Phase diagram of crushed powders

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% to 50% of initial grains are reduced to finer particles, depending on the initial size. Then 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 phase transition in liquid-vapour systems and powder compression with crush-up. Fragmentation diagram of soda lime glass granular beds 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

Solveur de Riemann à reconstruction interne (RSIR) pour les écoulements compressibles monophasiques et diphasiques hors d'équilibre

International audienceA new Riemann solver is built to address numerical resolution of complex flow models. The research direction is closely linked to a variant of the Baer and Nunziato (1986) model developed in Saurel et al. (2017a). This recent model provides a link between the Marble (1963) model for two-phase dilute suspensions and dense mixtures. As in the Marble model, Saurel et al. system is weakly hyperbolic with the same 4 characteristic waves, while the system involves 7 partial differential equations. It poses serious theoretical and practical issues to built simple and accurate flow solver. To overcome related difficulties the Riemann solver of Linde (2002) is revisited. The method is first examined in the simplified context of compressible Euler equations. Physical considerations are introduced in the solver improving robustness and accuracy of the Linde method. With these modifications the flow solver appears as accurate as the HLLC solver of Toro et al. (1994). Second the two-phase flow model is considered. A locally conservative formulation is built and validated removing issues related to non-conservative terms. However, two extra major issues appear from numerical experiments: The solution appears not self-similar and multiple contact waves appear in the dispersed phase. Building HLLC-type or any other solver appears consequently challenging. The modified Linde (2002) method is thus examined for the considered flow model. Some basic properties of the equations are used, such as shock relations of the dispersed phase and jump conditions across the contact wave. Thanks to these ingredients the new Riemann solver with internal reconstruction (RSIR), modification of the Linde method, handles stationary volume fraction discontinuities, presents low dissipation for transport waves and handles shocks and expansion waves accurately. It is validated on various test problems showing method's accuracy and versatility for complex flow models. Its capabilities are illustrated on a difficult two-phase flow instability problem, unresolved before

Modeling Heavy-Gas Dispersion in Air with Two-Layer Shallow Water Equations

International audienceComputation of gas dispersal in urban places or hilly grounds requires a large amount of computer time when addressed with conventional multidimensional models. Those are usually based on two-phase flow or Navier-Stokes equations. Different classes of simplified models exist. Among them, two-layer shallow water models are interesting to address large-scale dispersion. Indeed, compared to conventional multidimensional approaches, 2D simulations are carried out to mimic 3D effects. The computational gain in CPU time is consequently expected to be tremendous. However, such models involve at least three fundamental difficulties. The first one is related to the lack of hyperbolicity of most existing formulations, yielding serious consequences regarding wave propagation. The second is related to the non-conservative terms in the momentum equations. Those terms account for interactions between fluid layers. Recently, these two difficulties have been addressed in Chiapolino and Saurel (2018) and an unconditional hyperbolic model has been proposed along with a Harten-Lax-van Leer (HLL) type Riemann solver dealing with the non-conservative terms. In the same reference, numerical experiments showed robustness and accuracy of the formulation. In the present paper, a third difficulty is addressed. It consists of the determination of appropriate drag effect formulation. Such effects also account for interactions between fluid layers and become of particular importance when dealing with heavy-gas dispersion. With this aim, the model is compared to laboratory experiments in the context of heavy gas dispersal in quiescent air. It is shown that the model accurately reproduces experimental results thanks to an appropriate drag force correlation. This function expresses drag effects between the heavy and light gas layers. It is determined thanks to various experimental configurations of dam-break test problems

Simulation of Hydrogen Explosions in Closed or Vented Connected Vessels

International audienceThe aim of this study was to characterize the interaction of a shock wave with a parallelepipedal obstacle. Shock wave properties were quantified downstream of sixty configurations with different obstacle dimensions. With the introduction of new parameters, these experimental measurements were used to write evolution laws for the arrival time and the maximum overpressure downstream of a parallelepipedal obstacle. The accuracy of these laws was satisfactory. Then, the maximum overpressure law was compared with experimental measures from the literature. Despite differences in the obstacle geometry or experimental setup, these experimental data are in good agreement with the maximum overpressure law

Evaporation under cavity flow: laser speckle correlation of the wind velocity above the liquid surface

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Multiscale multiphase modeling of detonations in condensed energetic materials

International audienceHot spots ignition and shock to detonation transition modeling in pressed explosives is addressed in the frame of multiphase flow theory. Shock propagation results in mechanical disequilibrium effects between the condensed phase and the gas trapped in pores. Resulting subscale motion creates hot spots at pore scales. Pore collapse is modeled as a pressure relaxation process, during which dissipated power by the ‘configuration’ pressure produces local heating. Such an approach reduces 3D micromechanics and subscale contacts effects to a ‘granular’ equation of state. Hot spots criticity then results of the competition between heat deposition and conductive losses. Heat losses between the hot solid-gas interface at pore's scale and the colder solid core grains are determined through a subgrid model using two energy equations for the solid phase. The conventional energy balance equation provides the volume average solid temperature and a non-conventional energy equation provides the solid core temperature that accounts for shock heating. With the help of these two temperatures and subscale reconstruction, the interface temperature is determined as well as interfacial heat loss.The overall flow model thus combines a full disequilibrium two-phase model for the mean solid-gas flow variables with a subgrid model, aimed to compute local solid-gas interface temperature. Its evolution results of both subscale motion dissipation and conductive heat loss. The interface temperature serves as ignition criterion for the solid material deflagration. There is no subscale mesh, no system of partial differential equations solved at grain scale.The resulting model contains less parameter than existing ones and associates physical meaning to each of them. It is validated against experiments in two very different regimes: Shock to detonation transition, that typically happens in pressure ranges of 50 kbar and shock propagation that involves pressure ranges 10 times higher

Modelling spherical explosions with turbulent mixing and post-detonation

International audienceThis paper addresses post detonation modelling in spherical explosions. One of the challenges is thus related to compressible turbulent mixing layers modelling. A one-dimensional flow model is derived consisting in a reduced two-phase compressible flow model with velocity drift. To reduce the number of model parameters, the stiff velocity relaxation limit is considered. A semi-discrete analysis is used resulting in a specific artificial viscosity formulation embedded in the diffuse interface model of Kapila et al. [Phys. Fluids 13(10), 3002-3024 (2001)]. Thanks to the velocity non-equilibrium model and semi discrete formulation, the model fulfils the second law of thermodynamics in the global sense and uses a single parameter. Multidimensional mixing layer effects occurring at gas-gas unstable interfaces are thus summarized as artificial viscosity effects. Model's predictions are compared against experimental measurements of mixing layer growth in shock tubes at moderate initial pressure ratios as well as fireball radius evolutions in air explosions at high initial pressure ratios. Also, pressure signals recorded at various stations are compared, showing excellent agreement for the leading shock wave as well as the secondary one. With the help of various experiments in the low and high initial pressure ratios bounds, estimates for the interpenetration parameter are given. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4761835

Symmetric model of compressible granular mixtures with permeable interfaces

International audienceCompressible 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. (C) 2014 AIP Publishing LLC

Overpressure wave interaction with droplets: time resolved measurements by laser shadowscopy

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The Challenge of Critical Infrastructure Dependency Modelling and Simulation for Emergency Management and Decision Making by the Civil Security Authorities

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