Effects of Chemical Kinetics on Ignition of Hydrogen Jets

During the early phase of the transient process following a hydrogen leak into the atmosphere, a contact surface appears separating air heated by the leading shock from hydrogen cooled by expansion. Locally, the interface is approximately planar. Diffusion leads to a temperature decrease on the air side and an increase in the hydrogen-filled region, and mass diffusion, of hydrogen into air and of air into hydrogen, potentially resulting in ignition. This process was analyzed by Li ˜nan and Crespo [1] for unity Lewis number and Li ˜nan and Williams [2] for Lewis number less than unity. We included in the analysis the effect of a slow expansion [3, 4], leading to a slow drop in temperature, which occurs in transient jets. Chemistry being very temperature-sensitive, the reaction rate peaks close to the hot side of the interface, where only a small fuel concentration present close to the warm, air-rich side, which depends crucially upon the fuel Lewis number. For Lewis number unity, the fuel concentration due to diffusion is comparable to the rate of consumption by chemistry. If the Lewis number is less than unity, diffusion brings in more fuel than temperature-controlled chemistry consumes. For a Lewis number greater than unity, diffusion is not strong enough to bring in as much fuel as chemistry would burn; combustion is controlled by fuel diffusion. If the temperature drop due to expansion associated with the multidimensional jet does not lower significantly the reaction rate up to that point, analysis shows that ignition in the jet takes place. For fuel Lewis number greater than unity, chemistry does not lead to a defined explosion, so that eventually, expansion will affect the process; ignition does not take place [3, 4]. In the current paper, these results are extended to consider multistep chemical kinetics but for otherwise similar assumptions. High activation energy is no longer applicable. Instead, results are obtained in the short time limit, still as a perturbation superimposed to the self-similar solution to the chemically frozen diffusion solution. In that approximation, the initiation step, which consumes fuel and oxidant, is taken to be slow compared with steps that consume one of the reactants and an intermediate species. The formulation leads to a two point boundary value problem for set of coupled rate equations plus an energy equation for perturbations. These equations are linear, with variable co-effcients. The coupled problem is solved numerically using a split algorithm in which chemical reaction is solved for frozen diffusion, while diffusion is solved for frozen chemistry. At each time step, the still coupled linear problem is solved exactly by projecting onto the eigenmodes of the stiff matrix, so that the solution is unaffected by stiffness. Since in the short time limit, temperature is only affected at the perturbation level, the matrix depends only on the similarity variable x t but it is otherwise time-independent. As a result, determination of the eigenvalues and eigenvectors is only done once (using Maple), for the entire range of discretized values of the similarity variable. The diffusion problem consists of a set of independent equations for each species. Each of these is solved using orthogonal decomposition onto Hermite polynomials for the homogeneous part, plus a particular solution proportional to time for the non-homogeneous (source) terms. That approach can be implemented for different kinetic schemes.