One-step reduced kinetics for lean hydrogen–air deflagration

Abstract

A short mechanism consisting of seven elementary reactions, of which only three are reversible, is shown to provide good predictions of hydrogen-air lean-flame burning velocities. This mechanism is further simplified by noting that over a range of conditions of practical interest, near the lean flammability limit all reaction intermediaries have small concentrations in the important thin reaction zone that controls the hydrogen-air laminar burning velocity and therefore follow a steady state approximation, while the main species react according to the global irreversible reaction 2H 2 + O 2 → 2H 2 O. An explicit expression for the non-Arrhenius rate of this one-step overall reaction for hydrogen oxidation is derived from the seven-step detailed mechanism, for application near the flammability limit. The one-step results are used to calculate flammability limits and burning velocities of planar deflagrations. Furthermore, implications concerning radical profiles in the deflagration and reasons for the success of the approximations are clarified. It is also demonstrated that adding only two irreversible direct recombination steps to the seven-step mechanism accurately reproduces burning velocities of the full detailed mechanism for all equivalence ratios at normal atmospheric conditions and that an eight-step detailed mechanism, constructed from the seven-step mechanism by adding to it the fourth reversible shuffle reaction, improves predictions of O and OH profiles. The new reduced-chemistry descriptions can be useful for both analytical and computational studies of lean hydrogen-air flames, decreasing required computation times.

The structure of lean hydrogen-air flame balls

“…The plots show results corresponding to the stable branch of large flame balls, which begins at the flame-ball lean limit / l ¼ 0:0735. Note that, because of the large fuel diffusivity, this critical value / l ¼ 0:0735 is much smaller than that of planar flames for the same ambient conditions / l ¼ 0:251 [13,14].…”

“…2, the solutions of stable flame balls corresponding to points along the upper branch of the r f -/ curve exhibit moderate peak temperatures not far from the crossover value. As shown recently [13,14], under those conditions all intermediates appear in very small concentrations and can be assumed to follow a steady-state description, whereas the main species react according to the overall reaction 2H 2 + O 2 ? 2H 2 O, with a rate (moles per unit volume per unit time) given by…”

“…These flame balls are stable due to radiation, with a radius that increases in such a way that radiant heat losses keep the peak temperature at a value that barely exceeds T c . Under those conditions, the one-step chemistry recently developed for near-limit hydrogen-air deflagrations [13,14] can be used to describe with excellent accuracy the whole branch of stable flame balls. As may be seen in Fig.…”

“…The associated departures are however small, so that the reaction-sheet description is satisfactory, as demonstrated by the plots in Figs. 1 and 2. conditions exist only for equivalence ratios above a lean flammability limit / l ¼ 0:251 [13,14], determined by the condition that the flame temperature equals the crossover temperature T c , nonpropagating flames in the form of flame balls exist under microgravity conditions for much lower values of the equivalence ratio due to the high diffusivity of hydrogen enhanced by Soret effects. These flame balls are stable due to radiation, with a radius that increases in such a way that radiant heat losses keep the peak temperature at a value that barely exceeds T c .…”

“…In the formulation, C M represents the effective third-body concentration, which accounts for the non-unity third-body chaperon efficiencies of H 2 O and H 2 associated with reaction 4f . The subscripts f and b in (9) denote forward and backward reaction-rate constants, while G, H and a are functions of order unity of the composition and temperature [13].…”