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This paper reports an experimental study on the supersonic jet surface flow structure visualization and shear stress field measurement issuing from a rectangular nozzle with extended shelf. The evolution of the near-field surface flow structures with an increased Nozzle Pressure Ratio (NPR) is successfully captured by the surface oil flow, infrared detection technology, and the Shear-Sensitive Liquid Crystal Coating (SSLCC) technique. Results reveal that under smaller NPR, the wall flow structure is similar to that of a jet without the extended shelf i.e., clean jets, and this is caused by insufficient effect on the boundary layer. However, at higher amplitudes of NPR, there exists a significant effect of the boundary layer, as a near triangular separation forms on the trailing edge of the Mach stem due to the adverse pressure gradient, which is visualized for the very first time in this paper. Furthermore, the vector field of shear stress is measured quantitatively by SSLCC technique. Results shows that the magnitude of shear stress heightened with NPR increasing, and the directions of shear stress changes across the shock wave and expansion fans. In addition, surface streamlines measured by SSLCC is significantly consistent with the streamlines visualized using the oil flow technique.

This study evaluated the effects of the adding of flow momentum using artificial external source on the controlling of oblique shock wave of a supersonic flow in a three dimensional duct with low-aspect-ratio (based on experimental data) through a numerical investigation by employing an OpenFoam extended solver. The oblique shock occurred due to a 20° compression ramp which placed on the top of the low-aspect-ratio duct. The flow characteristics were consistent with the published data, suggesting that the numerical methodology successfully resolved the interaction between the shock-waves and flow boundary-layer. To investigate the effect of momentum adding, based on literature, three different cases with various forces exerted on the upper and lower walls of the duct were considered. The results showed that momentum adding led to a decrement in the separation region and shock strength. Moreover, adding the momentum sources on the lower wall of the duct suppressed the lambda shock that happened by the collision of separated and incident shocks and Mach stem. However, by applying the momentum source on the upper wall (upstream of the compression ramp) had more effects on the interaction between shock wave and boundary layer, as compared to the lower wall. Therefore, based on the obtained results, to achieve the best performance of momentum source, it must apply at the critical point with the greatest effect on discontinuities in the flow structure.

The purpose of this research work is to perform accurate numerical computations of supersonic flow in a converging nozzle and specifically to study Mach-disks. The latter process has been widely studied over the last years. In the present study numerical simulations are performed for transient supersonic flow, tracing the transition from a Mach reflection to a regular one. This has been done by enforcing the walls of a converging nozzle to come closer together, changing the deflection angle with time. Viscosity was taken into account and the full Navier- Stokes have been solved. The results obtained clearly show the gradual extinction of the Mach disk and the eventual wave intersection to a single point

During clinical procedures, the lithotripter shock wave (LSW) that is incident on the stone and resultant stress field is often asymmetric due to the respiratory motion of the patient. The variations of the LSW-stone interaction and associated fracture pattern were investigated by photoelastic imaging, phantom experiments, and three-dimensional fluid-solid interaction modeling at different lateral locations in a lithotripter field. In contrast to a T-shaped fracture pattern often observed in the posterior region of the disk-shaped stone under symmetric loading, the fracture pattern gradually transitioned to a tilted L-shape under asymmetric loading conditions. Moreover, the model simulations revealed the generation of surface acoustic waves (SAWs), i.e., a leaky Rayleigh wave on the anterior boundary and Scholte wave on the posterior boundary of the stone. The propagation of SAWs on the stone boundary is accompanied by a progressive transition of the LSW reflection pattern from regular to von Neumann and to weak von Neumann reflection near the glancing incidence and, concomitantly, the development and growth of a Mach stem, swirling around the stone boundary. The maximum tensile stress and stress integral were produced by SAWs on the stone boundary under asymmetric loading conditions, which drove the initiation and extension of surface cracks into the bulk of the stone that is confirmed by micro-computed tomography analysis.

The accidental release of hydrogen into enclosures can result in a flammable mixture with concentration gradients and possible deflagration-to-detonation transition (DDT). This numerical study aims to investigate the effect of obstacle spacing and mixture concentration on the DDT in a homogeneous and inhomogeneous hydrogen-air mixture. The paper focuses on the mechanisms behind the DDT in two mixtures with an average hydrogen concentration of 15% and 30%. Unlike the near-stoichiometric mixture, in the lean mixture, DDT only occurs in the inhomogeneous mixture. Depending on obstacle spacing, three different regimes of DDT were observed in the near-stoichiometric inhomogeneous mixture: i) Detonation was ignited when a strong Mach stem formed and propagated between the obstacles; ii) two explosion centers appeared when incident shock and Mach stem reflected from upper and lower obstacles, respectively; iii) Mach stem did not form but DDT occurred behind the flame front at the top of the obstacle.

In this paper, the initiation characteristics of the oblique detonation flow field induced by single- and double-wedge surfaces of finite length in a confined space are investigated. Numerical simulations with a detailed H2/air reaction and theoretical shock polar analyses are combined to study the influence mechanism of a complex wave system structure on the characteristics of the oblique detonation. The effects of expansion waves on the oblique detonation waves (ODWs) and their flow field characteristics for different equivalent ratios and geometric sizes are analyzed in single-wedge and double-wedge structures with the same inflow parameters. The results show that the length of the induced ODW is shorter in the double-wedge structure than in the single-wedge structure. For the single-wedge structure, the strength of the expansion wave increases, the wall temperature drops, and the characteristic length of the induction zone decreases with increasing deflection angle of the second wedge. If the strength of the expansion wave is sufficiently large, the ODW is initiated. For the double-wedge structure, the ODWs interact and form a complex wave system structure, consisting of a Mach stem, two reflected detonation waves and slip lines. The length and the temperature before and after the Mach stem decrease with an increase in the strength of the expansion waves. The effects of the expansion waves on the flow field of the ODW are relatively small at a large equivalent ratio and significantly larger at a small equivalent ratio.

The reflection of a moving shock wave over a wedge immersed in a still gas and the reflection of a wedge induced steady shock wave over symmetrical and asymmetrical reflecting surfaces have received intensive considerations since more than 70 years ago. Here we consider a different shock reflection problem—reflection of a moving shock wave over an initially steady oblique shock wave induced by a wedge immersed in supersonic flow. For the flow condition we considered, five moving triple points, with each connecting an incident shock wave, a reflected shock wave and a Mach stem, are identified. By using the reference frame co-moving with each triple point, the type of each shock wave of this triple point is clarified. The present study is significant in that it treats a new shock reflection problem leading to a new shock reflection configuration and showing potential applications in supersonic flow with unsteady shock interaction.

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.

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.

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.

The transition of an overdriven Mach stem in the Mach reflection of cellular detonations on the wedge is experimentally studied in mixtures of hydrogen and oxygen with different argon dilutions. This study focuses on the changes in the cell size of an overdriven Mach stem on the wedge surface other than those on the sidewall. The detonation cell pattern on the wedge surface has a complicated process, i.e., the cells decrease from a large to a small size and then increase asymptotically to a medium size, which can be considered a three-stage pattern. The changes in cell size in this case do not correspond to the normal cell-size change in a decaying overdriven detonation. This is primarily attributed to the mixed effect of Mach reflection and cellular instability. Furthermore, the cell-size ratio upon increasing the degree of overdrive is examined. It is found that the ratio decreases with increase in the degree of overdrive. However, as the wedge angle increases to a critical value, finer cells are not created on the smoke foils.

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.

We examine, via multi-material simulation in a two-dimensional planar geometry, the effects on steady detonation propagation of the presence of a low-density intermediate layer between a condensed-phase high explosive (HE) and a high-density metallic confiner of finite thickness. Such elastomer intermediate layers are often added to eliminate air-gaps and the associated jetting effects that can arise due to machining imprecisions, or to prevent HE cracking due to environmental changes. Without an intermediate layer, the flow structure of a steady detonation/metal confiner interaction is well understood. In particular, there is no reflected wave passed into the HE due to the metal confinement. With the elastomer layer present, we find that, as the intermediate layer width increases, a complex wave interaction and communication path develops between the HE, intermediate, and metal layers. For thin intermediate layers, a shock-driven subsonic flow develops in the intermediate layer, passing information from the metal layer to the HE, with the detonation speed decreasing as the intermediate layer width increases. For wider intermediate layers, a Mach stem configuration develops in the intermediate layer, forcing a shock to be reflected into the HE. Simultaneously, a localized Prandtl-Meyer fan emerges from the intersection of the detonation shock with the HE-intermediate layer material interface. These HE structures are shown to have a substantial effect on the structure of the detonation driving zone. The Prandtl-Meyer fan becomes the dominant structure for critically large intermediate layer widths, wherein the presence of the metal layer does not affect the detonation propagation. We examine the detonation propagation speed and reaction and driving zone structure as a function of varying intermediate layer width. Two confinement metals are examined, along with two high explosive and three metal layer widths.

Building on previous experiments conducted in an obstructed narrow rectangular channel, new details of the three-dimensional propagation behaviour of supersonic combustion waves have been revealed. In this study, a square channel equipped with 50% blockage ratio obstacles was used. Average velocity measurements coupled with high-speed schlieren photography and sooted glass sheets were used to simultaneously capture wave propagation and triple-point trajectories from multiple fields-of-view. Experiments were carried out in mixtures of stoichiometric hydrogen-oxygen at initial pressures between 9 kPa and 60 kPa in a 3.66 m long, by 7.62 cm square cross-section channel with optical access. Results show that the increased channel width results in a lower maximum pressure for which fast-flame propagation occurs. At higher initial pressures, detonation kernels were initiated at the obstacle face-sidewall interface in either a symmetrical (both sides) or an asymmetrical (single side) formation across the channel width. Wall reflection generated detonations evolve to form transverse detonations propagating diagonally across the channel width in the shock-compressed region following the obstacle. The single wall ignition was found to lead to a stable single-head “zig-zag” detonation (diagonal propagation driven by sidewall reflection) at initial pressures from 17 kPa to 24 kPa where transverse detonation reflection leads to the generation of a reactive Mach stem that survives diffraction at the next obstacle pair. Soot foils displayed a unique narrow vertical band of cells where the transverse wave collides with the channel sidewall in this propagation mode, which is the only mode to not involve obstacle reflection re-initiation. The channel width w, being larger than the obstacle opening d, makes it possible for the transverse modes seen in an obstacle-free channel to lock in, like the single-head detonation propagation observed. Continuous detonation propagation through the channel core was seen at high CJ velocity deficits beginning at d/λ = 6.3, where λ is the detonation cell width, with higher initial pressures having cellular structure reach the channel walls between obstacles. Thus, continuous detonation propagation is governed by the diffraction process around the obstacles and d is the governing length scale.

In this paper, nonlinearity associated with intense ultrasound is studied by using the one-dimensional motion of nonlinear shock wave in an ideal fluid. In nonlinear acoustics, the wave speed of different segments of a waveform is different, which causes distortion in the waveform and can result in the formation of a shock (discontinuity). Acoustic pressure of high-intensity waves causes particles in the ideal fluid to vibrate forward and backward, and this disturbance is of relatively large magnitude due to high-intensities, which leads to nonlinearity in the waveform. In this research, this vibration of fluid due to the intense ultrasonic wave is modeled as a fluid pushed by one complete cycle of piston. In a piston cycle, as it moves forward, it causes fluid particles to compress, which may lead to the formation of a shock (discontinuity). Then as the piston retracts, a forward-moving rarefaction, a smooth fan zone of continuously changing pressure, density, and velocity is generated. When the piston stops at the end of the cycle, another shock is sent forward into the medium. The variation in wave speed over the entire waveform is calculated by solving a Riemann problem. This study examined the interaction of shocks with a rarefaction. The flow field resulting from these interactions shows that the shock waves are attenuated to a Mach wave, and the pressure distribution within the flow field shows the initial wave is dissipated. The developed theory is applied to waves generated by 20 KHz, 500 KHz, and 2 MHz transducers with 50, 150, 500, and 1500 W power levels to explore the effect of frequency and power on the generation and decay of shock waves. This work enhances the understanding of the interactions of high-intensity ultrasonic waves with fluids.

Mach reflection in steady supersonic flow is an important phenomenon having received extensive studies, among which simplified theoretical models to predict the size of Mach stem and other flow structure are of particular interest. Past efforts for such models were based on inviscid assumption while in real cases the flow is viscous. Here in this paper we consider the influence of wedge boundary layer on the Mach stem height. This is done by including a simplified boundary layer model into a recently published inviscid model. In this viscous model, the wedge angle and the trailing edge height, which control the Mach stem height, are replaced by their equivalent ones accounting for the displacement effect of the wedge boundary layer, with the boundary layer assumed to be laminar or fully turbulent. This viscous model is shown to compare well with numerical results by computational fluid dynamics and gives a Mach stem height as function of the Reynolds number and Mach number. It is shown that due to the viscous effect, the Mach stem height is increased, through increasing the effective wedge angle. Keywords: Boundary-layer correction, Mach reflection, Shock waves, Supersonic flow, Viscous effect

The Jones-Wilkins-Lee (JWL) equation of state (EOS) is used to calculate expansion of detonation reaction products from the chemical equilibrium Chapman-Jouguet (C-J) state to large volumes. Overdriven detonation waves with shock pressures higher than C-J are created by high-velocity impacts or converging detonation waves. Reflection from high-impedance materials, multiple shock impacts, and Mach stem wave interactions creates similar pressures. When overdriven states were first measured experimentally, the original reaction product JWL EOSs predicted excess compression. This problem was resolved by modifying the JWL EOS to produce less compression at high pressures while still correctly calculating expansion from the C-J state. Zeldovich-von Neumann-Doring (ZND) reactive flow models, which include the measured reaction zone momentum, explained experimental observations that lower C-J pressures are required to smoothly connect the C-J state to overdriven states on the product Hugoniot curve. Experimental data on overdriven detonation waves for two octogen (HMX)-based plastic-bonded explosives (PBXs), PBX 9501 and PBX 9404, and for two triaminotrinitrobenzene (TATB)-based PBXs, LX-17 and PBX 9502, are compared to various JWL reaction product EOSs, including ones generated by the CHEETAH chemical equilibrium code. Excellent agreement is obtained using JWL EOSs for overdriven shock pressures and densities up to 130 GPa and 3.8 g/cm3 for both HMX- and TATB-based PBXs.

In this paper, we study the intersection (interaction) between several steady shocks traveling in the same direction. The interaction between overtaking shocks may be regular or irregular. In the case of regular reflection, the intersection of overtaking shocks leads to the formation of a resulting shock, contact discontinuity, and some reflected discontinuities. The type of discontinuity depends on the parameters of incoming shocks. At the irregular reflection, a Mach shock forms between incoming overtaking shocks. Reflected discontinuities come from the points of intersection of the Mach stem with the incoming shocks. We also consider the possible types of shockwave configurations that form both at regular and irregular interactions of several overtaking shocks. The regions of existence of overtaking shock waves with different types of reflected shock and the intensity of reflected shocks are defined. The results obtained in the study can potentially be useful for designing supersonic intakes and advanced jet engines.

The Mach stem height is an important parameter in the Mach reflection of steady supersonic flow. Various experimental, numerical, and theoretical works have been conducted to study this parameter in the past. However, much of the established work focuses around a single set of trailing edge heights. Here, we perform a study to show the dependence of Mach stem height on the trailing edge height for a wider range of geometry. Through numerical simulation for a set of trailing edge heights, we found that the normalized Mach stem height is almost linear with respect to the normalized wedge trailing edge height. The parameter used for normalization can be either the inlet height or the length of the lower wedge surface. The observation of this linear trend is justified through a simplified analysis, which leads to an expression of the Mach stem height that linearly depends on the trailing edge height. The present study extends our knowledge about how the geometry affects the Mach stem height, and provides a basis for future work to elaborate analytical models for Mach stem height.

Shock wave is a detriment in the development of supersonic aircrafts; it increases flow drag as well as surface heating from additional friction; it also initiates sonic boom on the ground which precludes supersonic jetliner to fly overland. A shock wave mitigation technique is demonstrated by experiments conducted in a Mach 2.5 wind tunnel. Non-thermal air plasma generated symmetrically in front of a wind tunnel model and upstream of the shock, by on-board 60 Hz periodic electric arc discharge, works as a plasma deflector, it deflects incoming flow to transform the shock from a well-defined attached shock into a highly curved shock structure. In a sequence with increasing discharge intensity, the transformed curve shock increases shock angle and moves upstream to become detached with increasing standoff distance from the model. It becomes diffusive and disappears near the peak of the discharge. The flow deflection increases the equivalent cone angle of the model, which in essence, reduces the equivalent Mach number of the incoming flow, manifesting the reduction of the shock wave drag on the cone. When this equivalent cone angle exceeds a critical angle, the shock becomes detached and fades away. This shock wave mitigation technique helps drag reduction as well as eliminates sonic boom.

In this study, we obtain the comparative analysis of methods of quick approximate analytical prediction of Mach shock height in planar steady supersonic flows (for example, in supersonic jet flow and in narrowing channel between two wedges), that are developed since the 1980s and being actively modernized now. A new analytical model based on flow averaging downstream curved Mach shock is proposed, which seems more accurate than preceding models, comparing with numerical and experimental data.

The effect of rapid wedge rotation on the transition from regular (RR) to Mach reflection (MR) is investigated. This unsteady shock reflection transition is compared with the steady-state transition. The dependence of various flow features such as the unsteady Mach stem height, position of the reflection point, and shock angle at the reflection or triple point on the wedge angle for a fixed Mach number is compared at various rotation rates. The study is further extended to compare the dynamic effects for various Mach numbers in the strong shock reflection domain at higher wedge speeds. Transition lines corresponding to different rotation speeds are obtained similar to the detachment transition line in steady cases. It is found that the pivot point has only marginal effect on the transition point, but it substantially affects the Mach stem growth and the movement of the reflection point, specifically at higher Mach numbers. The location of the transition from the inlet also depends on the pivot point and the rate of rotation.

High performance aircraft operate at high jet temperature and velocity. Measured noise data indicate that at afterburner condition their noise contain components not found in high temperature supersonic laboratory model jets. The combustion process inside an afterburner is highly unsteady and incomplete. Residual combustion takes place in the jet plume. This suggests that the flow from the afterburner into the jet nozzle would contain significant amount of hot and cold temperature blobs, generally referred to as entropy waves. It is known that when entropy waves move through a non-uniform mean flow, indirect combustion noise (also called entropy noise) would be generated. Military styled nozzles have a rather abrupt area change at and near the throat. This induces the formation of internal shocks inside the nozzle. This paper investigates the generation of entropy noise when strong entropy blobs or waves are convected through the internal shocks. It is found that the result of entropy blobs-shock interaction could lead to the radiation of intense entropy noise out of the nozzle exit into the jet plume as fast waves with a speed equal to sound speed plus jet flow speed. These fast waves create highly supersonic flow disturbances in the jet flow leading to strong Mach wave radiation. It is proposed that this Mach wave radiation is the source of a new noise component observed in the spectra of the F-22A aircraft. Detailed analysis of the F-22A noise data provides support for the proposal.

The canonical problem of transonic dense gas flows past two-dimensional compression/expansion ramps has recently been investigated by Kluwick & Cox (J. Fluid Mech., vol. 848, 2018, pp. 756–787). Their results are for unconfined flows and have to be supplemented with solutions of another canonical problem dealing with the reflection of disturbances from an opposing wall to finally provide a realistic picture of flows in confined geometries of practical importance. Shock reflection in dense gases for transonic flows is the problem addressed in this paper. Analytical results are presented in terms of similarity parameters associated with the fundamental derivative of gas dynamics$(\unicode[STIX]{x1D6E4})$, its derivative with respect to the density at constant entropy$(\unicode[STIX]{x1D6EC})$and the Mach number$(M)$of the upstream flow. The richer complexity of flows scenarios possible beyond classical shock reflection is demonstrated. For example: incident shocks close to normal incidence on a reflecting boundary can lead to a compound shock–wave fan reflected flow or a pure wave fan flow as well as classical flow where a compressive reflected shock attached to the reflecting boundary is observed. With incident shock angles sufficiently away from normal incidence regular reflection becomes impossible and so-called irregular reflection occurs involving a detached reflection point where an incident shock, reflected shock and a Mach stem shock which remains connected to the boundary all intersect. This triple point intersection which also includes a wave fan is known as Guderley reflection. This classical result is demonstrated to carry over to the case of dense gases. It is then finally shown that the Mach stem formed may disintegrate into a compound shock–wave fan structure generating an additional secondary upstream shock. The aim of the present study is to provide insight into flows realised, for example, in wind tunnel experiments where evidence for non-classical gas dynamic effects such as rarefaction shocks is looked for. These have been predicted theoretically by the seminal work of Thompson (Phys. Fluids, vol. 14 (9), 1971, pp. 1843–1849) but have withstood experimental detection in shock tubes so far, due to, among others, difficulties to establish purely one-dimensional flows.

Numerical simulations were performed to study reflection of a stable detonation wave with regular cellular patterns over a cylindrical concave wedge. The dynamics of this reflection phenomenon was described by the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model and solved numerically using the adaptive mesh refinement code AMROC. The effects of various parameters on the reflection evolution were analyzed in detail. The results indicate that the reflection-type transition of a stable cellular detonation is similar to that of a planar shock wave over a concave wedge. The triple-point trajectory resulted from the Mach reflection when the cellular detonation first encounters the concave wedge coincides with that of the planar shock propagating for the case with the same incident Mach number. As the effective wedge angle continuously increases, the Mach reflection of cellular detonation deviates from that of a planar shock with a reduced Mach stem height, and the transition from Mach to regular reflection occurs at a smaller angle. This observation is further explored by adopting the length-scale (or “corner-signal”) concept, examining the velocity variation of corner signals generated by fluid particles around the wedge tip. The reflection dynamics is described qualitatively by the ratio of two length scales characterizing the detonation structure, namely, the induction-zone and reaction-zone lengths. The increase of these length scales raises the Mach stem height and transition angle. Apart from the detonation length scales, the wedge curvature radius is found to have an opposite effect since the increase of radius expands the region where the corner signals are generated by the particles behind the induction zone, and makes the corner signals persist in a state with attenuating velocity.