WO2009059960A1

WO2009059960A1 - Method of modelling a multiphase fluid sheet

Info

Publication number: WO2009059960A1
Application number: PCT/EP2008/064913
Authority: WO
Inventors: Erick Meillot; Guillaume Balmigere; Stéphane Vincent; Jean-Paul Caltagirone
Original assignee: Commissariat A L'energie Atomique
Priority date: 2007-11-09
Filing date: 2008-11-04
Publication date: 2009-05-14
Also published as: EP2208156A1; FR2923628A1

Abstract

The present invention relates to a method of modelling a multiphase fluid sheet. The method comprises at least: a one-fluid bulk Eulerian description of the distribution of the phases in the calculation domain (1, 2, 3), discretized by a network of Eulerian grid cells, the phase information being carried by dummy particles, called markers, distributed within the network of grid cells; - Lagrangian modelling (4, 5, 6), inside the grid cells, of revolution of the interfaces, an interface separating the markers of a given phase from the markers of another phase. The invention applies in particular in respect of the simulation of multiphase flows, applied for example to the fragmentation of a liquid jet subject to thermal stresses. More generally, the invention applies to applications involving a free surface between two fluids.

Description

METHOD FOR MODELING A FLUID TABLE

MULTIPHASE

The present invention relates to a method for modeling a multiphasic fluid sheet. It applies in particular to the multiphase flow simulation, for example for the analysis of the fragmentation or flow of a liquid jet subjected to hydrodynamic and thermal stresses. More generally, the invention relates to applications involving a free surface between two fluids.

For the development of industrial activities involving flows with several fluids, it has been sought to fractionate the liquid layers in the form of droplets mainly for the purpose of economy, rationality and efficiency. Indeed, the transfers are all the more effective as the exchange surface between the different phases is large. Thus the use of liquid particles, of calibrated size or not, is involved in many industrial applications. Spraying paint and, more broadly, surface treatments or fuel injection in engines are examples of applications. Other industrial applications are known in the agri-food, pharmaceutical or cosmetic sectors in particular. Generally, the production of this type of droplet is carried out using sprayers whose major families include mechanical sprayers, pneumatic sprayers and wave sprayers. Each of them uses different fragmentation processes. In mechanical sprayers, the pressure difference applied to the fluid reservoir leads to the splitting of the outgoing liquid layer. The pneumatic sprayers use a gas assistance responsible for the fractionation of the liquid layer by shearing or tearing of the drops. The third family uses electrostatic waves that weaken and destroy the liquid layer as it leaves the injector.

We tried to quantify and qualify the generation of drops irrespective of their industrial application, most often experimentally. Empirical relationships have been developed between the operating conditions of sprayers and the physicochemical properties of fluids used to the macroscopic structure and the particle size of the jets from the sprayers. This particle size distribution is valid only locally, at the exit of a sprayer, and the evaluation of the size of the drops during their duration of flight in a hostile atmosphere, due in particular to a high temperature or to a chemical reactivity, does not can be accessed only by long, expensive and often difficult to implement experimental diagnoses.

Experimental methods are insufficient. Numerical modeling has been used. These use computerized means such as programming languages and powerful computers that will use fluid mechanics flow codes capable of handling immiscible fluids. The numerical representations of the interface between two immiscible fluids differ mainly in the way in which the field of study is discretized. Several methods of interface tracking are known.

A first category does not use mesh, in particular the method known as "Smoothed Particles Hydrodynamics" (SPH), for which the advection phase is represented by a finite number of interacting particles whose movement is ensured exclusively by a particle tracking . The fields and their spatial derivatives are calculated for each particle by summation and weighting of the properties of the other particles. Since it does not use a mesh for the spatial discretization of the domain, the SPH method avoids the difficulties related to interpolations and projections encountered with the other methods. It presents little digital diffusion and, because of its independence vis-à-vis a mesh, it makes it possible to treat problems involving irregular, mobile and deformable limits. On the other hand, it remains more expensive than the other methods for comparable results. It is generally used for compressible flow problems. An SPH method is described in particular in the JJ document. Monaghan "Simulating Free Surface Flows with SPH", Journal of Computational Physics, 110, pp 399-406, 1994.

A second family is that called Lagrangian methods. These methods are based on the discretization of the domain of one of the two fluids and consider the interface between the two fluids as a boundary of the domain. The Navier-Stokes equations used are solved only in the discretized fluid without taking into account the other fluid. Thus, Lagrangian methods rely on an adaptive mobile mesh whose boundaries follow the shape of the interfaces. The evolution of the free surface is therefore accurately described thanks to a local reconstruction or enrichment of the mesh over time as a function of the deformations of the interface. In addition, the boundary conditions can be rigorously imposed at the interface without bulk approximation. Nevertheless, the use of Lagrangian methods is limited to small deformations of the interface. In the case of significant deformations, their cost quickly becomes prohibitive due to the reconstruction and enrichment of the mesh at each time step or at each iteration. Moreover, excessive deformation of the mesh does not ensure a good resolution of the flow. These methods do not make it possible to apprehend the birth or the disappearance of the interfaces which occur in the phenomena of rupture or coalescence. Finally their programming is complex in three dimensions. A Lagrangian method is described in particular in the document by JM Floryan and H. Rasmussen "Numerical method for viscous flows with moving boundaries", Applied Mechanics Reviews, 42 (12), pages 323-341, 1989.

The so-called Eulerian methods, contrary to the approach described previously, rely on the discretization of the totality of the flow on a fixed mesh, independent of the spatial and temporal evolution of the interface. These methods require the introduction of an additional variable and an equation to follow the evolution. This type of approach is called the 1-fluid model because of the approximation of the mixture by a single medium fluid at the interfaces. The Eulerian approach is in turn divided into two categories, the front-end monitoring methods and the volume monitoring methods. The documents of JM Hyman "Numerical methods for tracking interfaces" Physical D: Nonlinear phenomena, 12, pages 396-407, 1984 and D. Lakehal & al "Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows" , International Journal of Heat and Fluid Flow, 23, pages 242-257, 2002 propose some of the most used Eulerian interface methods. Edge tracking methods use markers positioned on the interface and interconnected, thus forming a secondary mesh of the surface between the two fluids. The position of the interface is therefore known precisely in a finite number of points corresponding to the secondary mesh. This topological information is projected towards the Eulerian mesh on which the fields of speed, temperature and the phase function are discretized. These methods give a precise description of the position and the orientation of the interface, but their implementation remains delicate as long as the interfaces evolve temporally, split or reconnect, in particular because of the management of the markers. In the case of volume tracking methods, the stored information no longer relates to the explicit position of the interface, but to the presence rate of each of the phases in each calculation mesh.

Among the Eulerian methods, mention may be made of the so-called MAC methods, the so-called VOF methods and the so-called "Level-Set" methods. In the case of the so-called MAC methods, Markers and CeIIs, particles without mass are positioned in one of the fluids of the model and followed in their movement in a Lagrangian manner. The stored information is the number of particles in a mesh. Meshes containing no particles are said to be empty and are occupied entirely by one of the fluids. Meshes containing particles and adjacent to an empty mesh are necessarily traversed by the interface and the other meshes containing particles are occupied by the other fluid. The exact position of the interface is not known, as is its orientation and curvature. MAC methods can deal with problems of breakage or coalescence but require significant storage capacity for the position of the particles. They are notably described in the document by PE Raad et al. The Journal of Computational Physics, 203, pages 668-699, 2005. In the Fluid volume methods, called VOF, the notion of markers has a physical meaning. Fluids are localized by their rate of presence, or volume fraction, in each mesh, which has the advantage of considerably reducing the amount of information to be stored. These methods are usually coupled to an interface reconstruction method based on the distribution of the presence rate. The VOF methods ensure the conservation of the mass of each fluid and give a good knowledge of the position of the interfaces. They are notably described in the documents of M. Rudman "A volume-tracking method for incompressible multifluid flows with large density variations", International Journal for Numerical Methods in Fluids, 28, pages 357-378, 1998 and WJ. Ryder & al. Reconstructing Volume Tracking, Journal of Computational Physics, 141, pp. 112-152, 1998.

In the "Level-Set" method, edge tracking is provided by a discretized function on the global Eulerian mesh. This algebraic function, which constitutes the signed distance from each point to the interface, and whose sign depends on the fluid in which one is located, is canceled at the interface. It is a distance function to know the exact position of the interface through the resolution of a transport equation. It does not require projection or reconstruction. Nevertheless, it generates digital diffusion and does not respect the conservation of the mass. An algorithm for redistributing this distance function makes it possible to limit these effects.

The limits of the Eulerian methods are reached when the characteristic scales of the interface are smaller than the size of the mesh. This results in non-mass conservation effects for the "Level-Set" methods, artificial splitting for VOF methods, or significant digital diffusion. Mixed methods have recently emerged to combine the mass conservation properties of VOF methods with the precision of "Level-Set" or particle methods for interface description. These methods are notably presented in the documents of E. Aulisa & al. A mixed markers and volume-of-fluid method for the reconstruction and advection of two-phase and free-boundary-flow interfaces, Journal of Computational Physics, 188, pages 61-639, 2003 and E. Ishii & al. Hybrid Particle / Grid Method for Predicting Motion Micro-and-Macrofree Surfaces, Journal of Fluids Engineering, 128, pp. 921-930, 2006. In addition, modeling of physical effects such as surface tension and phase change is no longer taken into account when the characteristic scales of the diphasic medium are smaller than the mesh. None of the existing approaches makes it possible to understand all the mechanisms involved in the fragmentation of a liquid layer over a wide range of scales. The processes of liquid sheet fragmentation usually involve large scale ratios, leading to the impossibility of solving all the structures resulting from the successive fragmentations. The previous Eulerian methods offer the advantage of a volumic approach to the flow but are limited as regards the fineness of resolution, at the scale of the mesh. Therefore, they filter the interface structures that will be called "sub-meshes" later and therefore require a complementary approach to model sub-mesh phenomena for a given mesh.

An object of the invention is in particular to overcome the aforementioned limits and to make it possible to follow the fragmentation of a liquid sheet in the form of droplets until its complete disappearance as a continuous phase, and then to jointly monitor the population of drops as well as created. The invention thus makes it possible to understand the processes of fragmentation of the liquid layer inherent in many industrial processes.

For this purpose, the subject of the invention is a method of modeling a multiphase fluid layer on a computing domain to analyze the fragmentation of said sheet or its flow, said method being implemented by at least one computer performing at least one computer. minus: - a eulerian volumic description stage 1 -fluid of the phase distribution in the computational domain, discretized by an Eulerian mesh network, the phase information being carried by fictitious particles, called markers, distributed in the network of meshes and carriers of the fi phase information; a lagrangian modeling step, within the meshs, of revolution of the interfaces, an interface separating the markers of a given phase from the markers of another phase.

The Eulerian description may include a step of initial generation of the markers within the meshes. The markers are for example distributed substantially uniformly in the mesh network.

In a particular mode of implementation, the method being iterative, for each time step, the Eulerian description includes a step of solving the conservation equations of the momentum under their formulation 1-incompressible fluid giving the knowledge of the speed field on the mesh network from the physical properties of the computational domain.

Lagrangian modeling is preceded by a marker transport step, this transport step comprising, for example:

a step of interpolating the speed of the markers from the speed to the nodes of the mesh network;

a step realizing the displacement of the markers from the interpolated speeds; a marker management step that retains a substantially homogeneous distribution of the markers inside the meshes. Advantageously, the displacement of the markers is for example carried out according to a temporal scheme of the Euler, Runge-Kutta or "Time-Splitting" type. According to a particular mode, in the management step: the particles leaving the calculation domain during the displacement step are repositioned in the rarefied cells;

the particles are transferred from the densest zones to the rarefied zones;

the phase information is updated and its value depends on the fluid in which the particle is repositioned.

Advantageously, in Lagrangian modeling, the isolated markers are detected in order to apply to them a specific model of fragmentation. For example, Lagrangian modeling involves at least:

a first step where the Eulerian meshes containing liquid and mainly surrounded by gas mesh are identified, these Eulerian meshes indicating the zones of fragmentation of the fluid;

a second step where, in the cells thus identified, the fragmentation of the markers is modeled as drops of liquid.

Lagrangian modeling can be followed by a stage of projection of the phase information of the markers to their new positions, towards the Eulerian mesh network to build the volume fraction field at the next time step.

The method comprises for example a step of calculating the physical properties of the calculation domain from the volume fraction field.

The invention particularly requires the use of a computer performing a fluid mechanics treatment capable of working jointly in Eulerian and Lagrangian mode. The method according to the invention is advantageously integrated in any fluid mechanics processing block as a separate module dedicated to the treatment of the monitoring of the different phases of fluids in the presence.

Other features and advantages of the invention will become apparent with the aid of the following description made with reference to the appended drawings which represent: FIG. 1, a presentation of the possible steps for implementing the method according to the invention ;

FIG. 2, an example of initial distribution of markers in a discretized calculation domain;

- Figure 3, a presentation of possible intermediate steps forming a transport step;

FIG. 4, an illustration of the distribution of the phases of the fluid before the transport step;

FIG. 5, an illustration of a step of interpolation of the speeds of the markers; FIG. 6, an illustration of the distribution of the phases after the transport of the markers;

FIG. 7, an example of steps forming the Lagrangian modeling used by the method according to the invention.

Figure 1 shows the possible steps for implementing the method according to the invention. This method is based on the consideration of sub-mesh phenomena, inside the meshes, by reconciling the description of the phases by a population of markers, underlying the MAC methods described above, and the voluminal description of the properties. of the two-phase medium of the VOF methods. In a first step 1, an Eulerian description of the context is made. Thus, in this first step 1, the problem to be processed is translated numerically into the mechanical calculation code used. The problem to be treated is for example translated numerically by: the dimensions of the computation domain and the parameterization of the corresponding mesh;

the fluids in the presence and their physical properties;

- the boundary conditions;

- the initial conditions relating to the variables to be solved. The domain of calculation concerns a part of the liquid layer to be modeled. This domain is defined by the user. In particular, it must be chosen large enough to take into account the phenomena that the user wishes to simulate. For example, in the case of application to a fuel injection, the calculation domain may include a part of the interior of the injector and a part of the reaction chamber at the outlet of this injector.

Once the computational domain has been defined, the definition of the problem and its numerical translation make use of known techniques and are independent of the method according to the invention. In particular, a translation requires knowledge of the initial fields of physical properties, speed and phase distribution, as well as the nature of the boundaries of the domain, open, closed or periodic. These data are traditionally required in any fluid mechanics code. In a second step 2, a set of fictitious particles, forming markers, is generated in all or in a characteristic sub-part of the cells of the domain. In each of these meshes, the number of markers is arbitrary. These particles are provided with information relating to the initial distribution of the phases in the presence of at least fi phase information. In a third step 3, the Navier-Stokes equations, or conservation of the momentum, are solved so as to obtain the speed and temperature field in the whole of the computation domain. This step can be carried out independently of the method according to the invention thanks in particular to the computation code in fluid mechanics used. Only source terms corresponding to the taking into account of the Surface tension or phase change are added in the conservation equations.

In a fourth step 4, each particle is transported from its current position and the Eulerian velocity field interpolated to the positions of the particles in the mesh.

A fifth step 5 performs Lagrangian modeling. In this step, a scaling is performed by focussing at an isolated particle. The process thus passes from the scale of a mesh in Eulerian modeling to that of a subgrid, the isolated particle, in Lagrangian modeling. For this purpose, the isolated particles are detected so as to apply to them a specific model of fragmentation or phase change.

In a sixth step 6, the information carried by the particles of the Lagrangian model is projected onto the Eulerian mesh so as to obtain a volume description of the volume fraction field.

In a seventh step 7, the physical properties of the domain are recalculated from the Eulerian volume fraction field. At the end of this step, these physical properties are used for the next iteration, which starts again with the calculation of the Navier-Stokes equations for obtaining the velocity field for the next time step. The iteration of steps 3 to 7 is performed for all the successive time steps. Exemplary embodiments of these steps will be described later.

FIG. 2 illustrates an initial distribution of markers 20 in a discretization grid 21 obtained in the second stage 2 of generating markers according to an Eulerian method. These markers are distributed in meshes 22 of the Eulerian grid covering the discretization domain defined in the first step. In this first step 1, the computational domain is discretized by one or more networks of points 23, forming the Eulerian nodes of the discretization grid. An array of points 23, or mesh, can be assigned to the scalar values including in particular the pressure or the temperature to discretize the latter. Similarly another network of points can be used to discretize vector values such as speed by example. For example, a single network can be assigned to both scalar values and vector values.

The population of Eulerian nodes 23 of the calculation as well as their position in space are known. A user then defines a set of fictitious particles forming the aforementioned markers. Initially, for the sake of simplification of the method, for example, the same quantity of markers is present in each mesh 22. In the example of FIG. 2, each mesh thus has four markers 20. More generally, if n is the initial number of markers per unit cell, n = n _m ^d n where _m is the initial number of markers in each direction in each cell defined by the user and is the number of dimensions of the problem, where d is equal to two for a modeling according to a plane and d being equal to three for a volume modeling in space. In the latter case, the meshes 22 of Figure 2 correspond in fact to cubes, other mesh shapes being possible.

Four data can thus be stored for each marker i, i ^θmθ marker of a cell k:

the number of its reference node 23, corresponding to the mesh 22 in which the marker is located; its relative coordinates, calculated with respect to the reference node;

the phase in which it is situated, by means of a variable f i, a phase indicator of this marker ^iθ , equal to 0 or 1 depending on whether the marker is in one or the other of the fluids in the presence ; its participation in the weight W _k of fluid, where w _k D = -, expressing the

/ j J ι n portion of the fluid contained in the mesh k represented by its markers.

The initial position of the particles 23 in a mesh may, as desired, be imposed on a regular basis, as illustrated in FIG. 2, or randomly.

The third step 3 carries out the resolution of the conservation equations of the energy and the momentum of the system, these equations are the Navier-Stokes equations in incompressible or compressible regime, Euler, or Boltzmann. For example, a 1-fluid formulation, called mesoscopic, is used which makes it possible, in particular, to take into account the movements of the interface between the phases by introducing an advection equation of the local volume fraction C of one of the two fluids in presence. For example, in an incompressible regime, the equations to be solved are then the following equations (1) to (3):

V.M = 0 (1)

V. is the divergence operator and û is the velocity of the fluid.

For an incompressible flow, the divergence of the velocity is zero as specified by equation (1).

P \ γ + û.grad {u) \ = pg - grad (p) + grad {(μ + μ _t) (Vw + V ^τ u) + F _τs (2)

pC - + û.grad (T) \ = V.λ.grad (T) + F _C

grad being the gradient, vector size.

Scalar variables p, μ, μ _t, p, T, A, C _p, F _cp represent the density, the viscosity, the eddy viscosity obtained from any model of integrated turbulence, pressure, temperature, thermal conductivity, local specific heat and the phase change source term. The vector variables u, g, F _τs respectively represent the fluid velocity, the gravitational acceleration and the surface tension.

This system of conservation equations can be the same for the entire flow and the fluids in the presence are localized by the volume fraction. This approach is comparable to that of the VOF methods presented previously. It is based on the Eulerian volume representation of the phase distribution. The resolution of the Navier-Stokes equations by the calculation code used, in the previous step 3, provides the knowledge of the velocity field on the Eulerian grid 21 of the computation domain. Figure 3 shows the possible intermediate steps of the fourth step 4 of transporting the markers. In this implementation example, the fourth step comprises three steps 41, 42, 43. A first intermediate step 41 interpolates the speed field to the position occupied by the particles 20.

FIG. 4 illustrates the distribution of the phases of the fluid in the computation domain before the transport step, the phases being separated by an interface 51. This interface travels through the meshes 22 of the domain. Markers 20 include phase information. Thus, the markers located on one side of the interface carry the information specific to this phase, for example 0 if this information is binary. The markers located on the other side of the interface carry the information specific to the second phase, for example 1. By way of illustration, this binary phase information is represented in FIG. 5 by a color, the representations of the markers 20 located in one phase being white and the markers in the other phase being gray. Before the transport step, the markers remain uniformly distributed in the mesh.

FIG. 5 illustrates step 41 of interpolation of the speeds of the discretization grid towards the particles. The speed iij of a particle, in this case a marker of a mesh, is extrapolated from the velocities v _n1 , v _n2 , v _n3 , v _n4 of the nodes 23 of the mesh. The velocities v _n1 , v _n2 , v _n3 , v _n4 of the nodes were obtained for them in the previous step by solving the Navier-Stokes equations.

Lagrangian transport of particles requires an estimation of their speed. This is for example assumed equal to the speed of the fluid at the position of the particle. Since the discrete knowledge of the velocity field is not available, it must be interpolated from the Eulerian fixed mesh to the position of each particle. Several interpolation methods can be used. It is thus possible to use in particular a quadratic interpolation of order 1 or 2, a interpolation by Lagrange polynomial of order 1 to 3, a Pesquin interpolation, or an exponential interpolation. Each of these interpolation schemes can also be filtered on the phase function. The choice of the interpolation method is free and results from a compromise between the degree of precision sought and the calculation time to be devoted to the transport step. A second intermediate step 42 moves the markers. Each particle being assigned a speed iij calculated in the previous intermediate step 41, it can be transported according to a known time scheme, for example of the type "time splitting", Euler or Runge-Kutta. The relative coordinates of the particles 20 are then updated, as well as their reference node as soon as they cross a mesh of the computation domain.

A third intermediate step 43 performs the management of the markers. Indeed, the transport step 42 affects the distribution of the markers in the field of computation, leading to their rarefaction, especially in the injection zones, and their densification in the stagnation zones such as the walls. In the computational domain with open boundaries, it is possible that the domain is partially or totally empty of its particles.

FIG. 6 illustrates the distribution of the phases after the displacement of the markers 20. The interface 51 separating the two phases has moved. Figure 6 shows meshes 71 without particles, meshes 72 where the particles 20 have become rarefied. Other meshes 73 have a high density of particles 20.

The intermediate management step 23 makes it possible to maintain a substantially homogeneous distribution of the markers 20, which are moreover fictitious particles, in particular to guarantee a minimum number of these particles in each cell of the discretization grid. So, in this step:

the particles leaving the calculation domain during the transport step 42 are repositioned in the rarefied cells; the particles are transferred from the densest zones to the rarefied zones;

- The phase indicator / is updated and its value depends on the fluid in which the particle is repositioned. FIG. 7 shows intermediate steps constituting step 5 of Lagrangian modeling. This step is for example structured in three steps 81, 82, 83. This step performs the transition from solved scales, at the meshes of the Eulerian domain, to the unresolved scales, at the level of the sub-meshes formed markers.

In a first step 81, the Eulerian meshes containing liquid and mainly surrounded by gas Eulerian meshes are identified, these meshes indicating the zones of fragmentation of the liquid. In a second step 82, in the liquid cells thus isolated, the fragmentation of the markers 20 is modeled as drops of liquid using, for example, an empirical fractionation model based on the local characteristics of the liquid and the surrounding gas. In a third step 83, the fragmented or non-fragmented state of each marker as well as the characteristics of the drops created are stored. For a given marker, the drops created from this marker are assumed to be identical.

The Lagrangian modeling step 5 is followed by the step 6 of projection of the information carried by the fictitious particles, the markers, on the Eulerian mesh. In this step 6, the following information, stored in the previous step 83, is known for each marker:

the reference node, identified for example by a number;

the relative position of the marker in the mesh;

- the phase indicator /,. The volume fraction field is deduced from these data by projection on the mesh of the phase information.

At first the weight Wj is defined. Wj = V _ik where V _ik corresponds to the volume of the particle i contained in the cell k calculated from the initial phase information, translating the fluid portion in the mesh. The weight Wj is defined in order to calculate the volume fraction C _k in each cell k, defined by the following relation:

ΣW f,

C _k = ^ (4)

ΣW, The projection step therefore corresponds to the inter-scale transfer of the phase information, the transfer taking place from the resolved scales to the unresolved scales. Advantageously, the initial description of the distribution of the sub-mesh scale phases via fictitious markers is conserved throughout the calculation, by means of the tools for managing the markers exhibited, in particular during the fourth step 4. Projection step 6 thus forms a bridge between the Lagrangian description and the Eulerian approach for coupling, from a hydrodynamic point of view, the interactions between the phases. At the end of the projection step, in the seventh step 7, the physical properties of the fluid are evaluated at each point of the Eulerian mesh by means of laws of independent mixtures known elsewhere and independent of the method according to the invention. The Eulerian fields of these properties are subsequently used at the next iteration 10, i.e. at the next time step, for the calculation of the speed field at the next time step at step 3 Calculation of Navier-Stokes equations.

The invention advantageously makes it possible to obtain a two-phase flow modeling capable of describing both the macroscopic deformations of a sheet of liquid and of providing the drop size distribution at the end of the fragmentation process, which constitutes a clear advanced compared to the models available in academic and industrial simulation tools. These potentialities have been illustrated in the document by G. BALMIGERE et al. "Use of a mixed interface Eulerian / Lagrangian interface for two-phase flows", 18 ° French Congress of Mechanics, Grenoble, 21 -31 August 2007, without revealing the architecture of the invention.

The prospects of applications in terms of multi-scale and multi-physics flows (phase change, turbulence, energy transfer in particular) are numerous. The advantages of the invention include:

- multi-scale modeling;

- lack of digital broadcasting; - an absence of artificial fragmentation; - increased accuracy;

- accessibility to sub-mesh phenomena and conservation of phase information allowing the use of a mesh less dense than that required by the previous methods.

Thus, the invention allows industrial applications following very large areas, from the microscopic scale (fragmentation of drops or bubbles, presence of fluid filaments) to the macroscopic scale (free surface, dam rupture, wave description, jets, pockets or macro-drops ...).

The fields of industrial applications, very varied, are for example the dimensioning and the characterization of installations or industrial products such as a fuel injector for internal combustion engine or diesel, an atomizer or a sprayer, thermal projection of solution or suspension, the filling of molds and more generally the channelization of liquid fluids, the flows of free or confined fluids, the exchangers and the reactors with or without a phase change, the steel processes, the lubrication processes in industrial applications.

The invention therefore advantageously makes it possible to apprehend the process of fragmentation or flow of liquid sheets inherent in numerous industrial processes, by forming a representative model of the flows of fluids present in this context, and this in an efficient and economical way, especially in computing time.

More particularly, the invention makes it possible to follow the fractionation of a liquid layer at any moment of its evolution until its complete disappearance as a continuous phase and to follow together the population of drops formed. It provides access to the main physical quantities of liquid particles resulting from the fractionation of a liquid layer, such as in particular temperature, speed and diameter. It also allows to model the effects of surface tension and phase change over a wide range of scales ranging from that of the continuous phase to that of small interfacial structures.

Claims

A method of modeling a multiphasic fluid sheet on a computational domain for analyzing the fragmentation or the flow of said sheet, characterized in that said method is implemented by at least one computer performing at least: a Eulerian volumetric description step 1 -fluid of the phase distribution in the computational domain, discretized (21) by an Eulerian mesh lattice (22), the phase information being carried by fictitious particles (20), called markers, distributed in the mesh network; a lagrangian modeling step, inside the meshes (22), of revolution of the interfaces, an interface separating the markers of a given phase from the markers of another phase.

2. Method according to claim 1, characterized in that the eulerian description step comprises a step (2) of initial generation of the markers inside the meshes.

3. Method according to any one of the preceding claims, characterized in that the markers (20) are distributed substantially uniformly in the mesh network

4. Method according to any one of the preceding claims, characterized in that said method being iterative (10), for each step of time, the Eulerian description step comprises a step (3) of solving the conservation equations of the quantity of motion under their formulation 1-incompressible fluid giving the knowledge of the velocity field on the network of meshes from the physical properties of the domain of computation.

5. Method according to any one of the preceding claims, characterized in that the lagrangian modeling step is preceded by a step (4) for transporting markers (20), said transport step comprising: a step (41) for interpolating the speed of the markers from the speed of the nodes (23) of the mesh network;

a step (42) realizing the displacement of the markers from the interpolated speeds; a marker management step (43) retaining a substantially homogeneous distribution of the markers inside the meshes.

6. Method according to claim 5, characterized in that the displacement of the markers is carried out according to an Euler, Runge-Kutta or "Time-Splitting" type time scheme.

7. Method according to any one of claims 5 or 6, characterized in that in the management step (43):

the particles leaving the calculation domain during the displacement step (42) are repositioned in the rarefied meshes (71,

72);

the particles are transferred from the densest zones (73) to the rarefied zones;

- The phase information (/ J is updated and its value depends on the fluid in which the particle is repositioned.

8. Method according to any one of the preceding claims, characterized in that in the lagrangian modeling step, the isolated markers are detected in order to apply to them a specific model of fragmentation.

9. Method according to claim 8, characterized in that the Lagrangian modeling step comprises at least:

a first step (81) in which the Eulerian meshes containing liquid and mainly surrounded by gaseous mesh are identified, these Eulerian meshes indicating the zones of fragmentation of the fluid; a second step (82) in which, in the cells thus identified, the fragmentation of the markers (20) is modeled as drops of liquid.

10. Method according to any one of claims 4 to 9, characterized in that the lagrangian modeling step is followed by a step (6) of projecting the phase information of the markers (20) to their new positions, to the Eulerian mesh network to build the volume fraction field at the next time step.

11. The method of claim 10, characterized in that it comprises a step (7) for calculating the physical properties of the calculation domain from the volume fraction field.

12. Method according to any one of the preceding claims, characterized in that it is applied on a microscopic scale.

13. Method according to any one of the preceding claims, characterized in that it is applied to the macroscopic scale.

14. Computer program product, characterized in that it implements the method according to any one of the preceding claims.