The Time Evolution of Interactions Between Ultra Short Length Scale Pressure Distrubances and Premixed Flames.

Abstract

The non-linear wave equation governing the progress of short length scale pressure perturbations across a conventional premixed flame is solved numerically. The particular acoustic disturbances considered have length scales of the same order as that of the flame and fractional amplitudes limited to O(l/θ), where θ is the dimensionless activation energy. These restrictions imply that the effects of the reaction and diffusion processes within the flame are negligible over the time scale of the passage of the pressure signals. The length scale of such a disturbance is of the order of a typical diffusion length, so the spatially varying temperature and density profile within the preheat and reaction zones must be considered (McIntosh 1989, McIntosh and Wilce 1991). However, in this work the exact steady temperature distribution, generated numerically, is used in the hyperbolic governing equations, enabling disturbances with length scales near to those of shock waves to be considered.

Shock formation times are calculated for signals emerging from the flame, and are compared with those for signals crossing a temperature discontinuity equal in magnitude to the overall change in temperature across the flame. The plots of these shock formation times show a slight decrease when the interaction between the pressure gradients of the input and the temperature gradients within the flame are considered.

The passage of a pressure step with length scale of the order described above represents an effectively instantaneous change in the flow quantities which knocks the flame out of equilibrium. The subsequent readjustment is examined by solving numerically the coupled non linear reaction-diffusion equations in temperature and fuel mass fraction.

The results show that for small, O(1/θ), pressure changes, although the mass burning rate initially varies rapidly as the reaction rate responds instantaneously to temperature fluctuations, the flame eventually attains a new steady state through diffusion processes.