Theory of explosions and detonations for a three-step chain-branching chemistry model

Maflahi, Nabeil (2006). Theory of explosions and detonations for a three-step chain-branching chemistry model. University of Birmingham. Ph.D.

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Abstract

A three-step kinetics scheme is used to model chain-branching reactions but also thermal reactions that are traditionally modelled using a one-step scheme. The chain-branching crossover temperature \(T_B\) is adjusted to accommodate for the different reaction types. Two main scenarios are considered: a homogeneous reactive gas in a closed vessel, and the initiation of detonation waves in a tube induced by a shock that is driven either by a piston or a contact. In the homogeneous scenario, the reaction behaves more and more like a chain-branching reaction the smaller \(T_B\) is below the initial temperature (unity in our non-dimensionalized scales). For \(T_B > 1\) however, heat is released from the outset, and the reaction proceeds in a thermal manner similar to what occurs with one-step schemes. It is shown how the three-step scheme can be matched to widely used two-step and one-step models in the cases \(T_B < 1\) and \(T_B > 1\) respectively. With piston-driven shock-induced detonations and for \(T_B — 1\) sufficiently large, we reproduce situations similar to those which occur with one-step thermal schemes. For \(T_B ~ 1\), both thermal and chain-branching effects are witnessed. With \(T_B\) sufficiently below unity, chain-branching is very prominent from the outset, and since no secondary shock is formed, the situation is unlike what usually occurs with one-step thermal schemes, but is in good agreement with predictions of a simplified two-step chain-branching model. The major qualitative difference when using an acoustically permeable contact discontinuity to drive the shock instead of a piston occurs when \(T_B — 1\) is sufficiently large, where we witness the temperature maximum and the fuel minimum move away from the driving surface.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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