Measurements of the Concentrations of Free Hydrogen Atoms in Flames from Observations of Ions: Correlation of Burning Velocities with Concentrations of Free Hydrogen Atoms

Abstract

A mass spectrometer has measured the concentrations of ions generated when trace amounts of alkaline earth metals (Sr or Ca) were added to the gas supply of a nonturbulent, almost flat, premixed flame of H 2 + O 2 + N 2 at atmospheric pressure. In this case, the ions produced are largely Sr + and SrOH +; their relative concentrations are governed by the reaction Sr ++ H 2 O⇌ SrOH ++ H being sufficiently fast to be equilibrated everywhere in a flame. Detailed studies of [Sr +]/[SrOH +] provide a method for measuring the concentration of free hydrogen atoms. Calibration techniques allowed absolute concentrations of free hydrogen atoms to be determined along the length of five fuel-rich flames with temperatures of 1820–2400 K. It was found that Sr and Ca gave identical results; also, the addition of small amounts (<0.5 vol %) of C 2H 2 to the burner supplies had little effect on the concentrations of radicals. Furthermore, in a hot flame (>2200 K), the measured maximum concentration of the radical pool corresponds to chain branching being almost total and also at that stage the pool is hardly affected by any recombination of radicals. Thus, the initial reaction can be written as 3H 2 + O 2 → 2H 2O + 2H. This is a considerable simplification of the chemical changes occurring in the reaction zone. In cooler flames (<2000 K) radical recombination is more conspicuous, and the maximum concentration of radicals is significantly lower than this maximum yield. The reactions occurring in the reaction zone have been considered, and both the maximum concentration of radicals close to the reaction zone and the local temperature were derived from an extremely simple, steady-state model. Agreement with experimental values is good in all but the coolest flame. A new pneumatic method, based on the rate at which gas is sampled from a flame into a vacuum chamber, coupled with the measured [H], yielded both the composition and temperature of a flame at any point. The derived temperatures agree well with those computed from measurements of [H] using an enthalpy balance. A simple theory gave the burning velocity as ([H] m/2){ k 4D H/[O 2] u} 1/2 in one of these rich flames of H 2 + O 2 + N 2. Here [H] m is the maximum concentration of free H atoms, D H is their diffusivity, [O 2] u is the concentration of O 2 in the unburned gas mixture, and k 4 is the rate constant of H+ O 2→ OH+ O the rate-determining step for radical generation, evaluated at the temperature at which [H] is a maximum. This formula gives good predictions of S u for such rich flames with final temperatures above 1800 K; its basis is that the burning velocity is mainly determined by countercurrent diffusion of free H atoms into unreacted gas, coupled with more radicals being produced in reaction Eq. (4).