Normal Detonation Research Articles

Two-Gamma Jump Relations for Gaseous Detonation Waves

Accurate jump relations for Chapman-Jouguet (CJ) and overdriven gaseous detonation waves are derived. The difficulty in accurately approximating the energy equation in a perfect gas two-gamma detonation jump formulation is resolved by adjusting the authentic combustion heat release in terms of linearly approximated up- and down-stream sensible enthalpies at the CJ condition where it is exactly satisfied for CJ and well approximated for overdriven waves. The basis of the success of the derived two-gamma jump relations is explained. Explicit thermodynamic jump relations across a normal detonation wave are obtained. These approximate jump relations depend on the following four parameters: γ upstream isentropic exponent (or the gamma giving pertinent upstream sound speed for defining Mj); γJ, CJ isentropic exponent (or the gamma giving pertinent sound speed for a CJ state); Mj upstream Mach number; and MJ, CJ Mach number. γJ and Mj can be obtained numerically, or experimentally with the derived jump relations. Comparisons of exact numerical and the present approximate calculation for jump conditions of CJ and overdriven detonations for methane- and hydrogen-oxygen systems show excellent agreement over a wide range of upstream Mach number, temperature, pressure, and mixture conditions.

The Normal Detonation Shock Velocity–Curvature Relationship for Materials with Nonideal Equation of State and Multiple Turning Points

We present a model and a simple-to-implement numerical procedure that obtains the normal detonation shock velocity (Dn)–curvature (κ) relationships for an explosive material with nonideal equation of state and an arbitrary reaction rate law. In addition we illustrate numerically (for a nonideal equation of state) and analytically (for an ideal equation of state with a large activation energy rate law) that for sufficient rate-state–sensitive explosives, the corresponding Dn, κ-response curve can have two turning points, at Dn, κ,-pairs [(Dn)1, κ1], [(Dn)2, κ2], such that κ1 > κ2 > 0 for DCJ ≥ (Dn)1 ≥ (Dn)2, and such that the curve has a Z-shape. The top branch of the Z response curve has been previously associated with detonation extinction at a critical curvature. The bottom branch can be possibly associated with low-velocity detonation and rapid change from low-order detonation to high-order.

On Deflagration-to-Detonation Transition

A reduced model for the reactive gas flow in a tube is proposed, where the nonlinear effects are discarded everywhere but in the reaction rate term. While ruling out the formation of shock-waves the model transpires to be rich enough to cover detonation-like phenomena with the sound waves acting as a driving agency. It is shown that depending on the ignition conditions, the detonation wave is evoked either immediately or gradually emanates from the low velocity deflagration by virtue of friction between the burning gas and the tube walls. At sufficiently strong friction the normal near-sonic detonation is found to undergo a hysteresic transition to a low speed quasi-detonation dominated by dissipative effects.

Detailed flowfields of a RAMAC device in H2−O2 full chemistry

Numerical simulations of a RAMAC device were performed for a range of speeds and grid densities. For certain initial conditions the detonation was unstable and propagated ahead of the projectile in a normal detonation wave, similar to the experimental phenomenon of unstart. The unstart was observed to develop within the narrow space between projectile and tube wall (the throat), so we focus on that area. Detailed flowfield views of the throat reveal a separated flow rotating in one large vortex. The detonation is overdriven but steady for fast enough upstream velocities. The vortex has an important role in triggering off the unstart by creating a condition at the throat whereby the detonation can propagate against the flow.

Approximate calculation of the parameters of one-dimensional deflagration for an arbitrary velocity of the flame front

Analytical dependences are obtained which allow one to determine with high accuracy the distribution of all flow parameters for one-dimensional deflagration of gas mixtures with an arbitrary propagation velocity of the flame front up to the normal detonation regime.

On the dynamics of multi-dimensional detonation

We present an asymptotic theory for the dynamics of detonation when the radius of curvature of the detonation shock is large compared to the one-dimensional, steady, Chapman-Jouguet (CJ) detonation reaction-zone thickness. The analysis considers additional time-dependence in the slowly varying reaction zone to that considered ill previous works. The detonation is assumed to have a sonic point in the reaction- zone structure behind the shock, and is referred to as an eigenvalue detonation. A new, iterative method is used to calculate the eigenvalue relation, which ultimately is expressed as an intrinsic, partial differential equation (PDE) for the motion of the shock surface. Two cases are considered for an ideal equation of state. The first corresponds to a model of a condensed-phase explosive, with modest reaction rate sensitivity, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, the first normal time derivative of the normal shock velocity, Dn, and the shock curvature, K. The second case corresponds to a gaseous explosive mixture, with the large reaction rate sensitivity of Arrhenius kinetics, and the intrinsic shock surface PDE is a relation between the normal detonation shock velocity, Dn, its first and second normal time derivatives of the normal shock velocity, Dn, Dn, and the shock curvature, K, and its first normal time derivative of the curvature, k. For the second case, one obtains a one-dimensional theory of pulsations of plane CJ detonation and a theory that predicts the evolution of self-sustained cellular detonation. Versions of the theory include the limits of near-CJ detonation, and when the normal detonation velocity is significantly below its CJ value. The curvature of the detonation can also be of either sign, corresponding to both diverging and converging geometries.

95/04327 On the normal detonation shock velocity-curvature relationship for materials with large activation energy

95/04327 On the normal detonation shock velocity-curvature relationship for materials with large activation energy

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 angleθ 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 angleθ 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.

On the normal detonation shock velocity-curvature relationship for materials with large activation energy

We derive the normal detonation shock velocity-curvature relation for a near-Chapman-Jouguet detonation, for an explosive material with Arrhenius kinetics and a large activation energy. Large activation energy asymptotics are used to develop an explicit exponential formula relating the shock curvature κ to the normal detonation shock speed, D n. In this case, the D n- κ relation is multivalued and has a turning point with a critical curvature κ cr such that for κ > κ cr, the possibility of detonation extinction arises. The asymptotic formula is in excellent agreement with the exact solution found by a numerical shooting procedure.

H2-air and CH4-air detonations and combustions behindoblique shock waves

Two stoichiometric reactive mixtures (H 2 -air and CH 4 -air) at initial conditions of temperature and pressure, T 0 =293 K and p 0 <1 bar, respectively, very different from the point of view of their detonability, are used in order to study the conditions of the onset of combustion and/or detonation when submitted to the action of an oblique shock wave (OSW) at Mach number M of about 6 and at various angles of inclination θ. Generation of an OSW in the reactive mixture at rest is obtained via lateral expansion of the detonation products of a normal CJ detonation wave propagating in a bounded gaseous detonable mixture separated from the mixture under test by a 6- μ m-thick mylar film. Different steady combustion regimes are observed depending on θ and on the reactive mixture. Based on simple polars analysis, the possibility of observing an oblique detonation wave (ODW) are checked for the two mixtures. In the case of H 2 -air mixtures, ODWs are obtained with small degrees of overdrive ( D/D CJ ) (≊1) ofthe detonation (where D is the normal detonation velocity of the ODW) after a predetonation zone, where the OSW is followed by an oblique flame initiated at the beginning of the interaction between the two media. Minimal conditions for detonative combustion are deduced, which correspond to a postshock temperature T s ≊1000 K while the minimal condition for combustion as an oblique flame behind the OSW is T s ≊800 K. For CH 4 -air mixtures, no detonation appears even when the degree of overdrive of the theoretically possible solutions of stable ODW is increased up to 1.1 and beyond for T s up to 1480 K. Only the OSW and oblique flame configuration are observed. For T s <1000 K, no combustion occurs behind the shock wave. Thus, this mixture appears to be especially difficult to detonate.

Critical diameter for the transmission of a detonation wave into a porous medium

An experimental investigation has been undertaken to elucidate the existence of a critical diameter forthe transmission of gaseous detonation into a porous medium. A Chapman-Jouguet (CJ) detonation is first established in a tube and allowed to transmit through an orifice plate into a porous medium comprised of inert spheres of equal diameter. It is found that detonation can successfully transmit past the orifice for diameters much smaller than the normal critical diameter (dc) of the mixture. An immediate transition from detonation to quasi-detonation normally takes place upon wave entry in the porous medium. Failure of detonation is observed to take place downstream of the orifice in the near-limit regime and is followed by deflagration to detonation transition (DDT) within the porous medium. Wave velocities in the porous medium are found to be identical to the corresponding values measured for direct transmission (without an orifice). For subcritical conditions, there is complete quenching of combustion in the pores. The critical composition (lean and rich) for mixtures with high activation energy is found to be practically the same as the propagation limits in the porous medium without an orifice. This indicates that the phenomenon is governed by the smallest physical dimension of the pore size, and thus a local failure mechanism exists. In mixtures highly diluted with argon, i.e., (C2H2−O2)+75% Ar, which have a lower activation energy and for which the “dc=13λ” correlation (where λ is the cell size) is known to break down, the critical composition appears to depend on the orifice diameter. The orifice now introduces a larger controlling length scale at the limits compared to the pore size, indicating that a global failure mechanism may prevail for such mixtures. Present findings are consistent with a local and global failure mechanism for normal detonation failure recently proposed by Lee.

Measurements of normal detonation wave structure using Rayleigh imaging

Normal detonation waves have been studied using Rayleigh scattering to obtain two-dimensional density images surrounding the wave front. The detonations were generated in mixtures of H 2 , O 2 and Ar with [O 2 ]/[Ar] held at 0.21/0.79, equivalence ratios varying between 0.6 and 1.4 and initial pressures set between .272 and .578 atm. The fourth harmonic of a Nd:YAG laser provided a pulsed sheet, of UV laser light which cut through the detonation wave front as it traversed the test section to generate the Rayleigh scattering. An intensified CID camera was used to acquire and image the resulting signals. Schlieren images were acquired simultaneously for comparison. Cellular structure was clearly visible in the images and cell sizes have been correlated with detonation parameters for comparison with measurements and analyses by earlier investigators. The progression of wave front structure could be understood by observing images which were each acquired from different runs and at random times in the wave front development. Rayleigh signal ratios, comparing reactant and product densities were quantified at various locations within the wave front. They were compared with calculated values based on shock theory and equilibrium analysis and were found to be in good agreement.

Spin wave and attenuation of liquid explosive detonation

The detonation of nitromethane and a dinitrotoluene solution in bistrinitroxyethylnitramine when the diameter of the cylindrical charge is close to the critical was investigated with the aid of high-speed photography of the luminosity of the lateral and end cylinder surfaces and the recording of the spin wave surface using sampling plates with an air gap. It was discovered that the appearance of penetrating spinning absence-of-reaction waves, which are responsible for the attenuation of liquid explosive detonation, is closely related to the spread of detonation spin waves over the charge surface (or immediately below it). The spin waves, which are instrumental in the propagation of a normal detonation in weakly heterogeneous cast charges consisting of trotyl-hexogene and trotyl-PETN, in the case of liquid explosives probably inhibit the detonation process by inducing the formation of penetrating absence-of-reaction spin waves. It is shown that the spin wave velocity corresponds to the degree of material compression in the near-surface layer, as calculated according to the Dremin-Trofimov model (it can be only slightly above it.)

Morphology of standing oblique detonation waves

Proposals have been made to utilize stabilized oblique detonation waves (ODWs) for the propulsion of hypersonic air-breathing vehicles and hypervelocity mass launchers. There exists hypersonic flight regimes where premixing of fuel and air may be desirable or unavoidable due to finite chemical induction times. Consequently, it is essential to understand under what conditions detonations may occur in order to design supersonic combustors to either avoid or utilize them efficiently. A theoretical analysis is made of supersonic flow of a combustible gas mixture past a wedge or an inclined wall, which shows that, for approach velocities roughly 25% or more greater than the Chapman-Jouguet velocity of the reactant mixture, there exists a usefully wide range of turning angles within which ODWs may be attached or stabilized. For smaller wedge angles, either an incomplete ODW, shock-induced combustion, or no combustion at all may ensue. For larger wedge angles, the wave will detach and form an overdriven normal detonation or normal shock-induced combustion wave immediately upstream of the stagnation point, decaying off axis to either a single oblique Chapman-Jouguet wave, or bifurcating to form an oblique shock followed by a shock-induced deflagration.

Normal detonation regimes in relaxing media

Normal detonation regimes in relaxing media

Diffraction and transmission of a detonation into a bounding explosive layer

The results of an experimental and analytical study of the propagation of a gaseous detonation past a bounding explosive layer are presented. Two adjacent 1.6 cm square detonation tubes, separated at the test section by a 50 nm thick cellulose film, were used to observe the interaction which occurs when a normal detonation in the primary gas comes into contact with a bounding explosive mixture. A pulsed argon ion laser and a high speed camera system were used to obtain Schlieren framing photographs of the interacting waves at 2μ sec intervals with an exposure time of 12 ns. Wave velocities and the pressure variation behind the incident detonation and the wave induced in the bounding gas were also determined. Experiments were made using a stoichiometric H 2 −O 2 mixture as the primary explosive, and using H 2 −O 2 mixtures with equivalence ratios ranging from 0.15 to 4.5 for the secondary bounding explosive. At the first instant of contact a bubble or blast wave was observed to propagate into the secondary explosive, and in some cases a micro-explosion in this bubble led to almost instant transition to oblique detonation. Otherwise an oblique shock is induced in the bounding explosive which is reflected from the shock tube wall. As the equivalence ratio of the bounding mixture increases, the reflection of the induced oblique shock changes from a regular to a Mach reflection, and in many cases a detonation is initiated behind the reflected wave. Shock polar analysis was used to compute the details of the interaction at the interface between the primary and secondary explosives. A simplified method for rapid computation of oblique detonation polars was developed for this purposes, and used to compute the conditions behind the induced oblique detonations and shock waves. There was good agreement between computed and measured shock angles; but computed oblique detonation angles, while showing the proper variation with the equivalence ratio, were always lower than the observed values. Calculation of induction lengths indicated that initiation was only possible behind reflected oblique shocks in agreement with experimental observation.

Thermodynamic calculation of ideal and nonideal detonation

A method has been proposed for calculating ideal and nonideal detonation, the thermodynamic basis of which is the method of characteristic function extrema, with the integral equations of conservation of the hydrodynamic model of steady-state flow of a continuous medium supplemented by the Chapman-Jouguet condition in the form of a minimum in normal detonation rate.

Structure of the stationary zone and relaxation instability of a detonation wave in heterogeneous media

The authors consider the two-phase detonation of mixtures of a gas and condensed particles. A rule is formulated for selecting the velocity of the normal detonation, and the authors determine the Jouget point and the qualitative structure of the normal and supercompressed waves, depending on the relation between the characteristic heat-generation time, the particle heating time, and the relaxation time of the relative velocity of the phases.

Detonation in a relaxing gas

One-dimensional steady-state detonation has been theoretically investigated in a gas with internal degrees of freedom (not directly related to irreversible energy release) characterized by a finite relaxation time τ. Relaxing gas is a variant of a system with sound speed dispersion. Detonation in such a system has been studied in detail by Kirkwood and Wood, who have pointed out the difficulties in formulating the Chapman-Jouguet (C-J) condition in such a medium. Self-sustaining (normal) and strong detonations for an arbitrary α  τ τ Q (where τ Q is the characteristic heat release time) have been determined, using an ideal gas with relaxing vibrational energy of molecules. The “topology” of continuous (in α) evolution of normal and strong detonations in the p- ν (pressure and specific volume of gas) plane has been determined with varying α. For normal detonations two values α ∗ and α ∗∗ < α ∗ , both of the order of unity, have been found to exist such that for the equilibrium C f and frozen cf sound speeds and for gas velocity u relative to the detonation wave at the Jouguet point, we have u = c f if c f > α ∗, c f > u > c e if α ∗ > α > α ∗∗, and u c e if α < α ∗∗ . The steady detonation wave zone has been matched with the rarefaction wave. The C-J condition has been generalized and a procedure has been described for calculating the parameters at the Jouguet point and the normal detonation velocity in a real gas mixture with relaxation.

Loss of detonational stability in elongated charges

This article presents some experimental results for the features of the stability loss of detonation waves in elongated charges of heterogeneous condensed media of various classes. Detonation was initiated by plane-wave shock-wave generators separated from the basic charge by inert barriers and by plane, spherical, and cylindrical charges of initiating explosives in direct contact with the explosive of the basic charge. The influence of the initiation conditions (conditions of overcompression, undercompression, normal detonation) and also the compositions of the basic-charge material on the stability-loss length of the detonation waves was investigated. The character of the stability loss of the detonation wave with a steady front and the distance at which this wave is converted to a wave with a pulsating front depend on the composition of the materials and the properties of their components, and does not depend on the means and conditions of initiation. The results indicate that detonation waves may lose stability at distances exceeding the value required by the stationarity and stability condition.