The Effect of Finite Molecular Volume on the Propagation of Unsteady Spherical Flame Front

An asymptotic analysis on the dynamics of adiabatic and nonadiabatic spherically expanding laminar flame was performed for real gas described by the Noble-Abel equation of state. The effect of the finite molecular volume was considered and characterized by a covolume parameter. It was demonstrated that the non-ideal model leads to higher flame speed at quasi-steady state and to lower Markstein number compared to the perfect gas based solutions. The change of the value of these two parameters is proportional to the covolume parameter. For example, with a covolume of 0.1, the flame speed was increased by 10%, while the Markstein number could be reduced by up to 35%, depending on the value of the Lewis number. In addition, the finite molecular volume effect promotes the quenching of nonadiabatic flame in the vicinity of the critical state. New relations for extrapolation of the zero-stretch flame speed were established. It was shown that non-negligible modifications of the unstretched laminar flame speed and Markstein number are introduced by the finite molecular volume effect at high pressure. Strategies for high-pressure laminar flame speed extrapolation were discussed and the relative uncertainty related to the finite volume effect is of 20%–45% over the total uncertainty for pressures in the range 1–2.5 MPa, indicating that this effect cannot be neglected to determine the laminar flame speed under such pressure conditions. The impact of real gas effect was further illustrated with numerical flame simulations for a stoichiometric hydrogen–air mixture.Novelty and Significance Statement1. First asymptotic analysis of adiabatic and nonadiabatic unsteady expanding spherical flame in a Noble-Abel gas2. Covolume promotes higher flame speed but mitigates ignition3. Non-negligible effect of the covolume even at a pressure of few MPa is demonstrated4. First unsteady numerical simulations of spherical flame in a Noble-Abel gas