Detonation Stability Research Articles

Fuel detonation stability and authenticity and a method for measuring them

A new index is proposed in order to estimate the detonation stability of fuels, i.e., a combined detonation index depending on their electrophysical parameters. The real part of the index determines fuel detonation stability, and the imaginary part determines authenticity (corresponding to the standard). Relationships are studied between fuel octane and cetane numbers with the proposed indices. A block diagram of an instrument is provided for measuring these properties.

Stabilization of detonation for any incoming mach numbers

Stability of rotating detonation with different velocities of the incoming mixture in a combustion chamber consisting ot two coaxial cylinders is studied experimentally and theoretically. The detonation is demonstrated to stabilize at velocities both higher and lower than the Chapman-Jouguet detonation velocity.

Numa Manson on velocity deficits and detonation stability

This memorial paper pays tribute to Professor Numa Manson’s contributions to the understanding of detonation velocity deficits and wave stability. Manson and his colleague Guenoche postulated that a velocity deficit exists in a tube because the chemical reactions are inhibited in a thin layer adjacent to the tube walls. The hydrodynamic theory of detonation was modified to account for this, and it was shown that the deficit varies inversely with the tube diameter. Manson and his students measured detonation velocities in tubes of various diameter. An estimate of the detonation velocity for an infinite tube diameter was obtained by plotting the velocity against the reciprocal of the tube diameter, \({\phi^{-1}}\) , and extrapolating the line through the data to \({\phi^{-1}=0}\) . The relative contributions of tube geometry and surface roughness to the deficits were systematically studied. Manson was also one of the early investigators to shed light on the cellular structure of detonation by reporting “vibratory phenomena” seen as striations in streak schlieren photographs. An attempt was made to relate this phenomenon to “dispersions” in the propagation velocity and hence the wave stability. The author has extended Manson’s work by investigating detonations in tubes with yielding walls. Whereas boundary layers were responsible for the gasdynamic expansion and deficits in Manson’s rigid tubes, it was the moving boundaries that caused similar effects in the author’s investigations. The author has repeated the “nozzle” analysis of Fay and Dabora using the detonation cell length as the relevant chemical kinetic length scale, and found reasonable agreement between his experimental results and the model. When the Poitiers data are reinterpreted in light of the modified model, the trends are described quite well. More recent studies have shown that the measured deficits for mixtures characterized by irregular cellular structures do not agree with the Fay–Dabora model. Possible reasons for the discrepancy are discussed.

Stability of detonations for an idealized condensed-phase model

The stability of travelling wave Chapman–Jouguet and moderately overdriven detonations of Zeldovich–von Neumann–Döring type is formulated for a general system that incorporates the idealized gas and condensed-phase (liquid or solid) detonation models. The general model consists of a two-component mixture with a one-step irreversible reaction between reactant and product. The reaction rate has both temperature and pressure sensitivities and has a variable reaction order. The idealized condensed-phase model assumes a pressure-sensitive reaction rate, a constant-γ caloric equation of state for an ideal fluid, with the isentropic derivative γ=3, and invokes the strong shock limit. A linear stability analysis of the steady, planar, ZND detonation wave for the general model is conducted using a normal-mode approach. An asymptotic analysis of the eigenmode structure at the end of the reaction zone is conducted, and spatial boundedness (closure) conditions formally derived, whose precise form depends on the magnitude of the detonation overdrive and reaction order. A scaling analysis of the transonic flow region for Chapman–Jouguet detonations is also studied to illustrate the validity of the linearization for Chapman–Jouguet detonations. Neutral stability boundaries are calculated for the idealized condensed-phase model for one- and two-dimensional perturbations. Comparisons of the growth rates and frequencies predicted by the normal-mode analysis for an unstable detonation are made with a numerical solution of the reactive Euler equations. The numerical calculations are conducted using a new, high-order algorithm that employs a shock-fitting strategy, an approach that has significant advantages over standard shock-capturing methods for calculating unstable detonations. For the idealized condensed-phase model, nonlinear numerical solutions are also obtained to study the long-time behaviour of one- and two-dimensional unstable Chapman–Jouguet ZND waves.

The evolution and cellular structure of a detonation subsequent to a head-on interaction with a shock wave

This paper analyzes the results of a head-on collision between a detonation and a planar shock wave. The evolution of the detonation cellular structure subsequent to the frontal collision was examined through smoked foil experiments. It is shown that a large reduction in cell size is observed following the frontal collision, and that the detonation cell widths are correlated well with the chemical kinetic calculations from the ZND model. From chemical kinetic calculations, the density increase caused by shock compression appears to be the main factor leading to the significant reduction in cell size. It was found that depending on the initial conditions, the transition to the final cellular pattern can be either smooth or spotty. This phenomenon appears to be equivalent to Oppenheim's strong and mild reflected shock ignition experiments. The difference between these two transitions is, however, more related to the stability of the incident detonation and the strength of the perturbation generated by the incident shock.

Pointwise Green function bounds and stability of combustion waves

Generalizing similar results for viscous shock and relaxation waves, we establish sharp pointwise Green function bounds and linearized and nonlinear stability for traveling wave solutions of an abstract viscous combustion model including both Majda's model and the full reacting compressible Navier–Stokes equations with artificial viscosity with general multi-species reaction and reaction-dependent equation of state, under the necessary conditions of strong spectral stability, i.e., stable point spectrum of the linearized operator about the wave, transversality of the profile as a connection in the traveling-wave ODE, and hyperbolic stability of the associated Chapman–Jouguet (square-wave) approximation. Notably, our results apply to combustion waves of any type: weak or strong, detonations or deflagrations, reducing the study of stability to verification of a readily numerically checkable Evans function condition. Together with spectral results of Lyng and Zumbrun, this gives immediately stability of small-amplitude strong detonations in the small heat-release (i.e., fluid-dynamical) limit, simplifying and greatly extending previous results obtained by energy methods by Liu–Ying and Tesei–Tan for Majda's model and the reactive Navier–Stokes equations, respectively.

State of Detonation Stability Theory andIts Application to Propulsion

We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of primary importance and is largely unexplored, hence we point to possible areas of research both theoretical and numerical, that might help improve our understanding of detonation behavior in propulsion devices. We outline the basic formulation of detonation stability theory that starts from linearized Euler equations, describe the algorithm of solution, and present an example that illustrates typical results.

A detonation stability formulation for arbitrary equations of state and multi-step reaction mechanisms

A general normal-mode linear stability formulation of steady planar detonation waves is presented that is valid both for an arbitrary equation of state and for multi-step, multi-species chemical kinetics. The general formulation can be used for many purposes, including an examination of gaseous detonation stability with complex reaction kinetics in which the individual reacting species have variable thermochemical properties. In the present paper, we consider two cases that could not be obtained by previous one-step chemistry, polytropic gas formulations: the first concerns the effect of a difference in heat capacities between product and fuel species, as well as a possible mole change, in a single-step irreversible reaction. The second examines the effects of exothermic or endothermic heat release/absorption in the chain-initiation stage of a model three-step reaction.

Numerical Study of Detonation Stabilization by Finite Length Wedges

A numerical study is conducted of the interaction between the leading oblique detonation wave stabilized by a wedge ramp of finite length and the expansion waves generated by the sudden deflection of the wedge surface. The two-dimensional Euler equations for a reactive gas mixture are solved using a cell-centered finite volume technique on unstructured meshes. Mesh refinement and coarsening techniques are used to concentrate the computational volumes in regions of interest of the flowfield. A detailed chemical kinetic mechanism is employed to describe the combustion process in the mixtures of hydrogen and air considered. Computational results show that a Chapman‐ Jouguet oblique detonation wave is obtained for intermediate wedge angles within the range of stable detonations. For wedge angles near to the maximum angle that supports stable oblique detonations, decoupling of the oblique detonation wave is observed.

Cell structure and stability of detonations with a pressure-dependent chain-branching reaction rate model

We examine detonation waves with a four-step chain-branching reaction model that exhibits explosion limits close to the two lower limits of hydrogen–oxygen chemistry. The reaction model consists of a chain-initiation step and a chain-branching step, both temperature-dependent with Arrhenius kinetics, followed by two pressure-dependent termination steps. Increasing the chain-branching activation energy or the overdrive shortens the reaction length in the ZND wavelength and leads to more unstable detonations, according to multi-dimensional linear stability analysis. Corresponding numerical simulations show that detonations with weak chain-branching reactions have a wave structure similar to those with a single-step reaction; strong chain-branching detonations show distinct keystone features. Keystone regions are bounded by a discontinuity in reactivity across the shear layers emanating from the triple points at the intersection of the transverse waves and the main front. Especially in the strong case, chain-branching occurs within a thin front at the back side of the keystone figure, or immediately behind Mach stems.

Theory of Detonation with an Embedded Sonic Locus

A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions.

Effect of sodium oleate adsorption on the colloidal stability and zeta potential of detonation synthesized diamond particles in aqueous solutions

Surface properties of a nanometer-scale diamond prepared from detonation synthesis were discussed and the dispersion of this nanodiamond (ND) in aqueous solutions was actualized utilizing the method of mechanochemical treatment (MCT). While preparing a stable suspension in alkaline aqueous media, the addition of an anionic surfactant, sodium oleate (SO), can increase the absolute value of ND surface zeta potential, strengthen the electrostatic stabilization and improve the hydrophilicity of the particles. Mechanisms of the surfactant adsorption on ND surface were investigated using Fourier Transform Infrared Spectroscopy (FTIR) and the measures of particle size, surface potential and adsorption capacity of SO on particle surface. Interactions of electrostatic, hydrogen bonding, hydration, and hydrophobic have influence on the adsorption behavior of SO. Dispersion efficiency and colloidal stability behavior of ND particles are dominated markedly by the electrostatic, hydration and hydrophobic interactions among the modified particles.

On the dynamics of self-sustained one-dimensional detonations: A numerical study in the shock-attached frame

In this work we investigate the dynamics of self-sustained detonation waves that have an embedded information boundary such that the dynamics is influenced only by a finite region adjacent to the lead shock. We introduce the boundary of such a domain, which is shown to be the separatrix of the forward characteristic lines, as a generalization of the concept of a sonic locus to unsteady detonations. The concept plays a fundamental role both in steady detonations and in theories of much more frequently observed unsteady detonations. The definition has a precise mathematical form from which its relationship to known theories of detonation stability and nonlinear dynamics can be clearly identified. With a new numerical algorithm for integration of reactive Euler equations in a shock-attached frame, that we have also developed, we demonstrate the main properties of the unsteady sonic locus, such as its role as an information boundary. In addition, we introduce the so-called “nonreflecting” boundary condition at the far end of the computational domain in order to minimize the influence of the spurious reflected waves.

Numerical simulation of detonations in mixtures of gases and solid particles

This article examines the structure and stability of detonations in mixtures of gases and solid particles via direct numerical simulation. Cases with both reactive and inert particles are considered. First, the two-phase flow model is presented and the assumptions that it is based upon are discussed. Steady-wave structures admitted by the model are subsequently analysed. Next, the algorithm employed for the numerical simulations is described. It is a recently developed high-order shock-capturing algorithm for compressible two-phase flows. The accuracy of the algorithm has been verified through a series of code validation and numerical convergence tests, some of which are included in this article. Subsequently, numerical results for both one-dimensional and two-dimensional detonations are presented and discussed. These results show that the mass, momentum and energy transfers between the two phases result in detonation structures that are substantially different from those observed in the corresponding purely gaseous flows. The effect of certain important parameters, such as particle reactivity, particle volume fraction, and particle diameter, are examined in detail. The numerical results predict that increased particle reactivity suppresses the flow instabilities and increases the detonation velocities. It is further predicted that sufficiently high particle volume fractions can cause detonation quenching regardless of particle reactivity.

Numerical simulations of pulsating detonations: II. Piston initiated detonations

Extremely long time, high-resolution one-dimensional numerical simulations are performed in order to investigate the evolution of pulsating detonations initiated and driven by a constant velocity piston, or equivalently by shock reflection from a stationary wall. The results are compared and contrasted to previous simulations where the calculations are initiated by placing a steady detonation on the numerical grid. The motion of the piston eventually produces a highly overdriven detonation propagating into the quiescent fuel. The detonation subsequently decays in a quasi-steady manner towards the steady state corresponding to the given piston speed. For cases where the steady state is one-dimensionally unstable, the shock pressure begins to oscillate with a growing amplitude once the detonation speed drops below a stability boundary. However, the overdrive is still being degraded by a rarefaction which overtakes the front, but on a time-scale which is very long compared with both the reaction time and the period of oscillation. As the overdrive decreases, the detonation becomes more unstable as it propagates and the nature (e.g. period and amplitude) of the oscillations change with time. If the steady detonation is very unstable then the oscillations evolve in time from limit cycle to period doubled oscillations and finally to irregular oscillations. The ultimate nature of the oscillations asymptotically approaches that of the saturated nonlinear behaviour as found from calculations initiated by the steady state. However, the nonlinear stability of the steady detonation investigated in previous calculations represents only the very late time (O(105) characteristic reaction times) behaviour of the piston problem.

Stationary and Nonstationary Wave Structures that Arise in Stabilization of Detonation Over a Compression Surface

The paper reports results of numerical simulations of flow structures with oblique detonation waves that arise in supersonic flow of a uniformly mixed mixture of hydrogen with air over two–dimensional compression surfaces (wedge and cone). In the first series of calculations, the internal structure of the detonation front was not resolved but the physical processes in the remaining flow region were simulated with allowance for nonequilibrium chemical reactions. This flow is shown to have a complex wave structure, and the dependence of this structure on the parameters of the problem is studied. In the second series of calculations, nonstationary wave structures at the detonation front were obtained. These nonstationary waves are compared with the structure of the spin head in a nonstationary spin detonation.

Numerical simulations of pulsating detonations: I. Nonlinear stability of steady detonations

Very-long-time numerical simulations of an idealized pulsating detonation with one irreversible reaction having an Arrhenius form are performed using a hierarchical adaptive second-order Godunov-type scheme. The initial data are given by the steady solution and the truncation error produces the perturbation to trigger the instability. The detonation is allowed to run for thousands of half-reaction times of the underlying steady wave to ensure that the final amplitudes and periods of the nonlinear oscillations are achieved. Thorough resolution studies are performed for various representative regimes of the instability. It is shown that to obtain quantitatively good solutions over 50 numerical grid points in the half-reaction length of the steady detonation are required, while to obtain a converged solution over 100 points are required, even near the stability boundary. This is much higher resolution than has generally been used in previous papers in either one or two dimensions. Resolutions of less than approximately 20 points per half-reaction length give very poor predictions of the periods and amplitudes near the stability boundary or entirely spurious solutions for more unstable detonations. The evolution of the converged solutions as the activation energy increases, and the detonation becomes more unstable, is also investigated.

One-dimensional nonlinear stability of pathological detonations

In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A→B→C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes. The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation.

The power of distinguished limits: A comment on ‘On the two-dimensional instability of square-wave detonations’

The stability of both Chapman-Jouguet and overdriven square-wave detonations is investigated in the limit of a large detonation Mach number and a ratio of specific heats close to one.

Linear stability of pathological detonations

In this paper we investigate the linear stability of detonations in which the underlying steady one-dimensional solutions are of the pathological type. Such detonations travel at a minimum speed, which is greater than the Chapman–Jouguet (CJ) speed, have an internal frozen sonic point at which the thermicity vanishes, and the unsupported wave is supersonic (i.e. weak) after the sonic point. Pathological detonations are possible when there are endothermic or dissipative effects present in the system. We consider a system with two consecutive irreversible reactions A→B→C, with an Arrhenius form of the reaction rates and the second reaction endothermic. We determine analytical asymptotic solutions valid near the sonic pathological point for both the one-dimensional steady equations and the equations for linearized perturbations. These are used as initial conditions for integrating the equations. We show that, apart from the existence of stable modes, the linear stability of the pathological detonation is qualitatively the same as for CJ detonations for both one- and two-dimensional disturbances. We also consider the stability of overdriven detonations for the system. We show that the frequency of oscillation for one-dimensional disturbances, and the cell size based on the wavenumber with the highest group velocity for two-dimensional disturbances, are both very sensitive to the detonation speed for overdriven detonations near the pathological speed. This dependence on the degree of overdrive is quite different from that obtained when the unsupported detonation is of the CJ type.