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In this Note, we study numerically turbulent diffusion in the case of homogeneous stably stratified turbulence. This study is based on a linear analysis in spectral space. To express the Lagrangian velocity correlations using Eulerian correlations, we adapt the Corrsin assumption and then we calculate the tensor components of the mean square displacement. We begin by writing the basic linear equations governing the evolution of the spectra of double correlations then we present the Corrsin hypothesis as a model of turbulent diffusion. Subsequently, we describe the numerical method used and analyze the numerical results. Clearly, the Corrsin assumption can give the proper behavior, at large times, of the horizontal diffusion and improves the prediction of vertical diffusion. As an application of the numerical code elaborated, we study the influence of Prandtl number on the vertical diffusion which results in an accentuation of the suppression of vertical diffusion when the Prandtl number (less than 1) diminishes. © 2011 Académie des sciences.

Thamri Naffouti L.,Laboratoire Of Mecanique Des Fluides | Lili T.,Laboratoire Of Mecanique Des Fluides | Bouzaiane M.,Laboratoire Of Mecanique Des Fluides | Bouzaiane M.,University of Carthage
Journal of Applied Fluid Mechanics | Year: 2014

In this work, the asymptotic equilibrium behaviour of dimensionless parameters in stably stratified turbulence submitted to a horizontal shear is studied using two different methods. The first one is an analytic method and is based on linear solutions obtained when non linear effects of pressure and viscosity are neglected. The Laplace Transform is used for integrating differential system. The principal result of this first part of our work is the existence of asymptotic equilibrium states at high shear for all non dimensionless parameters. The second method is a numerical one and is based on a second-order modeling of equations. The Speziale Sarkar and Gatski (SSG) model is retained for pressure-strain correlation and dissipation time evolution equation, whereas, three of the most known second-order models are retained for the scalar field. The principal result of this second part is the big contribution of the SSG models for predicting asymptotic equilibrium states of non dimensional parameters.

Jmai R.,Laboratoire Of Mecanique Des Fluides | Ben-Beya B.,Laboratoire Of Mecanique Des Fluides | Lili T.,Laboratoire Of Mecanique Des Fluides
Superlattices and Microstructures | Year: 2013

Heat transfer and fluid flow in a square cavity with partially heated side walls filled with nanofluid has been studied numerically using different types of nanoparticles. A two heat sources maintained at a constant heat flux q″ are embedded in the right and the left wall. The enclosure was cooled from the top and bottom walls. The remaining boundary parts are kept insulated. Method of solution is based on the finite volume method and an accelerated multigrid which has been tested and compared with previously published work on the basis of special cases and proved excellent agreements. The influence of pertinent parameters such as Rayleigh number, the type of nanofluid, the solid volume fraction of nanoparticles and the location of the heat sources on the heat transfer and fluid flow is studied. Different configurations corresponding to the sources locations are investigated. Results were presented by streamlines, isotherms, average and local Nusselt numbers for Rayleigh number in the range (104 ≤ Ra ≤ 107), solid volume fraction of nanoparticles in the range (0 ≤ φ ≤ 0.2) and different types of nanoparticles (Cu, Ag, Al2O3 and TiO2). It was found that the heat transfer increases with increasing of Rayleigh number and volume fraction of nanoparticles. In addition, the maximum source temperature has been significantly affected when their locations are considered. Regardless the Rayleigh number and the solid volume fraction of nanoparticles, the highest heat transfer enhancement occurs for the down-top case, while the minimum is reached in the middle-middle case. Multiple correlations in terms of the Rayleigh numbers and the solid volume fraction of nanoparticles have been established. © 2012 Elsevier Ltd. All rights reserved.

Chebbi B.,Laboratoire Of Mecanique Des Fluides | Bouzaiane M.,Laboratoire Of Mecanique Des Fluides
Journal of Applied Fluid Mechanics | Year: 2012

In this work, the effect of rotation on the evolution of kinematic and passive scalar fields in two dimensional homogeneous sheared turbulence is studied using two different approaches. The first one is analytical and it consists on the resolution of differential linear equations governing the turbulence at high shear when the non linear effects are neglected. The second one is numerical and it consists on the modeling of governing equations using the most known second order models of turbulence and their numerical integration using the fourth order Runge-kutta method. In this second approach, the classic Launder Reece Rodi model, the Speziale Sarkar Gatski and the Shih Lumley models are retained for the pressure-strain correlation, pressure-scalar gradient correlation and for the time evolution equations of the kinematic and scalar dissipations. The evolution of turbulence is studied according to the dimensionless rotation number R which is varied from -0.75 to 0.5. The obtained results are compared to the recent results of the DNS of Brethouwer. Both methods have confirmed the existence of asymptotic equilibrium states for dimensionless kinematic and scalar parameters.

Philippe M.,Laboratoire Of Mecanique Des Fluides | Philippe M.,Ecole Centrale Nantes | Babarit A.,Laboratoire Of Mecanique Des Fluides | Babarit A.,Ecole Centrale Nantes | And 2 more authors.
Houille Blanche | Year: 2011

This study deals with a coupled dynamic analysis of a body consisting of a wind turbine, a floater and an anchoring system in order to investigate the effect on the system of crossed waves relatively to the wind. Hydrodynamic loads are calculated by linear frequency domain approach. Aerodynamic effect is taken into account by in-creasing hydrodynamic damping and restoring matrices with aerodynamic damping and gyroscopic stiffness. A modal analysis of the system let us know the natural frequencies and natural modes of the system. It explains the coupled motions obtained in forced motion; particularly it explains which modes of motions are excited by which wave frequency and di-rection. © 2011 Société Hydrotechnique de France.

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