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).     

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 of detonation propagation in a square tube filled with orifice plates

DDT experiments were conducted in a 6000 mm long square cross-section (112 mm × 112 mm) tube with various obstacle configurations with hydrogen-air mixtures and ethylene-air mixtures at ambient pressure (101 kPa) and room temperature (298 K). Square orifice plates with inner side 86.8 mm and 70.8 mm (BR = 0.4 and 0.6) and round orifice plates with inner diameter 80.0 mm (BR = 0.6) were used to assemble the obstacle configurations. The plates were installed at 1, 2 and 3 times the tube inner side. Soot foils were placed between the two orifice plates at the end of the tube for $S=3D$, where $S$ is the obstacle spacing and $D$ is the tube inner side. The DDT limits were determined based on the flame velocity above the isobaric sound speed of the burnt products. The results show that at the DDT limits, the criterion $d_{eff}/\lambda \approx 1$ is not pervasive, i.e., $d_{eff}/\lambda$ decreases with the obstacle spacing increase, in which $d_{eff}$ and $\lambda$ are the effective diameter of the orifice and the detonation cell size. Within the limits, the measured velocity for BR = 0.6 square orifice plates is higher than that for round orifice plates. On the other hand, no obvious difference in the limits can be observed for the BR = 0.6 obstacle configurations. Soot foils provide insights into the detonation propagation mechanism in the orifice plate section. It is shown that hot spots formed via the interactions between the decoupled shock wave and the tube wall can be responsible for the re-initiation of detonation. In addition, overdriven detonations induced by shock focus at the corners, followed by a band of fine cells. For less sensitive mixture and smaller orifice, the re-initiation distance is longer. Near the limits, no cellular structure can be observed, indicating longer cycle period for detonation re-initiation. This also accounts for the significant velocity fluctuation for larger spacing ($S=2D$ and $S=3D$) when the limits are approached.     

Experimental determination of critical conditions for hydrogen-air detonation propagation in partially confined geometry

An experimental investigation was performed to determine critical semi-open channel height (h*) and two-sided open channel width (w*) in which hydrogen-air detonation may propagate. Three types of gaseous mixture composition were used: 25%, 29.6% and 40% of hydrogen in air. Experimental setup was based on rectangular (0.11 × 0.11 × 2 m) test channel equipped with acceleration section (0.11 × 0.11 × 1 m). Different channel heights h in range of 15–40 mm and widths w in range of 30–50 mm were used in the test channel. The critical height h* and width w* were defined for each investigated configuration. To determine representative detonation cell sizes λ and to calculate their relationship to h* and w*, the sooted plate technique was used. The results showed that detonation in stoichiometric H₂-air mixture may propagate in semi-open channel only when the channel height is very close to or higher than approximately 3λ. For less reactive mixtures critical relation h*/λ reaches 3.1 or 3.6 for mixtures with 25% and 40% of hydrogen in air, respectively. For two-sided open channel similar relations w*/λ were close to 4.9 and 5.5 for 29.6%H₂ and 40%H₂ in air, respectively.     

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.     

Numerical study of acoustic coupling in spinning detonation propagating in a circular tube

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.     

Effects of boundary layer on wedge-induced oblique detonation structures in hydrogen-air mixtures

Oblique detonation wave (ODW) structures are studied widely in recent years, but most of them are solved by the Euler equations without considering viscosity and then effects of boundary layer. In this study, the Navier-Stokes Equations are used to simulate the wedge-induced ODWs in hydrogen-air mixtures, and the two types of ODW transition structures at different incident Mach number M_i are analyzed to clarify the effects of viscosity and hence the boundary layer. Results show that the effect of boundary layer on ODW structures should be classified by the types of ODW transition patterns. As for the smooth transition pattern of ODW at high Mach numbers, the effect of boundary layer can be neglected, but for the abrupt transition pattern of ODW at low Mach numbers, the effect of boundary layer is large and it changes the ODW structure greatly. Resulting from the interaction of shock and boundary layer, a recirculation zone is formed within the viscous ODW layer at M_i = 7, which leads to the phenomenon that the straight oblique shock wave evolves into two sections, with the downstream one having a larger shock angle. Additionally, the corresponding transition position moves upstream, and the initiation length becomes only one third of that in inviscid ODW. The great importance of considering viscosity in ODW simulations and future designs of combustor of oblique detonation engine has been addressed.     

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.     

The propagation mechanism of detonation wave in a round tube filled with larger blockage ratio orifice plates

In this study, the detonation propagation mechanisms for the stoichiometric hydrogen-oxygen mixture are explored systematically in a circular tube with 6-m in length and an inner diameter of 90-mm. The continuous orifice plates with BR = 0.93 are adopted to investigate the characteristics of detonation diffraction, failure and initiation. High-speed piezoelectric pressure transducers are used to obtain the average velocity, and the smoked foil technique is adopted to record the detonation cellular patterns. The results indicate that three various propagation regimes can be observed, i.e., steady detonation, quasi-detonation and fast flame. In the smooth tube, only the steady detonation and fast flame modes are seen. When the initial pressure is greater than the critical value, the detonation can propagate at about the theoretical CJ velocity. Near the critical pressure, a sudden velocity drop is observed. Of note is that the single-headed spin and double-headed detonation cannot occur because of the limitation of the aspect ratio. In the tube filled with obstacles, the averaged wave velocity is decayed severely. Only the mechanisms of the quasi-detonation and fast flame can be seen. In the quasi-detonation mode, the critical value of d/λ is greater than 7.36, which is far larger than 1. Two different detonation ignition regimes produced by the shock reflection from the wall are observed, i.e., the initiation positions occur in the vicinity of the tube wall and the surface of the orifice plate.     

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.     

Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube

In this paper, an experimental study on the near detonation limits for propane-hydrogen-oxygen is performed. Three mixtures (i.e., 8H₂–C₃H₈–9O₂, 4H₂–C₃H₈–7O₂ and 12H₂–C₃H₈–11O₂) are tested in a rectangular tube (52 mm × 32 mm). Photodiodes with regular intervals are mounted on the tube wall to measure the time of arrival of detonation waves, from which the detonation velocity is determined. Smoked foils are inserted into the tube to obtain the detonation cell pattern. The results indicate that well within the detonation limits, the detonation can propagate at a steady velocity. By reducing the initial pressure, the detonation velocity decreases gradually. Subsequently, the detonation fails as the initial pressure is below a critical pressure. The critical pressures for 8H₂–C₃H₈–9O₂, 4H₂–C₃H₈–7O₂ and 12H₂–C₃H₈–11O₂ mixtures are 4 kPa, 5 kPa and 6 kPa, and the corresponding detonation velocity deficits are 10%, 9%, 10%, respectively. The cellular detonation structures show that the cell size decreases with the decrease of the hydrogen concentration, and the cell structures are very irregular near the detonation limits.     

Experimental study of a hydrogen-air rotating detonation combustor

The rotating detonation engine can generate continuous thrust via one or more detonation waves. In this study, rotating detonation experiments were performed on a combined structure which included a rotating detonation combustor (RDC) and a centrifugal compressor. Air, which functioned as an oxidiser, was obtained from the environment by the compressor, and hydrogen, which was used as fuel, was provided by the supply system. The propagation velocity of the rotating detonation wave (RDW) reached 81% of the Chapman–Jouguet value in experiments. With the increase of the air-injection area, the detonation-wave pressure increased, but the stability decreased. An air-injection area of 495 mm² was selected for long-duration experiments, and the frequency of the RDW ranged from 3 to 3.5 kHz. Through the self-adjustment of the combined structure, the air pressure ultimately reached a stable state after a certain period of time, and a stable detonation wave was formed in the RDC.     

Numerical simulation of detonation wave propagation through a rigid permeable barrier

The results of calculation of the detonation propagation in a porous medium for hydrogen-air mixture are presented. The porous medium was specified explicitly and consisted of sets of individual obstacles in the form of solid walls or the sets of finite-size plates. Various modes of detonation propagation depending on obstacle parameters are obtained: propagation in a cellular mode, stationary propagation with destruction of the cellular structure of the detonation front, propagation of a monotonically attenuating detonation wave with destruction of the cellular structure of the front. The possibility of reducing the detonation propagation velocity by replacing solid plates with finite-size ones was shown. The effect of the geometrical parameters of the plates and the step of it installation on the degree of detonation attenuation was estimated. It was determined that an increase in the number of plates leads to a stronger attenuation of the detonation.     

Control of detonation combustion of rarefied hydrogen-air mixture in a laval nozzle

The possibility of stabilizing the detonative combustion of hydrogen-air mixtures coming into an axisymmetric Laval nozzle with a high supersonic velocity under conditions of atmosphere at altitudes up to 24 km is being studied. The appropriate parameters for the composition of the mixture and the nozzle channel are determined. Used mathematical model is based on the non-stationary two-dimensional equations of an axisymmetric flow of an inviscid multi-component gas with non-equilibrium chemical reactions. A detailed kinetic model is used to describe the detonative combustion of hydrogen-air mixtures. The heat capacity and enthalpy of the mixture are calculated from the reduced Gibbs energy of the gas components. Numerical simulation is performed on the basis of Godunov's finite-difference scheme and its modification of a higher order of accuracy.Most of the calculations are performed on a supercomputer "Lomonosov" of Lomonosov Moscow State University using OpenMp technology of parallel calculations.     

Modeling of attenuation and suppression of cellular detonation in the hydrogen-air mixture by circular obstacles

The results of numerical study of the interaction of the gaseous detonation with the regular obstacle consisting of checkered elements with circular cross section are presented. The aim of this work is to identify and generalize the parameters affected the attenuation of a cellular detonation propagating in a premixed stoichiometric hydrogen-air mixture. Studies of such problems are aimed at studying issues related to explosion and fire safety in the operation of highly efficient gaseous fuels, which are currently very widespread. As a result, the dependencies of the leading shock wave propagation velocity on the obstacle geometry are obtained. The contribution of each of the considered parameters to the detonation wave velocity deficit is estimated. Maps of detonation suppression and re-initiation modes for varying barrier parameters are obtained.     

Study on the effects of geometry on the initiation characteristics of the oblique detonation wave for hydrogen-air mixture

The Oblique Detonation Wave Engine (ODWE) may act as a hypersonic propulsion system operating at high Mach numbers, which is an important member in the family of Scramjet. Hydrogen is a promising fuel for Scramjet, which provides wider Mach number range and is environmentally friendly. The geometry of the engine greatly affects the performance of the ODWE using hydrogen fuel. This investigation focuses on a novel wedge proposed recently, which may be utilized in scramjet engines. The wedge consists of two sub-wedges and a step. This research focuses on how the geometry of the wedge affects the initiation characteristics of the oblique detonation. Simulations are conducted on basis of Euler equations and a 9-species and 19-reactions mechanism. It is found that a larger leading wedge angle leads to a shorter initiation length. A larger step angle induces a longer initiation length. Few effects are observed on the initiation characteristics for the current range of depth. The streamline surface at the rear of the step weakens the rear shock wave and induces a longer initiation length. The streamline surface at the tip of the step begins to take effect when the initiation position is away from the step. This research provides basis for understanding the performance of the oblique detonation wave under different geometries and provides theoretical basis for scramjet engine design.     

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.     

Experimental investigation of unconfined spherical and cylindrical flame propagation in hydrogen-air mixtures

This paper presents results of experimental investigations on spherical and cylindrical flame propagation in pre-mixed H₂/air-mixtures in unconfined and semi-confined geometries. The experiments were performed in a facility consisting of two transparent solid walls with 1 m² area and four weak side walls made from thin plastic film. The gap size between the solid walls was varied stepwise from thin layer geometry (6 mm) to cube geometry (1 m). A wide range of H₂/air-mixtures with volumetric hydrogen concentrations from 10% to 45% H₂ was ignited between the transparent solid walls. The propagating flame front and its structure was observed with a large scale high speed shadow system. Results of spherical and cylindrical flame propagation up to a radius of 0.5 m were analyzed. The presented spherical burning velocity model is used to discuss the self-acceleration phenomena in unconfined and unobstructed pre-mixed H₂/air flames.