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.     

Propagation process of H2/air rotating detonation wave and influence factors in plane-radial structure

The rotating detonation wave (RDW) propagation processes and influence factors are simulated in the plane-radial structure. The effects of inner radii of curvature, domain widths and stagnation pressures on propagation mode are studied. The RDW is initiated, and two kinds of propagation mode are obtained and analyzed. The flow field structure, parameters variation and influence factors on unstable propagation mode are explored in depth, and the geometrical and injection conditions of the unstable propagation are obtained. Results indicate that the decoupling and re-initiation occur repeatedly during the unstable propagation mode of the RDW, and the angular velocities of leading shock wave vary accordingly. When the domain width remains constant, the range of stagnation-pressure under unstable propagation mode increases as the inner radius increases. But the RDW propagates steadily when the inner radius increases to a certain value (Larger than 40 mm in this study). The effect of curvature radius and initial pressure ahead of detonation wave on the unstable propagation mode in this calculation model is similar to that in a curved channel. When r_i +0.464p_a > 80.932 or r_i ≥ 40 mm, the detonation wave can propagate steadily in the annular domain. When the curvature radius remains constant, the stagnation-pressure range of the unstable propagation mode decreases as the domain width increases.     

The influence of the cellular instability on lead shock evolution in weakly unstable detonation

The evolution of the normal detonation shock velocity (D_n) with local shock curvature (κ) is experimentally and numerically examined along entire evolving fronts of a weakly unstable cellular detonation cycle with the intention of extending the understanding of cellular evolution dynamics. As expected, a single velocity–curvature relation is not recovered due to the unsteady evolution of the cell. However, geometric features of the D_n–κ evolution during a cell cycle reveal some new details of the mechanisms driving cellular detonation. On the cell centerline, the local shock velocity and curvature monotonically decrease throughout the cellular cycle. Off centerline, a larger range of wavefront curvature was exhibited in expanding cells as compared to shrinking ones, indicating that most curvature variation in a detonation cell occurs near the Mach stem. In normal shock velocity–curvature space, the cell dynamics can be mapped to three features that are characteristic of (feature 1) a detonation with a spatially short reaction zone, (feature 2) a transitional regime of shock and reaction zone decoupling, and (feature 3) a diffracting inert blast wave. New, growing cells predominately exhibited features 1 and 2, while decaying cells only exhibited feature 3. The portions of all profiles with normal velocities below the Chapman–Jouguet velocity were characteristic of inert blast propagation, indicating the possibility that exceeding this velocity may be a necessary condition for the existence of shock and reaction zone coupling. In this inert blast regime, D_n and κ vary spatially across the wave front so each segment is not geometrically cylindrical, but when accumulated, the D_n–κ data map out a straight line, indicating elements of self-similar flow for each stage in the cell cycle.     

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.     

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).     

Detonation wave propagation in semi-confined layers of hydrogen–air and hydrogen–oxygen mixtures

This paper presents results of an experimental investigation on detonation wave propagation in semi-confined geometries. Large scale experiments were performed in layers up to 0.6 m filled with uniform and non-uniform hydrogen–air mixtures in a rectangular channel (width 3 m; length 9 m) which is open from below. A semi confined driver section is used to accelerate hydrogen flames from weak ignition to detonation. The detonation propagation was observed in a 7 m long unobstructed part of the channel. Pressure measurements, ionization probes, soot-records and high speed imaging were used to observe the detonation propagation. Critical conditions for detonation propagation in different layer thicknesses are presented for uniform H₂/air-mixtures, as well as experiments with uniform H₂/O₂ mixtures in a down scaled transparent channel. Finally detail investigations on the detonation wave propagation in H₂/air-mixtures with concentration gradients are shown.     

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.     

Supersonic cavity flows over concave and convex walls

Supersonic cavity flows are characterized by compression and expansion waves, shear layer, and oscillations inside the cavity. For decades, investigations into cavity flows have been conducted, mostly with flows at zero pressure gradient entering the cavity in straight walls. Since cavity flows on curved walls exert centrifugal force, the features of these flows are likely to differ from those of straight wall flows. The aim of the present work is to study the flow physics of a cavity that is cut out on a curved wall. Steady and unsteady numerical simulations were carried out for supersonic flow through curved channels over the cavity with L/H = 1. A straight channel flow was also analyzed which serves as the base model. The velocity gradient along the width of the channel was observed to increase with increasing the channel curvature for both concave and convex channels. The pressure on the cavity floor increases with the increase in channel curvature for concave channels and decreases for convex channels. Moreover, unsteady flow characteristics are more dependent on channel curvature under supersonic free stream conditions.     

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.     

Detonation propagation characteristic of H2–O2–N2 mixture in tube and effect of various initial conditions on it

As for the premixed H₂–O₂–N₂ gas ignited and induced by flame in tube, this paper represents systemic researches on its detonative formation process and flow field changes under different initial conditions (pressure, temperature, component concentration). The conservational Euler equation set with chemical reaction is taken as the basic gas phase equation model and the reduced elementary chemical reaction and shock wave problem are considered available so as to establish a theoretical model of premixed H₂–O₂–N₂ combustible gas detonation process. A unity coupling TVD format with second-order accuracy is adopted to solve the gas phase equation and deduce the two-dimension Riemann invariant, and the TVD format for solution of the polycomponent convection equation with elementary chemical reaction is proposed. Meanwhile, a time splitting format is adopted to perfectly treat with the rigid problem resulted from the higher time difference value between gas phase flow characteristic time and chemical reaction characteristic time. It is shown by the calculation results that the detonation waves form certain angle with relation to the tube wall surface at the initial stage of ignition, so as to incur reflections and form reflection waves; during the propagation of the detonation waves, the reflection wave structures are propagated backwards the back of waves constantly, so the whole flow field is characterized of obvious two-dimension. Besides, the excessive pressure detonation occurs at first before formation of the stable detonation propagation process, then a stable detonation propagation process forms finally. Mixed gas detonation characteristics resulted from different calculated-initially parameters are different. The higher the initial temperature and pressure of flame is, the shorter the induction time for detonation formed due to combustion acceleration of the mixed gas is, but which nearly brings no great influence on the later propagation process of the detonation waves. The initial mixed gas component can influence the detonation characteristic of the mixed gas observably, when the quantity relative ratio is close to 1 and the mixed gas with larger reaction activity, its detonation propagation speed is rapider and the pressure after detonation waves is higher. The simulation result keeps accordant with the calculated result of the typical C–J detonation theory model.     

Numerical simulation of hydrothermal behavior in a concentric curved annular tube

This study performs a numerical investigation of the steady‐state fully developed laminar flow and forced convection heat transfer characteristics in a concentric curved annular tube with two different curvature angles, a 90°‐bend annular tube and a U‐bend annular tube. A wide range of aspect ratios (r* = 0.1, 0.25, 0.5, and 0.75) and three curvature ratios (δ_c = 0.1, 0.2, and 0.5) were adopted in this study. The governing equations consisting of continuity, momentum, and energy equations are solved by considering the outer wall to be insulated (adiabatic), and a constant temperature is applied at the inner wall by using the finite‐volume method (FVM) to investigate the hydrothermal performance for these two different bend angles.Features of axial velocity contours, temperature patterns, and secondary flow streamlines at different cross‐sectional locations along the angular coordinate of curved annulus are observed with a Dean number range of (De = 32‐632). Additionally, the circumferential friction factor and averaged Nusselt number are obtained along the concentric curved annulus flow direction. The numerical results indicate that the normalized average Nusselt number and Performance Evaluation Criteria (PEC) increase with increasing De and curvature ratio for both curvature angles of concentric curved annular tube. Moreover, the normalized average Nusselt number, normalized friction factor‐Reynolds number product, and PEC increase with decreasing the aspect ratio because the annular gap between the surfaces of the inner and outer tubes (the boundaries of annulus) increases with decreasing aspect ratio. The hydrothermal performance of the concentric curved annular tube is higher than that of the straight annular tube attributed to the formation of secondary flows (Dean's vortices) in a cross‐sectional direction and the impact of the inner tube wall boundary. The value of PEC for both curvature angles of the curved annular tube at aspect ratio = 0.1 and De = 632 is approximately two‐fold of the straight annular tube under the same conditions while at aspect ratio = 0.75, it increases by nearly 80%.     

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.     

Propagation characteristics of unstable detonation waves in a round tube with annular perturbation

The detonation propagation characteristics of the mixtures, 2H₂ + O₂+3Ar and CH₄ + 2O₂, were investigated. Accordingly, the mixtures were tested in round tube with inner diameter of D = 80 mm and annular tubes with widths of w = 25 mm, 15 mm, and 5 mm. The two mixtures represent stable mixture with regular cell pattern and unstable mixture with irregular cell pattern, respectively. Smoked foils were utilized to record cellular structure under various initial conditions. Subsequently, the length scale L_dsc was measured, which represents the length from the start of the test section to the position where the cellular structure changes drastically (the cell size obviously increases or the structure disappears). The results reveal that both mixtures can successfully propagate in round tube and annular tubes of 25 mm and 15 mm, but fail in 5 mm annular tube. The L_dsc value of 2H₂ + O₂ + 3Ar is higher than that of CH₄ + 2O₂ in 80 mm and 15 mm tubes, but it is opposite in 25 mm tube. Moreover, the relationship between L_dsc and hydraulic diameter D_H was analysed. For a given tube, the values of L_dsc and L_dsc/D_H increased when the initial pressure increased. And the variation trend of L_dsc and L_dsc/D_H of CH₄ + 2O₂ is steeper. Furthermore, the mixtures 2H₂ + O₂ + 3Ar and CH₄ + 2O₂ resulted in over-driven detonation in 15 mm and 25 mm annular tubes, respectively. The ratio between the total reaction length (sum of the induction length and exothermic length) and the hydraulic diameter (D_H/(Δ_i + Δ_e)) correspond to critical values of 18 for hydrogen-oxygen-argon and 6 for methane-oxygen, below which the detonation will fail.     

Cellular pattern evolution in gaseous detonation diffraction in a 90°-branched channel

This paper presents recent results of an experimental investigation on gaseous detonation diffraction in a 90°-branched channel. The entire process of diffraction is demonstrated by cellular patterns and the analysis is mainly based on their evolution. Detonation pressure history and velocity are measured and the corresponding cellular patterns are recorded on soot foils around the branched segment. Results show that detonation propagation is notably disturbed by the branched wall geometry and that a complex wave configuration appears in both channels. Cellular patterns show that an expansion fan appears at the T-junction area with a Mach reflection taking place in the horizontal channel, while regular reflection takes place in the vertical channel. Subsequently, it appears that there is a transition from a regular reflection to a Mach reflection in the vertical channel. Details of the cellular pattern indicate that from the early stage to the end of diffraction, the detonation wave sequentially experiences attenuation, front decoupling, and degradation into deflagration, reinitiation, and recuperation. According to cellular pattern evolution and velocity measurement, a recuperated detonation with nearly the same velocity as the undisturbed incoming wave finally develops downstream in both channels, at a distance of about four times the channel height (160 mm). The mechanism of diffraction is explored based on the ZND (Zel'dovich-von Neumann-Döring) model, and the soot foils in both channels show a pattern consistent with air shock-wave diffraction in a 90°-branched channel.     

Flame acceleration and DDT of hydrogen-oxygen gaseous mixtures in channels with no-slip walls

Hydrogen-oxygen flame acceleration and transition from deflagration to detonation (DDT) in channels with no-slip walls were studied theoretically and using high resolution simulations of 2D reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, real equation of state and a detailed chemical reaction mechanism. It is shown that in “wide” channels (D > 1 mm) there are three distinctive stages of the combustion wave propagation: the initial short stage of exponential acceleration; the second stage of slower flame acceleration; the third stage of the actual transition to detonation. In a thin channel (D < 1 mm) the flame exponential acceleration is not bounded till the transition to detonation. While velocity of the steady detonation waves formed in wider channels (10, 5, 3, 2 mm) is close to the Chapman-Jouguet velocity, the oscillating detonation waves with velocities slightly below the CJ velocity are formed in thinner channels (D < 1.0 mm). We analyse applicability of the gradient mechanism of detonation ignition for a detailed chemical reaction model to be a mechanism of the deflagration-to-detonation transition. The results of high resolution simulations are fully consistent with experimental observations of flame acceleration and DDT in hydrogen-oxygen gaseous mixtures.     

Regime classification of an exothermic reaction with nonuniform initial conditions

The initial (t = 0) temperature distribution in a reacting mixture enables one to calculate the induction period t_i to the adiabatic explosion in each particle of the mixture. Isosurfaces t_i(x,y,z) = t give the location of the explosion front at the moment t_i if no physical interaction of adjacent layers occurs; the inverse gradient of the induction period | grad t_i |^?1 determines the propagation velocity of the intensive reaction zone. The comparison of this rate with the rate of normal flame propagation and the Chapman-Jouguet detonation speed enables conclusions to be drawn about the effects of heat conductivity or substance movement on chemical reaction under given initial conditions.     

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

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

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.     

High speed turbulent deflagrations and transition to detonation in H2air mixtures

An experimental investigation on flame acceleration and transition to detonation in H₂air mixtures has been carried out in a tube which had a 5 cm cross-sectional diameter and was 11 m long. Obstacles in the form of a spiral coil (6 mm diameter tubing, pitch 5 cm, blockage ratio BR = 0.44) and repeated orifice plates spaced 5 cm apart with blockage ratios of BR = 0.44 and 0.6 were used. The obstacle section was 3 m long. The compositional range of H₂ in air extended from 10 to 45%, the initial pressure of the experiment was 1 atm, and the mixture was at room temperature. The results indicate that steady-state flame (or detonation) speeds are attained over a flame travel of 10–40 tube diameters. For H₂ ? 13% maximum flame speeds are subsonic, typically below 200 m/s. A sharp transition occurs at about 13% H₂ when the flame speed reaches supersonic values. A second transition to the so-called quasi-detonation regime occurs near the stoichiometric composition when the flame speed reaches a critical value of the order of 800 m/s. The maximum value of the averaged pressure is found to be between the normal C-J detonation pressure and the constant volume explosion value. Of particular interest is the observation that at a critical composition of about 17% H₂ transition to normal C-J detonation occurs when the flame exits into the smooth obstacle-free portion of the tube. For compositions below 17% H₂, the high speed turbulent deflagration is observed to decay in this portion of the tube. The detonation cell size for 17% H₂ is about 150 mm and corresponds closely to the value of πD that has been proposed to designate the onset of single-head spinning detonation, in this case for the 5 cm diameter tube used. This supports the limit criterion, namely, that for confined detonations in tubes, the onset of single-head spin gives the limiting composition for stable propagation of a detonation wave.