今回の講演会は，対面形式で開催します．ご参加される方は下記の講義室へお越し下さい（事前申込は不要です）．
| 日時： | 2023年3月31日（金）14:30-16:30 |
| 場所： | 京都大学 桂キャンパスCクラスタ総合研究棟III（C3棟） 1階 b1N01室（講義室1） |
| 講演1： | A two-scale reduced-order model for two-phase flows with polydisperse deformed droplets relying on Hamilton’s principle and a geometric method of moments |
| Prof. Marc Massot (Centre de Mathématiques Appliquées, Ecole Polytechnique, France) | |
| 要旨1： | Two-scale multi-fluid models with diffuse interface, amenable to realistic computational time, can be predictive for atomization, as long as they rely on the proper modeling of the small-scale interface dynamics below a given length threshold. The derivation of this two-scale model relies on three ingredients: 1- Large- and small-scale energies and conserved variables describing the physics, 2- the Hamilton’s Stationary Action Principle (SAP), 3- the second principle of thermodynamics that provide together with SAP the framework for consistent momentum and energy equations. Instead of solving capillarity at all physical length-scales with a phase-field model, this work proposes a two-scale model where a large-scale diffuse interface model interacts with a small-scale model under the chosen threshold, where the flow structure is simplified. The capillarity at large scale is here treated with a “Continuum Surface Force” (CSF), while the small-scale is modelled with a method of moment on a spray of droplets relying on a kinetic level of description. The resulting set of geometric moments allows geometric exchanges between scales to preserve the consistency of the interface geometry. The resulting unified model naturally degenerate into a Eulerian method of moments in the polydisperse spray region downward the flow, while matching the usual multi-fluid model in the separated flow region near the injector and offers an interesting entropy-consistant framework for the transfer of scales. |
| 講演2： | Small-scale modelling of interface dynamics in two-phase flows: a kinetic approach based on a geometric method of moments |
| Mr. Arthur Loison (PhD student at Centre de Mathématiques Appliquées, Ecole Polytechnique, France) | |
| 要旨2： | In the context of multi-scale two-phase flows such as liquid atomization or bubbly flows, the small-scale dynamics of the interface are computationally unaffordable with classic DNS with interface tracking, yet they are necessary to predict the right size distribution of the spray downstream the flow or the bubble polydispersity. Two-scale models avoid this bottleneck by modeling the small-scale unresolved dynamics of the interface. We expect such a small-scale model to be defined for any flow regime, while being consistent with reduced-order models based on methods of moments and the kinetic modelling of the disperse regime. This requires using specific quantities related to the average geometry of the unresolved interface that are the foundation of a geometric method of moments. In this presentation, we start by reviewing an averaged approach of interface dynamics [Pope 1988] [Essadki et al 2018] providing criteria for choosing appropriate geometric variables that are defined in every flow regime. Then, the small-scale model is closed with a geometric method of moments consistent with the disperse regime. Finally, we overview several closures and extensions of this method that allows the description of geometric polydispersion in size, shape, and internal dynamics in the disperse regime while providing dynamics for averaged geometrical variables for any flow regimes. |