Chapman-Jouguet Detonation Research Articles

Numerical simulation of similarities between rotating detonation and high-frequency combustion instability under two mixing schemes

This paper presents an experimental study on rotating detonations in a hollow combustor with the slit-orifice nozzle. The experimental results reveal that the propagation speed of detonation waves increases with the rise of mass flow rates and is greater than the Chapman–Jouguet detonation speed (VC−J). Furthermore, numerical simulations of rotating detonation in a non-premixed three-dimensional cylindrical combustor have been conducted based on a multispecies reacting code. The influence of two mixing schemes—that is, slit-orifice and coaxial injector—on detonation waves are studied to determine whether the characteristics of detonation waves tend toward high-frequency combustion instability due to changes in the mixing scheme. It is found that the slit-orifice scheme’s detonation speed, pressure, and temperature are significantly higher than those of the coaxial injector scheme. In particular, the detonation speed of the former reaches 124% of the VC−J, while that of the latter is only 80.5% of the theoretical value. The numerical results reveal that the low-speed detonation is caused by the deterioration of the hydrogen (H2)/air mixing conditions. Moreover, the flow-field structures of two mixing schemes were comparable, both containing transverse detonation waves, oblique shocks, contact surfaces, and wedge-shaped reactant regions. Furthermore, the Rayleigh index analysis showed that the unsteady heat release was in phase with the pressure fluctuations, amplifying the pressure. Therefore, it is suggested that high-frequency combustion instability may be a manifestation of rotating detonation waves under poor mixing conditions.

Numerical study of direct initiation for one-dimensional Chapman–Jouguet detonations by reactive Riemann problems

Numerical study of direct initiation for one-dimensional Chapman–Jouguet detonations by reactive Riemann problems

Effect of losses on hydrogen–oxygen–argon detonation cell sizes

This work revisits the effect of losses on detonation characteristic length scales. Low-pressure experiments of the very regular hydrogen–oxygen–argon detonations in the straight narrow channel and along the exponentially diverging ramp were reported, demonstrating the significant role of losses in increasing detonation velocity deficits and cell sizes. Both the theoretically established and experimentally obtained relationships show the exponential sensitivity of detonation cell sizes to losses in terms of flow divergence, which is controlled by the global activation energy. The presence of losses modulates the lengthening of the characteristic detonation reaction zones and thus results in larger cell sizes, as indicated by the linear correlation characterizing the amplification of cell sizes and induction length. Moreover, the present work proposed an effective method for calibrating the ideal Chapman–Jouguet (CJ) detonation cell size from experiments, by adopting a revised formulism of Mirels' laminar-boundary-layer theory and also the generalized Zeldovich–von Neumann–Doering (ZND) model in the presence of flow divergence. Comparisons of the ZND-model calibrated ideal CJ detonation cell sizes from experiments with those from detailed numerical simulations show that, while differences still exist for the relatively high pressure cases, accounting for wall losses could excellently reconcile the discrepancy for the lower pressure cases, which appears to suggest no evident influence of the vibrational non-equilibrium effects for the hydrogen–oxygen–argon reactive system.

Detonation propagation limits in hydrogen-oxygen mixtures in a tube filled with repeated perforated plates

This study investigated the propagation behaviors of quasi-detonations in a round tube filled with repeated perforated plates. Stoichiometric hydrogen-oxygen mixtures at different initial pressures were tested. Photodiodes and soot foil were used to record detonation velocity and cellular structure between two adjacent perforated plates. The orifice diameter (d), hole spacing (l) of the perforated plate and the obstacle spacing (S) were varied. The results show that the ratio of the overall jet diameter (D0, defined as the diameter of the circumcircle of the orifices) to the detonation cell size (λ) is in the range of 12–14 for the occurrence of Chapman-Jouguet detonations. The combustion regimes are affected by l/d, i.e., smaller l/d results in higher combustion velocity. At the detonation propagation limits, the results confirm the criterion L/λ>7, in which L=(S+D)/[2(1−1−BR)], D and BR are, respectively, the tube diameter and blockage ratio of the perforated plate.

Numerical investigation of three deflagration-to-detonation transition conditions related to the velocity of the spontaneous reaction wave

In this work, the deflagration-to-detonation transition (DDT) process in a tube filled with quiescent and stoichiometric hydrogen/oxygen mixture is numerically simulated by a detailed chemical reaction model together with a high-resolution adaptive mesh refinement (AMR) mesh system. Then the flow field is analyzed in detail. It is found that for the onset of detonation in a DDT process there are three essential conditions related to the velocity of the spontaneous reaction wave DSpRW. The first condition is that on a hot spot the DSpRW should be slower than the speed of the Chapman–Jouguet (CJ) detonation wave DCJ to make sure that a spontaneous shock wave could arise originating from the spontaneous reaction wave. The spontaneous shock wave and the spontaneous reaction wave have conspicuous positive correlation to accelerate the spontaneous reaction wave to be faster than the local sound speed, which is the second DDT condition. With this condition the spontaneous reaction wave could catch up with its associated spontaneous shock wave and implement a coupling of the gasdynamics and the chemical energy release. This process is in line with Lee's SWACER idea, while throughout the process the spontaneous reaction wave propagates mainly through the Zel'dovich's reactivity gradients mechanism. Meanwhile, the gas velocity Vg is also essential to maintain the above two conditions and the resultant velocity meets the relation ∥DSpRW+Vg∥≥DCJ, which is the third condition. Distinctly this settles the wave speed gap between deflagration and detonation. More importantly, gas velocity plays an important role especially for the pressure build-up. The most important expressive differences between CJ deflagration and CJ detonation are the gas velocities of both the reactants and products as well as the pressure build-up. When these three relations successfully trigger a DDT and get a detonation wave, they still hold in the resulting detonation wave. They are delicately inherited as the inherent characters of the (detonation) wave. Formerly they are preconditioning-sustaining in the DDT process, and now they become self-sustaining in the detonation wave. Besides, the important role of the progress ratio of the induction period ε is emphasized for a spontaneous propagation.

Analysis on stationary window of oblique detonation wave in methane-air mixture

In order to obtain the standing conditions and stationary range of oblique detonation wave in methane-air combustible mixture, we use the Newton-Raphson iteration method to solve the perfect gas flow conservation equations of oblique detonation wave based on detonation theory. We investigate the variation laws of the oblique detonation stationary window and internal mechanism under different methane-air equivalence ratio, incoming flow velocity, initial pressure and initial temperature. The oblique detonation polar curve can be separated into three sections, each of which has different flow characteristics corresponding to different wave morphology. Among them, a stationary oblique detonation wave can be formed when the wedge angle is larger than the wedge angle of Chapman-Jouguet state oblique detonation wave, and smaller than the maximum wedge angle corresponding to the oblique detonation wave without detached. The wedge angle range is called the stationary window of the oblique detonation wave. We found that the oblique detonation is more easily formed when the methane-air mixture is under the oxygen-enriched condition, and the range of oblique detonation wave stationary window becomes larger as the incoming velocity increases. The changes of initial pressure and temperature have little influence on the stationary window. The change law of the stationary window of oblique detonation wave corresponds to the change law of Mach number behind CJ oblique detonation wave. In addition, the standing conditions are mainly related to the coupling of the incoming mixture kinetic energy and heat release.

Evaluation of the two-γ model and the energy balance process of a Chapman-Jouguet detonation

Two issues related to the application of Chapman-Jouguet (C-J) theory have been investigated in this study. Firstly, the solution of the two-γ analytical model cannot agree with the exact solution calculated from the Chemical Equilibrium Compositions and Applications (CEA) code even all the required parameters are substituted with the exact ones. To root the source, the original derivation has been reviewed. It is believed that the perfect gas approximation induces the discrepancy, which will result in a huge discrepancy in the heat release at C-J state. Hence, a four-γ model for ideal gases has been derived, whose results are consistent with those from the CEA code though it requires more input parameters. Sensitive analysis implies that the accuracy of the four-γ model is greatly impacted by γ2‾ and qCJ. Besides, a parabola function that can describe the heat release and the lower heating value correlation has been proposed. Using this function, about ±5% relative error of estimated MS can be achieved when γ2‾ is equal to 9/7 for most selected stoichiometric gas mixtures. Secondly, the energy distribution in a C-J detonation process is found quite different when attaching the reference frame to the ground or the detonation wave front. Hence, regarding the C-J state as the equivalent burned state at the exit of a detonation combustor is questionable. Accordingly, a four-step thermodynamic process for a closed system has been developed, which can quantitatively analyze the energy balance process of a C-J detonation. Discussion is made by comparing the process with a traditional steady thermodynamic process as well as constant-volume combustion.

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An experimental investigation was performed to study the pressure limits and mechanism of the detonation re-initiation behind the perforated plate with various thicknesses and hole diameters in H2–O2-Ar mixture by schlieren and soot track measurement. The Chapman-Jouguet (CJ) detonation and overdriven detonation were used to collide with the perforated plate. For the CJ detonation transmission, the detonation re-initiation distance is larger than 3.9 times the tube hydraulic diameter. Both the thickness and the hole size have significant effects on the critical pressure and the re-initiation distance. The ratios of the hole hydraulic diameter and the critical cell size (dH/λc) are less than 1. The cellular structure can be observed near the perforated plate on the smoked foils due to the collision of the arc-sharp shock waves via multi-jet structure. For the overdriven detonation transmission, the detonation can be re-initiated quickly, and the re-initiation distances are all less than twice the tube hydraulic diameter. The re-initiation distance increases with the hole size while the thickness has little effect on the re-initiation distance. The “abrupt” mode of the detonation re-initiation is transformed into the “gradual” mode with the increase of the initial pressure. The pressure limit of the re-initiation mode transformation also increases with the decrease of the hole size. Two mechanisms of the multi-jet initiation: rapid turbulent mixing initiation and the induction by the collisions of transverse waves were verified experimentally, corresponding to the “abrupt” and “gradual” modes, respectively. The critical condition of detonation propagation can be quantified as dH/λ∗ > 3.37 and 3.77 for the 3 mm-hole and 2 mm-hole perforated plates, respectively, where dH is the hydraulic diameter and λ is the detonation cell size.

Effect of perforated plate with high blockage rate on detonation re-initiation in H2–O2-Ar mixture

An experimental investigation was performed to study the pressure limits and mechanism of the detonation re-initiation behind the perforated plate with various thicknesses and hole diameters in H2–O2-Ar mixture by schlieren and soot track measurement. The Chapman-Jouguet (CJ) detonation and overdriven detonation were used to collide with the perforated plate. For the CJ detonation transmission, the detonation re-initiation distance is larger than 3.9 times the tube hydraulic diameter. Both the thickness and the hole size have significant effects on the critical pressure and the re-initiation distance. The ratios of the hole hydraulic diameter and the critical cell size (dH/λc) are less than 1. The cellular structure can be observed near the perforated plate on the smoked foils due to the collision of the arc-sharp shock waves via multi-jet structure. For the overdriven detonation transmission, the detonation can be re-initiated quickly, and the re-initiation distances are all less than twice the tube hydraulic diameter. The re-initiation distance increases with the hole size while the thickness has little effect on the re-initiation distance. The “abrupt” mode of the detonation re-initiation is transformed into the “gradual” mode with the increase of the initial pressure. The pressure limit of the re-initiation mode transformation also increases with the decrease of the hole size. Two mechanisms of the multi-jet initiation: rapid turbulent mixing initiation and the induction by the collisions of transverse waves were verified experimentally, corresponding to the “abrupt” and “gradual” modes, respectively. The critical condition of detonation propagation can be quantified as dH/λ∗ > 3.37 and 3.77 for the 3 mm-hole and 2 mm-hole perforated plates, respectively, where dH is the hydraulic diameter and λ is the detonation cell size.

Detonation propagation through a nonuniform layer of hydrogen-oxygen in a narrow channel

Experiments were carried out to study detonation propagation through a nonuniform layer of stoichiometric hydrogen-oxygen in a narrow channel. Premixed stoichiometric hydrogen-oxygen was injected through a series of 1.3 mm diameter, 4.8 mm spaced holes into a 7 mm wide optically accessible channel initially filled with an inert gas. A Chapman-Jouguet detonation wave was transmitted into the test section from a pre-detonator of equal height. The height of the layer was varied by changing the time of hydrogen-oxygen injection relative to the arrival-time of the detonation wave. Schlieren photography was used to record the progression of the detonation wave. Soot foils mounted to the back window, were used to record the detonation cellular structure and visualization of the soot incandescence provided tracking of the reaction zone. With the channel initially filled with argon, detonation propagation was only possible when the layer height accommodated at least 8–11 detonation cells. Detonation propagation was not possible when the channel initially contained nitrogen, or carbon dioxide, indicating strong mixing with the injected premixed hydrogen-oxygen. Numerical simulations confirmed the strong mixing between the injected premixed hydrogen-oxygen with the prefilled inert gas. The simplified mixing condition, i.e., injection of premixed hydrogen-oxygen, provides a unique data set for numerical code validation and verification for a linear RDE geometry.

A numerical investigation of oblique detonation waves in hydrogen-air mixtures at low mach numbers

Oblique detonation waves (ODWs) have potential applications in hypersonic propulsion, but the boundary of steady ODWs has not yet been examined comprehensively. In this study, Euler equations coupled with detailed chemical reaction models are used to simulate ODWs in hydrogen-air mixtures with relatively low flight Mach numbers (from 7 to 8) and different flight altitudes (30 km and 25 km). Decreases in the flight Mach number and altitude are shown to result in unsteady ODWs in a stoichiometric hydrogen-air mixture. These ODWs can be re-stabilized by decreasing the fuel‒air equivalence ratio. Regardless of different parameters of Mach number and altitude, unsteady ODWs appear only when the velocity in the induction zone exceeds that of the corresponding Chapman-Jouguet detonation. A low equivalence ratio also induces a long initiation length, limiting the availability of decreases in the equivalence ratio to maintain a steady ODW in practical applications. A flow‒combustion criterion is proposed for the application of ODWs, based on the steadiness of ODWs and fast initiation.

Standing window of oblique detonation with pathological behaviour

Standing of an Oblique Detonation Wave (ODW) on a wedge within combustor is the prerequisite of thrust generation for ODW engine which is regarded as a novel and conceptual propulsion device with hypersonic flight Mach number. Usually a standing window of ODW is defined as the wedge angle ranged from the ODW detached angle from wedge (upper limit) to the angle that a Chapman-Jouguet (CJ) detonation occurs (lower limit). For pathological detonation cases, however, the CJ detonation cannot be achieved, and thus the lower limit of the standing window of ODW should be revisited. In present study, two types of reactions in hypersonic incoming flow that include the behavior of pathological detonation, that is, the single-step irreversible reaction with mole variation and the two-step irreversible reactions with exothermic process followed by endothermic process, have been used for studying standing behavior of ODW. The steady detonation polar analysis of ODW is carried out for both reaction systems. The results reveal that the reaction with more mole decrement and the reactions with stronger endothermic process show the pathological detonation feature and therefore modify the lower limit of standing window of ODW. Three equivalent parameters are proposed to quantitatively measure the standing window range of ODW from points of view of thermodynamics, Mach number of incoming flow and heat effect of reactions. It is found that the standing window of ODW is determined by the specific heat ratio, the overdrive degree of detonation and the endothermic level of the hypersonic incoming flow, regardless of whether the detonation is pathological or not.

Numerical investigation of the operating process in an annular detonation chamber of low diameter

Burning in unsteady rotating detonation waves is one of the ways of operating process organization in future aircrafts engines. However, a minimum combustion chamber diameter in which the unsteady rotating detonation process can be actualized is a significant limitation of such engines. A possibility of hydrogen-air mixture burning in an annular chamber with a diameter of 78 mm is shown in this paper using methods of three-dimensional computational fluid dynamics. The geometry of the chamber and the modes of its operation were selected, and the influence of the total pressure of air at the inlet was studied. At the pressure of 32 bar, the mass flux in the critical section of the aerodynamic nozzle was 7349.2 kg/(s·m2). It is shown that in a rotating reference frame in which the detonation wave is at rest, streamlines come to the wavefront almost at right angles. This fact allows making simple estimates of the fresh mixture parameters in front of the wave. Comparison with the detonation parameters in a premixed hydrogen-air mixture in the tube showed that the velocity of the detonation wave in the chamber is 0.65-0.74 of the Chapman-Jouguet detonation velocity, and its height is approximately equal to the characteristic size of the cellular structure of the detonation.

Rotating Detonation: History, Results, Problems

Abstract Among of modern papers devoted to numerical modeling of rotated waves the greater part of papers are based on assumption that such wave propagates with velocity equals to the Chapman-Jouguet velocity of ideal detonation model with plane front. But the experimental velocities of rotated detonation waves, as a rule, are less (and even much less) the velocity of ideal Chapman-Jouguet detonation. Such regimes are named as low-velocity detonation or quasi-detonation and its characteristics are practically not investigated carefully. Moreover, similar to the spinning detonation, the strong connection of velocity of rotated transverse waves with the acoustic waves of reaction products was observed. So the new model with an allowance for the losses of impulse and energy must be used at numerical modeling of RDE and new experimental investigations of regimes with understated velocity must be carried out. In given paper some important aspects of rotated detonation waves and new experimental results are analyzed: the multifront system of rotated waves; correlation of rotation velocity of waves with acoustic characteristics of reaction products; streak-records trajectory of rotated waves on moving film; pressure and temperature profiles of rotating waves; velocity deficit and energy-release.

Autoignition and combustion wave propagation in a spatial reactivity gradient environment constructed using the shock-converging method

Abstract Studies on autoignition and combustion wave propagation in a spatial reactivity gradient environment constructed using the shock-converging method were conducted to obtain a new understanding of combustion modes and their mutual transition mechanism. Autoignition induced by the converging cylindrical shock wave and weak detonation can be observed by experiment and numerical simulation. Research indicates that for an appropriate spatial reactivity gradient, the velocity of the weak detonation wave can decrease and adjust to the local sound speed. This leads to the transformation of the weak detonation into the self-propagating Chapman-Jouguet (CJ) detonation. The speed of the spontaneous reaction wave characterizing the end of the chemical reaction is never less than the local sound speed; hence, there is no overdriven phenomenon throughout the weak-to-CJ detonation transition. This conforms to the fact that the overdriven phenomenon is not a necessary condition to initiate the detonation, and the combustion has higher thermal efficiency compared with isochoric combustion. Further research indicates that CJ detonation propagating in the preheated reactant can also transform into weak detonation for an appropriate spatial reactivity gradient. The initial CJ detonation degrades into a shock that decays and finally disappears. The wave-eliminating effect of the CJ-to-weak detonation transition can ensure the flow field quality and thermal efficiency of the combustion. In summary, performing a controllable weak detonation between isochoric combustion and CJ detonation in an engine has significant practical importance for improving combustion thermal efficiency and knock suppression.

Numerical analysis of the vibration-chemistry coupling effect on one-dimensional detonation stability

A one-dimensional numerical simulation of detonation propagation is performed with an introduction of the vibrational relaxation mechanism in a single-step chemical model for the first time. This coupling mechanism is constructed based on the energy transfer between the translational-rotational mode and the vibrational mode, together with an averaged two-temperature model in chemical kinetics. A time ratio τα between the characteristic chemical time scale and the characteristic vibrational time scale is introduced to illustrate whether this coupling effect is crucial in stabilizing the detonation. The simulation is initialized first with an extended steady-state profile and the inclusion of the vibrational energy in the equations. For the particular case considered in this study with a nondimensional heat release Q=50, a ratio of specific heat γ=1.2, and a nondimensional characteristic vibrational temperature ϑ=20, the stability boundary is indicated at an activation energy Ea=26.47 under thermal equilibrium. Two mildly unstable cases for a Chapman-Jouguet (CJ) detonation and an overdriven detonation are then studied with the variation of τα. The results reveal that the detonation is stabilized by the vibrational nonequilibrium effect with a smaller pulsation amplitude and a longer oscillation period in the shock pressure history, and the neutral stability is shifted. For the CJ detonation case, the critical τα below which the coupling effect is significant is 7.2. The stabilization of detonation can be attributed to the reduction of the overall chemical reaction rate by vibrational relaxation and thus a shift of the stability limit towards higher activation energy. For an overdriven detonation, the critical τα is approximately 21 for the studied cases. Since the changes in both overdriven factors f and τα contributed to the stabilization of detonation, a reduction of the neutral stability limit of f is foreseen when the coupling effect is significant. Lastly, the effect of different ϑ on the stability limit is demonstrated at equilibrium state with vibrational energy included and it is suggested that the shift of stability limit would reach the maximum at around ϑ=15. This inaugural work provides a reference on the importance of considering thermal nonequilibrium flow in detonation stability and the implication to the related engine design.

On the Mechanism of Detonation Combustion of Nanostructured Silicon with a Solid-Phase Oxidant

The physical mechanism of detonation combustion of nanostructured silicon with a solid-phase oxidant at a velocity of the combustion front of 1000–3000 m/s has been proposed. Thermodynamic characteristics of combustion of model solid-phase mixtures “silicon–ammonium perchlorate” with different equivalent ratios of their components have been calculated at different pressures. It has been established that a characteristic feature of detonation combustion of nanostructured silicon with a solid-phase oxidant is the stationary velocity of motion of the detonation front with a significant defect (10–15%) with respect to the Chapman–Jouguet detonation velocity. The detonation (supersonic) and subsonic regimes of combustion of nanostructured silicon with a solid-phase oxidant have been determined.

Prediction of Energetic Material Properties from Electronic Structure Using 3D Convolutional Neural Networks.

We develop a convolutional neural network capable of directly parsing the 3D electronic structure of a molecule described by spatial point data for charge density and electrostatic potential represented as a 4D tensor. This method effectively bypasses the need to construct complex representations, or descriptors, of a molecule. This is beneficial because the accuracy of a machine learned model depends on the input representation. Ideally, input descriptors encode the essential physics and chemistry that influence the target property. Thousands of molecular descriptors have been proposed, and proper selection of features requires considerable domain expertise or exhaustive and careful statistical downselection. In contrast, deep learning networks are capable of learning rich data representations. This provides a compelling motivation to use deep learning networks to learn molecular structure-property relations from "raw" data. The convolutional neural network model is jointly trained on over 20,000 molecules that are potentially energetic materials (explosives) to predict dipole moment, total electronic energy, Chapman-Jouguet (C-J) detonation velocity, C-J pressure, C-J temperature, crystal density, HOMO-LUMO gap, and solid phase heat of formation. This work demonstrates the first use of complete 3D electronic structure for machine learning of molecular properties.

Formation and characteristics of composite reaction – Shock clusters in narrow channels

High-speed schlieren visualizations show that a composite reaction-shock cluster structure is formed in the last flame acceleration stage prior to detonation transition for ethylene/oxygen mixture in a narrow channel. The composite structure is bounded by a normal shock at the leading edge of the structure, and series of parallel oblique shocks interweave with reaction front on the other end in the cluster. Propagating velocity of the reaction front at the inception of the cluster is ∼ 45–50% of Chapman-Jouguet detonation velocity of the mixture. Reaction front accelerates rapidly after the formation of the reaction-shock cluster, and run into detonation in tens of microseconds except for very lean mixtures. The angle between the parallel oblique shocks in the cluster and the side wall, defined as ω-angle, is found to be constant for a specific mixture as the reaction wave propagates. Dependence of ω-angle on mixture equivalence ratio and channel size are investigated in the study. Analysis shows that DDT distance is linearly proportional to ω-angle, and an empirical correlation is derived.

Influence of propagation direction on operation performance of rotating detonation combustor with turbine guide vane

Due to the pressure gain combustion characteristics, the rotating detonation combustor (RDC) can enhance thermodynamic cycle efficiency. Therefore, the performance of gas-turbine engine can be further improved with this combustion technology. In the present study, the RDC operation performance with a turbine guide vane (TGV) is experimentally investigated. Hydrogen and air are used as propellants while hydrogen and air mass flow rate are about 16.1 g/s and 500 g/s and the equivalence ratio is about 1.0. A pre-detonator is used to ignite the mixture. High-frequency dynamic pressure transducers and silicon pressure sensors are employed to measure pressure oscillations and static pressure in the combustion chamber. The experimental results show that the steady propagation of rotating detonation wave (RDW) is observed in the combustion chamber and the mean propagation velocity is above 1650 m/s, reaching over 84% of theoretical Chapman-Jouguet detonation velocity. Clockwise and counterclockwise propagation directions of RDW are obtained. For clockwise propagation direction, the static pressure is about 15% higher in the combustor compared with counterclockwise propagation direction, but the RDW dominant frequency is lower. When the oblique shock wave propagates across the TGV, the pressure oscillations reduces significantly. In addition, as the detonation products flow through the TGV, the static pressure drops up to 32% and 43% for clockwise and counterclockwise propagation process respectively.