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Abstract: Spinning detonations propagating in a circular tube were numerically investigated with a two-step reaction model by Korobeinikov et al. The time evolutions of the simulation results were utilized to reveal the propagation behavior of single-headed spinning detonation. Three distinct propagation modes, steady, unstable, and pulsating modes, are observed in a circular tube. The track angles on a wall were numerically reproduced with various initial pressures and diameters, and the simulated track angles of steady and unstable modes showed good agreement with those of the previous reports. In the case of steady mode, transverse detonation always couples with an acoustic wave at the contact surface of burned and unburned gas and maintains stable rotation without changing the detonation front structure. The detonation velocity maintains almost a CJ value. We analyze the effect of acoustic coupling in the radial direction using the acoustic theory and the extent of Mach leg. Acoustic theory states that in the radial direction transverse wave and Mach leg can rotate in the circumferential direction when Mach number of unburned gas behind the incident shock wave in the transverse detonation attached coordinate is larger than 1.841. Unstable mode shows periodical change in the shock front structure and repeats decoupling and coupling with transverse detonation and acoustic wave. Spinning detonation maintains its propagation with periodic generation of sub-transverse detonation (new reaction front at transverse wave). Corresponding to its cycle, whisker is periodically generated, and complex Mach interaction periodically appears at shock front. Its velocity history shows the fluctuation whose behavior agrees well with that of rapid fluctuation mode by Lee et al. In the case of pulsating mode, as acoustic coupling between transverse detonation and acoustic wave is not satisfied, shock structure of spinning detonation is disturbed, which causes failure of spinning detonation. [Copyright &y& Elsevier]

Abstract: Pulsating detonations propagating in circular and square tubes were numerically investigated with a two-step reaction model by Korobeinikov et al. The time evolution of the simulation results was utilized to reveal the propagation mechanism of pulsating detonation. Soot track images on the wall and flow features shows cyclic behavior in longitudinal direction including three regions of multi-headed, single-headed, and no detonation. Pulsating detonation shows strong oscillation in the longitudinal direction and periodic behavior as follows. Shock front separates from the reaction front, and the shock wave velocity becomes underdriven. Local explosion occurs near the flame front and develops on inner detonation propagating to the leading shock wave. After penetration of the inner detonation into the leading shock wave, an overdriven multiheaded detonation appears and is gradually transformed into a spinning detonation with diminishing velocity. After a while, the spinning detonation decays, and the shock front finally separates from the reaction front again. Pulsating detonation propagates with repetition of these processes and its velocity varies from underdriven to overdriven in one cycle of pulsation. In order to discuss the one-dimensional features of pulsating detonation, x–t diagrams of cross-sectionally averaged profile are directly compared with x–t diagram of one-dimensional detonation, and the two agree well in terms of periodicity, as observed in the unsteady mechanism of the large-disturbance regime. Characteristic values such as the velocity in the failed regime obtained by the one-dimensional detonation agree with those by the pulsating detonation in circular and square tubes. Therefore, pulsating detonation is essentially a one-dimensional phenomenon and is dominant to longitudinal instability. [Copyright &y& Elsevier]

The oscillation mechanism and reignition process of one-dimensional unsteady detonations are numerically studied using a one-step chemical reaction model governed by Arrhenius kinetics. A series of simulations, without perturbations from the outflow boundary to the detonation front, are carried out while the degree of overdrive, f, is varied between 1.10 and 1.74 (f = D²/D²[sub CJ]; where D is detonation velocity). Shock pressure histories and x-t diagrams are utilized in order to attain precise understanding of the one-dimensional unsteady detonations. At higher degrees of overdrive, f = 1.40-1.74, shock pressure histories agree with those of previous studies. The oscillation mechanism is the same as that of the large-disturbance regime of unsteady shock-induced combustion around a projectile. At lower degrees of overdrive, f < 1.30, grid resolution affects the eventual results, because half reaction time in the shock pressure exhibits considerable variation. Four typical kinds of oscillation pattern are discussed and are explained by their x-t diagrams and shock pressure histories. Each oscillation mechanism is essentially the same as that of the large-disturbance regime. The reignition process in the failed regime was numerically investigated at f = 1.01-1.25. The reignition points tend to converge on a specified point in study of grid refinement, although the oscillation of the shock pressure histories becomes chaotic, suggesting the existence of a unique solution for reignition. All the simulation results for f = 1.01-1.20 show the failed regime after initial disturbance at the early stage. The failed regime is compared with the solution of the Riemann problem, and analysis consisting of a Rayleigh line for weak leading shock and a partially burnt Hugoniot curve is adopted. Analysis suggests the concept of partial chemical heat release, indicating the possibility of discontinuous change in conditions, and, indeed, simulation indicates occurrence... [ABSTRACT FROM AUTHOR]

To analyze non-ideal phenomena, such as burned gas backflow and non-detonation combustion, which affect the rotating detonation wave Mach number, simultaneous self-luminous visualization, time-averaged static pressure, fluctuating pressure, and thrust measurements with gaseous ethylene and oxygen were performed. Consequently, by doubling the number density of the fuel injectors, the hydrodynamic blockage ratio at the oxidizer inlet increased approximately 1.7-fold under the same oxidizer inlet area conditions. This may be attributed to the increase in the detonation propagation Mach number owing to the enhanced mixing of fuel and oxidizer. The relationship between the parasitic combustion fraction in front of the rotating detonation wave and the Mach number was also investigated by using a distributed heat release model. Consequently, it was suggested that experimental Mach number decreased from approximately 4.1 to 2.8 with increase in a mixture mass flux, and the theoretical detonation wave propagation Mach number was 7.3. • Mach number of rotating detonation wave was experimentally estimated. • Hydrodynamic blockage ratio increased with number density of fuel injectors. • Propagation speed of detonation wave increased with mixture mass flux. • Fluctuating pressure ratio decreased with increase in mixture mass flux. • The Mach number decreased from 4.1 to 2.8 with increase in mixture mass flux. [ABSTRACT FROM AUTHOR]

Liquid propellants are commonly used in rocket engines due to their high energy density. In this study, we focused on the use of liquid ethanol and liquid nitrous oxide as propellants in a cylindrical rotating detonation engine (RDE) for practical applications, and examined the effects of various conditions on the bipropellant RDE performance. We varied the vapor quality of nitrous oxide in a mixture of liquid and gaseous nitrous oxide due to the flash boiling. In addition, we varied the liquid ethanol temperature, the injector stiffness, and momentum angle of the propellant. We then analyzed the effects of these changes on the propagation mode of the RDE under atmospheric pressure conditions. The results showed that a rotating detonation wave was observed under the combination of high vapor quality of nitrous oxide, high injector stiffness, high liquid ethanol temperature, and high momentum angle. The propagation velocity was obtained as 73∼83 % of the Chapman-Jouguet velocity. Long-duration combustion tests were also conducted, and the internal combustion structure was confirmed from the erosion of the carbon-carbon (C/C) composite material. The detonation wave was considered to propagate near the bottom of the RDE with liquid propellants from the erosion heights of the C/C composite. The erosion height was confirmed to be consistent with the fill height calculated using the sound speed of the nitrous oxide. In addition, characteristic exhaust velocity efficiencies of more than 85 % were achieved in all combustion tests. [ABSTRACT FROM AUTHOR]

Abstract: Spherical projectiles were launched into detonable mixtures over a wide range of projectile velocities from near to about 1.8 times the Chapman–Jouguet (C–J) velocity. Oblique detonation waves (ODWs) and shock-induced combustions (SICs) stabilized around the projectiles were visualized with high time and high spatial resolutions using the Schlieren technique and a high-speed camera with a 1-μs frame speed. Unsteady wave structures called Straw Hat type structures consisting of a SIC region followed by a C–J ODW were observed near stabilizing criticalities of a C–J ODW, and they were divided into two propagation types, depending on whether the C–J ODW could be stabilized . In the present study, we suggested wave structures of the Straw Hat types based on our examination of dozens of continuous images. Triple points were observed at the intersection of a bow shock, a C–J ODW and a transverse detonation or shock wave when projectile velocities were slightly higher than C–J velocities. Onsets of local explosions in the SIC region for stabilizing the ODW in the Straw Hat type structures have been reported . We observed this stabilizing mechanism by visualizing onsets of periodical local explosions and their transition to spherical detonation waves when the projectile velocity was much higher than the C–J velocity. We also determined stabilizing criticalities using a stoichiometric acetylene-oxygen mixture diluted with argon or krypton in 50% or 75% volumetric fractions, respectively. We found that the stabilizing criticalities did not depend only on the ratio of the projectile diameter and the cell size of the mixture. [Copyright &y& Elsevier]

Gas dynamics in a simplified pulse detonation engine (PDE) was theoretically analyzed. A PDE was simplified as a straight tube with a fixed cross section. One end of the tube was closed, namely, this end was the thrust wall, and the other end was open. A detonation wave was initiated at the closed end and simultaneously started to propagate toward the open end. When the detonation wave broke out from the open end, a rarefaction wave started to propagate from the open end toward the closed end. This rarefaction wave was reflected by the closed end. By considering this rarefaction wave to be self-similar in the analysis of the interference between this rarefaction wave and its reflection from the closed end, we analytically formulated the decay portion of the pressure history at the closed end (thrust wall) without any empirical parameters. By integrating the obtained pressure history at the thrust wall with respect to time, important performance parameters of a PDE were also formulated. The obtained formulas were compared with numerical and experimental results and agreed with them very well. [ABSTRACT FROM AUTHOR]

Abstract This article reports on an experimental investigation into dynamical behaviours of detonation in non-uniform mixtures, generated from stoichiometric propane–oxygen, oxygen and ethane, with initial temperature and pressure 290 K and 20 kPa, respectively. Composition gradients are parallel to the direction of detonation propagation, with an equivalence ratio (ER) that first decreases from lean values and then increases to rich ones. Composition distributions are characterized according to the depth of the ER sink. Gradients are generated in a 50 × 50-mm2-square cross-section and a 665-mm total length chamber. The mixture components are injected separately in the pre-evacuated chamber in their order of decreasing density through porous plates at the chamber top-end to ensure planar filling of the chamber. Non-uniform distributions are then precisely controlled as a function of time by means of optical oxygen sensors. A Chapman–Jouguet (CJ) detonation is transmitted at the chamber bottom-end from a 3.6-m-long driver tube. Fast pressure transducers, sooted plates and Schlieren visualizations coupled with high-speed cameras are used to characterize the longitudinal velocity, cellular structure and transmission, failure and re-initiation mechanisms of the detonation front. Shallowest ER sinks produce the supercritical transmission mode of the CJ detonation with continuous adaptation of velocity and multicellular structure to local composition. Deepest sinks lead to the subcritical behaviour characterized by sudden detonation failure from shock-flame decoupling when ER decreases, and without detonation re-initiation when ER increases again. Intermediate sink depths generate critical behaviour with detonation re-initiat ion at chamber walls from expanding combustion kernels and reflected transverse Mach waves and then from SWACER retro-active mechanism. An elaboration of the failure criterion used in a previous study is found to well predict conditions for shock-flame decoupling. [ABSTRACT FROM AUTHOR]

A reflective shuttling detention combustor (RSDC) is a two-dimensional combustor with two reflection walls. Unlike a rotating detonation combustor (RDC), an RSDC can visualize the entire area of the combustor via an optical technique. In addition, the RSDC can reproduce the counter-rotating detonation mode in RDC. In present study, CH* luminescence and schlieren image were observed to investigate the dynamics of the RSDC. The reflective wall distance was set to 45 mm (Type L) and 25 mm (Type S). As the results, the wave speed of 1226 ± 64 m / s in the single wave mode in Type S was 76% of that in Type L. It was found that the detonation propagation speed decreased with a reduction in the reflection wall distance. Superimposing the luminescence images on the schlieren images revealed that the mixture was mainly burned by deflagration behind shock wave. In addition, the experimental mixture fill height was in good agreement with model in which the mixture filling process was temporarily stopped by detonation and refilled at a constant speed. Using the maximum fill height obtained by the model, it was found that the detonation mode was in the region of 3 ± 0.6 of the dimensionless quantity (the reflection wall distance divided by the wave number and maximum value of the mixture fill height). [ABSTRACT FROM AUTHOR]

Abstract: The detonation propagation phenomena in curved channels were experimentally studied in order to determine the stable propagation condition. A stoichiometric ethylene–oxygen mixture gas and five types of rectangular-cross-section curved channels with different inner radii of curvature were employed. The detonation waves propagating through the curved channels were visualized using a high-speed video camera. Multi-frame short-time open-shutter photography (MSOP) was developed in the present study to simultaneously observe the front shock shape of the detonation wave and the trajectories of triple points on the detonation wave. The detonation wave became more stable under the conditions of a higher filling pressure of the mixture gas and/or a larger inner radius of curvature of the curved channel. The critical condition under which the propagation mode of the detonation wave transitioned from unstable to stable was having an inner radius of curvature of the curved channel (r i) equivalent to 21–32 times the normal detonation cell width (λ). In the stable propagation mode, the normal detonation velocity (D n) increased with the distance from the inner wall of the curved channel and approached the velocity of the planar detonation propagating through the straight section of the curved channel (D str). The smallest D n was observed on the inner wall and decreased with decreasing r i/λ. The distribution of D n on the detonation wave in the stable mode was approximately formulated. The approximated D n given by the formula agreed well with the experimental results. The front shock shape of the detonation wave could be reconstructed accurately using the formula. The local curvature of the detonation wave (κ) nondimensionalized by λ decreased with increasing distance from the inner wall. The largest λκ was observed on the inner wall and increased with increasing r i/λ. D n/D str decreased with increasing λκ. This nondimensionalized D n–κ relation was nearly independent of r i/λ. [Copyright &y& Elsevier]