Burning velocity and the influence of flame stretch
A new technique is presented for determining burning velocities and stretch effects in laminar flames, and applied to a range of fuel/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 one-dimensional flame speed by extrapolation to infinite radius. The validity of the simple model has been tested by using it to analyse the results of detailed simulations of expanding spherical flames. The true one-dimensional 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 for hydrogen/air mixtures over most of the stoichiometric range. This demonstrates that the extrapolation procedure is sound and will produce reliable results when applied to experimental data. Since the flame speeds derived from experiments are one-dimensional values, multiplying them by the density ratio gives one-dimensional burning velocities (s,'). Maximum burning velocities of hydrogen, methane, ethane, propane and ethylene mixtures with air were 2.85 ms-', 0.37 ms-', 0.41 ms-', 0.39 ms-' and 0.66 ms-' respectively. These are considerably smaller than most burner-derived values. The discrepancies can be explained by flow divergence and stretch effects perturbing burner measurements. 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, the influence of flame stretch, expressed as the Markstein length, can be derived. Again values are given across the whole stoichiometric range of all fuels listed above, and form the most complete set of Markstein lengths reported to date. The Markstein lengths are negative in lean hydrogen and methane and in rich ethane and propane mixtures: this means that stretch increases the burning rate. They are positive in all other mixtures, showing that stretch decreases the burning rate. The results are in line with predictions based on Lewis number considerations. An alternative method of deriving one-dimensional burning velocities and Markstein lengths has been investigated. Burning velocities were measured at different stretch rates in flames in stagnation-point flow. Particle tracking was used to derive burning velocities referred to the hot side of the flame from the upstream values. The two burning velocities extrapolated to different one-dimensional values, both of which differed slightly from the expanding flame results. The suggested reason is that the upstream velocity gradient is not an accurate measure of the stretch experienced by the flame. Markstein lengths were consistent with those from the expanding flame method but the uncertainties were much larger. The method in its present form is therefore useful qualitatively but not quantitatively.