Physics – Fluid Dynamics
Scientific paper
2008-04-22
Physics
Fluid Dynamics
27 pages, 11 figures, to appear in Physics Letters A
Scientific paper
10.1016/j.physleta.2008.04.066
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.
Akkerman V'yacheslav
Bychkov Vitaly
Eriksson Lars-Erik
Marklund Mattias
Valiev Damir
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