Flame propagation through a non-ideal gas

Advances in understanding the dynamics of premixed flames have been predominantly made by assuming that the combustible mixture behaves as an ideal gas. While this assumption is suitable in many circumstances, it does not properly describe combustion at high pressures that is of interest in some practical systems. In this paper, we derive an asymptotic model of premixed flame propagation through a non-ideal gas in closed vessels, but the results readily accommodate flame propagation under isobaric conditions. Specifically, we employ the Noble-Abel equation of state, accounting for finite molecular volume, which is known to be significant at high pressures. Our analysis resides within the framework of the hydrodynamic theory for which the flame is thin relative to all the other length scales in the problem. Multi-scale methods are used to resolve the internal flame structure, resulting in explicit equations that determine the pressure rise throughout the vessel, as well as the instantaneous flame location, the local mass burning rate and flame speed. The flame speed is modulated by a Markstein number which has an explicit dependence on the co-volume parameter, a measure of the volume occupied by the molecules involved in the combustion process. For the enclosed flame, the Markstein number is also found to depend on the mean pressure rise. Our model is used to examine non-ideal gas effects on the propagation of free and confined flames in simple geometries. Novelty and significance statement This work provides the first formal asymptotic model of premixed flame propagation through a non-ideal gas in free and confined environments, thereby extending the hydrodynamic theory to new parameter regimes. The work is significant in that many practical combustion systems, such as rocket engines, gas turbines and incinerators, operate under these conditions.