Modeling and Multi-Scale Simulation of Interfaces – MODEMI

Initially the project will bring together teams around two validation cases to be addressed by all partners: thin film instabilities and phase separation at very high Reynolds and Weber numbers under gravity. In a second step, the methods of direct simulation and multi-scale capabilities of the codes will be improved, to move to the third task, the simulation of the most complex physical conditions: atomization, films and surface waves, phase separation, dispersed media bubble. In the continuity of the previous ANR project «STI« the formalism of Large Eddy Simulation (LES) (Climent et al. 2006) will be extended and used in this project.

In a final step partners will compare the various approaches that have been used in simulations of task 3 and develop a methodology to monitor their quality and effectiveness.

1) phase inversion benchmark
The four partners have carried out simulations in the specified configuration. This configuration is specified in Task 1 of the initial project: a cube of side 1m, initially filled with water (Vincent et al 2008.) with the exception of a smaller cubic subdomain, placed at the bottom, occupied by a lighter oil. The rise in oil causes a turbulent flow that generates a population of very small oil droplets, which are increasingly numerous and small scale as the simulation is refined. We performed simulations of the 128**3 and 256**3 meshes and compared our results (Figures 1 and 2). These comparisons showed a good correspondence of results on the kinetic energy, potential, interfacial area ... but a significant difference in the enstrophy. Note however that the Gerris code (d'Alembert) is also a difference in kinetic energy. Further simulations are carried out by different partners to understand the differences of the various codes / approaches.

2) Lagrangian Particles
Modeling Lagrangian particles is either available or under development. The coupling is effected at CORIA and under testing, the I2M has implemented and validated it on the sedimentation of solid particles in sedimenting in a tank. The numerical results were compared successfully with PIV experiments of Mordant and Pinton.

4) Representation of capillary forces
A new method is being developed to calculate the capillary term more independently of the spreading of the interface (ie the attendance phase function). It is a new variant of the CSF method. This method is revisited to calculate a part of the capillary force with a pseudo-reconstruction of the interfacial area, allowing control of the location of the capillary term and control the extent of the spatial domain where the force is applied. A numerical study was conducted to quantify the magnitude of the eddy currents obtained by this method (satisfactory). Validations were then performed (axisymmetric coalescence of two drops of mercury ([3]) 2D bubble ascent / deformation ([2]) Discussions are still needed regarding optimization..

5) Atomization
The numerical difficulties that arise with large density ratio and high shear are being resolved for the establishment of a new convective scheme (method of Rudman). AMR mesh refinement method is being parallelized and preliminary results are obtained (Figure 3).

1. Fuster, D. “An Energy Preserving Formulation for the Simulation of Multiphase Turbulent Flows.” Journal of Computational Physics 235 (February 2013): 114–128. doi:10.1016/j.jcp.2012.10.029.

2. A. Berlemont, J.B. Blaisot, Z. Bouali, J. Cousin, P. Desjonqueres, M. Doring, C. Dumouchel, S. Idlahcen, N. Leboucher, K. Lounnaci, T. Ménard, C. Rozé, D. Sedarsky, G. Vaudor Numerical simulation of primary atomization: Interaction with experimental analysis Atomization and Sprays, DOI: 10.1615/AtomizSpr.2013007525.

The project aims to advance the methods of high performance computing in very complex areas of two-phase fluid mechanics that are of considerable applied importance. A case in point are breaking waves and ocean spray formation, atomising jets of liquid fuel, bubbly flow in nuclear power plants or in chemical process engineering. These flows combine very large ranges of scales, which for ocean waves go from several dozen meters for the wavelength to a few microns for the smallest bubbles or droplets. The problems posed by a numerical solution of the problem cannto be solved without using methods that systematically account for the multi-scale character of the flow. Moreover, the evolution of high performace computing offers an additional challenge, since multiscale methods are more difficult to adapt to massively parallel computing than single-scale methods, which involve a simpler algorithmic structure.

At the conclusion of the project a multi-scale simulation methodology will be extracted. It will give answers to the following questions: how does one choose the regions that require a finer grid, how to chose between the various methods allowing to simulate the unresolved small scale effects ? How does the modelling of turbulence, of Large Eddy Simulation (LES) type couple to the unresolved interface geometry and dynamics at sub-mesh scales ?

In a first stage all the participants will perform the same two validation test cases : film stability under areodynamic shear and phase separartion at very large Reynolds and Weber number under gravity. In a second stage, the methods of direct numerical simulation and the multi-scale abilities of the various codes will be improved, which will allow to move on to the third stage, the simulation of the most complex physical cases: atiomization, films and surface waves, phase separation, disperse bubbly flows.

In a final stage, one will compare the various multiscale approaches used in stage 3 and develop cirteria to select the mthods and control their quality and efficiency.