Yes / A two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave-maker. The propagation of a solitary wave travelling with a following/opposing current is simulated. The effects of the current velocity on the solitary wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width and higher travelling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and lower travelling speed with an opposing current. The regression equations for predicting the wave height, wave width and travelling speed of the resulting solitary wave are for practical engineering applications. The impacts of current flow on the induced velocity and the turbulent kinetic energy (TKE) of a solitary wave are also investigated. / National Natural Science Foundation of China Grant #51209083, #51137002 and #41176073, the Natural Science Foundation of Jiangsu Province (China) Grant #BK2011026, the 111 Project under Grant No. B12032, the Fundamental Research Funds for the Central University, China (2013B31614), and the Carnegie Trust for Scottish Universities

Le but de ce travail de recherche est de contribuer à une meilleure compréhension de la dynamique de propagation et de la miscibilité de jets gravitaires au-dessous d’un liquide ambiant. Des expériences ont été réalisées en laboratoire à l’aide d’une plateforme expérimentale constituée d’un bassin parallélépipédique contenant de l’eau douce et d’un canal d’injection de section rectangulaire de jets gravitaires de concentration constante initiale fixée. Les calculs mathématiques et numériques sont basés sur les modèles RANS (Reynolds-Averaged Navier Stokes equations), k-ε (K-epsilon) et DCE (Diffusion-Convective Equation) de la fraction volumique de l’eau salée pour décrire la propagation et le mélange du jet gravitaire. L’évolution du front du jet obtenue expérimentalement est utilisée pour valider le modèle numérique. Par ailleurs, la comparaison des résultats obtenus sur l’écoulement moyen (z⁄z0.5 =U/Umax) avec ceux des études 2D expérimentales et numériques antérieures ont montré des similarités. La simulation numérique des champs hydrodynamiques montre que la vitesse maximale est atteinte à la position 0.18 z0.5, où z0.5 est la hauteur d’eau pour laquelle la vitesse moyenne u est égale à la moitié de la vitesse maximale Umax. / The aim of this investigation is to contribute to a better understanding of the propagation dynamics and the mixing process of dense gravity currents. The Laboratory experiments proceeded with a fixed initial gravity current concentration in one experimental set-up. The gravity currents are injected using a rectangular injection channel into a rectangular basin containing the ambient lighter liquid. The injection studied is said in unsteady state volume, as the Reynolds number lies in the range 1111 - 3889. The experiments provided the evolution of the boundary interface of the jet, and it is used to validate the numerical model. The numerical model depends on the Reynolds-Averaged Navier Stokes equations (RANS). The k-ε (K-epsilon) and the Diffusion-Convective Equation (DCE) of the saline water volume fraction were used to model the mixing and the propagation of the gravity current jet. On the other hand, comparison of the mean flow (z⁄z0.5 =U/Umax) with previous two-dimensional numerical simulations and experimental measurements have shown similarities. The numerical simulations of the hydrodynamic fields indicate that the velocity maximum at 0.18 z0.5, where z0.5 is the height at which the mean velocity u is the half of the maximum velocity Umax.

[pt] Modelos RANS (Reynolds Average Navier-Stokes) estão entre os modelos mais empregados para resolver escoamentos turbulentos, devido a seu baixo custo computacional. A maioria dos modelos RANS usa a aproximação de Boussinesq, baseada em uma relação linear entre a parte deviatórica do tensor de Reynolds e o tensor taxa de deformação, com a viscosidade turbulenta sendo o parâmetro positivo de proporcionalidade. Contudo, esses modelos falham em várias situações, e um grande esforço tem sido feito pela comunidade científica com intuito de melhorar a previsibilidade do modelo desenvolvendo modelos não lineares. Análises de modelos de ordem superior empregando tensores ortogonais objetivos têm mostrado que estes são muito promissores para melhorar a previsão dos componentes normais do tensor de Reynolds. No presente trabalho, modelos não lineares baseados no quadrado do tensor taxa de deformação e no tensor não persistência de deformação foram avaliados para uma faixa de número de Reynolds baseados na velocidade de atrito, variando de 395 até 5200. Novas funções de parede foram desenvolvidas, utilizando energia cinética turbulenta e o módulo do tensor taxa de deformação para determinar a velocidade e comprimento característicos. Além disso, um novo modelo turbulento de uma-equação baseado somente na equação de transporte da energia cinética turbulenta foi proposto juntamente com uma equação de fechamento algébrica para modelar a dissipação da energia cinética turbulenta. Os resultados dos modelos para escoamento em canal foram comparados com os dados DNS, apresentando uma melhor aderência aos dados DNS em comparação com os resultados de outros modelos RANS encontrados na literatura. / [en] Reynolds Average Navier Stokes (RANS) models are among the most employed models to solve turbulent flows, due to their low computational cost. The majority of RANS models use the Boussinesq approximation, based on a linear relation between the deviatoric part of Reynolds stress tensor and the rate of strain tensor, with the turbulent viscosity as the positive proportionality parameter. However, these models fail in several situations, and a great deal of effort has been made by the scientific community aiming to improve model prediction through the development of non-linear models. Analysis of higher-order models employing objective orthogonal tensors has shown that these are very promising to improve the prediction of the normal components of the Reynolds stress. In this work, non-linear models based on the square of the rate-strain tensor and non-persistence tensor were examined for a range of friction Reynolds number from 395 to 5200. New wall damping functions were developed, employing the turbulent kinetic energy and intensity of the rate of strain tensor to determine the turbulent characteristic velocity and length. Further, a new one-equation turbulent model based only on the turbulent kinetic energy transport equation was proposed coupled with an algebraic closure equation to model the turbulent kinetic energy dissipation. The models prediction for a channel flow were compared with DNS data and presented a better adherence to the DNS data, than the results of other RANS models available in the literature.

La modélisation à l’aide de l’approche RANS (Reynolds Averaged Navier Stokes) a été menée en trois dimensions, en considérant les régimes permanent et non permanent, dans le but de simuler les écoulements au niveau des jonctions, bifurcations et déversoirs d’orage. A travers ces trois exemples d’étude, plusieurs stratégies de modélisation (différentes combinaison lois de paroi/modèles de turbulence, différents algorithmes de couplage pression/vitesse, différents schémas de discrétisation spatiale, différentes conditions aux limites, différents types et tailles de maille, etc.) ont été testées et évaluées à l’aide de plusieurs indicateurs de performance (de type RMS –Root Mean Square) en s’appuyant sur les données de vitesses (vitesses moyennes in situ et champs de vitesses obtenus par PIV en laboratoire), hauteurs d’eau, débits (répartition de débits en bifurcation en laboratoire ou débits déversés in situ). Les résultats obtenus sont transposables aux autres cas de singularités et ouvrages spéciaux rencontrés en réseau d’assainissement et montrent que : i) les résultats des simulations 3D sont sensibles à la rugosité, aux conditions limites de hauteur et de vitesse ; ii) dans les trois cas d’étude, les schémas de discrétisation du second ordre et l’algorithme de couplage pression/vitesse PISO sont appropriés ; ii) la loi de paroi scalable couplée aux modèles de turbulence de type k-ε pour le cas des jonctions (avec un débit latéral inférieur ou égal au débit principal) ou des déversoirs semblent convenir, tandis que le modèle de turbulence RSM associé à la loi de paroi enhanced ou scalable permet de mieux représenter les écoulements à travers les bifurcations ou au niveau des jonctions lorsque le débit latéral est dominant. Sur la base de ces résultats, une méthodologie de modélisation plus générale définie en six étapes et fondée sur le guide proposée par Jakeman et al. (2006) a été mise au point. La méthodologie ainsi définie a été utilisée pour i) améliorer l’instrumentation du déversoir OTHU (Observatoire de Terrain en Hydrologie Urbaine) situé à Ecully, à partir de la simulation de sa courbe de fonctionnement et en fournissant les incertitudes sur les débits déversés obtenus ; ii) simuler l’implémentation des capteurs débitmétriques à l’aval d’une jonction. Elle a permis de concevoir et de dimensionner un nouveau dispositif de maîtrise des flux d’eau et de polluants déversés (technologie DSM – dispositif de surveillance et de maîtrise des flux déversés au milieu naturel). Ce dispositif a fait l’objet d’un dépôt de brevet international. Enfin, la mise en œuvre de cette méthodologie a été à l’origine de la découverte d’une nouvelle structure d’écoulement dans la branche latérale d’une bifurcation à 90°. L’analyse des résultats des simulations des écoulements mettant en évidence cette nouvelle structure a montré qu’il était possible de prédire l’apparition de cette dernière à partir du rapport d’aspect et du nombre de Froude. / The understanding of sewer flows behaviour is a key component for better urban drainage monitoring and management. However, these flows are conveyed across singularities (such as bends, drops, deviations, etc.) and special structures (combined sewer overflows –CSOs–, channels junction, dividing flow structures, etc.). These singularities and specific structures exhibit complex geometries, leading to open channel turbulent, three-dimensional and multiphase (pollutants and storm and sewer waters) flows. Using three-dimensional CFD (Computational Fluid Dynamics) platform allows a better understanding of mechanisms of contaminants transport through these structures and singularities, leading to a better sewer monitoring. In this thesis, 3D-RANS (Reynolds Averaged Navier Stokes) modelling approach under steady-state conditions is used in order to study flows within CSOs, junctions and bifurcations. Through these three structures, several modelling strategies (wall law/turbulence model combination, velocity/pressure coupling algorithm, spatial discretisation schemes, boundary conditions, computational mesh –shape and size of cells–, etc.) are tested and evaluated thanks to performance indicators (such as RMS –Root Mean Square– indicators) based on velocities (in situ mean velocities and PIV velocity fields obtained in laboratory), water depths and discharge (discharge repartition for bifurcation in laboratory or in situ overflow discharge, for CSOs). Results deriving from these tests are transposable to other singularities or special structures encountered in sewer network and suggest that: i) simulated CFD results are sensitive to the roughness coefficient; ii) for the three studied structures, second-order discretisation schemes and SIMPLE or PISO velocity/pressure coupling algorithm are appropriate; iii) scalable wall function associated to the group of k-ε turbulence model for junction flows (with a lateral inflow lower or equal to the main inflow) or for CSOs is appropriate, whereas RSM turbulence model associated to enhanced wall function allows a better representation of bifurcation flows or junctions flows when the lateral inflow is greater than the main inflow. Based on these results and on Jakeman et al. (2006) guideline, a six steps-methodology focused on the using of RANS approach modelling has been proposed. This six steps-methodology is used in order to i) enhance the monitoring of an OTHU (Observatoire de Terrain en Hydrologie Urbaine) CSO located at Ecully accounting for uncertainties on overflow discharge values ;ii) simulate the performance of flowmeters downstream of a junction, defining the best location for these sensors. This methodology is used to design the new overflow discharge measurement device. This device is an international patent. Finally, the application of the methodology led to point out a new flow structure, occurring in the downstream lateral branch of a 90° bifurcation.

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