Effect of concentration inhomogeneity on the pulsating instability of hydrogen–oxygen detonations

One-dimensional, unsteady gaseous detonation propagation in a non-homogeneous medium is investigated numerically using the reactive, compressible Navier–Stokes equations with detailed chemistry. The effect of concentration inhomogeneity on the pulsating mode is modeled by a sinusoidal distribution of H₂ mole fraction in a H₂–O₂ mixture. The mixture inhomogeneity, varied by changing the disturbance frequency and amplitude, has significant effects on the pulsating behavior of the detonation due to the interaction of the leading shock with the local gradient. Initially exhibiting a four-period pulsation, the detonation wave entering a non-homogeneous medium can adapt and re-establish into a new propagation mode. For a fixed, large-amplitude sinusoidal disturbance, the period-doubling limit cycle is prone to be destroyed, resulting in a chaotic mode for the propagating detonation front in the non-homogeneous mixture; lowering the disturbance frequency also favors a transition from a periodic pulsation to a chaotic one. When the disturbance amplitude decreases, the propagating detonation can transit quickly to a new pulsating behavior, which tends to be more regular. For a very small amplitude of inhomogeneous variation, it is found that the frequency corresponding to the wavelength close to that of the intrinsic pulsation in the uniform mixture makes the original four-period mode become a double-period mode; for a frequency less than this value, the double-period mode is prone to become more unstable. Consequently, this demonstrates that inhomogeneity could have a positive effect on stabilizing a pulsating detonation.