Steady-State Analysis of Quasi-One-Dimensional Reactive Flow

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Abstract
Steady quasi-one-dimensional flow is investigated for a general multi-reaction system, for an arbitrary equation of state satisfying the Bethe-Weyl conditions, and for a general class of lateral-expansion specifications. The nature of the various solutions is investigated, particularly with reference to the approach to chemical equilibrium and to transonic flow, with a view toward establishing a correspondence between a downstream boundary condition, whether for a nozzle problem or a detonation, and various types of integral curve behavior. The question of unsupported detonation structure and the quasi-one-dimensional Chapman-Jouguet condition is discussed and judged to be analogous to the one-dimensional detonation problem. The frequently quoted Chapman-Jouguet condition based on a special non-equilibrium condition at a frozen-sonic point is obtained only as a special case analogous to the “weak” one-dimensional Chapman-Jouguet condition. The equilibrium Chapman-Jouguet condition based on equilibrium-sonic flow is suggested as the normal case.