Spherically Symmetric Flame Propagation in Hydrogen-Air Mixtures

Abstract

Abstract Abstract–A Lagragian finite difference procedure is outlined for the modelling of constant pressure, spherically summetric, laminar flames, with detailed chemistry and transport property representation. The procedure is used for modelling spherically expanding hydrogen-air flames such as are obtained during the early, pre-pressure period of constant volume bomb explosions with single spark ignition at the centre. For modelling purposes, such explosions have the advantage over hurning velocity measurements on stationary flames that the speeds of radial advance of the flames in space can be measured in a purely objective manner, and they thus provide a calibration standard for the other overall rate processes (such as key reaction rate or diffusion parameters, or indirectly, the burning velocity itself) in the flames. Sensitivity analyses on the hydrogen-air flame system took full account (a) of published data on the hydrogen-oxygen reaction from a variety of sources, including studies of radical recombination in flames themselves, and (b) of measurments by Clifford, Gray, Mason and Waddicor (1982) of the diffusive properties of hydrogen atoms at room temperature. Taking the "spherical" flame speed of the 41 percent hydrogen-air mixture, measured by Andrews and Bradley (1973), as the calibration standard, they ied, for an assumed activation energy E2 = 70.3 KJ mol-1, to a reaction rate coefficient K2 = (1.8 + 0.2) X 1014 exp(-8450/T) cm3 mol-1 s-1 between 700 and 1500 K, where reaction (ii) is: H+O2 = OH O (ii)Within this range of K2 complete sets of malched diffusion and reaction rate parameters could be obtained so as to predict the observed flame speed. Spherical flame speeds predicted with the use of a specific matched set of such parmeters agreed well with the measurements of Andrews and Bradly (1973) over the whole flammable range of hydrogen-air mixtures.For an initial temperature of 298 K, the observed flame speeds corresponded with a maximum planar, one-dimensional, laminar hydrogen-air burning velocity of 300 cm s -1, at a composition containing about 41 percent hydrogen. Burning velocities corresponding with other compositions, and a complete matched set of reaction rate and diffusion parameters, are tabulated in the paper. The results were not affected by the inclusion of radiative losses into the calculations. The flames results do not confine the remperature dependence of K2 to that of the simple Arrhenius expression above. Retaining the activation energy E2 = 70.3 KJ mol-1 as the base, combination of the flame results with results with recently published shock tube data leads to a three-parameter, modified Arrhenius expression: K2 = 1015 T-0.48 exp(-8450/T), or alternatively: K2 = 1015 T-0.48 exp(-8450/T)cm3mol-1s-1, over the temperature range from 700 to 2500 K. The exspressions have slightly different temperature dependences, but both have confidence limits of + to percent. In the 700 to 1500 K temperature range these limits allow for effects of imprecisions in other key reaction kinetic or difusion parameters in the context of the flame modelling.