Mach Stem Research Articles

Influence of concentration gradient on detonation re-initiation in a bifurcated channel

The effect of concentration gradient on detonation re-initiation behavior in a bifurcated tube full of oxyhydrogen mixture is numerically studied by employing an OpenFOAM based solver DCRFoam. The Naiver-Stokes equations (NS) with detailed chemical kinetics are solved to model the detonation diffraction, quenching and re-initiation process. The results show that compared with the homogeneous case, the second reflection is the key to the successful re-initiation of the detonation in mixture with concentration gradient instead of the first one, because multiple transverse waves are generated during the second reflection. With steepening the concentration gradient, the number and intensity of the transverse waves decreases, leading to the cellular structure more irregular and the decrease of detonation velocity. After the second reflection, the interaction between the concentration gradient and the leading shock leads to the concentration gradient existing not only in the transverse direction but also in the longitudinal direction. The longitudinal concentration provides the earlier H2 for the formation and propagation of transverse detonation. Also, the Mach stem front bends greatly, and the transition distance from regular reflection to Mach reflection increases with steepening the concentration gradient.

Interaction between Shock Waves Travelling in the Same Direction

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.

A Study of the Dependence of the Mach Stem Height on the Trailing Edge Height

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.

Micro-Ramp Control for Shock Train Structure and Oscillation

Micro-ramps for shock train control were investigated experimentally in a Mach 1.85 supersonic isolator flow using three device heights. A mechanical flap was mounted downstream and linearly choked, forcing the shock train to travel upstream of the micro-ramp from the exit. Wall static pressure measurements along the primary and corner regions obtained a more complete pressure distribution. Detailed structures of the shock train were recorded using schlieren visualization with circular, horizontal, vertical, and color knife edges. The results show that the wake and wave structures generated by the micro-ramp control the shock train. The taller the device, the stronger the wake and wave structures, and the greater the control. The wake and wave structures shorten or eliminate the Mach stem in the shock train leading edge, causing modification of shocks downstream from pseudonormal to oblique, inhibiting the thickening of the boundary layer that results from shock impingement, slowing down the contraction of the supersonic core flow, and allowing more high total pressure fluid to develop downstream. The wake structure was found to promote the oscillation and upstream motion of the shock train. The wave structure can restrain shock train oscillation and upstream propagation of the downstream adverse pressure gradient, enhancing the resistance backpressure of the flowfield downstream of the micro-ramp.

Numerical study of fragments from cylindrical casing with one of end caps fully constrained

In order to study the process and characteristic of the fragments in the warhead with one end cap under full constraint condition, we established a cylindrical casing with two end caps which one of them was fully constrained using the simulation analysis. The result showed that the fragmentation of cylindrical casing with one end full constrained has its own characteristic. The Mach stem was generated when the detonation wave propagated to the fully constrained end cap under the condition of one end detonation, working on unreactive explosives and causing the nearby fragment subjected to nearly 2.5 times the normal pressure to obtain a higher speed. The cylindrical casing first ruptured at the contact surface with the fully constrained end, and then at the end cover of the initiating end, and then the rupture extends to the whole cylindrical casing. The detonation products started to leak out from the rupture. driving fragments to fly, and forming two dense flying areas. The analysis of this paper can provide a reference for the optimal design of this kind of warhead.

Variations of stress field and stone fracture produced at different lateral locations in a shockwave lithotripter field

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.

Effects of Cowl-Induced Expansion on the Wave Complex Induced by Oblique Detonation Wave Reflection

Oblique detonation wave (ODW) reflection on the upper wall leads to a sophisticated wave complex, whose stability is critical to the application of oblique detonation engines. The unstable wave complex characterized with a continuous moving Mach stem has been observed, but the corresponding re-stability adjusting method is still unclear so far. In this study, the cowl-induced expansion wave based on the model with an upper-side expansion wall is introduced, and the ODW dynamics have been analyzed using the reactive Euler equations with a two-step induction–reaction kinetic model. With the addition of a cowl-induced expansion wave, the re-stabilized Mach stem has been distinguished. This re-stability is determined by the weakened secondary reflection wave of lower wall, while the final location of Mach stem is not sensitive to the position of the expansion corner. The re-stabilized ODW structure is also basically irrelevant to the expansion angle, while it may shift to unstable due to the merging of subsonic zones. Transient phenomena for the unstable state have been also discussed, clarifying fine wave structures further.

Effects of flow momentum enhancement using an artificial external source on shock wave strength, a CFD study

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.

Propagation of Shock Waves of Varying Curvature

When a shock wave having variable concave curvature propagates, it can develop a kink followed by the development of a reflected shock. A typical example is a plane incident shock encountering a surface with concave curvature, the part of the shock adjacent to the surface curves forward and subsequently develops into a Mach reflection with a Mach stem, shear layer and reflected shock. The physical mechanisms associated with the evolution of the shock profile was evaluated for shock waves with initial profiles comprising a cylindrical arc, placed in-between two straight segments, propagating in a converging channel. The temporal variation of the pressure distribution immediately behind the shock wave was studied using CFD. This revealed a pressure imbalance in the region where the curved (which was initially cylindrical) and straight shock segments meet. This imbalance occurs due to the difference in the propagation behaviour of curved and planar shock waves, and results in the development of reflected shocks on the shock front. The angle at which the channel walls converge, the initial curvature radius, and the shock Mach number, was varied between 40 and 60 degrees, 130 and 190 mm and 1.1 to 1.4, respectively. The variation with time of the pressure-gradient distribution and the maximum pressure gradient behind theshock wave was evaluated. From this, the trajectory angle of the triple points, and the rate at which the reflected shocks develop, was deduced. It was found that when shock waves with larger curvature radii propagate in channels with lower wall angles, the reflected shocks develop at a slower rate, and the triple points follow a steeper trajectory. Consequently, the likelihood of reflected shocks emerging on the shock front, within the duration of the shock propagation, is reduced. This is due to the triple points intersecting the walls, before reflected shocks can fully develop. Similarly, when the shock Mach number is higher, the trajectory angle of the triple points is greater, and they intersect the walls before the reflected shocks can emerge.

Study on cell size variation in overdriven gaseous detonations

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.

A method for predicting Mach stem height in steady flows

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.

Evolution of wall flow structure and measurement of shear stress issuing from supersonic jet with extended shelf

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.

Characteristics of the oblique detonation flow field induced by a complex wave structure

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.

Onset of the Mach Reflection of Zel'dovich-von Neumann-Döring Detonations.

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.

Steadiness of wave complex induced by oblique detonation wave reflection before an expansion corner

Oblique detonation wave (ODW) reflection before an expansion corner leads to a sophisticated wave complex, whose steadiness is critical to achieve a practical oblique detonation engine. Both steady and unsteady wave complexes have been observed before, but the features of unsteady wave dynamics with related unsteadiness rules are still unclear so far. In this study, the ODW reflections before an expansion corner have been simulated using the reactive Euler equations with a two-step induction–reaction kinetic model, and the wave complex structures and dynamics have been analyzed correspondingly. Three subsonic zones have been distinguished, and their interactions were found to determine the wave complex steadiness. The main subsonic zone derives from the ODW reflection, which locates behind the Mach stem, while two other subsonic zones form due to the shock reflection downstream. The two downstream subsonic zones might travel upstream and combine with the main subsonic zone, resulting in two different unsteadiness modes. These wave complex dynamics were analyzed with respect to the deflection location, deflection angle and inflow Mach number, leading to the boundaries of combustion modes and ascertaining the rule of mode regime. Some transient phenomena related with the flow instability have been also discussed, clarifying fine flow structures further.

Transition of an overdriven Mach stem in the Mach reflection of detonations in H<sub>2</sub>/O<sub>2</sub> mixtures

<p indent="0mm">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.

Viscous jetting and Mach stem bifurcation in shock reflections: experiments and simulations

Abstract

Mach reflection of a H2-O2-Ar detonation wave on the rough wedge based on soot track measurements

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.

Dynamics of detonation transmission and propagation in a curved chamber: a numerical and experimental analysis

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 ≤ p0 ≤ 26 kPa) in an argon diluted stoichiometric H2–O2 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.

The effect of the polytropic index γ on the structure of gaseous detonations

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.