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The ignition time of hydrogen-air diffusion flames is a quantity of utmost interest in a large number of applications, with implications regarding the viability of supersonic combustion and the safe operation of gas turbines. The underlying chemistry and the associated ignition history are very different depending on the initial temperature and pressure. This article addresses conditions that place the system above the so-called second explosion limit, as is typically the case in SCRAMJET operation, so that a branched-chain explosion characterizes the ignition process. The roles of local radical accumulation, molecular transport, and chemical reaction in nonpremixed ignition are clarified by considering the temporal evolution of an unstrained mixing layer formed between two semi-infinite spaces of hydrogen and air. The problem is formulated in terms of a radical-pool mass fraction, whose evolution in time is studied with a WKB expansion that exploits the disparity of chemical time scales present in the problem, leading to an explicit expression for the ignition time. The applicability of the analytical results for obtaining predictions of ignition distances in supersonic-combustion applications is also considered.