Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

Experimental observation of the onset of detonation downstream of a perforated plate

In this study, the onset of detonation downstream of a perforated plate subsequent to the reflection of a Chapman–Jouguet detonation upstream is investigated. The experiments were performed with C₃H₈ + 5O₂ and C₂H₂+2.5O₂+70%Ar. The former has a much more irregular transverse wave pattern whereas the latter is known to have a piecewise laminar structure with a regular cellular structure. The onset of detonation phenomenon was found to be significantly different for the two mixtures. For the high argon diluted mixtures, the onset of detonation occurs in the vicinity downstream of the perforated plate. However, if the onset of detonation does not occur close to the plate, the precursor shock decouples from the reaction zone and a deflagration results. For the propane–oxygen mixtures, the onset of detonation is found to occur relatively far from the perforated plate at critical conditions. The major difference between these two mixtures is that the metastable turbulent reaction front can be maintained for relatively long distances for the propane–oxygen mixture. This turbulent metastable regime is also observed to be able to maintain a relatively constant propagation velocity for many channel widths prior to the onset of detonation. For the propane–oxygen mixtures, the onset is caused by a strong local explosion within the turbulent reaction zone.     

Dynamics of a single bubble in a liquid in the presence of chemical reactions and interphase heat and mass exchange

The influence of inert and chemically reactive additives in the form of microdrops on the dynamics of a single bubble filled with an active gas mixture and collapsing under the action of a shock wave is considered. The development of a reaction during formation of the mixture is analyzed for instantaneous and dynamic evaporation of drops with allowance for various phases of their injection t _inj . It is shown that in instantaneous evaporation, an increase in the fraction of gaseous argon in the H₂+O₂ system raises the final temperature of the system under cryogenic conditions, lowers it under ordinary conditions, and causes appreciable oscillations of the values of γ, heat release, and molecular weight. It is noted that there are values of t _inj and D₀ at which the final temperature of the mixture decreases practically to the initial temperature. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 119–127, March–April. 1999.     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

Supersonic H2-air combustions behind oblique shock waves

In order to study the mechanisms of initiation and stabilization of H₂-Air combustions (stoechiometric mixture initially atT ₀=293 K andp ₀=0.5 bar) in supersonic flow conditions behind an oblique shock wave (OSW), an original technique is used where OSW is generated in this mixture by the lateral expansion of the burnt gas behind a normal CJ gaseous detonation propagating into a bounding reactive mixture. Four Mach numberM of propagation of OSW are considered in the study, namelyM=7.7-6.1-4.4 and 3. Depending on the Mach numberM and inclinaison angle of OSW different regimes of combustion may occur in the driven mixture. For high values ofM (6.1 and 7.7) delayed steady overdriven oblique detonation waves (SODW) were obtained with a near CJ detonation wave as the critical regime. It was found that SODW obtained correspond quite well to prediction of the polar method. When thermal conditions behind the OSW are lower, either for high Mach number 6.1 and 7.7 for smaller angle than the previous case, or for lower Mach number, 4.4 and 3, the flame initiated at the apex is stabilized as a turbulent oblique flame behind the OSW. With much lower conditions, no combustion appears in the H₂-Air mixture.     

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF₄ premixed in the test gas. The final product C₂F₄ is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C₂F₄ is correlated to the temperature of the reflected shock wave with the initial pressureP ₁ and test time τ as parameters in the temperature range 3 300 K<T<5 600 K, pressure range 5 kPa<P ₁<12 kPa and τ≅0.4 ms. The project supported by the China Aerodynamics Project for Basic Researches (J13.5.2 ZK04)     

Initiation of gaseous detonation by a high speed body

The investigation of detonation initiated by the passage of a high speed body is presented. The following experiments are carried out for mixture of C₂H₂ + 2.5 O₂ passed by a hemispherical or blunt cylinder with velocity ranging from 800 to 1400 m/s. A new mechanism of the transformation of shock waves to detonation waves is observed at near-critical regimes. The analytical correlation between the aerodynamical characteristics of high speed body and the physico-chemical parameters of explosive mixture is proposed as the initiation criterion of gaseous detonation. Analytical and experimental data agree well with each other.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Effect of wall heat transfer on shock-tube test temperature at long times

When performing chemical kinetics experiments behind reflected shock waves at conditions of lower temperature (<1,000 K), longer test times on the order of 10–20 ms may be required. The integrity of the test temperature during such experiments may be in question, because heat loss to the tube walls may play a larger role than is generally seen in shock-tube kinetics experiments that are over within a millisecond or two. A series of detailed calculations was performed to estimate the effect of longer test times on the temperature uniformity of the post-shock test gas. Assuming the main mode of heat transfer is conduction between the high-temperature gas and the colder shock-tube walls, a comprehensive set of calculations covering a range of conditions including test temperatures between 800 and 1,800 K, pressures between 1 and 50 atm, driven-tube inner diameters between 3 and 16.2 cm, and test gases of N₂ and Ar was performed. Based on the results, heat loss to the tube walls does not significantly reduce the area-averaged temperature behind the reflected shock wave for test conditions that are likely to be used in shock-tube studies for test times up to 20 ms (and higher), provided the shock-tube inner diameter is sufficiently large (>8cm). Smaller diameters on the order of 3 cm or less can experience significant temperature loss near the reflected-shock region. Although the area-averaged gas temperature decreases due to the heat loss, the main core region remains spatially uniform so that the zone of temperature change is limited to only the thermal layer adjacent to the walls. Although the heat conduction model assumes the gas and wall to behave as solid bodies, resulting in a core gas temperature that remains constant at the initial temperature, a two-zone gas model that accounts for density loss from the core to the colder thermal layer indicates that the core temperature and gas pressure both decrease slightly with time. A full CFD solution of the shock-tube flow field and heat transfer at long test times was also performed for one typical condition (800 K, 1 atm, Ar), the results of which indicate that the simpler analytical conduction model is realistic but somewhat conservative in that it over predicts the mean temperature loss by a few Kelvins. This paper presents the first comprehensive study on the effects of long test times on the average test gas temperature behind the reflected shock wave for conditions representative of chemical kinetics experiments.     

Interaction of detonation with inert gas zone

The results of experimental study on detonation interaction with the regions of low reactivity, generated by the injection of an inert gas into reactive mixture, are reported. A square cross-section 60×60 mm, 3.6 m long detonation channel was used. The experiments were done for stoichiometric H₂−O₂ mixture at 0.3 bar and 0.5 bar initial pressure and room temperature. The inert gas (Ar, He, N₂ or CO₂) was injected from 0.523 dm³ container into the main channel 1 s before ignition. The size of the inert zone was controlled by inert initial pressure. The behavior of detonation was studied using direct streak photography and pressure transducers. The study has shown that at low pressure of Ar, N₂ and CO₂ injection only a slight decrease of detonation velocity occurs. At higher injection pressures complete damping of detonation and flame extinguishment occur, followed by flame reigniton and DDT outside the inert zone. For low He injection pressures an increase in detonation velocity was recorded. For higher injection pressures, detonation damping occurred, followed by DDT process. The results have shown that CO₂ has the strongest effect on damping 2H₂+O₂ detonation, with N₂ and Ar in the next places, and He very far behind. The effectiveness of inert gas in detonation damping was found proportional to its molecular weight and reciprocal to its specific heat ratio. The numerical simulations of detonation propagation through inert gas zone were also performed using the one- dimensional Detonation Lagrangean code with simple energy release model. The results of simulations are in good qualitative agreement with experimental tendencies. In particular, the model has shown that the re-initiation of detonation is enhanced by smooth concentration gradients at inert/reactive interface. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Population inversion behind a detonation wave propagating in a variable-density medium

The creation of an active medium by means of detonation has been investigated on a number of occasions. It was suggested that one could use the expansion of the detonation products of an acetylene-air mixture in vacuum [1] or the cooling of the detonation products of a mixture of hydrocarbons and air through a nozzle [2, 3]. In [4], the detonation of a solid high explosive was used to produce population inversion in the gas mixture CO₂-N₂-He(H₂O). Stimulated emission from HF molecules was observed in [5] behind the front of an overdriven detonation wave propagating in an F₂-H₂-Ar mixture in a shock tube. Population inversion behind a detonation wave was studied in H₂-F₂-He mixtures in [6–8] and in H₂-Cl₂-He mixtures in [9] with energy release on a plane and on a straight line in a medium with constant density. Similar problems were solved for shock waves propagating in both a homogeneous gaseous medium [7, 10] and in the supersonic part of an expanding nozzle. In the present paper, we study theoretically population inversion behind an overdriven detonation wave propagating in a mixture (fine carbon particles + acetylene + air) which flows through a hypersonic nozzle. The propagation of detonation in media with variable density and initial velocity was considered, for example, in [11, 12]. Analysis of the gas parameters behind a detonation wave propagating in a medium with constant density (for a given fuel) showed that the temperature difference across the detonation front is insufficient to produce population inversion of the vibrational levels of the CO₂ molecule.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 65–71, January–February, 1980.I am grateful to V. P. Korobeinikov for a helpful discussion of the results.     

Inhibition of detonation wave with halogenated compounds

The influence of CF₃Br, CF₂HBr, CF₂HCl and CF₃H on a benchmark mixture composed of stoichiometric H₂−CO−O₂−Ar is experimentally investigated. Several ratios hydrogen/carbon monoxide are studied. For each benchmark mixture, the initial pressure is adjusted in such a way that the detonation cell sizes are quasi identical. The effect of the additives on the detonation velocity and the detonation cellular structure is analyzed. The experiments show that CF₃Br is the best inhibitor and CF₂HBr might be substituted for CF₃Br. CF₃H does not inhibit the detonation wave. Simple chemical kinetics analysis gives us a better understanding of the inhibiting and promoting effect of the halocarbons. An abridged version of this paper was presented at the 15th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Boulder, Colorado, from July 30 to August 4, 1995     

Structure cellulaire de la détonation des mélanges H2–NO2/N2O4Cellular structure of the detonation of gaseous mixtures H2–NO2/N2O4

Calculations of the detonation reaction zone of gaseous reactive mixtures of NO₂/N₂O₄ as oxidizer and H₂, CH₄ or C₂H₆ as fuel, in the range of equivalence ratio Φ between 0.5 and 2, show that, for Φ?1, the chemical energy is released in two distinct and successive exothermic steps with different chemical induction times. The first exothermic stage is mainly due to the reaction NO₂+H→NO+OH, NO being the main oxidizer of the second one.The experimental study conducted on the same range of equivalence ratio (0.5?Φ?2) shows that, for Φ?1, the detonation wave of these mixtures contains a double set of cellular structures. A similar result had already been obtained with the detonation of gaseous Nitromethane, the NO₂ group being here included in the molecule. Consequently, the oxidizer NO₂ being either initially separated from the fuel or included inside the molecule of a monopropellant (Nitromethane) is responsible, because of its specific chemical kinetics, of a chemical energy release in two main steps and of the existence of a double cellular structure in the detonation wave for the same range of equivalence ratio. These results reinforce the assumption that the cellular structure of the detonation finds its origin in the strong rates of chemical energy release inside the reaction zone. To cite this article: F. Joubert et al., C. R. Mecanique 331 (2003).     

A generalized Zel’dovich-Neumann-Döring model of steady gaseous detonation

A model of N-component gas mixture detonation whose combustion zone is formed by n (1 ≤ n ≤ N − 1) independent reactions satisfying the kinetic formulation of the mass action law is studied. In the framework of this model, it is found that there exist two possible types of self-sustaining detonation waves with asymptotically stable combustion zones. It is shown that it is possible to observe only a strong wave propagating in the Chapman-Jouguet regime relative to the flow on the critical surface. It is also shown that, for a perfect gas mixture, this wave appears only when a combustion zone is formed by one or two reactions.     

Shock tube study of n-decane ignition at low pressures

Ignition delay times for n-decane/O 2 /Ar mixtures were measured behind reflected shock waves using endwall pressure and CH* emission measurements in a heated shock tube. The initial postshock conditions cover pressures of 0.09-0.26 MPa, temperatures of 1 227-1 536 K, and oxygen mole fractions of 3.9%-20.7% with an equivalence ratio of 1.0. The correlation formula of ignition delay dependence on pressure, temperature, and oxygen mole fraction was obtained. The current data are in good agreement with available low-pressure experimental data, and they are then compared with the prediction of a kinetic mechanism. The current measurements extend the kinetic modeling targets for the n-decane combustion at low pressures.     

Nonequilibrium molecular radiation behind the front of a strong shock wave in the CO<Subscript>2</Subscript>-N<Subscript>2</Subscript>-O<Subscript>2</Subscript> mixture

Models of population of some radiating electron-vibrational states of CO, CN, and C₂ molecules are developed. The characteristics of radiation in a chemically nonequilibrium flow behind the front of a strong shock wave in a mixture of gases constituting the Martian atmosphere are calculated. The numerical data are compared with experimental results.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 13–22, March–April, 2005     

Behavior of the vorticity vector in supersonic axisymmetric swirl flows behind a detonation wave

The behavior of the vorticity vector on a discontinuity surface arising in a supersonic nonuniform combustible gas flow with the formation of a shock or detonation wave is studied. In the general case, it is a vortex flow with prescribed distributions of parameters. It is demonstrated that the ratio of the tangential component of vorticity to density remains continuous in passing through the discontinuity surface, while the quantities proper become discontinuous. Results calculated for flow vorticity behind a steady-state detonation wave in an axisymmetric supersonic flow of a combustible mixture of gases are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 15–21, November–December, 2007     

Investigation of detonation initiation in aluminium suspensions

Detonation initiation is investigated in aluminium/oxygen and aluminium/air mixtures. Critical conditions for initiation of spherical detonations are examined in analogy with the criteria defined for gaseous mixtures, which correlate critical parameters of detonation initiation to the characteristic size of the cellular structure. However, experimental data on the detonation cell size in these two-phase mixtures are very scarce, on account of the difficulty to perform large-scale experiments. Therefore, 2D numerical simulations of the detonation cellular structure have been undertaken, with the same combustion model for Al/air and Al/O₂ mixtures. The cell size is found to be λ = 37.5 cm for a rich (r = 1.61) aluminium–air mixture, and λ = 7.5 cm for a stoichiometric aluminium-oxygen mixture, which is in reasonable agreement with available experimental data. Calculations performed in large-scale configurations (up to 25 m in length and 1.5 m in lateral direction) suggest that the critical initiation energy and predetonation radius for direct initiation of the unconfined detonation in the aluminium–air mixture are, respectively, 10 kg of TNT and 8 m. Moreover, numerical simulations reveal that the structure of the detonation wave behind the leading front is even more complicated than in pure gaseous mixtures, due to two-phase flow effects. This paper is based on work that was presented at the 21st International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave

A simplified theoretic method and numerical simulations were carried out to investigate the characterization of propagation of transverse shock wave at wedge supported oblique detonation wave.After solution validation,a criterion which is associated with the ratio Φ (u 2 /u CJ) of existence or inexistence of the transverse shock wave at the region of the primary triple was deduced systematically by 38 cases.It is observed that for abrupt oblique shock wave (OSW)/oblique detonation wave (ODW) transition,a transverse shock wave is generated at the region of the primary triple when Φ < 1,however,such a transverse shock wave does not take place for the smooth OSW/ODW transition when Φ > 1.The parameter Φ can be expressed as the Mach number behind the ODW front for stable CJ detonation.When 0.9 < Φ < 1.0,the reflected shock wave can pass across the contact discontinuity and interact with transverse waves which are originating from the ODW front.When 0.8 < Φ < 0.9,the reflected shock wave can not pass across the contact discontinuity and only reflects at the contact discontinuity.The condition (0.8 < Φ < 0.9) agrees well with the ratio (D ave /D CJ) in the critical detonation.     

Properties of an equilibrium detonation model

A shock wave of zero width is studied as a detonation model in the case when detonation products are in chemical equilibrium behind this shock wave. Together with the well-known properties, some new properties of this model are found. In particular, it is found that there exist weak and strong self-sustaining detonation waves; the latter one propagates in the Chapman-Jouguet regime and corresponds to the point of contact of the Mikhelson line with a new-type adiabat called the extreme adiabat.     

Interaction of a high-speed combustion front with a closely packed bed of spheres

The head-on collision of a combustion front with a closely packed bed of ceramic-oxide spheres was investigated in a vertical 76.2 mm diameter tube containing a nitrogen diluted stoichiometric ethylene–oxygen mixture. A layer of spherical beads in the diameter range of 3–12.7 mm was placed at the bottom of the tube and a flame was ignited at the top endplate. Four orifice plates spaced at one tube diameter were placed at the ignition end of the tube in order to accelerate the flame to either a “fast-flame” or a detonation wave before the bead layer face. The mixture reactivity was adjusted by varying the initial mixture pressure between 10 and 100 kPa absolute. The pressure before and within the bead layer was measured by flush wall-mounted pressure transducers. For initial pressures where a fast-flame interacts with the bead layer peak pressures recorded at the bead layer face were as high as five times the reflected Chapman–Jouget detonation pressure. The explosion resulting from the interaction developed by two distinct mechanisms; one due to the shock reflection off the bead layer face, and the other due to shock transmission and mixing of burned and unburned gas inside the bead layer. The measured explosion delay time (time after shock reflection from the bead layer face) was found to be independent of the incident shock velocity. As a result, the explosion initiation is not the direct result of the shock reflection process but instead is more likely due to the interaction of the reflected shock wave and the trailing flame. The bead layer was found to be very effective in attenuating the explosion front transmitted through the bead layer and thus isolating the tube endplate. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.