A diffuse interface approach for disperse two-phase flows involving dual-scale kinematics of droplet deformation based on geometrical variables

The purpose of this contribution is to derive a reduced-order two-phase flow model in- cluding interface subscale modeling through geometrical variables based on Stationary Action Principle (SAP) and Second Principle of Thermodynamics in the spirit of [6, 14]. The derivation is conducted in the disperse phase regime for the sake of clarity but the resulting paradigm can be used in a more general framework. One key issue is the definition of the proper potential and kinetic energies in the Lagrangian of the system based on geometrical variables (Interface area density, mean and Gauss curvatures...), which will drive the subscale kinematics and dissipation, and their coupling with large scales of the flow. While [14] relied on bubble pulsation, that is normal deformation of the interface with shape preservation related to pressure changes, we aim here at tackling inclusion deformation at constant volume, thus describing self-sustained oscillations. In order to identify the proper energies, we use Direct Numerical Simulations (DNS) of oscillating droplets using ARCHER code and recently devel- oped library, Mercur(v)e, for mean geometrical variable evaluation and analysis preserving topological invariants. This study is combined with historical analytical studies conducted in the small perturba- tion regime and shows that the proper potential energy is related to the surface difference compared to the spherical minimal surface. A geometrical quasi-invariant is also identified and a natural definition of subscale momentum is proposed. The set of Partial Differential Equations (PDEs) including the conservation equations as well as dissipation source terms are eventually derived leading to an original two-scale diffuse interface model involving geometrical variables

Modélisation et simulation numérique des phénomènes de combustion en régime supercritique

PARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF

Nonmixing layers

International audienceWe investigate the impact of nonideal diffusion on the structure of supercritical cryogenic binary mixing layers. This situation is typical of liquid fuel injection in high-pressure rocket engines. Nonideal diffusion has a dramatic impact in the neighborhood of chemical thermodynamic stability limits where the components become quasi-immiscible and ultimately form a nonmixing layer. Numerical simulations are performed for mixing layers of H2 and N2 at a pressure of 100 atm and temperature around 120–150 K near chemical thermodynamic stability limits

Vers la simulation multi-physique avec la méthode JFNK

International audienceFor multi-physics simulations, the definition of an accurate implicit time integration scheme is of paramount importance to converge the multi-physics system efficiently towards its steady solution. Generally, the definition of the Jacobian approximation relies on scientist experience and is one of the biggest flaws since cross-solver coupling terms are generally disregarded. As a time integration method, a Jacobian-Free Newton-Krylov can improve the precision of the Jacobian approximation. In this context, we present the strategy adopted for our in-house computational fluid dynamics solver: CEDRE.Pour la simulation numérique des phénomènes multi-physiques, la définition d'une méthode d'intégration temporelle implicite est primordiale afin de faire converger le système multi-physique efficacement vers sa solution stationnaire. En général, le calcul de la matrice jacobienne du système se base sur l'expérience des développeurs et présente de grands défauts car les termes croisés correspondants aux couplages entre solveurs sont souvent ignorés. Comme méthode d'intégration temporelle, la méthode JFNK améliore la précision de l'évaluation de la matrice jacobienne. Dans ce cadre, nous présentons la stratégie adoptée pour notre solveur CEDRE

A diffuse interface approach for disperse two-phase flows involving dual-scale kinematics of droplet deformation based on geometrical variables

The purpose of this contribution is to derive a reduced-order two-phase flow model in- cluding interface subscale modeling through geometrical variables based on Stationary Action Principle (SAP) and Second Principle of Thermodynamics in the spirit of [6, 14]. The derivation is conducted in the disperse phase regime for the sake of clarity but the resulting paradigm can be used in a more general framework. One key issue is the definition of the proper potential and kinetic energies in the Lagrangian of the system based on geometrical variables (Interface area density, mean and Gauss curvatures...), which will drive the subscale kinematics and dissipation, and their coupling with large scales of the flow. While [14] relied on bubble pulsation, that is normal deformation of the interface with shape preservation related to pressure changes, we aim here at tackling inclusion deformation at constant volume, thus describing self-sustained oscillations. In order to identify the proper energies, we use Direct Numerical Simulations (DNS) of oscillating droplets using ARCHE