Viscous attenuation of a detonation wave propagating in a channel

The propagation of a detonation wave remains one of the challenging problems in physics. While it is possible to predict the average propagation velocity almost correctly using classical theory [1, 2], there is no theory to explain the internal flow structure satisfactorily. The famous Zel’dovich-von Neumann-Döring theory [3, 4, 5] is widely considered to describe the one-dimensional detonation structure correctly. Early experiments uncovered that the reduction to one space dimension is not entirely justified in long tubes. The detonation waves are non-planar and exhibit multi-dimensional substructures [18]. Numerical simulations have lately been used to examine these transient sub-structures but most of these studies thus have far neglected transport phenomena partly to simplify the approach. Moreover, neglecting transport phenomena appeared to be feasible in regions where such phenomena can be neglected. Nonetheless, the presence of walls requires careful consideration of transport phenomena [7]. Recent progress in computing power has enabled Navier-Stokes solutions of detonation waves [8, 9, 10]. A preliminary study on the effect of transport processes is reported here. The propagation of a detonation wave is examined by a comparison between an inviscid and a viscous solution.