Turbulent flame speeds in ducts and the deflagration/detonation transition

A methodology is proposed for determining whether a deflagration-to-detonation transition (DDT) might occur for flame propagation along a duct with baffles, closed at the ignition end. A flammable mixture can attain a maximum turbulent burning velocity. If this is sufficiently high, a strong shock is formed ahead of the flame. It is assumed that this maximum burning velocity is soon attained and on the basis of previous studies, this value can be obtained for the given conditions. The increase in temperature and pressure of the reactants, due to the shock, further increases the maximum turbulent burning velocity. The gas velocity ahead of the flame is linked to one-dimensional shock wave equations in a numerical analysis. The predicted duct flame speeds with the appropriate maximum turbulent burning velocities are in good agreement with those measured in the slow and fast flame regimes of a range of CH4–air and H2–air mixtures. DDTs are possible if autoignition of the reactants occurs in the time available, and if the projected flame speed approaches the Chapman–Jouguet velocity at the same temperature and pressure. Prediction of the first condition requires values of the autoignition delay time of the mixture at the shocked temperatures and pressures. Prediction of the second requires values of the laminar burning velocity and Markstein number. With the appropriate values of these parameters, it is shown numerically that there is no DDT with CH4–air. With H2–air, the onset of DDT occurs close to the values of equivalence ratio at which it has been observed experimentally. The effects of different duct sizes also are predicted, although details of the DDT cannot be predicted. Extension of the study to a wider range of fuels requires more data on their laminar burning velocities and Markstein numbers at higher temperatures and pressures and on autoignition delay times at lower temperatures and pressures.