On the viscous boundary layer of weakly unstable detonations in narrow channels

International audienceThe present study investigates, via high performance computing simulations, detonations propagating in small channel filled with a working fluid representative of the thermodynamic and transport properties of a stoichiometric mixture of propane and oxygen. With the help of a high-order compressible Navier--Stokes solver based on Weighted Essentially Non-Oscillatory (WENO5) scheme coupled with the Strang splitting method, we investigate the 2D mean structure of weakly unstable non-ideal detonations. The mean procedure is conducted on the instantaneous position of the shock. To overcome the expensive CPU time needed due to the long lengths required to get a self-similar solution that is independent from the initial solution, we implemented a recycling block technique (RBT). The RBT combined with the addition of a negative inflow in the detonation propagation direction allows to reduce the domain length by a factor of ten. Moreover, the investigation of the viscous boundary layer characteristics using different channel heights and different activation energies show that the displacement thickness scales in Re −αx , α≈0.56--0.65. For the skin-friction coefficient we find a scaling in Re −1 x