Response of counterflow diffusion flames to oscillating strain rates

The response of counterflow flames to oscillating strain rates is analyzed by using large activation energy asymptotics, as a potential application to turbulent combustion and acoustic instability of rocket engines. The characteristic oscillation time of practical interest is found to be of the same order as the characteristic diffusion time of the flame, so that the flame structure consists of a quasi-steady reactive-diffusive layer embedded in the outer unsteady-diffusive-convective zone. A linear analysis is conducted by assuming that the amplitude of the strain rate oscillation is small relative to the mean strain rate. Results show that the flame response is controlled mainly by two effects: (a) the response of the convective mass flux into the reaction sheet, which is directly related to the flow-field variation applied at the boundary, and (b) the response of the reaction sheet to adjust the reduced residence time due to finite-rate chemistry. For flames near equilibrium, the former effect tends to be dominant, so that the response of the net heat release is in phase with the strain rate oscillation. For flames near extinction, however, the finite-rate chemistry effect overtakes the fluid-dynamic effect such that increasing strain rate leads to a reduction of the reactivity of the flame during the oscillatory cycle. As such, the net heat release response of the near-extinction flame becomes out of phase with the strain rate oscillation in the sense of the Rayleigh's criterion. Results of the present study suggest the possibility that the unsteady characteristics of the near-extinction diffusion flame can be significantly different from those in the Burke-Schumann limit.