A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.     

On discretization errors and subgrid scale model implementations in large eddy simulations

We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier–Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.     

Influences of subgrid scale dynamics on resolvable scale statistics in large-eddy simulations

Recently, the -expansion and recursive renormalization group (RNG) theories as well as approximate inertial manifolds (AIM) have been exploited as means of systematically modeling subgrid scales in large-eddy simulations (LES). Although these theoretical approaches are rather complicated mathematically, their key approximations can be investigated using direct numerical simulations (DNS). In fact, the differences among these theories can be traced to whether they retain or neglect interactions between the subgrid-subgrid and subgrid-resolvable scales. In this paper, we focus on the influence of these two interactions on the evolution of the resolvable scales in LES: the effect^A which keeps only the interactions between the small and large scales; and, the effect^B which, on the other hand, keeps only the interactions among the subgrid-subgrid scales. The performance of these models is analyzed using the velocity fields of the direct numerical simulations. Specifically, our comparison is based on the analysis of the energy and enstrophy spectra, as well as higher-order statistics of the velocity and velocity derivatives. We found that the energy spectrum and higher-order statistics for the simulations with the effect^A (referred to, hereafter, as model^A) are in very good agreement with the filtered DNS. The comparison between the computations with effect^B (referred to, hereafter, as model^B) and the filtered DNS, however, is not satisfactory. Moreover, the decorrelation between the filtered DNS and model^A is much slower than that of the filtered DNS and model^B. Therefore, we conclude that the model^A, taking into acciunt the interactions between the subgrid and resolvable scales, is a faithful subgrid model for LES for the range of Reynolds numbers considered.     

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.     

Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzmann method

In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or test-filtering of super-grid turbulence dynamics and subsequent use of scale-invariance for two levels, circumvents the need for empiricism in determining the magnitude of the model coefficient of the SGS models. We employ the multiple relaxation times (MRT) formulation of LBM with a forcing term, which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non-hydrodynamic modes, for simulation of the grid-filtered dynamics of large-eddies. The dynamic procedure is illustrated for use with the common Smagorinsky eddy-viscosity SGS model, and incorporated in the LBM kinetic approach through effective relaxation time scales. The strain rate tensor in the SGS model is locally computed by means of non-equilibrium moments of the MRT-LBM. We also discuss proper sampling techniques or test-filters that facilitate implementation of dynamic models in the LBM. For accommodating variable resolutions, we employ conservative, locally refined grids in this framework. As examples, we consider the canonical anisotropic and inhomogeneous turbulent flow problem, i.e. fully-developed turbulent channel flow at two different shear Reynolds numbers Re_∗ of 180 and 395. The approach is able to automatically and self-consistently compute the values of the Smagorinsky coefficient, C_S. In particular, the computed value in the outer or bulk flow region, where turbulence is generally more isotropic, is about 0.155 (or the model coefficient ) which is in good agreement with prior data. It is also shown that the model coefficient becomes smaller and approaches towards zero near walls, reflecting the dampening of turbulent length scales near walls. The computed turbulence statistics at these Reynolds numbers are also in good agreement with prior data. The paper also discusses a procedure for incorporation of more general scale-similarity based SGS stress models.     

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.     

A hierarchically constrained kinetic Ising model

A concrete model for hierarchically constrained dynamics in the sense proposed by Palmer et al. (Phys. Rev. Lett.53, 958 (1984)) is presented. The model is a kinetic Ising chain with an asymmetric kinetic constraint, allowing a spin to flip only if its neighbour to the right is in the up spin state. The spin autocorrelation function is obtained by numerically exact calculation for finite chain length up toL=9 and by Monte Carlo simulation for effectively infinite chain length. The Kohlrausch-Williams-Watts formula is found to fit the results only with limited accuracy, and within limited time intervals. We also performed an analytical calculation using an effective-medium approximation. The approximation leads to a spurious blocking transition at a critical up spin concentrationc=0.5.     

A soluble model for quantum mechanical dissipation

In order to derive the equations for dissipation and noise in a quantum mechanical system it is necessary to include the equations of motion of a suitably chosen bath interacting with the system. In this way the standard treatment arrives at an approximate master equation for the density matrix of the system, at the expense of a number ofad hoc assumptions. These assumptions are here scrutinized on the basis of an exactly soluble model. The conclusion is: the bath must obey certain specifications; the interaction must be weak; and the temperature must be so high that the interaction energy is within the classical domain rather than occurring in quanta. Some additional comments concerning dissipation in quantum mechanics are relegated to an appendix.     

A priori analysis of subgrid scale pressure and heat flux in high pressure mixing and reacting shear layers

Direct Numerical Simulation (DNS) data on high pressure H₂/O₂ and H₂/air flames using the compressible flow formulation, detailed kinetics, a real fluid equation of state, and generalised diffusion are analysed. The DNS is filtered over a range of filter widths to provide exact terms in the Large Eddy Simulation (LES) governing equations, including unclosed terms. The filtered pressure and the filtered heat flux vector are extensively compared with the pressure and the heat flux vector calculated as a function of the filtered primitive variables (i.e. the exact LES term is compared with its form available within an actual LES). The difference between these forms defines the subgrid pressure and the subgrid heat flux vector. The analyses are done both globally across the entire flame, as well as by conditionally averaging over specific regions of the flame; including regions of large subgrid kinetic energy, subgrid scalar dissipation, subgrid temperature variance, flame temperature, etc. In this work, although negligible for purely mixing cases, the gradient of the subgrid pressure is shown to be of the same order as, and larger than, the corresponding divergence of the turbulent subgrid stresses for reacting cases. This is despite the fact that all species behave essentially as ideal gases for this flame and holds true even when the ideal gas law is used to calculate the pressure. The ratio of the subgrid pressure gradient to the subgrid stress tensor divergence is shown to increase with increasing Reynolds number. Both the subgrid heat flux vector and its divergence are found to be substantially larger in reacting flows in comparison with mixing due to the associated larger temperature gradients. However, the divergence of the subgrid heat flux vector tends to be significantly smaller than other unclosed terms in the energy equation with decreasing significance with increasing Reynolds number.     

A general model for power dissipation by domain wall movement in thin ferromagnetic films

In this work we present a model for magnetic domain wall (DW) dynamics in metallic ferromagnets with uniaxial anisotropy. The model allows us to consider both viscous and eddy current dampings. While the latter mechanism involves only one degree of freedom — the coordinate of the DW, the former involves all degrees of freedom of the spins in magnetic domains and in DW’s. The structure of the DW itself must then be considered, the conjecture used allowing one to describe the spin precessions which may appear in low quality factor Q materials. The model built is nonlinear, allowing one to deal with the set of complex susceptibilities characterizing the response to an ac drive field in strongly nonlinear circumstances, and has a general character, due to the normalized quantities used. In this work we analyze the susceptibility and the dissipated power spectra as functions of a dc transversal field, which can be treated only by this kind of models. We show that the viscous damping can become comparable to eddy current damping when precessions are excited.     

Modelling of the subgrid scale wrinkling factor for large eddy simulation of turbulent premixed combustion

We propose a model for assessing the unresolved wrinkling factor in the large eddy simulation of turbulent premixed combustion. It relies essentially on a power-law dependence of the wrinkling factor on the filter size and an original expression for the ‘active’ corrugating strain rate. The latter is written as the turbulent strain multiplied by an efficiency function that accounts for viscous effects and the kinematic constraint of Peters. This yields functional expressions for the fractal dimension and the inner cut-off length scale, the latter being (i) filter-size independent and (ii) consistent with the Damköhler asymptotic behaviours at both large and small Karlovitz numbers. A new expression for the wrinkling factor that incorporates finite Reynolds number effects is further proposed. Finally, the model is successfully assessed on an experimental filtered database.     

Large scale dissipation and filament instability in two-dimensional turbulence

Coherent vortices in two-dimensional turbulence induce far-field effects that stabilize vorticity filaments and inhibit the generation of new vortices. We show that the large-scale energy sink often included in numerical simulations of statistically stationary two-dimensional turbulence reduces the stabilizing role of the vortices, leading to filament instability and to continuous formation of new coherent vortices. This counterintuitive effect sheds new light on the mechanisms responsible for vortex formation in forced-dissipated two-dimensional turbulence, and it has significant impact on the temporal evolution of the vortex population in freely decaying turbulence. The time dependence of vortex statistics in the presence of a large-scale energy sink can be approximately described by a modified version of the scaling theory developed for small-scale dissipation.     

Direct evaluation of the subgrid scale scalar flux in turbulent premixed flames with conditioned dual-plane stereo PIV

With the dual-plane stereo PIV technique the instantaneous three-dimensional resolved rate-of-strain tensor is directly measured in turbulent premixed flames. Simultaneously, also the instantaneous subgrid scale (SGS) scalar flux is measured with fine resolution, where for the latter term the conditioned particle image velocimetry (CPIV) technique is applied. The subgrid resolution reaches 118 μm, allowing a 9 × 9 resolution of a subgrid filter with width Δ = 1 mm. This combined measurement approach allows the a-priori comparison of models for the SGS scalar flux term with direct measurements which is important for large eddy simulation methods in turbulent premixed flames. Two different flame conditions of a premixed V-shaped turbulent flame are investigated where the turbulence intensity is varied by a factor of nearly three. The instantaneous radial and axial SGS fluxes are compared with the following three models: gradient model with Smagorinsky approach for the turbulent viscosity, Clark model, and extended gradient model with an anisotropy term. None of these models shows a good correlation with the directly measured flux. The anisotropy term alone (being nearly similar to the Clark model) shows, however, a right trend behaviour. An analysis of the data indicates a significant dependency of the experimentally determined SGS flux on the Favre averaged reaction progress (spatially averaged over the SGS area). A relatively simple closure for the SGS flux, which describes the dilatation due to the gasdynamic expansion, and which is a function proportional to , shows a rather good correlation with direct measurement for some of the components. A successful SGS scalar flux model for premixed turbulent flames most likely needs to include at least two different effects.     

A compact 341 model at TeV scale

We build a gauge model based on the SU(3)_c⊗SU(4)_L⊗U(1)_X$SU{\left(3\right)}_c\otimes SU{\left(4\right)}_L\otimes U{\left(1\right)}_X$ symmetry where the scalar spectrum needed to generate gauge boson and fermion masses has a smaller scalar content than usually assumed in literature. We compute the running of its abelian gauge coupling and show that a Landau pole shows up at the TeV scale, a fact that we use to consistently implement those fermion masses that are not generated by Yukawa interactions, including neutrino masses. This is appropriately achieved by non renormalizable effective operators, suppressed by the Landau pole scale. Also, SU(3)_c⊗SU(3)_L⊗U(1)_N$SU{\left(3\right)}_c\otimes SU{\left(3\right)}_L\otimes U{\left(1\right)}_N$ models embedded in this gauge structure are bound to be strongly coupled at this same energy scale, contrary to what is generally believed, and neutrino mass generation is rather explained through the same effective operators used in the larger gauge group. Besides, their nice features, as the existence of cold dark matter candidates and the ability to reproduce the observed standard model Higgs-like phenomenology, are automatically inherited by our model. Finally, our results imply that this model is constrained to be observed or discarded soon, since it must be realized at the currently probed energy scale in LHC.     

A low composite scale preon model with complementarity

We have constructed the first “realistic candidate” preon model with low composite scale satisfying complementarity between the Higgs and confining phases. The model is based onSU(4) metacolor and predicts four generations of ordinary quarks and leptons together with heavy neutrinos at the level of the standard gauge groupSU(3) _c ×SU(2) _L ×U(1) _Y . There are no exotic massless fermions. The global family group isSU(2)×U(1).     

A scale mixer model for sis waveguide receivers

We report results from measurements of a scale mixer model, built to investigate the embedding impedance presented to a superconductor-insulator-superconductor (SIS) tunnel junction detector in a full height waveguide with two tuning elements. The embedding impedance is measured as a function of junction position across the waveguide channel. The results are compared to i) computer simulations of the embedding impedance using waveguide theory, ii) a lumped element circuit derived from the theory, iii) an SIS receiver operating between 200 and 280 GHz.     

A quark model based on QCD scale anomaly

We consider a quark model based on QCD scale anomaly in which the quarks move in the field of an effective glueball field. Hadrons correspond to solitonic bags of higher energy density in a nonperturbative sea of condensed gluons. We calculate the static properties of nucleon in this model and find that the nucleon mass is far too large (2.4–4 GeV) and the proton charge radius (0.37–0.54 fm) is low. The proton gyromagnetic ratio and g_A/g_v are in reasonable agreement with the experimental numbers.