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.     

Detonability of THDCPD-exo–air mixtures

In the frame of industrial risk and propulsive application, the detonability study of JP10–air mixtures was performed. The simulation and measurements of detonation parameters were performed for THDCPD-exo/air mixtures at various initial pressure (1 bar < P ₀ < 3 bar) and equivalence ratio (0.8 < Φ < 1.6) in a heated tube (T ₀ ~ 375 K). Numerical simulations of the detonation were performed with the STANJAN code and a detailed kinetic scheme of the combustion of THDCPD. The experimental study deals with the measurements of detonation velocity and cell size λ. The measured velocity is in a good agreement with the calculated theoretical values. The cell size measurements show a minimum value for Φ ~ 1.2 at every level of initial pressure studied and the calculated induction length L _i corresponds to cell size value with a coefficient k = λ/L _i = 24 at P ₀ = 1 bar. Based on the comparison between the results obtained during this study and those available in the literature on the critical initiation energy E _c, critical tube diameter d _c and deflagration to detonation transition length L _DDT, we can conclude that the detonability of THDCPD–air mixtures corresponds to that of hydrocarbon–air mixtures.

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This paper is based on the work presented at the 33rd International Pyrotechnics Seminar, IPS 2006, Fort Collins, July 16–21, 2006.     

DDT in fuel–air mixtures at elevated temperatures and pressures

An experimental study was carried out to investigate flame acceleration and deflagration-to-detonation transition (DDT) in fuel–air mixtures at initial temperatures up to 573 K and pressures up to 2 atm. The fuels investigated include hydrogen, ethylene, acetylene and JP-10 aviation fuel. The experiments were performed in a 3.1-m long, 10-cm inner-diameter heated detonation tube equipped with equally spaced orifice plates. Ionization probes were used to measure the flame time-of-arrival from which the average flame velocity versus propagation distance could be obtained. The DDT composition limits and the distance required for the flame to transition to detonation were obtained from this flame velocity data. The correlation developed by Veser et al. (run-up distance to supersonic flames in obstacle-laden tubes. In the proceedings of the 4th International Symposium on Hazards, Prevention and Mitigation of Industrial Explosions, France (2002)) for the flame choking distance proved to work very well for correlating the detonation run-up distance measured in the present study. The only exception was for the hydrogen–air data at elevated initial temperatures which tended to fall outside the scatter of the hydrocarbon mixture data. The DDT limits obtained at room temperature were found to follow the classical d/λ = 1 correlation, where d is the orifice plate diameter and λ is the detonation cell size. Deviations found for the high-temperature data could be attributed to the one-dimensional ZND detonation structure model used to predict the detonation cell size for the DDT limit mixtures. This simple model was used in place of actual experimental data not currently available. PACS 47.40.-x; 47.70.Fw This paper was based on work that was presented at the 19th Interna-tional Colloquium on the Dynamics of Explosions and Reactive Sys-tems, Hakone, Japan, July 27 - August 1, 2003     

Optimization of the deflagration to detonation transition: reduction of length and time of transition

The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L _DDT and t _DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L _DDT with λ_CJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L _DDT values of several meters. To shorten L _DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H₂, CH₄, C₃H₈, and C₂H₄ with oxygen and diluted with N₂ in order to obtain the same cell width λ_CJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L _DDT below 40 cm for the mixtures used and a ratio L _DDT/λ_CJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E _a/RT _c) and on the normalized heat of reaction (Q/a ₀ ²). The higher these quantities are, the shorter the ratio L _DDT/λ_CJ is. PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

氢气/丙烷/空气预混气体爆轰性能的实验研究

通过采用压力传感器和烟灰板两种测试设备,开展了常温常压下氢气/丙烷和空气混合气体爆轰性能的实验研究。实验过程中观察到自持爆轰波,爆轰速度比值在0.99~1之间,爆轰压力比值在0.8~1.2之间。爆轰胞格尺寸在10~50 mm范围内,建立了爆轰胞格尺寸和化学诱导长度的关系式。随着丙烷不断添加,爆轰速度减小,而爆轰压力和胞格尺寸增加。这种变化趋势起初较快,而后变缓。因为起初氢气摩尔分数较大,混合气体趋向于氢气/空气的爆轰性能;而后因丙烷摩尔质量较大,丙烷逐渐起主要作用,混合气体表现出丙烷/空气的爆轰性能。     

Transition layer thickness in a fluid-porous medium of multi-sized spherical beads

Momentum and mass transfer at fluid–porous interfaces occur in many technical and natural applications. The vertical extend below a fluid–porous interface within which the free fluid velocity reduces to a constant Darcy velocity in the porous medium is known as Brinkman layer. Recently, the Brinkman layer thickness (δ) has been measured for a porous bed of mono-sized spherical beads, and was found to be in the order of the particle diameter (d). In this study, we investigate a porous medium made of multi-sized spherical beads. The measured averaged interfacial velocity field clearly indicated that, in the case of multi-sized beads, δ is in the order of a characteristic diameter given by with x _i and d _i being the weight fraction and diameter of the component i in the mixture.     

Approach to local axisymmetry in a turbulent cylinder wake

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re _d  ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re _d  ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.     

Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme

The time dependent heating and cooling velocities are investigated in this paper. The temperature profile is found by using a keyhole approximation for the melted zone and solving the heat transfer equation. A polynomial expansion has been deployed to determine the cooling velocity during welding cut-off stage. The maximum cooling velocity has been estimated to be V _max ≈ 83°C s⁻¹.     

Aluminum Particles–air Detonation at Elevated Pressures

The effect of initial pressure on aluminum particles–air detonation was experimentally investigated in a 13 m long, 80 mm diameter tube for 100 nm and 2 μm spherical particles. While the 100 nm Al–air detonation propagates at 1 atm initial pressure in the tube, transition to the 2 μm aluminum–air detonation occurs only when the initial pressure is increased to 2.5 atm. The detonation wave manifests itself in a spinning wave structure. An increase in initial pressure increases the detonation sensitivity and reduces the detonation transition distance. Global analysis suggests that the tube diameter for single-head spinning detonation or characteristic detonation cell size would be proportional to (d ₀: aluminum particle size, p ₀: initial pressure). Its application to the experimental data results in m ~ O(1) and n ~ O(1) for 1 to 2 μm aluminum–air detonation, thus indicating a strong dependence on initial pressure and gas-phase kinetics for the aluminum reaction mechanism in detonation. Hence, combustion models based on the fuel droplet diffusion theory may not be adequate in describing micrometric aluminum–air detonation initiation, transition and propagation. For 2 μm aluminum–air mixtures at 2 atm initial pressure and below, experiments show a transition to a “dust quasi-detonation” that propagates quasi-steadily with a shock velocity deficit nearly 40% with respect to the theoretical C–J detonation value. The dust quasi- detonation wave can propagate in a tube with a diameter less than 0.4–0.5 times the diameter required for a spinning detonation wave.     

Detonation diffraction through different geometries

We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d _c  = k _c ·λ (with λ the detonation cell size and k _c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter (D/d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/λ. For ratios below k _c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k _lim (which depends on D/d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k _c by 50%. The results in configuration C show that the re-ignition process depends both on d/λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D _ch = 200 mm) at as small d/λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

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This paper was based on work that was partly presented at the International Conference on Combustion and Detonation, Zel’dovich Memorial II, Moscow, Russia, 30 August–3 September 2004, and at the 20th International Colloquium on the Dynamics of Explosions and Reactive systems, Montreal, Canada, 31 July–5 August 2005.     

Detonation diffraction from an annular channel

In this study, gaseous detonation diffraction from an annular channel was investigated with a streak camera and the critical pressure for transmission of the detonation wave was obtained. The annular channel was used to approximate an infinite slot resulting in cylindrically expanding detonation waves. Two mixtures, stoichiometric acetylene–oxygen and stoichiometric acetylene–oxygen with 70% Ar dilution, were tested in a 4.3 and 14.3 mm channel width (W). The undiluted and diluted mixtures were found to have values of the critical channel width over the cell size around 3 and 12 respectively. Comparing these results to values of the critical diameter (d _c ), in which a spherical detonation occurs, a value of critical d _c /W _c near 2 is observed for the highly diluted mixture. This value corresponds to the geometrical factor of the curvature term between a spherical and cylindrical diverging wave. Hence, the result is in support of Lee’s proposed mechanism [Lee in Dynamics of Exothermicity, pp. 321, Gordon and Breach, Amsterdam, 1996] for failure due to diffraction based on curvature in stable mixtures such as those highly argon diluted with very regular detonation cellular patterns.     

Measurement and scaling analysis of critical energy for direct initiation of gaseous detonations

In this paper, the critical energies required for direct initiation of spherical detonations in four gaseous fuels (C₂H₂, C₂H₄, C₃H₈ and H₂)–oxygen mixtures at different initial pressures, equivalence ratios and with different amounts of argon dilution are reported. Using these data, a scaling analysis is performed based on two main parameters of the problem: the explosion length R _o that characterizes the blast wave and a characteristic chemical length that characterizes the detonation. For all the undiluted mixtures considered in this study, it is found that the relationship is closely given by R_o ? 26 l{R_{\rm o} \approx 26 \lambda} , where λ is the characteristic detonation cell size of the explosive mixture. While for C₂H₂–2.5O₂ mixtures highly diluted with argon, in which cellular instabilities are shown to play a minor role on the detonation propagation, the proportionality factor increases to 37.3, 47 and 54.8 for 50, 65 and 70% argon dilution, respectively. Using the ZND induction length Δ _I as the characteristic chemical length scale for argon diluted or ‘stable’ mixtures, the explosion length is also found to scale adequately with R_o ? 2320 D_I{R_{\rm o} \approx 2320 \Delta_I} .     

Gas flow activated in an electron-beam plasma

Probe measurements of electron temperature and density, electron energy distribution functions, and plasma potential in a free gas jet activated in an electron-beam plasma and in a planar reactor are presented. The measurements are performed by single, double, and triple electrostatic probes in jets of helium-argon and helium-argon-monosilane gas mixtures. The latter mixture is used to deposit films of microcrystalline and epitaxial silicon. Microcrystalline silicon films of higher quality are obtained in a dense (n_e ≈ 10¹⁷ m⁻³) and cold (T_e ≈ 1.0–0.5 eV) plasma with a low potential (U_sp ≈ 10 V), whereas the growth of monocrystalline silicon films requires a hotter plasma (T_e ≈ 3–5 eV) with a potential U_sp ≈ 15 V. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 3–10, January–February, 2007.     

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.     

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     

On the Domain of Validity of Brinkman’s Equation

An increasing number of articles are adopting Brinkman’s equation in place of Darcy’s law for describing flow in porous media. That poses the question of the respective domains of validity of both laws, as well as the question of the value of the effective viscosity μ ^e which is present in Brinkman’s equation. These two topics are addressed in this article, mainly by a priori estimates and by recalling existing analyses. Three main classes of porous media can be distinguished: “classical” porous media with a connected solid structure where the pore surface S _p is a function of the characteristic pore size l _p (such as for cylindrical pores), swarms of low concentration fixed particles where the pore surface is a function of the characteristic particle size l _s , and fiber-made porous media at low solid concentration where the pore surface is a function of the fiber diameter. If Brinkman’s 3D flow equation is valid to describe the flow of a Newtonian fluid through a swarm of fixed particles or fibrous media at low concentration under very precise conditions (Lévy 1983), then we show that it cannot apply to the flow of such a fluid through classical porous media.     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998     

Viscosity of concentrated noncolloidal bidisperse suspensions

At the same solid volume fraction (Φ) the relative viscosity (η _r ) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension. In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method. In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction Φ _m which depends upon both the diameter ratio (λ) of large to small particles and the volume fraction of large particles (ξ=Φ _l /Φ). This model shows that at high solid volume fraction, Φ > 0.40, both λ and ξ significantly influence η _r . For example, at Φ=0.5, it predicts that for monodisperse suspensions η _r =70, while for bidisperse suspensions (λ=2 and ξ=0.7) η _r =40. Comparison shows that, at high solid volume fraction (0.4–0.5), the relative viscosity predicted by this model is in good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than that predicted by the work of others. Received: 27 February 2001 Accepted: 25 April 2001     

On detonation behavior of mixed fuels

An experimental study of detonation was carried out for mixed fuels (, and ). The results obtained demonstrate that detonation velocities of mixed fuels agree very well with normal C-J velocity and that detonation limits were not extended by the addition of a small amount of . As for mixed fuel, detonation velocities and detonation limits as a function of the equivalence ratio of the whole mixture of mixed fuel coincided with those of single fuel. However, the detonation induction time of a mixture of with a lower sensitivity to detonation decreased considerably with the addition of a small amount of . In addition, the influence of mixed fuels on the quasi-detonation and the fast deflagration in the process of DDT was investigated, showing interesting and complicated features in mixed fuel. Received 20 December 1994 / Accepted 20 November 1995     

Similarities Between Rotation and Stratification Effects on Homogeneous Shear Flow

Linear theory is applied to examine rotation and buoyancy effects on homogeneous turbulent shear flows with given vertical velocity shear, S=d/dx ₃. In the rotating shear case (where the rotation vector is perpendicular to the plane of the mean flow, Ω _i =Ωδ _{i 2}), general solutions for the Fourier components of the fluctuating velocity are proposed. These solutions are compared with those proposed in the literature for the Fourier components of the fluctuating velocity and density in the case of a homogeneous stratified shear flow with vertical density gradient, S _ρ=d/dx ₃. It is shown that from the normal mode stability stand point the Bradshaw parameter B=2Ω/S(1+2Ω/S) (in the rotating shear case) and the Richardson number R _i (in the statified shear case) play similar roles in identifying the stability for all the wave components except in the case where Ω·k=0, for which rotation has no effects on the flow. Analysis of the long-time behavior of the non-dimensional spectral density of energy, e ^g , is carried out. In the stable case, e ^g has decaying oscillations or undergoes a power law decay in time. Analytical solutions for the streamwise two-dimensional energy ℰ _ii ¹/2 (i.e. the limit at k ₁=0 of the one-dimensional energy spectra) are proposed. At large time, ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (3R _i +1)/(4R _i ) except at R _i =1 it stays constant in time. Similar behavior for ℰ _ii ¹(t)/ℰ _ii ¹(0) is also observed in the rotating shear case (ℰ _ii ¹(t)/ℰ _ii ¹(0) oscillates around the value (1+4B)/(4B)). Due to the behavior of the dimensionless spectral density of energy in both flow cases, the turbulent kinetic energy, /2, the production rate, ?, and the rate due to the buoyancy forces, ℬ, are split into two parts, , ?=?₁+?₂, ℬ=ℬ₁+ℬ₂ (in the stratified shear case, both ?₁ and ℬ₁ vanish when R _i >?, while in the rotating shear case one has ℬ=0). It is shown that when rotation is “cyclonic” (i.e. Ω/S>0), part reaches maximum magnitudes at St ≈2, independent of the B value, and the first time to a zero crossing of ?₂ occurs at this particular value. When rotation is “anticyclonic” (i.e. Ω/S<0) one finds St ≈1.6 instead of St ≈2. In the stratified shear case, both ?₂ and ℬ₂ cross zero at Nt=St ≈2, and part reaches maximum magnitudes at this particular value. These results and in particular those for the turbulent kinetic energy are compared with previous direct numerical simulation (DNS) results in homogeneous stratified shear flows. Received 30 July 2001 and accepted 19 February 2002