scholarly journals Fluctuation theorem and extended thermodynamics of turbulence

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200468
Author(s):  
Amilcare Porporato ◽  
Milad Hooshyar ◽  
Andrew D. Bragg ◽  
Gabriel Katul
Keyword(s):  
Energy Transfer ◽  
Steady State ◽  
Energy Balance ◽  
Turbulent Flows ◽  
Energy Supply ◽  
Planck Equation ◽  
Fluctuation Theorem ◽  
Spectral Energy ◽  
Small Scales ◽  
And Diffusion

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

Spectral analysis of energy transfer in turbulent flows laden with heated particles

2017 ◽  
Vol 813 ◽  
pp. 1156-1175 ◽  
Author(s):  
H. Pouransari ◽  
H. Kolla ◽  
J. H. Chen ◽  
A. Mani
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Turbulent Combustion ◽  
Stokes Number ◽  
Turbulence Modification ◽  
Wide Range ◽  
Small Scales ◽  
Divergence Free ◽  
Particle Heating ◽  
Transfer Term

In this study we consider particle-laden turbulent flows with significant heat transfer between the two phases due to sustained heating of the particle phase. The sustained heat source can be due to particle heating via an external radiation source as in the particle-based solar receivers or an exothermic reaction in the particles. Our objective is to investigate the effects of fluid heating by a dispersed phase on the turbulence evolution. An important feature in such settings is the preferential clustering phenomenon which is responsible for non-uniform distribution of particles in the fluid medium. Particularly, when the ratio of particle inertial relaxation time to the turbulence time scale, namely the Stokes number, is of order unity, particle clustering is maximized, leading to thin regions of heat source similar to the flames in turbulent combustion. However, unlike turbulent combustion, a particle-laden system involves a wide range of clustering scales that is mainly controlled by particle Stokes number. To study these effects, we considered a decaying homogeneous isotropic turbulence laden with heated particles over a wide range of Stokes numbers. Using a low-Mach-number formulation for the fluid energy equation and a Lagrangian framework for particle tracking, we performed numerical simulations of this coupled system. We then applied a high-fidelity framework to perform spectral analysis of kinetic energy in a variable-density fluid. Our results indicate that particle heating can considerably influence the turbulence cascade. We show that the pressure-dilatation term introduces turbulent kinetic energy at a range of scales consistent with the scales observed in particle clusters. This energy is then transferred to high wavenumbers via the energy transfer term. For low and moderate levels of particle heating intensity, quantified by a parameter $\unicode[STIX]{x1D6FC}$ defined as the ratio of eddy time to mean temperature increase time, turbulence modification occurs primarily in the dilatational modes of the velocity field. However, as the heating intensity is increased, the energy transfer term converts energy from dilatational modes to divergence-free modes. Interestingly, as the heating intensity is increased, the net modification of turbulence by heating is observed dominantly in divergence-free modes; the portion of turbulence modification in dilatational modes diminishes with higher heating. Moreover, we show that modification of divergence-free modes is more pronounced at intermediate Stokes numbers corresponding to the maximum particle clustering. We also present the influence of heating intensity on the energy transfer term itself. This term crosses over from negative to positive values beyond a threshold wavenumber, showing the cascade of energy from large scales to small scales. The threshold is shown to shift to higher wavenumbers with increasing heating, indicating a growth in the total energy transfer from large scales to small scales. The fundamental energy transfer analysis presented in this paper provides insightful guidelines for subgrid-scale modelling and large-eddy simulation of heated particle-laden turbulence.

scholarly journals Probability density function (PDF) models for particle transport in porous media

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Matteo Icardi ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Probability Density ◽  
Turbulent Flows ◽  
Concentration Field ◽  
Planck Equation ◽  
Transport Processes ◽  
Fokker Planck Equation ◽  
Mixing Problem ◽  
And Diffusion ◽  
Fokker Planck

AbstractMathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field). Recently, closer to the spirit of PDF models for turbulent flows, some approaches have used this statistical viewpoint also in pore-scale transport processes (fully resolved porous media models). When a concentration field is transported, by advection and diffusion, in a heterogeneous medium, in fact, spatial PDFs can be defined to characterise local fluctuations and improve or better understand the closures performed by classical upscaling methods. In the study of hydrodynamical dispersion, for example, PDE-based PDF approach can replace expensive and noisy Lagrangian simulations (e.g., trajectories of drift-diffusion stochastic processes). In this work we derive a joint position-velocity Fokker–Planck equation to model the motion of particles undergoing advection and diffusion in in deterministic or stochastic heterogeneous velocity fields. After appropriate closure assumptions, this description can help deriving rigorously stochastic models for the statistics of Lagrangian velocities. This is very important to be able to characterise the dispersion properties and can, for example, inform velocity evolution processes in continuous time random walk dispersion models. The closure problem that arises when averaging the Fokker–Planck equation shows also interesting similarities with the mixing problem and can be used to propose alternative closures for anomalous dispersion.

Introduction

1996 ◽  
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Turbulence Models ◽  
Spectral Energy ◽  
Wavelet Representations ◽  
Turbulent Closure ◽  
Scaling Parameters ◽  
The Subject ◽  
Compressible Turbulent Flow ◽  
Insightful Analysis

The aim of this book is to provide the engineer and scientist with the necessary understanding of the underlying physics of turbulent flows, and to provide the user of turbulence models with the necessary background on the subject of turbulence to allow them to knowledgeably assess the basis for many of the state-of-the-art turbulence models. While a comprehensive review of the entire field could only be thoroughly done in several volumes of this size, it is necessary to focus on the key relevant issues which now face the engineer and scientist in their utilization of the turbulent closure model technology. The organization of this book is intended to guide the reader through the subject starting from key observations of spectral energy transfer and the physics of turbulence through to the development and application of turbulence models. Chapter 1 focuses on the fundamental aspects of turbulence physics. An insightful analysis of spectral energy transfer and scaling parameters is presented which underlies the development of phenomenological models. Distinctions between equilibrium and nonequilibrium turbulent flows are discussed in the context of modifications to the spectral energy transfer. The non-equilibrium effects of compressibility are presented with particular focus on the alteration to the turbulent energy dissipation rate. The important topical issue of coherent structures and their representation is presented in the latter half of the chapter. Both Proper Orthogonal Decomposition and wavelet representations are discussed. With an understanding of the broad dynamic With an understanding of the broad dynamic range covered by both the turbulent temporal and spatial scales, as well as their modal interactions, it is apparent that direct numerical simulation (DNS) of turbulent flows would be highly desirable and necessary in order to capture all the relevant dynamics of the flow. Such DNS methods, in which all the important length scales in the energy-containing range and in the dissipation range are accounted for explicitly is presented in Chapter 2. Emphasis is on spectral methods for incompressible flows, including the divergence-free expansion technique. Vortex methods for incompressible bluff body flows are described and some techniques for compressible turbulent flow simulations are also discussed briefly.

Lagrangian pair dispersion in upper-ocean turbulent flows with mixed-layer instabilities

2021 ◽  
Author(s):  
Stefano Berti ◽  
Guillaume Lapeyre
Keyword(s):  
Turbulent Flows ◽  
Mixed Layer ◽  
Separation Distance ◽  
Vertical Shear ◽  
Spreading Process ◽  
Opposite Case ◽  
Dispersion Regime ◽  
Fluid Layers ◽  
Small Scales ◽  
Good Proxy

<p>Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth’s rotation and are characterized by quasi-two-dimensional turbulence. At scales around 300 km (in the mesoscale range), coherent vortices contain most of the kinetic energy in the ocean. At scales around 10 km (in the submesoscale range) the flow is populated by smaller eddies and filamentary structures associated with intense gradients (e.g. of temperature), which play an important role in both physical and biogeochemical budgets. Such small scales are found mainly in the weakly stratified mixed layer, lying on top of the more stratified thermocline. Submesoscale dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the generation of energetic small scales that are not trapped at the surface, as those arising from mesoscale-driven processes, but extend down to the thermocline. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited.</p><p>By means of numerical simulations, we explore Lagrangian pair dispersion in turbulent flows from a quasi-geostrophic model consisting in two coupled fluid layers (representing the mixed layer and the thermocline) with different stratification. Such a model has been previously shown to give rise to both meso and submesoscale instabilities and subsequent turbulent dynamics that compare well with observations of wintertime submesoscale flows. We focus on the identification of different dispersion regimes and on the possibility to relate the characteristics of the spreading process at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the experimentally more accessible (e.g. by satellite altimetry) surface ones.</p><p>Using different statistical indicators, we find a clear transition of dispersion regime with depth, which is generic and can be related to the statistical features of the turbulent flows. The spreading process is local (namely, governed by eddies of the same size as the particle separation distance) at the surface. In the absence of a mixed layer it rapidly changes to nonlocal (meaning essentially driven by the largest eddies) at small depths, while in the opposite case this only occurs at larger depths, below the mixed layer. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear and address the properties of the relative motion of subsurface particles with respect to surface ones. In the absence of a mixed layer, the properties of the spreading process are found to rapidly decorrelate from those at the surface, but the relation between the surface and subsurface dispersion appears to be largely controlled by vertical shear. In the presence of mixed-layer instabilities, instead, the statistical properties of dispersion at the surface are found to be a good proxy for those in the whole mixed layer.</p>

Luminescence Studies on Low Temperature Synthesized ZnGa2O4:Ln3+ (Ln = Tb and Eu) Nanoparticles

2008 ◽  
Vol 8 (11) ◽  
pp. 5776-5780 ◽  
Author(s):  
C. Manikyala Rao ◽  
V. Sudarsan ◽  
R. S. Ningthoujam ◽  
U. K. Gautam ◽  
R. K. Vatsa ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Oleic Acid ◽  
Steady State ◽  
Low Temperature ◽  
Ethylene Glycol ◽  
Urea Hydrolysis ◽  
Lanthanide Ions ◽  
X Ray Diffraction ◽  
X Ray ◽  
Broad Emission

ZnGa2O4 nanoparticles doped with lanthanide ions (Tb3+ and Eu3+) were prepared at a low temperature of 120 °C based on urea hydrolysis in ethylene glycol medium. X-ray diffraction studies have confirmed that strain associated with nanoparticles changes as Tb3+ gets incorporated in the ZnGa2O4 lattice. Based on steady state emission and excitation studies of ZnGa2O4:Tb nanoparticles, it has been inferred that ZnGa2O4 host is characterized by a broad emission around 427 nm and there exists energy transfer between the host and Tb3+ ions. Unlike this, for ZnGa2O4:Eu nanoparticles, very poor energy transfer between the host and Eu3+ ions is observed. These nanoparticles when coated with ligands like oleic acid results in their improved dispersion in organic solvents like chloroform and dichloromethane.

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