scholarly journals Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

2016 ◽  
Vol 799 ◽  
pp. 159-199 ◽  
Author(s):  
A. Briard ◽  
T. Gomez ◽  
C. Cambon
Keyword(s):  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Homogeneous Isotropic Turbulence ◽  
Scalar Flux ◽  
Anisotropic Turbulence ◽  
Theoretical Predictions ◽  
High Reynolds ◽  
Shear Driven Flows ◽  
Very High

The present work aims at developing a spectral model for a passive scalar field and its associated scalar flux in homogeneous anisotropic turbulence. This is achieved using the paradigm of eddy-damped quasi-normal Markovian (EDQNM) closure extended to anisotropic flows. In order to assess the validity of this approach, the model is compared to several detailed direct numerical simulations (DNS) and experiments of shear-driven flows and isotropic turbulence with a mean scalar gradient at moderate Reynolds numbers. This anisotropic modelling is then used to investigate the passive scalar dynamics at very high Reynolds numbers. In the framework of homogeneous isotropic turbulence submitted to a mean scalar gradient, decay and growth exponents for the cospectrum and scalar energies are obtained analytically and assessed numerically thanks to EDQNM closure. With the additional presence of a mean shear, the scaling of the scalar flux and passive scalar spectra in the inertial range are investigated and confirm recent theoretical predictions. Finally, it is found that, in shear-driven flows, the small scales of the scalar second-order moments progressively return to isotropy when the Reynolds number increases.

scholarly journals Dynamics of helicity in homogeneous skew-isotropic turbulence

2017 ◽  
Vol 821 ◽  
pp. 539-581 ◽  
Author(s):  
Antoine Briard ◽  
Thomas Gomez
Keyword(s):  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Early Stage ◽  
Helical Structure ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Scalar Flux ◽  
Antisymmetric Part ◽  
Decaying Turbulence ◽  
High Reynolds

The dynamics of helicity in homogeneous skew-isotropic freely decaying turbulence is investigated, at very high Reynolds numbers, thanks to a classical eddy-damped quasi-normal Markovian (EDQNM) closure. In agreement with previous direct numerical simulations, a $k^{-5/3}$ inertial range is obtained for both the kinetic energy and helical spectra. In the early stage of the decay, when kinetic energy, initially only present at large scales cascades towards small scales, it is found that helicity slightly slows down the nonlinear transfers. Then, when the turbulence is fully developed, theoretical decay exponents are derived and assessed numerically for helicity. Furthermore, it is found that the presence of helicity does not modify the decay rate of the kinetic energy with respect to purely isotropic turbulence, except in Batchelor turbulence where the kinetic energy decays slightly more rapidly. In this case, non-local expansions are used to show analytically that the permanence of the large eddies hypothesis is verified for the helical spectrum, unlike the kinetic energy one. Moreover, the $4/3$ law for the two-point helical structure function is assessed numerically at very large Reynolds numbers. Afterwards, the evolution equation of the helicity dissipation rate is investigated analytically, which provides significant simplifications and leads notably to the definition of a helical derivative skewness and of a helical Taylor scale, which is numerically very close to the classical Taylor longitudinal scale at large Reynolds numbers. Finally, when both a mean scalar gradient and helicity are combined, the quadrature spectrum, linked to the antisymmetric part of the scalar flux, appears and scales like $k^{-7/3}$ and then like $k^{-5/3}$ in the inertial range.

A numerical comparison of velocity-based and strain-based Lagrangian-history turbulence approximations

1979 ◽  
Vol 91 (3) ◽  
pp. 581-597 ◽  
Author(s):  
Jackson R. Herring ◽  
Robert H. Kraichnan
Keyword(s):  
Isotropic Turbulence ◽  
Direct Interaction ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Numerical Comparison ◽  
The Difference ◽  
High Reynolds ◽  
High Wavenumbers

The abridged Langrangian-history direct-interaction (ALHDI) approximation (Kraichnan 1966) and the strain-based abridged Lagrangian-history direct-interaction (SBALHDI) approximation (Kraichnan & Herring 1978) are integrated numerically for isotropic turbulence in two and three dimensions and compared with data. At moderate Reynolds numbers in three dimensions, comparison with the computer simulations by Orszag & Patterson (1972) shows that the ALHDI gives numerically excessive energy transfer in the dissipation range while the SBALHDI approximation displays satisfactory accuracy in all ranges. In two dimensions, both approximations are in reasonable agreement with the simulations of Herring et al. (1974), the ALHDI approximation showing the better accuracy of the two at low wavenumbers. At high wavenumbers the SBALHDI approximation again transfers less energy than the ALHDI approximation but the effect is less marked than in three dimensions and the two curves straddle the data. High Reynolds number integrations of both approximations in three dimensions agree well with the tidal-channel inertial- and dissipationrange data of Grant, Stewart & Moilliet (1962), the SBALHDI approximation yielding a somewhat larger value of Kolmogorov's constant than the ALHDI approximation. The origin of the difference in straining efficiency between the two approximations at high wavenumbers and of the dependence of this difference on dimensionality is exhibited by application to the stretching of small scales of a convected passive scalar field. In three dimensions the SBALHDI approximation gives markedly larger values of the constant in Batchelor's (1959) k−1 spectrum range than the ALHDI approximation and is in better agreement with experiment. The SBALHDI values of Batchelor's constant satisfy Gibson's (1968) lower bound while the ALHDI values do not.

scholarly journals Radiation and Energetic Analysis of Nanofluid Based Volumetric Absorbers for Concentrated Solar Power

Nanomaterials ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 838 ◽  
Author(s):  
Jan Eggers ◽  
Eckart Lange ◽  
Stephan Kabelac
Keyword(s):  
Radiation Energy ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Working Fluid ◽  
Concentrated Solar Power ◽  
Optical Efficiency ◽  
Solar Absorber ◽  
Energetic Analysis ◽  
High Reynolds ◽  
Very High

Recently, several publications gave attention to nanofluid based solar absorber systems in which the solar radiation energy is directly absorbed in the volume of the fluid. This idea could provide advantages over conventionally used surface absorbers regarding the optical and thermal efficiency. For the evaluation of this concept, a numerical approach is introduced and validated in this contribution. The results show that the optical efficiency of a volumetric absorber strongly depends on the scattering behavior of the nanofluid and can reach competitive values only if the particle size distribution is narrow and small. If this is achieved, the surface temperature and therefore the heat loss can be lowered significantly. Furthermore, the surface absorber requires very high Reynolds numbers to transfer the absorbed energy into the working fluid and avoid overheating of the absorber tube. This demand of pumping power can be reduced significantly using the concept of volumetric absorption.

scholarly journals Reynolds-number dependence of turbulence enhancement on collision growth

2016 ◽  
Vol 16 (19) ◽  
pp. 12441-12455 ◽  
Author(s):  
Ryo Onishi ◽  
Axel Seifert
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Homogeneous Isotropic Turbulence ◽  
Collision Efficiency ◽  
Cloud Droplets ◽  
Clustering Effect ◽  
Reynolds Number Dependence ◽  
Coagulation Kernel

Abstract. This study investigates the Reynolds-number dependence of turbulence enhancement on the collision growth of cloud droplets. The Onishi turbulent coagulation kernel proposed in Onishi et al. (2015) is updated by using the direct numerical simulation (DNS) results for the Taylor-microscale-based Reynolds number (Reλ) up to 1140. The DNS results for particles with a small Stokes number (St) show a consistent Reynolds-number dependence of the so-called clustering effect with the locality theory proposed by Onishi et al. (2015). It is confirmed that the present Onishi kernel is more robust for a wider St range and has better agreement with the Reynolds-number dependence shown by the DNS results. The present Onishi kernel is then compared with the Ayala–Wang kernel (Ayala et al., 2008a; Wang et al., 2008). At low and moderate Reynolds numbers, both kernels show similar values except for r2 ∼ r1, for which the Ayala–Wang kernel shows much larger values due to its large turbulence enhancement on collision efficiency. A large difference is observed for the Reynolds-number dependences between the two kernels. The Ayala–Wang kernel increases for the autoconversion region (r1, r2 < 40 µm) and for the accretion region (r1 < 40 and r2 > 40 µm; r1 > 40 and r2 < 40 µm) as Reλ increases. In contrast, the Onishi kernel decreases for the autoconversion region and increases for the rain–rain self-collection region (r1, r2 > 40 µm). Stochastic collision–coalescence equation (SCE) simulations are also conducted to investigate the turbulence enhancement on particle size evolutions. The SCE with the Ayala–Wang kernel (SCE-Ayala) and that with the present Onishi kernel (SCE-Onishi) are compared with results from the Lagrangian Cloud Simulator (LCS; Onishi et al., 2015), which tracks individual particle motions and size evolutions in homogeneous isotropic turbulence. The SCE-Ayala and SCE-Onishi kernels show consistent results with the LCS results for small Reλ. The two SCE simulations, however, show different Reynolds-number dependences, indicating possible large differences in atmospheric turbulent clouds with large Reλ.

Effect of Schmidt number on small-scale passive scalar turbulence

2003 ◽  
Vol 56 (6) ◽  
pp. 615-632 ◽  
Author(s):  
RA Antonia ◽  
P Orlandi
Keyword(s):  
Turbulent Flows ◽  
Schmidt Number ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence ◽  
Passive Scalars ◽  
First Case ◽  
Decaying 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.

A multiple relaxation time extension of the constant speed kinetic model

2016 ◽  
Vol 27 (08) ◽  
pp. 1650088 ◽  
Author(s):  
Abed Zadehgol ◽  
Mahmud Ashrafizaadeh
Keyword(s):  
Relaxation Time ◽  
Kinetic Model ◽  
Reynolds Numbers ◽  
Constant Speed ◽  
Benchmark Problems ◽  
Multiple Relaxation Time ◽  
Time Extension ◽  
High Reynolds ◽  
The Stability ◽  
Very High

In this work, a multiple relaxation time (MRT) extension of the recently introduced constant speed kinetic model (CSKM) is proposed. The CSKM, which is an entropic kinetic model and based on unconventional entropies of Burg and Tssalis, was introduced in [A. Zadehgol and M. Ashrafizaadeh, J. Comput. Phys. 274, 803 (2014)]; [A. Zadehgol Phys. Rev. E 91, 063311 (2015)] as an extension of the model of Boghosian et al. [Phys. Rev. E 68, 025103 (2003)] in the limit of fixed speed continuous velocities. The present extension improves the stability of the previous models at very high Reynolds numbers, while allowing for a more convenient orthogonal lattice. The model is verified by solving the following benchmark problems: (i) the lid driven square cavity and (ii) the Kelvin–Helmholtz instability of thin shear layers in a doubly periodic square domain.

Two-Dimensional Simulations of Turbulent Flow Past a Row of Cylinders using Lattice Boltzmann Method

2017 ◽  
Vol 14 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Yi-Kun Wei ◽  
Xu-Qu Hu
Keyword(s):  
Lattice Boltzmann Method ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Two Dimensional ◽  
Flow Past ◽  
High Reynolds ◽  
An Array Of Cylinders ◽  
Boltzmann Method

Two-dimensional simulations of channel flow past an array of cylinders are carried out at high Reynolds numbers. Considering the thickness fluctuating effect on the equation of motion, a modified lattice Boltzmann method (LBM) is proposed. Special attention is paid to investigate the thickness fluctuations and vortex shedding mechanisms between 11 cylinders. Results for the velocity and vorticity differences are provided, as well as for the energy density and enstrophy spectra. The numerical results coincide very well with some published experimental data that was obtained by turbulent soap films. The spectra extracted from the velocity and vorticity fields are displayed from simulations, along with the thickness fluctuation spectrum H(k). Our results show that the statistics of thickness fluctuations resemble closely those of a passive scalar in turbulent flows.

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