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AbstractAbstract
[en] From both the theoretical and the practical points of view, the problem of constitutive laws is a part and parcel of the modeling problem. In particular, the necessity to restore in the model, through topological laws, some of the information lost during the usual averaging process is emphasized. It is shown that the customary 'void fraction' topological law Psub(V)=Psub(L) should be proscribed whenever propagation phenomena are involved. A new void fraction topological law is proposed. The limitations of the current assumption of constant pressure within any phase in any cross section are also illustrated. The importance of proximity effects (neighborhood and history effects, related to characteristic lengths and times) is brought out. It results in the importance of the mathematical form of the constitutive laws. Various approaches to the constitutive law problem and possible mathematical forms for the transfer laws are reviewed. The simplest form (transfert terms as functions of the dependent variables only) may have some usefulness if interpretation of the results in terms of propagation phenomena is banned. A good compromise between the necessity to take proximity effects into account and to obtain a tractable set of equations is carried out when so called 'differential terms' are introduced in the transfer laws. The last part of the paper is devoted to some restrictions, which are imposed to the transfer terms because of some basic principles: indifference to Galilean changes of frame and to some changes of origins, second law of thermodynamics and assumption of local thermodynamic equilibrium, closure constraints. Practical recommendations are formulated
[fr]
On replace le probleme des lois constitutives dans le cadre general de celui de la modelisation, dont il n'est separable ni du point de vue theorique, ni du point de vue pratique. On insiste notamment sur la necessite de restituer, au niveau du systeme pratique d'equations, une partie des informations perdues au cours des habituelles operations de moyennes, par une loi 'topologique' de taux de vide. On montre que la loi topologique usuelle Psub(V)=Psub(L) est a proscrire pour l'etude des phenomenes de propagation et on propose une forme moins restrictive. On discute egalement les consequences de l'hypothese d'isobaricite phasique. On met enfin en evidence l'importance des effets dits de proximite (effets de voisinage et d'histoire lies a certaines longueurs et temps caracteristiques) et, partant, de la forme mathematique des lois constitutives, on rappelle les approches utilisables pour la recherche de lois constitutives et on examine les formes envisageables pour les lois des transferts. La forme la plus simple (fonctions des variables dependantes) peut rendre des services a conditions de s'interdire toute interpretation basee sur des phenomenes de propagation. La forme 'a termes differentiels' realise un bon compromis entre la necessite de prendre en compte les effets de proximite et celle de batir un modele maniable. On recherche enfin les restrictions qu'imposent aux lois de transfert certains axiomes fondamentaux: indifference aux changements de reperes galileens et a certains autres changements d'origine, second principe et hypothese de l'equilibre thermodynamique local, contraintes de fermeture. On en tire un certain nombre de recommandations pratiquesOriginal Title
Les lois constitutives des modeles d'ecoulements diphasiques monodimensionnels, a deux fluides - Formes envisageables - Restrictions resultant d'axiomes fondamentaux
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May 1978; 87 p
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