The initial stages of hydrogen–air flame propagation in tubes and the mechanism of tulip flame formation are investigated using a high-order numerical code to solve the fully compressible reactive Navier–Stokes equations for a spark or planar igniting flame at the closed end of a tube and propagating to the opposite closed or open end. It is shown that the mechanism of tulip flame formation is universal for both sparked and planar ignited flames in tubes with both ends closed. Flame front inversion results from the tulip-shaped profile of the unburned gas axial velocity near the flame front, which is the result of the superposition of the unburned gas flow generated by the accelerating flame and the reverse flow generated by the rarefaction wave during flame deceleration. In a half-open tube, this mechanism is valid for spark ignited flames. In the case of planar ignition, there is no rarefaction wave, but the growth of bulges on the sidewalls leads to the formation of a tulip flame.

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen–oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10–30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width $\delta x$ like $\delta x^{-1.4}$ down to $\delta x=0.2\text{μ}\mathrm{m}$. With the WENO scheme, solutions are smooth at $\delta x=10\text{μ}\mathrm{m}$, but no detonation is obtained for $\delta x=5\text{μ}\mathrm{m}$. This is argued to be an artifact of a decoupling between pressure and reaction fronts.

The early stages of hydrogen–air and methane–air flame dynamics and the development and evolution of tulip flames in closed tubes of various aspect ratios and in a semi-open tube are studied by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method coupled to detailed chemical models for stoichiometric hydrogen/air and methane/air mixtures. The use of adaptive mesh refinement (AMR) provides adequate resolution of the flame reaction zone, pressure waves, and flame–pressure wave interactions. The purpose of this study is to gain a deeper insight into the influence of chemical kinetics on the combustion regimes leading to the formation of a tulip flame and its subsequent evolution. The simulations highlight the effect of the flame thickness, flame velocity, and reaction order on the intensity of the rarefaction wave generated by the flame during the deceleration phase, which is the principal physical mechanism of tulip flame formation. The obtained results explain most of the experimentally observed features of tulip flame formation, e.g., faster tulip flame formation with a deeper tulip shape for faster flames compared to slower flames.

The early stages of flame dynamics and the development and evolution of tulip flames in closed tubes of various aspect ratios and in a half-open tube are studied by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method coupled to detailed chemical models in stoichiometric hydrogen/air and methane/air mixtures. The use of adaptive mesh refinement (AMR) provides adequate resolution of the flame reaction zone, pressure waves, and flame-pressure wave interactions. The purpose of this study is to gain a deeper insight into the influence of chemical kinetics on the combustion regimes leading to the formation of a tulip flame and its subsequent evolution. The simulations highlight the effect of laminar flame velocity and reaction order on the physical mechanism of tulip flame formation and evolution. It is shown that the intensity of the pressure and rarefaction waves generated by the flame at the acceleration and deceleration stages depends on the rate of flame acceleration and deceleration. Since the rate of flame acceleration and deceleration depends on the value of the laminar flame velocity, tulip flame formation and evolution are much faster in a highly reactive mixture.

The effects of pressure waves on the tulip flame formation in closed and semi-open tubes were studied using numerical simulations of the fully compressible Navier-Stokes equations coupled to a detailed chemical model for stoichiometric hydrogen air mixture. Rarefaction waves generated by the decelerating flame are shown to be the primary physical process leading to the flame front inversion and the tulip flame formation for spark and for planar ignited flames in closed tubes. In the case of a spark ignited flame, the first rarefaction wave is generated by the flame, which is decelerating due to the reduction in flame surface area as the flame skirt touches the tube walls. Flame collisions with pressure waves in a closed tube result in additional deceleration stages and rarefaction waves that shorten the time of the tulip flame formation.