For mass transfer applications, CFD codes need the turbulent Schmidt number . The aim of our study is the analysis of some theoretical closure results and analytical formulations for . We will investigate different formulations of from the basic conservation equations for sediment-water mixtures in turbulent open-channel flows based on a two-fluid description and a kinetic model. The kinetic model for turbulent two-phase flows provides which depends on particle Stokes number. Our study show that the two approaches provide that depends on turbulent kinetic energy (TKE), eddy viscosity and particles settling velocity. For the analysis, accurate analytical formulations for TKE and eddy viscosity calibrated by DNS data are presented.

For transient thermal performance of building envelops adequate parameters are needed to capture the time lag and decrement factor. It is surprising that, in the formal electrical analogy, "inertia" is not represented by same components in fluid mechanics and heat transfer. In Windkessel model for fluid flow in elastic tubes, the fluid inertia is represented by an electrical inductance while in thermal-electric analogy, thermal inertia is given by a capacitance. Some authors argued that the terminology of ''thermal inertia'' is used incorrectly in the literature. The aim of our communication is to provide some clarification about this controversy. We will show that the thermal effusivity which is the geometric mean of thermal conductivity and volumetric heat capacity plays the role of a "thermal mass". The revisited notion of inertia in mechanics will allow to show the analogy between: mechanical inertia (mass), thermal effusivity and electrical inductance. The three parameters show a tendency to keep invariant a certain physical quantity: velocity, temperature and current intensity respectively. However, the analogy is not complete, the capacitance used in the heat transfer seems to be similar to the one used in the Windkessel model which accounts for tube compliance and therefore to a local storage.

No abstract

Résumé :La forme des profils verticaux de concentration des sédiments en suspension sur un fond de rides, qui peut être concave ou convexe, dépend de la taille des sédiments. Pour améliorer la prédiction de ces profils, nous considérons d'une part, le modèle de longueur de mélange finie avec différentes descriptions du mélange turbulent et d'autre part, l'équation d'advection-diffusion classique basée sur l'approximation de Fick avec une description appropriée du paramètre  (rapport entre diffusivité et viscosité turbulente). L'analyse détaillée des données de mesures a permis d'identifier deux couches distinctes, une première proche du fond où le profil de concentration est concave et une seconde plus éloignée où le profil est convexe. La limite de passage d'une couche à l'autre dépend de la taille des sédiments. Mots-clés: SEDIMENTS -MELANGE TURBULENT -PROFILS DE SEDIMENTS -TAILLES DES PARTICULES Abstract :The shape of suspended sediment concentration vertical profiles over a wave ripples, which is upward concave or convex, depends on sand grain sizes. In order to improve the prediction of these profiles, we consider on the hand the finite mixing length model with different descriptions of turbulent mixing and on the other hand the classical advection-diffusion equation based on Fick's approximation with an appropriate description of the parameter  (ratio between sediment diffusivity and eddy viscosity). A detailed analysis of experimental data shows two layers, a first near the bottom where the concentration profile is Actes de Xèmes Journées Nationales Génie côtier Génie civil, SophiaAntipolis, 14-16 octobre 2008, ISBN 2-9505787-9-9, Tome 1, pp. 9-18. upward concave and a second where the profile is upward convex. The limit between these two layers depends on sediments size. Mots-clés:SEDIMENT -TURBULENT MIXING -SEDIMENT PROFILES -PARTICLE SIZE

RésuméPour décrire le profil de concentration des sédiments en suspension dans un écoulement turbulent, nous introduisons dans cette contribution une nouvelle écriture du profil vertical lm(z) de la longueur de mélange.Nous montrons que notre expression de lm ne tend en limite vers celle de Prandtl que dans le cas des faibles rugosités de surface (conditions aux limites du type « fond lisse »). Sous l'hypothèse de validité de la loi de Fick, le profil de concentration obtenu est qualitativement comparé aux prévisions théoriques usuelles, basées sur lm = κ z L'écart constaté permet d'expliquer -sans hypothèse arbitraire -certains résultats expérimentaux.Enfin, une critique est faite de l'usage de la loi de Fick pour l'écriture du flux de mélange dans le cas des forts gradients de concentration. Mots clés Sédiments, turbulence, diffusion, mélange, longueur, rugosité. AbstractIn order to describe the suspended sediment concentration profile in a turbulent flow, we introduce in this contribution a new vertical profile for the mixing length lm(z).We show that our expression tends to the Prandtl mixing length only in the case of small roughness (smooth bed boundary condition). Under the assumption of validity of the Fickian (or gradient) diffusion, the obtained concentration profile is qualitatively compared to usual theoretical predictions, based on lm= κ.z .The difference can explain -without arbitrary assumption -some m experimental data. Finally, a critical study is done on the use of the Fickian mixing flux in the case of high concentration gradients.