The use of expanding spherical flames to determine burning velocities and stretch effects in hydrogen/air mixtures

Abstract

A new technique is presented for determining burning velocities and stretch effects in laminar flames, and applied to hydrogen/air mixtures. The speeds of expanding spherical flames, measured by high-speed schlieren cine-photography, are shown to vary with flame radius. A simple phenomenological model has been developed to analyse the data and obtain the 1-D flame speed by extrapolation to infinite radius. A computer program has also been developed for detailed simulation of expanding flames. The validity of the simple model has been tested by using it to analyse the results of the detailed simulations. The true 1-D flame speeds in this case are known from planar flame modelling using the same kinetic scheme. The simple model predicted flame speeds within 2% of the true values over most of the stoichiometric range. This demonstrates that our extrapolation procedure is sound and will produce reliable results when applied to experimental data. Since the flame speeds derived from experiments are 1-D values, multiplying them by the density ratio gives 1-D burning velocities (S u 0 ). Burning velocities are reported for mixtures containing 9 to 68% hydrogen. The maximum S u 0 is 2.85 ms −1 , considerably less than most burner-derived values. The discrepancies can be explained by flow divergence and stretch effects perturbing burner measurements. Planar flame modelling reproduces the experimental burning velocities to within 3% over most of the stoichiometric range. The rate at which the measured flame speed approaches its limiting value depends on flame thickness and flame stretch. By subtracting the flame thickness term, Markstein lengths can be derived. Again values are given across the whole stoichiometric range. They are negative in lean mixtures (i.e. stretch increases the burning rate) but positive in stoichiometric and rich (stretch reducing burning rate). This is in line with predictions based on Lewis number considerations.