Numerical studies on the ignition and propagation for spherically expanding premixed cool flames under gravitational conditions

Cool flame speed is a fundamental parameter, which requires special consideration in terrestrial measurement due to the slow propagation of the cool flame, the intrusion of gravity, and multiple flame regimes (cool, hot, and double flames). The current study employs multiscale numerical simulations with and without gravity to investigate premixed spherical cool flame ignition and propagation. One-dimensional simulations without gravity are adopted to study the effects of initial ambient temperature T0 , pressure P0 , equivalence ratio phi, and ignition kernel temperature TH on feasible conditions for an isolated cool flame measurement, emphasizing the intrinsic couplings among the cool flame, hot flame, and autoignition. Besides considering the minimum and maximum ignition energies for low-temperature ignition (LTI), the results highlight the impacts of the auto -ignition upstream and hot flame downstream of the cool flame on speed measurement. Comprehensive effects of T0 , P0 , and phi are evaluated in order to obtain accurate flame speed versus stretch rate data for extrapolation. Two-dimensional simulations focus on the cool flame deformation with buoyancy. Buoyancy induces a toroidal vortex, causing the spherical cool flame to be mushroom-like at high Richardson numbers, a non-dimensional metric used to evaluate the relative importance of buoyancy. The flame deformation at different ambient temperatures and equivalence ratios are observed. Detailed analyses of the flow field, the deformed flame structure, and the effects of stretch and diffusion are performed. In addition, three equivalent flame radius definitions are proposed and compared to extrapolate cool flame speed. Different from the previous studies on the gravitational hot flames, the current results identify the flame volume-based radius (i.e., Req,V) to be the best one for extrapolating non-spherical cool flame speed, with which cool flames faster than 8 cm/s can be measured within 5% uncertainty. Finally, a systematic strategy is proposed to guide the experimental design. The current work reveals unique cool flame dynamics under gravity conditions and helps to measure the cool flame speed in a terrestrial environment.