Assessment of mixing time scales for a sparse particle method

A sparse particle implementation of the multiple mapping conditioning / large eddy simulation (MMC-LES) model is assessed against direct numerical simulations (DNS) of non-premixed syngas combustion in the double shear layer configuration of Hawkes et al. (2007). The considered configuration features strong extinction and reignition and therefore poses a stringent test of the model's capabilities to capture finite-rate chemistry effects. The investigation focuses on the modelling of the Lagrangian mixing time scale, τL, which emulates the dissipation of conditional subfilter scalar fluctuations. An a posteriori strategy is used to separate LES errors from potential shortcomings in modelling of τL. The DNS data are filtered on the LES grid to compute all LES-filtered quantities that are needed for the modelling of τL while the (unfiltered) DNS velocity and mixture fraction fields are used for particle transport and mixing model localization, respectively. The results show that the previously derived and most commonly used model for τL (Cleary & Klimenko, 2011) is capable of accurately capturing the temporal evolution of the mean quantities in the flame and that, by virtue of the controlled localisation of the generalised MMC mixing model in a reference mixture fraction space, statistical predictions are quite insensitive to variations in the spatial distance between particles. However, the model yields significant under-predictions of the conditional variances of the reactive scalars, both for the reference case and an additional case with a reduced reaction zone thickness. It is shown that for these particular flames the conditional variance under-predictions cannot be completely remedied by tuning the input parameter fm which determines the amount of mixing localisation in reference mixture fraction space. Instead, this shortcoming is attributed to the model for τL. Alternative model closures are suggested which are based on a consistent anisotropic or isotropic perspective on subfilter scalar mixing in sparse particle schemes. The anisotropic closure is demonstrated to significantly improve the model predictions, in particular for the conditional scalar variances. Additionally the predictions show less sensitivity to variations in fm providing good potential for improved robustness of sparse particle methods for MMC-LES. A series of tests involving a three order of magnitude increase in particle number is conducted to demonstrate numerical convergence. During those tests the two primary model parameters, fm and rm which control the mixing distance between particles in both mixture fraction space and physical space, are held constant so that those mixing distances are independent of the number of particles used and, at the same time, the sparse character of the mixing model is preserved.