NS simulations and mathematical modelling of minimum ignition energy for lean to stoichiometric methane-air mixtures for 1–30 bar

• Identifying the ignition threshold between non-ignition and successful ignition. • Quantification of the shoot temperature with time for successful flame evolution • NS simulation-based MIE model is developed for CH 4 -air mixtures for 1–30 bar. • A novel model is developed for MIE( φ , p ) = −0.1(ln p ) + 0.524( φ −3/2 ), up to 10 bar. • The MIE model is further extended to higher pressures, 20 and 30 bar. Efficient and reliable ignition is crucial for developing advanced combustion technologies in various industrial applications, such as internal combustion engines and gas turbines. Understanding the relationship between minimum ignition energy, equivalence ratio, and pressure conditions presents a fundamental challenge in combustion science. We investigate the predictive capabilities for effective ignition energy concerning the initiation and propagation of spherical flames in lean methane-air mixtures under quiescent conditions at equivalence ratios of 0.65, 0.8, 0.9, 0.95, and 1.0, across different pressures of 1, 5, and 10 bar, maintaining a constant initial temperature of 300 K. The mixtures undergo successful forced ignition at the centre of a 75 mm cubical domain with variable ignition power density q (W/m 3 ). The value of q is varied for an ignition duration of 10 ms to determine the minimum ignition energy (MIE) required for the flame to initiate and sustain itself until it reaches the adiabatic flame temperature (Tadia) and stabilizes. NS simulations of combustion are conducted using the reactingFOAM solver. Flame evolution is measured as a function of temperature for all numerical cases, including the shoot temperature (T s ) versus shoot time (t s ) and T adia . The effect of the equivalence ratio on MIE is more pronounced than that of an increase in pressure. MIE decreases slightly in a non-linear fashion with increasing pressure for the mixtures studied. A novel mathematical equation is proposed, linking MIE to both equivalence ratio and pressure terms, validated up to 30 bar. This formulation addresses a key gap in the literature, where predictive models for MIE in lean CH 4 –air mixtures under elevated pressures are lacking. The result of our novel method provides practical design guidelines for ignition systems, utilising the numerical estimation of Ts vs ts, as ignition indicators. These results contribute to the broader field of energy efficiency and engine design, providing insights that could lead to improvements in various applications where controlled combustion is essential.