A theory for fast‐igniting catalytic converters

Using asymptotic expansion and numerical analysis, we demonstrate how the step‐response ignition time of an automobile catalytic converter depends on the ratio of the reaction rate to the interphase heat‐transfer rate, as measured by a key Damköhler parameter χ and the degree of monolith subcooling ŋ.In the region of low reactionrate at smallχ, the normalized ignition time t ig scaled bythe homogeneous ignition time from the inlet gas temperature is (t ig t   ig ∞ ) = 1 + 2 χ 1/2 ∣ln( χ 1/2 /2 η)∣ 1/2 , and the ignition takes place at a thermal front deep in themonolith. At large χ when the reaction rate is high, ignition occursat the leading edge of the monolith with (t ig /t   ig ∞ ) = 2.50 + χ(ln η − 0.34).The delay in ignition time with increasing χ is due to a Taylor‐Aris dispersion mechanism induced by interphase heat transfer. Although the small‐ χ ignition mechanism is faster, its downstream ignition location leads to a very slow upstream propagation of the thermal front that follows ignition. An optimal converter system that ignites in 13 s, 25% of the current value in a standard step‐response test, is then designed by placing a small igniter, which ignites by the small‐ χ mechanism, upstream to preheat the current converter which then ignites by the large‐ χ mechanism. The length of the igniter is kept small by bypassing 2/3 of the exhaust since, from our theory, t   ig ∞is independent of the gas velocity.