Effects of Lewis numbers and kinetics on spontaneous ignition of hydrogen jets

Abstract

The transient process following a hydrogen leak into the atmosphere initiates as a contact surface appears separating air heated by the leading shock from hydrogen cooled by expansion. Diffusion of heat and species produces reactive mixture, potentially leading to ignition. Reactions being very temperature-sensitive, their rate peaks close to the hot air-rich side of the interface, where the small fuel concentration depends upon the fuel Lewis number. If the Lewis number is less than unity, diffusion brings in more fuel than temperature-controlled chemistry consumes. If greater, diffusion does not bring in as much fuel as chemistry would burn. Results from the current analysis for multistep kinetics also show that the role of the H Lewis number is crucial. In the short time limit, the evolution of the diffusion layer appears as a perturbation superimposed to the self-similar non-reactive diffusion solution. Initiation is very slow compared with steps consuming one reactant and an intermediate species, while some steps associated with termination are extremely fast. The approximation being made, assuming initiation much smaller than most rates, and termination much faster, is very accurate since the corresponding ratios are of the order of 105. The resulting problem still requires a numerical solution. A time-splitting algorithm combines exact solutions to three subproblems, avoiding issues such as stiffness of the kinetics. The problem is formulated not in physical space but in the similarity variable of the diffusion problem, hence avoiding difficulties associated with the initial singularity when the layer has zero thickness, and the resulting uncertainties. These are distinct advantages over numerical simulations, which however will retain a reasonable accuracy at later times. Results confirm the role of the Lewis number. They also show two distinct regimes: an early one mainly controlled by initiation, and a later one controlled by chain-branching, with a sharp transition.