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In this paper, we construct the Mach-type soliton solution of a coupled KP system on the Grassmannian Gr(4, 8). In particular, the amplitudes and critical angles are also obtained. Furthermore, we introduce the pipedream over the Young diagram, which gives a graphical interpretation of the permutation for the spatial structure of the coupled KP equation. [ABSTRACT FROM AUTHOR]

The paper analyzes the parameters of gas streams after the triple-shock configuration, which forms in Mach reflection with normal Mach shock (so-called stationary Mach configuration). We suppose that this stationary Mach configuration moves in a counter flow with arbitrary velocity (or Mach number). Analyzing the relation of dynamical pressures across the contact discontinuity, which issues from the triple point of the Mach reflection, we have shown that the streams after the triple-shock configuration differs much in their translational action of surrounding objects. [ABSTRACT FROM AUTHOR]

Shock wave reflections in laterally colliding laser-produced aluminum plasmas at 10–1 and 1 mbar argon ambient has been studied using fast imaging technique. In 10–1 mbar pressure regime, the two shock fronts interact to form an intense interaction region. In the case of 1 mbar pressure regime, at early stages of plume expansion, individual shock fronts interact to form a collision front resulting in regular reflection of shock waves. At later times, the collision front split and a channel-like structure was observed and the width of the channel increases with time which is the cause of Mach reflection of shock waves. Incident angle and Mach stem length were measured from ICCD images, and it is found that Mach stem length increases with angle of incidence and time delay. Thus, the transition from regular reflection to Mach reflection of shock waves is reported in this paper. [ABSTRACT FROM AUTHOR]

In this study, the propagation of internal solitary waves in oceans at great depths was analyzed. Using multi-scale analysis and perturbation expansion, the basic equation is simplified to the classical Benjamin–Ono equation with variable coefficients. To better describe the propagation characteristics of solitary waves, we derived a higher-order variable-coefficient integral differential (Benjamin–Ono) equation. Subsequently, the bilinear form of the model was derived using Hirota's bilinear method, and a multi-soliton solution was obtained. Based on the multi-soliton solution of the model, we further studied the interaction of the soliton, which led to the discovery of Mach reflection. Some conclusions were drawn, which are of potential value for further study of solitary waves in the ocean. [ABSTRACT FROM AUTHOR]

Reflections of hydraulic jumps on shallow water are studied. Theoretical criteria of the transition between the regular and Mach reflections are derived, and it is shown that there is a domain of angles of incidence where both types of reflection are possible. Numerical simulations reveal a hysteresis of this transition, which is consistent with theoretical predictions. It is shown that the hysteresis can be obtained by smoothly varying either the angle of the wedge generating the hydraulic jump or the freestream Froude number. [ABSTRACT FROM AUTHOR]

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The supersonic flow of a reactive gas mixture with Mach reflection of oblique shocks and pulsed energy supply at the Mach stem is considered within the framework of the Chapman–Jouguet theory. An approximate analytical model is proposed that quickly determines the shape and size of the shock-wave structure as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the "first barrel" of a highly overexpanded jet flow of an air-methane mixture with a high supersonic velocity, is studied. Flows of hydrogen–air and hydrogen–oxygen mixtures were also considered for comparison with preceding numerical results. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock. [ABSTRACT FROM AUTHOR]

To accurately predict the locations and trajectories of shock wave triple points in near-ground explosions, this study determined the propagation law of shock waves after the initiation of a detonator using a schlieren system. Moreover, it established a numerical simulation model using the Autodyn software and verified the accuracy of the model through a detonator explosion experiment. The propagation law of shock waves of TNT charges (1, 10 ​kg and 100 ​kg) at different heights of burst(0.5, 1.0, 1.5, 2.0 ​m,and 2.5 ​m) was studied through numerical simulations, and the triple point trajectories were fitted to an empirical formula. The results show that the maximum simulation error relative to the schlieren images of detonator explosions did not exceed 4 ​mm. As the scaled height of burst decreased, the positions of generated triple points were closer to the vertical projection of the explosion center and rose faster. As the scaled distance increased, the scaled height of triple points rose exponentially. The average error of triple point trajectories between the values predicted in this study and the experimental values was 4.1%, indicating that the accuracy of the fitted formula is acceptable. This study revealed the overpressure distribution law of shock waves and will provide a reference for shock wave overpressure measurements and explosion protection.

The supersonic flow of a reactive gas mixture with Mach reflection of emerging shocks and pulsed energy supply at the main shock is considered within the framework of the Zel'dovich–Neumann–Döring model. An approximate analytical model is proposed that allows one to quickly determine the shape and size of the resulting gas-dynamic discontinuities as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the initial "first barrel" of a highly overexpanded jet of an air-methane mixture with a high supersonic velocity is studied. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock. [ABSTRACT FROM AUTHOR]

In this study, the propagation of internal solitary waves in oceans at great depths was analyzed. Using multi-scale analysis and perturbation expansion, the basic equation is simplified to the classical Benjamin–Ono equation with variable coefficients. To better describe the propagation characteristics of solitary waves, we derived a higher-order variable-coefficient integral differential (Benjamin–Ono) equation. Subsequently, the bilinear form of the model was derived using Hirota’s bilinear method, and a multi-soliton solution was obtained. Based on the multi-soliton solution of the model, we further studied the interaction of the soliton, which led to the discovery of Mach reflection. Some conclusions were drawn, which are of potential value for further study of solitary waves in the ocean.

The shock instability, notably the disastrous carbuncle phenomenon, has plagued many low-dissipation Godunov-type numerical schemes in calculations of high Mach flows. In the current work, two popular stability analysis tools and corresponding numerical experiments are used to investigate the root cause of shock instability of the low-dissipation Harten, Lax, and van Leer with contact (HLLC) scheme. The local linear stability analysis reveals that the HLLC flux could attenuate all perturbations in the streamwise direction but not perturbations of density and shear velocity in the transverse direction. Numerical results also indicate that the shock instability of the HLLC scheme is only related to the transverse flux. The viscosity terms of entropy wave and shear wave are introduced into the transverse flux, and the stability analysis shows that with the help of additional viscosities the shock instability of the HLLC scheme is cured. To preserve the capability of resolving contact discontinuities and shear waves, a pressure-based switching function is incorporated into the expressions of viscosity terms so that the additional viscosities are activated only when calculating the transverse flux in the shock layer. A series of numerical experiments give evidence of the robustness and accuracy of the proposed scheme, and the strategy adopted here can be easily applied to cure shock instabilities of other low-dissipation numerical schemes, e.g., the Roe scheme and the AUSM+ scheme. [ABSTRACT FROM AUTHOR]

A Mach reflection structure in steady supersonic flow is studied in which a transonic region exists behind the reflected shock wave. Here, the measure of a strong Mach reflection is the total pressure loss of the shock reflection system. A corresponding classification chart provides a method to directly characterize the regions of the strong Mach reflection. An analytical model is proposed for predicting the Mach stem height in an explicit function. The theoretical results are in good agreement with the numerical simulations. Assumptions supporting the analytical model are thus validated. A linear relationship is found between the dimensionless Mach stem height and the dimensionless wedge length, which is validated with both analytical and numerical results. Taking advantage of this feature, a generalized method to determine the domain regarding the dimensionless wedge length in the strong Mach reflection is created. The analytical method provides a quick and precise prediction of boundaries for more detailed simulations and experiments. [ABSTRACT FROM AUTHOR]

The present study aims to investigate the reflection and refraction of a curved shock front as it slides along an air–water interface, using the time-resolved shadowgraph technique. The curved shock front is generated from a free-piston shock tube. The study successfully captured the propagation of a refracted shock wave in water along with that of the reflected shock wave in the air. The refracted shock moves much faster than the incident shock due to a higher acoustic speed in the water. It is seen that the reflected shock initially exhibits a regular reflection (RR), which then transitions to a Mach reflection (MR) as it propagates along the interface. As the shock wave propagates along the air–water interface, the incident shock wave angle with the interface keeps on increasing, leading to RR–MR transition. Shock polar analysis shows that as the Mach reflection structure propagates further along the interface, it transitions from a standard Mach reflection to a non-standard Mach reflection. It is seen that the distance the shock wave propagates along the interface before it transitions from RR to MR increases with the increase in the interface distance (distance between the water surface and the shock tube axis). It is also found that the reflection surface (water or solid) does not seem to have a significant effect on the shock transition criterion, especially the distance at which the shock wave transitions from RR to MR. [ABSTRACT FROM AUTHOR]

The supersonic flow of a reactive gas mixture with Mach reflection of oblique shocks and pulsed energy supply at the Mach stem is considered within the framework of the Chapman–Jouguet theory. An approximate analytical model is proposed that quickly determines the shape and size of the shock-wave structure as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the “first barrel” of a highly overexpanded jet flow of an air-methane mixture with a high supersonic velocity, is studied. Flows of hydrogen–air and hydrogen–oxygen mixtures were also considered for comparison with preceding numerical results. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock.

This paper is the review of modern studies of triple configurations of stationary and propagating shocks on supersonic steady and unsteady gas flows. Prospective directions of the further studies of the triple-shock configurations are defined as well as some their possible engineering applications. [ABSTRACT FROM AUTHOR]

Under investigation in this article is the propagation of the internal solitary waves in the finite depth ocean. According to the perturbation and multi-scale analysis method, the (2+1)-dimensional Kadomtsev–Patviashvili-intermediate long-wave (KP-ILW) equation is derived. This is a novel model for describing the ocean internal solitary waves for the first time. It should be noted that when a 2 = 0 , the model is converted to the ILW equation; when h 1 - h 0 → 0 , the model is converted to the KP equation; when h 1 → ∞ , the model is changed to the KP-BO equation. In order to further study the properties of the internal solitary waves, we explore the conservation of momentum, mass and energy of the internal solitary waves. Through the Hirota bilinear method, we obtain the Bäcklund transformation of the KP-ILW equation for the first time. This is of great significance to the construction of the infinite conservation law of the model. Then, the N-soliton solutions of the KP-ILW equation are given. Meanwhile, we study the oblique interaction of the internal solitary waves, which leads to the discovery of rogue waves and Mach reflection. In addition, we also discuss the effect of some parameters on Mach stem and get some conclusions. All these are particularly important for studies of large amplitude waves such as tsunamis in shallow water. [ABSTRACT FROM AUTHOR]

Resonant Y-shaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional soliton modulation equations, valid in the zero dispersion limit of the KPII equation, are demonstrated to reduce to a one-dimensional system. In this same limit, the rapid transition from the larger Y soliton stem to the two smaller legs limits to a travelling discontinuity. This discontinuity is a multivalued, weak solution satisfying modified Rankine–Hugoniot jump conditions for the one-dimensional modulation equations. These results are applied to analytically describe the dynamics of the Mach reflection problem, V-shaped initial conditions that correspond to a soliton incident upon an inward oblique corner. Modulation theory results show excellent agreement with direct KPII numerical simulation. [ABSTRACT FROM AUTHOR]

Numerical investigation is performed for Mach reflection phenomena in Earth and Mars atmospheric conditions considering real gas effects. Initial computation at lower enthalpy yields Mach reflection in either flow medium. It is found that with increment in the freestream enthalpy the reflection pattern changes from Mach to regular reflection more prominently for the Mars atmosphere. This change is believed to be due to the noticeable real gas effects at higher enthalpies. The shock polar analyses indicate that the flow properties variation at higher enthalpies increases the maximum deflection angle of the flow, which in turn introduces transition in the reflection pattern. • Mach reflection phenomenon is assessed in Earth and Mars atmospheric conditions. • Increased freestream stagnation enthalpy reduces the Mach stem height for real flows. • Real gas effects are more prominent in Martian conditions than Earth atmospheric conditions. • Higher enthalpies increase the maximum deflection angle of the flow to have attached shock. [ABSTRACT FROM AUTHOR]

A new model to predict internal axisymmetric shocks with Mach reflections at their centreline is developed, and results are compared with an Eulerian flow solver, termed CFD herein. The model combines the method of characteristics with the equations for quasi-one-dimensional flow. Calculations are conducted for a range of axisymmetric wedge geometries, and the effects of wedge length and shock angle at the wedge leading edge are studied. These various wedge geometries are found to generate flowfields with similar flow features, with Mach discs that vary greatly in size. This observation forms the basis of a method that uses the results from a CFD mesh convergence study, conducted for a single wedge geometry, to determine the mesh resolution requirements and uncertainty due to finite mesh resolution for all other wedge geometries. When uncertainties due to the effects of finite mesh resolution are considered, it is shown that either the differences between model results and CFD results for Mach disc radius are small, or the results are almost indistinguishable from one another. The model indicates that these geometries generate a flowfield that can be treated as two separate parts: one supported by the wedge surface and another supported by the sharp corner at the wedge trailing edge. The influence of these separate flowfields on the incident shock, flow properties along the slip-line, and the size of the Mach disc is assessed. [ABSTRACT FROM AUTHOR]

The cell size variation in overdriven gaseous detonations is studied in hydrogen/oxygen and acetylene/oxygen mixtures. The local self-similarity of Mach reflection of detonations on the wedge in the far field renders the presence of a steady overdriven Mach stem to be possible. The study focuses on the cell size change of overdriven Mach stem on the wedge surface other than on the sidewall. The detonation cell pattern on the wedge surface has a complicated process of three-stage pattern, i.e., the cells decreasing from large to small size, and then increasing asymptotically to a medium size and keeping constant. The cell size ratio with increasing the degree of overdrive is also examined. It is found that the ratio decays as the degree of overdrive increases. However, as the wedge angle increases to a critical value, finer cells are not created on the smoke foils. Ng's model used to predict the cell size is also found to be valid only for detonations with relative large instability parameters, but presents large errors for highly overdriven detonations with low instability. A modification to Ng's model is proposed based on the experimental results. [ABSTRACT FROM AUTHOR]

Numerical investigations were performed to study the reflection of cellular detonation over wedges with rounded corner, and for comparison, reflections over wedges with straight sharp corner were also calculated. Dynamics of the reflection phenomenon were described by the two-dimensional reactive Euler equations based on the platform of OpenFOAM-7, with the utilization of the adaptive mesh refinement (AMR) technology. The reflection process and the influence of the concave section and wedge angle on the reflection were discussed, as well as the transition from Mach reflection to regular reflection. Different kinds of reflection types including the Direct-Mach reflection (DiMR), the Stationary-Mach reflection (StMR) and the Inverse-Mach reflection (InMR) were observed in the concave section. When the detonation initially propagated to the straight section, the influence of the concave section was "remembered". Subsequently, the influence was "forgotten" at a certain point, and the reflection was controlled by the straight section. When the wedge angle was smaller than or equal to 50°, the asymptotic self-similarity approached in the far field, and the asymptotical triple-point angles decreased with the increase of wedge angle. The critical angle for the transition from Mach reflection to regular reflection was 64.17° for concave wedge, which was much larger than that of straight sharp corner wedge (51 ± 1°). • Simulation were taken on the platform of OpenFOAM using AMR technology. • Different kinds of Mach reflections were observed in the concave section. • Influence of the concave section was limited but should not be ignored. • Asymptotical triple-point angles decreased with the increase of the wedge angle. • Critical angle for rounded corner wedge was larger than that of straight wedge. [ABSTRACT FROM AUTHOR]

Gaseous detonation wave reflection on the rough wedge was experimentally investigated by soot track measurements. Various wedge angles, step numbers and initial pressures were taken into account. The results show that the Mach reflection can form on the rough surface due to the three-dimensional structure of the cellular detonation wave or the pseudo triple-point configuration. The wedge angle is still a significant parameter to affect the Mach stem height and the triple-point trajectory. The Mach stem on the rough surface is weaker and the triple-point is easily deflected due to the triple-point disappearance from the Mach stem. The wedge with smaller step number leads to the triple-point trajectory starting in the downstream region, instead of its starting from the wedge apex. As the step number increases, the Mach stem height on the rough wedge gradually approaches the one on the smooth wedge. The initial pressure has a more significant effect on the Mach reflection on the rough surface compared to that on the smooth surface. Moreover, the Mach reflection on the rough wedge keeps localized self-similarity, and satisfies the frozen limit in the near field and the equilibrium limit in the far field. The critical wedge angle of the transition from regular reflection to Mach reflection is dependent on the step number. [ABSTRACT FROM AUTHOR]

The theory of interaction of stationary gasodynamic discontinuities points to existence of Mach shock reflection with negative slope angle of the reflected shock. It forms in steady gas flows with large Mach numbers and small adiabatic index. Feasibility of such ("negative") triple-shock configurations, their stability and unambiguity of corresponding solutions seem traditionally doubtful. In the present study, conditions of existence and solution's unambiguity regarding "negative" configurations are analyzed. In addition, the possibilities of having other shock-wave structures, which can appear at the same parameters of supersonic steady flow and incident shock, are determined analytically. • Triple-shock structures with negative reflected shock slope angle are formally possible. • They appear at Mach reflection in high supersonic gas flows having small adiabatic index. • The feasibility and stability of observing such reflections in steady flows looks doubtful. • Solutions corresponding to Mach reflection with negative slope angle are ambiguous. • Regions of solution ambiguity and types of "alternatives" are found analytically. [ABSTRACT FROM AUTHOR]

The dynamics of detonation transmission from a straight channel into a curved chamber was investigated numerically and experimentally as a function of initial pressure (10 kPa ≤ p 0 ≤ 26 kPa) in an argon diluted stoichiometric H 2 –O 2 mixture. Numerical simulations considered the two-dimensional reactive Euler equations with detailed chemistry; hi-speed schlieren and OH* chemiluminescense were used for flow visualization. Results show a rotating Mach detonation along the outer wall of the chamber and the highly transient sequence of events (i.e. detonation diffraction, re-initiation attempts and wave reflections) that precedes its formation. An increase in pressure, from 15 kPa to 26 kPa, expectedly resulted in detonations that are less sensitive to diffraction. The decoupling location of the reaction zone and the leading shock along the inner wall determined where transition from regular reflection to a rather complex wave structure occurred along the outer wall. This complex wave structure includes a rotating Mach detonation (stem), an incident decoupled shock-reaction zone region, and a transverse detonation that propagates in pre-shocked mixture. For lower pressures, i.e. ≤ 10 kPa, the detonation fails shortly after ignition. However, the interaction of the decoupled leading shock with the curved section of the chamber results in detonation initiation behind the inert Mach stem. Thereafter, the evolution was similar to the 15 kPa case. Simulations and experiments qualitatively and quantitatively agree indicating that the global dynamics in this configuration is mostly driven by the geometry and initial pressure, and not by the cellular structure in highly compressed regions. [ABSTRACT FROM AUTHOR]

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

The transition boundary separating the regions of regular and Mach reflections for a planar shock moving in argon and interacting with an inclined wedge in a shock tube is investigated using flow-field simulations produced by high-resolution computational fluid dynamics (CFD). The transition boundary is determined numerically using a modern and reliable CFD algorithm to solve Euler's inviscid equations of unsteady motion in two spatial dimensions with argon treated as a polytropic gas. This numerically computed transition boundary for inviscid flow, without a combined thermal and viscous boundary layer on the wedge surface, is determined by post-processing many closely stationed flow-field simulations to accurately determine the transition-boundary point when the Mach stem of the Mach-reflection pattern just disappears, and this pattern then transcends into that of regular reflection. The new numerical transition boundary for argon is shown to agree well with von Neumann's closely spaced sonic and extreme-angle boundaries for weak incident shock Mach numbers from 1.0 to 1.55, but it deviates upward and above the closely spaced sonic and extreme-angle boundaries by almost 2 ∘ at larger shock Mach numbers from 1.55 to 4.0. This upward trend of the numerical transition boundary for this sequel case with monatomic gases like argon ( γ = 5 / 3 ) and no boundary layer on the wedge surface (inviscid flow) is similar to the previous finding for the case of diatomic gases and air ( γ = 7 / 5 ). An alternative method used to determine one point on the transition boundary between regular and Mach reflections, from a collection of Mach-reflection patterns with a constant-strength shock and different far-field wedge angles, by linear and higher-order polynomial extrapolations to zero for triple-point trajectories versus wedge angle, is compared to the present method of using near-field data that are close to and surround the new transition boundary. Such extrapolation methods are shown to yield a different transition-boundary estimate that corresponds to the mechanical-equilibrium boundary of von Neumann. Finally, the significance of the computed inviscid transition boundary between regular and Mach reflections for monatomic and diatomic gases is explained relative to the case of viscous flow with a combined thermal and viscous boundary layer on the wedge surface. [ABSTRACT FROM AUTHOR]

In this paper, we study the vibration excitation on the reflection of shock waves in hypersonic flows by using analytical and computational approaches. First, a theoretical approach is established to solve the shock relations which are further applied to develop the shock polar analytical method for high-temperature air. Then, a comparative investigation using calorically perfect gas model and thermally perfect gas model considering vibration excitation indicates an obvious change to the overall profile of the shock polar. The post-shock pressure increases within the strong branch of the shock polar while decreases within the weak branch due to vibration excitation of air molecules. A more notable phenomenon is the increase in the maximum deflection angle of the shock polar which can significantly influence the detachment criterion of shock reflection transition in high-temperature air flows. The shock polar analysis of shock reflection shows that the vibration excitation result in an obvious increase to the detachment criterion while a slight increase to the von Neumann criterion. A series of computations are conducted to confirm the above analytical findings on the shock reflection considering the vibration excitation. A slight difference of transition criterion between the theory and computations is found to be caused by the existence of the expansion fan which is an inherent flow structure. The proposed shock polar analytical method is proved to be an effective but simple approach for the study of shock wave reflections in hypersonic flows. [ABSTRACT FROM AUTHOR]

The triple configurations of stationary shock waves with negative slope angle of the reflected shock to the velocity vector of the supersonic stream in front of the triple point ("inverse" triple configurations) are considered. "Inverse" configurations with the maximum relations of flow parameters at the tangential discontinuity after the triple point are determined. Extreme relations of the flow parameters downstream the "inverse" configurations are compared with the analogous extreme parameters attained on the whole set of the triple-shock configurations that appear in supersonic streams of the inviscid perfect gas. [ABSTRACT FROM AUTHOR]

Abstract The detonation reflection over a cylindrical convex surface was investigated experimentally and numerically by focusing on the length-scale effect on the reflection process, such as the triple-point trajectory and the critical wedge angle at which a transition occurs from regular reflection to Mach reflection. The results show that the critical wall angle plots exhibit significant scatter because of the cellular properties of the detonation front. If the transverse spacing is large as compared to the radius of curvature, the scatter range extends. If the transverse spacing is small as compared to the radius of curvature, the scattering is dramatically reduced. The critical wall angle is found to mainly depend on the scaled length i.e., the radius of curvature (R) over the cell size λ (or the reaction zone thickness Δ). Moreover, the critical wall angle increases with the decrease in the detonation thickness or with the increase in the radius. As R /λ increases to approximately ten, the critical wall angle approaches a value calculated using the non-reactive two-shock theory for pseudo-steady flows. The numerical results reveal that the transition to Mach reflection occurs earlier in the case of a ZND detonation than in the case of an inert shock wave because of the higher sound speed due to the release of chemical heat. [ABSTRACT FROM AUTHOR]

• Directly show the propagation of the reaction zone in rotating detonation. • Calculate the radial thickness of the reaction zone with phase-averaged image. • Analysis the pressure distribution along the chamber radius. • Reconstruct the radial structure of the rotating detonation wave. This experimental study discusses the radial structure of the rotating detonation wave (RDW) in a hollow chamber. The head chamber wall could be fabricated with quartz glass for high-speed visualizations or metal cover for high-frequency pressure measurement. The entire radial-stratified reaction zone was directly and continuously captured. The wall-attached bright zone indicated that the main reaction zone propagated along the chamber wall, but some deflagration was still observed in the inner zone. Based on the phase-averaged CH* chemiluminescence image, the radial thickness of the reaction zone was determined to be about 15–20 mm. The diminishing pressure peaks and deteriorating waveforms of the high-frequency pressure signals proved that the intensity of shock waves decreased along the chamber radius. The structure of RDW was reconstructed using radially distributed pressure sensors. Due to the compression effect of the concave chamber wall, a Mach reflection of detonation wave might occur. The detonation wave was connected to a diffracted shock, which stretched in the radial direction with decreasing intensity. The central angles calculated with the time-difference analysis demonstrated that the entire RDW bent forward in the inner zone of the chamber. Moreover, the radial thickness of the reaction zone and the curvature of shock waves increased with decreasing nozzle contraction ratio, which mainly attributed to the increasing expansion effect. This study demonstrated the distribution of reaction zone and the radial structures of shock waves for the RDW in a hollow combustor, contributing to the exploration of the flow and combustion process in a rotating detonation engine. [ABSTRACT FROM AUTHOR]

Subject of Study. We study the interference of counterpropagating shock waves and oblique shock reflection from the wall. There are two fundamentally different interaction modes of counterpropagating shocks: four-wave regular and five-wave irregular ones. The transition from one mode to another can be abrupt or smooth; it can also be accompanied by hysteresis. Hysteresis is the existence of two different types of shock-wave structures with the same parameters of interference. The implementation of a particular decision depends on the direction and perhaps the rate of change of parameters. Hysteresis in the interference of counterpropagating shocks and oblique shock wave reflection from the wall has been studying since the mid-60s of the XX-th century, the most actively in the past 20 years. This is due to the development of new types of internal and mixed compression intakes, in particular, intended for high supersonic and hypersonic speeds. Despite of problem research for many years, many questions still remain unclarified and among them nonconcurrence of the numerical and physical experiment results with the data obtained by analytical theory of interference stationary gas-dynamic discontinuities, the effect of the rate change for parameters, the accuracy of calculations, the difference grid density. The present paper deals with the impact of two factors: the rank of difference grid and blurring degree of shock waves front. Main Results. Analytical and numerical calculations have shown that blurring of shock waves and the transition from small difference grid to a coarser one is accompanied by narrowing of the hysteresis domain, i.e. the transitions from regular to irregular reflection and backwards are more different from those predicted by the theory. Reducing the size of the difference grid cells leads to solution convergence to the results of interference theory of stationary gas-dynamic discontinuities. Practical Relevance. Obtained findings complement the interference theory of stationary gas-dynamic discontinuities and are usable in the design of advanced models of supersonic and hypersonic aircrafts.

Subject of Study. The paper deals with data on the interference of shock waves with different intensity and slope angles to the flow of them. This problem is related to the problem of designing air intakes to the internal compression and detonation combustion engines in stationary overdriven detonation wave. A regular form of interference and irregular Mach one are considered. Intensity calculations of reflected shock waves for both cases are given. As shown below, there is a possibility of a very large difference in the intensity of the reflected shocks. Main Results. We describe transition criteria from regular to irregular reflection of counter shocks: von Neumann criterion and a stationary Mach configuration criterion. Intensity dependences of the reflected intensity shocks from the interaction of colliding shock waves are presented both for the case of regular interaction, and irregular interference. We demonstrate intensity dependence of a reflected shock wave on the intensity of the two interacting shock waves, as in the transition from regular to irregular reflection, in accordance with von Neumann detaching criterion, and in accordance with a stationary Mach configuration criterion. In the first case, the transition is accompanied by an abrupt change in the intensity of the reflected shock; in the second case, the intensity varies in a continuous manner. Practical Relevance. The results supplement interference theory of stationary gas-dynamic discontinuities and are usable in the design of advanced air intakes of internal compression supersonic and hypersonic aircrafts.

Regular and Mach (irregular) reflection of an oblique shock wave from the wall is considered. Criteria for the transition from regular to irregular reflection are described: von Neumann criterion and the criterion for fixed Mach configuration. Specific incident shock wave intensities corresponding to the two criteria for the transition from regular to irregular reflection were plotted. The area of ambiguity solutions was demonstrated in which both regular and Mach reflection is not prohibited by the conditions of dynamic compatibility. Areas in which the transition from one type of reflection to another is possible only by a shock wave were described, as well as areas of a possible smooth transition. Dependence of the magnitude of this abrupt change in reflected discontinuity intensity from the intensity of the incident shock wave was plotted. Intensity dependences of the reflected discontinuity from the intensity of the shock wave incident on the wall for all types of reflections were shown.

The subject of study. We examined the interaction of counterpropagating shock waves. The necessity of counterpropagating shock waves studying occurs at designing of high Mach number modern internal compression air intakes, Ramjets with subsonic and supersonic combustion, in asymmetrical supersonic nozzles and in some other cases. In a sense, this problem is a generalization of the case of an oblique shock reflection from the wall or from the plane of symmetry. With the renewed vigor, the interest to this problem emerged at the end of the 90s. This was due to the start of the programs for flight study at hypersonic speeds. The first experiments performed with air intakes, which realized the interaction of counterpropagating shock waves have shown that the change in flow velocity is accompanied by abrupt alteration of shock-wave structure, the occurrence of nonstationary and oscillatory phenomena. With an increase of flow velocity these phenomena undesirable for aircraft structure became more marked. The reason is that there are two fundamentally different modes of interaction of counterpropagating shock waves: a four-wave regular and a five-wave irregular. The transition from one mode to another can be nonstationary abrupt or gradual, it can also be accompanied by hysteresis. Main results. Criteria for the transition from regular reflection of counterpropagating shock waves to irregular are described: the criterion of von Neumann and the stationary Mach configuration criterion. We described areas in which the transition from one reflection type to another is possible only in abrupt way, as well as areas of possible gradual transition. Intensity dependences of the reflected shock waves from the intensity of interacting counterpropagating shocks were given. Qualitative pictures of shock-wave structures arising from the interaction of counterpropagating shock waves were shown. Calculation results of the intensity of outgoing gas-dynamic discontinuities, the intensities corresponding to the transition from regular to irregular interference were described. Numerical calculations of the shock-wave structure transformation in the conditions of hysteresis were performed. The results were compared with the experiments carried out by hydraulic analogy method. Practical significance. Results of the work complement well the theory of stationary gas-dynamic discontinuities interference and can be used at designing of perspective images of supersonic and hypersonic aircraft.

The reflection of a two-dimensional cylindrical shock wave segment on a concave-cylindrical wall segment was investigated from an experimental and numerical perspective. Qualitatively, the experimental results show that a cylindrical shock behaves similarly to a plane shock when propagating up a concave-cylindrical wall segment. Thus, whatever differences exist must be quantitative. The length of the cylindrical shock’s Mach stem was plotted against the subtending angle. From the plots, two limits are highlighted, one where the shock’s radius is much larger than the wall’s radius and another where the wall has the larger radius. The former being akin to a plane shock interacting with a cylindrical wall segment. An increase in initial shock Mach number was observed to affect the type of Mach reflection that is formed (whether it is an inverse or stationary Mach reflection) as well as the transition point to a transitioned regular reflection. An expression which relates the shock’s Mach stem to the subtending angle was derived. Comparisons between the expression’s predictions, experimental and CFD data were completed, and they showed good correlation. Further, the expression was shown to reduce to that derived by Itoh et al. when the shock’s radius was much larger than the wall’s radius. [ABSTRACT FROM AUTHOR]

An experimental investigation was conducted to control a Mach reflection (MR)-induced flow separation in a Mach 2.05 flow using a 18∘ shock generator (SG). The study was extended to four SG exit heights (g / w) of 0.87, 0.81, 0.725, and 0.66 primarily to study its effect on the extent of flow separation as well as on Mach stem height, with and without control. Two vane-type vortex generator configurations, namely the ramp vane (RV) with device heights h/δ=0.3,0.5,0.8, and 1.0 and the rectangular vane (RRV) with h/δ=0.3 and 0.5, were studied for control. Each control device array was implemented 10δ upstream of the separation location for no control. For stable MR interactions (i.e., g/w=0.87,0.81), the extent of separation and the reattachment shock strength are seen to decrease with increase in RV height (with h/δ=1.0 device showing 17% reduction). However, for unstable MR condition (i.e., g/w=0.725), RV devices of h/δ=0.8 and 1.0 become ineffective. The RRV2 device (h/δ=0.5), on the other hand, was found to be more effective in reducing the extent of separation in both the stable (31%) and unstable (24%) MR conditions. The effectiveness of each control device is also accompanied with an increase in height of the Mach stem. This is, however, not seen as a serious limitation since in such strong interactions it is more important to prevent or avert an intake unstart condition. The separation shock unsteadiness or the σmax/Pw value, on the other hand, is seen to increase considerably with controls and seems to be almost independent for h/δ≥0.5. [ABSTRACT FROM AUTHOR]

An experimental study of the Mach reflection of cellular detonations over the wedge is reported in this paper. Throughout the experiments, high-quality smoked foil is obtained to record cell pattern variation. The initial pressures are varied to yield cellular detonations with varied transverse wave spacing (or cell size). This paper focuses on length scales controlling the deviation and recovery of self-similarity in an unsteady Mach reflection process. The results show that the frozen limit and equilibrium limit both exist for all the mixture compositions. The Mach reflection undergoes a frozen condition in the near field, and then goes through a transition process before asymptotically approaching an equilibrium state in the far field. The cell size variation in the Mach stem region also confirms the transient process. Although the final triple-point trajectory angle in the equilibrium state disagrees with classical three-shock theories, it is in agreement with the reactive three-shock theory when the wedge angle is less than 30°. The triple-point trajectory angle asymptotically approaches zero as the wedge angle increases to approximately 50°, indicating the critical wedge angle from Mach to regular reflection. The transition length associated with the equilibrium limit is found to be dependent on the mixture composition and has the same order of a hydrodynamic thickness, which is approximately a few cell lengths. This means that the hydrodynamic thickness is the characteristic length scale that most significantly dominates the Mach reflection process of cellular detonations. [ABSTRACT FROM AUTHOR]