Effects of Viscosity on the Multifront Structure of Gas Detonation Waves

Abstract

Highly resolved, two-dimensional reactive Navier-Stokes numerical simulations with accurate two-step kinetics were used to study the i nfluence of molecular transport processes on multifront detonation waves. Numerical simulations were performed for a hydrogenoxygen mixture in a flat channel. Simulati ons of viscous detonation in wide channels (the channel width is greater than or commensurable with the detonation cell size) show that the governing effect on the number of tra nsverse waves on the wave front is exerted by the absence or presence (owing to viscos ity and other transport phenomena) of boundary layers on the channel walls rather than by the absolute values of the transport coefficients for a particular mixture. Interaction of transverse waves with boundary layers on the channel walls alters the conditions of wave reflection from the channel walls, as compared with the case of an inviscid detonation wa ve. Different condition of detonation propagation results in a different number of transv erse waves on the leading shock front of the detonation wave. Numerical experiments in narrow channels (the channel width being smaller than the detonation cell size) show that th ere exists a geometric limit of propagation of a viscous detonation wave, i.e., there may be su ch a channel width where a quasi-steady self-sustained detonation mode cannot exist. A near -limit self-sustained marginal detonation wave, a decaying regime of detonations, and a sub-c ritical regime of detonation‐wave propagation are obtained in the present study. Nomenclature a0 = detonation cell width in the Chapman‐Jouguet regime DCJ = detonation velocity in the Chapman‐Jouguet regime H = height of the channel Nx = number of the grid cells in the x direction Ny = number of the grid cells in the y direction p0 = initial pressure of the mixture T = gas temperature, K Tw = channel walls temperature, K u = gas velocity in the x direction, m/s v = gas velocity in the y direction, m/s x = axis along the lower wall of the channel xfr = position of the detonation front along the chann el y = axis upwards, normal to the x axis µ = molecular viscosity