Saint-Zacharie, France
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Bodard S.,RS2N | Jalbaud O.,Polytechnic Marseille | Saurel R.,RS2N | Saurel R.,Aix - Marseille University | And 2 more authors.
Physics of Fluids | Year: 2016

Compression of monodisperse powder samples in quasistatic conditions is addressed in a pressure range such that particles fragmentation occurs while the solid remains incompressible (typical pressure range of 1-300 MPa for glass powders). For a granular bed made of particles of given size, the existence of three stages is observed during compression and crush up. First, classical compression occurs and the pressure of the granular bed increases along a characteristic curve as the volume decreases. Then, a critical pressure is reached for which fragmentation begins. During the fragmentation process, the granular pressure stays constant in a given volume range. At the end of this second stage, 20%-50% of initial grains are reduced to finer particles, depending on the initial size. Then the compression undergoes the third stage and the pressure increases along another characteristic curve, in the absence of extra fragmentation. The present paper analyses the analogies between the phase transition in liquid-vapour systems and powder compression with crush-up. Fragmentation diagram for a soda lime glass is determined by experimental means. The analogues of the saturation pressure and latent heat of phase change are determined. Two thermodynamic models are then examined to represent the crush-up diagram. The first one uses piecewise functions while the second one is of van der Waals type. Both equations of state relate granular pressure, solid volume fraction, and initial particle diameter. The piecewise functions approach provides reasonable representations of the phase diagram while the van der Waals one fails. © 2016 Author(s).

Saurel R.,Aix - Marseille University | Chinnayya A.,University of Poitiers | Carmouze Q.,RS2N | Carmouze Q.,French National Center for Scientific Research
Physics of Fluids | Year: 2017

Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none are able to cover accurately the entire range, in particular regarding waves propagation. In the present work, an alternative to the Baer and Nunziato (BN) model [Baer, M. R. and Nunziato, J. W., "A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials," Int. J. Multiphase Flow 12(6), 861 (1986)], initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble model [Marble, F. E., "Dynamics of a gas containing small solid particles," Combustion and Propulsion (5th AGARD Colloquium) (Pergamon Press, 1963), Vol. 175] based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 characteristic wave speeds as well, but with different velocities. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave speeds as the BN model, but at a given point of space, 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock-particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data showing clear improvements.

Patryl L.,CEA DAM Ile-de-France | Lapebie E.,CEA DAM Gramat | Hank S.,RS2N | Armand P.,CEA DAM Ile-de-France
HARMO 2014 - 16th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes, Proceedings | Year: 2014

Developed at CEA since 2008, CERES® CBRN-E is a computational tool designed for crisis management in case of accidental, malevolent or terrorist releases of hazardous radiological, chemical or biological materials. More precisely, CERES® computes atmospheric dispersion in complex environments including buildings (industrial sites or urban areas), assesses the health consequences of the toxic releases on the population and first responders, and delivers operational results (e.g. danger zones, intervention zones...) in less than 15 minutes to rescue teams and decision makers. CERES® is a flexible modular platform, thus capable to integrate both simplified and advanced models adapted to the description of the scenario (leakage from storage, evaporation from a pool, fire⋯), the AT&D of the hazardous material and the CBRN impact evaluation. This paper aims at discussing two recent developments in CERES®. The first one relates to high-Mach source terms simulation in case of an explosion preceding the toxic dispersion. The near-field unstationary source terms generated by energetic reactions are included in CERES® using either analytical relations (gathered in the so-called D2R2 modules) derived from multiphase pre-computations or a direct coupling between the pre-established transient results of the HI2LO code (a CFD model able to deal with the transition from high to low-Mach number flows) and CERES®. These models provide the source term geometry and the noxious material granulometry and spatial distribution after the explosion, taking into account the presence of the buildings in the simulation domain. The second development consists in the implementation in CERES® of a simple method for source term estimation using in-field sensors measurements. In a first step, retro-plumes are propagated individually from each of the detectors. In a second step, the possible locations of the source and associated releases rate are determined by retro-plumes overlapping. For both developments, the paper gives more details about the methodology and the validation of the new modules based on experimental data. © Crown Copyright 2014 Dstl.

Saurel R.,Aix - Marseille University | Le Martelot S.,RS2N | Tosello R.,Directorate General of Armaments | Lapebie E.,CEA DAM Gramat
Physics of Fluids | Year: 2014

Compressible granular materials are involved in many applications, some of them being related to energetic porous media. Gas permeation effects are important during their compaction stage, as well as their eventual chemical decomposition. Also, many situations involve porous media separated from pure fluids through two-phase interfaces. It is thus important to develop theoretical and numerical formulations to deal with granular materials in the presence of both two-phase interfaces and gas permeation effects. Similar topic was addressed for fluid mixtures and interfaces with the Discrete Equations Method (DEM) [R. Abgrall and R. Saurel, "Discrete equations for physical and numerical compressible multiphase mixtures," J. Comput. Phys. 186(2), 361-396 (2003)] but it seemed impossible to extend this approach to granular media as intergranular stress [K. K. Kuo, V. Yang, and B. B. Moore, "Intragranular stress, particle-wall friction and speed of sound in granular propellant beds," J. Ballist. 4(1), 697-730 (1980)] and associated configuration energy [J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, "Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues," Phys. Fluids 11, 378 (1999)] were present with significant effects. An approach to deal with fluid-porous media interfaces was derived in Saurel et al. ["Modelling dynamic and irreversible powder compaction," J. Fluid Mech. 664, 348-396 (2010)] but its validity was restricted to weak velocity disequilibrium only. Thanks to a deeper analysis, the DEM is successfully extended to granular media modelling in the present paper. It results in an enhanced version of the Baer and Nunziato ["A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials," Int. J. Multiphase Flow 12(6), 861-889 (1986)] model as symmetry of the formulation is now preserved. Several computational examples are shown to validate and illustrate method's capabilities. © 2014 AIP Publishing LLC.

Hank S.,RS2N | Saurel R.,Institut Universitaire de France | Le Metayer O.,Aix - Marseille University | Lapebie E.,CEA DAM Gramat
Journal of Hazardous Materials | Year: 2014

The numerical simulation of shock and blast waves as well as particles dispersion in highly heterogeneous media such as cities, urban places, industrial plants and part of countries is addressed. Examples of phenomena under study are chemical gas products dispersion from damaged vessels, gas dispersion in urban places under explosion conditions, shock wave propagation in urban environment. A three-dimensional simulation multiphase flow code (HI2LO) is developed in this aim. To simplify the consideration of complex geometries, a heterogeneous discrete formulation is developed. When dealing with large scale domains, such as countries, the topography is considered with the help of elevation data. Meteorological conditions are also considered, in particular regarding complex temperature and wind profiles. Heat and mass transfers on sub-scale objects, such as buildings, trees and other obstacles are considered as well. Particles motion is addressed through a new turbulence model involving a single parameter to describe accurately plumes. Validations against experiments in basic situations are presented as well as examples of industrial and environmental computations. © 2014 Elsevier B.V.

LeMartelot S.,Aix - Marseille University | Nkonga B.,RS2N | Nkonga B.,French National Center for Scientific Research | Saurel R.,Aix - Marseille University | Saurel R.,Institut Universitaire de France
Journal of Computational Physics | Year: 2013

All speed flows and in particular low Mach number flow algorithms are addressed for the numerical approximation of the Kapila et al. [1] multiphase flow model. This model is valid for fluid mixtures evolving in mechanical equilibrium but out of temperature equilibrium and is efficient for material interfaces computation separating miscible and non-miscible fluids. In this context, the interface is considered as a numerically diffused zone, captured as well as all present waves (shocks, expansion waves). The same flow model can be used to solve cavitating and boiling flows [2]. Many applications occurring with liquid-gas interfaces and cavitating flows involve a very wide range of Mach number, from 10-3 to supersonic (and even hypersonic) conditions with respect to the mixture sound speed. It is thus important to address numerical methods free of restrictions regarding the Mach number.To do this, a preconditioned Riemann solver is built and embedded into the Godunov explicit scheme. It is shown that this method converges to exact solutions but needs too small time steps to be efficient. An implicit version is then derived, first in one dimension and second in the frame of 2D unstructured meshes. Two-phase flow preconditioning is then addressed in the frame of the Saurel et al. [3] algorithm. Modifications of the preconditioned Riemann solver are needed and detailed. Convergence of both single phase and two-phase numerical solutions are demonstrated with the help of single phase and two-phase steady nozzle flow solutions. Last, the method is illustrated by the computation of real cavitating flows in Venturi nozzles. Vapour pocket size and instability frequencies are reproduced by the model and method without using any adjustable parameter. © 2013 Elsevier Inc.

Le Martelot S.,RS2N | Saurel R.,RS2N | Saurel R.,Institut Universitaire de France | Saurel R.,Aix - Marseille University | Nkonga B.,French National Center for Scientific Research
International Journal of Multiphase Flow | Year: 2014

A flow model is built to capture evaporating interfaces separating liquid and vapour. Surface tension, heat conduction, Gibbs free energy relaxation and compressibility effects are considered. The corresponding flow model is hyperbolic, conservative and in agreement with the second law of thermodynamics. Phase transition is considered through Gibbs energy relaxation, in the same mind as in Saurel et al. (2008). Surface tension effects are modelled following the lines of Brackbill et al. (1992). There is thus no need to resolve the interface structure as jump conditions are inherent features of the model formulation. With the present approach, the same set of partial differential equations is solved everywhere, in pure fluids as well as in the captured diffuse interface. There is thus a unique hyperbolic flow solver that handles flow dynamics, interface motion and eventually acoustic wave dynamics. To make distinction between "pure" fluids and liquid-vapour mixture treatment, different sets of algebraic equations are considered in the relaxation solver. To guarantee accurate computation of the liquid and gas dynamics the preconditioned implicit scheme of LeMartelot et al. (2013) is adapted to the present boiling flow model. The model and method are validated against a one-dimensional test problem having exact solution. Multidimensional computations are then shown to illustrate method capabilities. © 2014 Elsevier Ltd.

Fraysse F.,RS2N | Fraysse F.,Technical University of Madrid | Redondo C.,Technical University of Madrid | Rubio G.,Technical University of Madrid | Valero E.,Technical University of Madrid
Journal of Computational Physics | Year: 2016

This article is devoted to the numerical discretisation of the hyperbolic two-phase flow model of Baer and Nunziato. A special attention is paid on the discretisation of intercell flux functions in the framework of Finite Volume and Discontinuous Galerkin approaches, where care has to be taken to efficiently approximate the non-conservative products inherent to the model equations. Various upwind approximate Riemann solvers have been tested on a bench of discontinuous test cases. New discretisation schemes are proposed in a Discontinuous Galerkin framework following the criterion of Abgrall and the path-conservative formalism. A stabilisation technique based on artificial viscosity is applied to the high-order Discontinuous Galerkin method and compared against classical TVD-MUSCL Finite Volume flux reconstruction. © 2016 Elsevier Inc.

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