Modélisation des transferts de masse et de chaleur dans une cellule d'électrolyse de production de fluor. La production de fluor par électrolyse est une étape clé de la conversion de l’uranium dans l’industrie nucléaire. Afin d’optimiser ce procédé, les travaux de thèse décrits dans ce manuscrit se sont concentrés sur deux axes : le développement d’un modèle numérique de l’électrolyseur et l’étude du phénomène d’hyperpolarisation cathodique néfaste pour le bon fonctionnement de la cellule. Un modèle couplant plusieurs physiques (thermique avec solidification, diphasique, électrocinétique) a été développé et des essais expérimentaux ont été menés afin d’acquérir, d’une part, certaines propriétés physiques de l’électrolyte nécessaires aux simulations (conductivité thermique et capacité thermique à pression constante) et, d’autre part, des données expérimentales permettant de qualifier le modèle obtenu. Ce travail de modélisation a abouti à l’obtention d’un modèle 3D fiable couplant les physiques citées précédemment, ceci à l’échelle d’un pilote R&D semi-industriel. L’impact de la solidification de l’électrolyte sur le transfert de chaleur a également pu être simulé pour la première fois. Ces essais ont également permis de fournir des premières explications sur le phénomène d’hyperpolarisation cathodique en dressant des tendances claires quant à l’influence de certains paramètres de contrôle de l’électrolyseur comme le titre HF et la température de consigne. / Computer modeling of heat transfer and mass transfer in an electrolytic cell for production of fluorineElectrolytic production of fluorine is a key step in uranium conversion for the nuclear industry. In order to improve this process, the work described in this dissertation aims at two main objectives: to build a numerical simulation of the electrolysis cell and to understand the cathodic hyperpolarization effect which lowers the productivity of the cell. A model coupling several physics (heat transfer with solidification, two-phase flow, electrokinetics) has been developed and experiments were made in order to evaluate unknown physical properties of the electrolyte (thermal conductivity and heat capacity at constant pressure). Experimental data were also acquired in order to assess the capacity of the model to simulate various phenomena occurring inside the cell. Eventually, a reliable 3D model of a semi-industrial R&D cell coupling the physics above mentioned has been obtained. The negative impact of the solidification of the electrolyte on the cooling system was simulated for the first time. Thanks to these experiments, it was also possible to determine the major trends which drive the cathodic hyperpolarization effect. The influence of HF mass fraction and temperature on this phenomenon was clearly shown.

Em linhas gerais, esta dissertação de mestrado envolve o estudo de padrões de escoaomento durante a ebulição convectiva em microcanais. Resultados experimentais foram levantados para um tubo com diâmetro de 2,32 mm durante a evaporação convectiva dos refrigerantes R134a e R245fa. Para a investigação, técnicas experimentais e de análise foram desenvolvidas. A caracterização dos padrões de escoamento envolveu o tratamento simultâneo de sinais provenientes dos seguintes dispositivos: um par diodo/sensor-laser tendo um tubo transparente entre eles no interior do qual ocorre o escoamento bifásico; um transdutor de pressão piezo-elétrico de tamanho reduzido com o objetivo de determinar a variação local da pressão do escoamento; e de um micro-termopar em contato com o fluido refrigerante. A técnica de tratamento de dados utilizada envolve a aglomeração progressiva de dados que apresentem características médias similares através do algoritmo k-means. Os sinais de pressão, intensidade de radiação e temperatura foram adquiridos simultaneamente a uma freqüência de 25 kHz. Imagens simultâneas do escoamento bifásico a uma velocidade de captura em torno de 10.000 imagens/s foram levantadas através de uma câmera de filmagem rápida (até 100.000 imagens/s), e os padrões de escoamentos observados contrastados aos resultados fornecidos pelo método proposto. Baseado nesta análise, mapas de escoamento foram propostos, os quais incorporaram não apenas critérios subjetivos como a visualização, mas também objetivos como as variações transientes da pressão local do escoamento e da morfologia do escoamento através do seu efeito na dispersão da radiação emitida pelo foto-diodo. Os resultados previstos pelo método objetivo apresentam concordância razoável com os dados caracterizados com base em visualizações. Adicionalmente, características de bolhas alongadas foram determinadas. / The present research has been focused on the study of flow patterns inside channels of diameter less than 3 mm during the convective evaporation of refrigerants such as R134a and R245fa. For the investigation of such topics, experimental techniques and methods of analysis of results were developed. A broad database was gathered in an experimental test facility. The characterization of flow patterns involved the simultaneous processing of signals from the following devices: a pair diode / laser-sensor having a transparent tube between them, within which occurs the two-phase flow; a micro piezoelectric pressure transducer to determine the local variation of pressure of the flow and a micro-thermocouple fixed within the fluid. The technique used in data processing involves the gradual agglomeration of data having similar average characteristics; this method was developed based on the k-means clustering algorithm. The signals from the transducers were acquired simultaneously at a frequency of 25 kHz. The program for the acquisition and for processing of the signals was developed using LabView. Simultaneous images of two-phase flow at a speed of capture around 10,000 images / s were obtained through a high speed camera and the observed flow patterns were contrasted to the results provided by the objective method. Based on this analysis, flow maps were proposed, which incorporate not only subjective criteria such as visualization, but also objective criteria like the transient variations of local pressure of the flow, temperature of the fluid and the effect of the flow morphology based on the dispersion of light which effect was captured by the photo-diode. The maps obtained by the objective method were compared against flow pattern segregated based on visualization and a reasonable agreement was obtained. Besides the elongated bubble characteristics were determined.

Two-phase flow, ubiquitous to waterflood oil recovery, geological CO2 storage, and groundwater remediation, is strongly influenced by wettability, and made more complex under mixed-wet conditions. Optimum wettability for such operations is not well established due to limited experimental data and difficulties in their interpretation. This thesis investigates the impact of mixed-wettability, characterised by advancing contact angle θa on capillary pressure, relative permeability, and waterflood displacement. Using a Darcy scale simulator, relative permeability kr, capillary pressure Pc, and residual oil saturation Sor were extracted by history matching production and pressure drop data from centrifuge brine invasion and waterflood displacements completed for a range of θa. As θa increased, a larger |Pc| was required to displace oil from mixed-wet cores at high initial oil saturation. End point oil and brine permeability decreased with increasing θa. A permeability enhancement, such that kr > 1, was measured both when the flowing phase was wetting and non-wetting and was attributed to a slippage at the oil/brine interface directly correlated to θa. Residual oil saturation decreased monotonically with increasing θa while core-averaged remaining oil saturation at the end of the waterflood exhibited a non-monotonic dependence on θa. Simulations of the waterfloods revealed that both significant capillary end effects and premature termination of the waterflood in the laboratory contribute to the deviation between remaining and residual saturations. This work demonstrates that the former is not representative of the latter, as it has been assumed in a number of studies in the literature. Both corefloods and microfluidic waterfloods show the importance of combining experimental studies with simulation for correct interpretation of the measurements especially under capillary dominated flow.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Mohamed Tayeb Benchaita. / Ph.D.

abstract: The goal of this paper was to do an analysis of two-dimensional unsplit mass and momentum conserving Finite Volume Methods for Advection for Volume of Fluid Fields with interfaces and validating their rates of convergence. Specifically three unsplit transport methods and one split transport method were amalgamated individually with four Piece-wise Linear Reconstruction Schemes (PLIC) i.e. Unsplit Eulerian Advection (UEA) by Owkes and Desjardins (2014), Unsplit Lagrangian Advection (ULA) by Yang et al. (2010), Split Lagrangian Advection (SLA) by Scardovelli and Zaleski (2003) and Unsplit Averaged Eulerian-Lagrangian Advection (UAELA) with two Finite Difference Methods by Parker and Youngs (1992) and two Error Minimization Methods by Pilliod Jr and Puckett (2004). The observed order of accuracy was first order in all cases except when unsplit methods and error minimization methods were used consecutively in each iteration, which resulted in second-order accuracy on the shape error convergence. The Averaged Unsplit Eulerian-Lagrangian Advection (AUELA) did produce first-order accuracy but that was due to a temporal error in the numerical setup. The main unsplit methods, Unsplit Eulerian Advection (UEA) and Unsplit Lagrangian Advection (ULA), preserve mass and momentum and require geometric clipping to solve two-phase fluid flows. The Unsplit Lagrangian Advection (ULA) can allow for small divergence in the velocity field perhaps saving time on the iterative solver of the variable coefficient Poisson System. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2019

The Mechanical Engineering Department at California Polytechnic State University in San Luis Obispo currently maintains a lab-scale hybrid rocket motor for which nitrous oxide is utilized as the oxidizer in the combustion system. Because of its availability, the same two-phase (gas and liquid) nitrous oxide that is used in the combustion system is also routed around the throat of the hybrid rocket’s converging-diverging nozzle as a coolant. While this coolant system has proven effective empirically in previous tests, the physics behind the flow of the two-phase mixture is largely unexplained. This thesis provides a method for predicting some of its behavior by modeling it using the classic gas dynamics scenarios of Rayleigh and Fanno flows which refer to one-dimensional, compressible, inviscid flow in a constant area duct with heat addition and friction. The two-phase model produced utilizes a separated phase with interface exchange model for predicting whether or not dryout occurs. The Shah correlation is used to predict heat transfer coefficients in the nucleate boiling regime. The homogeneous flow model is utilized to predict pressure drop. It is proposed that a Dittus-Boelter based correlation much like that of Groeneveld be developed for modeling heat transfer coefficients upon the collection of sufficient data. Data was collected from a series of tests on the hybrid rocket nozzle to validate this model. The tests were first run for the simplified case of an ideal gas (helium) coolant to verify the experimental setup and promote confidence in subsequent two-phase experimental results. The results of these tests showed good agreement with a combined Rayleigh-Fanno model with a few exceptions including: (1) reduced experimental gas pressure and temperature in the annulus entrance and exit regions compared to the model and (2) reduced experimentally measured copper temperatures uniformly through the annulus. These discrepancies are likely explained by the geometry of the flowpath and location of the copper thermocouples respectively. Next, a series of two-phase cooled experiments were run. Similar trends were seen to the helium experiment with regards to entrance and exit regions. The two-phase Rayleigh homogeneous flow model underpredicted pressure drop presumably due to the inviscid assumption. Ambiguity was observed in the fluid temperature measurements but the trend seemed to suggest that mild thermal non-equilibrium existed. In both cases, the dryout model predicted that mist flow (a post-CHF regime) occurred over most of the annulus. Several modifications should be implemented in future endeavors. These include: (1) collecting more data to produce a heat transfer coefficient correlation specific to the nitrous oxide system of interest, (2) accounting for thermal non-equilibrium, (3) accounting for entrance and exit effects, and (4) developing a two-phase Fanno model.

The hydrodynamic phenomena occurring inside the enclosed downcomer section of a plunging jet bubble column are described in the study. The gas entrainment rate for a plunging liquid jet was found to consist of two components, namely the gas trapped within the effective jet diameter at the point of impact, and the gas contained within the film between the jet and induction trumpet surface at the point of rupture. Entrainment within the effective jet diameter has been examined by McCarthy (1972). In this study, a model was supported by the experimental results, provided the film attained a region of constant thickness. When the induction trumpet was ruptured prior to a constant film thickness being reached, the measured rate of filmwise entrainment was higher than the prediction. Filmwise entrainment was found to be initiated once a critical velocity along the surface of the induction trumpet was reached. The critical velocity was a function only of the liquid physical properties and was independent of the jet conditions and downcomer diameter. The velocity of the free surface of the induction trumpet was obtained from the velocity profile for the recirculating eddy generated by the confined plunging liquid jet. The jet angle used to describe the expansion of the submerged jet inside the downcomer was predicted from the radial diffusion of jet momentum into the recirculation eddy. The model was able to predict the jet angle when it was assumed that the radial diffusion of jet momentum was a function of the Euler number based on the jet velocity and absolute pressure in the headspace at the top of the downcomer. The model was also developed to predict the maximum stable bubble diameter generated within the submerged jet volume, where the energy dissipation attributed to bubble breakup was given by the energy mixing loss derived for the throat section of a liquid-jet-gas-pump. Good agreement was found between the measured and predicted maximum bubble diameter values. The average experimental Sauter mean/maximum diameter ratio was found to be 0.61, which was similar to that for other bubble generation devices. It was found that for turbulent liquid conditions in the uniform two-phase flow region, a transition from bubble to churn-turbulent flow occurred at a gas void fraction of approximately 0.2 when the gas drift-flux was zero. Under laminar liquid flow, this transition took place at a gas void fraction above 0.3. For the bubbly flow regime the Distribution parameter Co used by Zuber and Findlay (1965) to describe the velocity and gas void fraction profile, was found to be a function of the liquid Reynolds number. For laminar liquid flow, values of Co greater than unity were obtained. As the liquid Reynolds number was increased it was found that Co decreased, until a constant value of unity was obtained for fully turbulent flow. For the churn-turbulent regime it was found that the gas void fraction measurements for all of the experimental runs could be collapsed onto a single curve when a modified gas void fraction was plotted against the gas-to-liquid volumetric flow ratio. The modified gas void fraction included a correction factor to account for the difference in the bubble slip velocity between the experimental runs. The experimental results also indicated that the value of the constant in the gas void fraction correction factor was different for laminar and turbulent flow. Prior to bubble coalescence, it was found that the experimental drift-flux curves could be predicted from the measured bubble diameter, using the separated flow model development by Ishii and Zuber (1979). After the onset of coalescence the drift flux measurements departed from the original drift-flux curves at a rate which increased linearly with increasing gas void fraction. It was found that the slope of the line fitted to the coalesced region of the drift-flux curves increased with increasing liquid Reynolds number and reached a constant value under fully turbulent flow conditions. The model developed, together with the implications of the experimental results, are discussed with regard to optimising the design of an industrial plunging jet bubble column. / PhD Doctorate

A literature review of current phase separation publications was conducted. Data sets were collected and compiled into a Two-Phase Flow Separation Database. Examination of this database indicating a need for further investigation into the liquid entertainment phenomena for smaller hot-leg to branch diameters and intermittent flow regimes. A detailed analysis to the prototypic phase separation process is presented and the associated phenomena are identified. Appropriate scaling criteria were employed for the design of a scaled test facility. Geometry and the flow conditions of the test facility were determined accordingly to Wu et. al (1998). A series of phase separation tests conducted at the Air-water Test Loop for Advanced Thermal-hydraulic Studies (ATLATS) and Advanced Plan Experiment (APEX) has been completed. Results show that the criteria developed by Smoglie (1984) used in RELAP5, reasonably predicts the onset of liquid entrainment. However, the steady-state entrainment correlation in RELAP5 significantly underpredicts primary coolant removal rates. This discrepancy is due to the effects of downstream boundary conditions and pool entrainment and carry-over from the reactor vessel. Due to pool entrainment, entrainment through the branch continues when the reactor vessel mixture level drops below the bottom of the hot-leg. This investigation shows that RELAP5 is non-conservative when predicting coolant removal rates due to steady state liquid entrainment in a horizontal mainline with a vertical branch for stratified, stratified-wavy, transition, and stepped hot-leg flow regimes. / Graduation date: 2001

Flow mechanisms affect transport processes during condensation. Most studies on two-phase flow regimes are qualitative in nature, typically providing only information to guide the identification of the respective regimes and the transitions between them. These studies have, however, not yielded quantitative information to assist the development of pressure drop and heat transfer models. Such qualitative studies have also yielded results with considerable variability between investigators. A comprehensive investigation of flow mechanisms, void fraction, pressure drop and heat transfer during condensation of R404A in microchannels was conducted. In contrast to all prior investigations, high-speed video recordings and image analyses were used to directly measure void fraction, slug frequencies, vapor bubble velocity, vapor bubble dimensions and liquid film thicknesses in tube diameters ranging from 0.508 to 3.00 mm. Experiments were conducted at reduced pressures and mass fluxes ranging from 0.38 to 0.77 and 200 to 800 kg m-2 s-1, respectively, to document their influences on the condensation process at local vapor qualities ranging from 0 to 1. This information was used to develop a model for the void fraction in condensing flows. A complementing set of heat transfer and pressure drop measurements were conducted on the same geometries at similar conditions, and the void fraction model was used in conjunction with these measurements to develop improved heat transfer and pressure drop models. This comprehensive set of experiments and analyses yields a self-consistent and accurate treatment of high-pressure condensation in small hydraulic diameter geometries. Furthermore, the heat transfer model was found to agree well with condensing ammonia and carbon dioxide data that were obtained at significantly different conditions in different tube diameters. The added physical understanding of the condensation process and the models developed will serve as important building blocks for the design of microscale condensers and thermal systems.

The level set method is a powerful way of tracking surfaces by defining the surface as a zero level set of a continuous function that is usually a signed distance function. The level set method is one of the best methods for simulating multi-phase flow because it can easily handle fast topological changes, as well as splitting and merging of fluids. In this thesis, a standard level set method was implemented in C++, using the finite element method library deal.II, to simulate incompressible two-phase flow on some benchmark problems. The results show a significant change of mass in the simulations, something that should not be allowed to happen when simulating incompressible fluids. The mass changes mainly occur in the reinitialization phase, where the level set function is rebuilt to look more like a signed distance function.