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The present work exploits simplifications arising in weakly exothermic detonations when the postshock conditions are supersonic to investigate the structure of wedge-induced oblique detonations. These simplifications enable the linearized Euler equations (employed here in characteristic form) to be efficiently solved numerically, subject to the linearized Rankine-Hugoniot jump conditions across the leading oblique shock. A first set of computations employs one-step first-order Arrhenius chemistry appropriate for describing detonations when the postshock chemistry exhibits a thermal-explosion character. In that case, the relevant chemical-kinetic parameter of order unity ß is the product of the heat release and the activation energy divided by the square of the postshock thermal enthalpy. The transition from the shock to the detonation wave is continuous at small ß, begins to develop spatially decaying oscillations as ß increases, and develops a singularity at the shock at a critical value of ß; above which, the transition must become discontinuous and involve a triple point. Parametric results are presented in a plane of the wedge angle and the incident-flow Mach number: the two important controlling parameters. The triple point is found to develop when the incident-flow Mach number falls below a critical value that exhibits a U-shaped dependence on the wedge angle, becoming large at both high and low wedge angles and reflecting large differences between shock angles with and without heat release in those two extremes. Additional computations are performed for a three-step branched-chain scheme with the heat-release step having zero activation energy and for very fuel-lean hydrogen-air detonations with postshock temperatures above crossover. These cases, for which ignition develops as a chain-branching explosion, do not develop a singularity at the shock; although they display many of the features identified with the Arrhenius chemistry, including oscillations and appearance of a precursor point indicative of criticality. The results suggest a strong potential influence of the chemistry on the transition. [ABSTRACT FROM AUTHOR]

A simplified formulation, based on treating the ratio of the heat release to the postshock thermal enthalpy as a small parameter, accommodating arbitrary chemistry descriptions, is shown to reproduce computationally the same variety of phenomena as more complex formulations for oblique detonations with supersonic postshock flow. The resulting small relative variations of velocity and thermodynamic properties across the reaction region are described by linearized Euler equations written in characteristic form, supplemented by the linearized Rankine-Hugoniot jump conditions across the leading shock. The simplified formulation is used to analyze the interaction of the oblique detonation with a weak vortex sheet, for an Arrhenius irreversible reaction with an activation energy large compared with the postshock thermal enthalpy. The analysis reveals that, as β, the product of the activation energy and the heat release divided by the square of the postshock thermal enthalpy, increases through values of order unity, decaying spatial oscillations, found for small values, are replaced by persistent nonlinear oscillations of finite amplitude for larger values. Beyond a critical value of β the growth of the oscillation amplitude leads to the development of a singularity at the shock, an explosion, consistent with the formation of a triple point. Many related problems can be clarified with this formulation. [ABSTRACT FROM AUTHOR]

This paper examines the steady interaction of a shear layer separating two uniform supersonic streams of Mach numbers M1 and M2 with an oblique shock approaching from the faster stream at an incident angle σi sufficiently small for the postshock flow to remain supersonic everywhere. The development begins by considering the related problem of oblique-shock impingement on a supersonic vortex sheet of infinitesimal thickness, for which the region of existence of regular shock refractions with downstream supersonic flow is delineated in the parametric space (M1,M2,σi). The interaction region located about the impingement point, scaling with the shear-layer thickness, is described next by integrating the Euler equations in the postshock region, formulated in characteristic form, subject to the Rankine-Hugoniot jump conditions at the shock front. The results are used to investigate the accuracy and limitations of a simplified treatment, the so-called Moeckel-Chisnell approach, commonly employed for determining the shape of the shock wave in these scenarios, which does not account for the influence of the postshock flow. It is found that, although the Moeckel-Chisnell method predicts accurately the shape of the shock front as it evolves across the shear layer, it is unable to predict the final transition to the transmitted-shock solution, which occurs beyond the edge of the shear layer. The structure of the shear layer in the far field also is addressed here for the first time, with the objective being to lay the groundwork for future studies of shock-induced ignition in supersonic fuel-air mixing layers. [ABSTRACT FROM AUTHOR]