A review of theories currently being used to model steady plane flames on flame-holders

A review of theories currently being used to model steady plane flames on flame-holders

McIntosh, A.C.
Clarke, J.F.

Cranfield Institute of Technology, College of Aeronautics

1983-06-30

The stability of burner flames for arbitrary Lewis number is considered on the basis of large activation energy modelling. Previous leading-order-only approaches are now extended to second order in 0,-1 (the inverse activation energy). The assumption that the unsteady perturbations are small (order E) means that one must discuss the distinguished limit implicit in the product OE. It is demonstrated here that different governing equations (and in particular the inner zone equation) are obtained in the two cases, OE — O and OE — oo It is shown that there are two important complex frequency relations governing the behaviour of flames near burners and it is readily seen that the now classical free flame dispersion relation can be derived as a special case for flames with infinite stand-off distance, and Lewis number close to unity. However, for finite stand-off distances, the Lewis number can remain as an arbitrary O (1) parameter and the full description of the flame-behaviour for small perturbations will involve both these frequency relations. Starting in 1946 as the College of Aeronautics, the Cranfield Institute of Technology was granted university status in 1969. In 1993 it changed its name to Cranfield University.

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Cranfield Institute of Technology

College of Aeronautics Report 8316

Aerospace Engineering Reports

report

(c) 1983 Cranfield Institute of Technology