Simulations Of Homogeneous Isotropic Turbulence Research Articles

Source of acceleration intermittency in isotropic turbulence

Strong acceleration intermittency in fluid turbulence is interpreted in the context of different supports for local enstrophy and dissipation by introducing a new decomposition of acceleration. This paper proposes a simple Lamb Vortex Model that captures statistical features of acceleration, such as probability density functions, flatness factors, and correlation coefficients, observed in the direct numerical simulation of homogeneous isotropic turbulence.

Intermittency in premixed turbulent reacting flows

Intermittency in premixed reacting flows is studied using numerical simulations of premixed flames at a range of turbulence intensities. The flames are modeled using a simplified reaction mechanism that represents a stoichiometric H2-air mixture. Intermittency is associated with high probabilities of large fluctuations in flow quantities, and these fluctuations can have substantial effects on the evolution and structure of premixed flames. Intermittency is characterized here using probability density functions (pdfs) and moments of the local enstrophy, pseudo-dissipation rate (strain rate magnitude), and scalar (reactant mass fraction) dissipation rate. Simulations of homogeneous isotropic turbulence with a nonreacting passive scalar are also carried out in order to provide a baseline for analyzing the reacting flow results. In the reacting flow simulations, conditional analyses based on local, instantaneous values of the scalar are used to study variations in the pdfs, moments, and intermittency through the flame. For low intensities, pdfs of the local enstrophy vary substantially through the flame, with greater intermittency near the products. Changes in the pseudo-dissipation pdfs are, however, less pronounced. As the intensity increases, both the enstrophy and pseudo-dissipation pdfs become increasingly independent of position in the flame and are similar to results from the nonreacting simulations. The scalar dissipation intermittency is largest near the reactants and increases at all flame locations with increasing turbulence intensity. For low intensities and in the reaction zone, however, scalar dissipation pdfs approximately follow a Gaussian distribution, indicative of substantially reduced intermittency. Deviations from log-normality are observed in the pdfs of all quantities, even for intensities and flame locations characterized by strong intermittency. The implications of these results for the internal structure of the flame are discussed, and we also propose a connection between reacting flow intermittency and anisotropic vorticity suppression by the flame.

Statistical properties of the local structure of homogeneous isotropic turbulence and turbulent channel flows

Statistical properties of the local structure are investigated using the data of direct numerical simulation of homogeneous isotropic turbulence for Re λ=60.1∼287.6 and turbulent channel flows for Re τ = 180, 400, 800, and 1270. The dimensionless second invariant is used as the representative local structure, and is defined as the second invariant of a velocity gradient tensor normalized by the magnitude of the velocity gradient tensor. In homogeneous isotropic turbulence, the probability density function (pdf) profiles of the dimensionless second invariant show good agreement for different values of Reynolds number. The volume fraction, the average, and the variance of the dimensionless second invariant converge to certain values at high Reynolds number, respectively. For the turbulent channel flows, the pdf profiles of the dimensionless second invariant for different values of Reynolds number coincide very well for the distance from the wall in wall units. The probability density and the volume fraction of the dimensionless second invariant at the center of the channel are in good agreement with those of homogeneous isotropic turbulence.

Helicity and geometric nature of particle trajectories in homogeneous isotropic turbulence

The role of helicity in Lagrangian turbulence is investigated using direct numerical simulation of homogeneous isotropic turbulence. Probability density functions and autocorrelations along a fluid particle trajectory associated with geometric quantities such as curvature and torsion of the Lagrangian trajectory are provided. The relationship between helicity and the ratio of torsion to curvature is investigated. We found that probability density functions of torsion and torsion normalized by curvature clearly show well-established slope in log–log plots. Finally, the relationship between helicity, acceleration and geometric quantities are discussed.

Analysis of the turbulence–radiation interactions for large eddy simulations of turbulent flows

In large eddy simulations (LES) of radiative heat transfer, the subgrid-scale (SGS) radiative emission and the SGS radiative absorption are two unclosed terms that arise after applying the filtering operation to the radiative transfer equation and which represent the effect of the SGS motions on the evolution of the resolved radiative heat flux. In the present work, a-priori tests based on direct numerical simulation of homogeneous isotropic turbulence have been carried out. It was found that the effect of the SGS radiative absorption may be neglected in LES, whereas the SGS radiative emission has to be modelled, particularly for engineering applications where the grids are generally coarse, and in flows with high turbulence intensities. Future works should be devoted to the development of SGS models for radiative transfer.

Quantifying Turbulence-Induced Segregation of Inertial Particles

Particles with different density from the advecting turbulent fluids cluster due to the different response of light and heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute polydisperse inertial particles evolving in turbulent flow, as obtained from direct numerical simulation of homogeneous isotropic turbulence. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg}, quantifying the segregation degree between two particle types, is deduced.

Local and nonlocal strain rate fields and vorticity alignment in turbulent flows

Local and nonlocal contributions to the total strain rate tensor S(ij) at any point x in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor S(ij)(B)(x) to be obtained from S(ij)(x). In turbulent flows, where the vorticity naturally concentrates into relatively compact structures, this allows the local alignment of vorticity with the most extensional principal axis of the background strain rate tensor to be evaluated. In the vicinity of any vortical structure, the required radius R and corresponding order n to which the expansion must be carried are determined by the viscous length scale lambda(nu). We demonstrate the convergence to the background strain rate field with increasing R and n for an equilibrium Burgers vortex, and show that this resolves the anomalous alignment of vorticity with the intermediate eigenvector of the total strain rate tensor. We then evaluate the background strain field S(ij)(B)(x) in direct numerical simulations of homogeneous isotropic turbulence where, even for the limited R and n corresponding to the truncated series expansion, the results show an increase in the expected equilibrium alignment of vorticity with the most extensional principal axis of the background strain rate tensor.

Effects of molecular diffusion on the subgrid-scale modeling of passive scalars

The spectral eddy-viscosity and eddy-diffusivity closures derived from the eddy-damped quasinormal Markovian (EDQNM) theory, and one of its physical space counterparts, i.e., the structure function model [Métais and Lesieur, J. Fluid Mech. 239, 157 (1992)], are revisited to account for molecular viscosity and diffusivity effects. The subgrid-scale Schmidt number (usually set to Sct≈0.6) is analytically derived from the EDQNM theory and shown to be Reynolds number dependent, a property of utmost importance for flows involving scalar transport at moderate Reynolds numbers or during the transition to turbulence. A priori tests in direct numerical simulation of homogeneous isotropic turbulence [da Silva and Pereira, Phys. Fluids 19, 035106 (2007)] and in spatially evolving turbulent plane jets [da Silva and Métais, J. Fluid Mech. 473, 103 (2002)], as well as a posteriori (large eddy simulation) tests in a round jet are carried out and show that the present viscous structure function model improves the results from the classical approaches and at a comparatively small computational cost.

Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: A wavelet viewpoint

Coherent vortices are extracted from data obtained by direct numerical simulation (DNS) of three-dimensional homogeneous isotropic turbulence performed for different Taylor microscale Reynolds numbers, ranging from Reλ=167 to 732, in order to study their role with respect to the flow intermittency. The wavelet-based extraction method assumes that coherent vortices are what remains after denoising, without requiring any template of their shape. Hypotheses are only made on the noise that, as the simplest guess, is considered to be additive, Gaussian, and white. The vorticity vector field is projected onto an orthogonal wavelet basis, and the coefficients whose moduli are larger than a given threshold are reconstructed in physical space, the threshold value depending on the enstrophy and the resolution of the field, which are both known a priori. The DNS dataset, computed with a dealiased pseudospectral method at resolutions N=2563,5123,10243, and 20483, is analyzed. It shows that, as the Reynolds number increases, the percentage of wavelet coefficients representing the coherent vortices decreases; i.e., flow intermittency increases. Although the number of degrees of freedom necessary to track the coherent vortices remains small (e.g., 2.6% of N=20483 for Reλ=732), it preserves the nonlinear dynamics of the flow. It is thus conjectured that using the wavelet representation the number of degrees of freedom to compute fully developed turbulent flows could be reduced in comparison to the standard estimation based on Kolmogorov’s theory.

Analysis of the gradient-diffusion hypothesis in large-eddy simulations based on transport equations

The gradient-diffusion hypothesis is frequently used in numerical simulations of turbulent flows involving transport equations. In the context of large-eddy simulations (LES) of turbulent flows, one modeling trend involves the use of transport equations for the subgrid-scale (SGS) kinetic energy and SGS scalar variance. In virtually all models using these equations, the diffusion terms are lumped together, and their joint effect is modeled using a “gradient-diffusion” model. In this work, direct numerical simulations of homogeneous isotropic turbulence are used to analyze the local dynamics of these terms and to assess the performance of the “gradient-diffusion” hypothesis used in their modeling. For this purpose a priori tests are used to assess the influence of the Reynolds and Schmidt numbers and the size of the implicit grid filter in this modeling assumption. The analysis uses correlations, variances, skewnesses, flatnesses, probability density functions, and joint probability density functions. The correlations and joint probability density functions show that provided the filter width is within or close to the dissipative range the diffusion terms pertaining to the SGS kinetic energy and SGS scalar variance transport equations are well represented by a gradient-diffusion model. However, this situation changes dramatically for both equations when considering inertial range filter sizes and high Reynolds numbers. The reason for this lies in part in a loss of local balance between the SGS turbulent diffusion and diffusion caused by grid/subgrid-scale (GS/SGS) interactions, which arises at inertial range filter sizes. Moreover, due to the deficient modeling of the diffusion by SGS pressure-velocity interactions, the diffusion terms in the SGS kinetic energy equation are particularly difficult to reconcile with the gradient-diffusion assumption. In order to improve this situation, a new model, inspired by Clark’s SGS model, is developed for this term. The new model shows very good agreement with the exact SGS pressure-velocity term in a priori tests and better results than the classical model in a posteriori (LES) tests.

Coherent vortex extraction and simulation of 2D isotropic turbulence

We present a method to extract coherent vortices out of turbulent flows, based on thresholding the wavelet coefficients of vorticity. We compare two ways of choosing the threshold and show how one can thus split each flow realization into coherent vortices and quasi-Gaussian white noise. We then describe a new method, called CVS (coherent vortex simulation), for computing deterministically the time evolution of the coherent vortices while neglecting or modelling the incoherent background noise. We develop a hierarchy of model equations based on the nonlinear Galerkin approach. In the first CVS method there is no modelling of the effect of the discarded coefficients and filtering out the incoherent background at each time step plays the role of turbulent dissipation. For the second approach we derive an additional linear equation to compute the effect of the incoherent background flow whose coefficients have been discarded. Finally, to validate both CVS approaches, we analyse the different terms of the filtered equations and present different simulations of homogeneous isotropic turbulence.

On the local equilibrium of the subgrid scales: The velocity and scalar fields

Direct numerical simulations of homogeneous isotropic turbulence are used to analyze the local equilibrium assumption between large and small scales of motion in the context of large-eddy simulations. The local imbalance, between grid/subgrid scales transfer (of kinetic energy and scalar variance) and molecular dissipation, increases with the Reynolds and Schmidt numbers and with the filter size. It is shown that the correlations between SGS production and dissipation (for the velocity and scalar fields) are higher in regions dominated by strain and where vorticity and strain are comparably large, and smaller in regions where vorticity dominates.

Homogeneous isotropic turbulence in dilute polymers

The modification of the turbulent cascade by polymeric additives is addressed by direct numerical simulations of homogeneous isotropic turbulence of a FENE-P fluid. According to the appropriate form of the Karman-Howarth equation, two kinds of energy fluxes exist, namely the classical transfer term and the coupling with the polymers. Depending on the Deborah number, the response of the flow may result either in a pure damping or in the depletion of the small scales accompanied by increased fluctuations at large scale. The latter behaviour corresponds to an overall reduction of the dissipation rate with respect to an equivalent Newtonian flow with identical fluctuation intensity. The relevance of the position of the crossover scale between the two components of the energy flux with respect to the Taylor microscale of the system is discussed.

3006 差分格子ボルツマン法による一様等方性乱流の直接シミュレーションに関する研究(OS-30B 格子ボルツマン・ガス法,OS-30 格子ボルツマン・ガス法)

3006 差分格子ボルツマン法による一様等方性乱流の直接シミュレーションに関する研究(OS-30B 格子ボルツマン・ガス法,OS-30 格子ボルツマン・ガス法)

Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations

Energy transfers within large-eddy simulation (LES) and direct numerical simulation (DNS) grids are studied. The spectral eddy viscosity for conventional dynamic Smagorinsky and variational multiscale LES methods are compared with DNS results. Both models underestimate the DNS results for a very coarse LES, but the dynamic Smagorinsky model is significantly better. For moderately to well-refined LES, the dynamic Smagorinsky model overestimates the spectral eddy viscosity at low wave numbers. The multiscale model is in good agreement with DNS for these cases. The convergence of the multiscale model to the DNS with grid refinement is more rapid than for the dynamic Smagorinsky model.

Large eddy simulations of decaying rotating turbulence

Large eddy simulations of homogeneous isotropic turbulence subjected to system rotation were performed using the truncated Navier-Stokes method. In the method the Navier-Stokes equations are solved through a sequence of direct numerical simulation runs and a periodic processing of small scales to provide the necessary dissipation. The method is evaluated by comparing simulation results with theoretical analysis, direct numerical simulations, as well as with other large eddy simulation results. Obtained results demonstrate several advantages of the method over traditional large eddy simulations models. The method captures important features of rotating turbulence: the energy decay is inhibited, the energy spectrum departs from the classical k−5/3 form, and initially isotropic turbulence becomes anisotropic. For increasing rotation rate three distinct regimes are observed. At low rotation rates, the influence of rotation is weak and flow behaves like for nonrotating cases. At intermediate rotation rates strong coupling between rotation and nonlinear interactions has a significant influence on turbulence. At high rotation rates viscous effects dominate over nonlinear effects. Furthermore, for high Reynolds numbers, small Rossby numbers, and large elapsed time, the k−3 energy spectrum is observed due to the anisotropy identified by various indicators, rather than the k−2 form found under the assumption of isotropy.

Non-Fickian diffusion and tau approximation from numerical turbulence

Evidence for non-Fickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly time-dependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The first-order smoothing approximation is shown to be inapplicable.

Effect of Schmidt number on small-scale passive scalar turbulence

Previous reviews of the behavior of passive scalars which are convected and mixed by turbulent flows have focused primarily on the case when the Prandtl number Pr, or more generally, the Schmidt number Sc is around 1. The present review considers the extra effects which arise when Sc differs from 1. It focuses mainly on information obtained from direct numerical simulations of homogeneous isotropic turbulence which either decays or is maintained in steady state. The first case is of interest since it has attracted significant theoretical attention and can be related to decaying turbulence downstream of a grid. Topics covered in the review include spectra and structure functions of the scalar, the topology and isotropy of the small-scale scalar field, as well as the correlation between the fluctuating rate of strain and the scalar dissipation rate. In each case, the emphasis is on the dependence with respect to Sc. There are as yet unexplained differences between results on forced and unforced simulations of homogeneous isotropic turbulence. There are 144 references cited in this review article.

Subgrid-Scale Models for Compressible Large-Eddy Simulations

An a priori study of subgrid-scale (SGS) models for the unclosed terms in the energy equation is carried out using the flow field obtained from the direct simulation of homogeneous isotropic turbulence. Scale-similar models involve multiple filtering operations to identify the smallest resolved scales that have been shown to be the most active in the interaction with the unresolved SGSs. In the present study these models are found to give more accurate prediction of the SGS stresses and heat fluxes than eddy-viscosity and eddy-diffusivity models, as well as improved predictions of the SGS turbulent diffusion, SGS viscous dissipation, and SGS viscous diffusion.

Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence

A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padé approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τL and τE. An analysis of a high resolution (5123 grid points) direct numerical simulation database at large Reynolds number suggests the scalings τL∝k−2/3 and τE∝k−1 for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed.