Heating of the fuel mixture due to viscous stress ahead of accelerating flames in deflagration-to-detonation transition

TL;DR

This paper investigates how viscous stress contributes to heating the fuel mixture during deflagration-to-detonation transition, combining analytical theory and numerical simulations to understand wall effects and shock interactions.

Contribution

It develops an analytical low Mach number theory and performs numerical simulations to analyze viscous heating effects in DDT, highlighting wall-localized heating and multi-dimensional explosion dynamics.

Findings

Viscous stress causes significant heating at the walls.

Heating effects become comparable to compression wave at high Mach numbers.

Detonation develops through wall-spreading reactions and shock interactions.

Abstract

The role of viscous stress in heating of the fuel mixture in deflagration-to-detonation transition in tubes is studied both analytically and numerically. The analytical theory is developed in the limit of low Mach number; it determines temperature distribution ahead of an accelerating flame with maximum achieved at the walls. The heating effects of viscous stress and the compression wave become comparable at sufficiently high values of the Mach number. In the case of relatively large Mach number, viscous heating is investigated by direct numerical simulations. The simulations were performed on the basis of compressible Navier-Stokes gas-dynamic equations taking into account chemical kinetics. In agreement with the theory, viscous stress makes heating and explosion of the fuel mixture preferential at the walls. The explosion develops in an essentially multi-dimensional way, with fast spontaneous reaction spreading along the walls and pushing inclined shocks. Eventually, the combination of explosive reaction and shocks evolves into detonation.