Subgrid-scale Closure Research Articles

Large Eddy Simulation of Titanium Dioxide Nanoparticle Formation and Growth in Turbulent Jets

Large eddy simulations (LES) of titanium dioxide nanoparticles in three dimensional turbulent reacting planar jets are performed. The spatio-temporal evolution of the particle field is obtained by utilizing a nodal representation of the general dynamic equation. Gradient-diffusion, Smagorinsky-type subgrid-scale closures are employed to account for the unresolved stresses, fluid-scalar fluxes, and fluid-particle fluxes. The effect of the unresolved fluctuations on coagulation are neglected. Simulations are performed at two different precursor concentration levels. Comparison between results obtained via direct numerical simulation (DNS) and LES is performed to assess the performance of the closures. The LES performs fairly well in predicting the particle concentration as a function of size as well as the mean diameter. Additionally the polydispersity of the LES particle field is greater than that of the DNS. The results also suggest that at as the precursor concentration increases, neglect of the unresolv...

Leray-α LES of magnetohydrodynamic turbulence at low magnetic Reynolds number

A series of large eddy simulations is performed for decaying homogeneous magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number (Rem <<1) with different strengths of magnetic field. The initial isotropic turbulence problem has the Taylor scale Reynolds number (Re λ) of 120. The regularization-based Leray-α model is used for sub-grid scale (SGS) closure for the first time and comparisons are made with our own direct numerical simulation (DNS) calculations conducted as part of this study. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields are made between the varying magnetic field cases. The SGS model assessments are also made between the Leray-α model and the classic non-dynamic Smagorinsky with several model coefficients. Overall, the Leray-α model was unable to capture the anisotropy associated with MHD flows as well as the non-dynamic Smagorinsky model in this study or even the dynamic Smagorinsky model in previous studies.

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.

Novel developments in subgrid-scale modeling of space plasma: weakly compressible turbulence in the local interstellar medium

A survey of various subgrid-scale (SGS) models for the study of compressible magnetohydrodynamic (MHD) turbulence of space plasma is given. A large eddy simulation (LES) method for the study of compressible MHD turbulence of polytropic fluid is developed. A theory of SGS turbulent flow for the new SGS terms, appearing after the Favre-filtering procedure in the system of MHD equations, is proposed. Modeling of decaying compressible MHD turbulence under various similarity numbers is carried out and the validity of the LES method for the modeling of a polytropic is shown. Numerical studies are performed for five different SGS closures: the Smagorinsky model, the Kolmogorov model, the cross-helicity model, the scale-similarity model and the mixed model. Suggested SGS parameterizations are studied and SGS models that demonstrate the most exact results for decaying compressible MHD turbulence, under various similarity numbers, are shown. Using the advantages of the LES method, a nontrivial space plasma compressible MHD turbulence regime is studied when initially supersonic fluctuations become weakly compressible. An as yet unexplained observation is that density fluctuations in the local interstellar medium exhibit a Kolmogorov-like spectrum over an extraordinary range of scales with a spectral index close to −5/3. In spite of the compressibility and the presence of a magnetic field in the local interstellar medium, density fluctuations nevertheless admit a Kolmogorov-like power law. Supersonic flows with high large-scale Mach numbers are characterized in the interstellar medium. Nevertheless, there are subsonic fluctuations of weakly compressible components of the interstellar medium. These weakly compressible subsonic fluctuations are responsible for the emergence of a Kolmogorov-type spectrum in the interstellar turbulence which is observed from experimental data. It is shown that density fluctuations are a passive scalar in a weakly compressible MHD turbulence velocity field and demonstrate a Kolmogorov-like spectrum.

Prediction of Small-Scale Cavitation in a High Speed Flow Over an Open Cavity Using Large-Eddy Simulation

Large-eddy simulation of flow over an open cavity corresponding to the experimental setup of Liu and Katz (2008, “Cavitation Phenomena Occurring Due to Interaction of Shear Layer Vortices With the Trailing Corner of a Two-Dimensional Open Cavity,” Phys. Fluids, 20(4), p. 041702) is performed. The filtered, incompressible Navier–Stokes equations are solved using a co-located grid finite-volume solver with the dynamic Smagorinsky model for a subgrid-scale closure. The computational grid consists of around 7×106 grid points with 3×106 points clustered around the shear layer, and the boundary layer over the leading edge is resolved. The only input from the experimental data is the mean velocity profile at the inlet condition. The mean flow is superimposed with turbulent velocity fluctuations generated by solving a forced periodic duct flow at a freestream Reynolds number. The flow statistics, including mean and rms velocity fields and pressure coefficients, are compared with the experimental data to show reasonable agreement. The dynamic interactions between traveling vortices in the shear layer and the trailing edge affect the value and location of the pressure minima. Cavitation inception is investigated using two approaches: (i) a discrete bubble model wherein the bubble dynamics is computed by solving the Rayleigh–Plesset and the bubble motion equations using an adaptive time-stepping procedure and (ii) a scalar transport model for the liquid volume fraction with source and sink terms for phase change. Large-eddy simulation, together with the cavitation models, predicts that inception occurs near the trailing edge similar to that observed in the experiments. The bubble transport model captures the subgrid dynamics of the vapor better, whereas the scalar model captures the large-scale features more accurately. A hybrid approach combining the bubble model with the scalar transport is needed to capture the broad range of scales observed in cavitation.

내부조파기법을 활용한 Navier-Stokes 방정식 모형의 고립파 처오름 수치모의

급경사에서의 고립파의 처오름을 예측하기 위해 3차원 수치모형에 내부조파기법을 도입하여 수치모형실험을 수행하였다. 수치모형은 Navier-Stokes 방정식을 유한차분법을 이용하여 계산하는 동수압 모형으로서, 난류의 해석을 위해서 상대적으로 큰 에디(eddy)만을 고려하는 SANS(spatially averaged Navier-Stokes) 방정식을 푸는 LES(large-eddy-simulation) 기반의 수치모형을 사용한다. 엇갈림 격자체계에서 유한차분법을 사용하여 지배방정식을 해석하는 모형으로서 수치기법으로 Two-step projection 기법을 사용하여 SANS 방정식을 풀었으며, Poisson 방정식을Bi-CGSTAB 기법을 이용하여 풀고 압력장을 계산하였다. 또한, 자유수면의 추적을 위하여 2차 정확도의 VOF(volume-of-fluid) 기법을 사용하였다. 먼저 고립파를 3차원 공간의 일정 수심상에서 내부조파하여 해석해와 비교한 후 분산오차에 대해 분석하였다. 그리고 고립파를 내부조파하여 급경사에서의 고립파의 처오름 및 처내림 현상을 예측하고 수리모형 실험결과와 비교 및 분석하였다. A three-dimensional numerical model called NEWTANK is employed to investigate solitary wave run-up with an internal wave-maker on a steep slope. The numerical model solves the spatially averaged Navier-Stokes equations for two-phase flows. The LES (large-eddy-simulation) approach is adopted to model the turbulence effect by using the Smagorinsky SGS (sub-grid scale) closure model. A two-step projection method is adopted in numerical solutions, aided by the Bi-CGSTAB (Bi-Conjugate Gradient Stabilized) method to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate VOF (volume-of-fluid) method is used to track the distorted and broken free surface. A solitary wave is first internally generated and propagated over a constant water depth in the three-dimensional domain. Numerically predicted results are compared with analytical solutions and numerical errors are analyzed in detail. The model is then applied to study solitary wave run-up on a steep slope and the obtained results are compared with available laboratory measurements.

Large eddy simulation of a stenosed artery

A large eddy simulation is conducted of a 50% stenosed artery. The inlet boundary condition is a physiologically accurate pulsatile flow, representative of that found in a femoral artery. The transient, three dimensional results show the non-axisymmetric nature of the flow field; high values of wall shear stress, oscillatory in both space and time are also observed. The identification of such fluid dynamic quantities within a stenosed vessel is important in understanding the likely causes and ongoing effects on the integrity of the vessel. References S. A. Berger and L-D. Jou. Flows in Stenotic Vessels. Annu. Rev. Fluid Mech. 32:347--382. 2000. doi:10.1146/annurev.fluid.32.1.347 M. Li, J. Beech-Brandt, L. John, P. Hoskins, W. Easson. Numerical Analysis of Pulsatile Blood Flow and Vessel Wall Mechanics in Different Degrees of Stenoses. J. Biomechanics 40:3715--3724. 2007. doi:10.1016/j.jbiomech.2007.06.023 S. S. Varghese and S. H. Frankel. Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels. J. Biomech. Eng. 125 (445--460). 2003. doi:10.1115/1.1589774 S. S. Varghese, S. H. Frankel and P. F. Fischer. Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow. Journal of Fluid Mechanics., 582:281--318. 2007. doi:10.1017/S0022112007005836 B. Xiao and Y. Zhang. Numerical simulation of pulsatile turbulent flow in tapering stenosed arteries. Int. J. Numerical Meth. Heat Fluid Flow, 19(5):561--573. 2009. doi:10.1108/09615530910963526 B. Lieber and D. Giddens. Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress. J. Biomech., 23(6):597--605. 1990. doi:10.1016/0021-9290(90)90052-5 M. Paul, Md. M. Molla and G. Roditi. Large eddy simulation of pulsatile blood flow. Medical Engineering and Physics, 31:153--159. 2009. doi:10.1016/j.medengphy.2008.04.014 W. W. Nichol and M. F. O'Rourke. McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles, Hodder Arnold, London, 5th edition. 2005. D. N. Ku. Blood flow in arteries. Annu. Rev. Fluid Mech. 29:399--434. 1997. doi:10.1146/annurev.fluid.29.1.399 D. Lilly. A Proposed Modification of the Germano Subgrid-Scale Closure Model. Physics of Fluids, 4:633--635. 1992. doi:10.1063/1.858280 B. Geurts. Elements of direct and large eddy simulation. R. T. Edwards, 2004.

Large-eddy simulation of mixing in a recirculating shear flow

The flow field and mixing in an expansion-ramp geometry is studied using large-eddy simulation (LES) with subgrid scale (SGS) modelling. The expansion-ramp geometry was developed to investigate enhanced mixing and flameholding characteristics while maintaining low total-pressure losses. Passive mixing was considered without taking into account the effects of chemical reactions and heat release, an approximation that is adequate for experiments conducted in parallel. The primary objective of the current work is to validate the LES–SGS closure in the case of passive turbulent mixing in a complex configuration and, if successful, to rely on numerical simulation results for flow details unavailable via experiment. Total (resolved-scale plus subgrid contribution) probability density functions (p.d.f.s) of the mixture fraction are estimated using a presumed beta-distribution model for the subgrid field. Flow and mixing statistics are in good agreement with the experimental measurements, indicating that the mixing on a molecular scale is correctly predicted by the LES–SGS model. Finally, statistics are shown to be resolution-independent by computing the flow for three resolutions, at twice and four times the resolution of the coarsest simulation.

Validation of large eddy simulation method for study of flatness and skewness of decaying compressible magnetohydrodynamic turbulence

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.

Numerical studies of large-amplitude internal waves shoaling and breaking at shelf slopes

Hydro carbon fields beyond the shelf break are presently being explored and developed, which has increased the scientific focus in this area. Measurements from the slopes reveal large variability in temperature and velocity, and some of the observed events are due to interactions between large-amplitude oscillations of the thermocline and the topography. The present study focuses on the strong currents that are generated near the seabed during shoaling and breaking of internal waves along shelf slopes. The parameter regime used is similar to the one for the Nordic Seas. The results show that, during shoaling of large internal waves along (gentle) slopes, the energy is transferred towards smaller scales and strong velocities (over 1 m s − 1) can be generated. To resolve all scales involved is still not feasible, and therefore, the model results are sensitive to the grid size and the subgrid scale closure.

A compressible wall-adapting similarity mixed model for large-eddy simulation of the impinging round jet

Wall-jet interaction is studied with large-eddy simulation (LES) in which a mixed-similarity subgrid scale (SGS) closure is combined with the wall-adapting local eddy-viscosity (WALE) model for the eddy-viscosity term. The macrotemperature and macropressure are introduced to deduce a weakly compressible form of the mixed-similarity model, and the relevant formulation for the energy equation is deduced accordingly. LES prediction capabilities are assessed by comparing flow statistical properties against experiment of an unconfined impinging round jet at Reynolds numbers of 23 000 and 70 000. To quantify the benefit of the proposed WALE-similarity mixed model, the lower Reynolds number simulations are also performed using the standard WALE and Lagrangian dynamic Smagorinsky approaches. The unsteady compressible Navier–Stokes equations are integrated over 2.9 M, 3.5 M, and 5.5 M node Cartesian grids with an explicit fourth-order finite volume solver. Nonreflecting boundary conditions are enforced using a methodology accounting for the three-dimensional character of the turbulent flow at boundaries. A correct wall scaling is achieved from the combination of similarity and WALE approaches; for this wall-jet interaction, the SGS closure terms can be computed in the near-wall region without the necessity of resorting to additional specific treatments. The possible impact of turbulent energy backscatter in such flow configurations is also addressed. It is found that, for the present configuration, the correct reproduction of reverse energy transfer plays a key role in the estimation of near-wall statistics, especially when the viscous sublayer is not properly resolved.

A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean

A three-dimensional numerical model for large-eddy simulation (LES) of oceanic turbulent processes is described. The numerical formulation comprises a spectral discretization in the horizontal directions and a high-order compact finite-difference discretization in the vertical direction. Time-stepping is accomplished via a second-order accurate fractional-step scheme. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy-viscosity parametrization for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky parametrization for which the model coefficient is computed dynamically as a function of the flow. Validation studies are presented demonstrating the temporal and spatial accuracy of the formulation for laminar flows with analytical solutions. Further validation studies are described involving direct numerical simulation (DNS) and LES of turbulent channel flow and LES of decaying isotropic turbulence. Sample flow problems include surface Ekman layers and wind-driven shallow water flows both with and without Langmuir circulation (LC), generated by wave effects parameterized via the well-known Craik–Leibovich (C–L) vortex force. In the case of the surface Ekman layers, the inner layer (where viscous effects are important) is not resolved and instead is parameterized with the Smagorinsky models previously described. The validity of the dynamic Smagorinsky model (DSM) for parameterizing the surface inner layer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in Ekman layers with wave effects, the implicit LES grid filter leads to LC subgrid-scales requiring ad hoc modeling via an explicit spatial filtering of the C–L force in place of a suitable SGS parameterization.

Non-hydrostatic pressure in σ-coordinate ocean models

Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed. The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure.

Coupled Effects of Small-Scale Turbulence and Phytoplankton Biomass in a Small Stratified Lake

Recent laboratory studies demonstrated that small-scale fluid motion mediates phytoplankton physiological responses. We have investigated to what extent the laboratory studies are consistent with field measurements in a small stratified lake. We propose the rate of energy dissipation and corresponding Kolmogorov velocity are important scaling variables that describe the enhanced algal growth and the uptake of nutrients in a moving fluid under laboratory and field conditions. The ratio of nutrient flux to an alga in a moving fluid versus the nutrient flux in a stagnant fluid (Sherwood number) is quantified by the ratio of advective nutrient transport to molecular diffusion of a nutrient (Péclet number, PeK). The advective transport of nutrients is described by the layer-averaged Kolmogorov velocity (ũK). An enhanced algal growth due to fluid motion is proposed over the Péclet number range 6.7>PeK>1.3, with the maximal growth at PeK=2.9. Field measurements recorded by a microstructure profiler demonstrated encouraging agreement between laboratory and field findings. The current mechanistic models of phytoplankton population dynamics could consider the proposed Péclet number with redefined characteristic velocity scale (ũK) in the formulation of subgrid scale closure fluxes on nutrient uptake and growth rate. Furthermore, the laboratory and field results presented in this study are intended to motivate researchers to question the validity of standard laboratory biotoxicity protocols and to modify existing procedures in the examination of effluent toxicity in the environment by including the fluid motion.

Three-dimensional liquid sloshing in a tank with baffles

A numerical model has been developed to study three-dimensional (3D) liquid sloshing in a tank with baffles. The numerical model solves the spatially averaged Navier–Stokes equations, which are constructed on a non-inertial reference frame having six degree-of-freedom (DOF) of motions. The large-eddy-simulation (LES) approach is employed to model turbulence by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. The baffles in the tank are modeled by the concept of virtual boundary force (VBF) method. The numerical model is first validated against the available analytical solution and experimental data for two-dimensional (2D) liquid sloshing in a tank without baffles. The 2D liquid sloshing in tanks with baffles is then investigated. The numerical results are compared with other results from available literatures. Good agreement is obtained. Finally, the model is used to study 3D liquid sloshing in a tank with vertical baffles. The effect of the baffle is investigated and discussed.

Numerical studies of internal waves at a sill: Sensitivity to horizontal grid size and subgrid scale closure

A non-hydrostatic terrain following model in cross sectional form is applied to study the generation and propagation of tidally forced internal waves near a sill in an idealized loch. On inflow internal waves are generated behind the sill, and they propagate from the sill. There is a transfer of energy from the barotropic tide to internal waves and then to irreversible mixing. The range of length scales involved goes from the scale of the forced tide to scales associated with wave breaking. This wide range of scales makes it very difficult to resolve all relevant length scales with a numerical model using a uniform finite difference grid. The sensitivity of the numerical results to the grid resolution and the parameterisation of subgrid scale mixing is investigated. Initial calculations are performed with constant values of viscosity and diffusivity, and subsequently they are repeated using large eddy simulations and including Richardson number dependant vertical mixing. In the studies with sub-critical flow over the sill, the results are robust to changes in the grid size. With stronger forcing, the flow over the sill becomes super-critical during maximum inflow, and the frequency and the nature of the internal waves generated in the lee of the sill becomes grid size dependant. For the super-critical case, the solution is sensitive to the subgrid scale closure scheme. Calculations show that with constant and small values of vertical viscosity and diffusivity, strong internal waves are generated on inflow in the lee of the sill. When using Richardson number dependant vertical viscosity and diffusivity, more of the tidal energy goes into vertical irreversible mixing, and less into internal waves.

Large-eddy simulation of H2–air auto-ignition using tabulated detailed chemistry

Large-eddy simulation (LES) of an igniting turbulent hydrogen/air jet for which experimental data are available is reported. A sub-grid scale closure is proposed that is based on a tabulation of detailed chemistry combined with a presumed probability density function, to be implemented into a fully compressible LES solver. The simulations are performed in a frame moving with the mean flow. The obtained results are shown to reproduce the experimental findings in terms of ignition length. A dynamic closure is used for the unknown sub-grid scale (SGS) scalar dissipation rate of mixture fraction and the sensitivity of the chemical response to SGS modelling is studied.

A numerical study of three-dimensional liquid sloshing in tanks

A numerical model NEWTANK (Numerical Wave TANK) has been developed to study three-dimensional (3-D) non-linear liquid sloshing with broken free surfaces. The numerical model solves the spatially averaged Navier–Stokes equations, which are constructed on a non-inertial reference frame having arbitrary six degree-of-freedom (DOF) of motions, for two-phase flows. The large-eddy-simulation (LES) approach is adopted to model the turbulence effect by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. Laboratory experiments are conducted for both 2-D and 3-D non-linear liquid sloshing in a rectangular tank. A linear analytical solution of 3-D liquid sloshing under the coupled surge and sway excitation is also developed in this study. The numerical model is first validated against the available analytical solution and experimental data for 2-D liquid sloshing of both inviscid and viscous fluids. The validation is further extended to 3-D liquid sloshing. The numerical results match with the analytical solution when the excitation amplitude is small. When the excitation amplitude is large where sloshing becomes highly non-linear, large discrepancies are developed between the numerical results and the analytical solutions, the former of which, however, agree well with the experimental data. Finally, as a demonstration, a violent liquid sloshing with broken free surfaces under six DOF excitations is simulated and discussed.

Large-eddy simulation of a dispersed particle-laden turbulent round jet

The numerical results obtained by large-eddy simulation (LES) of a particle-laden axisymmetric turbulent jet are compared with the available experimental data. The results indicate that with a new stochastic subgrid-scale (SGS) closure, the effects of the particles on the carrier gas and those of the carrier gas on the particles are correctly captured by the LES. Additional numerical experiments are conducted and used to investigate the effects of particle size, mass-loading ratio, and other flow/particle parameters on the statistics of both the carrier gas phase and the particle dispersed phase.

Development of large eddy simulation for modeling of decaying compressible magnetohydrodynamic turbulence

The large eddy simulation technique is developed for the study of decaying compressible magnetohydrodynamic turbulence. In the present paper the obtained results of numerical computations for large eddy simulation are compared with the results of direct numerical simulation of three-dimensional compressible magnetohydrodynamic turbulence under various similarity parameters, namely, magnetic Reynolds numbers, hydrodynamic Reynolds numbers, and Mach numbers. The comparison of five subgrid-scale closures of large eddy simulation for the magnetohydrodynamic case is made. The comparison between large eddy simulation and direct numerical simulation is carried out regarding the time evolution of kinetic and magnetic energy, cross helicity, subgrid-scale and molecular dissipations for kinetic and magnetic energy, turbulent intensities and quantities that describe anisotropy of flow, that is, skewness and kurtosis of velocity and magnetic field. It is shown that some subgrid-scale models proposed in the paper provide sufficient dissipation of kinetic and magnetic energy, reduce computational efforts and produce adequate results of magnetohydrodynamic turbulent modeling for various values of similarity parameters of flows.