Detonation Limits Research Articles

Numerical study of cellular structure in detonation of a stoichiometric mixture of vapor JP-10 in air using a quasi-detailed chemical kinetic model

Regularity of cellular structure that forms in the detonation of a stoichiometric gaseous JP-10/air mixture was investigated using a quasi-detailed chemical kinetic model consisting of 275 elementary reactions among 54 chemical species. Two-dimensional numerical simulations were conducted for the cases of a wave front structure that develops in a channel following strong initial perturbations. The effect that the grid resolution has on the detonation structure was examined. With a low grid resolution, relatively regular detonation structure was achieved, but an irregular structure developed at moderately high resolutions. The formation process of irregular structure can be divided into three states: overdriven state, regular state and irregular state. The detonation cell size obtained from numerical results about 50 mm is similar with the experimental results. Meanwhile, new modes appear earlier in wider domains than in narrower domains. This preliminary work provides references for our future research on detonation limits and fuel selection in cloud explosion.

Effect of Inert Micro- and Nanoparticles on the Parameters of Detonation Waves in Silane/Hydrogen–Air Mixtures

Physicomathematical modeling of interaction of detonation waves in silane/hydrogen composite mixtures with clouds of inert micro- and nanoparticles ranging from 10 nm to 100 µm is performed. The normalized detonation velocity is calculated as a function of the volume concentration of particles. It is found that the efficiency of detonation suppression increases only as the particle diameter decreases to 1 µm. The influence of the thermodynamic parameters of particles on the detonation suppression efficiency is identified. The concentration limits of detonation are determined. It is demonstrated that a certain equilibrium asymptotic level of the concentration limits of detonation is reached as the particle diameter decreases below 1 µm. An approximation of the concentration limits of detonation is obtained in the form of an analytical dependence of the limiting volume concentration of particles on their diameter and fuel concentration in a composite two-fuel mixture of silane, hydrogen, and air.

Effects of nitrogen and carbon monoxide on the detonation of hydrogen-air gaseous mixtures

Nitrogen inhibition is considered as a mitigation measure against chemically sensitive mixtures in industry and carbon monoxide is possibly generated during molten corium concrete interaction in a severe accident of nuclear power plants. To study the effects of the N2 and CO on the detonation of H2-air mixtures, a detonation facility of 78 mm inner diameter and 10 m length is set up. Key measured parameters includes detonation cell size, flame velocity, lean and rich detonation limits. All the measured detonation parameters are theoretically predicted by CJ theory or one-dimensional ZND model. Detailed chemical kinetics mechanism for H2-air and H2-CO-air mixtures is coupled with reactive Euler equations. Experiments and theoretically analysis has been performed mostly at 0.101 MPa and 293 K. Results shows that N2 increases the detonation cell size and narrows down the detonable range significantly. Especially when N2 concentration is more than 43%, all mixtures are unable to detonate. Moreover, when the added N2 concentration is larger than 20%, detonation velocity does not increase with hydrogen concentration for rich mixtures. The above effects of N2 is explained by the replacement of O2 with N2 and by the weak chemical reaction of N2. CO significantly decreases the cell size of lean H2-air mixtures and increased the cell size for rich H2-air mixtures. For lean H2-air mixtures, the added CO linearly decreases the lean detonation limit, thus increasing the possibility of detonation to occur in the severe accidents. Therefore, the contribution of CO must be carefully considered in the safety assessment. Results also shows that pure CO is difficult to detonate in the air, while small quantity of hydrogen can significantly enhance the rate of CO oxidation reactions.

On the detonation behavior of methane-oxygen in a round tube filled with orifice plates

Abstract In this study, the detonation behaviors of stoichiometric methane-oxygen mixture were examined in a round tube filled with orifice plates. The blockage ratio was 0.56 and the plate spacings were 1, 1.5 and 2 times the tube diameter. Detonation velocity measurement and soot foils were adopted to study the propagation characteristics. Experimental results show that the abrupt velocity jump was only observed for the obstacle configuration with S = 2 D , where S and D are the plate spacing and the tube diameter. For a fixed plate spacing, the detonation velocity as well as the detonation limits are independent of the orifice geometry, since the effective diameters ( d e f f ) of the orifices are almost the same. The ratios of d e f f to the detonation cell size ( λ ) were found to be 0.4–0.5. For sensitive mixtures, the soot foils indicate that the detonation re-initiation occurs via hot spots formed on the wall. As the initial pressure decreases, the detonation can travel without hot spots generation. At the limits, no indication of detonation can be observed for obstacle configurations with smaller spacings in spite of the higher velocity (compared with the isobaric sound speed of the products). The propagation mechanism near the limits is left, however, for further investigation.

The propagation characteristics of curved detonation wave: Experiments in helical channels

The propagation characteristics of curved detonation have been extensively investigated in the present study using three types of stoichiometric test mixtures (2H2+O2+3Ar, C2H4+3O2, and CH4+2O2) in a new experimental facility consisting of a straight channel joined to a helical channel. The helical channel with different inner radii (Ri = 60 mm, 70 mm, and 80 mm) and uniform outer radius (Ro = 100 mm) were used. Flame propagation through the helical channel was observed by high-speed CCD camera, and the trajectories of triple points on the detonation waves were obtained using a soot-deposition plate. The results clearly identify three detonation propagation modes, namely, a stable mode, critical mode, and unstable mode. A definite flame shape, which is perpendicular to the inner wall of the channel, is observed for the stable mode. The smooth flame front becomes more wrinkled as p0 and/or Ri decreases. Three types of patterns of cellular structure are observed for unstable mode, which present specific features of the periodical variation with various mixtures and curvatures, such as periodical disappearance near the inner wall, “petals”-like structure, and intermittent structure. Moreover, the ratio Ri/λ is introduced as a sensitivity parameter to characterize the ability of a detonation. The detonation limits are found to be at the range of 2.6 ≤ Ri/λ ≤ 4.8 in the present study.

Continuous Detonation of Methane/Hydrogen–Air Mixtures in an Annular Cylindrical Combustor

Regimes of continuous detonation of methane/hydrogen–air mixtures in spin and opposing transverse detonation waves are obtained for the first time in a flow-type annular cylindrical combustor 503 mm in diameter. A two-component (methane/hydrogen) fuel with the H2 mass fractions of 1/9 to 1/2 in the range of specific flow rates of the mixture from 64 to 1310 kg/(s ·m2) and the fuel-to-air equivalence ratio ϕ = 0.78–1.56 is considered. In methane/hydrogen–air mixtures with two compositions of the fuel (CH4 + 8H2 and CH4 + 4H2), one-wave and two-wave regimes of continuous spin detonation are obtained; the frequency of rotation of transverse detonation waves is 0.56–1.66 kHz at ϕ = 0.78–1.02. For the fuel compositions CH4 + 2H2 and CH4 + 1.5H2, continuous multifront detonation with two opposing transverse detonation waves rotating with the frequency of 0.86–1.34 kHz at ϕ = 1.0–1.23 is obtained. For the CH4 + H2 + air mixture, both combustion in the chamber and continuous spin detonation outside the combustor with transverse detonation waves rotating with the frequency of 1.01–1.1 kHz are observed. The lean limits of continuous detonation are obtained in terms of the specific flow rate of the mixture: 64, 100, 200, and 790 kg/(s · m2) for the fuel compositions CH4 + 8H2, CH4 + 4H2, CH4 + 2H2, and CH4 + 1.5H2, respectively, for the mass fraction of hydrogen in the methane/hydrogen fuel of ≈0.16. Violation of regularity of the continuous detonation wave structure and the wave velocity with a decrease in the fraction of hydrogen in the two-component fuel is detected.

The three-dimensional structure of a detonation wave propagating in a round tube with orifice plates

Experiments were performed to study detonation propagation in a round tube equipped with repeating orifice plates, equally spaced at two tube diameters. Tests were performed with stoichiometric hydrogen–oxygen over a range of initial pressures up to 60 kPa absolute. The self-luminous high-speed video was used to visualize the detonation for two sizes of orifice plate, i.e., 50 and 75% cross-sectional area blockage. The high-speed videos were used to obtain the average combustion wave velocity, from which the detonation propagation regime was determined, and the propagation mechanism for each orifice plate geometry was identified. For the 50% blockage ratio orifice plate tests, the detonation limit was measured to be 6 kPa, and detonation propagation was characterized by cycles of detonation failure and re-initiation after each orifice plate, resulting in a CJ detonation velocity deficit of the order of 20%. The high-speed video, captured at an oblique camera angle, showed that the detonation wave forms at hot spot(s) on the tube wall just downstream from the orifice plate, following shock reflection. For the 75% blockage orifice plates, the detonation propagation limit was measured to be 20 kPa. For initial pressures between 20 and 40 kPa, a galloping detonation mode was observed, which was not observed in a previous study performed in the same tube and orifice plates but with one-tube-diameter orifice plate spacing. The galloping mode consists of repeating cycles of fast-flame propagation between successive obstacles, followed by detonation wave propagation between the following pair of orifice plates. The experimental results were used to explain why the well-established requirement that the orifice accommodates one cell for detonation propagation (i.e., $$d/\lambda >1$$ ) is sufficient for low blockage ratio orifice plates; however, for high blockage ratio plates it is necessary but not sufficient.

Detonation behaviors of syngas-oxygen in round and square tubes

The present study reports the detonation behaviors of syngas-oxygen mixtures in three 2 m long tubes, including two circular tubes (D = 32 mm and 18.5 mm, D is the inner diameter) and a square tube (H = 32 mm, His the inner side). Three stoichiometric syngas-oxygen mixtures, i.e., CO+H2+O2, 2CO+H2+1.5O2, 3CO+H2+2O2 were used. Evenly spaced photodiodes were used to determine the detonation velocity while the soot foil technique was adopted to record the cellular structure. The results indicate that well with the limits, the detonation propagates at a steady velocity close to the Chapman-Jouguet value. The velocity deficits are more prominent at decreased initial pressure (equivalently, larger cell size and less sensitivity). At the limiting pressure, the velocity deficits of three mixtures in various tubes are approximate 14%–17%. The experimental velocity deficits were compared with a modified model based on Fay's theory, in which the cell size as well as the corresponding cell length are measured. The experimental velocity deficit is in excellent agreement with the theoretical prediction. The effective diameter, De, rather than the hydraulic diameter, is found to be a more appropriate parameter for the characterization of the detonation velocity in both round and square tubes. Further, a linear correlation between the normalized detonation velocity and (De·p0)−1 is observed. The cellular structure shows that the single-headed spin occurs in all tubes when the detonation limits are approached.

Quantitative effect of Ar dilution on the dynamic detonation parameters in acetylene–oxygen mixtures

In order to clarify the effect of Ar dilution on the dynamic parameters of detonation quantitative, smoked foil records of C2H2–O2 with different Ar dilutions are investigated. With the Ar concentration increasing, the instability will decrease and detonation can fail more easily. Histograms, variance measurements, and studies of the autocorrelation function are systematically considered to quantitative define the irregularity parameters. The other kinetics characteristics, such as detonation limits, velocity, and cell size, are also analyzed to illustrate the dilution effects via the smoke foils from different Ar dilution. It was found that the results from histograms, variance studies, and the autocorrelation function consistently show the tendency that mixtures with different Ar dilutions exhibited different degrees of irregularity. Quantitative irregularity can be examined by the values of the ratio Max discrepancy/Relevant mean cell size of C2H2 + 2.5O2. For the mixtures with higher Ar concentration, the main cell size shown by the peak in the histogram and the first peak of the autocorrelation function were much closer to the cell size measured visually because of the stronger dominant mode and more regular trajectory of triple-point patterns. Predictions of the cell size considering the participation of Ar in the mixtures were also given.

Physical and mathematical modeling of interaction of detonation waves in mixtures of hydrogen, methane, silane, and oxidizer with clouds of inert micro- and nanoparticles

ABSTRACTThe physical and mathematical models for the description of the detonation process in mixtures of hydrogen–oxygen, methane–oxygen, and silane–air in the presence of inert nanoparticles were proposed. On the basis of these models, the dependencies of detonation wave (DW) velocity deficit versus the size and concentration of inert nanoparticles were found. Three regimes of detonation flows in gas suspensions of reactive gases and inert nanoparticles were revealed: (1) stationary propagation of weak DW in the gas suspension, (2) galloping propagation of detonation, (3) destruction of the detonation process and transformation to wave of turbulent burning. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lie in the splitting of a DW to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that concentration limits (on particle volume concentration) of detonation are quite similar for particles with diameters ranging from 10 nm to 1 µm.

Attenuation and Suppression of Detonation Waves in Reacting Gas Mixtures by Clouds of Inert Micro- and Nanoparticles

Physicomathematical models are proposed to describe the processes of detonation propagation, attenuation, and suppression in hydrogen–oxygen, methane–oxygen, and silane–air mixtures with inert micro- and nanoparticles. Based on these models, the detonation velocity deficit is found as a function of the size and concentration of inert micro- and nanoparticles. Three types of detonation flows in gas suspensions of reacting gases and inert nanoparticles are observed: steady propagation of an attenuated detonation wave in the gas suspension, propagation of a galloping detonation wave near the flammability limit, and failure of the detonation process. The mechanisms of detonation suppression by microparticles and nanoparticles are found to be similar to each other. The essence of these mechanisms is decomposition of the detonation wave into an attenuated frozen shock wave and the front of ignition and combustion, which lags behind the shock wave. The concentration limits of detonation in the considered reacting gas mixtures with particles ranging from 10 nm to 1 μm in diameter are also comparable. It turns out that the detonation suppression efficiency does not increase after passing from microparticles to nanoparticles.

Influence of the Fluid on the Parameters and Limits of Bubble Detonation

The compression and inflammation of reactive gas bubbles in bubble detonation waves have been studied, and the considerable influence of the fluid (liquid or vapor) on the detonation parameters has been found. It has been shown numerically that the final values of the pressure and temperature significantly decrease if the temperature dependence of the adiabatic index is taken into account at the compression stage. The parameters of reactive gas combustion products in the bubble have been calculated in terms of an equilibrium model, and the influence of the fluid that remains in the bubble in the form of microdroplets and vapor on these parameters has been investigated.

Mathematical description of ignition, combustion and propagation of detonation in reacting gas mixtures in the presence of micro- and nanoparticles

The physical and mathematical models for the description of the processes of ignition, combustion and propagation of detonation in mixtures of hydrogen-oxygen, methane-oxygen and silane-air in the presence of inert micro- and nanoparticles were proposed. On the basis of these models the dependencies of detonation velocity deficit vs the size and concentration of inert micro- and nanoparticles were found. Two modes of detonation flows in gas suspensions of reactive gases and inert nanoparticles were revealed: - propagation of weak detonation wave in the gas suspension, - destruction of the detonation process. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lies in the splitting of a detonation wave to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that in the transition from microparticles to nanoparticles the detonation suppression efficiency does not increase.

Detonation propagation limits in highly argon diluted acetylene-oxygen mixtures in channels

In this study, the velocity deficits and detonation limits of highly argon (70% and 85% vol.) diluted stoichiometric acetylene-oxygen mixtures in a small diameter circular tube (D=36mm) and three annular channel widths (w=2, 4.5 and 7mm) were investigated. The purpose is to explore the velocity behavior of stable mixture due to its different failure mechanism by investigating the scaling law between the hydraulic diameter (DH) of the circular tube and annular channels with the characteristic length scale (i.e., cell size λ and ZND induction zone length ΔI) of stable detonations. The experimental results suggest the detonation velocity decreases with the decreasing of initial pressure, when the initial pressure reaches a critical value corresponding the maximum velocity deficit, the detonation fails and the detonation limits are approached. The results indicate that the average maximum velocity deficit is approximately 14% of the corresponding CJ value VCJ for the highly argon diluted mixtures in the tubes with different geometries. The scaling between the hydraulic diameter and the cell size (DH/λ) or ZND induction zone length (DH/ΔI) gives an average estimation for the highly argon diluted mixtures at the detonation limits 0.66 and 15, respectively.

Detonation velocity behavior and scaling analysis for ethylene-nitrous oxide mixture

In this study, a detailed experimental investigation of the detonation propagation velocity behavior of stoichiometric ethylene-nitrous oxide in narrow channels is conducted. The experimental results in 4mm (inner diameter) round tube indicate the detonation experiences three propagation modes with the decreasing of initial pressure (p0), i.e., steady mode (p0>40kPa), unstable mode (40–27kPa) and decay mode (p0<27kPa), it is confirmed that below pc=27kPa the failure of detonation occurs. The maximum of the velocity deficit at the critical pressure is 35% VCJ. However, only steady and decay detonation modes are observed in 14mm round tube, and the critical pressure for the detonation limits is 15kPa, at which the maximum velocity deficit is 15% VCJ. In 36mm round tube, there are steady and decay modes can be found, the critical pressure for detonation limits is 5.2kPa, its corresponding maximum velocity deficit is 12% VCJ. The results indicate that with the decreasing initial pressure and tube diameter, boundary layer displacement thickness increases and causes more losses through the flow divergence and hence the increasing of velocity deficits. A linear relationship is obtained between the normalized detonation average velocity and (p0·d)−1 by scaling analysis. It suggests the normalized velocity and dimensionless parameter of length scale, i.e., ratio of tube diameter and ZND induction zone length (d/ΔI) collapse to a single exponential curve.

On the detonation propagation behavior in hydrogen-oxygen mixture under the effect of spiral obstacles

Detonation propagation velocity behavior and cellular structure of stoichiometric hydrogen-oxygen mixture in spiral obstacles with four roughness (ξ = 0.133, 0.231, 0.4, 0.625) are systematically examined, at the conditions outside-, near- and within the propagation limits. The experimental results indicate that, at p0 = 10 kPa (outside the limits), spirals with roughness smaller than 0.4 facilitate the initiation of detonation, but ξ = 0.625 spiral causes the detonation quench earlier than that in smooth tube without spiral, and suggests it has prohibiting effect on the detonation propagation. At p0 = 12 kPa (near the detonation limits), spirals with ξ = 0.133 and 0.231 extend the detonation limits and therefore they have the facilitating effect on the detonation propagation, but this positive effect is not obvious in the spiral with larger roughness (i.e., ξ = 0.4 and 0.625). As the initial pressure is higher than 15 kPa, under such condition detonations are well within the limits, the dual effects of promoting and prohibiting of the spiral on the detonation propagation are more obvious, which are confirmed by the cellular structures obtained from smoked foil. The ZND induction zone length (ΔI) analysis confirms ΔI is shorter at higher initial pressure, under this condition detonation is more sensitive and easier to survive from failure as it enters into the spiral section.

An experimental study of the propagation characteristics for a detonation wave of ethylene/oxygen in narrow gaps

To investigate the propagation characteristics of a detonation wave in a narrow gap, the detonation processes of a stoichiometric ethylene-oxygen mixture were studied at different initial pressures in narrow gaps ranging 1.0–4.0mm in height. Flame propagation through the narrow gap was observed with a high-speed camera, and the trajectories of triple points on the detonation waves were obtained using a soot-deposition plate. The results showed that both higher initial pressure p0 and lower narrow gap height h could accelerate the deflagration-to-detonation transition process and determine how the detonation wave propagates, e.g., galloping detonation, stuttering detonation, and stable detonation. To attain unstable detonation propagation, the corresponding range of initial pressures increased with decreasing height of the narrow gap. A smaller height of the narrow gap led to a higher initial pressure threshold corresponding to the detonability limit. This could be determined by the range of h/λ; the onset of galloping detonation occurred when 0.17<h/λ<0.27. Since the effect of the boundary layer on detonation propagation could not be neglected in narrow gaps, the velocity deficits were relatively large compared with those from a large scale channel. It was found that the velocity deficits were inversely proportional to the narrow gap height and initial pressure, and the relation between them was obtained by fitting the experimental data, i.e., ΔD=0.65h-0.8p0-0.5.

Experimental investigation of methane-oxygen detonation propagation in tubes

In this study, the detonation behaviors of methane-oxygen with five equivalence ratios (φ=0.5, 0.667, 1, 1.333, 2) were investigated experimentally. Two 32-mm inner diameter round tubes were used, i.e., a smooth tube and a porous tube, to study the effect of different walls on the detonation limits. Fiber optical sensors was employed to capture the signals of the detonation wave, from which the velocity can be determined. Smoked foils were inserted into the smooth to register the cellular structure. The results indicate that in the smooth tube, the detonation propagates at a steady velocity within the limit. The stable spinning detonation is observed in a range of the initial pressure. Below the limits, no steady velocity and cell structure can be observed. In the porous tube, the detonation limits are elevated significantly. Within the limits, the detonation propagates at a velocity more than 0.70VCJ. Below the limits, the decoupled deflagration can hold a steady velocity at about 0.4VCJ∼0.5VCJ. The failure condition for the mixture at φ=0.5 is d/λ≈6. For other mixtures, the detonation fails at d/λ≈4.

A computational study of the interaction of gaseous detonations with a compressible layer

The propagation of two-dimensional cellular gaseous detonation bounded by an inert layer is examined via computational simulations. The analysis is based on the high-order integration of the reactive Euler equations with a one-step irreversible reaction. To assess whether the cellular instabilities have a significant influence on a detonation yielding confinement, we achieved numerical simulations for several mixtures from very stable to mildly unstable. The cell regularity was controlled through the value of the activation energy, while keeping constant the ideal Zel’dovich - von Neumann - Döring (ZND) half-reaction length. For stable detonations, the detonation velocity deficit and structure are in accordance with the generalized ZND model, which incorporates the losses due to the front curvature. The deviation with this laminar solution is clear as the activation energy is more significant, increasing the flow field complexity, the variations of the detonation velocity, and the transverse wave strength. The chemical length scale gets thicker, as well as the hydrodynamic thickness. The sonic location is delayed due to the presence of hydrodynamic fluctuations, for which the intensity is increased with the activation energy as well as with the losses to a lesser extent. The flow field has been studied through numerical soot foils, detonation velocities, and 2D detonation front profiles, which are consistent with experimental findings. The velocity deficit increases with the cell irregularity. Moreover, the relation between the detonation limits obtained numerically and in detonation experiments with losses is discussed.

Study on Behavior of Methane/Oxygen Gas Detonation Near Propagation Limit in Small Diameter Tube: Effect of Tube Diameter

ABSTRACTThe unstable behavior of the detonation is an important issue in predicting detonation limits and safety problems. The present study aims to obtain information of the unstable behavior near the detonation propagating limit in methane/oxygen gas mixture for various initial pressures and tube diameters. The detonation velocity rapidly decreases near α = 1.0 and deviates from the theoretical value for α < 1.0 conditions (α = πd/λ; d: tube diameter; λ: cell width). The onset of the single-head spinning is α = 1.0. For α < 1.0 conditions, the transition to the single-head spinning from small cells and the failure of cellular patterns were observed. For α > 1.0 conditions, the propagation mode was unstable. The unstable phenomenon means that the cellular pattern repeats multi-head and single-head spinning in turn.