THE LINEARIZED RESPONSE OF THE MASS BURNING RATE OF A PREMIXED FLAME TO RAPID PRESSURE CHANGES

An investigation is made into the response of the mass burning rate of a premixed flame to small but sharp changes in pressure. In this paper a fast time scale is considered such that tau = diffusion time/acoustic time = K'/u01'2/l(a)'/a01' = theta2 (K' = thermal diffusivity, u01' = initial burning velocity, l(a)' = a typical acoustic length, a01' = frozen sound speed, theta = nondimensional activation energy). Previous studies by the author (McIntosh 1990) and by other researchers (e.g. Ledder and Kapila 1991) have considered the case of tau = 1 which is the usual value corresponding to audible resonance of flames in tubes, burner ports etc, However the case tau = theta2 (McIntosh 1991) is a most interesting and distinct case since then the fast time scale alters the inner reaction zone which consequently obeys a different and essentially unsteady diffusion-reaction equation. The mass burning rate is then on an appreciably larger scale. The time response of the mass burning rate to pressure fluctuations at this fast time scale is governed in general by a non-linear partial differential equation whose solution has already been investigated for small amplitudes of harmonic pressure fluctuations. In this paper the solution is extended to second order in theta-1 and it is found that the effect of activation energy on the peak amplitude of mass burning rate fluctuation is substantial. The work is further extended to include different types of non-harmonic pressure inputs. It is found that the transient mass burning rate response can vary by large amounts particularly at early times. Sudden acceleration or extinction are distinct possibilities.