C. B. da Silva

On the influence of coherent structures upon interscale interactions in turbulent plane jets

The influence of the coherent structures on grid/subgrid-scale (GS/SGS) interactions in free shear layers is analysed through the application of a top-hat filter to several plane jet direct numerical simulations (DNS). The Reynolds number based on the plane jet inlet slot width is Re h = 3000. The study deals with energy containing (Kelvin–Helmholtz) and inertial range (streamwise) vortices, from the far field of the turbulent plane jet. The most intense kinetic energy exchanges between GS and SGS occur near these structures and not randomly in the space. The GS kinetic energy is dominated by GS advection and GS pressure/velocity interactions which appear located next to the Kelvin–Helmholtz rollers. Surprisingly, GS/SGS transfer is not very well correlated with the coherent vortices and GS/SGS diffusion plays an important role in the local dynamics of both GS and SGS kinetic energy. The so-called ‘local equilibrium assumption’ holds globally but not locally as most viscous dissipation of SGS kinetic energy takes place within the vortex cores whereas forward and backward GS/SGS transfer occurs at quite different locations. Finally, it was shown that SGS kinetic energy advection may be locally large as compared to the other terms of the SGS kinetic energy transport equation.

Radiation statistics in homogeneous isotropic turbulence

An analysis of turbulence?radiation interaction (TRI) in statistically stationary (forced) homogeneous and isotropic turbulence is presented. A direct numerical simulation code was used to generate instantaneous turbulent scalar fields, and the radiative transfer equation?(RTE) was solved to provide statistical data relevant in TRI. The radiation intensity is non-Gaussian and is not spatially correlated with any of the other turbulence or radiation quantities. Its power spectrum exhibits a power-law region with a slope steeper than the classical ?5/3 law. The moments of the radiation intensity, Planck-mean and incident-mean absorption coefficients, and emission and absorption TRI correlations are calculated. The influence of the optical thickness of the medium, mean and variance of the temperature and variance of the molar fraction of the absorbing species is studied. Predictions obtained from the time-averaged RTE are also included. It was found that while turbulence yields an increase of the mean blackbody radiation intensity, it causes a decrease of the time-averaged Planck-mean absorption coefficient. The absorption coefficient self-correlation is small in comparison with the temperature self-correlation, and the role of TRI in radiative emission is more important than in radiative absorption. The absorption coefficient?radiation intensity correlation is small, which supports the optically thin fluctuation approximation, and justifies the good predictions often achieved using the time-averaged RTE.

Energy spectra in elasto-inertial turbulence

Direct numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model are presented. Emphasis is given to large polymer relaxation times compared to the eddy turnover time, which is a regime recently termed elasto-inertial turbulence. In this regime the polymers are ineffective in dissipating kinetic energy but they play a lead role in transferring kinetic energy to the small solvent scales which turns out to be concomitant with the depletion of the usual non-linear energy cascade. However, we show that the non-linear interactions are still highly active, but they lead to no net downscale energy transfer because the forward and reversed energy cascades are nearly balanced. Finally, we show that the tendency for a steeper elasto-inertial power-law spectra is reversed for large polymer relaxation times and the spectra tend towards the usual k−5/3 functional form.

The Dynamics of Turbulent Scalar Mixing near the Edge of a Shear Layer

In free shear flows a sharp and convoluted turbulent/nonturbulent (T/NT) interface separates the outer fluid region, where the flow is essentially irrotational, from the shear layer turbulent region. It was found recently that the entrainment mechanism is mainly caused by small scale (nibbling) motions (Westerweel et al. (2005)). The dynamics of this interface is crucial to understand important exchanges of enstrophy and scalars that can be conceived as a three-stage process of entrainment, dispersion and diffusion (Dimotakis (2005)). A thorough understanding of scalar mixing and transport is of indisputable relevance to control turbulent combustion, propulsion and contaminant dispersion (Stanley et al. (2002)). The present work uses several DNS of turbulent jets at Reynolds number ranging from Reλ = 120 to Reλ = 160 (da Silva & Taveira (2010)) and a Schmidt number Sc = 0.7 to analyze the scalar interface and turbulent mixing of a passive scalar. Specifically, we employ conditional statistics, denoted by I, in order to eliminate the intermittency that affects statistics close to the jet edge. The physical mechanisms behind scalar mixing near the T/NT interfaces, their scales and topology are investigated detail. Analysis of the instantaneous fields showed intense scalar gradient sheet-like structures along regions of persistent strain, in particular at the T/NT interface. The scalar gradient transport equation, at the jet edge, showed that almost all mixing mechanisms are taking place in a confined region, beyond which they become reduced to an almost in perfect balance between production and dissipation of scalar variance. At the T/NT interface transport mechanisms are the ones responsible for the growth in the scalar fluctuations to the entrained fluid, where convection plays a dominant role, smoothing scalar gradients inside the interface and boosting them as far as

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 [Metais 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 Metais, 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...

Grid and subgrid-scale interactions in viscoelastic turbulent flow and implications for modelling

ABSTRACT Using direct numerical simulations of turbulent plane channel flow of homogeneous polymer solutions, described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model, a-priori analyses of the filtered momentum and FENE-P constitutive equations are performed. The influence of the polymer additives on the subgrid-scale (SGS) energy is evaluated by comparing the Newtonian and the viscoelastic flows, and a severe suppression of SGS stresses and energy is observed in the viscoelastic flow. All the terms of the transport equation of the SGS kinetic energy for FENE-P fluids are analysed, and an approximated version of this equation for use in future large eddy simulation closures is suggested. The terms responsible for kinetic energy transfer between grid-scale (GS) and SGS energy (split into forward/backward energy transfer) are evaluated in the presence of polymers. It is observed that the probability and intensity of forward scatter events tend to decrease in the presence of polymers.

Analysis of the viscous/molecular subgrid-scale dissipation terms in LES based on transport equations: A priori tests

One trend in large-eddy simulations (LES) involves the use of a transport equation for the subgrid-scale (SGS) kinetic energy. For problems involving active or passive scalar fields a SGS scalar variance transport equation is also used. The terms from these equations involve sub-filter scale quantities that are not accessible during LES and thus require modelling. By far the greatest challenge for modelling in these equations comes from the viscous and the molecular SGS dissipation terms that represent the final (dissipation) stages of the ‘energy cascade mechanism’ whereby the SGS kinetic energy and SGS scalar variance are dissipated through the action of the molecular viscosity and diffusivity, respectively. In this work direct numerical simulations (DNS) of statistically stationary (forced) homogeneous, isotropic turbulence are used to (i) analyse the topology and spatial localisation of the viscous and the molecular SGS dissipation terms, (ii) assess three models currently used for these terms and (iii) present some guidelines to improve or develop future models for these terms. The models analysed here are (a) the classical model used by e.g. Schumann [1] and Yoshizawa [2], (b) the model used in hybrid RANS/LES by Paterson and Peltier [3], and by Hanjalic [4], and (c) the model for the molecular SGS dissipation of SGS scalar variance from Jiménez et al. [5]. The classical models for the molecular SGS dissipation give very good results in terms of topology, spatial localisation (in the physical space), statistical behaviour and spectral characteristics. Moreover, the model constants approach asymptotically the theoretical values as the Reynolds number and filter sizes increase which supports the use of a constant value in engineering and geophysical applications, instead of using a dynamic procedure for their computation as in Ghosal et al. [6]. For the molecular SGS dissipation of SGS scalar variance the model from Jiménez et al. [5] performs even better than the classical model and should be the preferred model for this term when the Schmidt number is close to 1.0. Finally, all the tests showed that the models used in hybrid RANS/LES tested here give very poor results either in terms of their topological, statistical or spectral characteristics. The reason behind this is connected with the deficient spectral representation of the exact molecular SGS dissipation terms.

The Imbalance Between Enstrophy Production and Destruction in Homogeneous Isotropic Unsteady Turbulence

We show in direct numerical simulations of homogeneous isotropic non-stationary turbulence that there is a systematic and significant imbalance between enstrophy production and its destruction which is concomitant with the previously observed imbalance between the non-linear energy cascade to fine scales and its dissipation (Valente, Onishi, da Silva, Phys Rev E 90(023003), 2014, [12]). However, contrary to the former, the imbalance between enstrophy production and destruction is affected by the ‘cascade time-lag’, i.e. the time it takes for the energy injected on the large-scales to reach the fine-scales.