On the prediction of hot spot induced ignition by the Livengood-Wu integral

Abstract

The Livengood-Wu (L-W) integral is popularly used to predict the occurrence of homogeneous autoignition without heat and mass transport; yet it has not been used for non-homogeneous forced ignition which usually occurs in fire or explosion accidents. In this study, the forced ignition process caused by a hot spot in a flammable mixture is considered, and a method using the L-W integral is developed to predict the critical ignition temperature. In this method, the evolution of the temperature at the hot spot center is first obtained by solving the one-dimensional unsteady heat conduction equation. Then the L-W integral is evaluated based on the central temperature evolution and the corresponding homogenous ignition delay time. The critical ignition temperature is determined at the condition when the L-W integral reaches unity. The present method based on the L-W integral can reduce the computational cost by two to three orders compared to the transient simulation considering detailed chemistry and transport. Different fuels including methane, hydrogen, n-heptane, and dimethyl ether are considered. The predicted critical ignition temperature based on the L-W integral is compared with that predicted by one-dimensional transient simulations considering detailed chemistry and transport. For hydrogen, the present method based on the L-W integral can accurately predict the critical ignition temperature. However, for the other three fuels, the predicted critical temperature is lower than that from detailed simulation. Such under-prediction is interpreted by the ratio between the time scales for ignition and mass diffusion. Nevertheless, the method based on the L-W integral can give a conservative prediction of the critical ignition temperature, which is important for fire safety considerations. Besides, the effects of low temperature chemistry (LTC) on hot spot induced ignition are examined. It is found that the hot spot induced ignition is mainly controlled by high temperature chemistry.