Diffusion and hydrodynamic instabilities in gaseous detonations

To clarify the role played by diffusion in detonation structure, two-dimensional numerical simulations are performed by solving the Navier–Stokes equations and considering the single step Arrhenius kinetic as reaction model. The effect of diffusion on the generation of vortices produced by hydrodynamic instabilities (Richtmyer–Meshkov (RM) and Kelvin Helmholtz (KH) instabilities) is investigated. Mixtures with both low and high activation energies, characterized by their regular and irregular detonation structures, are considered. The computations are performed with resolutions ranging from 25 to 103 cells per half reaction length of the ZND structure. Resolution studies of the Navier–Stokes solution for irregular detonations in moderate activation energy mixtures shows that to capture a proper structure, to be at least in qualitative agreement with experimental observations, resolution more that 300 cells per half reaction length is required. However, in mixtures with low activation energy a resolution of 25 cells per half reaction length gives a reasonable physical structure of the detonation. Results provided by very high resolution for irregular structure detonations reveal that the major effect of diffusion occurs at shear layers and unburned pockets boundaries. Diffusion suppresses the small-scale vortices produced by KH instabilities and decreases the turbulent mixing rate of burned and partly burned gases at shear layers. However, behind the shock front, where less concentration of small-scale vortices exist, the diffusion of heat and mass from neighboring hot regions of burned material to the unreacted gases increases the burning rate of the un-reacted pockets. Comparison of the structure obtained by solving the Euler equations with the solution of the Navier–Stokes equations shows that, the strength of the shock front in Navier–Stokes solution is higher than that in Euler solution. Due to the absence of hydrodynamic instabilities behind the main front of regular structure detonations, the results obtained by solving the Euler equations and Navier–Stokes equations are similar for detonations with regular structure even in high resolution simulations.