Statistical modeling of the gas–liquid interface using geometrical variables: Toward a unified description of the disperse and separated phase flows

•Statistical formalism for gas–liquid interface based on geometrical properties.•Link of local interface geometry with NDF of objects using topological invariants.•Algorithm to compute average geometrical properties preserving the topological invariants.•Assessment on DNS post-processing with and wi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:International journal of multiphase flow Jg. 120; S. 103084
Hauptverfasser: Mohamed, Essadki, Florence, Drui, Stéphane, de Chaisemartin, Adam, Larat, Thibault, Ménard, Marc, Massot
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.11.2019
Elsevier
Schlagworte:
computational geometry
Differential Geometry
disperse/separated phases
Engineering Sciences
Fluid mechanics
gas-liquid interface
Gauss-Bonnet formula
Mathematics
Mechanics
moments method
Numerical Analysis
Physics
Reactive fluid environment
surface and number density function
surface and number density function
76A99
76T10
disperse/separated phases
35Q35
65D99
computational geometry
Gauss-Bonnet formula
53A17
gas-liquid interface
moments method
Gauss- Bonnet formula
surface and number density function 2010 MSC: 76T10
ISSN:0301-9322, 1879-3533
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:•Statistical formalism for gas–liquid interface based on geometrical properties.•Link of local interface geometry with NDF of objects using topological invariants.•Algorithm to compute average geometrical properties preserving the topological invariants.•Assessment on DNS post-processing with and without topological changes.•NDF obtained for non-spherical objects in the proposed geometrical phase space. In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas–liquid two-phase flows through geometrical variables. The contribution is two-fold. First it participates in the theoretical design of a unified reduced-order model for the description of two regimes: a disperse phase in a carrier fluid and two separated phases. The first idea is to propose a statistical description of the interface relying on geometrical properties, such as the mean and Gauss curvatures, and to define an associated Surface Density Function (SDF). The second main idea consists in using such a formalism in the disperse case, where a clear link is proposed between local statistics of the interface and the statistics of countable objects, such as a number density function. To this end we make essential the use of topological invariants in geometry through the Gauss-Bonnet formula. This strategy strictly includes the works conducted on sprays of spherical droplets, but it also yields a statistical treatment of populations of non-spherical objects, such as ligaments, as long as they are homeomorphic to a sphere. Second, we propose an original statistical post-processing of DNS data of interfacial flows. Starting from the proposed theoretical approach, we identify a kernel for the spatial averaging of geometrical quantities which preserves the topological invariants. Coupled to a new algorithm for the evaluation of the surface and its curvatures, that also preserves these invariants, we analyze two sets of DNS results obtained with the ARCHER code from CORIA, with and without topological changes, and assess the approach. Indeed, this procedure allows us to transform the interfacial information provided by a Level-Set function into a number distribution of a collection of objects in the proper geometrical phase space.
ISSN:0301-9322
1879-3533
DOI:10.1016/j.ijmultiphaseflow.2019.103084