Detonation propagation with velocity deficits in narrow channels

Propagation limits of detonations in narrow channels have been studied with a focus on velocity deficits and variation in cell widths. A channel was formed by a pair of metal plates of 1500 mm length which were inserted in a detonation tube of 50.5 mm inner diameter. Test gases were hydrogen–oxygen mixtures diluted with argon or nitrogen, which were selected as representatives of regular and irregular mixture systems. The velocity deficits predicted using the concept of negative boundary layer displacement thickness were compared to those obtained experimentally. From good agreement between the predicted and the experimental velocity deficits, the cell width enlarged in the channel was calculated using the induction zone length behind the decelerated leading shock front. Although this calculation underestimates the cell widths, the calculated cell widths were found to be well predicted when they were multiplied by an appropriate proportionality factor. It is found that for given mixtures, a combination of the calculated velocity deficit and the number of cells in a channel contributes to the prediction of propagation limits of detonations.     

Detonability limits in thin annular channels

In this paper, detonability limits in two-dimensional annular channels are investigated. Since the channel heights are small in comparison to the tube diameter, curvature effects can be neglected and the annular channels can be considered to be essentially two-dimensional. Mixtures that are highly diluted with argon are used since previous investigations seem to indicate that detonations in such mixtures are “stable” in that cellular instabilities play minor roles on the propagation of the detonation. For stable detonations where the ZND structure is valid, boundary layer effects can be modeled as a flow divergence term in the conservation of mass equation following the pioneering work of Fay [J.A. Fay, Phys. Fluids 2(3) (1959) 283–289]. Expansion due to flow divergence in the reaction zone results in a velocity deficit. There exists a maximum deficit when an eigenvalue detonation velocity can no longer be found, which can be taken as the onset of the detonability limits. Experimentally, it was found that unlike “unstable” detonations, the detonability limits for “stable” detonations are well-defined. No unstable near-limit phenomena (e.g., galloping detonations) was observed. Good agreement is found between the theoretical predictions and the experimentally obtained velocity deficits and limits in the two channel heights of 2.2 and 6.9 mm for hydrogen–oxygen and acetylene–oxygen mixtures diluted with over 50% argon. It may be concluded that at least for these special mixtures where the detonation is “stable,” the failure mechanism is due to flow divergence caused by the negative displacement thickness of the boundary layer behind the leading shock front of the detonation wave.     

Pulsating instability of detonations with a two-step chain-branching reaction model: theory and numerics

The nonlinear dynamics of Chapman–Jouguet pulsating detonations are studied both numerically and asymptotically for a two-step reaction model having separate induction and main heat release layers. For a sufficiently long main heat release layer, relative to the length of the induction zone, stable one-dimensional detonations are shown to be possible. As the extent of the main reaction layer is decreased, the detonation becomes unstable, illustrating a range of dynamical states including limit-cycle oscillations, period-doubled and four-period solutions. Keeping all other parameters fixed, it is also shown that detonations may be stabilized by increasing the reaction order in the main heat release layer. A comparison of these numerical results with a recently derived nonlinear evolution equation, obtained in the asymptotic limit of a long main reaction zone, is also conducted. In particular, the numerical solutions support the finding from the analytical analysis that a bifurcation boundary between stable and unstable detonations may be found when the ratio of the length of the main heat release layer to that of the induction zone layer is O(1/ε), where ε (?1) is the inverse activation energy in the induction zone.     

Spinning detonation and velocity deficit in small diameter tubes

Detonation velocities and soot patterns of H₂/O₂ mixtures were measured in glass tubes of 3, 6 and 10 mm diameters at pressures ranging from 70 to 400 Torr and equivalence ratios of 0.5–1.5. It was confirmed that the transition from a multi-head to a spinning detonation occurred at the pressure where the cell size is equal to the length of circumference. At this transition pressure, the velocity was 95% of the C-J detonation. Stable spinning detonations were observed at wide range of initial pressures below the transition point. Detonation velocities were continuously decreasing with decreasing initial pressures in this pressure region. Spinning detonations with velocities down to 85% of the C-J detonation were observed. Those deficits in detonation velocities were well predicted by the modified ZND model with full detailed chemical kinetics. Heat and momentum losses were taking into account in this model. Validity of the modified ZND model to define the limit of detonation propagation was discussed.     

Dynamics of shock induced ignition in Fickett’s model: Influence of χ

Using Fickett’s model for reactive compressible flows, i.e., the reactive form of Burgers’ equation, we address the problem of shock induced ignition by a piston in a reactive medium characterized by a 2 step induction-reaction kinetics. Owing to the model’s simplicity, the ignition and acceleration mechanism is explained using the two families of characteristics admitted by the model. The energy release along the particle paths provides the amplification of forward-traveling pressure waves. These waves pre-compress the medium in the induction layer ahead of the reaction zone, therefore changing the induction delays of successive particles. The variation of the induction delay provides the modulation of the amplification of the forward traveling pressure waves by controlling the residence time of the pressure waves in the reaction zone. A closed form analytical solution is obtained by the method of characteristics and high activation energy asymptotics. The acceleration of the reaction zone was found to be proportional to the product of the activation energy, the ratio of the induction to reaction time and the heat release. This finding provides a theoretical justification for the previous use of this non-dimensional number to characterize the ignition regimes observed experimentally in detonations and shock induced ignition phenomena. Numerical simulations are presented and analyzed. Both subsonic and supersonic internal flame propagation are observed, consistent with experiment and previous reactive Euler models.     

Analytical solution to a mode of mixed elastohydrodynamic lubrication with mixed contact regimes: Part I. Without consideration of contact adhering layer in the inlet zone

In 2005, Zhang presented a Grubin-like inlet zone analysis to the isothermal line contact elastohydrodynamic lubrication under relatively heavy loads when the hydrodynamic film thickness in the Hertzian zone approaches zero and the EHL fluid is Newtonian [Zhang, Y.B. A justification of the load-carrying capacity of elastohydrodynamic lubrication film based on the Newtonian fluid model. Industrial Lubrication and Tribology, 2005, Vol. 57, pp. 224–232]. His results showed that in this EHL, when the rolling speed is lower than the characteristic rolling speed (U_ch =) 0.0372W^1.50/G, the Hertzian zone is in physical adsorbed layer boundary lubrication while the inlet zone is in conventional hydrodynamic lubrication. This mode of EHL represents a mode of mixed EHL with mixed contact regimes, where hydrodynamic films with different rheological behaviors occur in different areas of the contact. The present paper presents an analysis to this mode of mixed EHL by using the Grubin type method when the contact adhering layer in the inlet zone is neglected. Pressures, film thicknesses and load partition in the contact are obtained from this analysis. It is also found that the formula for the characteristic rolling speed U_ch = 0.0372W^1.50/G obtained by Zhang [Zhang, Y.B. A justification of the load-carrying capacity of elastohydrodynamic lubrication film based on the Newtonian fluid model. Industrial Lubrication and Tribology, 2005, Vol. 57, pp. 224–232] may be valid for the dimensionless load W > 1.0E−7, while it may be invalid for the dimensionless load W < 1.0E−8. In part II [Zhang, Y.B. Analytical solution to a mode of mixed elastohydrodynamic lubrication with mixed contact regimes: Part II. Considering the contact adhering layer effect in the inlet zone. Journal of Molecular Liquids, 2006, Vol. 117. (doi:10.1016/j.molliq.2006.04.007)] will be presented an analysis to other two modes of mixed EHL with mixed contact regimes for relatively heavy loads, low rolling speeds and Newtonian fluids, where the conventional hydrodynamic lubrication, physical adsorbed layer boundary lubrication and oxidized chemical layer boundary lubrication can simultaneously occur in the inlet zone while the oxidized chemical layer boundary lubrication or the fresh metal-oxidized chemical boundary layer dry contact occur in the Hertzian zone, considering the contact adhering layer effect in the inlet zone.     

Rapid communication: Permeability of hydrogen in two-dimensional graphene and hexagonal boron nitride sheets

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.     

On the characteristics of two-dimensional double cellular detonations with two successive reactions model

Double cellular detonations were numerically investigated using two-dimensional Euler equations with two successive chemical reactions, whose reaction lengths differ one order of magnitude. Simulated soot track images showed the double cellular structure with two cell widths that differ one order of magnitude, as well as previous experiments and numerical simulations. We successfully divided the double cellular detonation with two successive exothermic reactions into two detonations, primary and secondary detonations, with a single exothermic reaction, based on p–v relation of Rayleigh line and Hugoniot curves with the addition of the hypothetical condition of intermediate initial state. The ratio of cell widths of primary and secondary detonations showed good agreement with that caused by the first and second reactions of double cellular detonation, and there was no interaction between two successive chemical reactions. The linear stability analysis of planar detonation and the soot rack images of double, primary and secondary detonations showed that instabilities of primary and secondary detonations are dominant to that of double cellular detonation with two successive reactions. We confirmed the validity of division of two successive reactions to clarify the detonation instability and its cellular structure.     

Effect of Cellular Instability on the Initiation of Cylindrical Detonations

The direct initiation of detonations in one-dimensional(1 D) and two-dimensional(2 D) cylindrical geometries is investigated through numerical simulations. In comparison of 1 D and 2 D simulations, it is found that cellular instability has a negative effect on the 2 D initiation and makes it more difficult to initiate a sustaining 2 D cylindrical detonation. This effect associates closely with the activation energy. For the lower activation energy,the 2 D initiation of cylindrical detonations can be achieved through a subcritical initiation way. With increasing the activation energy; the 2 D cylindrical detonation has increased difficulty in its initiation due to the presence of unreacted pockets behind the detonation front and usually requires rather larger source energy.     

Analytical solution to a mode of mixed elastohydrodynamic lubrication with mixed contact regimes: Part II—Considering the contact adhering layer effect in the inlet zone

The present paper presents the researches succeeding the first part of the paper [Y.B. Zhang, Analytical Solution to A Mode of Mixed elastohydrodynamic lubrication with Mixed Contact Regimes: Part I—Without Consideration of Contact Adhering Layer in the Inlet Zone. Journal of Molecular Liquids, 2006, Vol.117, (10.1016/j.molliq.2006.04.006)], which analyzed one mode of mixed elastohydrodynamic lubrication with mixed contact regimes for the relatively heavy load and low rolling speed which make the conventional hydrodynamic lubrication occur in the inlet zone while make the physical adsorbed layer boundary lubrication occur in the Hertzian zone, based on the Newtonian fluid model. The present paper presents analysis to other two modes of mixed EHL with mixed contact regimes for relatively heavy loads, low rolling speeds and Newtonian fluids, where the conventional hydrodynamic lubrication, physical adsorbed layer boundary lubrication and oxidized chemical layer boundary lubrication can simultaneously occur in the inlet zone while the oxidized chemical layer boundary lubrication or the fresh metal-oxidized chemical boundary layer dry contact occur in the Hertzian zone, considering the contact adhering layer effect in the inlet zone. The present analysis is also extended to the first mode of mixed EHL with mixed contact regimes as analyzed in Part I [Y.B. Zhang, Analytical Solution to A Mode of Mixed elastohydrodynamic lubrication with Mixed Contact Regimes: Part I—Without Consideration of Contact Adhering Layer in the Inlet Zone. Journal of Molecular Liquids, 2006, Vol.117, (10.1016/j.molliq.2006.04.006)] when the contact adhering layer effect in the inlet zone is considered. Results of contact pressures, film thicknesses, load partitions in the contact and characteristic rolling speeds for approaching to zero averaged hydrodynamic film thickness in the Hertzian zone are obtained from this analysis respectively as functions of the contact adhering layer thickness in the inlet zone. The results show that the contact adhering layer effect in the inlet zone in the present EHL is reduced with the increase of load; At large loads, this effect may be negligible; At small loads, it may be very significant. The results also show that at low rolling speeds, when the contact adhering layer effect in the inlet zone is considered, the load-carrying capacity of the present EHL contact is increased especially for small loads. This means that at low rolling speeds the contact adhering layer effect in the inlet zone may reduce the elastohydrodynamic lubrication deviation from classical EHL theory predictions especially for small loads.     

Critical diffraction of irregular structure detonations and their predictability from experimentally obtained D−κ data

The present work reports new experiments of detonation diffraction in a 2D channel configuration in stoichiometric mixtures of ethylene, ethane, and methane with oxygen as oxidizer. The flow field details are obtained using high-speed schlieren near the critical conditions of diffraction. The critical initial pressure for successful diffraction is reported for the ethylene, ethane and methane mixtures. The flow field details revealed that the lateral portion of the wave results in a zone of quenched ignition. The dynamics of the laterally diffracting shock front are found in good agreement with the recent model developed by Radulescu et al. (Physics of Fluids 2021). The model provides noticeable improvement over the local models using Whitham’s characteristic rule and Wescott, Bdzil and Stewart’s model for weakly curved reactive shocks. These models provide a link between the critical channel height and the critical wave curvature. The critical channel heights and global curvatures are found in very good agreement with the critical curvatures measured independently by Xiao and Radulescu (Combust. Flame 2020) in quasi-steady experiments in exponential horns for three mixtures tested. Furthermore, critical curvature data obtained by others in the literature was found to provide a good prediction of critical diffraction in 2D. These findings suggest that the critical diffraction of unstable detonations may be well predicted by a model based on the maximum curvature of the detonation front, where the latter is to be measured experimentally and account for the role of the cellular structure in the burning mechanism. This finding provides support to the view that models for unstable detonations at a meso-scale larger than the cell size, i.e., hydrodynamic average models, are meaningful.     

Enhanced DDT mechanism from shock-flame interactions in thin channels

We show experimentally and numerically that when a weak shock interacts with a finger flame in a narrow channel, an extremely efficient mechanism for deflagration to detonation transition occurs. This is demonstrated in a 19-mm-thick channel in hydrogen-air mixtures at pressures below 0.2 atm and weak shocks of Mach numbers 1.5 to 2. The mechanism relies primarily on the straining of the flame shape into an elongated alligator flame maintained by the anchoring mechanism of Gamezo in a bifurcated lambda shock due to boundary layers. The mechanism can increase the flame surface area by more than two orders of magnitude without any turbulence on the flame time scale. The resulting alligator-shaped flame is shown to saturate near the Chapman–Jouguet condition and further slowly accelerate until its burning velocity reaches the sound speed in the shocked unburned gas. At this state, the lead shock and further adiabatic compression of the gas in the induction zone gives rise to auto-ignition and very rapid transition to detonation through merging of numerous spontaneous flames from ignition spots. The entire acceleration can occur on a time scale comparable to the laminar flame time.     

Laboratory simulation of rotating atmospheric boundary layer flows over obstacles

Summary The present study fits in the frame of a research program concerning in general the dynamics of airflow in the atmospheric boundary layer and in particular the influence of terrestrial rotation on the movements of air masses interacting with natural extended obstacles (mountains). The experiment has been performed by the method of hydraulic simulation, using schematic models at reduced scale in a channel placed on a rotating platform. We only considered the case of a neutral atmosphere and studied the wake of an obstacle with semi-circular section and the reciprocal interaction of two obstacles of this kind placed perpendicularly to the flow. In this last case we investigated the influence of the distance between the obstacles on their wake length and on the vorticity conditions inside the wakes. Among the various results we obtained, the modifications of the velocity profiles over the reliefs and their dependence on the rotation velocity are particularly interesting. We discuss here our results from two different points of view, namely the purely hydraulic one (which includes the effects of different rotation velocities) and the atmospheric one, according to which the model simulates—with given reduction scales—an actual situation characterized by a fixed value of the Coriolis parameter. As to the first approach to the problem, we found that: 1) The roll with horizontal axis, which is observed behind an obstacle, becomes narrower and narrower as the rotation velocity of the platform increases, while its stability in time and its definition in space increase. In general, it may be said that rotation plays a stabilizing role for vortex dimensions and velocity profiles. 2) The transversal velocity behind the obstacles may attain values about twice the mean longitudinal velocity of the flow. 3) When rotating, the roll is thicker at its left edge than on the right one, due to the transversal flux which provides fluid supply. 4) When the thickness of the boundary layer is increased by making the channel bottom rough, the above-mentioned phenomena are emphasized; moreover, with a second obstacle placed in the flow (and not too far from the first) the transversal velocity components increase, due to a canalization effect. 5) The accelerations of the low layers over the obstacles are strongly amplified by rotation, due to the action of Coriolis' force. As for the second approach, we checked the extent to which the simulation procedures adopted for our laboratory flows, and for their boundary conditions, can be representative of the features of atmospheric phenomena. In order to do that, we compared the dynamical structure of the low flow layers over the obstacle with the analogous structure observed in the field and in wind tunnel by other authors, as well as with the predictions of a few theoretical models. Inside the lowest part of the planetary boundary layer, where the overshooting due to the relief is confined, a good consistency was found among all these results, in particular for what concerns the maximum of overflow velocity. This work has been carried out during 1981–1982 on the rotating platform of Institut de Mécanique, Université de Grenoble, within the ambit of a research convention with Istituto di Cosmogeofisica of C.N.R., Torino.     

Visualizing shear stress in Görtler vortex flow

Shear stress distributions were obtained from velocity measurements in a concave surface boundary layer flow in the presence of Görtler vortices by means of a single hot-wire probe for several streamwise (x) locations. A set of vertical wires of 0.20 mm diameter were positioned at a distance of 10 mm upstream from the leading edge of a concave surface of radius of curvature R=1.0 m to pre-set the wavelength of the vortices so to obtain the most amplified wavelength Görtler vortices. Consequently, the wavelength of the vortices was set equal to the wire spacing and preserved downstream. In addition to the high shear regions near the wall, one positive peak at the head of the mushroom-like structures and two relatively weak negative peaks at the vicinity of the low-speed streaks are found in the iso-?u/?y contours. They are believed to be related to the formation of the inflectional point in the velocity profile across boundary layer. The occurrence of the inflection points in the spanwise distributions of streamwise velocity component u is associated with the appearance of the second peak of the ?u/?z shear near the boundary layer edge. The nonlinear effect of Görtler instability is to increase the wall shear stress, and further enhancement beyond the turbulent values is due to the presence of secondary instability.     

Anomalies of radiation absorption and superluminal propagation of light: I. An isotropic layer

The features of superluminal propagation of light through an isotropic layer are investigated and the group velocity is calculated. Multilayer systems providing superluminal propagation of light over large distances with compensation of losses upon light transmission through the system are considered. The situations in which the propagation speed of a light pulse decreases or in which it is equal to zero are also investigated. The features of radiation absorption in a thin isotropic layer are considered. The effects of anomalously high and anomalously low absorption are found. It is shown that these effects are caused by an increase (decrease) in the density of light energy in the layer and by changes in the group velocity. The possibility of experimental observation of the effects discovered is discussed.     

Transverse rarefaction of a layer behind the front of a longitudinal wave of nonlinear thermal conductivity and features of plasma formation inside the target cavity

A solution of the two-dimensional problem is presented for a transverse rarefaction wave of a plane layer behind a wavefront of nonlinear thermal conductivity produced by an instantaneous cylindrical energy source with its axis normal to the layer surface. The matter can rarefy through the free surfaces of the layer or through holes in the boundary walls, which are coaxial with the energy source axis. Analytic solutions are obtained describing the formation of the rear boundary in the heated zone due to transverse matter rarefaction. The energy fraction transferred to the energy of hydrodynamic motion is also determined. Models of plasma formation inside the inner target cavity under the action of pulsed energy sources are considered as applications of the approach suggested. Requirements on the source and target parameters are formulated for efficient matter heating with minimum energy losses caused by hydrodynamic rarefaction of the matter. Translated from Preprint No. 14 of the P. N. Lebedev Physical Institute, Moscow (1998).     

The kinetic boundary layer around an absorbing sphere and the growth of small droplets

Deviations from the classical Smoluchowski expression for the growth rate of a droplet in a supersaturated vapor can be expected when the droplet radius is not large compared to the mean free path of a vapor molecule. The growth rate then depends significantly on the structure of the kinetic boundary layer around a sphere. We consider this kinetic boundary layer for a dilute system of Brownian particles. For this system a large class of boundary layer problems for a planar wall have been solved. We show how the spherical boundary layer can be treated by a perturbation expansion in the reciprocal droplet radius. In each order one has to solve a finite number ofplanar boundary layer problems. The first two corrections to the planar problem are calculated explicitly. For radii down to about two velocity persistence lengths (the analog of the mean free path for a Brownian particle) the successive approximations for the growth rate agree to within a few percent. A reasonable estimate of the growth rate for all radii can be obtained by extrapolating toward the exactly known value at zero radius. Kinetic boundary layer effects increase the time needed for growth from 0 to 10 (or 2 1/2) velocity persistence lengths by roughly 35% (or 175%).     

Dynamics of Chapman-Jouguet pulsating detonations with Chain-Branching kinetics: Fickett’s analogue and Euler equations

The present study examines the spatiotemporal nonlinear dynamics of detonations over a wide range of reaction time scales away from the neutral stability region. This is addressed by one-dimensional numerical simulations with chain-branching kinetics. Fickett’s detonation analogue and Euler’s equations were used as evolution equations. A shock-fitting solver is used to reduce CPU time. Up to four thousand five hundred simulations have been carried out. Detailed bifurcation diagrams have been generated to explore the detonation dynamics. For long/intermediate reaction time scales, away from the neutral boundary, the traditional period-doubling cascade to chaos is seen. For square wave detonations, away from the neutral stability, almost periodic oscillations are recorded. This result might have implications for the existence of a characteristic length scale, the cell size, on typical cellular detonations which have a short reaction length.     

DNS analysis of boundary layer flashback in turbulent flow with wall-normal pressure gradient

The presence of swirl in combustion systems produces a marked change in their boundary layer flashback behaviour. Two aspects of swirling flow are investigated in this study: the effect of the swirl-generated wall-normal pressure gradient, and the effect of misalignment between the mean flow direction and the direction of flame propagation. The analysis employs Direct Numerical Simulation (DNS) of fuel-lean premixed hydrogen-air flames in turbulent planar channel flow with friction Reynolds number of 180. The effect of swirl on the flashback process is investigated by imposing a wall-normal pressure gradient profile. Analysis of the DNS data shows how the resulting differences in flow field and flame topology contribute to the differences in the overall flashback speed. Misalignment of the flow and propagation directions leads to asymmetry in the flame shape statistics as streaks of high velocity fluid in the boundary layer cleave into the flame front at an angle, yielding an increase in flame surface density away from the wall. Swirl has a stabilising effect on the turbulent flame front during flashback along the centre-body of a swirling annular flow due to the density stratification across the flame front, and produces a reduction in turbulent consumption speed. However the swirl also sets up a hydrostatic pressure difference that drives the flame forward, and the net effect is that the flashback speed is increased. The dominance of hydrostatic effects motivates development of relatively simple modelling for the effect of swirl on flashback speed. A model accounting for the inviscid momentum balance and for confinement effects is presented which adequately describes the effect of swirl on flashback speed observed in previous experimental studies.     

A flame technique to isolate the detonation/product interface relevant to rotating detonation engines

A novel experimental technique is proposed to study the detonation propagation in a layer of non-reacted gas weakly confined by combustion products. This problem is relevant to rotating detonation engines, where transverse detonations are confined by products of a previous rotation cycle, and other applications such as industrial safety. The experimental technique utilizes a flame ignited along the top wall in a long channel. The preferential growth of the flame along the long direction of the channel creates a finger flame and permits to create a narrow layer of unburned gas. A detonation ignited outside of this layer then propagates through the layer. This permits to conduct accurate observations of the detonation interaction with the inert gas and determine the boundary condition of the interaction. The present paper provides a proof-of-concept demonstration of the technique in a 3.4 m by 0.2 m channel, in which long finger flames were observed in ethylene-oxygen mixtures. The flame is visualized by high-speed direct luminosity over its entire travel, coupled with pressure measurements. A direct simulation of the flame growth served to supplement the experiments and evaluate the role of the induced flow by the flame growth, which gives rise to a non-uniform velocity distribution along the channel length. Detonation experiments were also performed at various layer heights in order to establish the details of the interaction. The structure was visualized using high speed Schlieren video. It was found that an inert shock always runs ahead of the detonation wave, which gives rise to a unique double shock reflection interaction.