No description available.

Safe and reliable operation of nuclear power plants is the basic requirement for the utilization of nuclear energy since accidents can release radioactivity and with that cause irreversible damage to human beings. Reliability and safety of nuclear reactors are highly dependent on the stability of thermal hydraulic processes occurring in them. Nucleate boiling occurs in Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) as well as in their passive safety systems during an accident. Passive safety systems are solely driven by thermal gradients and gravitational force removing residual heat from the reactor core independent of any external power supply in the case of accidents. Instability of flow boiling in these passive circuits can cause flow oscillations. These oscillations may induce insufficient local cooling and mechanical loads, which threatens the reactors’ safety. Analysis of boiling two-phase flow and associated heat and mass transfer requires an accurate modeling of flow regime transitions and prediction of boiling parameters such as void fraction, steam bubble sizes, heat transfer coefficient, etc. Flow boiling has been intensively investigated through experiments, one-dimensional codes, and Computational Fluid Dynamics (CFD) methods. Costly hardware and no accessibility to all locations in complex geometries restrict the experimental investigation of flow boiling. Since one-dimensional codes such as ATHLET, RELAP and TRACE are ”lumped parameter” codes, they are unable to simulate complex flow boiling transition patterns. In the last decades, with the development of supercomputers, CFD has been considered as a useful tool to model heat and mass transfer occurring in flow boiling regimes. In many industrial applications and system designs, CFD codes and particularly the Eulerian-Eulerian (E-E) two-fluid model are quickly replacing the experimental and analytical methods. However, the application of this approach for flow boiling modelling poses a challenge for the development of bubble dynamics and wall boiling models to predict heat and mass transfer at the heating wall as well as phase-change mechanism. Many empirical and mechanistic models have been proposed for bubble dynamics modelling. Nevertheless, the validity of these models for only a narrow range of operating conditions and their uncertainties limit their applicability and consequently presently necessitate us to calibrate them for a given boundary condition via calibration factors. For that reason, the first aim of this thesis is the development of a bubble dynamics model for subcooled boiling flow, which needs no calibration factor to predict the bubble growth and detachment. This mechanistic model is formulated based on the force balance approach, physics of a single nucleated bubble and several well-developed models to cover the whole bubble life cycle including formation, growth and departure. This model considers dynamic inclination angle and contact angles between the bubble and the heating wall as well as the contribution of microlayer evaporation, thermal diffusion and condensation around the bubble cap. Validation against four experimental flow boiling data sets was conducted with no case-dependent recalibration and yielded good agreement. The second goal is the implementation of the developed bubble dynamics model in the E-E two-fluid model as a sub-model to improve the accuracy of boiling flow simulation and reduce the case dependency. This implementation requires an extension of the nucleation site activation and wall heat-partitioning models. The bubble dynamics and heat-partitioning models were coupled with the Population Balance Model (PBM) to handle bubble interactions and predict the Bubble Size Distribution (BSD). In addition, the contribution of bubble sliding to wall heat transfer, which has been rarely considered in other modelling approaches, is considered. Validation for model implementation in the E-E two-fluid model was made with ten experimental cases including R12 and R134a flow boiling in a pipe and an annulus. These test cases cover a wide range of operating parameters such as wall heat flux, fluid velocity, subcooling temperature and pressure. The validated parameters were the bubble diameter, void fraction, bubble velocity, Interfacial Area Density (IAD), bubble passing frequency, liquid and wall temperatures. Two-phase flow morphologies for an upward flow in a vertical heating pipe may change from bubbly to slug, plug, and annular flow. Since these flow patterns have a great impact on the heat and mass transfer rates, an accurate prediction of them is critical. The aim of this thesis is the implementation of the developed bubble dynamics and heat-partitioning models in the recently developed GENeralized TwO-Phase flow (GENTOP) framework for the modelling of these flow patterns transition as well. An adopted wall heat-partitioning model for high void fractions is presented and for a generic test case, flow boiling regimes of water in a vertical heating pipe were modelled using ANSYS CFX 18.2. Moreover, the impacts of wall superheat, subcooling temperature and fluid velocity on the flow boiling transition patterns and the effects of these patterns on the wall heat transfer coefficient were evaluated.:Nomenclature xi 1 Introduction 1 1.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 State-of-the-art in modelling of subcooled flow boiling 11 2.1 Physics of boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Bubble growth modelling . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 CFD simulation of boiling flows . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 The Eulerian-Eulerian two-fluid model . . . . . . . . . . . . . 21 2.3.2 The Population Balance Model (PBM) . . . . . . . . . . . . . 22 2.3.3 Governing equations of the two-fluid model . . . . . . . . . . 25 2.3.4 Closure models for adiabatic bubbly flow . . . . . . . . . . . . 28 2.3.5 Phase transfer models . . . . . . . . . . . . . . . . . . . . . . 37 2.3.6 The Rensselaer Polytechnic Institute (RPI) wall boiling model 37 2.4 Flow boiling transition patterns in vertical pipes . . . . . . . . . . . . 42 2.5 The GENeralized TwO-Phase flow (GENTOP) concept . . . . . . . . . 45 2.5.1 Treatment of the continuous gas . . . . . . . . . . . . . . . . 46 2.5.2 The Algebraic Interfacial Area Density (AIAD) model . . . . . 46 2.6 Interfacial transfers of continuous gas . . . . . . . . . . . . . . . . . 47 2.6.1 Drag and lift forces . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6.2 Cluster and surface tension forces . . . . . . . . . . . . . . . . 49 2.6.3 Complete coalescence . . . . . . . . . . . . . . . . . . . . . . 50 2.6.4 Entrainment modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.6.5 Turbulence modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3 An improved bubble dynamics model for flow boiling 55 3.1 Modelling of the bubble formation . . . . . . . . . . . . . . . . . . . 55 3.1.1 Bubble growth rate . . . . . . . . . . . . . . . . . . . . . . . . 57 3.1.2 Force balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 ix 3.1.3 Detachment criteria . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.4 Wall heat flux model . . . . . . . . . . . . . . . . . . . . . . . 69 3.1.5 Heat transfer in the heating wall . . . . . . . . . . . . . . . . 70 3.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1 Discretization dependency study . . . . . . . . . . . . . . . . 72 3.2.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4 An improved wall heat-partitioning model 85 4.1 The cavity group activation model . . . . . . . . . . . . . . . . . . . . 85 4.1.1 Bubble sliding length and influence area . . . . . . . . . . . . 88 4.1.2 Model implementation in the Eulerian-Eulerian framework . . 89 4.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.1 DEBORA experiments . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2 Subcooled flow boiling of R134a in an annulus . . . . . . . . 102 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5 Modelling of flow boiling patterns in vertical pipes 115 5.1 Adopted wall heat-partitioning model for high void fractions . . . . . 115 5.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2.1 Effect of wall superheat on the flow boiling transition patterns 118 5.2.2 Effect of flow morphologies on the wall heat transfer coefficient124 5.2.3 Comparison of GENTOP and Eulerian-Eulerian two-fluid models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2.4 Effect of subcooling on the flow boiling transition patterns . . 129 5.2.5 Effect of inlet fluid velocity on the flow boiling transition patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 Conclusions and outlook 133 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 References 137 Declaration 155

Carbon dioxide hydrates were synthesized in a 0.10m I.D. and 1.22m tall bubble column equipped with a cooling jacket for heat removal. Visual observations at different driving forces (pressures between 2.75 and 3.60 MPa and temperatures between 0 and 8ºC) were recorded with a digital camera through a sight glass of 118.8 by 15.6 mm. The superficial gas velocity was varied from 20 to 50 mm/s to attain different levels of turbulence in the liquid. The growth rate was found to be dependent on the sequence/method used to reach the operating temperature and pressure. A greater supersaturation was obtained when the system temperature and pressure were reached with very low or no bubble-induced mixing. As a result, hydrates nucleated and grew immediately when starting the gas flow with the reactor volume being quickly filled with hydrates. Moreover, the hydrate growth rate and solution final density were higher when operating conditions partially condensed CO2 resulting in greater interphase mass transfer rates. In parallel, since hydrate formation is an exothermic process and the reaction is often limited by the rate of heat removal, heat transfer measurements were achieved in a simulated hydrate environment. The instantaneous heat transfer coefficient and related statistics gave insight on the role of bubbles on heat transfer and hydrodynamics.

This dissertation aims to better understand the evolution of single hydrogen gas bubbles evolved during the water electrolysis at microelectrodes. In particular, the growth and detachment processes were studied in detail experimentally by means of electrochemical and optical methods in terrestrial, micro-, and hypergravity conditions. The combination of microelectrode and sulfuric acid promoting the bubble coalescence results in a periodical growth and the detachment of single bubbles. This provides a systematic view on the phenomena under study. A shadowgraphy system was used to provide general insight into the bubble behaviour, while Particle Tracking Velocimetry (PTV) was used for the flow velocity measurements around the growing hydrogen bubble. By applying high electric potentials considerably exceeding that in industrial electrolysers, it is possible to analyse the evolution of hydrogen bubbles under extreme conditions and for a wide range of electrolyte concentrations, overall shedding more light on bubble dynamics in general, and especially the underlying balance of forces. The growth of single hydrogen bubbles at micro-electrodes was studied in an acidic electrolyte over a wide range of concentrations and cathodic potentials. New bubble growth regimes were identified which differ in terms of whether the bubble evolution proceeds in the presence of a monotonic or oscillatory variation in the electric current and a carpet of microbubbles underneath the bubble. Key features such as the growth law of the bubble radius, the dynamics of the microbubble carpet, the onset time of the oscillations and the oscillation frequencies were characterised as a function of the concentration and electric potential. Furthermore, the system's response to jumps in the cathodic potential was studied. The electrode, tilted to the horizon, promotes faster growth and, therefore, earlier detachment at the smaller volume of the bubble. During its evolution, the bubble moves laterally from the electrode centre, releasing the electrode area and enabling higher electric current, therefore faster hydrogen generation and bubble-bubble coalescence rates. The duration of the bubble position oscillations found on the horizontal electrode gradually reduces upon tilt angle increase, with an almost complete disappearance at 5°. Based on the analysis of the forces involved and their scaling with the concentration, potential and electric current, a sound hypothesis was formulated regarding the mechanisms underlying the micro-bubble carpet and oscillations. A detailed look was also taken on the dynamics of single hydrogen bubbles in microgravity during parabolic flights. Three bubble evolution scenarios were identified depending on the electric potential applied and the acid concentration. The dominant scenario, characterised by lateral detachment of the grown bubble, was studied in detail. For that purpose, the evolution of the bubble radius, electric current and bubble trajectories as well as the bubble lifetime were comprehensively addressed for different potentials and electrolyte concentrations. The bubble-bubble coalescence events, which are responsible for reversals of the direction of bubble motion, were particularly analysed. Finally, as parabolic flights also permit hypergravity conditions, a detailed comparison of the characteristic bubble phenomena at various levels of gravity was drawn. Finally, the Marangoni convection at the foot of hydrogen gas bubbles mainly induced by the thermocapillary effect is systematically studied during the bubble evolution, the bubble position oscillations, at horizontal and tilted electrodes both in terrestrial and hyper-g environments. The flow structure progressively modifies with the bubble evolution or during the bubble position oscillations, i.e. as per electric current and bubble geometry variation. The velocity increases both with the bubble size and the electric current magnitude. It reaches up to 50 mm/s and 125 mm/s shortly before the bubble detachment at horizontal and tilted electrodes, correspondingly. The bubble position oscillations characterised by the large variation of the electric current govern the velocity of around ~80 mm/s at the highest and ~40 mm/s at the lowest positions. In the case of tilted electrodes, both in terrestrial and hyper-g environments, the lateral movement of the bubble enables higher values of the current and, therefore, stronger convection. The non-homogeneous distribution of the electric current lines at the tilted electrode results in the asymmetrical Marangoni convection around the bubble. There is a certain limitation in terms of the maximal magnitude of the velocity at different tilt angles, governed by the optimal size of the bubble and electric current. At last, the effects of the particles and laser used for PTV measurements were shown to reduce the duration of the oscillations and to retard the bubble evolution. Both effects were considered during the measurements.

In order to elucidate the progression mechanism of cavitation erosion, the behaviors of a single cavitation bubble collapse near a pit on a wall and both the resulting pressure wave in fluid and stress wave in material are investigated in detail. To find out the mechanism of cavitation erosion, many experimental studies on the bubble collapse behavior near a flat rigid wall and the resulting material damage have been conducted so far. A lot of numerical studies using only fluid analysis have been also carried out. In recent years, a few studies on the bubble collapse near a more complex geometry were made and it is reported that more complex geometry has an effect on the bubble collapse behavior, jet formation and subsequent wave dynamics. It is, however, very challenging to introduce a material analysis and investigate detailed stress wave propagation in the material and its effect on the material damage i.e. cavitation erosion. This study tackles this problem using an in-house fluid/material two-way coupled numerical analysis method which considers reflection and transmission of plane waves with acoustic impedance at the fluid/material boundary. In the fluid domain, the locally homogeneous model of compressible gas-liquid two-phase medium is used for capturing the gas-liquid interface. The compressibility of two-phase flow is also considered in this model so that the propagation of pressure wave can be also be taken into account. The governing equations are the 3D compressible gas-liquid two-phase Navier-Stokes equations. In the material domain, the governing equations are composed of the motion equations and the time-differential constitutive equations assuming that the material is a homogeneous isotropic elastic medium, which can simulate the stress wave propagation in the material. Results show that the stress waves are concentrated at the bottom of the pit regardless of the initial bubble position. It is also found that the surface pressure in the fluid side does not necessarily correlate with the stresses in the material, suggesting the importance of material analysis. Moreover, under high pressure conditions, a rapid bubble collapse causes a gas phase generation at the bottom of the pit and its gas phase is contracted and collapsed by the pressure wave, which leads to pressure and stress peaks at the bottom of the pit. Furthermore, through the study of the effect of initial bubble position on its collapse behavior, it is confirmed that, when the initial bubble position is shifted horizontally, bubble collapses asymmetrically and the pressure waves tend to be directed away from a pit. This research numerically reveals that a single bubble collapse near a pit on a wall results in high strain energy concentration at the bottom of the pit, which gives rise to deeper erosion progression at the bottom of the pit. / För att klargöra framstegsmekanismen för kavitationserosion kollapsar beteendet hos en enda kavitationsbubbla nära en grop på en vägg och både den resulterande tryckvågen i vätska och stressvåg i material undersöks i detalj. För att ta reda på mekanismen för kavitationserosion har många experimentella studier av bubblans kollapsbeteende nära en platt styv vägg och den resulterande materialskada genomförts hittills. Många numeriska studier med endast vätskeanalys har också genomförts. Under de senaste åren gjordes några studier om bubblans kollaps nära en mer komplex geometri och det rapporteras att mer komplex geometri har en effekt på bubblans kollapsbeteende, strålbildning och efterföljande vågdynamik. Det är dock mycket utmanande att införa en materialanalys och undersöka detaljerad spänningsvågförökning i materialet och dess inverkan på materialskadorna, dvs. kavitationserosion. Denna studie hanterar detta problem med hjälp av en inbyggd tvåvägs kopplad numerisk analysmetod som tar hänsyn till reflektion och överföring av plana vågor med akustisk impedans vid vätska / materialgränsen. I fluiddomänen används den lokalt homogena modellen av tvåfasmedium för komprimerbar gas-vätska för att fånga gas-vätskegränssnittet. Komprimerbarheten av tvåfasflöde beaktas också i denna modell så att utbredningen av tryckvågen också kan beaktas. De styrande ekvationerna är de 3D-komprimerbara tvåfasiga gasvätska Navier-Stokes-ekvationerna. I materialdomänen är de styrande ekvationerna sammansatta av rörelseekvationer och tidsdifferentialkonstitutiva ekvationer förutsatt att materialet är ett homogent isotropiskt elastiskt medium, vilket kan simulera spänningsvågutbredningen i materialet. Resultaten visar att stressvågorna är koncentrerade längst ner i gropen oavsett den ursprungliga bubbelpositionen. Man har också funnit att yttrycket i vätskesidan inte nödvändigtvis korrelerar med spänningarna i materialet, vilket tyder på vikten av materialanalys. Vidare orsakar en snabb bubbelskollaps under högtrycksförhållanden en gasfasgenerering vid botten av gropen och dess gasfas dras samman och kollapsas av tryckvågen, vilket leder till tryck och spänningstoppar vid botten av gropen. Vidare bekräftas det genom studien av effekten av den ursprungliga bubbelpositionen på dess kollapsbeteende att när den ursprungliga bubbelpositionen förskjuts horisontellt kollapsar bubblan asymmetriskt och tryckvågorna tenderar att riktas bort från en grop. Denna undersökning avslöjar numeriskt att en enda bubbla kollapsar nära en grop på en vägg resulterar i hög spänningsenergikoncentration längst ner i gropen, vilket ger upphov till djupare erosionsprogression längst ner i gropen.

L’ébullition est un mode de transfert de chaleur intervenant dans de nombreux systèmes thermiques ou énergétiques de par son efficacité. Dans certains, elle se produit à basse pression. La pression statique induite par la colonne de liquide au-dessus de la surface de formation des bulles n’est alors pas négligeable devant la pression de saturation à la surface libre. Dès lors, la pression et le sous-refroidissement induit ne peuvent plus être considérés homogènes autour des bulles, d’où des inhomogénéités des propriétés thermophysiques dans le fluide. Les influences relatives des forces s’exerçant sur une bulle pendant sa croissance sont modifiées par rapport aux pressions plus élevées : une dynamique de bulles différente apparaît. Ces conditions particulières affectent également les transferts thermiques. L’influence de la pression sur l’ébullition en vase a été étudiée expérimentalement dans le régime de bulles isolées en site unique. L’eau a d’abord été testée sur une large gamme de pressions subatmosphériques. Quatre comportements de dynamique de bulles ont été identifiés d’après la visualisation par caméra rapide. Plusieurs paramètres de la dynamique ont été quantifiés grâce à un traitement d’images adapté appliqué aux vidéos. Pour généraliser le concept d’ébullition à « basse pression » et mieux en appréhender les phénomènes fondamentaux, de nouveaux essais ont été réalisés avec un second fluide, le cyclohexane, choisi pour sa similitude thermodynamique avec l’eau bouillant en deçà de la pression atmosphérique. La comparaison des comportements des deux fluides a permis d’identifier certains paramètres responsables des spécificités du phénomène. En outre, de nouvelles fonctionnalités sont apportées au dispositif expérimental pour – notamment – effectuer la mesure rapide du flux transféré sous la bulle pendant sa croissance, synchroniser ces mesures thermiques avec l’acquisition d’images et étudier des surfaces d’ébullition structurées. Les résultats obtenus sont encourageants pour l’analyse des comportements spécifiques de l’ébullition à basse pression et ses applications. / Boiling is an efficient heat transfer mode used in numerous thermal or energy systems. In some systems boiling takes place at low pressure. The static head of the liquid column over the wall where bubbles nucleate is then not negligible against the saturation pressure at the free surface level. The pressure and the induced subcooling degree therefore cannot be considered as homogeneous around growing bubbles, resulting in non-homogeneous thermophysical properties in the fluid. The relative influence of the forces acting on a growing bubble differs from higher pressure conditions, yielding specific bubble dynamics features. Heat transfer is consequently also affected. The effect of the pressure on pool boiling was experimentally investigated during the isolated bubbles regime taking place from a single activated nucleation site. Experiments were first conducted with water for a wide range of subatmospheric pressures. Four distinct bubble dynamics behaviors were identified through high-speed camera visualizations. An adapted image processing of the recordings enabled the measurement of several bubble dynamics characteristics. In order to generalize the concept of pool boiling at "low pressure" and to get a better understanding of the related fundamental phenomena, new experiments were performed with a second fluid, cyclohexane, chosen from original thermodynamic similarity with water boiling at pressures lower than atmospheric. The comparison of fluids’ behaviors made possible the identification of parameters governing the specific phenomena occurring during boiling at low pressure. Besides, the experimental facility was improved to provide new functionalities. The high-speed measurement of the heat flux transferred under the growing bubble, its synchronization with the high-speed videos images and the study of boiling on enhanced surfaces are in particular made possible. Results are encouraging for a better understanding of the specific behaviors of low pressure boiling and for its future implementation in practical applications.

Cette thèse est consacrée aux écoulements homogènes de bulles, ainsi qu'à leur couplage avec le transport d'un scalaire et la turbulence. Elle s'intéresse plus spécifiquement aux effets de taille finie, des interactions hydrodynamiques et de la microstructure de la suspension qui sont étudiés à l'aide de simulations numériques directes à l'échelle d'une seule bulle. La dynamique d'une suspension laminaire de bulles induite par la seule gravité est d'abord revisitée. L'influence de la fraction volumique sur la vitesse de dérive des bulles est établie analytiquement et numériquement pour une suspension parfaitement ordonnée, puis des ressemblances entre suspensions ordonnées et suspensions désordonnées sont mises en évidence. Ces résultats sont ensuite mis à profit pour la modélisation du transport d'un scalaire passif au sein d'une suspension laminaire, tel que décrit par une diffusivité effective tensorielle, et des différences essentielles entre systèmes ordonnés et systèmes désordonnés concernant le transport de scalaire sont mises en exergue. Enfin, la turbulence est prise en compte dans les simulations et son interaction avec une bulle de taille finie est caractérisée. Il est montré que le comportement dynamique d'une bulle de taille comparable à la microéchelle de Taylor ressemble qualitativement à celui d'une microbulle, avec, notamment, une préférence pour certaines régions caractéristiques de l'écoulement. Une définition de l'écoulement vu par la bulle compatible avec les modèles standards de masse ajoutée et de portance est finalement proposée / This thesis is devoted to the study of homogeneous bubbly flows and their coupling with scalar transport and turbulence. It focuses on the effects of finite size, hydrodynamic interactions, and suspension microstructure, which are investigated using direct numerical simulations at the bubble scale. The dynamics of laminar buoyancy-driven bubbly suspensions is first revisited. More specifically, the effect of volume fraction on the bubble drift velocity is clarified by connecting numerical results to theory for dilute ordered systems, and similarities between perfectly ordered and free disordered suspensions are evidenced. These results are then used for the modeling of passive scalar transport in laminar suspensions as described by an effective diffusivity tensor, and crucial differences between ordered and disordered systems with respect to scalar transport are highlighted. Lastly, turbulence is included in the simulations, and its interaction with a finite-size bubble is characterized. The behavior of a bubble as large as Taylor microscale is shown to share a number of common features with that of a microbubble, most notably, the flow sampled by the bubble is biased. A definition of the liquid flow seen by the bubble, as it enters in usual models for the added mass and the lift forces, is finally proposed

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The present thesis deals with two-phase electrohydrodynamic simulations of bubble and droplet dynamics under externally applied electric fields. We used the Coupled Level-Set and Volume-of-fluid method (CLSVOF) and two different electrohydrody-namic formulations to study the process of bubble and drop formation from orifices and needles, the interactions of two conducting drops immersed in a dielectric medium, and the oscillations of sessile drops under two different ways of applying external elec-tric field. For the process of bubble formation in dielectric liquids due to the injection of air from submerged orifices and needles, we show that a non-uniform electric field pro-duces smaller bubbles while a uniform electric field changes only the bubble shape. We further explain the reason behind the bubble volume reduction under a non-uniform electric field. We show that the distribution of the electric stresses on the bubble inter-face is such that very high electric stresses act on the bubble base due to a non-uniform electric field. This causes a premature neck formation and bubble detachment lead-ing to the formation of smaller bubbles. We also observe that the non-uniform elec-tric stresses pull the bubble interface contact line inside the needle. With oscillatory electric fields, we show that a further reduction in bubble sizes is possible, but only at certain electric field oscillation frequencies. At other frequencies, bubbles bigger than those under a constant electric field of strength equal to the amplitude of the AC electric field, are produced. We further study the bubble oscillation modes under an oscillatory electric field. We implemented a Volume-of-fluid method based charge advection scheme which is charge conservative and non-diffusive. With the help of this scheme, we were able to simulate the electrohydrodynamic interactions of conducting-dielectric fluid pairs. For two conducting drops inside a dielectric fluid, we observe that they fail to coalesce when the strength of the applied electric field is beyond a critical value. We observe that the non-coalescence between the two drops occur due to the charge transfer upon drop-drop contact. The electric forces which initially bring the two drops closer, switch direction upon charge transfer and pull the drops away from each other. The factors governing the non-coalescence are the electric conductivity of the drop’s liquid which governs the time scale of charge transfer relative to the capillary time scale and the magnitude of the electric forces relative to the capillary and the viscous forces. Similar observations are recorded for the interactions of a charged conducting drop with an interface between a dielectric fluid and a conducting fluid which is the same as the drop’s liquid. For the case of a pendant conducting drop attached to a capillary and without any influx of liquid from the capillary, we observed that the drop undergoes oscillations at lower values of electric potential when subjected to a step change in the applied electric potential. At higher values of electric potential, we observed the phenomenon of cone-jet formation which results due to the accumulation of the electric charges and thus the electric forces at the drop tip. For the formation of a pendant conducting drops from a charged capillary due to liquid injection, we observed that the drops are elongated in presence of an electric field. This happens because the free charge which appears at the drop tip is attracted towards the grounded electrode. This also leads to the formation of elongated liquid threads which connect the drop to the capillary during drop detachment. We plotted the variation of total electric charge inside the drops with respect to time and found the charge increases steeply as the drop becomes elongated and moves towards the grounded electrode. For sessile drop oscillations under an alternating electric field, two different modes of operations are studied. In the so called ‘Contact mode’ case, the droplet is placed on a dielectric coated grounded electrode and the charged needle electrode remains in direct contact with the drop as it oscillates. In the ‘Non-contact mode’ case, the drop is placed directly on the grounded electrode and electric potential is applied to a needle electrode which now remains far from the drop. We show that the drop oscillations in the contact mode are caused by concentration of electric forces near the three phase contact line where the electric charge accumulates because of the repulsion from the needle. For the non-contact mode, we observe that the electric charge is attracted by the needle towards the drop apex resulting in a concentration of the electric forces in that region. So the drop oscillates due to the electric forces acting on a region near the drop tip. We also present the variation of the total electric charge inside the drop with respect to time for the two cases studied.

Dans ce document, nous présentons nos travaux sur les décharges dans l'heptane. L'une des conditions retenue pour ces études est le choix d'un gap micrométrique. Nous avons travaillé avec des gaps compris entre 10 et 150 µm qui correspondent à des tensions de claquage comprises entre 1 et 15 kV. Du claquage jusqu'à 1 µs, la décharge a été caractérisée par ombroscopie et par spectroscopie d'émission optique (SEO). L'ombroscopie a montré que la vitesse de propagation de l'onde de choc et de la bulle est de l'ordre de 1200 m s-1 et 100 m s-1, respectivement. Au-delà de 1 µs, la dynamique de la bulle a été étudiée. Une nouvelle méthode est proposée pour estimer la pression à l'initiation de la décharge. La technique est basée sur la réponse d'une "bulle test" qui se trouve dans le champ acoustique d'une nouvelle décharge dont on veut connaître la pression. Elle est aux environs 80 bar. La SEO a montré une dominance des rayonnements continus pendant les premières 200 ns qui ont été attribués à la recombinaison électron-ion. Au-delà de 200 ns, les rayonnements continus s'effondrent et les raies d'émission deviennent dominantes. L'étude de l'élargissement de la raie H[alpha] de l'hydrogène a montré que la densité électronique peut atteindre 1019 cm-3. En ce qui concerne l'interaction plasma-surface, nous avons pu démontrer que l'impact créé est gouverné par la quantité de charges déposée. Sa morphologie est une résultante d'un équilibre entre la force due à la pression et la force de Marangoni. Nous avons étudié dans une dernière partie la synthèse des nanoparticules de platine (diamètre 5 nm) insérées dans une matrice de carbone hydrogéné présentant un ordre à courte distance / In this document, we report our work on discharges in heptane. One of the specific conditions selected is the choice of a micrometric gap distance. Typically, gaps were between 10 and 150 µm, corresponding to breakdown voltages between 1 and 15 kV. From breakdown up to 1 µs, the plasma discharge was characterized by shadowgraphy and optical emission spectroscopy (OES). Shadowgraphy results showed that the velocities of shock wave and bubble interface are about 1200 m s-1 and 100 m s-1, respectively. Beyond 1 µs, experimental and theoretical studies of the oscillatory dynamics of the bubble are made. Then, we proposed a new method to estimate the pressure at discharge breakdown. The technique is based on the response of a 'test bubble' present in the acoustic field of a new discharge whose pressure is to be known. It is estimated to be about 80 bar. OES, between 300 and 800 nm, showed a dominance of continuous radiations during the first 200 ns which were attributed to electron-ion recombination processes. Beyond 200 nm, continuous radiations collapse and then, the emission lines dominate the spectrum. The study of the H? line broadening showed that the electron density can reach 1019 cm-3. Regarding the interaction of the discharge with the electrode surfaces, we demonstrated that the diameter of the impact is governed by the quantity of charges deposited by the discharge. However, the impact morphology is determined by a balance between the force exerted by the plasma pressure and the Marangoni's force. Finally, we studied the possibility to synthesize platinum nanoparticles (5 nm in diameter) embedded in a matrix of hydrogenated carbon exhibiting a short range order