A mathematical model for three dimensional detonation as pure gas-dynamic discontinuity

TL;DR

This paper introduces a mathematical model for three-dimensional detonation treating it as a modified hydrodynamic discontinuity, incorporating internal structure effects like chemical reactions, curvature, and stretching.

Contribution

It develops a new model that modifies classical jump conditions to include detonation internal structure based on first principles.

Findings

Derived modified Rankine-Hugoniot conditions for detonation

Model accounts for curvature, flame thickness, and stretching effects

Provides a physically interpretable framework for 3D detonation analysis

Abstract

A model for three dimensional detonation is proposed based on the approximation that the detonation thickness is small compared to the characteristic scales of the fluid motion. In this framework detonations are treated as a modified hydrodynamic discontinuity. The altered Rankine-Hugoniot jump conditions take into account the internal structure of the detonation including the chemical reaction. The position of the discontinuity surface and the corresponding jump conditions are derived from first principles. The final modified conditions are dependent on curvature, flame thickness and stretching and allow for simple physical interpretation.