Accelerating flames in cylindrical tubes with nonslip at the walls

An analytical theory of flame acceleration in cylindrical tubes with one end closed is developed. It is shown that all realistic flames with a large density drop at the front accelerate exponentially because of the nonslip at the tube walls. Such acceleration mechanism is not limited in time and, eventually, it may lead to detonation triggering. It is found that the acceleration rate decreases with the Reynolds number of the flow. On the contrary, the acceleration rate grows with the thermal expansion of the burning matter. It is shown that the flame shape and the velocity profile remain self-similar during the flame acceleration. The theory is validated by extensive direct numerical simulations. The simulations are performed for the complete set of combustion and hydrodynamic equations including thermal conduction, diffusion, viscosity, and chemical kinetics. The simulation results are in very good agreement with the analytical theory.