Sub-grid Scale Scalar Dissipation Research Articles

Local Equilibrium and Discretization Effects on the Prediction of Scalar Dissipation Rates in Large Eddy Simulation of Turbulent Non-Premixed Combustion

ABSTRACT The effects of discretization and local equilibrium on the prediction of scalar dissipation rates are investigated by performing large-eddy simulation (LES) of a turbulent-piloted jet diffusion flame, Sandia Flame D. As a way to reduce the discretization errors on the prediction of scalar dissipation, an approach to use a higher-order finite difference scheme only for the evaluation of scalar gradients in a scalar dissipation model, while keeping the overall accuracy of the numerical method at second order, is investigated. Results indicate that the fourth-order scheme improves the accuracy with negligible addition to computational cost. With the improved evaluation of scalar gradients, the local equilibrium assumption, which is used in the algebraic model, is investigated by solving the subgrid-scale variance transport equation, where a model coefficient in a scaling-based relaxation model for subgrid-scale scalar dissipation is varied. It is found that the conditional mean scalar dissipation rates are insensitive to the model coefficient. This insensitivity is attributed to the prevalence of local equilibrium. A rapid decay of imbalance between production and dissipation of subgrid-scale scalar fluctuations is seen in both the predicted scalar dissipation and the transport budget in the variance equation. It is argued that since, at high Reynolds numbers, the transport of the scalar fluctuations occurs over a timescale larger than the subgrid-scale mixing timescale, its contribution to the evolution of subgrid-scale variance is statistically insignificant except near the nozzle exit where different streams begin to mix and scalar layers evolve rapidly. Consequently, the conditional (and unconditional) mean scalar dissipation rates in LES tend to depend solely on the production of subgrid-scale scalar fluctuations in most regions of turbulent jet flames, when the modeling is based on the Kolmogorov scaling.

A further evaluation of the mixing controlled direct chemistry (MCDC) combustion model for diesel engine combustion using large eddy simulation

The local mixing effect at sub-grid scale (SGS) is explored using Large Eddy Simulation (LES) turbulence model with a mixing controlled direct chemistry (MCDC) model. The MCDC model is developed using the computation of chemical kinetics, thermo-chemical equilibrium state and SGS mixing effects by combining a mixing time scale and a kinetic time scale with the integration of direct chemistry solver (DCS) solutions. The mixing time scale is based on the SGS scalar variance and SGS scalar dissipation rate. The kinetic time scale is based on thermal–chemical equilibrium state and the kinetic reaction rate. These two time scales have been previously evaluated in experiments and computations, showed reasonable quantifications of local mixing and kinetic progress, which improved accuracy of combustion modeling.In this study, the conventional diffusion-type operating conditions are represented by a Caterpillar 3401™ single cylinder oil test engine (SCOTE). The cylinder-averaged results are compared between the DCS model, MCDC model and ‘Kong-Reitz’ model. A grid dependence study for the MCDC model on a baseline grid and a coarse grid is performed. The mixing time scale and kinetic time scale analysis for the MCDC model and ‘Kong-Reitz’ model is provided to investigate the differences in predictions. Compared to the DCS model and ‘Kong-Reitz’ model, the MCDC model shows improved capability in modeling mixing effects at the SGS level, which is represented by the improved prediction of combustion phasing and good matching with experimental results.

A priori analysis of subgrid mass diffusion vectors in high pressure turbulent hydrogen/oxygen reacting shear layer flames

Direct numerical simulations of high pressure (100 atm), turbulent H2/O2 non-premixed temporally developing shear layer flames are conducted at initial Reynolds numbers ranging from 850 ⩾ Reδ0 ⩾ 4500, with up to ∼3/4 × 109 grid points. A real gas equation of state, real property models, detailed chemistry, and generalized diffusion models are included. The results of the simulations focus on the mass diffusion vectors and their subgrid contributions relevant to large eddy simulation of turbulent combustion. Comparisons of the actual filtered mass flux vectors with their corresponding forms evaluated with filtered primitive variables are shown through correlation coefficients, probability density functions (PDFs) of the ratios between the vector magnitudes, and PDFs of the angles between the vectors. The results show a reasonable correlation (⩾0.75) for all species and simulations when evaluated globally. However, the correlations weaken substantially in regions of large temperature subgrid scale (SGS) variance and filtered SGS scalar dissipation. Within these regions, the correlations are also shown to vary inversely with Reynolds number. Vector analysis indicates that evaluating the mass flux vector using only the filtered primitive variables accurately predicts the direction of the actual filtered flux; however, the magnitude is poorly predicted in the aforementioned regions. Comparisons of the subgrid mass fluxes to the subgrid scalar fluxes are also represented as PDFs of the ratios between the vector magnitudes. These results show the subgrid mass flux to be significantly smaller (≲5%) than the subgrid scalar flux, and this ratio is shown to diminish with increasing Reynolds number. A final comparison of the divergence of the subgrid mass fluxes to the subgrid scalar fluxes are also represented as PDFs of the ratios between the magnitudes. At lower Reynolds numbers, these ratios suggest comparable values between the subgrid diffusion and turbulent stirring terms in regions of large temperature SGS variance and filtered SGS scalar dissipation. However, this ratio is shown to diminish, but remain significant, with increasing Reynolds number.

A mixing controlled direct chemistry (MCDC) model for diesel engine combustion modelling using large eddy simulation

A mixing controlled direct chemistry (MCDC) combustion model with sub-grid scale (SGS) mixing effects and chemical kinetics has been evaluated for Large Eddy Simulation (LES) of diesel engine combustion. The mixing effect is modelled by a mixing timescale based on mixture fraction variance and sub-grid scalar dissipation rate. The SGS scalar dissipation rate is modelled using a similarity term and a scaling factor from the analysis of Direct Numerical Simulation (DNS) data. The chemical reaction progress is estimated from a kinetic timescale based on local internal energy change rate and equilibrium state internal energy. An optical research engine operating at conventional operating conditions and Low Temperature Combustion (LTC) conditions was used for evaluation of the combustion model. From the simulation results, the effect of SGS scalar mixing is evaluated at different stages of combustion. In the context of LES, the new approach provides improved engine modelling results compared to the Direct Chemistry Solver (DCS) combustion model.

Dynamic structure subgrid‐scale models for large eddy simulation

AbstractLarge eddy simulation (LES) is based on separation of variable of interest into two parts—resolved and subgrid. The resolved part is obtained numerically using modified transport equation while the effect of the subgrid part is modelled using subgrid‐scale (SGS) models. In this paper we present and discuss new one‐equation LES models for SGS scalar flux, SGS scalar dissipation and SGS energy dissipation. The proposed models belong to a new family of SGS models—dynamic structure (DS) models. The DS models borrow the structure of the modelled term from the corresponding Leonard term, and a special scaling factor is then used which does not contain user‐specified constants. The models are evaluated a priori using available DNS data for a non‐reacting mixing layer and decaying isotropic turbulence; the evaluation results compare well with viscosity and similarity models. During the a priori tests, the DS models were found to perform better than dynamic viscosity and similarity models for various test‐to‐base filter size ratios and non‐symmetric filters. For a posteriori evaluation, the models are implemented into a high‐order finite‐difference code and an LES of decaying isotropic turbulence is performed. The results match the data available from the literature and DNS simulations. Copyright © 2005 John Wiley & Sons, Ltd.