Ignition Condition of a Stagnation Premixed Flow Impinging on a Heated Surface

Insights into ignition of a premixed flow impinging on a hot surface are important from a fire-safety point of view. This paper theoretically discusses the critical conditions for ignition of a stagnation flow near a surface heated at a constant power. A one-dimensional, diffusive-thermal model is developed, and a shooting method is used to numerically obtain a steady-state solution for a given heat flux at the solid surface. It is found that there are three solution branches when the heat flux is within a certain range. The upper branch corresponds to a gas-phase combustion solution, and the lower branch to an extinguished solution, whereas the middle branch to a solution with weak (but not negligible) reaction. When the heat flux exceeds the upper limit of the three-branch range, there exists only the upper solution, meaning that ignition always occurs. The result indicates that there is the critical heat flux for ignition, agreeing with previous experimental observations. Asymptotic analysis is additionally conducted to analytically obtain the critical condition for ignition.