The influences of fuel Lewis number Le F on localised forced ignition of inhomogeneous mixtures are analysed using three-dimensional compressible Direct Numerical Simulations (DNS) of turbulent mixing layers for Le F = 0.8, 1.0 and 1.2 and a range of different root-mean-square turbulent velocity fluctuation u values. For all Le F cases a tribrachial flame has been observed in case of successful ignition. However, the lean premixed branch tends to merge with the diffusion flame on the stoichiometric mixture fraction isosurface at later stages of the flame evolution. It has been observed that the maximum values of temperature and reaction rate increase with decreasing Le F during the period of external energy addition. Moreover, Le F is found to have a significant effect on the behaviours of mean temperature and fuel reaction rate magnitude conditional on mixture fraction values. It is also found that reaction rate and mixture fraction gradient magnitude |∇ξ | are negatively correlated at the most reactive region for all values of Le F explored. The probability of finding high values of |∇ξ | increases with increasing Le F . For a given value of u , the extent of burning decreases with increasing Le F . A moderate increase in u gives rise to an increase in the extent of burning for Le F = 0.8 and 1.0, which starts to decrease with further increases in u . For Le F = 1.2, the extent of burning decreases monotonically with increasing u . The extent of edge flame propagation on the stoichiometric mixture fraction ξ = ξ st isosurface is characterised by the probability of finding burned gas on this isosurface, which decreases with increasing u and Le F . It has been found that it is easier to obtain self-sustained combustion following localised forced ignition in case of inhomogeneous mixtures than that in the case 126 Flow Turbulence Combust (2010) 84:125-166 of homogeneous mixtures with the same energy input, energy deposition duration when the ignition centre is placed at the stoichiometric mixture. The difficultly to sustain combustion unaided by external energy addition in homogeneous mixture is particularly prevalent in the case of Le F = 1.2.

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A consistent linearisation, using perturbation methods, is obtained for the structural degrees of freedom of flexible slender bodies with large rigid-body motions. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of a reference configuration. This gives equations of motion with cubic terms in the rigid-body degrees of freedom and constant coefficients which can be pre-computed prior to the time-marching simulation. Numerical results are presented to illustrate the approach and to show its advantages with respect to mean-axes approximations.

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