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 wnsidered have length scales of the same order as that of the flame and fractional amplitudes limited to 0(1/9), where 0 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 wnsidered (Mclntosh 1989, McIntosh and Wilce 199i): 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 arc 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 wnsidered.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 reactiondiffusion equations in temperature and fuel mass fraction.The results show that for small, 0(1/8), 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.
The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.
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