R. Knystautas

The critical tube diameter for detonation failure in hydrocarbon-air mixtures

Abstract Critical tube diameters dc for the successful transformation of a planar to a spherical detonation have been measured in nine gaseous fuels (CH4, C2H2, C2H4, C2H6, C3H6, C3H8, C4H10, MAPP and H2) in stoichiometric fuel-oxygen mixtures diluted with nitrogen at atmospheric initial pressure. In agreement with the previous work of Matsui and Lee. acetylene is found to have the smallest critical tube diameter of 12 cm at stoichiometric composition with air. However, in contrast with the earlier estimate of Matsui and Lee, hydrogen is now found to be the second most sensitive fuel with a critical tube diameter of 20 cm. Both ethylene and MAPP, with critical diameters of about 38 and 53 cm, respectively, have nearly the same sensitivity. The heavier hydrocarbons (i.e., C4H10, C2H6, C3H6, and C3H8) are found to belong to the same sensitivity class with critical diameters of 64, 67, 70, and 70 cm, respectively. Direct measurements of detonation cell sizes λ in both atmospheric fuel-oxygen-nitrogen mixtures and subatmospheric fuel-oxygen mixtures demonstrate that the observation of Mitrofanov and Soloukhin in low-pressure ( p 0 ⋍ 80 Torr) C2H2O2 mixtures that dc3- 13λ is valid for other fuels as well and can be used as an empirical law to estimate critical tube diameter from cell size data. Based on the preseent results for the critical tube diameter, initiation energies have been estimated using the work-done formula of Lee and Matsui to evaluate the detonation hazard numbers DH as proposed previously by Matsui and Lee. For stoichiometric fuel-air mixtures at 1 atm initially, acetylene ranks first (DH = 8.4 × 105), followed by hydrogen (DH = 3.4 × 106) and ethylene oxide (DH = 1.1 × 107) and MAPP (DH = 7.2 × 107) have nearly the same sensitivity. The other alkanes (DH = 1.5 × 108 for ethane, DH = 1.7 × 108 for n-butane, DH = 1.73 × 108 for propane) and the alkenepropylene (DH = 1.6 × 108) belong to the same sensitivity class.

Photochemical initiation of gaseous detonations

Abstract Direct initiation of detonations in gaseous mixtures of C 2 H 2 -O 2 , H 2 -O 2 and H 2 -Cl 2 in the pressure range of 10–150 torr using flash photolysis was studied. Similar to blast initiation using a concentrated powerful energy source, it was found that for photochemical initiation, there exists a certain threshold of flash intensity and energy for each mixture at any given initial pressure and composition below which a deflagration is formed. At the critical threshold, however, a fully developed detonation is rapidly formed in the immediate vicinity of the window of incident UV radiation. However, at super critical flash energies, the amplitude of the detonation formed decreases and combustion of the entire irradiated volume approaches a constant volume explosion. It was found that photo-chemical initiation requires both a certain minimum peak value of the free radical concentration generated by the photo-dissociation as well as an appropriate gradient of this free radical distribution. The minimum peak radical concentration permits rapid reaction rates for the generation of strong pressure waves, while the gradient is necessary for the amplification of the shock waves to a detonation. If the gradient is absent and the free radicals are uniformly distributed in the mixture, then the entire volume simply explodes as in a constant volume process. The present study reveals that the mechanism of photochemical initiation is one of proper temporal synchronization of the chemical energy release to the shock wave as it propagates through the mixture. In analogy to the LASER, the term SWACER is introduced to represent this mechanism of Shock Wave Amplication by Coherent Energy Release. There are strong indications that this SWACER mechanism is universal and plays the main role in the formation of detonations whenever a powerful concentrated external source is not used to generate a strong shock wave in the explosive.

Flame acceleration due to turbulence produced by obstacles

Abstract This paper reports on an investigation of the influence of obstacles on the propagation of freely expanding cylindrical flames. The flame speed is found to depend critically on the obstacle configuration and flame speeds up to 130 m/sec in stoichiometric methane-air mixtures are readily achieved by placing appropriate turbulence producing obstacles in the flame path. This is ∼ 24 times the flame speed observed with no obstacles. The dramatic influence of obstacles is interpreted in terms of the positive feedback coupling between the flame itself and the turbulence and flow field distortions produced by the obstacles. It is also shown that the flame is unable to maintain its large turbulent flame speed without repeated obstacles to provide flow field distortions and turbulence continuously.

High speed turbulent deflagrations and transition to detonation in H2air mixtures

Abstract An experimental investigation on flame acceleration and transition to detonation in H 2 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 H 2 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 H 2 ≲ 13% maximum flame speeds are subsonic, typically below 200 m/s. A sharp transition occurs at about 13% H 2 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% H 2 transition to normal C-J detonation occurs when the flame exits into the smooth obstacle-free portion of the tube. For compositions below 17% H 2 , the high speed turbulent deflagration is observed to decay in this portion of the tube. The detonation cell size for 17% H 2 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.

Propagation mechanism of quasi-detonations

The propagation mechanism of quasi-detonations in very rough tubes is studied using high speed schlieren photography. Stoichiometric mixtures of H2, C2H4 and C3H8 in oxygen at an initial pressure range 10≤po≤160 torr are investigated in a 61.8×61.8 mm by 1.5 m long channel with two-dimensional obstacles with a height of 25.4 mm and for various obstacle spacings. The results indicate that shock reflections (transition from regular to Mach reflections) from the walls lead to re-initiation. The obstacle spacing is found to represent an effective reaction zone length (or cell length) of the quasi-detonation. At the critical condition of transition from the choking to the quasi-detonation regime, this effective reaction zone length is found to be about twice the normal cell length of the mixture in accordance with Shchelkins stability criterion for a perturbed wave. The minimum open dimension of the channel is found to be of the order of a cell size λ for transition to the quasi-detonation regime in agreement with the previous results of Peraldi17 and Gu8 for rough tubes. Photographic observations of the propagation mechanism in the choking regime reveal the absence of ignition via shock reflection. The placement of wire screens to damp the shock reflections at the channel walls suppresses the transition to quasi-detonations indicating the essential role of shock reflections. It is not clear whether the adiabatic heating or the turbulent vortex mixing associated with the shear layer wall jet by the Mach stem near the wall is the responsible mechanism for re-initiation.

Turbulent jet initiation of detonation

Abstract Experiments have been carried out on the direct initiation of detonation by means of a jet of hot product gases, produced in a constant volume explosion, which is vented into another mixture through an opening. Stoichiometric mixtures of C2H4, C2H2, H2, and C3H8 with oxygen and with different degrees of dilution with nitrogen were used. The initial pressure of the mixtures was 1 atm in all cases. The orifice opening was initially closed by a diaphragm set to rupture at about the peak constant volume explosion pressure of the product gases prior to venting. The results are highly reproducible and the phenomenon is not affected by the fine-scale turbulence generated by the diaphragm fragments. The results suggest that under optimal conditions of initiation there exists a minimum value of the ratio of the orifice diameter d to the cell size λ of the mixture to be detonated. This minimum value d λ is comparable to that for detonation transmission or the critical tube diameter situation (i.e., d λ ⋍ 13 ). However, if the free radical concentration is high, the critical value of d λ at which initiation occurs increases. The effect of orifice geometry on the initiation of detonation is similar to that for detonation transmission. For example, the result for detonation initiation via a square orifice of identical cross-sectional area is about the same as for circular orifice, while rectangular slits are more effective in that detonation in less sensitive mixtures can be initiated. This trend corresponds identically to that observed in our earlier work for detonation transmission through similar orifices.

On the effective energy for direct initiation of gaseous detonations

Abstract The present paper demonstrates that the effective and hence the true critical energy E c for direct initiation of gaseous detonations using electrical sparks corresponds to the total energy deposited into the gas up to the time t f of the peak averaged power, i.e., (E(t) t) max , of the spark. The energy subsequent to this time is found to have no noticeable influence on the initiation processes. The method for demonstrating this experimentally is via the “crowbarred” discharge which was used to initiate cylindrically expanding detonation waves. Almost all previous investigations had implied that the direct initiation process can be characterized by a unique critical value of the source energy where the source energy was invariably taken as the total energy initially stored in the source or its equivalent. The present results indicate that the critical energy E c is non unique but depends on its rate of deposition. It is found that E c increases very rapidly with increasing time of energy deposition t f . Howerver, a minimum limiting value of the critical energy is found to exist as t f →0. The present results, in fact, suggest that the direct initiation process should be characterized by two parameters, namely, the peak power of the source and the energy release up to the peak power. The critical peak averaged power of the source, i.e., P c = E c (t f ) t f , also exhibits a minimum value which corresponds to shock strengths of the order of the autoignition limit for the explosive mixture.

Hydrogen-air detonations

The Three Mile Island nuclear plant accident has triggered renewed interest in fundamental combustion studies in hydrogen-air mixtures. The present study is concerned with the problem of detonation of atmospheric, hydrogen-air mixtures and reports new experimental results on cell sizes lambda and critical tube diameters d/sub c/. The results confirm the empirical correlation d/sub c/ = 13lambda. Comparison of the critical tube diameter of stoichiometric hydrogen-air mixtures (d/sub c/ = 20 cm) with that of stoichiometric acetylene-air mixtures (d/sub c/ = 12 cm) indicates that hydrogen is slightly less sensitive than acetylene. The relatively slow increase in d/sub c/ for H/sub 2/-rich mixtures (as compared to lean mixtures) indicates that fuel-rich mixtures are more hazardous from the detonation point of view than fuel-lean mixtures. Regarding the detonability limits, the present paper formally defines limit criteria for different boundary conditions based on the cell size of the mixture. For fully confined detonations in tubes, limits are set by the onset of single-headed spin.

Effect of geometry on the transmission of detonation through an orifice

Abstract An experimental study has been carried out to investigate the transmission of a planar detonation wave through an orifice into an unconfined medium. Mixtures of 2H 2 + O 2 + βN 2 and C 2 H 4 + 3(O 2 + βN 2 ) for a range of nitrogen concentrations corresponding to 1 ≤ β ≤ 3.76 and at an initial presure of 1 atm were used in the experiments. It is found that the critical diameter for the transmission through an orifice is identical to that for a straight tube and both follow the empirical correlation of d c ≅ 13 λ . The transmission through square, triangular, elliptical, and rectangular orifices has led to the development of a correlation based on the effective diameter similar to the case of circular geometry (i.e., d eff ≅ 13 λ ). The effective diameter is defined as the mean value of the longest and shortest dimensions of the orifice shape. The effective diameter correlation suggests that the criterion for transmission may be based on the mean curvature of the wave front, the implication being that it is not to exceed a certain critical value. The results suggest that local properties in the immediate vicinity of the wave front are the controlling parameters for reinitiation rather than the properties of the gas dynamic flow structure in the wake. Expressions are developed to provide estimates for the critical transmission dimensions for arbitrarily shaped openings. For the two-dimensional limit when one of the characteristic linear dimensions becomes very large compared to the other, it is found that the transmission is based on a critical value for the shorter dimension of the order of 3 times the cell diameter. This result is in accordance with the recent large scale experiments of Benedick in two-dimensional channels of an aspect ratio L.W as large as 35. These observed results can also be successfully explained in terms of the critical wave curvature criterion.

Direct initiation of spherical detonations in gaseous explosives

This paper summarizes the salient results of a recent theoretical and experimental study of the propagation of spherical detonation waves initiated by a laser-induced spark. In this study, theoretical solutions of the blast-wave model were obtained using a novel analytical technique that yields a complete description of the spherical detonation wave from its initial overdriven state to its asymptotic C-J condition. Based on the approximation that hydrodynamic motion is not influenced by chemical reactions, solutions were also obtained for the propagation of spherical blast waves with finite kinetic rates. Three regimes of propagation were established experimentally: the subcritical energy regime, where decoupling of shock and reaction zone occurs; the supercritical energy regime, where the initially overdriven spherical detonation decays asymptotically to its C-J state; and the critical energy regime, where decoupling first occurs followed by the reestablishment of a highly asymmetrical multi-head detonation.