Alain Berlemont

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.

Heat and mass transfer coupling between vaporizing droplets and turbulence using a lagrangian approach

A Lagrangian approach is developed for droplet vaporization in turbulent fields, with two-way coupling between phases. Specific source terms induced by phase changes are described and results are presented for methyl alcohol droplet vaporization in a heated turbulent round jet. A high coupling is observed between production and diffusion processes for the vapour mass fraction and fluid temperatures. Droplet diameter distributions are strongly dependent on the turbulent dispersion and droplet history.

On the Lagrangian simulation of turbulence influence on droplet evaporation

A Lagrangian approach is developed to study the influence of turbulence on droplet evaporation. Two models can be used for the droplet heating, infinite conductivity and conduction limit. Convection is taken into account by correlation laws, where fluctuating quantities for velocities, temperature or concentration are introduced. The influence of turbulence on the droplet evaporation in homogeneous turbulence is discussed, the results also being compared with simulations which involve mean quantities only.

Dispersion of discrete particles by continuous turbulent motions. Extensive discussion of the Tchen’s theory, using a two‐parameter family of Lagrangian correlation functions

The theory of dispersion of discrete particles by continuous turbulent motions is first expressed in a 3‐D formalism, as a synthesis between the 1‐D Tchen’s theory of dispersion and the 3‐D Batchelor’s theory of diffusion. Then it is exemplified with the aid of a two‐parameter Frenkiel family of Lagrangian correlation functions, taking into account the Basset’s term or neglecting it. It is then shown and explained that even dense discrete particles may disperse faster than fluid particles. That work is included in a more general framework aiming at modeling and predicting the behavior of discrete particles in turbulent flows.

Dispersion of discrete particles by continuous turbulent motions: New results and discussions

A number of results for the Tchen theory of dispersion of discrete particles by continuous turbulent motion are recalled. A Frenkiel family of Lagrangian correlation functions is used and the main results are rewritten in nondimensional form. The theory is completed by a new relation expressing the mean square of the relative particle velocity. The validity of the Stokes contribution to the Tchen equation of motion is examined. Numerical results are given and discussed.

Numerical simulation of surface tension- and combined buoyancy-driven convection in a liquid layer heated by a hot wire

Abstract The characteristics of convection in liquid layers heated below the free surface are numerically studied. The mechanisms for convection are buoyancy and variation of surface tension with respect to temperature. Specific computations are performed to stress the influence of heat transfer at the interface and of interfacial viscosities. The transition between Marangoni and buoyancy regimes, when heating by an infinite hot wire located below the free surface, is investigated.

Lagrangian Simulation of Particle Dispersion

Eulerian and Lagrangian approaches have been studied at Rouen for the prediction of particle dispersion in turbulent flows. A first computer code DISCO (Dispersion computing) has been developed during the past Years for predicting turbulence and the dispersion of discrete particles in the framework of an Eulerian approach. In that method, the particles are considered as a continuum and satisfy a transport equation which involves a dispersion tensor linked to particles and fluid characteristics. The Tchen theory (on discrete particle displacement) and the Batchelor theory (for diffusion of fluid particles) are used to determine the dispersion tensor, and a correction factor is defined to take into account for the crossing trajectories effects.

Prediction and Simulation of the Behaviour of Discrete Particles Transported by Turbulent Flows: a Review Paper

The realm of multiphase flows and problems is very vast and indeed potentially infinite. In the Universe fluids are nearly everywhere, and when they occur they almost invariably contain particles. Inside our bodies we can take the example of blood transporting a vital procession of red and white cells. Around us, we can find various particles in the air we breathe, bubbles in the champagne or the soda we drink, or natural and artificial (polluting!) particles in the lakes we swim in. These examples correspond to the case when discrete particles are transported by flows. They could be filed as suspensions of particles in fluids, bubbly flows and drop flows. But considering only these cases would be forgetting about slug and annular flows, and the various combinations and transitions between all these regimes. Numerous models have been designed to understand and study all these situations, from empirical correlations and homogeneous models to more sophisticated approaches : separated flows, drift-flux models, differential or integral analysis... It is impossible to do justice to such a large topic in a limited review paper. Consequently we shall limit our discussion to the case of discrete particles transported by turbulent flows for which our personal knowledge is a bit more than scholar.