Flame propagation in a tube with wall quenching of radicals

In micro- and meso-scale combustion, there exists strong flame-wall interaction and flame can be quenched by thermal and kinetic mechanisms. The thermal quenching mechanism has been well studied while the kinetic quenching mechanism has received little attention. To provide an incremental advance to former analytical models, we conduct theoretical analysis on flame propagation in a tube with emphasis on both thermal and kinetic quenching mechanisms. A two-step chemistry model for gaseous combustion is employed and it consists of a chain-branching reaction and a completion reaction. To mimic the wall quenching of radicals, a one-step surface quenching reaction of radicals is considered. A general theoretical description of quasi-one-dimensional flame propagation in a tube with both heat loss and radical quenching is presented. An analytical correlation, which describes the change of the flame propagation speed with heat loss and radical quenching coefficients, is derived. Based on this correlation, the effects of radical Lewis number, cross-over temperature, wall temperature, and tube diameter on flame speed and quenching limit are examined. The results show that the impacts of both heat loss and radical quenching become stronger at smaller radical Lewis number. With the increase of cross-over temperature, flame extinction due to heat loss and that due to radical quenching are shown to be promoted and inhibited, respectively. With the increase of wall temperature, both the thermal and kinetic quenching limits are significantly extended. With the decrease of the tube diameter, flame extinction occurs due to thermal and/or kinetic quenching. It is found that the radical quenching effect becomes stronger at higher wall temperature and/or lower cross-over temperature.