The Richtmyer-Meshkov instability (RMI) in the convergent geometry is numerically studied in the framework of ideal magnetohydrodynamics (MHD) and two-fluid plasma in this thesis. The converging RMI usually occurs along with the Rayleigh-Taylor instability (RTI) due to the non-uniform motion or continuous acceleration of the interface. First, we investigate the interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field with ideal MHD model. We show that the RMI is suppressed by the magnetic field . However, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry increases when the seed field strength increases. The perturbation amplitude is affected by the competition mechanism between RMI and RTI. It increases when RMI dominates RTI while decreases when RTI dominates. Then, we research the two-fluid plasma RMI of a cylindrical density interface without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. The charge separation is responsible for the self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling effect is weak. In addition to the RT stabilization effect during flow deceleration, the interfaces are accelerated by the induced Lorentz force. As a consequence, the perturbations develop into the RTI, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case. Finally, we investigate the linear evolution of two-fluid plasma RMI. We show that the increase of perturbation amplitude is almost contributed by the ion shock-interface interaction. We also examine the effect of magnetic field in the streamwise direction. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. As time progresses the suppression of the instability due to the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the vorticity being transported away from the interface.

The Richtmyer-Meshkov Instability (RMI) (Commun. Pure Appl. Math 23, 297-319, 1960; Izv. Akad. Nauk. SSSR Maekh. Zhidk. Gaza. 4, 151-157, 1969) occurs due to an impulsive acceleration acting on a perturbed interface between two fluids of different densities. In the experiments presented in this thesis, single mode 3D RMI experiments are performed. An oscillating speaker generates a single mode sinusoidal initial perturbation at an interface of two gases, air and SF6. A Mach 1.19 shock wave accelerates the interface and generates the Richtmyer-Meshkov Instability. Both gases are seeded with propylene glycol particles which are illuminated by an Nd: YLF pulsed laser. Three high-speed video cameras record image sequences of the experiment. Particle Image Velocimetry (PIV) is applied to measure the velocity field. Measurements of the amplitude for both spike and bubble are obtained, from which the growth rate is measured. For both spike and bubble experiments, amplitude and growth rate match the linear stability theory at early time, but fall into a non-linear region with amplitude measurements lying between the modified 3D Sadot et al. model (Phys. Rev. Lett. 80, 1654-1657, 1998) and the Zhang & Sohn model (Phys. Fluids 9. 1106-1124, 1997; Z. Angew. Math Phys 50. 1-46, 1990) at late time. Amplitude and growth rate curves are found to lie above the modified 3D Sadot et al. model and below Zhang & Sohn model for the spike experiments. Conversely, for the bubble experiments, both amplitude and growth rate curves lie above the Zhang & Sohn model, and below the modified 3D Sadot et al. model. Circulation is also calculated using the vorticity and velocity fields from the PIV measurements. The calculated circulation are approximately equal and found to grow with time, a result that differs from the modified Jacobs and Sheeley's circulation model (Phys. Fluids 8, 405-415, 1996).

Richtmyer-Meshkov instability (RMI) occurs when an interface of two fluids with different densities is impulsively accelerated. The main interest in RMI is to understand the growth of perturbations, and numerous theoretical models have been developed and validated against experimental/numerical studies. However, most of the studies assume very simple initial conditions. Recently, more complex RMI has been studied, and this study focuses on two cases: reshocked RMI and multiphase RMI. It is well known that reshock to the species interface causes rapid growth of interface perturbation amplitude. However, the growth rates after reshock are not well understood, and there are no practical theoretical models yet due to its complex interface conditions at reshock. A couple of empirical expressions have been derived from experimental and numerical studies, but these models are limited to certain interface conditions. This study performs parametric numerical studies on various interface conditions, and the empirical models on the reshocked RMI are derived for each case. It is shown that the empirical models can be applied to a wide range of initial conditions by choosing appropriate values of the coefficient. The second part of the study analyzes the flow physics of multiphase RMI. The linear growth model for multiphase RMI is derived, and it is shown that the growth rates depend on two nondimensional parameters: the mass loading of the particles and the Stokes number. The model is compared to the numerical predictions under two types of conditions: a shock wave hitting (1) a perturbed species interface surrounded by particles, and (2) a perturbed particle cloud. In the first type of the problem, the growth rates obtained by the numerical simulations are in agreement with the multiphase RMI growth model when Stokes number is small. However, when the Stokes number is very large, the RMI motion follows the single-phase RMI growth model since the particle do not rapidly respond while the RMI instability grows. The second type of study also shows that the multiphase RMI model is applicable if Stokes number is small. Since the particles themselves characterize the interface, the range of applicable Stokes number is smaller than the first study. If the Stokes number is in the order of one or larger, the interface experiences continuous acceleration and shows the growth profile similar to a Rayleigh-Taylor instability.

A computational and experimental study of the Richtmyer-Meshkov instability is presented here for an inclined interface perturbation. The computational work is composed of simulation studies of the inclined interface RMI performed using the Arbitrary Lagrange Eulerian (ALE) code called ARES. These simulations covered a wide range of Mach numbers (1.2 to 3.5), gas pairs (Atwood numbers 0.23to 0.95), inclination angles (30° to 85°), and explored various perturbation types (both inclined interface and sinusoidal). The computational work included the first parametric study of the inclined interface RMI. This study yielded the first scaling method for the inclined interface RMI mixing width growth rates. It was extended to explore the effect of perturbation linearity and identified that a sharp transition in growth regimes occurs for an initial perturbation inclination angle of 75° with angles below (above) this growing faster (slower). Finally a study of the effects of incident shock strength on the refracted shock wave perturbation decay rate is presented. This study examined how the perturbations induced on the transmitted shock front by the RMI decay with time and found that the decay rates follow a power law model, Alpha=Beta∗S^(Epsilon). When the coefficients from the power law decay model were plotted versus Mach number, a distinct transition region was found which is likely a result of the post-shock heavy gas velocity transitioning from the subsonic to supersonic range. The experimental portion of this work was conducted using the TAMUFMSTF, completed in May of 2012. This facility uses a variable inclination shock tube, with a modular construction design for incident shock strengths of up to Mach 3.0. It employs optical systems for measuring density and velocity fields simultaneously using the planar laser induced fluorescence and particle imaging velocimetry techniques. The design and construction of this facility is reviewed in detail in chapter 4 of this work. The initial experiments performed in the TAMUFMSTF provided the first known extensive experimental data for an inclined interface RMI. Planar laser Mie scattering images and velocity vectors were obtained for a N_(2)/CO_(2) interface at a 60° inclination angle and an incident shock strength of Mach 1.55. These images have been compared with simulations made using the ARES codes and have been shown to have some distinct differences. Some of these differences indicate that the initial conditions in the experiments deviate from the ideal planar interface. Other differences have revealed features which have not been resolved by the simulations due to resolution limitations.

High explosive charges when detonated ensue in a flow field characterized by several physical phenomena that include blast wave propagation, hydrodynamic instabilities, real gas effects, fluid mixing and afterburn effects. Solid metal particles are often added to explosives to augment the total impulsive loading, either through direct bombardment if inert, or through afterburn energy release if reactive. These multiphase explosive charges, termed as heterogeneous explosives, are of interest from a scientific perspective as they involve the confluence and interplay of various additional physical phenomena such as shock-particle interaction, particle dispersion, ignition, and inter-phase mass, momentum and energy transfer. In the current research effort, chemical explosions in multiphase environments are investigated using a robust, state-of-the-art Eulerian-gas, Lagrangian-solid methodology that can handle both the dense and dilute particle regimes. Explosions into ambient air as well as into aluminum particle clouds are investigated, and hydrodynamic instabilities such as Rayleigh- Taylor and Richtmyer-Meshkov result in a mixing layer where the detonation products mix with the air and afterburn. The particles in the ambient cloud, when present, are observed to pick up significant amounts of momentum and heat from the gas, and thereafter disperse, ignite and burn. The amount of mixing and afterburn are observed to be independent of particle size, but dependent on the particle mass loading and cloud dimensions. Due to fast response times, small particles are observed to cluster as they interact with the vortex rings in the mixing layer, which leads to their preferential ignition/ combustion. The total deliverable impulsive loading from heterogeneous explosive charges containing inert steel particles is estimated for a suite of operating parameters and compared, and it is demonstrated that heterogeneous explosive charges deliver a higher near-field impulse than homogeneous explosive charges containing the same mass of the high explosive. Furthermore, particles are observed to introduce significant amounts of hydrodynamic instabilities in the mixing layer, resulting in augmented fluctuation intensities and fireball size, and different growth rates for heterogeneous explosions compared to homogeneous explosions. For aluminized explosions, the particles are observed to burn in two regimes, and the average particle velocities at late times are observed to be independent of the initial solid volume fraction in the explosive charge. Overall, this thesis provides useful insights on the role played by solid particles in chemical explosions.

We present an Embedded Boundary with Adaptive Mesh Refinement technique for solving the compressible Navier Stokes equations in arbitrary complex domains; followed by a numerical studies for the effect of circular cylinders on the transient dynamics of the Richtmyer-Meshkov Instability. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The Navier Stokes equations are numerically solved by the second order multidimensional upwind method. Block-structured AMR, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the Embedded Boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The effects on the transient dynamics of the Richtmyer-Meshkov instability due to small scale perturbations introduced on the shock-wave or the material interface by a single or set of solid circular cylinders were computationally investigated using the developed technique. First, we discuss the RMI initiated on a flat interface by a rippled shock-wave that is disturbed by a single circular cylinder. Then, we study the effect of introducing a number of circular cylinders on the interface. The arrangement of the cylinders set mimic (in a two dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in the experimental setup. We analyzed their effects on the mixing layer growth and the mixedness level, and qualitatively demonstrate the cylinders' perturbation effects on the mixing layer structure. We modeled the cylinders' influence based on their diameters; and showed the model ability to predict the variation of the mixing layer growth for different flow parameters.

Le travail de thèse présenté dans ce manuscrit propose une analyse expérimentale du dé-veloppement spatio-temporel d’une zone de mélange (air/hélium) initiée par instabilité deRichtmyer-Meshkov (IRM). Cette étude s’appuie sur la mise en oeuvre d’un tube à chocspositionné verticalement et sur le développement d’un nouveau protocole expérimental associéà un système innovant de génération de l’interface initiale entre les deux espèces gazeuses enprésence. Ce système est basé sur un dispositif d’obturation/ouverture composé d’un rideau rigiderétractable et d’une série volets mobiles. La caractérisation de l’interface initiale et de l’évolutionspatio-temporelle de la zone de mélange ainsi obtenue est effectuée en exploitant les résultats dedifférentes techniques de mesures telles que la visualisation strioscopique (Schlieren) résolue entemps, la tomoscopie plan laser (TPL) et la Vélocimétrie par Imagerie de Particules (PIV). Enpremier lieu, différentes campagnes de mesures visant à caractériser l’interface initiale ont permisde quantifier la répétabilité du système et de démontrer ses capacités à générer une interfacepériodique faiblement diffuse. Dans un second temps, une étude du mélange gazeux obtenu pourun jeu de paramètres expérimentaux donné, est proposée. L’analyse s’intéresse en particulieraux mécanismes d’initiation et de transition a la turbulence de la zone de mélange produite parl’IRM. L’interaction entre cette zone de mélange en cours de développement et le choc réfléchisur l’extrémité supérieure du tube (phénomène de rechoc) est également étudiée dans l’optique deconfirmer la transition turbulente de la zone de mélange. / This work proposes an experimental analysis of the spatio-temporal development of an air/heliummixing zone promoted by the Richtmyer-Meshkov instability (RMI). This study relies on the useof a vertical shock tube and on the development of a new experimental protocol associated with aninnovative device for the generation of an initial interface between two gazeous species. This deviceconsists a rigid retractable curtain and of a series of rotating shutters. The characterization ofthis initial interface and the spatio-temporal evolution of the RMI-induced mixing zone is carriedout by exploiting the results of various experimental methods such as time resolved Schlierenvisualizations, planar laser mie scattering and Particle Image Velocimetry (PIV). In a first step,various measurement campaigns have made it possible to quantify the repeatability of the newdevice and to demonstrate its ability to generate a periodic, weakly diffused interface. In a secondstep, a study of the gaseous mixing for a given set of experimental parameters is proposed. Theanalysis focuses on the understanding of the underlying mechanisms driving the gaseous interfaceformation and the transition to turbulence of the RMI-induced mixing. The interaction betweenthis mixing zone and the reflected shock from the upper end of the tube (re-shock phenomenon)is also studied in order to confirm the turbulent transition of the mixing zone.

Ce travail s’intéresse à l’analyse expérimentale du développement de la zone de mélange turbulente (ZMT) produite par une instabilité de Richtmyer-Meshkov (IRM). Les expériences sont réalisées au sein d’un tube à chocs vertical, et l’analyse s’appuie sur des mesures simultanées mettant en œuvre des techniques expérimentales de type capteurs de pression pariétaux, visualisations strioscopiques résolues en temps et mesures de vitesse par Vélocimétrie Laser Doppler (LDV). Une caractérisation de l’installation expérimentale est tout d’abord effectuée en situation homogène (air pur, sans mélange), afin de déterminer la qualité de l’écoulement de base et connaître le niveau de turbulence de fond du tube à chocs. Les configurations de mélange, principalement entre de l’air et de l’hexafluorure de soufre (SF6), sont ensuite abordées. On s’intéresse dans un premier temps aux caractéristiques globales de la zone de mélange : en particulier à l’évolution de son épaisseur et à son taux de croissance. Plusieurs configurations de mélange sont étudiées en faisant varier différents paramètres expérimentaux tels que la hauteur de la veine d’essais du tube à chocs, la forme de la perturbation initiale de l’interface entre les deux gaz et le nombre d’Atwood, dans le but de déterminer leur influence sur le développement de la ZMT. On montre ainsi une sensibilité du taux de croissance post-rechoc à plusieurs de ces paramètres. Des comparaisons avec des simulations numériques réalisées par nos partenaires du Commissariat à l’Énergie Atomique (CEA) montrent des tendances similaires entre expériences et simulations sur ce point. L’étude est ensuite complétée par une caractérisation plus locale de la ZMT, en mesurant les niveaux de turbulence en différents points de la veine d’essais à l’aide de la LDV. Après avoir quantifié les contraintes de convergence statistique imposées par l’expérience pour ce type de mesures, on donne une estimation des intensités turbulentes produites par l’écoulement de mélange à différents stades de son développement. / This experimental study sheds some light on the development of the turbulent mixing zone (TMZ) arising from a Richtmyer-Meshkov instability (RMI). The experiments are conducted in a vertical shock tube, and the analysis relies on simultaneous measurements involving pressuretransducers, time-resolved Schlieren visualizations and Laser Doppler Velocimetry (LDV). In a first step, a thorough characterization of the experimental apparatus is conducted in order to qualify the basic flow configuration corresponding to homogeneous situations (pure air withoutmixing), and to evaluate the « background » turbulence level of the shock tube. Mixing configurations (mainly between air and sulfur hexafluoride, SF6) are then investigated. We first focus on a global description of the mixing zone such as the time evolution of its thickness and the corresponding growth rate. We consider several mixing configurations, varying the length of the test section, the shape of the initial interface between the two gases and the Atwood number. A clear influence of some of these parameters is shown on the the post-reshock increasing rate of the mixing zone, in good accordance with numerical results obtained from the Commissariat à l’Energie Atomique (CEA, french atomic energy commission). A more local description of the flow is then obtained in a second step by measuring the turbulence levels at different locations inside the test section thanks to the LDV technique. After quantifying the issues linked to the statistical convergence of the turbulent quantities in such specific configurations, we provide an estimation of the turbulent intensities produced by the mixing at various stages of its development.

Les différents dimensionnements et expériences de Fusion par Confinement Inertiel (FCI) en attaque directe comme indirecte montrent qu'une des principales limites à l'atteinte de l'ignition est l'instabilité de Rayleigh-Taylor (IRT) qui cause la rupture de la coquille de la cible en vol et potentiellement le mélange du combustible chaud du coeur avec celui, froid, de la coquille. La connaissance, la compréhension et la maîtrise des conditions initiales de ce mécanisme sont donc d'un grand intérêt. Nous présentons ainsi une étude expérimentale et théorique des conditions initiales de l'IRT ablative en attaque directe au travers de deux campagnes expérimentales réalisées sur le laser OMEGA (LLE, Rochester). La première campagne concerne l'étude de l'instabilité de Richtmyer-Meshkov (IRM) ablative imprimée par laser ; cette instabilité commence à se développer au début de l'irradiation laser et fixe l'ensemencement de l'IRT. Nous avons mis en place une configuration expérimentale qui a permis de mesurer l'évolution temporelle de l'IRM ablative imprimée par laser pour la première fois. Nous présentons ensuite une interprétation des résultats de cette expérience par des simulations hydrodynamiques réalisées avec le code CHIC, ainsi que par un modèle théorique de l'IRM ablative imprimée par laser. Nous montrons que le moyen le plus direct de contrôler cette instabilité est de réduire l'amplitude des défauts d'intensité laser. Ceci peut être accompli en utilisant des cibles couvertes par une couche de mousse de basse densité. Ainsi, lors de la deuxième campagne, nous avons étudié pour la première fois l'effet de mousses sous-denses sur la croissance de l'IRT ablative. Au cours de ces expériences, des feuilles de plastique recouvertes d'une couche de mousse ont été irradiées par un faisceau laser portant une perturbation d'intensité destinée à imprimer des modulations sur la cible. Différentes données expérimentales sont présentes : rétrodiffusion de l'énergie laser, dynamique de la cible obtenue par mesure de côté d'auto-émission et radiographies de face faisant apparaître l'effet des mousses sur les modulations de densité surfacique des cibles. Ces données ont ensuite été interprétées à l'aide de simulations CHIC et du code d'interaction laser-plasma PARAX. Nous montrons qu'une des mousses réduit l'amplitude des modulations de l'intensité laser d'un facteur 2. Par conséquent, cette thèse a donné lieu au développement de configurations expérimentales et d'un ensemble d'outils de dépouillement numériques pour l'étude approfondie des instabilités hydrodynamiques en FCI. / Numerous designs and experiments in the domain of Inertial Confinement Fusion (ICF) show that, in both direct and indirect drive approaches, one of the main limitations to reach the ignition is the Rayleigh-Taylor instability (RTI). It may lead to shell disruption and performance degradation of spherically imploding targets. Thus, the understanding and the control of the initial conditions of the RTI is of crucial importance for the ICF program. In this thesis, we present an experimental and theoretical study of the initial conditions of the ablative RTI in direct drive, by means of two experimental campaigns performed on the OMEGA laser facility (LLE, Rochester). The first campaign consisted in studying the laser-imprinted ablative Richtmyer-Meshkov instability (RMI) which starts at the beginning of the interaction and seeds the ablative RTI.We set up an experimental configuration that allowed to measure for the first time the temporal evolution of the laser-imprinted ablative RMI. The experimental results have been interpreted by a theoretical model and numerical simulations performed with the hydrodynamic code CHIC. We show that the best way to control the ablative RMI is to reduce the laser intensity inhomogeneities. This can be achieved with targets covered by a layer of a low density foam. Thus, in the second campaign, we studied for the first time the effect of underdense foams on the growth of the ablative RTI. A layer of low density foam was placed in front of a plastic foil, and the perturbation was imprinted by an intensity modulated laser beam. Experimental data are presented : backscattered laser energy, target dynamic obtained by side-on selfemission measurement, and face-on radiographs showing the effect of the foams on the target areal density modulations. These data were interpreted using the CHIC code and the laser-plasma interaction code PARAX. We show that the foams noticeably reduce the amplitude of the laser intensity inhomogeneities and the level of the subsequent imprinted ablation front modulations. In conclusion, this thesis allowed us to develop an experimental platform and a suite of numerical tools for future, more detailed studies of hydrodynamic instabilities for ICFapplications.

Cette thèse a pour objet la simulation d'une zone de mélange turbulente issue de l'instabilité de Richtmyer-Meshkov à l'aide d'un modèle à fonction de densité de probabilité (PDF). Nous analysons plus particulièrement la prise en charge par le modèle PDF du transport de l'énergie cinétique turbulente dans la zone de mélange.Dans cette optique, nous commençons par mettre en avant le lien existant entre les statistiques en un point de l'écoulement et ses conditions initiales aux grandes échelles. Ce lien s'exprime à travers le principe de permanence des grandes échelles, et permet d'établir des prédictions pour certaines grandeurs de la zone de mélange, telles que son taux de croissance ou son anisotropie.Nous dérivons ensuite un modèle PDF de Langevin capable de restituer cette dépendance aux conditions initiales. Ce modèle est ensuite validé en le comparant à des résultats issus de simulations aux grandes échelles (LES).Enfin, une analyse asymptotique du modèle proposé permet d'éclairer notre compréhension du transport turbulent. Un régime de diffusion est mis en évidence, et l'expression du coefficient de diffusion associé à ce régime atteste l'influence de la permanence des grandes échelles sur le transport turbulent.Tout au long de cette thèse, nous nous sommes appuyés sur des résultats issus de simulations de Monte Carlo du modèle de Langevin. A cet effet, nous avons développé une méthode spécifique eulérienne et à l'avons comparé à des alternatives lagrangiennes. / The aim of the thesis is to simulate a turbulent mixing zone resulting from the Richtmyer-Meshkov instability using a probability density function (PDF) model. An emphasis is put on the analysis of the turbulent kinetic energy transport.To this end, we first highlight the link existing between the one-point statistics of the flow and its initial conditions at large scales. This link is expressed through the principle of permanence of large eddies, and allows to establish predictions for quantities of the mixing zone, such as its growth rate or its anisotropy.We then derive a Langevin PDF model which is able to reproduce this dependency of the statistics on the initial conditions. This model is then validated by comparing it against large eddy simulations (LES).Finally, an asymptotic analysis of the derived model helps to improve our understanding of the turbulent transport. A diffusion regime is identified, and the expression of the diffusion coefficient associated with this regime confirms the influence of the permanence of large eddies on the turbulent transport.Throughout this thesis, our numerical results were based on Monte Carlo simulations for the Langevin model. In this regard, we proceeded to the development of a specific Eulerian method and its comparison with Lagrangian counterparts.