Flame Flashback Critical Damköhler Number for CO$_2$ Diluted CH$_4$ and C$_3$H$_8$ Mixtures with Air

Abstract

The premixed laminar flame flashback phenomenon in tubes has been known and studied for several decades. However, the effect of the CO$_2$ dilution has not been addressed, which is relevant for assessing the safety of oil-producing facilities. Furthermore, even if numerical studies have underscored the important role played by the mixture Lewis number (Le), these lack an experimental validation. For this reason, specific studies of premixed flame flashback in laminar flows have been undertaken. The objective is to assess the flame flashback critical conditions in mixtures of hydrocarbons — methane or propane diluted by various amounts of CO$_2$ — with air. This is effected by determining the critical Damköhler number, which is computed using both experimental and numerical data. The former leads to the flashback critical velocity gradient, whereas the latter to a characteristic chemical time scale. The effect of different flame thickness definitions on the Damköhler number (Da) is examined, evidencing than an order of magnitude discrepancy may arise depending on the definition choice. For methane/air mixtures the critical Da increases with the equivalence ratio, whereas a decrease of nearly two orders of magnitude has been obtained for propane/air mixtures. The original results show that CO$_2$ dilution increases Da only when the fuel dilution percentage is larger than 25 and 50%, for methane and propane, respectively, situations which correspond to flame extinction after flashback. The propane/air/CO$_2$ mixture results exhibit a $Da \propto Le^{5.06}$ dependency which closely follows the trend computed previously, whereas the methane/air/CO$_2$ results evidence the thermal boundary condition at the tube wall influence.