On the critical pressure pulse width for ignition of hydrogen–air and dimethyl ether–air mixtures

Abstract

Under certain situations, such as a water hammer event, a volume of gas can undergo a rapid compression immediately followed by a rapid expansion, which could lead to auto-ignition under certain conditions. The goal of the present study was to investigate under which critical conditions such a pressure pulse could lead to an ignition event. To simulate the pressure pulse, a simplified Gaussian pressure pulse model was implemented in Cantera. Hydrogen–air and dimethyl ether–air mixtures were employed to study the ignition dynamics of chemical systems with a single and a double step of heat release. The numerical simulations were performed for three peak pressures of 101.3, 1013.2, and 5066 kPa, for a range of compression ratios between 5 and 45, and various pulse widths, which determine the characteristics of the pressure pulse. Depending on the width of the Gaussian pulse, either ignition or chemical quenching were observed. Critical ignition, just at the limit between ignition and quenching, is the result of the competition between chemical reaction and volumetric expansion due to the imposed specific volume changes. This competition can be summarized by the concept of critical pressure pulse width, which is an extension of the critical decay rate concept. To further investigate the mechanisms responsible for critical ignition and quenching, quantitative thermo-chemical analyses were performed for sub-critical, critical and super-critical conditions. A Damköhler number was defined as the ratio of characteristic time of expansion to ignition delay time to characterize the competition between ignition and quenching. A simplified non-dimensional pressure pulse model for which the derivative of the naperian logarithm of density was assumed to follow a linear law was established. It can be employed to derive the critical conditions for which ignition fails. The evolution of non-dimensional temperature was obtained numerically and showed the existence of a critical pulse width for successful ignition and that the location of ignition delay time moves from the expansion phase to the compression phase as the non-dimensional pulse width is increased.