Ignition by a concentrated heat source in an unbounded space and near a cold wall: eliminating singularities in boundary conditions, the influence of the heat release time and the Lewis number

• A new formulation for ignition from a point source of heat. • Resolution issues and singular points are avoided by coordinate and variable changes. • Results show an optimal energy deposition time minimizing the required energy (MIE). • Fuel Lewis number variation from 1 to 0.3 results in an O(10 7 ) decrease in MIE. • This has major safety implications for hydrogen or hydrogen-containing fuels. Flame initiation in a homogeneous fuel-oxidizer mixture generated by a concentrated heat source is considered. A method is proposed for eliminating singularities in the boundary conditions, thereby improving the accuracy of calculations. This is achieved through appropriate transformations of both the independent and dependent variables. Two configurations are compared: ignition from a point source located in an unbounded space and ignition from a point source located near a cold wall. The latter configuration is equivalent to ignition from a thermal dipole. Two heat release modes are also considered: instantaneous heat release and release of the same amount of energy over a finite time. The main objective is to determine the minimum critical energy required for successful ignition and the dependence of this minimum ignition energy on the problem parameters. An unexpectedly strong dependence of the minimum energy required for ignition on the Lewis number was obtained, with the minimum energy variation ranging seven order of magnitude for Lewis number variations from values of order of unity to 0.3.