Flame speed and particle image velocimetry measurements of laminar burning velocities and Markstein numbers of some hydrocarbons

Abstract

Particle image velocimetry, PIV, is described for measuring laminar burning velocities during flame propagation in spherical explosions, by the measurement of the flame speed and gas velocity just ahead of the flame. Measurements made in this way are compared with those obtained from the flame speed method, which is based on the flame front propagation speed and the ratio of unburned to burned gas densities. Different values arise between the two methods, and the principal reason is the common assumption in the flame speed method that the burned gas density is at the equilibrium, burned gas, adiabatic temperature. When allowance is made for the effects of flame stretch rate and Lewis number on this density, the differences in burning velocities are significantly decreased. The PIV methodology enables mass rate of burning velocities to be expressed in terms of the burning velocity at zero stretch rate and the Markstein numbers for strain rate and flame curvature. Burning velocities and Markstein numbers are presented for methane, i-octane, ethanol, and n-butanol over a range of equivalence ratios at atmospheric pressure and, in the case of n-butanol, also over a range of pressures. Account is taken of the low stretch rate at which a laminar flame becomes unstable, and, below which, the burn rate increases due to the enhanced flame surface area. The critical stretch rates for the transition are identified. In measuring Markstein numbers, there is a dependency upon the isotherm employed for the measurement of the stretch rate. This aspect is studied by comparing measurements with two different isotherms. It is concluded that the measured PIV flame measurements might under-estimate the Markstein numbers by about 12%.