Subgrid Quantities Research Articles

On the subgrid dissipation concept for large eddy simulation of turbulent combustion

A new subgrid turbulent combustion model for LES is derived based on the eddy dissipation concept (EDC). To be consistent with the LES framework, the relationship between the subgrid quantities and the fine structure ones is built from the unresolved part of the energy cascade, hence the subgrid dissipation concept (SDC). The fine structure quantities are directly computed using the subgrid scale ones. Resolving local laminar flame structures is allowed if the grid resolution permits. The model is examined using premixed piloted jet flames and non-premixed swirl flame. Satisfactory predictions from the SDC model are obtained in the test cases, showing improvements with respect to the standard EDC model. The new SDC model is relatively insensitive to the grid resolution.

The partially stirred reactor model for combustion closure in large eddy simulations: Physical principles, sub-models for the cell reacting fraction, and open challenges

For their ability to account for finite-rate chemistry, reactor-based models are well suited Turbulence–Chemistry Interactions (TCI) Sub-Grid Scale (SGS) closures for Large Eddy Simulations (LES). The SGS closure in the Partially Stirred Reactor (PaSR) model relies on the determination of the reacting fraction of each computational cell, whose definition is based on estimates of the characteristic mixing and chemical time scales. Direct Numerical Simulations (DNS) of turbulent combustion can supply key information on TCI for the development, validation, and comparison of combustion models. In particular, a priori testing allows the direct validation of model assumptions. In the present work, an a priori assessment of the PaSR model is conducted. Its ability to reconstruct thermo-chemical quantities of interest is investigated along with model assumptions. Sub-grid quantities are extracted from the DNS to investigate the role of the cell reacting fraction. Various definitions are then proposed to estimate the characteristic chemical timescale in the PaSR model. Modeled chemical source terms and heat release rates are compared against the filtered quantities from DNS data of a two-dimensional, spatially developing, turbulent nonpremixed jet flame with detailed kinetics. The results demonstrate the importance of accounting for the fine structures quantities in the context of reactor-based models. A new formulation of the chemical timescale is proposed and provides improved overall predictions. Several issues are raised in the discussion, representing realistic prospects for further developments of the PaSR model as a SGS combustion closure for LES.

Dynamic tensorial eddy viscosity model: Effects of compressibility and of complex geometry

A previous paper by Cimarelli et al. [“General formalism for a reduced description and modelling of momentum and energy transfer in turbulence,” J. Fluid Mech. 866, 865–896 (2019)] has shown that every decomposition of turbulent stresses is naturally approximated by a general form of tensorial eddy viscosity based on velocity increments. The generality of the formalism is such that it can also be used to give a reduced description of subgrid scalar fluxes. In the same work, this peculiar property of turbulent stresses and fluxes has been dynamically exploited to produce tensorial eddy viscosity models based on the second-order inertial properties of the grid element. The basic idea is that the anisotropic structure of the computational element directly impacts, although implicitly, the large resolved and small unresolved scale decomposition. In the present work, this new class of turbulence models is extended to compressible turbulence. A posteriori analysis of flow solutions in a compressible turbulent channel shows very promising results. The quality of the modeling approach is further assessed by addressing complex flow geometries, where the use of unstructured grids is demanded as in real world problems. Also in this case, a posteriori analysis of flow solutions in a periodic hill turbulent flow shows very good behavior. Overall, the generality of the formalism is found to allow for an accurate description of subgrid quantities in compressible conditions and in complex flows, independent of the discretization technique. Hence, we believe that the present class of turbulence closures is very promising for the applications typical of industry and geophysics.

Stochastic modeling for subgrid-scale particle dispersion in large-eddy simulation of inhomogeneous turbulence

We consider Lagrangian modeling of heavy particle motion in inhomogeneous turbulence. The dynamics of point particles is one-way coupled to the large-eddy simulation (LES) of fluid flow. To account for the effect of non-resolved (subgrid) flow scales on particle motion, we propose a model for the fluid velocity along the particle trajectories. The model, based on a stochastic diffusion process, accounts for turbulence anisotropy and utilizes the statistical estimates of subgrid quantities: the velocity components (the r.m.s. and covariance) and the Lagrangian time scales. The turbulent channel flow case is taken for validation. First, we discuss the outcome of an a priori LES study. Then, the proposed subgrid dispersion model is tested in a true LES computation. The resulting velocity statistics, particle concentration profiles, and the deposition velocity are compared against available reference data from direct numerical simulations.

Inhomogeneous drag models for gas-solid suspensions based on sub-grid quantities

Inhomogeneous structures have significant impact on the drag. In this work, direct numerical simulations of flows past fluidized spheres are performed to investigate the effect of inhomogeneities on the drag at low Reynolds numbers. The inhomogeneities are quantified using various sub-grid quantities including a newly defined quantity named the solid drift flux, which is a measure of the correlation between the gas volume fraction and the particle phase velocity. Following the methodology of Rubinstein et al. (2017), a new drag model that depends simultaneously on the solid drift flux and the scalar variance of solid volume fraction is then developed. Given that these two sub-grid quantities are readily available in Eulerian-Lagrangian (EL) simulations, the developed model can be directly used in EL simulations without any additional closures for sub-grid quantities. An a priori analysis demonstrates that this model achieves satisfactory performance in predicting the drag in inhomogeneous structures.

Theoretical and numerical analysis of key sub-grid quantities' effect on filtered Eulerian drag force

An expression of the filtered Eulerian drag force is proposed based on the second order Taylor polynomial approximation of a microscopic drag coefficient. Theoretical computations of the expression at low particle Reynolds numbers show that four sub-grid quantities, the gas drift velocity, the solid drift velocity, the scalar variance of solid volume fraction and a third-order moment, are significant for an accurate estimation of the filtered drag force. Various drag models with different combinations of the four sub-grid quantities are proposed and their coefficients are optimized based on fine-grid two fluid model results. The gas drift velocity is demonstrated to be the most important marker in predicting the filtered drag force. The model with the solid drift velocity and the scalar variance of the solid volume fraction is found to be promising in computational fluid dynamic-discrete element model simulations due to the ready availability of the two sub-grid quantities.

Towards filtered drag force model for non-cohesive and cohesive particle-gas flows

Euler-Lagrange simulations of gas-solid flows in unbounded domains have been performed to study sub-grid modeling of the filtered drag force for non-cohesive and cohesive particles. The filtered drag forces under various microstructures and flow conditions were analyzed in terms of various sub-grid quantities: the sub-grid drift velocity, which stems from the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and the scalar variance of solid volume fraction, which is a measure to identify the degree of local inhomogeneity of volume fraction within a filter volume. The results show that the drift velocity and the scalar variance exert systematic effects on the filtered drag force. Effects of particle and domain sizes, gravitational accelerations, and mass loadings on the filtered drag are also studied, and it is shown that these effects can be captured by both sub-grid quantities. Additionally, the effect of cohesion force through the van der Waals interaction on the filtered drag force is investigated, and it is found that there is no significant difference on the dependence of the filtered drag coefficient of cohesive and non-cohesive particles on the sub-grid drift velocity or the scalar variance of solid volume fraction. The assessment of predictabilities of sub-grid quantities was performed by correlation coefficient analyses in a priori manner, and it is found that the drift velocity is superior. However, the drift velocity is not available in “coarse-grid” simulations and a specific closure is needed. A dynamic scale-similarity approach was used to model drift velocity but the predictability of that model is not entirely satisfactory. It is concluded that one must develop a more elaborate model for estimating the drift velocity in “coarse-grid” simulations.

CFD Analysis of Combustion and Pollutant Formation Phenomena in a Direct Injection Diesel Engine at Different EGR Conditions

In this work, exhaust gas recirculation (EGR) is varied in a direct injection constant speed diesel engine using extended coherent flame model for 3-zones by CFD. The three zones are unmixed fuel zone, mixed gases zone, unmixed air plus EGR zone. The three zones are too small to be resolved by the mesh and are therefore modeled as sub-grid quantities. The mixed zone is the result of turbulent and molecular mixing between gases in the other two zones, where combustion takes place. Grid and time independent tests are carried out further to find the appropriate space and time steps respectively. The preliminary studies are carried out to validate the model with the experiments. The present study is conducted towards varying the EGR in the cylinder. CFD results indicate that as EGR increases, nitrogen oxides decreases in a general trend observed in diesel engines. The predicted model shows that flame temperature is lowered in the combustion chamber with the increase in EGR. However, as oxides of nitrogen decreases, soot increases due to lowered oxygen concentration. Reaction variable and temperature contours in the cylinder reveal that combustion regresses as EGR is increased.

Hybrid RANS/LES modelling with an approximate renormalization group. I: Model development

A hybrid RANS/LES model based on renormalization group (RG) calculations is presented. The result of the RG approach is a one-equation LES subgrid model in well-resolved regions of the flow, and a two-equation RANS model otherwise. The two modes of the model are linked by comparing the filter width with a length scale constructed from subgrid quantities. The one-equation subgrid model uses a transport equation for the mean rate of dissipation, in which the inverse time scale is explicitly filter width dependent. The model is free of adjustable parameters (after the truncations of the approximate RG are made) in its high-Reynolds formulation, has a clear physical interpretation and is easy to implement.

Theoretical and numerical study of highly anisotropic turbulent flows

We present a detailed numerical study of anisotropic statistical fluctuations in stationary, homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors, and the relative importance of isotropic and anisotropic fluctuations at different scales on a direct numerical simulation of a three-dimensional random Kolmogorov flow. We review a simple argument to predict the dimensional scaling for all velocity moments, in all anisotropic sectors. We extend a previous analysis made on the same data set (Phys. Rev. Lett. 86 (2001) 4831) presenting (i) the statistical behavior of spectra and co-spectra; (ii) high-order longitudinal structure functions; (iii) anisotropic fluctuations of the full tensorial two-points velocity correlations. Among the many issues discussed, we stress the problem of the return-to-isotropy, the universality of anisotropic fluctuations and the foliation mechanism. A new a priori test on sub-grid quantities used in Large-Eddy Simulations is also presented.

Passive scalar anisotropy in a heated turbulent wake: new observations and implications for large-eddy simulations

The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modelling for large-eddy simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated cylinder, using an array of four X-wire and four cold-wire probes. By varying the separation distance among probes in the array, we obtain filtered and subgrid quantities at three different filter sizes. We compute several terms that comprise the subgrid dissipation tensor of kinetic energy and scalar variance and test for isotropic behaviour, as a function of filter scale. We find that whereas the kinetic energy dissipation tensor tends towards isotropy at small scales, the SGS scalar-variance dissipation remains anisotropic independent of filter scale. The eddy-diffusion model predicts isotropic behaviour, whereas the nonlinear (or tensor eddy diffusivity) model reproduces the correct trends, but overestimates the level of scalar dissipation anisotropy. These results provide some support for so-called mixed models but raise new questions about the causes of the observed anisotropy.

Upscaling Immiscible Gas Displacements: Quantitative Use of Fine-Grid Flow Data in Grid-Coarsening Schemes

Summary This paper presents and assesses grid-coarsening schemes based on the quantitative use of fine-scale two-phase-flow information. The basic approach is motivated from a volume-average analysis of the fine-scale saturation equation including gravitational effects. Extensive results for layered systems are presented. We show that coarse-grid simulation error correlates closely with specific subgrid quantities involving higher moments of fine-grid variables, which can be computed from the fine-scale simulations. With formation of a coarse grid that minimizes the appropriate subgrid property, optimal coarse-scale descriptions can be generated. The overall approach is shown to be applicable to coarse-scale descriptions with either rock or pseudorelative permeability curves. The accuracy of the coarse-grid calculations is, however, significantly better when pseudofunctions are used. The method is applied to determine the optimal number and configuration of coarse-grid layers in more general cases and it is shown that coarse-grid results do not always improve as the number of coarse layers is increased.