Mathematical model of continuous detonation in an annular combustor with a supersonic flow velocity

A two-dimensional unsteady mathematical model of a continuous spinning detonation wave in a supersonic incoming flow in an annular combustor is formulated. The wave dynamics in a combustor filled by a gaseous hydrogen-oxygen mixture is studied. The possibility of continuous spin detonation with a supersonic flow velocity at the diffuser entrance is demonstrated numerically for the first time; the structure of transverse detonation waves and the range of their existence depending on the Mach number are studied. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 6, pp. 83–91, November–December, 2008.     

Estimation of critical conditions for the detonation-to-deflagration transition

An estimate is proposed for the critical Mach number of the shock wave that can ensure the deflagration-to-detonation transition (DDT): M_min ≈ 0.56M₀ for expanding waves and M_min ≈ 0.33M₀ for plane waves propagating in a constant-section straight tube (M₀ is the Mach number of an ideal Chapman—Jouguet detonation wave). The condition M > M_min ensures the DDT mode, whereas only laminar or turbulent burning without the DDT is observed for lower Mach numbers. The estimate is based on the equiprobable transition from the compressed state of the initial mixture both to the detonation and to the deflagration branch of the adiabat of reaction products (with respect to the initial state of the combustible mixture). __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 91–96, March–April, 2006.     

Numerical study of the reflection of detonation waves from a wedge

The reflection of a nonstationary multifront two-dimensional gas-detonation wave from a wedge is simulated numerically for a 2H₂+O₂ mixture. The value of the critical angle of the wedge at which the regular reflection of the detonation wave becomes Mach reflection is determined forp ₀=0.2 bar. In the case of Mach reflection, it is established for various angles of the wedge that the growth of the Mach stem is not self-similar, i.e., the triple-point trajectory is not a straight line. Numerical analysis shows that the limiting height of the Mach stem depends on the angle of the wedge. The effect of the detonation-cell size and the gradients of the incident-wave parameters on the specific growth of the Mach stem and on the critical angle of the wedge is studied. Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 6, pp. 97–104, November–December 1999.     

Reflection of a bubble-detonation wave from a rigid obstacle

The process of detonation-wave reflection from a rigid obstacle in mono- and polydisperse bubble media is studied experimentally. The evolution of the reflected wave formed upon interaction of the detonation wave with the butt-end of a shock tube is traced. The structure of the detonation and reflected waves is studied and the wave pressures are measured at various parameters of the bubble media. The damping constants of the reflected waves are determined. In addition, the velocities of the detonation and reflected waves are measured. The effect of the gas-bubble size on the characteristics of these waves is investigated. The energy-dissipation mechanisms in the detonation and reflected waves in the bubble media are analyzed qualitatively. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 3, pp. 107–113, May–June, 2000. This work was supported by the Russian Foundation for Fundamental Research (Grant No. 98-03-32325).     

Detonation of a thin explosive layer in evacuated tubes

Detenation of thin layers of dispersed primary and secondary high explosives (HE) on the outer surface of glass and plastic tubes 0.6–3 mm in diameter was examined at an initial air pressure inside the tube of 0.1 MPa to 30 Pa. It is shown that, under these conditions, the air practically does not influence the detonation velocity, which for secondary explosives (PETN, RDX, and HMX), is lower than or approximately equal to the Chapman-Jouguet detonation velocityD _CJ for a homogeneous mixture of the same substances. Experiments with a primary HE (lead azide) revealed regimes with a wave velocity higher thanD _CJ and a varying reaction zone pattern. When tubes containing a layer of a secondary HE were filled with an explosive gas mixture, waves of a hybrid detonation with a velocity both higher and lower than that in the evacuated tubes was observed. In tubes with diameter 2–3 mm, detonation proceeded in a spinning regime over the entire range of the initial pressure and at a velocity higher thanD _CJ. It is concluded that in the evacuated tubes with a thin HE layer on the walls, ignition is transferred by the stream of hot detonation products moving at the head of the detonation wave. Translated fromFizika Goreniya i Vzryva, Vol. 36, No. 4, pp. 56–67, November–December 1998     

Continuous spin detonation of hydrogen-oxygen mixtures. 2. Combustor with an expanding annular channel

A comprehensive numerical and experimental study of continuous spin detonation of a hydrogen-oxygen mixture in an annular combustor with the components supplied through injectors is performed. The hydrogen-oxygen mixture is burned in the regime of continuous spin detonation in an annular combustor 4 cm in diameter with subsequent channel expansion. The flow structure is considered for varied flow rates of the components of the mixture and the counterpressure of the ambient medium. The dynamics of the transverse detonation wave is numerically studied in a two-dimensional unsteady gas-dynamic statement of the problem with the geometric parameters of the combustor consistent with experimental ones. Reasonable agreement with experiments is reached in terms of the shape of detonation fronts, detonation velocity, and height of the wave front. The optimal point of channel expansion beginning is chosen, which ensures the maximum specific impulse in the spin detonation regime. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 3, pp. 95–108, May–June, 2008.     

Effect of a nanosecond gas discharge on deflagration to detonation transition

The possibility of using a high-voltage nanosecond discharge to initiate gaseous detonation was shown experimentally. The experiments were performed with C₃H₈ + 5O₂ and C₃H₈/C₄H₁₀ + 5O₂ + xN₂ (x = 0–10) mixtures at an initial pressure of 0.15–0.6 atm. The discharge was initiated by a voltage pulse of duration ≈60 nsec and amplitude 4–70 kV; the energy input was 0.07–12 J. Under the conditions of the experiment, three flame propagation regimes were observed: slow combustion, transient detonation, and Chapman—Jouguet detonation. For the initiation of the C₃H₈+ 5O₂ mixture in a tube of diameter 140 mm, the length of the deflagration to detonation transition was 130 mm at an initial pressure of 0.3 atm and an initiation energy of 70 mJ. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 2, pp. 80–90, March–April, 2006.     

Two-dimensional cellular structure of a kinetically unstable detonation front

Based on previously published results on the detonation of gaseous and liquid explosives, an explanation is given to the formation of the two-dimensional cellular structure of the detonation front of some gas mixtures undergoing a two-step exothermic transformation at the wave front and suggestions are proposed for the mechanism of development of the two-dimensional cellular structure in the case of detonation transformation of gas mixtures with one-step chemical kinetics. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 4, pp. 80–86, July–August, 2008.     

Continuous detonation in the regime of self-oscillatory ejection of the oxidizer. 1. Oxygen as a oxidizer

Results of an experimental study of continuous spin and pulsed detonation of hydrogen-oxygen and acetylene-oxygen mixtures in a flow-type annular combustor 10 cm in diameter with channel expansion in the regime of oxidizer ejection are presented. Through comparisons with the mechanical analogy of a piston-driven pump, it is found that the detonation wave serves as a pump for the oxidizer, and the rarefaction wave serves as a suction piston. Stable regimes of continuous spin detonation with one transverse wave are observed under the test conditions used; the wave velocity is D = 1.76–1.6 km/sec for hydrogen and D = 1.46–1.2 km/sec for acetylene. The frequency of the pulsed detonation wave is 7.3-5 kHz in the H₂-O₂ mixture and approximately 2.5 kHz in the C₂H₂-O₂ mixture.     

Nonclassical steady-state detonation regimes in pressed TNETB

The reaction zones and the dependence of the velocity of steady-state detonation waves on the initial density of pressed TNETB are studied using a VISAR interferometer. It is shown that, in the range of initial densities of TNETB 1.56–1.77 g/cm³, the propagation of a steady-state detonation wave is possible without the range of elevated pressures (chemical spike) in the reaction zone predicted by the classical theory. The dependence of the detonation velocity on the initial density shows singularities which indicate that a steady-state underdriven regime can occur in this range of initial densities. Based on the well-known theoretical concepts of the hot-spot decomposition mechanism of heterogeneous explosives, it is shown that the possibility of the existence of a steady-state detonation wave without a chemical spike, in particular, underdriven detonation, and the effect of the internal structure of the charge on the detonation regime are explained by the decomposition of explosives at the shock-wave front. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 6, pp. 97–103, November–December, 2007.     

Numerical Study of Formation of a Detonation Wave in a Supersonic Flow over a Wedge by an H2-O2 Mixture with Nonequilibrium Excitation of Molecular Vibrations of Reagents

Specific features of formation of an oblique detonation wave in a supersonic hydrogen-oxygen mixture flow over a plane wedge are analyzed. Preliminary excitation of molecular vibrations of H₂ is shown to lead to a noticeable (severalfold) decrease in the induction-zone length and the distance at which the detonation wave is formed. These effects are manifested even if H₂ molecules are excited in a narrow region in the vicinity of the flow centerline. The reason for these effects is intensification of chain reactions in the H₂-O₂ (air) mixture owing to the presence of vibrationally excited hydrogen molecules in the flow. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 78–86, January–February, 2006.     

Continuous spin detonation of hydrogen-oxygen mixtures. 1. Annular cylindrical combustors

A comprehensive numerical and experimental study of continuous spin detonation of a hydrogen-oxygen mixture in annular combustors with the components supplied through injectors is performed. In an annular combustor 4 cm in diameter, burning of a hydrogen-oxygen gas mixture in the regime of continuous spin detonation is obtained. The flow structure is considered for varied flow rates of the components of the mixture and the combustor length and shape. The dynamics of the transverse detonation wave is numerically studied in a two-dimensional unsteady statement of the problem with the geometric parameters of the combustors consistent with experimental ones. A comparison with experiments reveals reasonable agreement in terms of the detonation velocity and pressure in the combustor. The calculated size and shape of detonation fronts are substantially different from the experimental data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 2, pp. 32–45, March–April, 2008.     

Mathematical modeling of a rotating detonation wave in a hydrogen-oxygen mixture

A two-dimensional unsteady mathematical model of spin detonation in an annular cylindrical ramjet-type combustor is formulated. The wave dynamics in the combustor filled by a hydrogen-oxygen mixture is studied numerically. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 4, pp. 90–101, July–August, 2007.     

Physical model of low-velocity detonation in plasticized HMX

A physical model of low-velocity detonation in plasticized HMX is considered. In this model, a low-velocity detonation wave is a combination of a weak leading shock wave and a subsequent compression wave. This combination is formed by the simultaneous effects of energy release and spreading of the reacting medium. The main features of low-velocity detonation observed in experiments are reproduced in two-dimensional calculations. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 1, pp. 102–112, January–February, 2008.     

Radiographic study of interaction of shock and detonation waves in a high explosive

Collisions of shock and detonation waves in an HMX-based high explosive are experimentally studied with the use of flash radiography. Based on X-ray patterns, specific features of the wave-interaction process are identified, and qualitative differences are found in detonation formation and evolution in an explosive precompressed by a weak shock wave and in an undisturbed explosive. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 3, pp. 132–138, May–June, 2007.     

Effect of the degree of dispersion on the detonation wave structure in pressed TNETB

A VISAR interferometer was used to study the reaction zone in steady-state detonation waves in pressed TNETB at different initial densities (1.23–1.71 g/cm³) and degrees of dispersion (5 and 80 μm) of the initial powdered high explosive (HE). The initial density range in which a pressure rise was observed instead of the theoretically predicted chemical spike is shown to depend on the degree of dispersion of the HE. The unusual change in the parameters in the reaction zone is explained by the heterogeneous structure of pressed HEs, whose decomposition has a local nature and proceeds partially at the compression wave front. A technique for recording wave profiles using LiF windows was developed, which confirmed that all qualitative features observed when using aluminum foils ≈200 μm thick and a water window reliably reflect the detonation wave structure. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 5, pp. 90–95, September–October, 2007.     

Critical conditions for initiation of cylindrical multifront detonation

A quantitative relation between the characteristic scales determining the excitation and propagation of cylindrical and spherical detonation waves is found with the use of a technique for diffraction reinitiation of multifront detonation. The effect of the channel depth on the reinitiation conditions is studied. The ideal character (the smallness of losses) of a cylindrical multifront wave is estimated, and this estimate is found to be in agreement with experimental data. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 2, pp. 114–120, March–April, 1998.     

Detonation waves in interstellar gas

In astronomy there is a large amount of observational data on the phenomenon of sequential star formation from a single molecular cloud. In this process, a cluster of stars of the same generation creates favorable conditions for the formation of stars of the next generation. A star-forming wave whose velocity is estimated to be10–30 km/sec travels over a molecular cloud of interstellar gas. In the present paper, the self-sustained star-formation phenomenon is claimed to have all features of a detonation process and the star-forming wave is treated as a detonation one. The velocities of the detonation and star-forming waves are estimated to be (∼27 km/sec) and (∼13 km/sec), respectively. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Fizika Goreniya i Vzryva, Vol. 33, No. 1, pp. 88–93, January–February, 1997     

Bubble detonation as a self-sustained solitary wave with energy release

Previous experiments have shown that a bubble detonation wave is a resonant or self-sustained solitary wave in a bubble medium. Bubble detonation is modeled by a solitary wave with energy release in bubbles. The equation describing a solitary wave of small amplitude is shown to be an analog of nonlinear Boussinesq equation of the fourth order. A comparison of the solution obtained with averaged experimental pressure profiles shows that the analytical solution is suitable for describing bubble detonation waves with a finite pressure amplitude. In the model proposed, the time of action of solitary-wave compression on a separate bubble is several times the bubble oscillation period. This result agrees with experimental data and confirms the presence of a collective resonant effect in a bubble medium. Satisfactory agreement is obtained between experimental and theoretical data on the pressure profile and extent and velocity of bubble detonation waves. __________ Translated from Fizika Goreniya i Vzryva, Vol. 43, No. 6, pp. 104–111, November–December, 2007.