Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modelling

Abstract

Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constantcoefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.

A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

“…Vreman et al 1996b;Berselli, Iliescu & Layton 2006) have reported the GR model to be numerically unstable; however, other authors used it successfully for both singlephase and two-phase flow LESs of temporal mixing layers (e.g. Leboissetier et al 2005). Because the GRC simulations of § 6.1 showed that the GR model is very sensitive to the p correction, the conjecture is here that the poor performance of the GRDA-IC0 model may be due to the initial p-transients, which can be very substantial (Okong'o & Bellan 2002b).…”

Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation

“…Because ψ f is not available in LES, it must be modelled from the simulated flow field (φ), leading to ψ f ,m . We follow here the strategy of Leboissetier, Okong'o & Bellan (2005) in using the filtered flow field at the drop location as a model for the unfiltered flow field (i.e. ψ f ,m =ψ f ), meaning that we neglect direct SGS flow effects on the drop evolution.…”

Characteristics of transitional multicomponent gaseous and drop-laden mixing layers from direct numerical simulation: Composition effects

“…The next stage of this study will be devoted to a priori and a posteriori investigations, so as to reduce the large computational time of DNS and replace DNS with computationally efficient large eddy simulations, akin to the studies of Leboissetier et al 41 Currently, there are no data available for MC model validation. The diagnostics for producing experimental data for model validation are still in their infancy.…”