A PDF closure model for compressible turbulent chemically reacting flows

The objective of the proposed research project was the analysis of single point closures based on probability density function (pdf) and characteristic functions and the development of a prediction method for the joint velocity-scalar pdf in turbulent reacting flows. Turbulent flows of boundary layer type and stagnation point flows with and without chemical reactions were be calculated as principal applications. Pdf methods for compressible reacting flows were developed and tested in comparison with available experimental data. The research work carried in this project was concentrated on the closure of pdf equations for incompressible and compressible turbulent flows with and without chemical reactions

Large Eddy simulation of supersonic combustion using a probability density function method

The scramjet propulsion system is regarded to be a key technology to deliver the next generation of hypersonic planes. It consists of a ramjet engine in which the combustion occurs at supersonic speed. Experiments have been used to investigate the scramjet engine, however, the high costs of gathering data is a limiting factor in its development. In this context, the numerical simulation is an affordable alternative to shed a light into supersonic combustion. The simulation of high-speed compressible and reactive flows, however, is not straightforward, including shock/boundary layer interactions and combustion. Nonetheless, most combustion models have been designed for subsonic flames and their portability to high-speed flows is non-trivial. This work investigates the use of the Probability Density Function (PDF) method for supersonic combustion within the Large Eddy Simulation (LES) framework. Two methods are considered: one is an extension of a joint scalar PDF model (SPDF) for high speed flows and the other is a new joint velocity-scalar PDF formulation (VSPDF). The LES-PDF equations are solved using the Eulerian stochastic fields method, which is implemented into the in-house compressible code CompReal. Their performance are evaluated through a reactive shock-tube, mixing layers and a homogeneous isotropic turbulence cube simulation. Two supersonic burner configurations are simulated to validate the code against experimental data. The results show that sub-grid contributions are important at coarse meshes and the stochastic fields approach can reproduce experimental results. The University of Virginia scramjet configuration A is also simulated using the joint scalar PDF model. Results of topwall pressure, temperature and molar fractions are compared with experimental data. Overall, the results suggest that the joint scalar PDF is the most robust and reliable formulation and the sub-grid closures for the joint velocity-scalar PDF require further investigation.Open Acces

Predictability: a way to characterize Complexity

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kind of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports. Related information at this http://axtnt2.phys.uniroma1.i

Hindered diffusion of nanoparticles

Brownian theory provides us with a powerful tool which can be used to delve into a microscopic world of molecules, cells and nanoparticles, that was originally presumed to be beyond our reach. Consequently, modeling the inherent dynamics of a system through a Brownian transport equation is of relevance to several real-word problems that involve nanoparticles including, the transport and mitigation of particulate matter (PM) generated though fossil fuel combustion and nanocarrier mediated drug delivery. Experimentally forecasting these systems is challenging due to the simultaneous prevalence of disparate length and time scales in them. Correspondingly, an in-silico driven assessment at such nanoscales can complement existing experimental techniques.Hence, in this thesis, a novel multiphase direct numerical simulation (DNS) framework is proposed to address the transport at these nanoscales. A coupled Langevin-immersed boundary method (LaIBM), that solves the fluid as an Eulerian field and the particle in a Lagrangian basis, is developed in this thesis. This framework is unique in its capability to include the resolved instantaneous hydrodynamics around the Brownian nanoparticle (without the need for an a-priori determination of the relevant mobility tensors) into the particle (Langevin) equation of motion. The performance of this technique is established and validated using well-established theoretical bases including the well-known theories for unbounded and hindered diffusion (wherein hydrodynamic interactions mediated by the fluid such as particle-particle or particle-wall influence the governing dynamics) of Brownian particles in a liquid. Correspondingly, it is shown that directional variations in mean-squared displacements, velocity auto-correlation functions and diffusivities of the Brownian nanoparticle correspond well with these standard theoretical bases. Moreover, since the resolved flow around the particle is inherently available in the proposed DNS method, the nature of the hydrodynamic resistances (on the particle) including the inherent anisotropies and correlated inter-particle interactions (mediated by the fluid) are further identified and shown to influence particle mobility. Furthermore, this framework is also extended towards Brownian transport in a rarefied gas using first order models to account for the non-continuum effects. Thus, the utility of this novel method is established in both colloids and aerosols, thereby aiding in modeling the transport of a fractal shaped PM (in the latter) and a spherical nanocarrier in a micro-channel (in the former)

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy

Modélisation numérique directe et des grandes échelles des écoulements turbulents gaz-particules dans le formalisme eulérien mésoscopique

Une nouvelle approche eulérienne aux grandes échelles (LES) pour simuler un nuage de particules inertielles soumis à une turbulence fluide est présentée. Elle est basée sur le formalisme eulérien mésoscopique (Février et al. (2005)) qui permet de décomposer la vitesse de chaque particule en une partie spatialement corrélée et une partie décorrélée. La dérivation des équations LES particulaires comprend deux étapes : une moyenne d'ensemble conditionnée par une réalisation du champ fluide turbulent est suivie d'un filtrage spatial LES classique des équations de transport. En conséquence, les termes à modéliser sont de deux sortes : ceux provenant de la moyenne d'ensemble sont modélis es par analogie avec les fermetures statistiques de la méthode aux moments, alors que l'effet des termes de sous-maille est prédit par des modèles similaires à ceux employés en turbulence monophasique compressible. Les différents modèles sont testés a priori à l'aide de résultats de simulations lagrangiennes pour la phase dispersée couplées à une résolution numérique directe du fluide en turbulence homogène isotrope décroissante. Les nombres de Stokes des écoulements simulés correspondent à des régimes de concentration préférentielle des particules. Le couplage inverse ainsi que les collisions interparticulaires ne sont pas pris en compte. L'interprétation de ces résultats lagrangiens en terme de champs eulériens mésoscopiques nécessite l'emploi d'une procédure de projection. Une projection de type gaussienne, spécialement développée permet de limiter les erreurs spatiales et statistiques. Les champs mésoscopiques sont, tout d'abord analysés en détail : évolution des grandeurs moyennes, spectres de vitesses, champs locaux instantanés. Puis ces champs sont filtrés spatialement. Les tests a priori des modèles de sous-mailles sont effectués et donnent des résultats similaires aux tests effectués en écoulements monophasiques en ce qui concerne le tenseur de sous-maille. ABSTRACT : The purpose of the paper is to develop a new large eddy simulation (LES) approach for a dispersed phase suspended in a fluid turbulent flow in the framework of the Eulerian modelling for inertial particles. Local instantaneous Eulerian equations for the particles are first written using the Mesoscopic Eulerian Formalism, which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Then, particle LES equations are obtained by volume filtering of mesoscopic Eulerian equations. In such approach, the particulate flow at larger scales than the filter width is recovered while subgrid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed subgrid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of the proposed modelling approaches is performed using seven sets of particle Lagrangian results computed from discret particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turubulence. Fluid acts on the particle through the Stokes drag force, two-way coupling and inter-particle collisions are not considered. Simulated Stokes numbers corresponds to prefential concentration regimes. Mesoscopic Eulerian fields are extracted from Lagrangian results by a projection process, which is equivalent to a spatial filter. A specific projector is develop to limit statistical bias and spatial error and is validated. First mesoscopic fields are analysed in detail including correlated velocity power spectra and uncorrelated energy modelling. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle subgrid stress models gives comparable agreement than fluid compressible turbulence tests. The standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients. The scale similarity model shows very good correlation coefficient but strongly underestimates the subgrid dissipation. The mixed model is on the whole superior to pure eddy-viscosity mode

Holographic fluids: a thermodynamic road to quantum physics

Quantum mechanics, superfluids, and capillary fluids are closely related: it is thermodynamics that links them. In this paper, the Liu procedure is used to analyze the thermodynamic requirements. A comparison with the traditional method of divergence separation highlights the role of spacetime. It is shown that perfect Korteweg fluids are holographic. The conditions under which a complex field can represent the density and velocity fields of the fluid, and where the complex scalar field becomes a wave function of quantum mechanics, are explored. The bridge between the field and particle representations of a physical system is holography, and the key to holography is the Second Law of thermodynamics.Comment: 33 pages, no figures, accepted in Physics of Fluid

Lagrangian stochastic modeling of turbulent gas-solid flows with two-way coupling in homogeneous isotropic turbulence

Dans ce travail de thèse, réalisé à l'IMFT, nous nous sommes intéressés aux écoulements turbulents diphasiques gaz-solides et plus particulièrement au phénomène de couplage inverse qui correspond à la modulation de la turbulence par la phase dispersée. Ce mécanisme est crucial pour les écoulements à forts chargements massiques. Dans cette thèse, nous avons considéré une turbulence homogène isotrope stationnaire sans gravité dans laquelle des particules sont suivies individuellement d'une façon Lagrangienne. La turbulence du fluide porteur est obtenue par des simulations directes (DNS). Les particules sont sphériques, rigides et d'une taille inférieure aux plus petites échelles de la turbulence. Leur densité est bien plus grande que la densité du fluide. Dans ce cadre, la force la plus importante agissant sur les particules est celle de traînée. Les interactions inter-particules ainsi que la gravité ne sont pas prises en compte. Pour modéliser ce type d'écoulement, une approche stochastique est utilisée pour laquelle l'accélération du fluide est modélisée par une équation de Langevin. L'originalité de ce travail est la prise en compte de l'effet de la modulation de la turbulence par un terme additionnel. Nous avons proposé deux modèles : une force de couplage moyenne qui est définie à partir des vitesses moyennes des phases, et une force instantanée qui est définie à l'aide du formalisme mésoscopique Eulérien. La fermeture des modèles s’appuie sur la fonction d’autocorrélation Lagrangienne et l’équation de transport de l’énergie cinétique. Les modèles sont testés en terme de prédiction de la vitesse de dérive et des corrélations fluide-particule. Les résultats montrent que le modèle moyen, plus simple, prend en compte les effets principaux du couplage inverse. Cependant, le problème de fermeture pratique est reporté sur la modélisation de l’échelle intégrale Lagrangienne et l’énergie cinétique de la turbulence du fluide vue par les particules. ABSTRACT : In this thesis, performed in IMFT, we are interested in the turbulent gas-solid flows and more specifically, in the phenomenon of turbulence modulation which is the modification of the structure of the turbulence due to the solid particles. This mechanism is crucial in flows with high particle mass-loadings. In this work, we considered a homogeneous isotropic turbulence without gravity kept stationary with stochastic type forcing. Discrete particles are tracked individually in Lagrangian manner. Turbulence of the carrier phase is obtained by using DNS. The particles are spherical, rigid and of a diameter smaller than the smallest scales of turbulence. Their density is very large in comparison to the density of the fluid. In this configuration the only force acting on the particles is the drag force. Volume fraction of particles is very small and inter-particle interactions are not considered. To model this type of flow, a stochastic approach is used where the fluid element accel- eration is modeled using stochastic Langevin equation. The originality in this work is an additional term in the stochastic equation which integrates the effect of the particles on the trajectory of fluid elements. To model this term, we proposed two types of modeling: a mean drag model which is defined using the mean velocities from the mean transport equations of the both phases and an instantaneous drag term which is written with the help of the Mesoscopic Eulerian Approach. The closure of the models is based on the Lagrangian auto- correlation function of the fluid velocity and on the transport equation of the fluid kinetic energies. The models are tested in terms of the fluid-particle correlations and fluid-particle turbulent drift velocity. The results show that the mean model, simple, takes into account the principal physical mechanism of turbulence modulation. However, practical closure problem is brought forward to the Lagrangian integral scale and the fluid kinetic energy of the fluid turbulence viewed by the particles