Asymptotic study of pulsating evolution of overdriven and CJ detonation with a chain-branching kinetics model
- Los Alamos National Laboratory
The pulsating dynamics of gaseous detonations with a model two-step chain-branching kinetic mechanism are studied both numerically and asymptotically. The model studied here was also used in [4], [3] and [2] and mimics the attributes of some chain-branching reaction mechanisms. Specifically, the model comprises a chain-initiationlbranching zone with an Arrhenius temperature-sensitive rate behind the detonation shock where fuel is converted into chain-radical with no heat release. This is followed by a chain-termination zone having a temperature insensitive rate where the exothermic heat of reaction is released. The lengths of these two zones depend on the relative rates of each stage. It was determined in [4] and [3] via asymptotic and numerical analysis that the ratio of the length of the chain-branching zone to that of the chain-initation zone relative to the size of the von Neumann state scaled activation energy in the chain initiation/branching zone has a primary influence of the stability of one-dimensional pulsating instability behavior for this model. In [2], the notion of a specific stability parameter related to this ratio was proposed that determines the boundary between stable and unstable waves. In [4], a slow-time varying asymptotic study was conducted of pulsating instability of Chapman-Jouguet (CJ) detonations with the above two-step rate model, assuming a large activation energy for the chain-initiation zone and a chain-termination zone longer than the chain-initiation zone. Deviations D{sub n}{sup (1)} ({tau}) of the detonation velocity from Chapman-Jouguet were of the order of the non-dimensional activation energy. Solutions were sought for a pulsation timescale of the order of the non-dimensional activation energy times the particle transit time through the induction zone. On this time-scale, the evolution of the chain-initation zone is quasi-steady. In [4], a time-dependent non-linear evolution equation for D{sub n}{sup (1)} ({tau}) was then constructed via a perturbation procedure for cases where the ratio of the length of the chain-termination zone to chain-initiation zone was less than the non-dimensional activation energy. To leading order, the steady CJ detonation was found to be unstable; higher-order corrections lead to the construction of a stability limit between stable and unsteady pulsating solutions. One conclusion from this study is that for a stability limit to occur at leading order, the period of pulsation of the detonation must occur on the time scale of particle passage through the longer chain-termination zone, while the length of the chain-termination zone must be of order of the non-dimensional activation energy longer than the chain-initiation zone. The relevance of these suggested scalings was verified via numerical solutions of the full Euler system in [3], and formed the basis of the stability parameter criteria suggested in [2]. In the following, we formulate an asymptotic study based on these new suggested scales, studying the implications for describing pulsating behavior in gaseous chain-branching detonations. Specifically, we find that the chain-induction zone structure is the same as that studied in [4]. However, the study of unsteady evolution in the chain-termination region is now governed by a set of asymptotically derived nonlinear POEs. Equations for the linear stablity behavior of this set of POE's is obtained, while the nonlinear POEs are solved numerically using a shock-attached, shock-fitting method developed by Henrick et aJ. [1]. The results thus far show that the stability threshold calculated using the new ratio of the chain-termination zone length to that of the chain-initiation zone yields a marked improvement over [2]. Additionally, solutions will be compared with predictions obtained from the solution of the full Euler system. Finally, the evolution equation previously derived in [4] has been generalized to consider both arbitrary reaction orders and any degree of overdrive.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1048796
- Report Number(s):
- LA-UR-11-00414; LA-UR-11-414; TRN: US1204299
- Resource Relation:
- Conference: Int Colloquium on the dynamics of explosives and reactive systems ; July 24, 2011 ; Irvine, Ca
- Country of Publication:
- United States
- Language:
- English
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