The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. Here, we aim to present a coherent and comprehensive review encompassing the rapid progress made recently in the analysis, understanding and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally-coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

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Coupling functions:universal insights into dynamical interaction mechanisms

Due to computational time limitations, fully resolved simulations using the two-fluid model of the flow inside industrial-scale fluidized beds are unaffordable. The filtered approach is used to account for the effect of small unresolved scales on the large resolved scales computed with “coarse” realistic meshes. Using a fully resolved simulation, we highlight the need to account for a subgrid drift velocity to obtain the correct bed expansion when using coarse meshes. This velocity, defined as the difference between the filtered gas velocity seen by the particle phase and the resolved filtered gas velocity, modify the effective relative velocity appearing in the drag law. We close it as a correction of the resolved relative velocity depending on the filtered particle concentration and the filter size. A dynamic procedure is used to adjust a tuning parameter. Bed expansion obtained with a posteriori test on coarse-grid simulations matches well to fully resolved simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012

A functional subgrid drift velocity model for filtered drag prediction in dense fluidized bed

Some thermal hydraulic challenges in sodium cooled fast reactors

Implementation of an iterative solution procedure for multi-fluid gas–particle flow models on unstructured grids

CATHARE-3: A new system code for thermal-hydraulics in the context of the NEPTUNE project

The NEPTUNE project constitutes the thermal-hydraulic part of the long-term Electricite de France and Commissariat a l’Energie Atomique joint research and development program for the next generatio...

NEPTUNE : A new software platform for advanced nuclear thermal hydraulics

General Overview of the TOPFLOW-PTS Experimental Program

Un programme a long terme de developpement commun d'outils de simulation pour la prochaine generation de reacteurs nucleaires a ete lance en 2001 par EDF (Electricite De France) et CEA (Commissariat a l'Energie Atomique). Le projet NEPTUNE constitue la partie thermo-hydraulique de ce programme complet. Naturellement, dans le developpement de cette nouvelle plateforme de logiciel d'ecoulement diphasique, la validation de la modelisation physique impliquee est une question cruciale,quelle que soit l'echelle , et l'article traite de ce sujet. Apres un bref rappel sur la plateforme NEPTUNE, la strategie generale de validation a adopter est tout d'abord eclairee par trois caracteres majeurs : (i) validation physique en connexion etroite avec les applications industrielles interessees, (ii) impliquer (autant que possible) un processus en deux etapes se concentrant successivement sur des modeles dominants separes et l'evaluation des possibilites de modelisation globale, (iii) grâce a l'utilisation des donnees appropriees respectivement aux objectifs de validation. Base sur ce procede general de validation, une approche generique a quatre phases de travail a etedefinie ; elle inclut : (i) une analyse complete des applications industrielles interessees pour identifier les phenomenes physiques principaux impliques et les modeles de base dominants associes, (ii) une evaluation de ces modeles par rapport aux elements d'information disponibles pour la validation, pour indiquer les besoins supplementaires de validation et definir des plans consacres a la validation, (iii) inventaire et evaluation des donnees existantes de validation(en fonction des exigences definies dans la tâche precedente) pour identifier les besoins reels de nouvelles donnees de validation, (iv) specifications des nouveaux programmes experimentaux a installer pour fournir les nouvelles donnees necessaires. Cette approche de travail a ete appliquee au logiciel NEPTUNE, en se concentrant sur 8 applications industrielles fortement prioritaires, et a abouti a la definition : (i) du plan de validation et des programmes experimentaux a installer pour la modelisation 3D en milieu ouvert , en connexion etroite successivement avec le coeur DNB des-PWR et les applications PTS, et, (ii) des programmes experimentaux fortement prioritaires, en ce qui concerne les milieux poreux multi-domaine et le transport interfacial, en connexion avec l'application LB-LOCA. Ces programmes experimentaux exigeront l'utilisation d'une instrumentation specifique pour fournir des caracteristiques locales des deux phases de liquide et de vapeur, telles que la fraction de vide locale, la concentration locale d'interface et la vitesse locale du liquide. Pour remplir ces besoins, les techniques suivantes de mesure ont respectivement ete developees/ameliorees et evaluees : la tomographie par rayonsX, les sondes optiques a 4-capteurs et l'anemometrie a film chaud.

Physical validation issue of the NEPTUNE two-phase modelling: Validation plan to be adopted, experimental programs to be set up and associated instrumentation techniques developed : Progrès des méthodes de modélisation des écoulements diphasiques

Pierre Péturaud

Papers

NEPTUNE : A new software platform for advanced nuclear thermal hydraulics

General Overview of the TOPFLOW-PTS Experimental Program

Physical validation issue of the NEPTUNE two-phase modelling: Validation plan to be adopted, experimental programs to be set up and associated instrumentation techniques developed : Progrès des méthodes de modélisation des écoulements diphasiques