The Crucial Role of the Lewis Number in Jet Ignition

During the early phase of the transient process following a hydrogen leak into the atmosphere, a contact surface appears separating hot air from cold hydrogen. Locally, the interface is approximately planar. Diffusion occurs, potentially leading to ignition. This process was analyzed by Lin˜a´n and Crespo (1976) for Lewis number unity and Lin˜a´n and Williams (1993) for Lewis number less than unity. In addition  to conduction, these processes are affected by expansion due to the flow, which leads to a temperature drop. If chemistry is very temperature-sensitive, then the reaction rate peaks close to the hot region, where relatively little fuel is present. Indeed the Arrhenius rate drops rapidly as temperature drops, much more so than fuel concentration. However, the small fuel concentration present close to the airrich side depends crucially upon the balance between fuel diffusion and heat diffusion, hence the fuel Lewis number. For Lewis number unity, the fuel concentration present due to diffusion is comparable to the rate of consumption due to chemistry. If the Lewis number is less than unity, fuel concentration brought in by diffusion is large compared with temperature-controlled chemistry. For a Lewis number greater than unity, diffusion is not strong enough to bring in as much fuel as chemistry would be able to burn, and combustion is controlled by fuel diffusion. In the former case, combustion occurs faster, leading to a localized ignition at a finite time determined by the analysis. As long as the temperature drop due to the expansion associated with the multidimensional nature of the jet does not lower significantly the reaction rate up to that point, ignition in the jet takes place. For fuel Lewis number greater than unity, first, the reaction rate is much lower. Second, chemistry does not lead to a defined ignition. Eventually, expansion will affect the process and ignition does not take place. In summary, it appears that the reason why hydrogen is the only fuel for which jet ignition has been observed is a Lewis number effect, coupled with a high speed of sound hence a high initial temperature discontinuity.