We investigate the effect of thermal expansion and gravity on the propagation and stability of flames in inhomogeneous mixtures. We focus on laminar flames in the simple configuration of an infinitely long channel with rigid porous walls in order to understand the effect of inhomogeneities on these fundamental structures. The first part of the thesis is concerned with premixed flames propagating against a prescribed parallel (Poiseuille) flow and subject to thermal expansion. We show that in a narrow channel (corresponding to a relatively thick flame), if the Peclet number is fixed and of order unity, a premixed flame propagating against a parallel flow is governed by the equation for a planar premixed flame with an effective diffusion coefficient. The enhanced diffusion is shown to correspond to Taylor dispersion, or shear-enhanced diffusion. Several important applications of the results are discussed. One of the topics of relevance is the bending effect of turbulent combustion. The results of our analysis show that, for a large flow intensity, the effective propagation speed of the premixed flame for depends only on the Peclet number (which is equal to the Reynolds number if the Prandtl number is unity). This mimics the behaviour of the turbulent premixed flame when the effective propagation speed is plotted versus the turbulence intensity for fixed values of the Reynolds number. The second part of the thesis is concerned with triple flames, subject to thermal expansion and buoyancy. A study is undertaken to investigate the stability of a diffusion flame subject to these effects, which gives rise to a problem analogous to the classical Rayleigh--B\'nard convection problem. A linear stability analysis in the Boussinesq approximation is performed, which leads to analytical results showing that the Burke-Schumann flame is unstable if the Rayleigh number is above a critical value which is determined. Numerical results confirm and complement the analytical results. A full numerical investigation of the effects of gravity and thermal expansion on triple flames propagating in a direction perpendicular to the direction of gravity is then carried out. This configuration does not seem to have received dedicated attention in the literature. It is found that the well-known monotonic relationship between the propagation speed $U$ and the flame-front thickness $\epsilon$, which exists in the constant density case when the Lewis numbers are of order unity or larger, persists for triple flames undergoing thermal expansion. Under strong enough gravitational effects, however, the relationship is no longer found to be monotonic, exhibiting hysteresis if the Rayleigh number is large enough. Finally, the initiation of triple flames from a hot two-dimensional ignition kernel is investigated. Particular attention is devoted to the energy required for ignition and the transient evolution of triple flames after initiation. Steady, non-propagating, two-dimensional solutions representing "flame tubes" are determined; their thermal energy is used to define a minimum ignition energy for the two-dimensional triple flame in the mixing layer. The transient behaviour of triple flames following "energy-increasing" or "energy-decreasing" perturbations to the flame tube solutions is described in situations where the underlying diffusion flame is either stable or unstable.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:644525 |
| Date | January 2015 |
| Creators | Pearce, Philip |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/propagation-and-stability-of-flames-in-inhomogeneous-mixtures(348733fb-7c95-4a9a-b524-de63549cd839).html |
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