The structure and propagation of laminar flames under autoignitive conditions

The laminar flame speed sl is an important reference quantity for characterising and modelling combustion. Experimental measurements of laminar flame speed require the residence time of the fuel/air mixture (τf) to be shorter than the autoignition delay time (τ). This presents a considerable challenge for conditions where autoignition occurs rapidly, such as in compression ignition engines. As a result, experimental measurements in typical compression ignition engine conditions do not exist. Simulations of freely propagating premixed flames, where the burning velocity is found as an eigenvalue of the solution, are also not well posed in such conditions, since the mixture ahead of the flame can autoignite, leading to the so called “cold boundary problem”. Here, a numerical method for estimating a reference flame speed, sR, is proposed that is valid for laminar flame propagation at autoignitive conditions. Two isomer fuels are considered to test this method: ethanol, which in the considered conditions is a single-stage ignition fuel; and dimethyl ether, which has a temperature-dependent single- or two-stage ignition and a negative temperature coefficient regime for τ. Calculations are performed for the flame position in a one-dimensional computational domain with inflow-outflow boundary conditions, as a function of the inlet velocity UI and for stoichiometric fuel-air premixtures. The response of the flame position, LF, to UI shows distinct stabilisation regimes. For single-stage ignition fuels, at low UI the flame speed exceeds UI and the flame becomes attached to the inlet. Above a critical UI value, the flame detaches from the inlet and Lf becomes extremely sensitive to UI until, for sufficiently high UI, the sensitivity decreases and Lf corresponds to the location expected from a purely autoignition stabilised flame. The transition from the attached to the autoignition regimes has a corresponding peak dLf/dUI value which is proposed to be a unique reference flame speed sR for single-stage ignition fuels. For two-stage ignition fuels, there is an additional stable regime where a high-temperature flame propagates into a pool of combustion intermediates generated by the first stage of autoignition. This results in two peaks in dLf/dUI and therefore two reference flame speed values. The lower value corresponds to the definition of sR for single-stage ignition fuels, while the higher value exists only for two-stage ignition fuels and corresponds to a high temperature flame propagating into the first stage of autoignition and is denoted sR′. A transport budget analysis for low- and high-temperature radical species is also performed, which confirms that the flame structures at UI=sR and UI=sR′ do indeed correspond to premixed flames (deflagrations), as opposed to spontaneous ignition fronts which do not have a unique propagation speed.