Thibaut Menard

A Level Set Method for vaporizing two-phase flows

Development and applications of numerical methods devoted to reactive interface simulations are presented. Emphasis is put on vaporization, where numerical difficulties arise in imposing accurate jump conditions for heat and mass transfers. We use both the Level Set Method and the Ghost Fluid Method to capture the interface motion accurately and to handle suitable jump conditions. A local vaporization mass flow rate per unit of surface area is defined and Stefan flow is involved in the process. Specific care has been devoted to the extension of discontinuous variables across the interface to populate ghost cells, in order to avoid parasitic currents and numerical diffusion across the interface. A projection method is set up to impose both the velocity field continuity and a divergence-free condition for the extended velocity field across the interface. The d^2 law is verified in the numerical simulations of the vaporization of an isolated static drop. Results are then presented for a water droplet moving in air. Vapor mass fraction and temperature fields inside and outside the droplet are presented.

A LES Simulation of Atomisation

Large Eddy Simulation has been used with a lot of success for single phase flows. Its extension to multiphase flows is underway. As far as liquid-gas flows are concerned, two limit cases have been addressed: In one hand, if the liquid phase corresponds to a set of droplets with diameters smaller than the LES filter size, a subgrid spray is described. In the other hand, if the characteristic sizes of the surface wrinkles are greater than the LES filters size, the surface is resolved and LES models concern the velocity field. An example of the first approach is a dilute spray and an example of the second approach is waves at ocean surface. The issue with LES simulation of atomization is that a surface resolved LES is expected close to the injector together with a subgrid sprays LES far from the injector when the spray is finally formed. If only a resolved LES is used, the drop diameter cannot be smaller than the LES filter size. It follows that smaller diameters cannot be described and the breakup process is blocked numerically at a size related to the filter size. At the contrary if a subgrid spray LES is used a model is necessarily used that is accurate only for given type of injector. The present work addresses the problem induced by this transition between resolved and unresolved spray. A first approach is proposed that is able to reach both limits. The transition is performed using a filtered surface density equation to avoid the assumption that ligaments, sheets and other surface topologies becomes spherical droplet abruptly at the subgrid level. Results will be shown to demonstrate the ability of the model to recover the essential characteristics of a spray in a Diesel like application.Copyright

DNS Study of Collision and Coalescence Over a Wide Range of Volume Fraction

Among the different processes that play a role during the atomization process, collisions are addressed in this work. Collisions can be very important in dense two-phase flows. Recently, the Eulerian Lagrangian Spray Atomization (ELSA) model has been developed. It represents the atomization by taking into account the dense zone of the spray. Thus in this context, collisions modeling are of the utmost importance. In this model results of collisions are controlled by the value of an equilibrium Weber number, We*. It is defined as the ratio between the kinetic energy to the surface energy. Such a value of We* has been studied in the past using Lagrangian collision models with various complexity. These models are based on analysis of collisions between droplets that have surface at rest. This ideal situation can be obtained only if droplet agitation created during a collision has enough time to vanish before the next collision. For a spray, this requirement is not always fulfill depending for instance on the mean liquid volume fraction. If there is not enough time, collisions will occur between agitated droplets changing the issue of the collision with respect to the ideal case. To study this effect, a DNS simulation with a stationary turbulence levels has been conducted for different liquid volume fractions in a cubic box with periodic condition in all directions. For liquid volume fraction close to zero the spray is diluted and collisions between spherical droplets can be identified. For a volume fraction close to one, collisions between bubbles are found. For a middle value of the volume fraction no discrete phase can be observed, instead a strong interaction between both liquid and gas phases is taking place. In all this case the equilibrium value of the Weber number We* can be determined. First propositions to determine We* as a function of the kinetic energy, density ratio, surface tension coefficient and the volume fraction will be proposed.Copyright