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<p dir="ltr">This thesis delves into the dynamics and driving factors of thermal transport via natural convection, the onset and severity of quiescent cavitation and its impact of auto-injector device performance, and the controlled release of rapidly swelling pharmaceutical tablets. In each of these instances showcases how variations in external conditions or the introduction of new variables can disrupt the equilibrium of fluid systems, leading to complex behaviors. Vertical thermal convection illustrates how temperature gradients induce fluid movement and patterns; cavitation inception focuses on the formation of vapor cavities due to pressure drops within a fluid; and rapid tablet swelling explores the interaction between solid materials and liquids, leading to significant changes in concentration and mass transfer. These studies collectively enhance our understanding of transport dynamics, highlighting pathways to achieve optimal transport and delivery conditions for various industrial and pharmaceutical processes.</p>

Convection set up in a fluid due to the presence of two components of differing diffusivities is known as double diffusive convection. Double diffusive convection is observed in nature, in oceans, in the formation of certain columnar rock structures and in stellar interiors. The major engineering applications of double diffusive convection are in the fields metallurgy and alloy solidification in casting processes. The two components may be any two substances which affect the density of the fluid, heat and salt being the pair found most commonly in nature. Depending upon the initial stratifications of the two components, double diffusive convection can be set up in either the diffusive mode or the finger mode. In this thesis, the linear stability of a double diffusive system prone to finger instability has been studied in the presence of temporally varying non-linear background profiles of temperature and salinity. The motivation for the present study is to bridge the gap between existing theories, which mainly concentrate on linear background profiles independent of time, on the one hand and experiments and numerical simulations, which have time dependent step-like non-linear background profiles, on the other. The general stability characteristics of a double diffusive system with step-like background profiles have been studied using the standard normal mode method. The background temperature and salinity profiles are assumed to follow the hyperbolic tangent function, since it has a step-like character. The sharpness of the step can be altered by changing a suitable parameter in the hyperbolic tangent function. It is found that changing the degree of non-linearity of the background profile of one of the components keeping the background profile of the other component linear affects the growth rate, Wave number and the form of the disturbances. In general, increasing the degree of nonlinearity of background salinity profile makes the system more unstable and results in a reduction in the vertical extent of the disturbances. On the other hand, increasing the degree of non-linearity of the background temperature profile with the salinity profile kept linear results in a reduction in the growth rate and increase in the wave number. The form of the disturbance may change due to enhanced modal competition between the gravest odd and even modes in this case. The method of normal modes inherently assumes that the background profiles of temperature and salinity are independent of time and hence, it cannot be used for studying the stability of systems with time varying background profiles. A pseudo-similarity method has been used to handle such background profiles. Initial steps of temperature and salinity diffuse according to the error function form, and hence, the case of error function background profiles has been studied in detail. Taking into account the time-dependence of background profiles has been shown to significantly change the wave number and the incipient flux ratio. The dependence of the critical wave number (kc) on the thermal Rayleigh number (RaT ) can be determined analytically and is found to change from kc ~ Ra T1/4 for linear background profiles to kc ~ Ra T1/3 for error function profiles. The region of instability in the Rp (density stability ratio) space is found to increase from 1 ≤ R ρ ≤ r−1 for linear background profiles to 1 ≤ Rρ < r−3/2 for error function background profiles, where T denotes the ratio of the diffusivity of the slower diffusing component to that of the faster diffusing one. A parametric study covering a wide range of parameter values has been carried out to determine the effect of the parameters density stability ratio (Rp), diffusivity ratio (ρ ) and Prandtl number (Pr) on the onset time, critical wavenumber and the incipient flux ratio. The wide range of governing parameters covered here is beyond the scope of experimental and numerical studies. Such a wide range can be covered by theoretical approaches alone. It has been shown that the time of onset of convection determines the thicknesses of the temperature and salinity boundary layers, which in turn determine the width of salt fingers. Finally, the theoretical predictions of salt finger widths have been shown to be in agreement with the results of two dimensional numerical simulations of thermohaline system.

Turbulent mixed convection is a complicated flow where the buoyancy and shear forces compete with each other in affecting the flow dynamics. This thesis deals with the near wall dynamics in a turbulent mixed convection flow over an isothermal horizontal heated plate. We distinguish between two types of mixed convection ; low-speed mixed convection (LSM) and high-speed mixed convection (HSM). In LSM the entire boundary layer, including the near-wall region, is dominated by buoyancy; in HSM the near-wall region, is dominated by shear and the outer region by buoyancy. We show that the value of the parameter (* = ^ determines whether the flow is LSM or HSM. Here yr is the friction length scale and L is the Monin-Obukhov length scale. In the present thesis we proposed a model for the near-wall dynamics in LSM. We assume the coherent structure near-wall for low-speed mixed convection to be streamwise aligned periodic array of laminar plumes and give a 2d model for the near wall dynamics, Here the equation to solve for the streamwise velocity is linear with the vertical and spanwise velocities given by the free convection model of Theerthan and Arakeri [1]. We determine the profiles of streamwise velocity, Reynolds shear stress and RMS of the fluctuations of the three components of velocity. From the model we obtain the scaling for wall shear stress rw as rw oc (UooAT*), where Uoo is the free-stream velocity and AT is the temperature difference between the free-stream and the horizontal surface.A similar scaling for rw was obtained in the experiments of Ingersoll [5] and by Narasimha et al [11] in the atmospheric boundary layer under low wind speed conditions. We also derive a formula for boundary layer thickness 5(x) which predicts the boundary layer growth for the combination free-stream velocity Uoo and AT in the low-speed mixed convection regime.

Natural turbulent convection studies encompass a wide range of flows occurring in nature, for example, atmospheric and oceanic flows, con-vection in the Earth’s mantle, convection in the stars and also in many engineering applications. Rayleigh-Benard convection (RBC), i.e. con-vection in a horizontal fluid layer confined between two plates with a temperature differential maintained across them, has been a proto-type problem in the studies of turbulent natural convection. Many small scale and global features of the flow in the turbulent regime of RBC are known, yet the flow dynamics is not fully understood, es-pecially at high Rayleigh numbers (Ra). Present work comprises of experimental investigations of a different type of flow, high Rayleigh number turbulent convection in a long vertical tube (abbreviated as tube convection or TC). The tube of aspect ratio (length to diameter) of about 10, open at both the ends interconnects two large tanks. The flow driven by an unstable density difference created between the two tanks, has some unique features, different from RBC. The net flow at any tube cross-section is zero and the time averages of the velocities, the Reynolds shear stress and the mean shear are also zero. Turbu-lent energy production is therefore solely due to buoyancy. The flow is axially homogeneous and axisymmetric. In the homogeneous region, the mean density gradient is linear. Rayleigh number in TC is conve-niently defined based on the mean (linear) density gradient (denoted by Rag). Two sets of experiments are carried out. In one set of experiments, the density difference is created using brine and fresh water and in another set, it is created using heat. The ranges of Rag achieved are 3 × 108 < Rag < 8 × 109 in the experiments using salt (Schmidt number, Sc ≈ 600) and 5 × 104 < Rag < 5 × 106 in the experiments using heat (Prandtl number, P r ≈ 6). From the measured salt and heat fluxes in both the sets of experiments, the non dimensional flux 1 1 scaling above a certain value of Rag is obtained as N ug ∼ Rag2 P r 2 and from the velocity measurements in the experiments using salt, the 1 Reynolds number scaling is obtained as Re ∼ Rag2 P r− 12 . Both these are as per the predicted scalings by the mixing length model proposed by Arakeri et al. (2000) for high Rag convection in the vertical tube. The flux scaling N u ∼ (RaP r)2 , also known as the ‘ultimate regime’ of convection, expected at very high Ra but not yet observed in the experiments in classical RBC, is easily achieved in TC at relatively lower values of Ra. The fluxes and Reynolds numbers in TC are orders of magnitude higher as compared to those obtained in RBC for similar values of Ra and P r. In the lower range of Rag values for P r ≈ 6, a transition to a new flux scaling, N u ∼ (RaP r)0.29 is found. Similar transitions are also found to be present in the results of Tovar (2002) for Sc ≈ 600 and in the DNS results of Schmidt et al. (2012) for P r = 1, at different values of Rag. Collecting all these data, it is shown that the transition occurs at a fixed Grashof number of 1.6 × 105, independent of P r. Velocity measurements are carried out using particle image velocime-try (PIV) in the salt experiments. Kinetic energy spectra computed from the velocity fields are presented for the locations from the tube axis to the wall, for the lowest and the highest values of Rag achieved in the experiments. The spatial energy spectrum of lateral velocity at the tube axis follows Kolmogorov-Obukhov (KO) scaling (−5/3 scaling exponent) while the spatial spectrum of longitudinal velocity shows a scaling slightly higher than −5/3 but lower than −11/5 (the Bolgiano-Obukhov (BO) scaling). The scalar spectra is computed from the concentration fields obtained from planar laser induced fluorescence (PLIF) in the experiments using salt, and also from the temperature measurements from the experiments using heat. Both the concentra-tion and temperature fluctuations spectra show some evidence of dual scaling - BO scaling (−7/5 scaling exponent) in the inertial subrange followed by Obukhov-Corrsin (OC) scaling (−5/3 scaling exponent) over a narrow range of scales. Light propagation through the buoyancy driven turbulent flow in TC has also been experimentally investigated. Light propagation through convective turbulence is encountered in many situations. In some cases e.g. in observational astronomy it is undesirable, while in some other cases it is useful, e.g. in remote sensing of meteorological parameters. In the present study, light intensity and angle of arrival fluctuations in a parallel beam of light are measured. Laser shadowgraphy is used in the intensity measurements while the angle of arrival is obtained by measuring deflections of narrow laser beams, created by passing collimated laser light through a mask having equispaced grid of holes. Background oriented schlieren (BOS) measurements have also been carried out to obtain the displacements, which are proportional to the angle of arrivals. The equations for frequency spectrum of intensity and angle of arrival from the literature, developed for isotropic, ho-mogeneous turbulent media, are modified for the flow in the present case and the asymptotic scalings for high and low frequency ranges are obtained. The scalings in the frequency spectra computed from the measurements of intensity and angle of arrival fluctuations are com-pared with the obtained asymptotic scalings. The results from the present work are also compared with results from studies in the atmo-sphere and lab experiments.

Les modèles de prévision opérationnelle du temps résolvent numériquement les équations de la mécanique des fluides en calculant l'évolution de champs (pression, température, humidité, vitesses) définis comme moyennes horizontales à l'échelle des mailles d'une grille (et à différents niveaux verticaux).<p><p>Les processus d'échelle inférieure à la maille jouent néanmoins un rôle essentiel dans les transferts et les bilans de chaleur, humidité et quantité de mouvement. Les paramétrisations physiques visent à évaluer les termes de source correspondant à ces phénomènes, et apparaissant dans les équations des champs moyens aux points de grille.<p><p>Lorsque l'on diminue la taille des mailles afin de représenter plus finement l'évolution des phénomènes atmosphériques, certaines hypothèses utilisées dans ces paramétrisations perdent leur validité. Le problème se pose surtout quand la taille des mailles passe en dessous d'une dizaine de kilomètres, se rapprochant de la taille des grands systèmes de nuages convectifs (systèmes orageux, lignes de grain).<p><p>Ce travail s'inscrit dans le cadre des développements du modèle à mailles fines ARPÈGE ALADIN, utilisé par une douzaine de pays pour l'élaboration de prévisions à courte échéance (jusque 48 heures).<p><p>Nous décrivons d'abord l'ensemble des paramétrisations physiques du modèle.<p>Suit une analyse détaillée de la paramétrisation actuelle de la convection profonde. Nous présentons également notre contribution personnelle à celle ci, concernant l'entraînement de la quantité de mouvement horizontale dans le nuage convectif.<p>Nous faisons ressortir les principaux points faibles ou hypothèses nécessitant des mailles de grandes dimensions, et dégageons les voies pour de nouveaux développements.<p>Nous approfondissons ensuite deux des aspects sortis de cette discussion: l'usage de variables pronostiques de l'activité convective, et la prise en compte de différences entre l'environnement immédiat du nuage et les valeurs des champs à grande échelle. Ceci nous conduit à la réalisation et la mise en œuvre d'un schéma pronostique de la convection profonde.<p>A ce schéma devraient encore s'ajouter une paramétrisation pronostique des phases condensées suspendues (actuellement en cours de développement par d'autres personnes) et quelques autres améliorations que nous proposons.<p>Des tests de validation et de comportement du schéma pronostique ont été effectués en modèle à aire limitée à différentes résolutions et en modèle global. Dans ce dernier cas l'effet du nouveau schéma sur les bilans globaux est également examiné.<p>Ces expériences apportent un éclairage supplémentaire sur le comportement du schéma convectif et les problèmes de partage entre la schéma de convection profonde et le schéma de précipitation de grande échelle.<p><p>La présente étude fait donc le point sur le statut actuel des différentes paramétrisations du modèle, et propose des solutions pratiques pour améliorer la qualité de la représentation des phénomènes convectifs.<p><p>L'utilisation de mailles plus petites que 5 km nécessite enfin de lever l'hypothèse hydrostatique dans les équations de grande échelle, et nous esquissons les raffinements supplémentaires de la paramétrisation possibles dans ce cas.<p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Dans ce mémoire on s'intéresse à la modélisation du changement de phase solide-liquide en convection naturelle et en convection forcée en utilisant l'équation de diffusion de la chaleur et une forme modifiée de la conductivité. Comme on ne cherche pas à résoudre le champ des vitesses, on intègre à l'intérieur de la conductivité modifiée les effets thermiques des mouvements convectifs, puis on résout l'équation de conduction en utilisant ces conductivités modifiées. L'objectif du mémoire est de prédire la position de l'interface solide-liquide en fonction du temps dans un processus de fusion ou de solidification en présence de convection, et ce avec un modèle conductif. Dans les deux cas types que nous avons traités, la valeur de la conductivité modifiée à utiliser dans le modèle conductif simplifié est d'abord estimée par une étude d'ordre de grandeur. Le premier cas type étudié est celui du changement de phase en présence de convection forcée se déroulant dans une conduite à paroi froide. On a réussi à développer une relation permettant d'obtenir la valeur de la conductivité modifiée directionnelle à utiliser dans le modèle conductif en fonction du nombre de Reynolds de l'écoulement ainsi que du facteur de forme de la conduite. Cette relation a montré de bons résultats en comparaison avec ceux issus d'un modèle numérique complet plus classique (CFD). Le deuxième cas type étudié est celui de la fusion d'un matériau sous l'effet de la convection naturelle à l'intérieur d'une enceinte. Nous avons réussi à paramétrer l'évolution des valeurs de conductivité modifiée à utiliser par notre modèle conductif, celles-ci sont fonction de l'avancement du front de fusion et du nombre de Nusselt. Cette modélisation est comparée à la fois avec les résultats fournis par un modèle numérique complet (CFD) mais aussi avec des résultats expérimentaux issus de la littérature. Ces comparaisons ont montré une bonne concordance entre notre modélisation et la réalité. / In this work we have developed an enhanced conduction model for predicting solid-liquid interface positions in convection-dominated phase-change processus. The flow field is not calculated and the effects of convection are taken into account via the modification of the material conductivity. Our objective is to obtain a good approximation of the solid-liquid interface evolution. It is shown that the enhanced thermal conductivity of the melt may be formulated in terms of directional thermal conductivity components and that their value may be correlated in terms of dimensional numbers obtained from an order of magnitude analysis. The proposed approach is then tested for two different cases. The first test case is devoted to forced convection dominated solidification in a duct while the second test case is concerned with buoyancy dominated melting in an enclosure. The results of the simulations using our conduction model are then compared with a full CFD model and in the case of melting in an enclosure experimental data, they show good agreements.

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published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

A numerical code for solving the time-dependent incompressible 3D Navier-Stokes equations with finite volumes on overlapping staggered grids in cylindrical and rectangular geometry is developed. In the code, written in FORTRAN, the momentum equation for the velocity is solved by projection method and Poisson equation for the pressure is solved by ADI implicit method in two directions combined with discrete fast Fourier transform in the third direction. A special technique for overcoming the singularity on the cylinder's axis is developed. This code, taking into account dependence upon temperature of the viscosity, density and surface tension of the liquid, is used to study the fluid motion in a cylinder with free cylindrical surface (under normal and zero-gravity conditions); and in a rectangular closed cell with a source of thermocapillary convection (bubble inside attached to one of the cell's faces). They are significant problems in crystal growth and in general experiments in fluid dynamics respectively. Nevertheless, the main study is dedicated to the liquid bridge problem. The development of thermocapillary convection inside a cylindrical liquid bridge is investigated by using a direct numerical simulation of the 3D, time-dependent problem for a wide range of Prandtl numbers, Pr = 0.01 - 108. For Pr > 0.08 (e.g. silicon oils), above the critical value of temperature difference between the supporting disks, two counter propagating hydrothermal waves bifurcate from the 2D steady state. The existence of standing and traveling waves is discussed. The dependence of viscosity upon temperature is taken into account. For Pr = 4, 0-g conditions, and for Pr = 18.8, 1-g case with unit aspect ratio an investigation of the onset of chaos was numerically carried out. For a Pr = 108 liquid bridge under terrestrial conditions , the appearance and the development of thermoconvective oscillatory flows were investigated for different ambient conditions around the free surface. Transition from 2D thermoconvective steady flow to a 3D flow is considered for low-Prandtl fluids (Pr = 0.01) in a liquid bridge with a non-cylindrical free surface. For Pr < 0.08 (e.g. liquid metals), in supercritical region of parameters 3D but non-oscillatory convective flow is observed. The computer program developed for this simulation transforms the original non-rectangular physical domain into a rectangular computational domain. A study of how presence of a bubble in experimental rectangular cell influences the convective flow when carrying out microgravity experiments. As a model, a real experiment called TRAMP is numerically simulated. The obtained results were very different from what was expected. First, because of residual gravity taking place on board any spacecraft; second, due to presence of a bubble having appeared on the experimental cell's wall. Real data obtained from experimental observations were taken for the calculations.