Effect of obstacles behind the pre-detonator tube on the re-initiation of diffracted detonation wave

The re-initiation of diffracted detonation wave is simulated by the DCRFoam. The detonation waves propagated from the pre-detonator tube to the main chamber are formed by 2H₂-O₂-7Ar. Due to the sudden expansion of cross-section, the detonation wave will be attenuated by the rarefaction effect, resulting in detonation failure. Introducing obstacles behind the pre-detonator is an effective method to realize the diffracted detonation re-initiation. This study aims to optimize the detonation transmission by considering the height (h) of obstacles and the distance (w) between obstacles and the exit of the pre-detonator. Results show that, when 15.31311w²-1342.52507w+29435.20137≤h ≤ 0.00239w²+0.38038w+10.95694 (10 mm ≤ h ≤ 30 mm, 10 mm ≤ w ≤ 50 mm), the diffracted detonation wave can realize re-initiation. When w is constant, the formation distance of stable detonation first decreases and then increases with the increase of h. The same law of w can be found when h is unchanged.     

Transmission of near-limit detonation wave through a planar sudden expansion in a narrow channel

Transmission of single-cell and spinning detonation waves in C₂H₄ + 3(O₂ + βN₂) mixtures through a 2-D sudden expansion experimentally studied using high-speed cinematography and soot film visualization. Nitrogen dilution ratio, β, is utilized to control cell size and detonation mode. Detonation wave of ethylene/oxygen/nitrogen mixture was initiated via DDT in the 1 mm × 1 mm cross-section and 250 mm long initiator channel before propagating into the 3 mm × 1 mm receptor channel. Visualizations show that detonation waves were extinct and accompanied with abrupt decrease in visible reaction front propagating velocities right after passing through the sudden expansion. However, re-acceleration of the reaction front and re-initiation of the detonation wave were observed downstream in the expanded receptor section. Two re-initiation modes with large disparity in the re-initiation distance were experimentally characterized. For mixtures with nitrogen dilution ratio equals 0.3 or less, the cellular detonation front propagated with single cell in the initiator section before entering the sudden expansion. The re-initiation distance was less than 50 mm and was likely achieved via shock reflection. Velocity characterization shows that steady propagating speed of the detonation wave is ～100 m/s higher in receptor section than in the initiator section. Since the cell size became larger than 1 mm for mixtures with β ? 0.3, the detonation wave propagated in spinning detonation mode before transmitting into the expanded section. The reaction front would have to go through another DDT process to reach detonation state in the receptor section, and the re-initiation distance was increased to more than 150 mm. Moreover, step height of the sudden expansion was proposed as the characteristic length scale to obtain a unified non-dimensional correlation between re-initiation distance and detonation cell size.     

Effect of orifice shapes on the detonation transmission in 2H2–O2 mixture

In this study, the effect of orifice geometries on the detonation propagation is considered systematically in stoichiometric 2H₂–O₂ mixture. Three various orifice shapes with the same blockage ratio (BR = 0.889) are used firstly, i.e., round, square and triangular. Eight PCB pressure transducers are employed to obtain the average velocity through two adjacent signals while the smoked foil technique is used to record the detonation cellular pattern. The experimental results indicate that three different propagation modes can be observed: (1) when the initial pressure (P₀) is smaller than the critical value (P_c), the steady detonation wave cannot be produced before the orifice plate, afterwards, the mechanism of deflagration to detonation transition (DDT) is seen; (2) near the critical pressure, a steady detonation wave is formed prior to the obstacle, but the failure of detonation is seen after its propagation through the orifice plate due to the diffraction effect and the mass and momentum loss from the wall, and then the phenomenon of detonation re-initiation is observed due to the reflection from the wall; (3) at the initial pressure larger than the critical value, the steady detonation wave can propagate through the orifice plate without decay. Moreover, although the effect of orifice shapes on the critical pressure can be nearly ignored, the re-ignition position is different among three various orifice geometries. For the cases of round and square orifices, the ignition position is produced near the center of the wall. However, the detonation wave is re-ignited from the corner in the case of triangular orifice. Finally, the critical condition of detonation propagation can be quantified as D_H/λ > 1. But the critical values of D_H/λ are not uniform among three different orifice geometries. For the cases of round, square and triangular orifices, the critical values of D_H/λ are 8.94, 5.88 and 3.84, respectively.     

Influence of longitudinal obstacle spacing on the deflagration-to-detonation transition through a bank of obstacles in a hydrogen-air mixture

Flame acceleration and deflagration-to-detonation transition (DDT) in a channel containing an array of staggered cylindrical obstacles and a stoichiometric hydrogen-air mixture were studied by solving the fully-compressible reactive Navier-Stokes equations using a high-order numerical algorithm and adaptive mesh refinement. Four different longitudinal spacings (ls) of the neighboring obstacle rows (i.e., ls = 15.28, 19.1, 25.4, and 38.2 mm, corresponding to 1.2, 1.5, 2 and 3 times of obstacle diameter, respectively) were used to examine the effect of obstacle spacing on flame acceleration and DDT. The results show that the main mechanisms of flame acceleration and transition to detonation in all the cases studied are consistent. While the flame acceleration is caused by the growth of flame surface area in the initial stage, it is governed by shock-flame interactions in the later stage when shock waves are generated. The focusing of strong shocks at flame front is responsible for the initiation of detonation. It was found that the flame propagation speed and the DDT run-up distance and time are highly dependent on ls. Specifically, the flame acceleration declines as ls increases, since a larger ls leads to less disturbance of flow by obstacles per unit channel length. For detonation initiation, both the run-up distance and time increase with the increase of ls. It is interesting to note that the DDT distance and time increase significantly as ls increases from 19.1 mm to 25.4 mm. This is related to the slowdown of the increase rate of energy release over a period before DDT occurs under large ls condition, because every time the flame passes over an obstacle row the shock-flame interaction is delayed and numerous isolated pockets of unburned gas material are formed.     

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 ($d_H/{\lambda }_c$) 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 d_H/λ¹ > 3.37 and 3.77 for the 3 mm-hole and 2 mm-hole perforated plates, respectively, where d_H is the hydraulic diameter and λ is the detonation cell size.     

Effect of orifice plate on the transmission mechanism of a detonation wave in hydrogen-oxygen mixtures

In this paper, a square orifice plate with 60 mm thick and the blockage ratio (BR) of 0.889 is employed to systematically explore the transmission regime of a steady detonation wave in hydrogen-oxygen mixtures. The influence of hydrogen mole fraction is also considered. The average velocity of combustion wave can be determined by evenly mounting eight high-speed pressure sensors on the tube wall, and the detonation cellular patterns can be also registered by the soot foil technique. The experimental results indicate that for the condition of smooth tube, the hydrogen concentration limits range of detonation successful propagation is 37.5%–73.68%. Two propagation modes can be obtained, i.e., the regimes of fast flame and steady detonation. The hydrogen concentration limits range is narrowed to 42.53%–69.51% in the tube with a square orifice plate. Three propagation regimes are observed: (1) near the low limit, a steady detonation wave can be produced before the obstacle, and the phenomenon of detonation decay is seen across the square orifice plate because of the influence of diffraction resulting in the mechanism of detonation failure. The failed detonation wave is not re-ignited because of the lower hydrogen concentration; (2) as the hydrogen mole fraction is increased to 42.53%, the mechanism of detonation re-ignition can be seen after the detonation decay. Well within the limits, the same detonation re-initiation phenomenon also can be observed; (3) as the hydrogen concentration is further enhanced to 69.7% beyond the upper limit, a stable detonation wave is not produced prior to the orifice plate, and the combustion wave front maintain the mode of fast flame until the end of the channel. Finally, it can be found that the detonation wave can successfully survive from the diffraction only when the effective diameter (d_eff) is at least greater than one cell size (λ).     

Experimental and numerical research on rotating detonation combustor under non-premixed conditions

In order to investigate the formation process and propagation characteristics of detonation wave, developing process of detonation wave from initiation to stable detonation formation under non-premixed conditions has been studied by experiments and numerical simulation. The results show that when mass flow rates of air and hydrogen are 158.957 g/s and 2.728 g/s respectively, stable detonation can be formed in the combustor. Due to the lower inlet pressure, there is an unstable stage in combustor before the stable detonation is formed. Reducing the air pressure will increase the lowest detonation limit of combustor and lead to flame-out and re-initiation in the combustor. The propagation direction of detonation wave may change after re-initiation. Non-premixed intake structure lead to the inconsistency of rotating detonation combustion fluid in the radial direction. Moreover, peak pressure appears near the outer wall, while peak temperature appears near the inner wall.     

Effect of bundle geometries on the detonation velocity behaviors in stoichiometric hydrogen-air mixture

In this study, the effects of pipe bundle geometries on the detonation velocity behaviors are examined systematically in a circular tube with 6 m long and an inner diameter of 90 mm. The tube bundle structures are created by inserting several small pipes (20 mm outer diameter, 2 mm wall thickness) into the tube. Three different bundle structures can be obtained by varying the number of small pipes n of 3, 4 and 5. The ionization probes and pressure transducers (PCB102B06) are used to determine the average velocity while the smoked foil technique is employed to register the detonation cellular structures. The experimental results indicate that detonation can propagate at about the theoretical CJ velocity with a small deficit when the initial pressure (P₀) is greater than the critical value (P_c). The average velocity gradually decreases and deviates from the CJ value as the approaches of critical condition by gradually decreasing the initial pressure. The failure of detonation can be observed below the critical pressure. In the smooth tube, three different propagation mechanisms can be observed, i.e., super-critical condition, critical condition and sub-critical condition. After the bundle structures are introduced into the tube, a sudden velocity drop is seen at the critical pressure. Moreover, the detonation re-initiation phenomenon occurs with the velocity from the flame back to over-driven state quickly. Of note is that nearly no difference is seen between n = 3 and 4. However, in the case of n = 5, the detonation velocity experiences a more violent fluctuation with a high frequency, and the critical pressure is also increased to 28 kPa sharply. Finally, the critical condition analysis of detonation successful transmission is performed. The critical condition can be quantified as D_H/λ > 1. However, the critical values of D_H/λ are not uniform among various bundle geometries, but in a small range, i.e., from 1.52 to 1.97.     

Experimental study on the detonation propagation behaviors through a small-bore orifice plate in hydrogen-air mixtures

In this study, the regimes of detonation transmission through a single orifice plate were investigated systematically in a 6-m length and 90-mm inner diameter round tube. A series of experiments on the detonation propagation mechanisms in hydrogen-air mixtures were performed. A single obstacle with different orifice size (d) from 10 to 60 mm was adopted to study the effects of the induced perturbations on the detonation propagation. Here, the thickness of orifice plate (δ) was fixed at 10.33 mm. Detonation velocity was determined from the time-of-arrival (TOA) of the detonation wave recorded by eight high-speed piezoelectric pressure transducers (PCB102B06). Detonation cellular size was obtained by the smoked foil technique. The characteristic of detonation velocity evolution were quantitatively analyzed after it passes through a single obstacle, and particular attention was paid to the cases for which the blockage ratio (BR) is greater than 0.9, i.e., the cases of small hole diameter of d < 25 mm. The experimental results showed that, in a smooth tube, only super-critical condition and sub-critical condition can be observed. After the orifice plate is introduced into the tube, critical condition occurs. The detonation re-initiation with distinct cellular structures was experimentally observed. Of note is that when the blockage ratio (BR) values in the range of 0.802–0.96, it was easier to detonate at the fuel-lean side. Finally, the critical condition for detonation propagation through an orifice plate was quantified as d/λ > 1 where λ is the detonation cell size.     

Numerical study of detonation diffraction through 90-degree curved channels to expansion area

The adaptive mesh refinement program AMROC was adopted to conduct numerical study of detonation diffraction through 90-degree curved channels to expansion area. The detonation diffraction processes through straight and curved channels were compared. The effect of curved channel on the re-initiation of diffracted detonation and its mechanism were analyzed in depth. The influence of curvature radius on the deflection of detonation front was discussed. Results indicate that the detonation wave is highly asymmetric when diffracted through the curved channel, which results in the wave front deflection with a certain angle. The value of deflection angle θ decreases with the increase of inner wall curvature radius r₀, while the deflecting direction is the same as the propagating direction of the triple point in the Mach reflection. The utilization of the curved channel can promote the re-initiation of diffracted detonation. The mechanism of this promoting effect is the redistribution of detonation energy produced by the interaction from the curved boundaries, which concentrates most of the energy into the compressed area to initiate local detonation and realizes re-initiation eventually. The promoting effect is weakened as r₀ gets enlarged and the initial pressure p₀ decreases. The critical condition for the re-initiation of diffracted detonation wave through the curved channels was obtained by analyzing the detonation re-initiation results.     

Detonation propagation characteristics of H2/O2/AR in multi-angle bifurcation tubes

The propagation characteristics of the detonation wave in the bifurcated tube with the angular variation range of 30°–90° are simulated with 25% AR as dilution gas for H₂/O₂ mixture fuel at chemical equivalence ratio using the solver DCRFoam built on the OpenFOAM platform. The diffraction and reflection phenomena of detonation waves passing through bifurcation tubes with different angles are studied and analyzed. The results show that the distance from regular reflection to Mach reflection increases with the increase of the bifurcation angle so that after one reflection, the detonation forms three reflection forms with the angle of the different bifurcation tubes. After the first reflection, the detonation waves are more likely to induce the formation of transverse waves in the low-angle bifurcation tube. The lowest collision pressure after the detonation collides with the upper wall to form a secondary reflection occurs in the bifurcation tube between 50° and 60°.     

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.     

Detonation propagation characteristics for CH4-2H2-3O2 mixtures in a tube filled with orifice plates

In this study, the detonation propagation characteristics of stoichiometric CH₄-2H₂-3O₂ mixture are investigated comprehensively in a round tube with an inner diameter of 90-mm and 6-m in length. Three different orifice plates with the blockage ratios (BR) of 0.7 and 0.8 including circular, triangular and square orifice, are considered for the first time to investigate the effect of obstacle geometries on the detonation evolution. Eight high-speed piezoelectric pressure transducers are mounted on the outer wall to obtain the detonation velocity while the smoked foil technique is adopted to record the detonation cellular patterns. The results indicate that well within the limit, the detonation can propagate at about the theoretical CJ velocity (V_CJ). Near the limit, the velocity deficit is sharply enhanced but the detonation still can propagate at about 0.6V_CJ, which seems to be a universal phenomenon before the failure of the detonation. In the smooth tube, a sudden velocity drop and the single-headed spin can be seen near the critical condition, and the critical pressure (P_c) is 3 kPa. In the tube filled with obstacles, the effect of obstacle geometries on the detonation transmission can be ignored approximately for the BR = 0.7 case, and the critical pressures are increased to 7, 7 and 10 kPa, respectively. In the case of BR = 0.8, the effect of the orifice plates structures on the detonation propagation becomes more significant. The square orifice has the most serious impact on the detonation transmission, followed by triangular ones and the round hole has the least impact. The critical pressures are sharply enhanced to 10, 12 and 18 kPa, respectively. Finally, the effective diameter (d_eff) and the characteristic parameter (L) are introduced to analyze the critical condition of the detonation propagation. The critical condition can quantified as d_eff/λ > 1 and L/λ > 7 where λ is the detonation cell size.     

Suppression of hydrogen–air detonation using porous materials in the channels of different cross section

Propagation of a detonation wave in a porous channel with different cross–section was experimentally studied. Experiments were performed in three rectangular channels with cross–sectional dimensions of 20 × 40 mm, 10 × 40 mm and 10 × 30 mm with two opposite walls covered with porous material to study the detonation suppression in stoichiometric hydrogen–air mixtures at atmospheric pressure. Detonation was initiated in 3000 mm long circular channel 20 mm in diameter. Porous material was covering 1/2 or 1/3 of the channel internal surface. Polyurethane foam with a number of pores per inch ranging from 10 to 80 was used for detonation attenuation. Piezoelectric pressure sensors were used to obtain the shock wave pressure. Detonation decay into the shock wave and the flame front was visualized using schlieren photography. Shock wave velocity was also calculated using high–speed schlieren image sequences. The strongest pressure attenuation was recorded in a 10 mm wide channel with a porous coating with largest pores (2.5 mm) covering 1/3 of the internal walls. The results indicate that even covering 1/3 of the internal surface of the channel leads to detonation decay and significant shock wave attenuation.     

Effect of fluidic obstacles on flame acceleration and DDT process in a hydrogen-air mixture

Using solid obstacles to accelerate the deflagration to detonation transition (DDT) process induces additional thrust loss, and fluidic obstacles can alleviate this problem to a certain extent. A detailed simulation is conducted to investigate the effects of multiple groups of fluidic obstacles on the flame acceleration and DDT process under different initial velocities and gas types. The results show that, initially, the propagation of reflected shock wave formed by jet impingement is opposite to the flame acceleration direction, thus increasing the initial jet velocity will hinder the flame acceleration. Later, the vortex structure and enhanced turbulence can promote flame acceleration. As the flame accelerates, the virtual blockage ratio of the fluidic obstacles decreases, and increasing initial jet velocity or using reactive jet gases both affect the virtual blockage ratio. Further, increasing initial jet velocity or using reactive jet gases can shorten the detonation initiation time and distance. Compared with solid obstacles, it is concluded that fluidic obstacles can achieve faster detonation initiation with a smaller blockage ratio. Overall, the detonation phenomena in this study are all triggered by hot spots formed by the interaction between reflected waves and distorted flame, but the formation of reflected waves varies.     

Self-organized generation of transverse waves in diverging cylindrical detonations

Self-organized generation of transverse waves associated with the transverse wave instabilities at a diverging cylindrical detonation front was numerically studied by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. After solution validation, four mechanisms of the transverse wave generation were identified from numerical simulations, and referred to as the concave front focusing, the kinked front evolution, the wrinkled front evolution and the transverse wave merging, respectively. The propagation of the cylindrical detonation is maintained by the growth of the transverse waves that match the rate of increase in surface area of the detonation front to asymptotically approach a constant average number of transverse waves per unit length along the circumference of the detonation front. This cell bifurcation phenomenon of cellular detonations is discussed in detail to gain better understanding on detonation physics.     

Numerical simulation on the operating characteristics of rotating detonation ramjet engines at high flight mach number

For high-Mach-number incoming flow circumstances, a rotating detonation ramjet engine configuration is proposed in this research. By installing supporting blocks at the rear of the combustor, this configuration achieves continuous rotating detonation operation. Based on the Comparison of the flow structures obtained from the engine configuration with and without the supporting block before and after detonation ignition respectively, we obtain the intrinsic mechanism of detonation wave's propagation and re-initiation under the action of the supporting block. The supporting block creates a deflagration wave that is almost stationary before detonation ignition. In the detonation-ignited state, the deflagration wave is continually formed and traveling upstream under the influence of the supporting block, which is analogous to the periodical before detonation ignition of a transverse wave structure. The dynamic deflagration wave will cause the incomplete reactants behind the detonation wave to burn as the intensity of the detonation wave decreases. As a result, the incident shock wave is transformed into a Mach stem to achieve the re-initiation of the detonation wave.     

Experimental study of a hydrogen-air rotating detonation engine with variable air-inlet slot

Rotating detonation engines have attracted considerable attentions in recent years. In this study, the experiments of initiating rotating detonation waves were performed on a H₂/air rotating detonation wave with the variable air-inlet slot. The results showed that the stability of detonation-wave pressure and velocity both initially increased and then decreased with the increase of slot width, and it could improve the stability of detonation-wave velocity via increasing the equivalence ratio. The intensity of reflected wave was strong for the tests of d = 0.5 mm, which leaded to the advance ignition of fresh mixture and a velocity deficit reaching up to 20%. The strong interaction between air plenum and combustor and bad mixing effect may be the reasons of forming unstable detonation wave for the tests of large-scale slots. The air-inlet slot of d = 1 mm, which got a best experiment results relative to other tests, had a wide equivalence-ratio scope to produce stable detonation wave.     

Numerical investigation of a non-premixed hollow rotating detonation engine

Rotating detonation engines (RDEs) are widely studied because of their compact configurations and high thermal cycle efficiency. In this paper, a series of numerical investigations of a non-premixed hollow RDE are performed. The transient explicit density-based solver in ANSYS Fluent is used to perform the simulations. For a hollow RDE without Laval nozzle, there is only one rotating detonation wave in the combustion chamber. Compared to the traditional annular RDE, the mixing quality is deteriorated, and the thrust of the engine decreases and becomes more unstable. When the hollow RDE is attached with a Laval nozzle, there are two rotating detonation waves in the combustion chamber. The pressure within the combustion chamber increases while the axial velocity decreases. The mixing quality is improved. The height of detonation waves decreases with larger contraction ratio of the nozzle. A Laval nozzle is beneficial for a hollow RDE to achieve steadier operation and higher thrust output. When the contraction ratio is 4, the propulsive performance of the engine is the highest. The maximum thrust achieved is 840 N.     

Experimental investigation on propagation characteristics of liquid-fuel/preheated-air rotating detonation wave

The rotating detonation combustor can be applied to the turbine engine to develop into a new power device, and the liquid-fuel/air rotating denotation has important research significance for engine applications. In this research, the propagation characteristics of liquid-fuel/air rotating detonation wave were experimentally investigated. A hydrocarbon mixture—liquid gasoline was employed for the fuel, the oxidizer was high-temperature air preheated by a hydrogen-oxygen heater, and the rotating detonation wave was initiated via a hydrogen-oxygen pre-detonator. The effects of the equivalence ratio, ignition pressure, and air total temperature on the propagation characteristics of the liquid-fuel rotating detonation wave were analyzed. The liquid-fuel/air continuous rotating detonation wave can be successfully obtained with a single-wave mode, and the velocity and peak pressure of the rotating detonation waves increase as the equivalence ratio increases. As the detonation-wave pressures at the outlet of the pre-detonator increase, the establishment time of the rotating detonation wave gradually decreases, and the average establishment time is 4.01 ms. Stable rotating detonation waves are obtained with the air total temperature of 600–800 K, but the intensity of the detonation wave has a large deficit due to some instabilities.