The Detonation Layer
The perturbation methods developed in fluid mechanics over the past three decades have made it possible to resolve many problems of regular or singular perturbation (see, e.g., Van Dyke ). Thus Germain and Guiraud , in particular, studied shock waves by considering the dissipative effects as a singular perturbation of the Hugoniot model  in a perfect fluid. In this chapter we adopt—on the subject of detonations—an analogous approach: detonation is seen as a layer of steep gradients in a Navier-Fourier dissipative fluid, this layer being localized in the neighborhood of the surface ∑(t) to which it is reduced by the Crussard model  in a perfect fluid. Analysis of flow in such a remarkable zone calls for the use of curvilinear coordinates z, ξ′, ξ″ which are associated, respectively, with the normal direction N and the principal directions N′, N″ of ∑(t). (N.B. Throughout this chapter the normal N is expressly oriented from upstream to downstream, as in Section II.2.) That is why (§1.2) the corresponding form of the equations (I.28) is established first of all: the expressions are those of Germain and Guiraud, made more manageable by appropriate notations. We then specify the hypotheses adopted to represent the law of chemical evolution (see §1.3). Finally, we go on to the necessary definitions and transformations (§1.4 and §1.5) for development of the perturbation method itself, ending up (§1.6) at zero-order structures and the notion of quasi C-J detonation.
KeywordsPerfect Fluid Perturbation Parameter Detonation Product Downstream State Upstream State
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