The Effect of the Polytropic Index {\gamma} on the Structure of Gaseous Detonations

TL;DR

This study uses two-dimensional simulations to investigate how the polytropic index affects gaseous detonation structures, revealing that lower indices enhance convective mixing and shorten reaction lengths, with gas dynamics playing a key role.

Contribution

It provides new insights into the influence of the polytropic index on detonation behavior through simplified numerical models, isolating gasdynamic effects from chemical kinetics.

Findings

Lower polytropic indices increase convective mixing.

Detonation reaction length decreases with lower polytropic index.

Mach stem bifurcation is primarily driven by gas dynamics.

Abstract

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.