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Theory of direct initiation of gaseous detonations and comparison with experiment
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In this work we discuss the application of an evolution equation that we have developed for the dynamics of a slowly evolving weakly-curved detonation to a problem of direct detonation initiation. Despite the relative simplicity of the theory, it successfully explains basic features of the initiation process which are observed in experiments and numerical simulations. Moreover, the theory allows one to calculate initiation energies based on the explosive chemical and thermodynamic properties only, without having to invoke significant modeling assumptions. The evolution equation exhibits the competing effects of the exothermic heat release, curvature, and shock acceleration. The detonation dynamics during the initiation depends on the relative strength of the heat release and flow divergence, resulting in successful initiation of self-sustained detonation if the heat release is sufficiently stronger than divergence or in failure if otherwise. Using global kinetic data from Caltech detonation database, which are derived from detailed chemical calculations, we have calculated critical initiation energies of spherical detonation for hydrogen-oxygen, hydrogen-air, and ethylene-air mixtures at various equivalence ratios and found a very good agreement with recent experimental data. published or submitted for publication is peer reviewed
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... Eckett et al. [18] demonstrated the importance of unsteadiness using one-dimensional DDI simulations and developed the critical decay rate (CDR) model. A general, rational theory of the self-sustained detonation waves was developed by Kasimov and Stewart [19], which is an unsteady generalisation of the detonation shock dynamics proposed by Stewart and coworkers [20]. Liu et al. [21] proposed the critical decay time (CDT) model based on a global initiation criterion that utilises the features of sub-CJ minimum in the near-critical regime of successful DDI processes. ...
Chemical kinetics plays an important role in the direct detonation initiation (DDI) of various combustible mixtures. However, its impact on detonation dynamics has rarely been studied with detailed mechanisms. This study introduces the active subspace method to systematically explore the chemical kinetics impact on the unsteady detonation dynamics in DDI of H2-O2-Ar mixture, with a 13-species detailed mechanism. The kinetic effects on the ZND structure with sub-CJ shock speed (subCJ ZND structure) is first investigated, where three important reactions to the sub-CJ minimum shock speed, H + O2 = O + OH, H + O + M = OH + M and H2O + H2O = H + OH + H2O are identified. Then the active subspace method is further employed to analyze the kinetics impact on the critical initiation energy (Ecr) predicted with the critical decay rate (CDR) model and critical decay time (CDT) model. Results show that the CDT model, which utilises the sub-CJ ZND model to compute the critical parameters, can properly capture the one-dimensional detonation dynamics. All the important reactions identified with the CDT model agree well with those of one-dimensional simulations. In contrast, the CDR model shares a similar active subspace with the constant volume auto-ignition process and fails to identify the less important reactions. The consistency in the key reactions between one-dimensional simulations and the CDT model implies that it is viable to employ the CDT model as an efficient surrogate for quantifying the kinetic effects in unsteady detonation dynamics
... It is noted that the numerical simulations of Eckett et al., as well as an order of magnitude analysis, have shown that the unsteadiness is the dominant effect [5]. The interaction of the two effects were considered by Kasimov et al. [6,7,8] and Clavin et al. [9,10], who give a more complete picture of the detonation dynamics during DDI. ...
The critical decay rate theory (C.A. Eckett, J.J. Quirk, J.E. Shepherd, Journal of Fluid Mechanics 421(2000) 147-183) on detonation initiation in unsteady flow was extended from ideal to Noble-Abel and van der Waals gas, in which the finite molecular volume effect (or repulsion force) and the inter-molecular attraction effect (or attraction force) were included. Considering the reactive Euler equations, the reaction zone temperature-gradient equation was established independently of the equation of state and wave geometry , and then solved asymptotically by assuming large activation energy, planar wave front and a one-step irreversible reaction model. A critical decay time was derived as the critical condition for detonation initiation. It was found that the inter-molecular attraction effect makes initiation more difficult by increasing the critical decay time, whereas the finite molecular volume effect promotes initiation. The real gas effects are enhanced when increasing the reduced activation energy or/and decreasing the heat capacity ratio of perfect gas. The applicability and generality of the asymptotic solutions were evaluated by comparison with quasi-unsteady simulation employing detailed reaction models for hydrogen-air and ethylene-air mixtures, and with the further simplified, fully analytical solutions based on strong-shock assumption. The critical conditions of the asymptotic solutions are qualitatively consistent with those obtained with the detailed mechanisms. The asymptotic solutions can also be well reproduced by the simple analytical solutions in most conditions. This study thus establishes a simple, yet reliable, method to evaluate the real gas effect on detonation initiation in high-pressure conditions.
... Taking detonation curvature and unsteadiness into account, Kasimov and Stewart (2004) establish a prediction model named as ̅ − −κ ( ̅ is detonation wave acceleration, D the detonation speed, and κ the curvature), using single-step chemistry. Their model is improved by Soury and Mazaheri (2009), who incorporate detailed chemical kinetics and predict better relations between Ec and the 3 equivalence ratio. ...
Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressure and composition are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and supercritical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the nonreactive hotspots. Two cell diverging patterns (i.e., abrupt and gradual) are identified and the detailed mechanisms are analyzed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growing. We also consider nonuniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation, and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction respectively, i.e., 1 to 0.9, 1 to 0.5 and 1 to 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated, and eventually become almost constant at the cell diverging stage, within which the sonic plane shows a sawtooth pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no sawtooth sonic plane can be observed.
... Different models have been proposed to predict the critical energy of direct detonation initiation (e.g., [3] and references therein). For simplicity, one-step chemistry model was popularly used to analyze the direct detonation initiation process (e.g., [2,[4][5][6][7] ). He and Clavin [2] found that the curvature effect can cause detonation initiation failure. ...
... Different models have been proposed to predict the critical energy of direct detonation initiation (e.g., [3] and references therein). For simplicity, one-step chemistry model was popularly used to analyze the direct detonation initiation process (e.g., [2,[4][5][6][7] ). He and Clavin [2] found that the curvature effect can cause detonation initiation failure. ...
Direct detonation initiation is simulated considering detailed chemistry for H2/O2/Ar mixture. The objective is to examine and interpret the effects of local temperature perturbation on direct detonation initiation. Temperature perturbations with different amplitudes are introduced in the region where the blast wave decays quickly. For the case without temperature perturbation, the supercritical, critical and subcritical regimes for direct detonation initiation are identified by continuously decreasing the initiation energy. The quasi-steady period in the critical case is investigated in details. The thermal states of flow particles at different initial locations within the quasi-steady region are tracked and analyzed; and the mechanism for the development of an over-driven detonation after the quasi-steady period is discussed. When a cold spot with large amplitude of temperature perturbation is introduced, the direct detonation initiation is prohibited, which is expected since low temperature in a cold spot greatly reduce the chemical reaction rate. However, it is observed unexpectedly that a cold spot with small amplitude of temperature perturbation can promote direct detonation initiation. Similarly, a hot spot with small amplitude of temperature perturbation inhibits direct detonation initiation; and it promotes direct detonation initiation when its amplitude is large enough. Such unexpected observation is caused by the opposite effects of temperature perturbation: local low temperature reduces the chemical reaction rate while it also increases the local volumetric energy density.
... Equivalently, the critical tube diameter and critical energy are experimentally measured simultaneously at the same mixture sensitivity controlled by the initial pressure p o . Although there exist several semi-empirical correlations [31,32] or theoretical models to estimate the critical energy for direct initiation (e.g., [33][34][35][36]), to compare the experimental results with theoretical predictions here we focus on an initiation model proposed by Lee [31,37] which relates specifically the two measured quantities in this work, namely the critical initiation energy E c and the critical tube diameter d c as the length scale. The surface energy model is a semi-empirical phenomenological model; its formulation originates from the relationship between direct initiation and the critical tube diameter phenomena. ...
In this investigation, the dynamic detonation parameters for stoichiometric acetylene–oxygen mixtures diluted with varying amount of argon are measured and analyzed. The experimental results show that the critical tube diameter and the critical energy for direct initiation of spherical detonations increase with the increase of argon dilution. The scaling behavior between the critical tube diameter d c and the detonation cell size k as well as the critical direct initiation energy E c is systematically studied with the effect of argon dilution. The present results again validate that the relation d c = 13k holds for 0– 30% argon diluted mixtures and breaks down when argon dilution increases up to 40%. It is found that the explosion length scaling of R o $ 26k becomes also invalid when the mixture contains approximately this same amount of argon dilution or more. This critical argon dilution is indeed close to that found from experiments in porous-walled tubes by Radulescu and Lee (2002) which exhibit a distinct transition in the failure mechanism. Cell size analysis in literature also indicates that the cellular detonation front starts to become more regular (or stable) when the argon dilution reaches more than 40–50%. Regardless of the degree of argon dilution or mixture sensitivity, the phenomenological model developed from the surface energy concept by Lee, which provides a relation that links the critical tube diameter and the critical energy remains valid. The present experimental results also follow qualitatively the observation from chemical kinetic and detonation instability analyses.
Two-dimensional simulations are conducted to investigate the direct initiation of cylindrical detonation in hydrogen/air mixtures with detailed chemistry. The effects of hotspot condition and mixture composition gradient on detonation initiation are studied. Different hotspot pressures and compositions are first considered in the uniform mixture. It is found that detonation initiation fails for low hotspot pressures and the critical regime dominates with high hotspot pressures. Detonation is directly initiated from the reactive hotspot, whilst it is ignited somewhere beyond the non-reactive hotspots. Two cell diverging patterns (i.e. abrupt and gradual) are identified and the detailed mechanisms are analysed. Moreover, cell coalescence occurs if many irregular cells are generated initially, which promotes the local cell growth. We also consider non-uniform detonable mixtures. The results show that the initiated detonation experiences self-sustaining propagation, highly unstable propagation and extinction in mixtures with a linearly decreasing equivalence ratio along the radial direction, i.e. 1 → 0.9, 1 → 0.5 and 1 → 0. Moreover, the hydrodynamic structure analysis shows that, for the self-sustaining detonations, the hydrodynamic thickness increases at the overdriven stage, decreases as the cells are generated and eventually becomes almost constant at the cell diverging stage, within which the sonic plane shows a ‘sawtooth’ pattern. However, in the detonation extinction cases, the hydrodynamic thickness continuously increases, and no ‘sawtooth’ sonic plane can be observed.
Proper characterization of the transient interaction between shock front motion and chemical energy release is the key for further understanding of unsteady detonation dynamics. We have shown that the gradients could be the adequate intermediate quantities to reflect the transient interaction between shock front motion and chemical energy release through the Lagrangian particle analysis of the simulated direct detonation initiation (DDI) process in H2-O2-Ar mixtures. Specifically, the "shock change equations" are verified to describe the direct relation between the shock front motion and the gradients immediately behind the shock. Moreover, given the time derivatives of shock speed, the gradient evolution in the induction zone can be reproduced by the gradient evolution equations that are deduced from the Euler equations, no matter the shock front undergoes rapid deceleration or acceleration. While in the reaction zone where the heat release is significant, it is demonstrated that the evolutions of velocity, pressure and their gradients can be described by the Zel'dovich-von Neumann-Döring (ZND) model with a constant wave speed that is below the Chapman-Jouguet (CJ) speed, no matter the shock front undergoes rapid deceleration or acceleration. These two distinct controlling mechanisms are verified in both planar and spherical DDI processes, showing their general applicability. This work suggests a new perspective, in terms of gradient evolution, for further understanding the unsteady detonation dynamics.
The present study compares the critical initiation energy predicted by the critical curvature (CC) and critical decay rate (CDR) models. To ensure a fair and meaningful comparison between these two theoretical approaches, the Taylor-Sedov (TS) blast wave model, which enables to relate the critical state to the energy of the point source, has been employed in both models. Simplified as well as detailed chemical mechanisms were employed for the comparison. By using the same blast wave model, the ratio of critical initiation energy calculated with the CC and CDR models was found to be one to two order of magnitude smaller than the results in previous studies. Although the choice of the blast wave model is important, the critical energy predicted by the CC model is invariably larger than the one predicted by the CDR model. This was explained by analyzing the relationship between the shock front radius and decay time as well as the ignition delay-time around the critical conditions of the two models. It was demonstrated that the critical conditions of the CDR model can be fulfilled more easily than those of the CC model. As a result, the main source of discrepancy between the CDR and CC models is that they adopt different initiation failure mechanisms, namely curvature for the CC model against unsteadiness for the CDR model.
We report results of Eulerian hydrodynamic simulations of detonation shock waves propagating through open cell foams constructed of aluminum, polymethylmethacrylate, and lead at approximately 20 % relative density in nitromethane. By varying pore sizes, as well as material impedance, we predict the dynamic responses at the mesoscale using a reactive flow model in the ALE3D software package. We explain predictions of the detonation profile of each explosive system, along with the stress-strain response of the foams therein. Finally, we describe predictions of a radially expanding detonation front and apply the theory of Detonation Shock Dynamics to the expansion rate of the shock front.
Time-resolved particle-image velocimetry measurements are made in the streamwise-wall-normal plane of turbulent channel flow at Re τ = 550 and 1747. Temporal and convective derivatives of velocity are computed from this data in order to evaluate the small-scale behaviour of these quantities as well as of the velocity itself. Instantaneous velocity fields indicate that the flow is dominated by small-scale vortex cores believed to be associated with hairpin/hairpin-like vortices. These vortices have been observed in realizations of the random velocity in other wall turbulence studies. In this work, a deterministic ‘vortex signature’ is determined by conditional averaging techniques. This average signature is consistent with the hairpin vortex signature defined by Adrian and co-workers: circular streamlines with a strong ejection of low-speed fluid away from the wall (a Q 2 event) just upstream of the vortex head. In addition, the spatial extent of these small-scale vortices appears to remain relatively constant within the Reynolds-number range studied herein.
(1) Introduction: some conditions for nonmaterial interfaces; (2) The need for a configurational force balance; (3) A framework for the study of evolving nonmaterial interfaces; (4) The normal configurational force balance and the dissipation inequality; (5) Relation of the normal configurational force balance to the classical equations; (6) A final remark. published or submitted for publication is peer reviewed
PZT (52/48) film response is measured as a function of externally applied mechanical stress using a double-beam laser-Doppler heterodyne interferometer. One laser beam is focused on the front film surface and a second is focused on the back of the substrate. This arrangement successfully eliminates any displacement contribution from flexural vibration of the substrate and enables measurement of the strain-electric field hysteresis loops as a function of applied stress. The field-induced strain in the PZT film increases as the applied uniaxial compressive stress increases, and the opposite trend is observed for applied tensile stress. The dependence of electromechanical response on the external stress is attributed to the initial tensile residual stress state in the film. Tensile stress creates an in-plane clamping effect on the domains in the film, hindering polarization switching. The application of a compressive stress reduces the tensile residual stress hi the film and the constraint on the domains, hence more 90° polarization switches are allowed to occur under applied electric field, leading to higher field-induced strains. Applied tensile stress amplifies the clamping effect, leading to lower field-induced strains.
Inspired by biological systems in which damage triggers an autonomic healing response, a polymer composite material that can heal itself when cracked has been developed. In this paper we summarize the self-healing concept for polymeric composite materials and we investigate fracture mechanics issues consequential to the development nd optimization of this new class of material. The self-healing material under investigation is an epoxy matrix composite, which incorporates a microencapsulated healing agent that is released upon crack intrusion. Polymerization of the healing agent is triggered by contact with an embedded catalyst. The effects of size and concentration of the catalyst and microcapsules on fracture toughness and healing efficiency are investigated. In all cases, the addition of microcapsules significantly toughens the neat epoxy. Once healed, the self-healing polymer exhibits the ability to recover as much as 90 percent of its virgin fracture toughness.
We discuss the effects of an external constraint of rotation on convection, driven mainly by compositional buoyancy, in a porous layer adjacent to the solid-liquid interface during directional solidification of a binary alloy. In the solidification literature such a porous layer is referred to as a mushy layer. The analyses carried out by several studies in the past and the subsequent results are reviewed first, the latest results unpublished elsewhere are presented briefly, and then in the second-half of the work the investigation of effects of rotation on convection in a horizontal porous layer of melt and dendrite solids is carried out subject to a simple model. The results based on this simple model indicate that the Coriolis force can have stabilizing effects on both the stationary and oscillatory mode of convection, while the oscillatory mode of convection experiences an additional destabilization due to the Coriolis force effect.
We develop a general dynamical theory for the epitaxial growth of an elastic film, a theory that accounts for both stress and diffusion within the epitaxial surface. Our approach relies on recent ideas concerning configurational forces. In addition to an equation that expresses the balance of classical Newtonian forces, our theory gives rise to equations for the epitaxial surface that impose the balance of atoms for each species and a normal configurational force balance. The latter balance can be viewed as a generalization, to a dynamical context involving dissipation, of a condition that would arise in equilibrium by considering variations of the total free-energy with respect to the configuration of the epitaxial surface. It is the counterpart of similar conditions that arise in theories for dislocation, crack, and interface propagation. A key and somewhat surprising result of our theory is that, for sufficiently small or large values of the interfacial stretch, a convex dependence of the surface free-energy density on the surface stretch may be destabilizing.
An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.
A transformation of the point vortex equations is introduced and studied. The transformation substitutes two point vortices for each vortex used in the calculation of induced velocity at a point, in particular in the calculation of the velocity of another vortex in the system. For certain symmetric configurations, such as the vortex polygons, this substitution simplifies the calculation of velocity very considerably. The case of three vortices is also considered, where the circumcircle of the vortex triangle may be used for the transformation. The transformation suggests a new differential relation for the vortex velocities in a many-vortex system. Applications of this result are given.