Este trabalho é dedicado à análise e implementação de esquemas "upwind" de alta ordem modernos e o modelo de turbulência k-epsilon padrão no Freeflow-2D; um ambiente integrado para simulação numérica em diferenças finitas de problemas de escoamentos incompressíveis com superfícies livres. O propósito do estudo é a simulação de escoamentos de fluidos newtonianos incompressíveis, bidimensionais, confinados e/ou com superfícies livres e a altos valores do número de Reynolds. O desempenho do código Freeflow-2D atual é avaliada na simulação do escoamento numa expansão brusca e de um jato livre incidindo perpendicularmente sobre uma superfície rígida impermeável. O código é então aplicado na simulação de um jato planar turbulento em uma porção de fluido com superfície livre e estacionário. Os resultados numéricos obtidos são comparados com dados experimentais, soluções analíticas e soluções numéricas de outros trabalhos. / This work is devoted to the analysis and implementation of modern high-order upwind schemes and the standard k-epsilon turbulence model into the Freeflow-2D; a finite difference integrated environment for the numerical simulation of incompressible free surface flow problems. The purpose of this study is the two-dimensional simulation of high-Reynolds incompressible newtonian confined and/or free surface flows. The performance of the current Freeflow-2D code is assessed by applying it to the simulation of flow over a backward facing step and of an impinging free jet onto an impermeable rigid surface. The code is then applied to a turbulent planar jet into a pool. The numerical results are compared with experimental data, analytical solution, and numerical simulations of other works.

The incompressible Navier-Stokes equations have proven formidable for nearly a century. The present difficulties are mathematical and computational in nature; the computational requirements, in particular, are exponentially exacerbated in the presence of high Reynolds number. The issues are further compounded with the introduction of markers or an immiscible fluid intended to be tracked in an ambient high Reynolds number flow; despite the overwhelming pragmatism of problems in this regime, and increasing computational efficacy, even modest problems remain outside the realm of direct approaches. Herein three approaches are presented which embody direct application to problems of this nature. An LES model based on an entropy-viscosity serves to abet the computational resolution requirements imposed by high Reynolds numbers and a one-stage compressive flux, also utilizing an entropy-viscosity, aids in accurate, efficient, conservative transport, free of low order dispersive error, of an immiscible fluid or tracer. Finally, an integral commutator and the theory of anti-dispersive spaces is introduced as a novel theoretical tool for consistency error analysis; in addition the material engenders the construction of error-correction techniques for mass lumping schemes.

Nous nous intéressons au transport turbulent de particules de taille grande devant l’échelle de Kolmogorov. Cette situation se retrouve à la fois dans les écoulements naturels (comme le transport de sédiments) et dans les écoulements industriels (solutés solides dans un mélangeur par exemple). Pour aborder ce problème, nous étudions la dynamique de particules de taille proche de l’échelle intégrale, de densité égale ou légèrement différente de celle du fluide, dans un écoulement turbulent de von Kármán contra-rotatif, à l’aide d’un montage de suivi lagrangien rapide. L’étude de la dynamique rapide des particules montre une diminution forte des fluctuations selon la taille, mais aussi l’apparition d’un phénomène nouveau : à partir d’une certaine taille, les particules n’explorent plus l’écoulement de façon homogène. Cette exploration préférentielle est liée à la structure moyenne de l’écoulement de von Kármán, qui crée une force de piégeage. Cette force devient alors supérieure aux fluctuations des particules quand leur taille dépasse une taille critique. Une étude dans le régime laminaire, où l’écoulement moyen domine largement les fluctuations, a en effet mis en évidence un piégeage fortement accru. Les particules orbitent alors pendant des temps très longs autour des attracteurs stables des particules fluides de l’écoulement laminaire. Même en régime pleinement turbulent, le déplacement des particules entre ces zones s’effectue sur des durées longues, décorrélées des temps de la dynamique turbulente. Nous avons adapté les outils d’analyse pour caractériser cette dynamique et l’avons comparée à celle de particules isodenses dans un écoulement de von Kármán qui possède deux états asymétriques. Nous avons également élaboré un modèle qui reproduit ces caractéristiques dans les cas symétrique et asymétrique. Ces questions sont intimement liées au transfert de masse ou de chaleur entre une particule et l’écoulement. Nous avons donc aussi étudié la fusion de grosses billes de glace en turbulence développée, analysant l’influence de la taille des billes et de la vitesse de glissement sur le transfert thermique, à l’aide d’un montage d’ombroscopie afocale. Nous avons notamment montré que les grosses billes de glace fondent dans un régime ultime de convection forcée lorsqu’elles sont librement advectées par l’écoulement. / We are interested in the turbulent transport of particles whose size is bigger than the Kolmogorov length scale. This issue takes place as much in natural flows (such as sediment transport) as in industrial flows (solid solute in mixer for instance). To tackle this problem, we study the dynamics of particle with size close to the integral length scale, whose density can be neutral or slightly different from the one of the fluid, in a turbulent counter-rotating von Kármán flow, through a fast Lagrangian tracking setup. Studying the fast scale motions, we find out that the fluctuations decrease strongly with particle diameter, but we also discover a new phenomena: particles bigger than a certain size do not sample the flow homogeneously. This preferential sampling is link to the von Kármán mean structure, which applies a trapping force on the particles, overcoming their fluctuations as their size becomes bigger than a critical size. A study in the laminar flow regime, where the mean flow is much greater than the fluctuations, showed an strongly increased trapping effect. The particles indeed orbit for very long times around stable attractors of the fluid particles of the laminar flow. Even in turbulent regime, the motion of the particle between these areas occurs at long times intervals, in a decorrelated way of the turbulent motion. We adapted our analysis tools to characterize this dynamics, comparing it to the one of large neutrally-buoyant particles in a von Kármán flow which presents two asymmetric states. We also designed a model that can reproduce these characteristics in both symmetrical and asymmetrical cases. These issues are tightly linked to mass or heat transfer between a particle and the carrier flow. Therefore, we also studied the melting dynamics of large ice balls in fully developed turbulence, analyzing the impact of particles size and sliding velocity on the turbulent heat transfer, through an afocal shadowgraphy setup. We showed in particular that large freely advected ice balls melt in the ultimate regime of heat transfer.

Flow separation and reattachment happens in many fluid mechanical situations occurring in engineering applications as well as in nature. The flow over a backward-facing step represents a geometrically simple flow situation exhibiting both flow separation and reattachment. Broadly speaking there are only two important parameters in the problem, the Reynolds number(Re) based on the step height(h),and a geometrical parameter, referred to as the Expansion ratio(ER), defined as the downstream channel height to the upstream channel height. In spite of the relative simplicity of this geometry, the flow downstream is quite complex. The main focus of the present work is to elucidate the unsteady three-dimensional coherent structures present in this flow at large Re, Re>36,000,based on the step height(h). For this, we use velocity field measurements from Particle Image Velocimetry (PIV)in conjunction with hotwire anemometry measurements. The time-averaged structure of this flow is first studied in detail, including the effect of Reynolds number(Re) and Expansion Ratio(ER), on it. These studies show that at sufficiently large Re (Re>20,000), the reattachment length becomes independent of Re. The detailed internal structure of the separation bubble is also found to be independent of Re, but for Revalues that are relatively larger(Re>36,000). At large Re, the main effect of ER ,is found to be on the reattachment length, which increases with ER and saturates for ER values greater than about 1.8. The detailed internal structure of the separation bubble has been mapped at high Re and is found to be nearly the same for all ER, when the streamwise length is normalized by the reattachment length. In order to elucidate the unsteady coherent vortical structures, PIV measurements are done in two orthogonal planes downstream of the backward-facing step. These measurements are done for ER= 1.50 at large Re(Re=36,000) and in a large aspect ratio facility(AR= span length/step height= 24); the latter being important to avoid any effects due to span-wise confinement. In the spanwise plane parallel to the lower wall(x-z plane),instantaneous velocity fields show counter rotating vortex pairs, which is a signature of the three-dimensional vortical structures in this plane. Using conditional averaging, this counter-rotating vortex pair signature is captured right from upstream of the step, to well after reattachment. Spatial correlations are used to get the length scale of these coherent vortical structures, which varies substantially from the attached boundary layer before separation to the region after reattachment. The variation of these structures in the cross-stream (vertical) direction at reattachment and beyond gives an idea about their three dimensional shape. The circulation of these counter-rotating pairs is measured from the conditionally aver-aged fields, and is found to increase with streamwise distance reaching normalized circulation values (Γ/Uoh) of about 0.5 around reattachment. Velocity spectra downstream of the step show peaks corresponding to both the shear layer frequency(Stsl)and a relatively lower frequency that corresponds to large-scale shedding from the separation bubble (Stb); the latter in particular being quasi-periodic. Small amplitude sinusoidal forcing at the shedding frequency(Stb) is applied close to the step, by blowing and suction, to make the quasi-periodic shedding more regular. Measurements show that this has a very small effect on both the mean separation bubble and on the counter-rotating structures in the x-z plane. This mild forcing however enables phase locked PIV measurements to be made which shows the bubble shedding phenomenon in the cross-stream plane(side view or x-y plane). The phase-averaged velocity fields show significant variations from phase to phase. Although there is some hint of structures being shed, from these phase-averaged fields, it is not very clear. One of the primary reasons is the fact that the flow is effectively spanwise averaged, as the three-dimensional structures are not locked in the spanwise direction. To get a three dimensional view of the sheddin gphenomenon, it is necessary to lock the spanwise location with respect to the three-dimensional vortical structures before averaging across the different phases. We use the condition, u’<- urms, to locate the central plane between the counter-rotating structures, which in effect are the “legs” of the three-dimensional structure. With this condition, we effectively get a slice of the shedding cycle cutting through the “head” of the three-dimensional structure. Apart from this cut, we also get a cut between adjacent structures from the weak sweep events, with the condition u’<- urms. Using these conditions, on the phase-locked velocity fields, we effectively lock the structures in time, as well as in the spanwise direction. With this ,a clearer picture of the shedding process emerges. The flow is highly three-dimensional near reattachment and the shedding of the separation bubble is modulated in the spanwise direction owing to the three-dimensional hairpin like vortical structures in the flow. The separation bubble is seen bulged out and lifted high at locations where the head of the hairpin vortex passes, owing to the strong ejection of fluid caused by the vortical structure. On the other hand, outside the hairpin vortices, weak sweep events push the flow towards the wall and make it shallow and less prominent, with the shedding being very weak in this plane. From these observations, a three-dimensional picture of the flow is proposed.