Computational study of detonation wave propagation in narrow channels

Abstract

A numerical study of the propagation of regular detonation waves is conducted in the context of narrow channels undergoing strong wall confinement. To deal with shock waves, chemical reactions, heat and viscous stresses, a high-order Navier-Stokes solver based on Weighted Essentially Non-Oscillatory (WENO) scheme, coupled with the Strang splitting method, is used in the framework of multi-species reacting mixtures. Results show that the wall dissipative effects decrease the speed of the detonation wave compared to the Chapman-Jouguet (CJ) detonation velocity. In addition, the multidimensional results reveal that the development of the thermo-diffusive boundary layers behind the leading shock wave induces an expansion flow, which then determines the contour of the sonic envelope. From the Master Equation and the generalized CJ condition, which are derived and compared to the results of the current simulations, the main energy withdrawals are found to be related to the streamline divergence as well as to the growth of the boundary layer. Moreover, a fraction of the released energy is trapped in the vicinity of the wall and does not contribute to drive the shock front. The influence of the channel height is also investigated. It was found that the transverse instabilities are damped when the channel is scaled down, which results in an increase of the dissipative effects. Finally, the validity of the Fay model is discussed with regard to the channel height and the curvature of the detonation front.

Mean structure of one-dimensional unstable detonations with friction

“…For the spatial derivative, ∂F/∂ξ , a fifth-order weighted essentially non-oscillatory scheme (WENO5) 1997;Ngomo et al 2010;Chaudhuri et al 2011). The coupling between the hydrodynamic solver and the source terms is made through the Strang splitting (Chinnayya, Hadjadj & Ngomo 2013). It is assumed that no reaction takes place upstream of the shock, i.e.…”

Computational study of non-ideal and mildly-unstable detonation waves

“…(2) is solved using the fractional step approach [32,12]. Without loss of generality and for simplicity, the fractional step method is briefly presented.…”

“…For steady state solutions, the generalized CJ criterion [2,11,12] can be used to determine the subsonic reaction zone. In unsteady detonations, Kasimov and Stewart [3] defined the sonic locus as a separatrix of the family of forward characteristics.…”

“…Lines represent computed results without condition(12) and symbols results obtained with condition(12).…”

“…Of course, for condition(12) to be valid the search of the local pressure starts from the undisturbed flow to the shocked one.…”