| A weak second-order accurate mid-point scheme for the stochastic differential equations (SDEs) arising in the composition PDF method for turbulent reactive flows is proposed and tested in Chapter 2 of this thesis. In contrast to most higher-order schemes for SDEs, the present scheme uses a mid-point, which makes it especially suitable for the implementation of the position-advance fractional step in the composition PDF method. The scheme can also be applied to the PDF method used in conjunction with large eddy simulation (LES), since the SDEs considered in this paper include explicit time dependence of the drift and diffusion coefficients.; Recent joint velocity-turbulent frequency-composition PDF calculations on turbulent lifted flames in vitiated coflows are shown in Chapter 3. The numerical model used in these calculations is found to capture the most interesting feature of this particular lifted flame: the extremely strong sensitivity of lift-off height to the coflow temperature.; In Chapter 4, a series of calculations is reported of the Barlow & Frank non-premixed piloted jet methane/air flames with the aim of determining the level of description of the chemistry necessary to account accurately for the turbulence-chemistry interactions observed in these flames. The calculations are based on the modelled transport equation for the joint probability density function of velocity, turbulence frequency and composition (enthalpy and species mass fractions). Seven chemical mechanisms are investigated, ranging from a five-step reduced mechanism to the 53-species GRI 3.0 mechanism for methane. The results show that, for C-H-O species, accurate results are obtained with the GRI 2.11 and GRI 3.0 mechanisms, as well as with 12 and 15-step reduced mechanisms based on GRI 2.11. But significantly inaccurate calculations result from use of the 5-step reduced mechanism (based on GRI 2.11), and from two different 16-species skeletal mechanisms. As has previously been observed, GRI 3.0 over-predicts NO by up to a factor of two; whereas NO is calculated reasonably accurately by GRI 2.11 and the 15-step reduced mechanism. |
