Subfilter-scale Research Articles

Statistical Variability of Dispersion in the Convective Boundary Layer: Ensembles of Simulations and Observations

A Lagrangian particle dispersion model (LPDM) driven by velocity fields from large-eddy simulations (LESs) is used to determine the mean and variability of plume dispersion in a highly convective planetary boundary layer (PBL). The total velocity of a “particle” is divided into resolved and unresolved or random (subfilter scale, SFS) velocities with the resolved component obtained from the LES and the SFS velocity from a Lagrangian stochastic model. This LPDM-LES model is used to obtain an ensemble of dispersion realizations for calculating the mean, root-mean-square (r.m.s.) deviation, and fluctuating fields of dispersion quantities. An ensemble of 30 realizations is generated for each of three source heights: surface, near-surface, and elevated. We compare the LPDM calculations with convection tank experiments and field observations to assess the realism of the results. The overall conclusion is that the LPDM-LES model produces a realistic range of dispersion realizations and statistical variability (i.e., r.m.s. deviations) that match observations in this highly convective PBL, while also matching the ensemble-mean properties. This is true for the plume height or trajectory, vertical dispersion, and the surface values of the crosswind-integrated concentration (CWIC), and their dependence on downstream distance. One exception is the crosswind dispersion for an elevated source, which is underestimated by the model. Other analyses that highlight important LPDM results include: (1) the plume meander and CWIC fluctuation intensity at the surface, (2) the applicability of a similarity theory for plume height from a surface source to only the very strong updraft plumes—not the mean height, and (3) the appropriate variation with distance of the mean surface CWIC and the lower bound of the CWIC realizations for a surface source.

Shear driven purging of negatively buoyant fluid from trapezoidal depressions and cavities

Experimental data and large eddy simulation results are analysed to investigate shear driven entrainment of a negatively buoyant fluid from trapezoidal depressions and cavities. This flow is of relevance to a number of environmentally significant applications including purging of saline pools in rivers and pollutant dispersion in cities and towns situated within topographic depressions. New scaling relations for the entrainment rate are developed based on physical arguments. Our scaling relations are shown to agree well with both experiments and numerical simulations of this flow in trapezoidal cavities with aspect ratios ranging between 7 and 17, entry beach angles between 8° and 33°, and an exit beach angle of 33°. For the numerical simulations, a sub-filter scale turbulence model is used that combines the dynamic mixed model of Zang et al. [“A dynamic mixed subgrid-scale model and its application to recirculating flows,” Phys. Fluids A 5, 3186 (1993)]10.1063/1.858675 with the dynamic localization procedure of Piomelli and Liu [“Large eddy simulation of rotating channel flows using a localized dynamic model,” Phys. Fluids 7, 839 (1995)]10.1063/1.868607 and a buoyancy correction similar to that proposed by Brown et al. [“Large-eddy simulation of stable atmospheric boundary-layers with a revised stochastic subgrid model,” Q. J. R. Meteorol. Soc. 120, 1485 (1994)]10.1002/qj.49712052004 based on data measured in the stable atmospheric boundary layer. Simulations run using this model give significantly closer agreement with the experimental data than simulations run using a version of the dynamic Smagorinsky model with similar modifications. Support for the physical arguments upon which the scaling relations are based is obtained through a statistical analysis of the turbulent flow fields generated by the numerical simulations.

Implementation and Evaluation of Dynamic Subfilter-Scale Stress Models for Large-Eddy Simulation Using WRF*

Abstract The performance of a range of simple to moderately-complex subfilter-scale (SFS) stress models implemented in the Weather Research and Forecasting (WRF) model is evaluated in large-eddy simulations of neutral atmospheric boundary layer flow over both a flat terrain and a two-dimensional symmetrical transverse ridge. Two recently developed dynamic SFS stress models, the Lagrangian-averaged scale-dependent (LASD) dynamic model and the dynamic reconstruction model (DRM), are compared with the WRF model’s existing constant-coefficient linear eddy-viscosity and (as of version 3.2) nonlinear SFS stress models to evaluate the benefits of more sophisticated and accurate, but also more computationally expensive approaches. Simulation results using the different SFS stress models are compared among each other, as well as against the Monin–Obukhov similarity theory. For the flat terrain case, vertical profiles of mean wind speed from the newly implemented dynamic models show the best agreement with the similarity solution, improving even upon the nonlinear model, which likewise yields a significant improvement compared to the Smagorinsky model. The more sophisticated SFS stress models more successfully predict the expected production and inertial range scaling of power spectra, especially near the surface, with the dynamic models achieving the best scaling overall. For the transverse ridge case, the nonlinear model predicts the greatest amount of reverse flow in the lee of the ridge, and also demonstrates the greatest ability to duplicate qualitative features of the highest-resolution simulations at coarser resolutions. The dynamic models’ flow distributions in the lee of the ridge did not differ significantly from the constant-coefficient Smagorinsky model.

Large-Eddy Simulation of the Stable Boundary Layer with Explicit Filtering and Reconstruction Turbulence Modeling

AbstractLarge-eddy simulation (LES) of the stably stratified atmospheric boundary layer is performed using an explicit filtering and reconstruction approach with a finite difference method. Turbulent stresses are split into the resolvable subfilter-scale and subgrid-scale stresses. The former are recovered from a reconstruction approach, and the latter are represented by a dynamic eddy-viscosity model. The resulting dynamic reconstruction model (DRM) can sustain resolved turbulence with less stringent resolution requirements than conventional closure models, even under strong atmospheric stability. This is achieved by proper representation of subfilter-scale (SFS) backscatter of turbulent kinetic energy (TKE). The flow structure and turbulence statistics for the moderately stable boundary layer (SBL) are analyzed with high-resolution simulations. The DRM simulations show good agreement with established empirical formulations such as flux and gradient-based surface similarity, even at relatively coarse resolution. Similar results can be obtained with traditional closure models at the cost of higher resolution. SBL turbulence under strong stability is also explored. Simulations show an intermittent presence of elevated TKE below the low-level jet. Overall, the explicit filtering and reconstruction approach is advantageous for simulations of the SBL. At coarse resolution, it can extend the working range of LES to stronger stability, while maintaining agreement to similarity theory; at fine resolution, good agreement with theoretical formulations provides confidence in the results and allows for detailed investigation of the flow structure under moderate to strong stability conditions.

The Canopy Horizontal Array Turbulence Study

The Canopy Horizontal Array Turbulence Study (CHATS) took place in spring 2007 and is the third in the series of Horizontal Array Turbulence Study (HATS) experiments. The HATS experiments have been instrumental in testing and developing subfilterscale (SFS) models for large-eddy simulation (LES) of planetary boundary layer (PBL) turbulence. The CHATS campaign took place in a deciduous walnut orchard near Dixon, California, and was designed to examine the impacts of vegetation on SFS turbulence. Measurements were collected both prior to and following leafout to capture the impact of leaves on the turbulence, stratification, and scalar source/sink distribution. CHATS utilized crosswind arrays of fast-response instrumentation to investigate the impact of the canopy-imposed distribution of momentum extraction and scalar sources on SFS transport of momentum, energy, and three scalars. To directly test and link with PBL parameterizations of canopy-modified turbulent exchange, CHATS also included a 30-m profile tower instrumented with turbulence instrumentation, fast and slow chemical sensors, aerosol samplers, and radiation instrumentation. A highresolution scanning backscatter lidar characterized the turbulence structure above and within the canopy; a scanning Doppler lidar, mini sodar/radio acoustic sounding system (RASS), and a new helicopter-observing platform provided details of the PBL-scale flow. Ultimately, the CHATS dataset will lead to improved parameterizations of energy and scalar transport to and from vegetation, which are a critical component of global and regional land, atmosphere, and chemical models. This manuscript presents an overview of the experiment, documents the regime sampled, and highlights some preliminary key findings.

Modeling of turbulent gas–liquid bubbly flows using stochastic Lagrangian model and lattice-Boltzmann scheme

In this paper we present detailed, three-dimensional and time-resolved simulations of turbulent gas–liquid bubbly flows. The continuous phase is modeled using a lattice-Boltzmann (LB) scheme. The scheme solves the large-scale motions of the turbulent flow using the filtered conservation equations, where the Smagorinsky model has been used to account for the effects of the sub-filter scales. A Lagrangian approach has been used for the dispersed, bubbly phase. That is we update the equations of motion of individual bubbles. It is shown that the incorporation of the sub-filter scale fluid fluctuations along the bubble trajectory improves the predictions. Collisions between bubbles are described by the stochastic inter-particle collision model based on kinetic theory developed by Sommerfeld (2001). It has been found that the collision model not only dramatically decreases computing time compared to the direct collision method, but also provides an excellent computational efficiency on parallel platforms. Furthermore, it was found that the presented modeling technique provides very good agreement with experimental data for mean and fluctuating velocity components.

From Large-Eddy Simulation to Direct Numerical Simulation of a lean premixed swirl flame: Filtered laminar flame-PDF modeling

Large-Eddy Simulations (LES) and Direct Numerical Simulation (DNS) are applied to the analysis of a swirl burner operated with a lean methane–air mixture and experimentally studied by Meier et al. [ 19]. LES is performed for various mesh refinements, to study unsteady and coherent large-scale behavior and to validate the simulation tool from measurements, while DNS enables to gain insight into the flame structure and dynamics. The DNS features a 2.6 billion cells unstructured-mesh and a resolution of less than 100 microns, which is sufficient to capture all the turbulent scales and the major species of the flame brush; the unresolved species are taken into account thanks to a tabulated chemistry approach. In a second part of the paper, the DNS is filtered at several filter widths to estimate the prediction capabilities of modeling based on premixed flamelet and presumed probability density functions. The similarities and differences between spatially-filtered laminar and turbulent flames are discussed and a new sub-grid scale closure for premixed turbulent combustion is proposed, which preserves spectral properties of sub-filter flame length scales. All these simulations are performed with a solver specifically tailored for large-scale computations on massively parallel machines.

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ w /Δ, where Λ w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.

The Effect of Subfilter-Scale Physics on Regularization Models

The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations’ performance as SFS models. Suppression of spectrally local SFS interactions and conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α-model (LANS-α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k +1 as the SFS spectra is resolved. The Clark-α and Leray-α models, truncations of LANS-α, do not conserve small-scale circulation and do not develop rigid bodies. LANS-α, however, is closest to Navier-Stokes in intermittency properties. All three models are found to be stable at high Reynolds number. Differences between L 2 and H 1 norm models are clarified. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES.

A Mixed Scheme for Subgrid-Scale Fluxes in Cloud-Resolving Models

Abstract A large-domain large-eddy simulation of a tropical deep convection system is used as a benchmark to derive and test a mixed subgrid-scale (SGS) scheme for scalar and momentum fluxes in cloud-resolving models (CRMs). The benchmark simulation resolves a broad range of scales ranging from mesoscale organizations, through gravity waves and individual clouds, down to energy-containing turbulent eddies. A spectral analysis shows that the vertical-velocity kinetic energy peaks at scales from hundreds of meters in the lower cloud layer to several kilometers higher up; these scales are typical grid sizes of today’s CRMs. The analysis also shows that a significant portion of the scalar and momentum fluxes in the benchmark simulation are carried by motions smaller than several kilometers (i.e., smaller than a typical grid resolution of CRMs). The broad range of scales of the benchmark simulation is split into two components: filter scale (mimicking CRM resolvable scale) and subfilter scale (mimicking CRM SGS), using filter widths characteristic of a typical CRM grid spacing. The local relationship of the subfilter-scale fluxes to the filter-scale variables is examined. This leads to a mixed SGS scheme to represent the SGS fluxes of scalars and momentum in CRMs. A priori tests show that the mixed SGS scheme yields spatial distributions of subfilter-scale fluxes that correlate much better with those retrieved from the benchmark when compared with an eddy viscosity/diffusivity scheme that is commonly used in today’s CRMs.

Implementation of a Nonlinear Subfilter Turbulence Stress Model for Large-Eddy Simulation in the Advanced Research WRF Model

Abstract Two formulations of a nonlinear turbulence subfilter-scale (SFS) stress model were implemented into the Advanced Research Weather Research and Forecasting model (ARW-WRF) version 3.0 for improved large-eddy simulation performance. The new models were evaluated against the WRF model’s standard Smagorinsky and 1.5-order turbulence kinetic energy (TKE) linear eddy-viscosity SFS stress models in simulations of geostrophically forced, neutral boundary layer flow over both flat terrain and a shallow, symmetric transverse ridge. Comparisons of simulation results with similarity profiles indicate that the nonlinear models significantly improve agreement with the expected profiles near the surface, reducing the overprediction of near-surface stress characteristic of linear eddy-viscosity models with no near-wall damping. Comparisons of simulations conducted using different mesh sizes indicate that the nonlinear model simulations at coarser resolutions agree more closely with the higher-resolution results than corresponding lower-resolution simulations using the standard WRF SFS stress models. The nonlinear models produced flows featuring a broader range of eddy sizes, with less spectral power at lower frequencies and more spectral power at higher frequencies. In simulated flow over the transverse ridge, distributions of flow separation and reversal near the surface simulated at higher resolution were likewise better depicted in coarser-resolution simulations using the nonlinear models.

An efficient numerical method for RANS/LES turbulent simulations using subfilter scale stress transport equations

SUMMARY We propose a numerical method for performing hybrid non-zonal RANS/LES simulations by using a subfilter scale stress transport model in the framework of finite volume technique. The turbulent equations are derived from the new partial integrated transport modeling (PITM) method. The PITM method has been initially developed for devising subfilter energy models based on the viscosity concept (Theoretical Computational Fluid Dynamics 2005; 18:443–468), and has been then extended to subfilter stress models relying on second-moment closures (Physics of Fluids 2005; 17(6); Int. J. Heat and Fluid Flow 2009; 30:602–616; Theoret. Comput. Fluid Dyn. 2007; 21(3):201–229.). The numerical method put in place is developed in a general framework of large eddy simulations and can be applied to almost all subfilter scale models based on transport equations of subfilter scale turbulent quantities. In this work, we have developed specific numerical schemes for solving the turbulent transport equations of compressible flows including the density, velocity, energy, subfilter scale turbulent stresses and subfilter scale dissipation rate that are strongly coupled together. When performing LES or VLES simulations, this coupling between the motion and turbulent equations poses some numerical problems because the subfilter scale turbulent stresses and dissipation rate are more fluctuating in time and space than in the case of RANS computations, so that a specific numerical treatment has been proposed. In this framework, new implicit iterative algorithms in time are especially developed for solving the unsteady equations of the turbulent energy, stresses and dissipation rate by ensuring the positivity of the normal stresses at each step of the computation. We show that the convective fluxes resulting from the volume technique including the main and turbulent variables can be computed by an approximate Riemann solver using new tensorial operators. The numerical solver is calibrated on the decay of isotropic spectrum and on the well-known fully turbulent channel flow for assessing the performances of the numerical method. Then, we perform numerical simulations of the turbulent channel flow over periodic hills on coarse and medium grids. This flow encountered in aeronautical applications is of complex physics as it is governed by interacting turbulence mechanisms associated with separation, recirculation and reattachment. As a result, it is found that the proposed numerical method used in conjunction with the subfilter stress model performs fairly well with these turbulent flows on different grids. From a practical point of view, this numerical method can be easily implemented in CFD codes for tackling engineering applications. Copyright © 2010 John Wiley & Sons, Ltd.

The Das–Moser commutator closure for filtering through a boundary is well-posed

When filtering through a wall with constant averaging radius, in addition to the subfilter scale stresses, a non-closed commutator term arises. We consider a proposal of Das and Moser to close the commutator error term by embedding it in an optimization problem. This report shows that this optimization-based closure, with a small modification, leads to a well-posed problem showing the existence of a minimizer. We also derive the associated first order optimality conditions.

Large-Eddy Simulation for an Axisymmetric Piston-Cylinder Assembly With and Without Swirl

Large-eddy simulation (LES) has been performed for an axisymmetric piston-cylinder assembly with and without swirl. For both cases, the LES mean and rms velocity profiles show better agreement with experimental data than profiles obtained using a Reynolds-averaged Navier–Stokes (RANS) approach with a standard k − e turbulence model. The sum of the resolved and modeled contributions to turbulence kinetic energy (TKE) approaches grid independence for the meshes used in this study. The sensitivity of LES to key numerical and physical model parameters has been investigated. Results are especially sensitive to mesh and to the subfilter-scale (SFS) turbulence models. Satisfactory results can be obtained using simple viscosity-based SFS turbulence models, although there is room for improvement. No single model gives uniformly best agreement between model and measurements at all spatial locations and at all times. The strong sensitivity of computed mean and rms velocity profiles to variations in the SFS turbulence model suggests that better results might be obtained using more sophisticated models.

LES of a laboratory-scale turbulent premixed Bunsen flame using FSD, PCM-FPI and thickened flame models

Large-eddy simulations (LES) of a turbulent premixed Bunsen flame were carried out with three subfilter-scale (SFS) modelling approaches for turbulent premixed combustion. One approach is based on the artificially thickened flame and power-law flame wrinkling models, the second approach is based on the presumed conditional moment (PCM) with flame prolongation of intrinsic low-dimensional manifolds (FPI) tabulated chemistry, and the third approach is based on a transport equation for the flame surface density (FSD). A lean methane–air flame at equivalence ratio ϕ=0.7, which was studied experimentally by Yuen and Gülder, was considered. The predicted LES solutions were compared to the experimental data. The resolved instantaneous three-dimensional structure of the predicted flames compares well with that of the experiment. Flame heights and resolvable flame surface density and curvature were also examined. In general, the average flame height was well predicted. Furthermore, the flame surface data extracted from the simulations showed remarkably good qualitative agreement with the experimental results. The probability density functions of predicted flame curvature displayed a Gaussian-like shape centred around zero as also observed in the experimental flame, although the experimental data showed a slightly wider profile. The results of the comparisons highlight the weaknesses and the strengths of SFS modelling approaches commonly used in LES of turbulent premixed flames.

Large Eddy Simulation of the Sandia Flame Series (D–F) using the Eulerian stochastic field method

Three turbulent piloted methane jet flames with increasing levels of local extinction (Sandia Flames D–F) have been computed using Large Eddy Simulation. The smallest unresolved scales of the flow, in which combustion occurs, are represented using the filtered probability density function method where the corresponding evolution equation is solved directly. A dynamic model for the sub-grid stresses together with a simple gradient diffusion approximation for the scalar fluxes is applied in conjunction with the linear mean square estimation closure for sub-filter scale mixing. An augmented reduced mechanism (ARM) derived from the full GRI 3.0 mechanism is incorporated to describe the chemical reaction. The results demonstrate the ability of the method in capturing quantitatively finite rate effects such as extinction and re-ignition in turbulent flames.

Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling

Law-of-the-wall (LOTW) scaling implies that at sufficiently high Reynolds numbers the mean velocity gradient ∂U/∂z in the turbulent boundary layer should scale on u∗/z in the inertia-dominated surface layer, where u∗ is the friction velocity and z is the distance from the surface. In 1992, Mason and Thomson pointed out that large-eddy simulation (LES) of the atmospheric boundary layer (ABL) creates a systematic peak in ϕ(z)≡(∂U/∂z)/(u∗/z) in the surface layer. This “overshoot” is particularly evident when the first grid level is within the inertial surface layer and in hybrid LES/Reynolds-averaged Navier–Stokes methods such as “detached-eddy simulation,” where the overshoot is identified as a “logarithmic layer mismatch.” Negative consequences of the overshoot—spurious streamwise coherence, large-eddy structure, and vertical transport—are enhanced by buoyancy. Several studies have shown that adjustments to the modeling of the subfilter scale (SFS) stress tensor can alter the degree of the overshoot. A comparison among simulations indicates a lack of grid independence in the prediction of mean velocity that originates in surface layer deviations from LOTW. Here we analyze the broader framework of LES prediction of LOTW scaling—including, but extending beyond, “the overshoot.” Our theory includes a criterion that is necessary to remove the overshoot but is insufficient for LES to produce constant ϕ(z)≡1/κ through the surface layer, and fully satisfy the LOTW. For mean shear to scale on u∗/z in the surface layer, we show that two additional criteria must be satisfied. These criteria can be framed in terms of three nondimensional variables that define a parameter space in which systematic adjustments can be made to the simulation to achieve LOTW scaling. This occurs when the three parameters exceed critical values that we estimate from basic scaling arguments. The essential difficulty can be traced to a spurious numerical LES viscous length scale that interferes with the dimensional analysis underlying LOTW. When this spurious scale is suppressed sufficiently to retrieve LOTW scaling, the LES has been moved into the supercritical “high accuracy zone” (HAZ) of our parameter space. Using eddy viscosity closures for SFS stress, we show that to move the simulation into the HAZ, the model constant must be adjusted together with grid aspect ratio in coordinated fashion while guaranteeing that the surface layer is sufficiently well resolved in the vertical by the grid. We argue that, in principle, both the critical values that define the HAZ and the surface layer constant κ when LOTW scaling is achieved can depend on details of the SFS (and surface stress) models applied in the LES. We carried out over 110 simulations of the neutral rough-surface ABL to cover a wide portion of the parameter space using a low dissipation spectral code, the Smagorinsky SFS stress model and a standard model for fluctuating surface stress. The overshoot was found to systematically reduce and ϕ(z) was found to systematically approach a constant value in the surface layer as the three parameters exceeded critical values and the LES moved into the HAZ, consistent with the theory. However, whereas constant ϕ(z) was achieved over nearly the entire surface layer as the LES is moved into the HAZ, the model for surface shear stress continues to disrupt LOTW scaling at the first couple grid levels, and the predicted von Kármán constant κ is lower than traditional values. In a comprehensive discussion, we summarize the primary results of subsequent studies where we minimize the spurious influence of the surface stress model and show that the surface stress model and the SFS stress model constant influence the predicted value of the von Kármán constant for LES in the HAZ.

Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks

We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) alpha model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of approximately 200 when compared to a direct numerical simulation on a large grid of 1536;{3} points at the same Reynolds number.

Large eddy simulation modelling of spray-induced turbulence effects

This study is focused on the development of spray models for large eddy simulations (LESs) of high injection pressure diesel sprays. Basic governing equations are numerically solved using the Lagrangian—Eulerian approach for liquid and gas phases respectively, in the KIVA-3V code. Non-reacting simulations of evaporating spray are performed using a dynamic structure LES model in which the subgrid stress tensor is modelled with a non-viscosity tensor coefficient. This is a one equation based model, in which an extra transport equation for the subgrid kinetic energy ( k) is solved. Subgrid scale energy exchange between droplets and the gas phase is identified as an important mechanism to capture the correct scaling of k, which eventually feeds back to both the spray droplets and the gas phase turbulent mixing. Hence, to account for spray-induced gas turbulence, a LES spray source model for k is developed. This model requires subfilter scale velocities, which are obtained by defiltering the filtered velocity field available from LES. Results are compared with corresponding RANS results and available experimental data for various physical spray variables such as spray penetration, gas phase penetration, droplet distribution, etc. The LES spray model was found to be important in predicting the correct liquid spray evolution and responds correctly to varying parameters such as nozzle size and ambient density.

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.