Numerical investigation of ethylene flame bubble instability induced by shock waves

In this paper, the ethylene/oxygen/nitrogen premixed flame instabilities induced by incident and reflected shock wave were investigated numerically. The effects of grid resolutions and chemical mechanisms on the flame bubble deformation process are evaluated. In the computational frame, the 2D multi-component Navier–Stokes equations with second-order flux-difference splitting scheme were used; the stiff chemical source term was integrated using an implicit ordinary differential equations (ODEs) solver. The two ethylene/oxygen/nitrogen chemical mechanisms, namely 3-step reduced mechanism and 35-step elementary skeletal mechanism, were used to examine the reliability of chemistry. On the other hand, the different grid sizes, Δx × Δy = 0.25 × 0.5mm and Δx × Δy = 0.15 × 0.2mm, were implemented to examine the accuracy of the grid resolution. The computational results were qualitatively validated with experimental results of Thomas et al. (Combust Theory Model 5:573–594, 2001). Two chemical mechanisms and two grid resolutions used in present study can qualitatively reproduce the ethylene spherical flame instability process generated by an incident shock wave of Mach number 1.7. For the case of interaction between the flame and reflected shock waves, the 35-steps mechanism qualitatively predicts the physical process and is somewhat independent on the grid resolutions, while the 3-steps mechanism fails to reproduce the instability of ethylene flame for the two selected grid resolutions. It is concluded that the detailed chemical mechanism, which includes the chain elementary reactions of fuel combustion, describes the flame instability induced by shock wave, in spite of the fact that the flame thickness (reaction zone) is represented by 1–2 grids only.