 1.2), the boundary layer is able to remain laminar further downstream of the bubble, which consequently results in a later reattachment of the boundary layer. The pressure distribution at the interaction onset for all laminar cases shows excellent agreement with the free-interaction theory, therefore supporting its validity even for incipiently separated laminar oblique shock wave reflections. [ABSTRACT FROM AUTHOR]

The non-stationary transition from regular reflection (RR) to Mach reflection (MR) over convex segments has been the focus of many recent studies. Until recently, the problem was thought to be very complicated because it was believed that many parameters such as the radius of curvature, initial angle and geometrical shape of the reflecting surface influenced this process. In this study, experiments and inviscid numerical computations were performed in air (“ 1:4) at an incident shock-wave Mach number of 1.3. The incident shock waves were reflected over cylindrical and elliptical convex surfaces. The computations were validated by high-resolution experiments, which enabled the detection of features in the flow having characteristic lengths as small as 0.06 mm. Therefore, the RR→MR transition and Mach stem growth were successfully validated in the early stages of the Mach stem formation and closer to the surface than ever before. The evolution of the RR, the transition to MR and the Mach stem growth were found to depend only on the radius of the reflecting surface. The reflected shock wave adjusts itself to the changing angles of the reflecting surface. This feature, which was demonstrated at Mach numbers 1.3 and 1.5, distinguishes the unsteady case from the self-similar pseudo-steady case and requires the formulation of the conservation equations. A modification of the standard two-shock theory (2ST) is presented to predict the flow properties behind a shock wave that propagates over convex surfaces. Until recently, the determination of the time-dependent flow properties was possible solely by numerical computations. Moreover, this derivation explains the controversial issue on the delay in the transition from the RR to the MR that was observed by many researchers. It turns out that the entire RR evolution and the particular moment of transition to MR, are based on the essential 'no-penetration' condition of the flow. Therefore, we proposed a simple geometrical criterion for the RR→MR transition. [ABSTRACT FROM AUTHOR]

The fluid mechanics of the interaction between a porous material confiner and a steady propagating high explosive (HE) detonation in a two-dimensional slab geometry is investigated through analytical oblique wave polar analysis and multi-material numerical simulation. Two HE models are considered, broadly representing the properties of either a high- or low-detonation-speed HE, which permits studies of detonation propagating at speeds faster or slower than the confiner sound speed. The HE detonation is responsible for driving the compaction front in the confiner, while, in turn, the high material density generated in the confiner as a result of the compaction process can provide a strong confinement effect on the HE detonation structure. Polar solutions that describe the local flow interaction of the oblique HE detonation shock and equilibrium state behind an oblique compaction wave with rapid compaction relaxation rates are studied for varying initial solid volume fractions of the porous confiner. Multi-material numerical simulations are conducted to study the effect of detonation wave driven compaction in the porous confiner on both the detonation propagation speed and detonation driving zone structure. We perform a parametric study to establish how detonation confinement is influenced both by the initial solid volume fraction of the porous confiner and by the time scale of the dynamic compaction relaxation process relative to the detonation reaction time scale, for both the high- and low-detonation-speed HE models. The compaction relaxation time scale is found to have a significant influence on the confinement dynamics, with slower compaction relaxation time scales resulting in more strongly confined detonations and increased detonation speeds. The dynamics of detonation confinement by porous materials when the detonation is propagating either faster or slower than the confiner sound speed is found to be significantly different from that with solid material confiners. [ABSTRACT FROM AUTHOR]

Experimental and numerical investigations on the interaction of a planar shock wave with two-dimensional (2-D) and three-dimensional (3-D) light gas cylinders are performed. The effects of initial interface curvature on flow morphology, wave pattern, vorticity distribution and interface movement are emphasized. In experiments, a wire-restriction method based on the soap film technique is employed to generate N2 cylinders surrounded by SF6 with well-characterized shapes, including a convex cylinder, a concave cylinder with a minimum-surface feature and a 2-D cylinder. The high-speed schlieren pictures demonstrate that fewer disturbance waves exist in the flow field and the evolving interfaces develop in a more symmetrical way relative to previous studies. By combining the high-order weighted essentially non-oscillatory construction with the double-flux scheme, numerical simulation is conducted to explore the detailed 3-D flow structures. It is indicated that the shape and the size of 3-D gas cylinders in different planes along the vertical direction change gradually due to the existence of both horizontal and vertical velocities of the flow. At very early stages, pressure oscillations in the vicinity of evolving interfaces induced by complex waves contribute much to the deformation of the 3-D gas cylinders. As time proceeds, the development of the shocked volume would be dominated by the baroclinic vorticity deposited on the interface. In comparison with the 2-D case, the oppositely (or identically) signed principal curvatures of the concave (or convex) SF6/N2 boundary cause complex high pressure zones and additional vorticity deposition, and the upstream interface from the symmetric slice of the concave (or convex) N2 cylinder moves with an inhibition (or a promotion). Finally, a generalized 3-D theoretical model is proposed for predicting the upstream interface movements of different gas cylinders and the present experimental and numerical findings are well predicted. [ABSTRACT FROM AUTHOR]

Taylor blast wave (TBW) theory and geometrical shock dynamics (GSD) theory describe a radially expanding shock wave front through an inert material, typically an ideal gas, in the strong blast wave limit and weak acoustic limit respectively. We simulate a radially expanding blast shock in air using a hydrodynamic simulation code and numerically describe the intermediate region between these two limits. We test our description of the intermediate shock phase through a two-dimensional simulation of the Bryson and Gross experiment. We then apply the principles of GSD to materials that follow the Mie-Gruneisen equation of state, such as plastics and metals, and derive an equation that accurately relates the acceleration, velocity and curvature of the shock through these materials. Along with detonation shock dynamics (DSD), which describes detonation shock propagation through high explosive fluids, we develop a hybrid DSD/GSD model for the simulation of heterogeneous explosives. This model enables computationally efficient simulation of the shock front in high explosive/inert mixtures consisting of simple or complex geometric configurations. We simulate an infinite two-dimensional slab consisting of one half explosive, PBXN-9, and one half aluminium and model the boundary angle conditions using shock polar analysis. We also simulate a series of high explosive unit cells embedded with aluminium spherical particles, and we compare the propagation of the detonation shock front with a direct numerical simulation performed with the ALE3D code. [ABSTRACT FROM AUTHOR]

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3% and 9.2 %, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within 1:3° is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, Ms = 1.2 and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, Ms = 3 and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g. Ms = 4, the temperature increment in the water is up to 7.3 K. [ABSTRACT FROM AUTHOR]

In this paper the asymmetric shock reflection configurations in two-dimensional steady flows have been studied theoretically. For an overall Mach reflection, it is found that the horizontal distance between both triple points in the Mach stem is related to the angles of two slip streams. Based on the features of the converging stream tube, several assumptions are put forward to perform better the wave configurations near the slip streams. Therefore, we present an analytical model here to describe the asymmetric overall Mach reflection configurations which agrees well with the computational and experimental results. [ABSTRACT FROM AUTHOR]

The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening and eventual overturning of a wave. Using self-similar variables in two space dimensions and a power series expansion based on powers of t0 - t1/2, t0 being the singularity time, we show that the spatial structure of this process, which starts at a point, is equivalent to the formation of a caustic, i.e. to a cusp catastrophe. The lines along which the profile has infinite slope correspond to the caustic lines, from which we construct the position of the shock. By solving the similarity equation, we obtain a complete local description of wave steepening and of the spreading of the shock from a point. The shock spreads in the transversal direction as t0 - t1/2 and in the direction of propagation as t0 - t3/2, as also found in a one-dimensional model problem. [ABSTRACT FROM AUTHOR]

Detonation propagation in the limit of highly spatially discretized energy sources is investigated. The model of this problem begins with a medium consisting of a calorically perfect gas with a prescribed energy release per unit mass. The energy release is collected into sheet-like sources that are embedded in an inert gas that fills the spaces between them. The release of energy in the first sheet results in a planar blast wave that propagates to the next source, which is triggered after a prescribed delay, generating a new blast, and so forth. The resulting wave dynamics as the front passes through hundreds of such sources is computationally simulated by numerically solving the governing one-dimensional Euler equations in the laboratory-fixed reference frame. Two different solvers are used: one with a fixed uniform grid and the other using an unstructured, adaptively refined grid enabling the limit of highly concentrated, spatially discrete sources to be examined. The two different solvers generate consistent results, agreeing within the accuracy of the measured wave speeds. The average wave speed for each simulation is measured once the wave propagation has reached a quasi-periodic solution. The effect of source delay time, source energy density, specific heat ratio and the spatial discreteness of the sources on the wave speed is studied. Sources fixed in the laboratory reference frame versus sources that convect with the flow are compared. Simulations using an Arrhenius-rate-dependent energy release are performed as well. The average wave speed is compared to the ideal Chapman-Jouguet (CJ) speed of the equivalent homogenized media. Velocities in excess of the CJ speed are found as the sources are made increasingly discrete, with the deviation above CJ being as great as 15%. The deviation above the CJ value increases with decreasing values of specific heat ratio. The total energy release, delay time and whether the sources remain laboratory-fixed or are convected with the flow do not have a significant influence on the deviation of the average wave speed away from CJ. A simple, ad hoc analytic model is proposed to treat the case of zero delay time (i.e. source energy released at the shock front) that exhibits qualitative agreement with the computational solutions and may explain why the deviation from CJ increases with decreasing. When the sources are sufficiently spread out so as to make the energy release of the media nearly continuous, the classic CJ solution is obtained for the average wave speed. Such continuous waves can also be shown to have a time-averaged structure consistent with the classical Zel'dovich-von Neumann-Döring (ZND) structure of a detonation. In the limit of highly discrete sources, temporal averaging of the wave structure shows that the effective sonic surface does not correspond to an equilibrium state. The average state of the flow leaving the wave in this case does eventually reach the equilibrium Hugoniot, but only after the effective sonic surface has been crossed. Thus, the super-CJ waves observed in the limit of highly discretized sources can be understood as weak detonations due to the non-equilibrium state at the effective sonic surface. These results have implications for the validity of the CJ criterion as applied to highly unstable detonations in gases and heterogeneous detonations in condensed phase and multiphase media. [ABSTRACT FROM AUTHOR]

The role of the global curvature on the structure and propagation of cylindrical detonations is studied allowing and without allowing the development of cellular structures through two-dimensional (2-D) and 1-D simulations, respectively. It is shown that as the detonation transitions from being overdriven to the Chapman–Jouguet (CJ) state, its structure evolves from no cell, to growing cells and then to diverging cells. Furthermore, the increased dimension of the average structure of the cellular cylindrical detonation, coupled with the curved transverse wave, leads to bulk un-reacted pockets as the cells grow, and consequently lower average propagation velocities as compared to those associated with smooth fronts. As the global detonation front expands and its curvature decreases, the extent of the un-reacted pockets diminishes and the average velocity of the cellular cylindrical detonation eventually degenerates to that of the smooth fronts. Consequently, the presence of cellular instability renders detonation more difficult to initiate for weakly unstable detonations. [ABSTRACT FROM AUTHOR]

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process. [ABSTRACT FROM AUTHOR]

We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area-Mach-number-shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as ∈-1, where ∈ is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. [ABSTRACT FROM AUTHOR]

Compressible flows frequently exhibit multiple features of disparate length scales and orientation which interact with each other. Detection of the local flow phenomena is of significant importance to several areas of flow studies including computational grid adaptation, formulation of numerical schemes (limiters for upwinding, sensors that control local addition of artificial dissipation), interrogation of the physics of a computed or experimentally measured flow field, as well as training and evaluation of neural networks. The present work focuses on effective detection of both individual and multiple flow phenomena, as well as their interaction. Detection of the weak features of a flow field in the presence of strong ones is also an aim of the present study. An appropriate " intensity index " for each of the flow features is proposed. Detection functions (sensors), based on local flow field variation are employed. A new type of sensor, which combines elementary sensors, is proposed and applied. A quantitative approach for sensors evaluation and comparison is presented. The tool for the study is a numerical flow solver and the phenomena encountered include boundary layers, flow separation regions, vortices, jets, wakes, as well as supersonic flow phenomena (normal and oblique shock waves, compressions/expansions, contact discontinuities). Statistical analysis of the shapes of the sensor distribution curves is performed. An analytic expression for setting the threshold for automatic detection is proposed and evaluated. • Flow sensors for a wide spectrum of compressible flow fields. • Accurate detection of multiple and interacting features of different strength. • The developed new type of composite sensors proved effective. • Novel correlations between the statistical parameters of the sensor distributions. • Determination of an automatic threshold based on the statistics of the sensors. [ABSTRACT FROM AUTHOR]

We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius (Ri), the arc thickness (Re-Ri, where Re is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linear Dn-κ model, in which the normal surface velocity Dn = DCJ(1 - Bκ), where DCJ is the planar Chapman-Jouguet velocity, κ is the total surface curvature and B is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratio B/Ri ≪ 1 is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where (Re - Ri)/Ri = O(B/Ri), the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where (Re - Ri)/Ri = O(1), the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only on DCJ and Ri, and corresponds to a Huygens limit (zero curvature) propagation model where Dn = DCJ, assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameter B, while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test. [ABSTRACT FROM AUTHOR]

This investigation concerns the problem of detonation attenuation in stoichiometric methane-oxygen and its re-establishment following its interaction with obstacles, using high resolution numerical simulation. The main focus was on the role of the transverse detonation on the re-establishment of the detonation wave, and the importance of applying a numerical combustion model that responds appropriately to the thermodynamic state behind the complex shock wave dynamics. We applied an efficient thermochemically derived four-step global combustion model using an Euler simulation framework to investigate the critical regimes present. While past attempts at using one- or two- step models have failed to capture transverse detonations, for this scenario, our simulations have demonstrated that the four-step combustion model is able to capture this feature. We thus suggest that to correctly model detonation re-initiation in characteristically unstable mixtures, an applied combustion model should contain at least an adequate description to permit the correct ignition and state variable response when changes in temperature and pressure occur, i.e., behind shocks. Our simulations reveal that (1) there is a relationship between the critical outcomes possible and the mixture cell size, and (2) while pockets of unburned gas may exist when a detonation re-initiates, it is not the direct rapid consumption of these pockets that gives rise to transverse detonations. Instead, the transverse detonations are initiated through pressure amplification of reaction zones at burned/unburned gas interfaces whose combustion rates have been enhanced through Richtmyer–Meshkov instabilities associated with the passing of transverse shock waves, or by spontaneous ignition of hot spots, which can form into detonations through the Zeldovich gradient mechanism. In both situations, non-uniform ignition delay times are found to play a role. Finally, we found that the transverse detonations are in fact Chapman–Jouguet detonations, but whose presence contributes to overdriving the re-initiated detonation along the Mach stem. [ABSTRACT FROM AUTHOR]

The Richtmyer–Meshkov instability on a ‘V’ shaped air/SF$_{6}$ gaseous interface is experimentally studied in a shock tube. By the soap film technique, a discontinuous interface without supporting mesh is formed so that the initial conditions of the interface can be accurately controlled. Five ‘V’ shaped air/$\text{SF}_{6}$ interfaces with different vertex angles ($60^{\circ }$, $90^{\circ }$, $120^{\circ }$, $140^{\circ }$ and $160^{\circ }$) are created where the ratio of the initial interface amplitude to the wavelength varies to highlight the effects of initial condition on the flow characteristics. The wave patterns and interface morphologies are clearly identified in the high-speed schlieren sequences, which show that the interface deforms in a less pronounced manner with less vortices generated as the vertex angle increases. A regime change is observed in the interface width growth rate near a vertex angle of $160^{\circ }$, which provides an experimental evidence for the numerical results obtained by McFarland et al. (Phys. Scr. vol. T155, 2013, 014014). The growth rate of interface width in the linear phase is compared with the theoretical predictions from the classical impulsive model and a modified linear model, and the latter is proven to be effective for a moderate to large initial amplitude. It is found that the initial growth rate of the interface width is a non-monotone function of the initial vertex angle (amplitude–wavelength ratio), i.e. the interface width growth rate in the linear stage experiences an increase and then a decrease as the vertex angle increases. A similar conclusion was also reached by Dell et al. (Phys. Plasmas, vol. 22, 2015, 092711) numerically for a sinusoidal interface. Finally, the general behaviour of the interface width growth in the nonlinear stage can be well captured by the nonlinear model proposed by Dimonte & Ramaprabhu (Phys. Fluids, vol. 22, 2010, 014104). [ABSTRACT FROM PUBLISHER]