Explicit analytic prediction for hydrogen–oxygen ignition times at temperatures below crossover

Abstract

This paper addresses homogeneous ignition of hydrogen-oxygen mixtures when the initial conditions of temperature and pressure place the system below the crossover temperature associated with the second explosion limit.A three-step reduced mechanism involving H 2 , O 2 , H 2 O, H 2 O 2 and HO 2 , derived previously from a skeletal mechanism of eight elementary steps by assuming O, OH and H to follow steady state, is seen to describe accurately the associated thermal explosion. At sufficiently low temperatures, HO 2 consumption through HO 2 + HO 2 → H 2 O 2 + O 2 is fast enough to place this intermediate in steady state after a short build-up period, thereby reducing further the chemistry description to the two global steps 2H 2 + O 2 → 2H 2 O and 2H 2 O → H 2 O 2 + H 2 . The strong temperature sensitivity of the corresponding overall rates enables activation-energy asymptotics to be used in describing the resulting thermal runaway, yielding an explicit expression that predicts with excellent accuracy the ignition time for different conditions of initial temperature, composition, and pressure.

Four-step and three-step systematically reduced chemistry for wide-range H2–air combustion problems

“…As seen in [6], while the H 2 O 2 steady state is an excellent assumption for flames and also during high-temperature autoignition, it is, however, never a valid approximation during the thermal-runaway events that characterize autoignition below crossover. It then seems natural, in searching to extend the range of validity of the reduced chemistry, to consider the four-step reduced mechanism that follows from assuming that only O and OH are in steady state, while H, HO 2 and H 2 O 2 are not.…”

“…The relevance of the first two of these to flames has been explained previously [1], and the importance of the third in high temperature autoignition has been described [4], while the mathematically convenient fourth step, combined with the first and third, reflects the low-temperature net radical production through H 2 O 2 [6,5]. The computation of the rates x 1b , x 7f and x 8f requires knowledge of the concentrations of O and OH, which can be obtained in explicit form by solving their steady-state equations.…”

“…The procedure involved chain-branching reaction-rate modifications, based on analytical ignition-time studies, keyed to switch on when HO 2 departed sufficiently from its steady-state, to account for the fact that O and OH do not maintain steady states in high-temperature autoignition. While the procedure was shown [4] to work well for the intended range of conditions, it cannot apply to low-temperature autoignition, below crossover, for which suitable reduced chemistry is different [5,6]. The present contribution addresses extending the previous [4] approach to include, as well, the lowtemperature autoignition, a regime of interest in applications involving gas-turbine combustion.…”

“…1f, 2f, 3f, 4f, 6b, 10f, 11f, 12f) is included in the subset of 12 reactions considered here. We shall see below that modifications to the chemistry, guided by knowledge gained in [6], can lead to derivations of reduced descriptions that can successfully describe not only flames and high-temperature autoignition, but also autoignition events below the second explosion limit.…”

“…Only eight elementary reactions have to be considered to accurately describe the low-temperature autoignition regime [5,6,9], and each of them (resp. 1f, 2f, 3f, 4f, 6b, 10f, 11f, 12f) is included in the subset of 12 reactions considered here.…”