On the performance of relaxation filtering for large-eddy simulation

In this work, the performance of large-eddy simulation (LES) based on the relaxation-filtering (RF) technique has been investigated quantitatively. In RF-based LES, the velocity field is filtered each nth time step, using a standard finite-difference filter, characterized by a specific order of accuracy m, and a fixed filtering strength σ. Hence, the procedure dissipates the amount of energy related to the residual stresses, and thus models the dissipative effect of the unresolved scales on the resolved scales. Since the order m and strength σ are related to the spectral distribution and the magnitude of the dissipation, respectively, these predefined parameters are crucial for the success of the method. Here, their influence is systematically investigated for the Taylor–Green vortex flow at a Reynolds number of 3000. First, the effects of m and σ are studied a priori in Fourier space. Further, 36 LESs are performed, each with a different combination of order m=4, 6, 8, 10, 12, 14 and strength σ=0.15, 0.2, 0.4, 0.6, 0.8, 1, and the turbulent statistics are compared with those of a direct numerical simulation, filtered at identical resolutions. The a priori, as well as the a posteriori results indicate that, for low filter orders m?4, the LES accuracy is rather poor and depends strongly on the filtering strength σ. However, for higher order filters, i.e. m?8, the accuracy is quite good and the results, including the resolved and subgrid dissipation rates, are nearly independent of the strength σ for σ?0.4. In this case, the spectral dissipation-distribution, determined by m, turns out to be the dominant parameter, whereas the dissipation strength, determined by σ, is of minor importance.     

A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence

Clustering (or preferential concentration) of inertial particles suspended in a homogeneous, isotropic turbulent flow is strongly influenced by the smallest scales of the turbulence. In particle-laden large-eddy simulations (LES) of turbulence, these small scales are not captured by the grid and hence their effect on particle motion needs to be modelled. In this paper, we use a subgrid model based on kinematic simulations of turbulence (Kinematic Simulation based SubGrid Model or KSSGM), for the first time in the context of predicting the clustering and the relative velocity statistics of inertial particles. This initial study focuses on the special case of inertial particles in the absence of gravitational settling. We show that the KSSGM gives excellent predictions for clustering in a priori tests for inertial particles with St ≥ 2.0, where St is the Stokes number, defined as the ratio of the particle response time to the Kolmogorov time-scale. To the best of our knowledge, the KSSGM represents the first model that has been shown to capture the effect of the subgrid scales on inertial particle clustering for St ≥ 2.0. We also show that the mean inward radial relative velocity between inertial particles (?w_r?^(?), which enters into the formula for the collision kernel) is accurately predicted by the KSSGM for all St. We explain why the model captures clustering at higher St?but not for lower St?, and provide new insights into the key statistical parameters of turbulence that a subgrid model would have to describe, in order to accurately predict clustering of low-St?particles in an LES.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Finite-size particles in turbulent channel flow: quadrant analysis and acceleration statistics

The interaction between finite-size particles and turbulent channel flow in the absence of gravity is studied by direct numerical simulations (DNS). The study is motivated by DNS observations of a turbulent channel flow with high-density, pointwise particles, that cluster in regions of high streamwise root-mean-square (RMS) acceleration close to the wall, contrary to what is observed in homogeneous isotropic turbulence. The aim of the present study is to explore if this is still the case when size effects are taken into account in the DNS. Based on the analysis of the velocity and acceleration statistics, the present DNS shows that, close to the wall, particles with ρ_p/ρ_f ranging from 2 to 4 are surrounded by regions with low streamwise RMS velocity but high streamwise RMS acceleration. According to the normalised particle acceleration probability density functions (PDFs), size effects become important in the near-wall region. As particle inertia increases, the normalised PDFs of particle acceleration tend to a Gaussian distribution. The tails of the normalised PDFs of the fluid conditioned by the presence of particles are higher than that of the unconditioned fluid close to the wall.     

Periodic Filtering as a subgrid-scale model for LES of laminar separation bubble flows

Laminar separation bubbles develop over many blades and airfoils at moderate angles of attack and Reynolds numbers ranging from 10⁴ to 10⁵. More accurate simulation tools are necessary to enable higher fidelity design optimisation for these airfoils and blades as well as to test flow control schemes. Following previous investigators, an equivalent problem is formulated by imposing suitable boundary conditions for flow over a flat plate which allows to use a high accuracy spectral solver. Large eddy simulation (LES) of such a flow were performed at drastically reduced resolution to assess the accuracy of several LES modelling approaches: the explicit dynamic Smagorinsky model, implicit LES, and the truncated Navier–Stokes approach (TNS). To mimic dissipation that occurs in implicit LES, the solution on a coarse mesh is filtered at every time step and two different filter strengths are used. In the TNS approach, the solution is filtered periodically, every few hundred time steps. The performance of each approach is evaluated against benchmark direct numerical simulation (DNS) data focusing on pressure and skin friction distributions, which are critical to airfoil designers. TNS results confirm that periodic filtering can act as an apt substitute for explicit subgrid-scale models, whereas filtering at every time step demonstrates the dependence of implicit LES on details of numerics.     

Study of mass consistency LES/FDF techniques for chemically reacting flows

A hybrid large eddy simulation/filtered density function (LES/FDF) approach is used for studying chemically reacting flows with detailed chemistry. In particular, techniques utilised for ensuring a mass consistent coupling between LES and FDF are discussed. The purpose of these techniques is to maintain a correct spatial distribution of the computational particles representing specified amounts of fluid. A particular mass consistency technique due to Y.Z. Zhang and D.C. Haworth (A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193) and their associated algorithms are implemented in a pressure-based computational fluid dynamics code suitable for the simulation of variable density flows, representative of those encountered in actual combustion applications. To assess the effectiveness of the referenced technique for enforcing LES/FDF mass consistency, two- and three-dimensional simulations of a temporal mixing layer using detailed and reduced chemistry mechanisms are carried out. The parametric analysis performed focuses on determining the influence on the level of mass consistency errors of parameters such as the initial number of particles per cell and the initial density ratio of the mixing layers. Particular emphasis is put on the computational burden that represents the use of such a mass consistency technique. The results show the suitability of this type of technique for ensuring the mass consistency required when utilising hybrid LES/FDF approaches. The level of agreement of the computed results with experimental data is also illustrated.     

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

Large Eddy Simulation of a swirl stabilized spray flame

Large Eddy Simulations (LES) of kerosene spray combustion in an axial-swirl combustor have been carried out focusing on the effect of the evaporating droplets on the flame temperature and species concentrations. The LES-PDF methodology is used for both dispersed (liquid) and gas phases. The liquid phase is described using a Lagrangian formulation whilst an Eulerian approach is employed for the gas phase. The predictive capability of LES with sub-grid scale models for spray dispersion and evaporation is assessed placing emphasis on the effect of the unresolved velocity and temperature fields on the droplet evaporation rate. The results of the fully coupled LES formulation exhibit good agreement between the measured and simulated mean velocity fields. The global behaviour of the spray combustion, such as droplet dispersion and evaporation, are captured reasonably well in the simulations. It was found that the large velocity fluctuations observed in the shear layer strongly affect the evaporation rate and thus the temperature distributions. The present work also demonstrated the feasibility of LES to study complex flow features which are typical of gas-turbine combustion chambers.     

分散相颗粒几何因素对电流变液体反应时间的影响

瞬变的反应时间是电流变液体的一个重要参数．本文通过实验和理论分析，建立了考虑分散相颗粒几何因素的电流变反应时间模型根据此模型，长椭球状颗粒的电流变液体反应时间比等效球状颗粒的短，扁椭球状和片状颗粒的电流变液体反应时间比等效球状颗粒的长，而棒状颗粒的电流变液体反应时间则视ε_p/ε_f比值大小或快于或慢于等效球状颗粒的反应时间．且反应时间与分散相尺寸的关系是（１）随体积增大，各种形状颗粒的电流变液体反应时间均变短；（２）同体积下，随长径比增大，长椭球状颗粒的电流变液体反应时间变短，而扁椭球状颗粒和片状颗粒的电流变液体反应时间变长，棒状颗粒的电流变液体反应时间则视。ε_p/ε_f比值大小或增快或减慢．因此，要获得反应快的电流变液体，颗粒形状除选择球状外，还可在使雷诺数较小范围内，选择一定尺寸的长椭球状或棒状颗粒。 关键词：     

Poloidal Structure of the Turbulence and the Turbulent Flux During Edge Plasma Biasing in the Castor Tokamak

The poloidal structure of the turbulence and the turbulent particle flux in the scrape-off layer (SOL) of the CASTOR tokamak are analysed by means of a poloidal ring of 124 probes distributed uniformly along the whole poloidal circumference. Fluctuation measurements are performed in standard ohmic regime as well as in discharges when a biased electrode is inserted either into the SOL or deeper into the confinement region. It is found that in both cases a strongly sheared radial electric field is created in the SOL, which de-correlates the density and radial velocity fluctuations and reduces their levels. Consequently, the turbulent flux is reduced. However, no phase shift is observed between density and radial velocity fluctuations. When the electrode is localized in the confinement region, all the above effects are less pronounced because of a smaller shear. In addition, the increase of the E × B velocity at biasing leads in both cases to the formation of oscillations in the temporal correlation function. These oscillations are specifically associated to the poloidal mode (m = q), which is created for a limited time and rotates poloidally. This mode does not modify the phase between density and radial velocity fluctuations and has no further effect on the turbulent flux.     

A non-diagonal singularity-free model in torsion gravity

In the context of torsion (teleparallel) gravity, we focus on discussing the spin effects of Dirac particles associated with the non-diagonal singularity-free model (Mars space-time). We see that the vector part depends on the radial r and z directions and the axial-vector will be along the radial direction, that is, it will be symmetric about radial direction. Furthermore, the t = 0 case of the Mars metric is considered, thence it is seen that the axial-vector vanishes.     

Possible measurement of the gravitational acceleration of antiprotons in the presence of “strong” patch effect electrical fields

The role of electrical fields due to the patch effect in a Penning trap used to measure the Earth's gravitational accelerationg on antiprotons is analyzed. Theg measurement method is based on the study of the gravity-induced shift of the center of the radial orbits of particles stored in a Penning trap having the magnetic field perpendicular to the direction of the force of gravity. The analysis of the radial motion shows that forces originating from patch effect electrical fields about ten times stronger than the force of gravity, still allow a differential measurement ofg for antiprotons and matter particles (H^–). As the precision of the measurement is affected by the particle axial energy distribution, particular care must be devoted to injecting antiprotons and H^– ions into the trap with very similar initial conditions.     

Density fluctuations in lattice-Boltzmann simulations of multiphase fluids in a closed system

A two-dimensional single component two-phase lattice Boltzmann model was used to simulate the Rayleigh–Taylor instability in a closed system. Spatiotemporally variable densities were generated by gravity acting on the fluid density. The density fluctuations were triggered by rapid changes in the fluid velocity induced by changes in the interface geometry and impact of the dense fluid on the rigid lower boundary of the computational domain. The ratio of the maximum density fluctuations to the maximum fluid velocity increased more rapidly at low velocities than at high velocities. The ratio of the maximum density fluctuations in the dense phase to its maximum velocity was on the order of the inverse of the sound speed. The solution became unstable when the density-based maximum local Knudsen number exceeded 0.13.     

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth’s gravitational field measured from the gravity field and steady-state ocean circulation explorer(GOCE),up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry(SGG) are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth’s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth’s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.     

Diffusion of a single particle in a 3D random packing of spheres

We report an experimental study of the dispersion properties of individual spherical particles of size d, moving under gravity in a dry random packing of large spheres of size D. The diameter ratio d/D is below the critical value 0.1547 above which beads get pinned inside the packing . They move in this regime at a constant mean velocity decreasing with the ratio d/D. We analyse dispersion parallel and transverse to the mean velocity by studying the bead distribution in the x-y plane at the exit of the packing (radial dispersion) and the transit time distribution (longitudinal dispersion) while varying the height H of the bed. Diffusion in both directions is found to be governed essentially by the diameter D of packed spheres and not by the size d of the small beads. A dispersivity length characterising the spreading amplitude is determined. Comparisons between transverse and longitudinal dispersion demonstrate that both processes have similar properties. A key parameter is the diameter D which controls the path length of the particles. Received 5 November 1999 and Received in final form 30 March 2000     

Large-eddy simulation of evaporating spray in a coaxial combustor

Large-eddy simulation of an evaporating isopropyl alcohol spray in a coaxial combustor is performed. The Favre-averaged, variable density, low-Mach number Navier-Stokes equations are solved on unstructured grids with dynamic subgrid scale model to compute the turbulent gas-phase. The original incompressible flow algorithm for LES on unstructured grids by [Mahesh et al., J. Comp. Phys. 197 (2004) 215–240] is extended to include density variations and droplet evaporation. An efficient particle-tracking scheme on unstructured meshes is developed to compute the dispersed phase. Experimentally measured droplet size distribution and size-velocity correlation near the nozzle exit are used as the inlet conditions for the spray. The predictive capability of the LES approach on unstructured grids together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail. The mean and turbulent quantities for the gas and particle phases are compared to experimental data to show good agreement. It is shown that for low evaporation rates considered in the present study, a well resolved large-eddy simulation together with simple subgrid models for droplet evaporation and motion provides good agreement of the mean and turbulent quantities for the gas and droplet phases compared to the experimental data. This work represents an important first step to assess the predictive capability of the unstructured grid LES approach applied to spray vaporization. The novelty of the results presented is that they establish a baseline fidelity in the ability to simulate complex flows on unstructured grids at conditions representative of gas-turbine combustors.     

Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model

We analyse the performance of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) in large eddy simulation (LES) of plane channel flow and the flow in a channel with streamwise periodic hill-shaped constrictions (periodic hill flow) which induce separation. The LESs are performed with the Code_Saturne which is an unstructured collocated finite volume solver with a second-order spatial discretisation suitable for LES of incompressible flow in complex geometries. At first, performance of the EASSM in LES of plane channel flow at two different resolutions using the Code_Saturne and a pseudo-spectral method is analysed. It is observed that the EASSM predictions of the mean velocity and Reynolds stresses are more accurate than the conventional dynamic Smagorinsky model (DSM). The results with the pseudo-spectral method were, in general, more accurate. In the second step, LES with the EASSM of flow separation in the periodic hill flow is compared to LES with the DSM, no SGS model and a highly resolved LES data using the DSM. Results show that the mean velocity profiles, the friction and pressure coefficients, the length and shape of the recirculation bubble, as well as the Reynolds stresses are considerably better predicted by the EASSM than the DSM and the no SGS model simulations. It was also observed that in some parts of the domain, the resolved strain-rate and SGS shear stress have the same sign. The DSM cannot produce a correct SGS stress in this case, in contrast to the EASSM.     

TiO2包覆石墨颗粒/硅油电流变液的研究

理论计算表明,介质包覆导体颗粒用作电流变液的分散相,可以获得高剪切应力的电流变液.采用溶胶-凝胶技术在尺度为5—10μm的石墨颗粒表面成功地包覆了TiO₂,获得了金红石相TiO₂包覆石墨的复合颗粒.配制成复合颗粒/硅油电流变液,其剪切应力与纯TiO₂/硅油电流变液相比,可提高一个数量级.当电场强度为1.7kV/mm时,复合颗粒/硅油电流变液的剪切应力可达1.25kPa,电流密度小于10μA/cm². 关键词： 电流变液 包覆 2')" href="#">TiO₂ 石墨     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

Simulation of diesel spray combustion using LES and a multicomponent vapourisation model

Diesel spray and combustion in a constant-volume engine cylinder was simulated by a large eddy simulation (LES) approach coupling with a multicomponent vapourisation (MCV) modelling. The simulation focused on the inclusion of the interaction between fuel spray and gas-phase turbulence flow at the sub-grid scale. The LES was based on the dynamic structure sub-grid model, and an additional source term was added to the filtered momentum equation to account for the effect of drop motion on the gas-phase turbulence. The multicomponent drop vapourisation modelling was based on the continuous thermodynamics approach using a gamma distribution to describe the complex diesel fuel composition and was capable of predicting a more complex drop vapourisation process. The effect of gas-phase turbulence flow on the fuel drop vapourisation process was evaluated through the solution of the gas-phase moments of the distribution in the present LES framework. A non-evaporative spray in a constant-volume engine cylinder was first simulated to examine the behaviours of LES, in comparison with a Reynolds-averaged Navier–Stokes (RANS) simulation based on the RNG k–? model. More realistic diesel spray structures and improved agreement on liquid penetration length with the corresponding experimental data were predicted by the LES, using a grid resolution close to that of RANS. A more comprehensive simulation of diesel spray and combustion in cylindrical combustor was also performed. Predicted distributions of soot particles were compared to the experimental image, and improved agreement with the experimental data was also observed by using the present LES and MCV models. Consequently, results of the present models proved that improved overall performance of the fuel spray simulation can be achieved by the LES without a significant increase in the computational load compared to the RANS.