The impact of pressure fluctuation and scalar dissipation rate closures in turbulent flames

Abstract

The present thesis features computational studies of turbulent flames with different degrees of premixing. The flow field is computed using Reynolds–Averaged Navier–Stokes (RANS) equations closed at the second–moment level and the scalar field is modelled by either a presumed probability density function (pdf) or a joint scalar transported pdf approach. The focus is on the turbulence–chemistry interactions for the different types of flames. For turbulent premixed flames, the impact of combustion–induced variable density on the pressure fluctuation correlations is investigated. Derivations are presented for pressure dilatation, flamelet scrambling and pressure transport terms in the flamelet regime where “dilatation effects” are found to be significant. A bimodal presumed pdf and a bridged algebraic reaction rate closure are adopted for illustration purposes. The complete closure is assessed by comparisons with direct numerical simulations (DNS) of statistically “steady" fully developed premixed turbulent planar flames at different expansion ratios and the prediction of lean premixed turbulent methane–air flames featuring fractal grid generated turbulence in an opposed jet geometry. Results show that “dilatation" effects contribute to counter–gradient transport and the overall agreement is promising in both cases. Overall, the derived models offer significant improvements and can readily be applied to the modelling of premixed turbulent flames at practical rates of heat release. For turbulent partially premixed flames and turbulent diffusion flames, the impact of mixing models and scalar time–scale forms is studied within a hybrid joint scalar transported pdf (jpdf)/RANS approach with systematically reduced chemistry. The hybrid approach features a naturally closed chemical reaction source term and the study on the molecular mixing term is important for the understanding of combustion regime independent methods. The sensitivity to molecular mixing closures is investigated using variants of the Euclidean Minimum Spanning Tree (EMST) and modified Curl’s (MC) models. Extensions to scalar time–scale forms for premixed turbulent flames are included via an algebraic scalar dissipation closure that accounts for local Damköhler number effects and a conceptually related blended scalar time-scale approach. The hybrid jpdf/RANS approach is first applied to turbulent partially premixed flames with inhomogeneous jets. Different composition profiles (homogeneous or inhomogeneous) at the burner exit lead to diverse combustion modes and both transit to diffusion–dominated combustion downstream. The MC model with standard scalar time–scale is found to achieve the best agreement and applied to investigate the joint statistics of mixture fraction and reaction progress variable. These two parameters, assumed to be independent in flamelet–based models, are investigated for both types of composition profiles. The correlation of mixture fraction and reaction progress variable is found to be related to local extinction and combustion modes. A second application of the hybrid jpdf/RANS approach features bluff-body turbulent flames approaching blow-off (HM1, HM2 and HM3). Such flames exhibit gradually increasing periodic and shear layer instabilities. The current second moment closure provides a partial resolution of the unsteady fluid motion. The impact of mixing models and scalar time–scale forms is investigated by comparing MC, EMST and two extended scalar time–scale forms. The latter include Extended scalar time–scale coupled with MC (EMC) and Blended scalar time–scale used with EMST (BEMST). The sensitivity to solution parameters affecting the temporal resolution is quantified using Fourier transforms of the time histories of velocity and scalar traces. Results are found be to similar to well–resolved jpdf /Large Eddy Simulation (LES) for two flames with relatively lower bulk velocities (HM1 and HM2). For flame HM3, the results of EMC and BEMST/EMST essentially enclose the experimental data. In addition, vortex related instabilities ~ 1 kHz in the outer shear layer are captured by all thermochemical closures. However, only the MC based models show periodic extinction/re-ignition in the neck region. The latter result in flame turbules (i.e. discrete pockets of hot gas) separating periodically at frequencies ~ 85 Hz.