Weak Detonation Waves Research Articles

Autoignition and combustion wave propagation in a spatial reactivity gradient environment constructed using the shock-converging method

Abstract Studies on autoignition and combustion wave propagation in a spatial reactivity gradient environment constructed using the shock-converging method were conducted to obtain a new understanding of combustion modes and their mutual transition mechanism. Autoignition induced by the converging cylindrical shock wave and weak detonation can be observed by experiment and numerical simulation. Research indicates that for an appropriate spatial reactivity gradient, the velocity of the weak detonation wave can decrease and adjust to the local sound speed. This leads to the transformation of the weak detonation into the self-propagating Chapman-Jouguet (CJ) detonation. The speed of the spontaneous reaction wave characterizing the end of the chemical reaction is never less than the local sound speed; hence, there is no overdriven phenomenon throughout the weak-to-CJ detonation transition. This conforms to the fact that the overdriven phenomenon is not a necessary condition to initiate the detonation, and the combustion has higher thermal efficiency compared with isochoric combustion. Further research indicates that CJ detonation propagating in the preheated reactant can also transform into weak detonation for an appropriate spatial reactivity gradient. The initial CJ detonation degrades into a shock that decays and finally disappears. The wave-eliminating effect of the CJ-to-weak detonation transition can ensure the flow field quality and thermal efficiency of the combustion. In summary, performing a controllable weak detonation between isochoric combustion and CJ detonation in an engine has significant practical importance for improving combustion thermal efficiency and knock suppression.

Experimental research on ignition, quenching, reinitiation and the stabilization process in rotating detonation engine

This paper presents an experimental research on ignition, quenching, reinitiation and the stabilization process in hydrogen-air rotating detonation engine with an array of injection holes. The stabilization process can be divided into six sections, including deflagration, deflagration to detonation transition (DDT) process, coexistence of detonation with deflagration, coexistence of strong & weak detonations, unstable to stable detonation transition and stable detonation. The phenomenon of single-double-single wave transition is found and analyzed for the first time in the experiment. During the transition, the initial strong detonation wave weakens until it disappears, and the weak detonation wave becomes stronger until it propagates steadily. The reinitiation phenomenon is related to the injection pressures of the propellant. Increasing the injection pressure helps to reinitiate, thus avoiding the occurrence of the quenching phenomenon.

Mathematical description of ignition, combustion and propagation of detonation in reacting gas mixtures in the presence of micro- and nanoparticles

The physical and mathematical models for the description of the processes of ignition, combustion and propagation of detonation in mixtures of hydrogen-oxygen, methane-oxygen and silane-air in the presence of inert micro- and nanoparticles were proposed. On the basis of these models the dependencies of detonation velocity deficit vs the size and concentration of inert micro- and nanoparticles were found. Two modes of detonation flows in gas suspensions of reactive gases and inert nanoparticles were revealed: - propagation of weak detonation wave in the gas suspension, - destruction of the detonation process. It was determined that the mechanisms of detonation suppression by micro- and nanoparticles are closed and lies in the splitting of a detonation wave to frozen shock wave and ignition and combustion wave. Concentration limits of detonation were calculated. It turned out that in the transition from microparticles to nanoparticles the detonation suppression efficiency does not increase.

Rotating detonation in a combustor of trapezoidal cross section for the hydrogen–air mixture

Rotating detonation engines are being studied widely because of high thermodynamic efficiency and high specific impulse. The combustors studied before were annular or hollow cylinders. Here, a combustor of annular trapezoidal cross section is numerically studied for the first time. The transient density-based solver with explicit formulation, the laminar finite-rate model with one step reaction and the standard k-epsilon model with standard wall functions are used. Numerical results show that reflected shock waves, explosions and new detonation waves occur near the corners of the combustor, but they do not stop the continuous propagation of the rotating detonation wave. Reactant gap of low temperature tends to intrude into weak detonation waves. Transverse waves move back and forth between the inner and outer walls due to the unsteady heat release along the detonation wave front. The unsteady heat release is mainly caused by the collisions between the detonation and corners. Since the detonation can pass the corners of right, acute and obtuse angles, it may be concluded that a detonation combustor of any convex polygon section is feasible. Thus, the study helps to design many new structures for rotating detonation engines, such as rectangle, rhombus, or trapezoid cross section.

Stability of Viscous Weak Detonation Waves for Majda’s Model

Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a simplified model for gas-dynamical combustion. Combining these new spectral stability results with the pointwise Green function analysis of Lyng, Raoofi, Texier, & Zumbrun [22], we conclude that these waves are nonlinearly stable. The principal novelty of this analysis is the treatment of weak detonation waves. In contrast to the case of strong detonation waves, weak detonation waves are undercompressive and the stability of these waves is delicate and has not been treated by standard weighted-norm techniques. The present analysis thus provides a case study illustrating the flexibility and power of the Evans-function- based approach to stability. As in the case of strong detonations, we find that all tested waves are spectrally stable, hence nonlinearly stable.

Ignition and combustion of disperse and nanodisperse gas suspensions under dynamic conditions

Results of mathematical modeling of propagation of heterogeneous detonation waves in a mixture of fine aluminum particles in oxygen and ignition of fine metal particles in reflected and transmitted shock waves and high-temperature gas flows, which were obtained at the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, are briefly reviewed. One-dimensional steady flows and one-dimensional and two-dimensional unsteady flows of reactive mixtures are considered. Flows in the form of weak and overdriven detonation waves and the Chapman-Jouguet detonation are found. Stability of the Chapman-Jouguet flow and weak detonation to interactions with rarefaction waves is demonstrated. Regimes of strong and weak initiation are determined; the calculated and experimental values of the initiation energy are found to be in reasonable agreement. Laminar detonation and cellular detonation for monodisperse and polydisperse mixtures are found within the framework of two-dimensional unsteady detonation flows. New numerical codes are developed for solving nonlinear-boundary-value problems of ignition of individual particles. Particular attention is paid to the accuracy of reproduction of integral parameters (burning time) of some experimental data, depending on the ambient temperature, etc. A solution of a single-phase Stefan problem of nanosized particle melting is described.

Structure of shock wave for a viscous combustion model

In this article, the existence of weak and strong detonation waves for a viscous combustion model is proved. In order to prove the existence of this kind of waves, it is necessary to consider a 3-dimensional system of ordinary differential equations and prove the existence of heteroclinic orbits of it. In order to prove this, topological arguments are mainly tools.

Ignition of thermally sensitive explosives between a contact surface and a shock

The dynamics of ignition between a contact surface and a shock wave is investigated using a one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing and contrasting the solutions with those of the ignition process between a piston and a shock, considered previously. The large activation energy asymptotic solutions are found to be qualitatively different from the piston driven shock case, in that thermal runaway first occurs ahead of the contact surface, and both forward and backward moving reaction waves emerge. These waves take the form of quasisteady weak detonations that may later transition into strong detonation waves. For the finite activation energies considered in the numerical simulations, the results are qualitatively different to the asymptotic predictions in that no backward weak detonation wave forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance of the contact surface. The above conclusions are relevant to gas phase equation of state models. However, when a large polytropic index more representative of condensed phase explosives is used, the large activation energy asymptotic and finite activation energy numerical results are found to be in quantitative agreement.

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.

A stability index for detonation waves in Majda’s model for reacting flow

Using Evans function techniques, we develop a stability index for weak and strong detonation waves analogous to that developed for shock waves in [SIAM J. Math. Anal. 32 (2001) 929; Commun. Pure Appl. Math. 51 (7) (1998) 797], yielding useful necessary conditions for stability. Here, we carry out the analysis in the context of the Majda model, a simplified model for reacting flow; the method is extended to the full Navier–Stokes equations of reacting flow in [G. Lyng, One dimensional stability of detonation waves, Doctoral Thesis, Indiana University, 2002; G. Lyng, K. Zumbrun, Stability of detonation waves, Preprint, 2003]. The resulting stability condition is satisfied for all nondegenerate, i.e., spatially exponentially decaying, weak and strong detonations of the Majda model in agreement with numerical experiments of [SIAM J. Sci. Statist. Comput. 7u (1986) 1059] and analytical results of [Commun. Math. Phys. 204 (3) (1999) 551; Commun. Math. Phys. 202 (3) (1999) 547] for a related model of Majda and Rosales. We discuss also the role in the ZND limit of degenerate, subalgebraically decaying weak detonation and (for a modified, “bump-type” ignition function) deflagration profiles, as discussed in [SIAM J. Math. Anal. 24 (1993) 968; SIAM J. Appl. Math. 55 (1995) 175] for the full equations.

Convergence of a finite difference method for combustion model problems

We study a finite difference scheme for a combustion model problem. A projection scheme near the combustion wave, and the standard upwind finite difference scheme away from the combustion wave are applied. Convergence to weak solutions with a combustion wave is proved under the normal Courant-Friedrichs-Lewy condition. Some conditions on the ignition temperature are given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Convergence to strong detonation wave solutions for the random projection method is also proved.

Finite difference method for a combustion model

We study a projection and upwind finite difference scheme for a combustion model problem. Convergence to weak solutions is proved under the Courant-Friedrichs-Lewy condition. More assumptions are given on the ignition temperature; then convergence to strong detonation wave solutions or to weak detonation wave solutions is proved.

Chapman-Jouguet Oblique Detonation Structure Around Hypersonic Projectiles

How to generate a steady-state detonation around a hypersonic projectile in stoichiometric hydrogen-oxygen premixed gases is studied. The speed of the hypersonic projectiles was beyond the Chapman ‐Jouguet(C‐J) detonation speed. The e owe eld around the projectile was visualized by using a gate intensie ed charge-coupled device camera(single-frame schlieren picturesand OHradical self-emissionimages ). Threeparameters are varied:1 ) the projectile e ight length from diaphragm rupture location, 2 )the initial pressure of mixture below/above the critical pressureforsteady detonation initiation around a hypersonicprojectile, and3 )theprojectilespeed.Atthepressure condition below the criteria, the detonation structure is composed of three different shock and detonation waves, which appear just after a diaphragm rupture and evolve in time: an overdriven bow detonation wave, a strong detonation wave, and a diffracted shock wave. Their propagation after diaphragm rupture is investigated, and it is found that the C ‐J detonation wave moved away from the projectile and only a reactive bow shock wave remained around projectile far away from the diaphragm. At the pressure condition above the criteria, a steady oblique detonation wave was generated around the projectile as soon as the projectile broke the diaphragm. In this steady-state detonation-wave case, with respect to the e ow Mach number behind the wave front, the whole detonation wavewas divided into fourparts: 1 )strong overdriven detonation wave, 2 ) weak overdriven detonation wave, 3) quasi-C‐J detonation wave, and 4 ) C‐J detonation wave. It has been found that a rarefaction wave is generated at the projectile shoulder and that curvature of the wave has a signie cant effect on the structure of the detonation wave.

Detonatlve travelling waves for combustions

The existence of travelling wave solution to equations of a viscous heat conducting combustible fluid is proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas. Instead of assuming the ideal gas conditions we consider a general thermodynamics which is described by a fairly mild set of hypotheses. Travelling waves for detonations reduce to specific heteroclinic orbits of a discontinuous system of ODE's. The existence proof for heteroclinic orbits corresponding to weak and strong detonation waves is carried out by some general topological arguments in ODE. The uniqueness and nonuniqueness of these waves are also considered.

Experimental study of interaction between oblique detonation wave and rarefaction wave around a hypersonic free projectile

Hypersonic projectiles whose speed was beyond the Chapman-Jouguet (C-J) detonation speed, were fired into stoichiometric hydrogen-oxygen premixed gases. The flowfield around the projectile was visualized using a gated CCD camera. A steady-state detonation wave was generated around the projectile. With respect to the flow Mach number behind the wave front, the whole detonation-wave was partitioned into four parts; (i) strong overdriven detonation wave, (ii) weak overdriven detonation wave, (iii) quasi C-J detonation wave, and (iv) C-J detonation wave. It has been found that a rarefaction wave generated at the projectile shoulder has a significant effect on the structure of the detonation wave.

Nonlinear Stability of Weak Detonation Waves¶for a Combustion Model

We show that the weak detonation waves for a combustion model of Rosales–Majda are nonlinearly stable. Because of the strongly nonlinear nature of the wave, usual stability analysis of weakly nonlinear nature does not apply. The chemical switch on-off is the main feature of nonlinearity. In particular, the propagation of the wave depends sensitively on the tail behaviour of the flow in front of it. Unlike the strong detonation waves, a weak detonation is supersonic and there is the separation of the gas waves from the reacting front. As a consequence, the reacting front needs to be traced.

Dynamics and Stability of a Weak Detonation Wave

One dimensional weak detonation waves of a basic reactive shock wave model are proved to be nonlinearly stable, i.e. initially perturbed waves tend asymptotically to translated weak detonation waves. This model system was derived as the low Mach number limit of the one component reactive Navier-Stokes equations by Majda and Roytburd [SIAM J. Sci. Stat. Comput. 43, 1086–1118 (1983)], and its weak detonation waves have been numerically observed as stable. The analysis shows in particular the key role of the new nonlinear dynamics of the position of the shock wave, The shock translation solves a nonlinear integral equation, obtained by Green's function techniques, and its solution is estimated by observing that the kernel can be split into a dominating convolution operator and a remainder. The inverse operator of the convolution and detailed properties of the traveling wave reduce, by monotonicity, the remainder to a small L1 perturbation.

極超音速飛行体近傍に発生する定常斜めデトネーション波の構造

Hypersonic projectiles, whose speed was beyond the Chapman-Jouguet (C-J) detonation speed, were fired into stoichiometric hydrogen-oxygen premixed gases. The flowfield around the projectile was visualized using a gated CCD camera. Around the projectile, a steady-state detonation wave was generated. With respect to the flow Mach number behind the wave front, the whole detonation-wave was partitioned into four parts; (i) strong overdriven detonation wave, (ii) weak overdriven detonation wave, (iii) quasi C-J detonation wave, and (iv) C-J detonation wave, It has been found that a rarefaction wave delivered from the projectile shoulder has a significant effect on the structure of the detonation wave.

A numerical study of the Riemann solutions for gasdynamic combustion

The effects of viscosity v and reaction rate k on the Riemann solutions of Navier-Stokes equations for a reacting gas are analyzed numerically. In this numerical experiment, a set of Riemann initial values is designed, such that only detonation can occur under the classical Chapman-Jouguet (CJ) theory. Based on the set of Riemann initial values, a family of solutions is computed corresponding to different values of reaction rate k and viscosity v. Furthermore, the structure of the limit solution, as k → +∞, v → 0, is studied. Our results show that the structure of the limit solution depends on the parameter C = kv. The strong, CJ detonation and weak detonation waves are all possible to appear.

Wave angle for oblique detonation waves

The flow field associated with a steady, planar, oblique detonation wave is discussed. A revision is provided forβ-θ diagrams, whereβ is the wave angle andθ is the ramp angle. A new solution is proposed for weak underdriven detonation waves that does not violate the second law. A Taylor wave, encountered in unsteady detonation waves, is required. Uniqueness and hysteresis effects are also discussed.