Understanding the physics of multiphase plumes and their simulation through numerical modeling has been an important area of research in recent times in the area of environmental fluid mechanics. The two renowned numerical modeling types that are commonly used by researchers today to simulate multiphase plumes in nature are the mixed-fluid and the two-fluid integral models. In the present study, a detailed review was performed to study and analyze the two modeling approaches for the case of a double plume (upward moving inner plume with downward moving annular outer plume) with the objective of ascertaining which of these models represent the prototype physics in the integral plume model equations with a higher degree of completeness and accuracy. A graphical user interface was designed to facilitate running the models. By comparison to laboratory scale experimental data and through sensitivity analyses, a rigorous effort was made to determine the most appropriate choice of initial conditions needed at the start of the model computation and at the peeling locations and to obtain the most consistent values of the different model parameters that are necessary for calibration of the two models. Consequently, with these selected sets of initial conditions and model parameters, the models were run and their outputs compared against each other for three different case studies with ambient conditions typical of real environmental data. The dispersed phases considered were air bubbles in two cases and liquid CO2 droplets for the third case, with water as the continuous phase in all cases. The entrainment coefficient was found to be the most important parameter that affected the model results. In all the three case studies conducted, the mixed-fluid model was found to predict about 30% higher values for the peel heights and the DMPR (Depth of Maximum Plume Rise) than the two-fluid model.

Soit R un anneau de valuation discrète de corps de fractions K. Soit X_K un K- schéma propre géométriquement normal. On montre que X_K possède des modèles X sur R, propres, plats, normaux et tels que tout faisceau inversible sur X_K se prolonge en un faisceau inversible sur X. On peut alors reconstruire le modèle de Néron de la variété de Picard de X_K, à partir du foncteur de Picard de X/R.Lorsque R est hensélien à corps résiduel algébriquement clos, on en tire des informations sur le prolongement de l’équivalence algébrique de X_K à X. En particulier, on peut décrire le symbole de Néron entre 0-cycles de degré zéro et diviseurs algébriquement équivalents à zéro sur X_K, en termes de multiplicités d’intersection sur le modèle X. Ceci nous permet de reformuler la conjecture de dualité de Grothendieck pour les modèles de Néron des variétés abéliennes, en termes d’équivalence algébrique relative. / Let R be a discrete valuation ring with fraction field K. Let X_K be proper geometrically normal scheme over K. One shows that X_K admits models X over R which are proper, flat, normal an such that any invertible sheaf on X_K can be extended to an invertible sheaf on X. Then, one can recover the Néron model of the Picard variety of X_K from the Picard functor of X/R.When R is henselian with algebraically closed residue field, one obtains some consequences about the extension of algebraic equivalence from X_K to X. In particular, one can describe the Néron symbol between 0-cycles of degree zero and divisors which are algebraically equivalent to zero on X_K, in terms of intersection multiplicities on the model X. This allows us to reformulate Grothendieck’s duality conjecture for Néron models of abelian varieties, in terms of relative algebraic equivalence.