Detonation Reflection Research Articles

Curved detonation and its reflections

This paper investigates the effect of curvature on curved detonation and its reflections. Specifically, the study focuses on two aspects: the effect of curvature on the postwave parameters and their gradients, and the stabilization of Mach reflection. Relationships are established between the curvature and the gradients of the postwave parameters, thus providing a basis for examining detonation reflections and obtaining a comprehensive understanding of curved detonation. In particular, these relationships offer a valuable analytical tool to predict the postwave gradients, as well as providing a fresh perspective to understand the transformation from Mach reflection to regular reflection in curved detonation. The validity of these relationships is confirmed by comparison with simulation results. Two mechanisms by which curvature influences the stationarity of Mach reflection are identified. An increase in wave angle and interference between wave systems leading to the generation and integration of subsonic zones are the reasons for the non-stationarity of the Mach reflection in curved detonation. Besides, the effect mechanisms of choked flow which is considered to be the root cause are analysed in detail. On the basis of a theoretical model, the development of a quantitative criterion for the stability of detonation reflection is proposed, and its validity is confirmed by simulations. This criterion is used in a comprehensive investigation of the primary factors affecting the stability of detonation wave reflections, providing insights that will be of great value for the further development of detonation engines.

Analysis of shock wave acceleration from normal detonation reflection

Analysis of shock wave acceleration from normal detonation reflection

Numerical study on detonation reflections over concave and convex double wedges

The solver DCRFoam is used to analyze the characteristics of detonation reflection over concave and convex double wedges. Seven reflection processes are observed depending on the wedge angles (θ1 and θ2), the critical angle of a single surface (θc,single), and the angle difference (Δθ). For concave wedges with small θ1 and Δθ, a Mach reflection is established along the first surface and the leading edge of the second surface. At the end of the second surface, either a Mach reflection or a regular reflection could be observed depending on the θ2. For concave wedges with large θ1 and Δθ, the Mach stem formed over the first surface regularly reflects at the leading edge of the second surface. Then the incident wave regularly reflects over the tail of the second surface. For concave wedges, the actual critical angle of the second surface is found to be larger than the θc,single. While the second surfaces of convex double wedges are found to have the same as a single surface. The detonation reflection processes over convex wedges are much simpler.

Numerical investigation on cellular detonation reflection over wedges with rounded corner

Numerical investigations were performed to study the reflection of cellular detonation over wedges with rounded corner, and for comparison, reflections over wedges with straight sharp corner were also calculated. Dynamics of the reflection phenomenon were described by the two-dimensional reactive Euler equations based on the platform of OpenFOAM-7, with the utilization of the adaptive mesh refinement (AMR) technology. The reflection process and the influence of the concave section and wedge angle on the reflection were discussed, as well as the transition from Mach reflection to regular reflection. Different kinds of reflection types including the Direct-Mach reflection (DiMR), the Stationary-Mach reflection (StMR) and the Inverse-Mach reflection (InMR) were observed in the concave section. When the detonation initially propagated to the straight section, the influence of the concave section was “remembered”. Subsequently, the influence was “forgotten” at a certain point, and the reflection was controlled by the straight section. When the wedge angle was smaller than or equal to 50°, the asymptotic self-similarity approached in the far field, and the asymptotical triple-point angles decreased with the increase of wedge angle. The critical angle for the transition from Mach reflection to regular reflection was 64.17° for concave wedge, which was much larger than that of straight sharp corner wedge (51 ± 1°).

Three-dimensional behaviour of quasi-detonations

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.

Experimental and numerical studies on detonation reflections over cylindrical convex surfaces

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

Observations on the normal reflection of gaseous detonations

Experimental results are presented examining the behavior of the shock wave created when a gaseous detonation wave normally impinges upon a planar wall. Gaseous detonations are created in a 7.67-m-long, 280-mm-internal-diameter detonation tube instrumented with a test section of rectangular cross section enabling visualization of the region at the tube-end farthest from the point of detonation initiation. Dynamic pressure measurements and high-speed schlieren photography in the region of detonation reflection are used to examine the characteristics of the inbound detonation wave and outbound reflected shock wave. Data from a range of detonable fuel/oxidizer/diluent/initial pressure combinations are presented to examine the effect of cell-size and detonation regularity on detonation reflection. The reflected shock does not bifurcate in any case examined and instead remains nominally planar when interacting with the boundary layer that is created behind the incident wave. The trajectory of the reflected shock wave is examined in detail, and the wave speed is found to rapidly change close to the end-wall, an effect we attribute to the interaction of the reflected shock with the reaction zone behind the incident detonation wave. Far from the end-wall, the reflected shock wave speed is in reasonable agreement with the ideal model of reflection which neglects the presence of a finite-length reaction zone. The net far-field effect of the reaction zone is to displace the reflected shock trajectory from the predictions of the ideal model, explaining the apparent disagreement of the ideal reflection model with experimental reflected shock observations of previous studies.

Numerical application of additive Runge-Kutta methods on detonation interaction with pipe bends

A detailed reaction model comprised of 9 species and 48 reactions is employed in simulating two-dimensional cellular detonations propagating through smooth pipe bends in a stoichiometric H2/O2 mixture diluted by Argon. Additive Runge-Kutta (ARK) methods are applied to solve the stiff reactive Euler equations, in which the stiff and non-stiff terms are solved implicitly and explicitly. The numerical results indicate that, as the regular cellular detonation wave propagating through the bend section, the diffraction near the inner wall causes an increase in detonation cell size while the detonation reflection occurring on the bottom wall leads to a decrease in cell size. In addition, an expansion wave is generated continuously. The expansion wave causes the failure as well as the partial failure of the detonations near the inner and outer walls, respectively. On the contrary, the transverse re-initiation waves evolve into a detonation in the decoupling zone just downstream of the bend outlet owing to continuous compression imposed by other transverse waves propagating right behind. Meanwhile, there exists a transition length after the detonation propagating out of the bend and entering the sloped tube section.

Numerical Study on Critical Wedge Angle of Cellular Detonation Reflections

The critical wedge angle (CWA) for the transition from regular reflection (RR) to Mach reflection (MR) of a cellular detonation wave is studied numerically by an improved space-time conservation element and solution element method together with a two-step chemical reaction model. The accuracy of that numerical way is verified by simulating cellular detonation reflections at a 19.3° wedge. The planar and cellular detonation reflections over 45°–55° wedges are also simulated. When the cellular detonation wave is over a 50° wedge, numerical results show a new phenomenon that RR and MR occur alternately. The transition process between RR and MR is investigated with the local pressure contours. Numerical analysis shows that the cellular structure is the essential reason for the new phenomenon and the CWA of detonation reflection is not a certain angle but an angle range.

The evolution of a detonation wave in a variable cross-sectional chamber

A two-dimensional numerical simulation has been performed to study the interaction of a gaseous detonation wave with obliquely inclined surfaces in a variable cross-sectional chamber. The weighted essentially non-oscillatory (WENO) numerical scheme with a relatively low resolution grid is employed. A detailed elementary chemical reaction model with 9 species and 19 elementary reactions is used for a stoichiometric oxy-hydrogen mixture diluted with argon. In this work, we study the effect of area expansion and contraction on the main/gross features of the detonation cellular structures in the presence of detonation reflection, diffraction and localized explosion. The result shows that there exists a transition region as the detonation wave propagates through the converging/diverging chamber. Within the transition region, the initial regular detonation cells become distorted and irregular before they re-obtain their regularity. While the ultimate regular cell size and the length of the transition region are strongly affected by the converging/diverging angle, the width/length ratio of the cells is fairly independent of it. A localized explosion near the wall is found as the detonation wave propagates in the diverging chamber.

Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H (2)/O (2) diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.