Subgrid-scale Effects Research Articles

The influence of sub-grid scale motions on particle collision in homogeneous isotropic turbulence

The absence of sub-grid scale (SGS) motions leads to severe errors in particle pair dynamics, which represents a great challenge to the large eddy simulation of particle-laden turbulent flow. In order to address this issue, data from direct numerical simulation (DNS) of homogenous isotropic turbulence coupled with Lagrangian particle tracking are used as a benchmark to evaluate the corresponding results of filtered DNS (FDNS). It is found that the filtering process in FDNS will lead to a non-monotonic variation of the particle collision statistics, including radial distribution function, radial relative velocity, and the collision kernel. The peak of radial distribution function shifts to the large-inertia region due to the lack of SGS motions, and the analysis of the local flowstructure characteristic variable at particle position indicates that the most effective interaction scale between particles and fluid eddies is increased in FDNS. Moreover, this scale shifting has an obvious effect on the odd-order moments of the probability density function of radial relative velocity, i.e. the skewness, which exhibits a strong correlation to the variance of radial distribution function in FDNS. As a whole, the radial distribution function, together with radial relative velocity, can compensate the SGS effects for the collision kernel in FDNS when the Stokes number based on the Kolmogorov time scale is greater than 3.0. However, it still leaves considerable errors for $${ St}_\mathrm{k }<3.0$$ .

Model Selection: Using Information Measures from Ordinal Symbolic Analysis to Select Model Subgrid-Scale Parameterizations

Abstract The use of information measures for model selection in geophysical models with subgrid parameterizations is examined. Although the resolved dynamical equations of atmospheric or oceanic global numerical models are well established, the development and evaluation of parameterizations that represent subgrid-scale effects pose a big challenge. For climate studies, the parameters or parameterizations are usually selected according to a root-mean-square error criterion that measures the differences between the model-state evolution and observations along the trajectory. However, inaccurate initial conditions and systematic model errors contaminate root-mean-square error measures. In this work, information theory quantifiers, in particular Shannon entropy, statistical complexity, and Jensen–Shannon divergence, are evaluated as measures of the model dynamics. An ordinal analysis is conducted using the Bandt–Pompe symbolic data reduction in the signals. The proposed ordinal information measures are examined in the two-scale Lorenz-96 system. By comparing the two-scale Lorenz-96 system signals with a one-scale Lorenz-96 system with deterministic and stochastic parameterizations, the study shows that information measures are able to select the correct model and to distinguish the parameterizations, including the degree of stochasticity that results in the closest model dynamics to the two-scale Lorenz-96 system.

Two-fluid sub-grid-scale viscosity in nonlinear simulation of ballooning modes in a heliotron device

A large eddy simulation (LES) approach is introduced to enable the study of the nonlinear growth of ballooning modes in a heliotron-type device, by solving fully 3D two-fluid magnetohydrodynamic (MHD) equations numerically over a wide range of parameter space, keeping computational costs as low as possible. A model to substitute the influence of scales smaller than the grid size, at sub-grid scale (SGS), and at the scales larger than it—grid scale (GS)—has been developed for LES. The LESs of two-fluid MHD equations with SGS models have successfully reproduced the growth of the ballooning modes in the GS and nonlinear saturation. The numerical results show the importance of SGS effects on the GS components, or the effects of turbulent fluctuation at small scales in low-wavenumber unstable modes, over the course of the nonlinear saturation process. The results also show the usefulness of the LES approach in studying instability in a heliotron device. It is shown through a parameter survey over many SGS model coefficients that turbulent small-scale components in experiments can contribute to keeping the plasma core pressure from totally collapsing.

Large eddy simulation of piloted pulverised coal combustion using extended flamelet/progress variable model

An extended flamelet/progress variable (EFPV) model for simulating pulverised coal combustion (PCC) in the context of large eddy simulation (LES) is proposed, in which devolatilisation, char surface reaction and radiation are all taken into account. The pulverised coal particles are tracked in the Lagrangian framework with various sub-models and the sub-grid scale (SGS) effects of turbulent velocity and scalar fluctuations on the coal particles are modelled by the velocity-scalar joint filtered density function (VSJFDF) model. The presented model is then evaluated by LES of an experimental piloted coal jet flame and comparing the numerical results with the experimental data and the results from the eddy break up (EBU) model. Detailed quantitative comparisons are carried out. It is found that the proposed model performs much better than the EBU model on radial velocity and species concentrations predictions. Comparing against the adiabatic counterpart, we find that the predicted temperature is evidently lowered and agrees well with the experimental data if the conditional sampling method is adopted.

A new statistical model for subgrid dispersion in large eddy simulations of particle-laden flows

Dispersed multiphase turbulent flows are present in many industrial and commercial applications like internal combustion engines, turbofans, dispersion of contaminants, steam turbines, etc. Therefore, there is a clear interest in the development of models and numerical tools capable of performing detailed and reliable simulations about these kind of flows. Large Eddy Simulations offer good accuracy and reliable results together with reasonable computational requirements, making it a really interesting method to develop numerical tools for particle-laden turbulent flows. Nonetheless, in multiphase dispersed flows additional difficulties arises in LES, since the effect of the unresolved scales of the continuous phase over the dispersed phase is lost due to the filtering procedure. In order to solve this issue a model able to reconstruct the subgrid velocity seen by the particles is required. In this work a new model for the reconstruction of the subgrid scale effects over the dispersed phase is presented and assessed. This innovative methodology is based in the reconstruction of statistics via Probability Density Functions (PDFs).

Subgrid-Scale Modeling of Reaction-Diffusion and Scalar Transport in Turbulent Premixed Flames

ABSTRACTA numerical study of premixed flame-turbulence interaction is performed to investigate the effects of turbulence on the structural features of the flame and the subgrid-scale (SGS) effects on vorticity dynamics, energy transfer mechanism, and turbulent transport across the flame. We consider a freely propagating methane-air turbulent premixed flame interacting with a decaying isotropic turbulence under three different initial conditions corresponding to the corrugated flamelet (CF), the thin reaction zone (TRZ), and the broken/distributed reaction zone (B/DRZ) regimes. We employ the well-established linear eddy mixing (LEM) model in large-eddy simulation (LEMLES), a new subgrid closure for reaction-diffusion occurring in the small-scales based on LEM (RRLES), and a quasi-laminar chemistry based closure in large-eddy simulation (QLLES) to simulate flame-turbulence interactions and to compare predictions with direct numerical simulation (DNS). We assess the accuracy and robustness of the closures by comparing statistical features to highlight their abilities and limitations. The newly proposed RRLES subgrid closure uses a dual-resolution grid for solving the species transport equations. Such an approach is shown to improve the existing LEMLES subgrid model especially at low Reynolds numbers. All SGS closures reveals good agreement, although there are some differences due to the closure used for convective transport of the scalar field and the reaction rate. Further analysis of the DNS dataset shows that there is a significant contribution by dilatation and baroclinic torque terms across the flame. In particular, at higher Karlovitz number, there is an abrupt change in the sign of the dilatation term, which is related to the competing effects of thermal expansion due to heat release and enhanced molecular mixing by the turbulence across the flame brush region. The enhanced mixing leads to localized pockets of cold reactants surrounded by hot products, which is only partly captured by the employed closures. The analysis of SGS kinetic energy and scalar dissipation rates indicates the presence of back-scatter of turbulent kinetic energy, and we also observe counter-gradient transport across the flame. The results suggest that further improvement of the traditional closures is needed to accurately capture the dynamics of flame-turbulence interaction.

A multi-column vertical mixing scheme to parameterize the heterogeneity of oceanic conditions under sea ice

The heterogeneity of ocean surface conditions associated with a spatially variable sea ice cover needs to be represented in models in order to represent adequately mixed layer processes and the upper ocean density structure. This study assesses the sensitivity of the ocean-sea ice model NEMO-LIM to a subgrid-scale representation of ice-ocean interactions. The sea ice component includes an ice thickness distribution, which provides heterogeneous surface buoyancy fluxes and stresses. A multi-column ocean scheme is developed to take them explicitly into account, by computing convection and turbulent vertical mixing separately in the open water/lead fraction of grid cells and below each ice thickness category. For the first time in a three-dimensional simulation, the distinct temperature and salinity profiles of the ocean columns are allowed to be maintained over several time steps. It is shown that the model response is highly sensitive to the homogenization time scale between the columns. If the latter are laterally mixed with time scales shorter than 10 h, subgrid-scale effects exist but the mean state is practically unaffected. For longer mixing time scales, in both hemispheres, the main impacts are reductions in under-ice mean mixed layer depths and in the summer melt of sea ice, following decreased oceanic heat flux at the ice base. Large changes in the open water temperature in summer suggest that the scheme could trigger important feedback processes in coupled simulations.

Efficient implicit LES method for the simulation of turbulent cavitating flows

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.

Shallow water equations with depth-dependent anisotropic porosity for subgrid-scale topography

This paper derives a novel formulation of the depth-averaged shallow water equations with anisotropic porosity for computational efficiency reasons. The aim is to run simulations on coarser grids while maintaining an acceptable accuracy through the introduction of porosity terms, which account for subgrid-scale effects. The porosity is divided into volumetric and areal porosities, which are assigned to the cell volume and the cell edges, respectively. The former represents the volume in the cell available to flow and the latter represents the area available to flow over an edge, hence introducing anisotropy. The porosity terms are variable in time in dependence of the water elevation in the cell and the cumulative distribution function of the unresolved bottom elevation. The main novelty of the equations is the formulation of the porosities which enables full inundation of the cell. The applicability of the equations is verified in five computational examples, dealing with dam break and rainfall-runoff simulations. Overall, good agreement between the model results and a high-resolution reference simulation has been achieved. The computational time decreased significantly: on average three orders of magnitude.

The role of wind forcing from operational analyses for the model representation of Antarctic coastal sea ice

An accurate representation of Antarctic coastal sea ice in Earth System Models is important as it affects the rate of Antarctic Bottom Water formation. Here we investigate the effect of using relatively high-resolution (∼20 km) near-surface wind fields of two different operational analyses (from the European Centre for Medium-Range Weather Forecasts (ECMWF), and the Antarctic Mesoscale Prediction System (AMPS)) to force a sea-ice - ocean model. We focus on the wind impact on coastal polynya formation in winter. Even though the horizontal resolution of both analyses is about the same, striking differences emerge in simulated coastal sea ice and thus the representation of coastal polynyas and net freezing rates. In AMPS, offshore winds are up to 10 m s−1 stronger than those of ECMWF, and mostly overestimated compared to weather station data. This leads to major differences in simulated coastal ice drift, concentration, and thickness, as well as discrepancies in the annual net freezing rate of up to 5 m per year. To identify the reasons for the discrepancies in the coastal wind fields of the analyses we scrutinized their orography, boundary-layer stratification, sea-ice boundary conditions, large-scale atmospheric circulations, data assimilation and initialization schemes, and their parameterization of subgrid-scale orographic effects. The final factor explained most of the discrepancies along steep coastlines, whereas the differences in boundary-layer stratification are mainly a consequence of the differences in surface winds. The data assimilation and initialization procedure biased the AMPS wind fields toward those of the NCEP analyses, which probably overestimate offshore winds as a result of coarse-resolution orography. The sea-ice boundary conditions and the large-scale circulations turned out to have a minimal effect.

Upscaling the shallow water model with a novel roughness formulation

This study presents a novel roughness formulation to conceptually account for microtopography and compares it to four existing roughness models from literature. The aim is to increase the grid size for computational efficiency, while capturing subgrid scale effects with the roughness formulation to prevent the loss in accuracy associated with coarse grids. All roughness approaches are implemented in the Hydroinformatics Modeling System and compared with results of a high resolution shallow water model in three test cases: rainfall-runoff on an inclined plane with sine-wave shaped microtopography, flow over an inclined plane with random microtopography and rainfall-runoff in a small natural catchment. Although the high resolution results can not be reproduced exactly by the coarse grid model, e.g. local details of flow processes can not be resolved, overall good agreement between the upscaled models and the high resolution model has been achieved. It is concluded that the accuracy increases with the number of calibration parameters available, however the calibration process becomes more difficult. Using coarser grids results in significant speedup in comparison with the high resolution simulation. In the presented test cases the speedup varies from 20 up to 2520, depending on the size and complexity of the test case and the difference in cell sizes. The proposed roughness formulation generally shows the best agreement with the reference solution, compared to the other models investigated in this study.

Contrasting Local versus Regional Effects of Land-Use-Change-Induced Heterogeneity on Historical Climate: Analysis with the GFDL Earth System Model

Abstract The effects of land-use and land-cover change (LULCC) on surface climate using two ensembles of numerical experiments with the Geophysical Fluid Dynamics Laboratory (GFDL) comprehensive Earth System Model ESM2Mb are investigated in this study. The experiments simulate historical climate with two different assumptions about LULCC: 1) no land-use change with potential vegetation (PV) and 2) with the CMIP5 historical reconstruction of LULCC (LU). Two different approaches were used in the analysis: 1) the authors compare differences in LU and PV climates to evaluate the regional and global effects of LULCC and 2) the authors characterize subgrid climate differences among different land-use tiles within each grid cell in the LU experiment. Using the first method, the authors estimate the magnitude of LULCC effect to be similar to some previous studies. Using the second method, the authors found a pronounced subgrid signal of LULCC in near-surface temperature over majority of areas affected by LULCC. The signal is strongest on croplands, where it is detectable with 95% confidence over 68.5% of all nonglaciated land grid cells in June–July–August, compared to 8.3% in the first method. In agricultural areas, the subgrid signal tends to be stronger than LU–PV signal by a factor of 1.3 in tropics in both summer and winter and by 1.5 in extratropics in winter. This analysis for the first time demonstrates and quantifies the local, subgrid-scale LULCC effects with a comprehensive ESM and compares it to previous global and regional approaches.

Large Eddy Simulation of piloted pulverized coal combustion using the velocity-scalar joint filtered density function model

Abstract A piloted pulverized coal jet flame was simulated by Large Eddy Simulation (LES). For the sub-grid scale (SGS) effects of the turbulence velocity and the scalar fluctuation of the gas flow on the coal particles, the velocity-scalar joint filtered density function (VSJFDF) model was used. Other models such as the governing equations for particles and coal combustion sub-models were also presented. Simulation results with the VSJFDF model, non-VSJFDF model and those by Franchetti et al. [7] were compared with the experimental data, including the mean and RMS (root mean square) velocity, temperature and species concentrations. The results showed that VSJFDF can distinctly improve the predictions, both in quantity and quality. The location where coal particles start burning could be roughly predicted along the centerline of the flame by VSJFDF model.

Numerical investigation of droplet evaporation and transport in a turbulent spray with LES/VSJFDF model

A velocity–scalar joint filtered density function (VSJFDF) transport equation was derived for the fluid flow field experienced by the particles in the evaporating gas–droplet two-phase flow. In this model, the large eddy simulation (LES) is used to simulate the fluid flow and the Lagrangian method is used to simulate the motion of the particle. In order to consider the sub-grid scale (SGS) effects of the gas velocity and scalar fluctuation transport and evaporation, we utilized the transport equation of the velocity–scalar joint filtered density function (VSJFDF) of the gas flow experienced by the droplets. With the developed LES/VSJFDF model, numerical simulations of an evaporating two-phase spray flow were carried out. The numerical results with the VSJFDF model, the VFDF (velocity filtered density function) model and non-FDF (filtered density function) model were compared with the experimental data, simultaneously. The comparison proved that the LES/VSJFDF model can definitely improve the accuracy of the prediction on the droplets׳ mean diameter.

Estimating the effective Reynolds number in implicit large-eddy simulation

In implicit large-eddy simulation (ILES), energy-containing large scales are resolved, and physics capturing numerics are used to spatially filter out unresolved scales and to implicitly model subgrid scale effects. From an applied perspective, it is highly desirable to estimate a characteristic Reynolds number (Re)-and therefore a relevant effective viscosity-so that the impact of resolution on predicted flow quantities and their macroscopic convergence can usefully be characterized. We argue in favor of obtaining robust Re estimates away from the smallest scales of the simulated flow-where numerically controlled dissipation takes place and propose a theoretical basis and framework to determine such measures. ILES examples include forced turbulence as a steady flow case, the Taylor-Green vortex to address transition and decaying turbulence, and simulations of a laser-driven reshock experiment illustrating a fairly complex turbulence problem of current practical interest.

Computation of transitional flow past a circular cylinder using multiblock lattice Boltzmann method with a dynamic subgrid scale model

Lattice Boltzmann method (LBM) is a kinetic based numerical scheme for the simulation of fluid flow. While the approach has attracted considerable attention during the last two decades, there is a need for systematic investigation of its applicability for complex canonical turbulent flow problems of engineering interest, where the nature of the numerical properties of the underlying scheme plays an important role for their accurate solution. In this paper, we discuss and evaluate a LBM based on a multiblock approach for efficient large eddy simulation of three-dimensional external flow past a circular cylinder in the transitional regime characterized by the presence of multiple scales. For enhanced numerical stability at higher Reynolds numbers, a multiple relaxation time formulation is considered. The effect of subgrid scales is represented by means of a Smagorinsky eddy-viscosity model, where the model coefficient is computed locally by means of a dynamic procedure, providing better representation of flow physics with reduced empiricism. Simulations are performed for a Reynolds number of 3900 based on the free stream velocity and cylinder diameter for which prior data is available for comparison. The presence of laminar boundary layer which separates into a pair of shear layers that evolve into turbulent wakes impose particular challenge for numerical methods for this condition. The relatively low numerical dissipation introduced by the inherently parallel and second-order accurate LBM is an important computational asset in this regard. Computations using five different grid levels, where the various blocks are suitably aligned to resolve multiscale flow features show that the structure of the recirculation region is well reproduced and the statistics of the mean flow and turbulent fluctuations are in satisfactory agreement with prior data.

Characterization of Dispersive Fluxes in Mesoscale Models Using LES of Flow over an Array of Cubes

Field studies have shown that local climate is strongly influenced by urban structures. This influences both energy consumption and the pedestrian comfort. It is thus useful to be able to simulate the urban environment to take these effects into account in building and urban design. But for computational reasons, conventional computational fluid dynamics (CFD) codes cannot be used directly on a grid fine enough to resolve all scales found in a city. For this, we use mesoscale models, variants of CFD codes in which the 3D conservation equations are solved on grids having a resolution of a few kilometers. At this resolution, the effects of subgrid scales need implicit representations. In other words, phenomena such as momentum and energy exchanges averaged over the mesoscale grid contribute necessary sources/sinks to the corresponding equations. Such spatial averaging results in additional terms called dispersive fluxes. Until now these fluxes have been ignored. To better understand these fluxes, we have conducted large eddy simulations (LESs) over an array of cubes for different inter-cube spacings. The study shows that these fluxes are as important as the turbulent fluxes and exhibit trends which are related to the eddy formations inside the canopies.

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

In this paper, large-eddy simulation has been performed to investigate the impacts of the centrifugal and Coriolis forces on a heated plane channel flow subjected to streamwise system rotations. In order to study the rotation effects, a variety of rotation numbers Roτ ranging from 0 to 15 have been tested in conjunction with a fixed low Reynolds number Reτ=300. The subgrid-scale effects on the budget balance of turbulent stresses and heat fluxes have been investigated, and the physical mechanisms underlying the transport of resolved turbulent stresses under the influence of streamwise system rotations have been thoroughly analyzed. Numerical simulations were performed using two dynamic subgrid-scale stress models and two dynamic subgrid-scale heat flux models; namely, the conventional dynamic model (DM) and an advanced dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and the conventional dynamic eddy thermal diffusivity model (DEDM) and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The predictive performances of the DM and DNM have been carefully compared in conjunction with the same subgrid-scale heat flux model DFLTDM. In order to validate the numerical approach, turbulent statistics obtained from the simulations have been compared with the available direct numerical simulation data.

Large-eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp

Results of a large-eddy simulation (LES) of a supersonic turbulent boundary layer flow along a compression–expansion ramp configuration are presented. The numerical simulation is directly compared with an available experiment at the same flow conditions. The compression–expansion ramp has a deflection angle of β=25°. The flow is characterized by a free-stream Mach number of Ma∞=2.88 and the Reynolds number based on the incoming boundary layer thickness is Reδ0=132840. The Navier Stokes equations for compressible flows are solved on a cartesian collocated grid. About 32.5×106 grid points are used to discretize the computational domain. Subgrid scale effects are modeled implicitly by the adaptive local deconvolution method (ALDM). A synthetic inflow-turbulence technique is used, which does not introduce any low frequency into the domain, therefore avoiding any possible interference with the shock/boundary layer interaction system. Statistical samples are gathered over 800 characteristic time scales δ0/U∞. The numerical data are in good agreement with the experiment in terms of mean surface-pressure distribution, skin-friction, mean velocity profiles, velocity and density fluctuations. For the first time the full compression–expansion ramp configuration was taken into account. The computational results confirm theoretical and experimental findings on fluctuation-amplification across the shockwave/boundary layer interaction region and on turbulence damping through the interaction with rarefaction waves. The LES provide evidence of the existence of Görtler-like structures originating from the recirculation region and traveling downstream along the ramp. An analysis of the wall pressure field clearly shows the presence of a low frequency motion of the shock and strong influence of the Görtler-like vortices on the wall pressure spectra.

Large Eddy Simulation of Turbulent Flow and Mixing Time in a Gas–Liquid Stirred Tank

Mixing time is a key parameter relevant to the scale-up and design of agitated reactors. Although there have been many published papers on mixing times in stirred tanks predicted by computational fluid dynamics (CFD), there are few reports on the large eddy simulation (LES) based prediction of the mixing time in a gas liquid stirred tank. In this work, an LES method based on an Eulerian-Eulerian model is presented for predicting the mixing time in a gas liquid stirred tank agitated by a Rushton turbine. In order to verify the simulated results, mixing time experiments were carried out using a conductivity technique. In the present LES, the Smagorinsky subgrid scale model was used to model the effect of subgrid scale on the resolved scales. The concentration distributions and operating parameters such as feed positions, impeller speeds, and gas flow rates on the mixing time were examined. It is shown that the predicted concentration distributions of tracers are more irregular and realistic by using LES. Also, the mixing time decreases with the increase of impeller speed. However, with increasing gas flow rate, the mixing time first increases and then levels off. The predicted mixing time by the LES method shows good agreement with the measured values.