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Experimental Investigation On Sharp Crested Rectangular WeirsGharahjeh, Siamak 01 June 2012 (has links) (PDF)
This study is an experimental research to formulate the discharge over sharp-crested rectangular weirs. Firstly, a series of measurements on different weir heights were conducted to find the minimum weir height for which channel bed friction has no effect on discharge capacity. After determining the appropriate weir height, weir width was reduced to collect data on discharge-water head over weir relationship for a variety of different weir openings. Then, the data was analyzed through regression analysis along with utilization of global optimization technique to reach the desired formulation for the discharge. By taking advantage of a newly-introduced &ldquo / weir velocity&rdquo / concept, a simple function was eventually detected for the discharge where no discharge coefficient was involved. The behavior of the weir velocity function obtained in the present study illustrates the transition between the fully contracted and partially contracted weirs. In addition, the proposed weir velocity formulation is simple and robust to calculate the discharge for full range of weir widths.
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Generalized non-dimensional depth-discharge rating curves tested on Florida streamflowMueses-Pérez, Auristela 01 June 2006 (has links)
A generalized non-dimensional mathematical expression has been developed to describe the rating relation of depth and discharge for intermediate and high streamflow of natural and controlled streams. The expressions have been tested against observations from forty-three stations in West-Central Florida. The intermediate-flow region model has also been validated using data from thirty additional stations in the study area. The proposed model for the intermediate flow is a log-linear equation with zero intercept and the proposed model for the high-flow region is a log-linear equation with a variable intercept. The models are normalized by the depth and discharge values at 10 percent exceedance using data published by the U.S. Geological Survey. For un-gauged applications, Q10 and d10 were derived from a relationship shown to be reasonably well correlated to the watershed drainage area with a correlation coefficient of 0.94 for Q10 and 0.86 for d10. The average relative error for this parameter set shows that, for the intermediate-flow range, better than 50% agreement with the USGS rating data can be expected for about 86% of the stations and for the high-flow range, better than 50% for 44% of the stations. Testing the model outside West Central Florida, in some stations at North Florida, and South Alabama and Georgia, show some reasonable relative errors but not as good as the results obtained for West Central Florida. Using a model with a different slope, developed specific for those particular stations improved the results significantly.
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On unsteady open-channel flows: a contribution to non-stationary sediment transport in runoff flows and to unstable non-Newtonian mudflow studies / Des écoulements instationnaires à surface libre: contribution aux études du transport instationnaire de sédiments en écoulement ruisselant et des instabilités de coulées de boue non-newtonienne / Escoamentos não-permanentes de superficie livre: uma contribuição para o estudo do transporte não estacionario de sedimentos em escoamentos superficiais e para instabilidades em corridas de lamasFiorot, Guilherme Henrique [UNESP] 01 July 2016 (has links)
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Previous issue date: 2016-07-01 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Dentro da temática de riscos naturais, mais precisamente no contexto das corridas de lama, esta tese surge da necessidade que existe na literatura em melhor se conhecer as características temporais destes eventos. A chuva, fonte da vazão liquida, conduz aos escoamentos superficiais, responsáveis pela redução da coesão do material sedimentar do solo (areia e argila) e seu consequente transporte. Em locais de topografia íngreme, de montante a jusante, a vazão sólida do escoamento principal pode, eventualmente, evoluir devido às contribuições laterais de pequenos escoamentos, alterando não só as propriedades reológicas do fluido e dinâmicas do escoamento, como se manter até que o transporte sólido atinja elevada concentração na composição do fluido. Na primeira parte desta tese, um experimento de superfície livre foi projetado para reproduzir escoamentos superficiais sobre um fundo móvel, com o objetivo de estudar propriedades não-permanentes do transporte de sedimentos. Um sistema de medição foi projetado e construído com o intuito de medir quase instantaneamente a vazão sólida e suas correlações com as propriedades hidráulicas do escoamento. Este aparato é também utilizado para observar a influência de instabilidades de superfície livre sobre o transporte. Um conjunto de resultados é apresentado e analisado e mostra que a presença de ondas pode, em média, reduzir a quantidade total de sedimentos transportada. Na segunda parte desta tese, a dinâmica de escoamentos com elevada concentração de sedimentos é estudada. Neste trabalho, executa-se a aplicação de um modelo de primeira ordem de roll waves para fluidos de reologia Herschel-Bulkley para simular um evento natural registrado na literatura. Os resultados apresentados mostram que roll waves poderiam, de fato, ser identificadas no evento e que a amplitude média observada poderia ter sido estimada com 8% de incerteza. Assim, um modelo mais complexo para a solução do perfil de velocidade é proposto, adicionando a porosidade do solo ao problema. Resultados do modelo são comparados com simulações numéricas. Uma análise paramétrica é efetuada e o caso de estudo é novamente avaliado. Como conclusão geral do trabalho, a presença de fenômenos não-estacionários durante a evolução escoamento superficial - corrida de lama afeta a dinâmica global do sistema acoplado hidráulica-transporte de sedimentos, quando comparado ao caso permanente e uniforme. Assim, a verificação de que tais fenômenos podem aparecer deve constituir parte de projetos engenharia, especialmente quando estes, em situações de catástrofes, envolvem danos a infraestruturas civis e quase sempre perdas de vidas, como é o caso das corridas de lama. / This thesis was motivated by the need to better understand time-dependent features related to mudflow evolution on natural sloped channels. Basically, the research is focused on events that are confined in channels formed due to the topography. The rain, source of the liquid discharge, generates the runoff flow which is responsible for wetting the soil surface, promoting reduction of soil cohesiveness and erosion of small particles such as clay and sand. From this point, the sediment transport can increase as small water flows merge and form greater streams. The scenario keeps its evolution until it reaches high concentration of particles in the fluid mixture. In the first part, to study the non-permanent feature of sediment transport, an open-channel experiment was designed for simulating runoff flow over a mobile bed. A measurement system was designed and constructed to instantaneously inspect the solid discharge of particles and the flow friction at the bed. This apparatus is further used to explore the influence of free-surface waves on the sediment transport. Hydraulic properties of flows are qualitatively and quantitatively studied and data are used to correlate characteristics of flow and sediment transport. A set of experimental runs is presented and explored. Analysis of results shows that for fixed flow conditions, waves induce an overall smaller quantity of transported sediment. In a second part, the dynamics of high concentrated flows is addressed and this thesis attempts to apply a first-order roll-wave model for Herschel-Bulkley laminar fluid flow to a registered natural event. Results presented point out that roll waves could have occurred during this already published case-study event. Simulations could predict wave heights within 8% on uncertainty with respect to the mean amplitude of measured waves. Finally a new theoretical solution for the velocity profile is proposed taking into account the porosity of the bed. Results are then compared with numerical simulation performed in FLUENT. A parametric analysis is employed and the case-study is once again evaluated. As general conclusion, the non-permanent phenomena that can appear during the evolution of a mudflow event affect the overall dynamics of the coupled system (hydraulic-sediment transport) in comparison to the steady and uniform case. Verifying that such phenomena could appear should indeed be an important part in hydraulic engineering projects, especially when dealing with lives, which is the case of mudflows. / CNPq: 201557/2012-6
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On unsteady open-channel flows : a contribution to non-stationary sediment transport in runoff flows and to unstable non-Newtonian mudflow studies /Fiorot, Guilherme Henrique. January 2016 (has links)
Orientador: Geraldo de Freitas Maciel / Abstract: This thesis was motivated by the need to better understand time-dependent features related to mudflow evolution on natural sloped channels. Basically, the research is focused on events that are confined in channels formed due to the topography. The rain, source of the liquid discharge, generates the runoff flow which is responsible for wetting the soil surface, promoting reduction of soil cohesiveness and erosion of small particles such as clay and sand. From this point, the sediment transport can increase as small water flows merge and form greater streams. The scenario keeps its evolution until it reaches high concentration of particles in the fluid mixture. In the first part, to study the non-permanent feature of sediment transport, an open-channel experiment was designed for simulating runoff flow over a mobile bed. A measurement system was designed and constructed to instantaneously inspect the solid discharge of particles and the flow friction at the bed. This apparatus is further used to explore the influence of free-surface waves on the sediment transport. Hydraulic properties of flows are qualitatively and quantitatively studied and data are used to correlate characteristics of flow and sediment transport. A set of experimental runs is presented and explored. Analysis of results shows that for fixed flow conditions, waves induce an overall smaller quantity of transported sediment. In a second part, the dynamics of high concentrated flows is addressed and this the... (Complete abstract click electronic access below) / Resumo: Dentro da temática de riscos naturais, mais precisamente no contexto das corridas de lama, esta tese surge da necessidade que existe na literatura em melhor se conhecer as características temporais destes eventos. A chuva, fonte da vazão liquida, conduz aos escoamentos superficiais, responsáveis pela redução da coesão do material sedimentar do solo (areia e argila) e seu consequente transporte. Em locais de topografia íngreme, de montante a jusante, a vazão sólida do escoamento principal pode, eventualmente, evoluir devido às contribuições laterais de pequenos escoamentos, alterando não só as propriedades reológicas do fluido e dinâmicas do escoamento, como se manter até que o transporte sólido atinja elevada concentração na composição do fluido. Na primeira parte desta tese, um experimento de superfície livre foi projetado para reproduzir escoamentos superficiais sobre um fundo móvel, com o objetivo de estudar propriedades não-permanentes do transporte de sedimentos. Um sistema de medição foi projetado e construído com o intuito de medir quase instantaneamente a vazão sólida e suas correlações com as propriedades hidráulicas do escoamento. Este aparato é também utilizado para observar a influência de instabilidades de superfície livre sobre o transporte. Um conjunto de resultados é apresentado e analisado e mostra que a presença de ondas pode, em média, reduzir a quantidade total de sedimentos transportada. Na segunda parte desta tese, a dinâmica de escoamentos com eleva... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor
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Cavitation assessment of the Baihetan discharge tunnel – Using Computational Fluid Dynamics / Bedömning av risken för kavitation i utskovstunneln för Baihetankraftverket med CFD-beräkningar.Alderman, Carin, Andersson, Sophia January 2012 (has links)
Recently it has become more common in the construction of large dams to reuse diversion tunnels as flood discharge tunnels in the final structure. These tunnels handle large flows with the characteristics of open channel flow. When such large hydrological forces act upon a structure there are several problems to be expected. One of these is the occurrence of cavitation, which could have potential hazardous erosion as a consequence. Cavitation is the formation and collapse of bubbles that create a shockwave strong enough to erode the underlying material. The Baihetan dam is one of the largest hydro power projects in China at present. It has three discharge tunnels that all run the risk of developing cavitation damages. By modelling one of the tunnels using Computational Fluid Dynamics (CFD) it is possible to investigate where in the tunnel structure cavitation is likely to occur. This degree project assesses the risk of cavitation erosion in the Baihetan tunnel using the static pressure distribution, the velocity distribution and modern cavitation theory. Several modifications of the tunnel – including alterations in the gradient and construction parameters – are simulated in order to investigate if changes in the design can mitigate the cavitation problem. None of the analysed modifications completely eliminate the problem and aeration is recommended to counteract the problem. This study indicates where cavitation might be a problem in the Baihetan tunnel and can be used as a basis for further research.
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Numerical modeling of a slotted flip bucket spillway system – The Shibuya Hydropower Project. / Numerisk modellering av ett skidbacksutskov i Shibuya vattenkraftsystem.Axelsson, Johan, Knutsson, Roger January 2011 (has links)
CFD is today a big part of the design process in hydraulic engineering and is more economical and time efficient than traditional scale models. But, there are still issues concerning the agreement with scale models in large and complex geometries. In this degree project a high head, five channeled, slotted flip bucket spillway system is analyzed with the CFD software FLUENT and compared with existing scale model results. The sought hydraulic parameters in each channel were the discharge capacity, the pressure distribution and the throw distance from the flip buckets. The discharge capacity and pressure distribution was practically equal for all five channels and only the throw distance from Channel 1 deviated from the others. The agreement with data from the scale model is quite low. The biggest error sources behind the bad agreement may depend on the lack of computational power which led to bad choice of cell size, model delimitations and simplifications. CFD models can easily be built up by people without experience in hydraulics which can lead to fatal errors when building up the model and interpreting results. Hence, long experience in CFD or verification of the numerical results with several different hydraulic parameters is the only way to guarantee qualitative results from CFD modeling.
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LONGITUDINAL SOLUTE TRANSPORT IN OPEN-CHANNEL FLOW - A Numerical Simulation Study on Longitudinal Dispersion, Surface Storage Effects, Transverse Mixing, Uncertainties and Parameter-Transferring ProblemsZhang, Wei January 2011 (has links)
The longitudinal solute transport modeling is critical in river and stream water quality management, control, and the mitigation of hazardous riverine spills. One of the widely used "deadzone" model is the transient storage model (TSM). TSM is a significant improvement over the advection-dispersion model (ADM), but it cannot simulate the breakthrough curve (BTC) immediately after a large pool. Additionally, the calibration (parameterization) method is challenged by the non-identifiability which is common to all inverse modeling, and it seems TSM cannot be easily used as a predictive tool, more of an interpretive tool of solute transport, i.e., is the parameter set calibrated via inverse modeling transferable? Pools are fundamental stream morphology unit in streams with mixed bed materials in pool-riffle or pool-step sequences. Understanding of how a pool impacts the longitudinal solute transport is the first step towards improving current model such as TSM or developing new models. By introducing a dimensionless group, e= Q/(Dt W) (where, Q is the average volumetric flow rate; Dt is an average transverse dispersion coefficient; W is the channel flow width), derived from non-dimensionalization of the governing equations of one of the most rigorous 2-dimansional (2D) (depth-averaged) model, Mike21, this work presents an alternative way of longitudinal solute transport investigation. Using the 2D fully hydrodynamic Mike21, numerical experiments were conducted on hypothetical streams in this dissertation. Simulation study on hypothetical stream with pool reveals that a pool's effects on longitudinal solute transport are manifested by three aspects: boosting longitudinal spreading (concentration peak attenuation), causing a solute plume delay and increasing solute residence time. These effects fade like a "wake" as the solute plume moves downstream. e provides an insight into the physics of longitudinal transport; it outlines a relative transverse mixing intensity of a stream. The internal transport and mixing condition (including the secondary circulations) in a pool together with the pool's dimensions determine the pool's storage effects especially when e >>1. The BTCs downstream from a pool may be "heavy tailed" (i.e., have enormously slow decaying rate) which cannot be modeled by the TSM. Results also suggest that the falling limb of a BTC more accurately characterizes the pool's storage effects because the corresponding solute has more chance to sample the entire storage area. n a more fundamental perspective, the predictive ability of inverse modeling parameterized model is discussed and conclusion is made about the role of a stream/river system's nonlinearity in determining the predictability; a misleading mis-nomenclature in TSM application is also demonstrated with a numerical experiment. / Civil Engineering
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Laminar and turbulent analytical dam break wave modelling on dry-downstream open channel flowTaha, T., Lateef, A.O.A., Pu, Jaan H. 26 September 2018 (has links)
Yes / A dam break wave caused by the discontinuity in depth and velocity of a flow is resulted from instantaneous release a body of water from a channel and classified naturally as a rapidly varied unsteady flow. Due to its nature, it is hard to be accurately represented by analytical models. The aim of this study is to establish the modelling differences and complexity echelons between analytically simulated explicit laminar and turbulent dry bed dam break wave free surface profiles. An in-depth solution to the free surface profile has been provided and evaluated by representing the reported dam break flow measurements at various locations. The methodology adopted utilizes the free surface profile formulations presented by Chanson 1,2, which are developed using the method of characteristics. In order to validate the results of the presented analytical models in illustrating the dam break wave under dry bed conditions, published experimental data provided by Schoklitsch 3, Debiane 4 and Dressler 5 are used to compare and analyze the performance of the dam break waves under laminar and turbulent flow conditions.
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Approximations d'ordre réduit des équations de Saint-Venant pour la modélisation de vallée hydroélectrique / Reduced order approximations of the Saint-Venant equations for hydropower valley modelingDalmas, Violaine 10 December 2018 (has links)
L'hydroélectricité est la première des énergies renouvelables électriques. Sa production repose en partie sur des centrales au fil de l'eau dont les capacités de modulation sont encore faiblement exploitées. Les capacités d'ajustement des centrales hydrauliques sont d'autant plus essentielles aujourd'hui que la pénétration d'énergies intermittentes dans un mix énergétique décarboné est indispensable.Dans cette thèse, nous nous intéressons aux centrales au fil de l'eau turbinant le débit de cours d'eau aux marnages limités. Les enjeux de sûreté, notamment liés au multi-usage de l'eau, ainsi que la perspective de moduler les débits turbinés nous ont amenés à considérer le problème de la modélisation des écoulements dans les canaux reliant les centrales au fil de l'eau. Les équations de Saint-Venant sont les plus pertinentes pour ce type de modélisation. Nous avons proposé plusieurs approches à partir de ces dernières pour caractériser analytiquement la dynamique de l'écoulement à des variations de débits turbinés. Nous avons considéré la dynamique du système autour d'un régime fluvial stationnaire non-uniforme caractéristique des configurations hydroélectriques. La première approche est basée sur une approximation basses fréquences. La seconde approche est basée sur une méthode de réduction de modèle avec une paramétrisation selon le débit support. Une troisième approche est proposée en considérant explicitement la recherche d'une solution approximée des équations de Saint-Venant linéarisées autour d'une configuration hydroélectrique. Un critère spatio-fréquentiel est alors introduit, l'existence d'un biais en basses fréquences nous conduit à proposer un modèle d'ordre réduit dont la dynamique basses fréquences est imposée selon les résultats de la première approche. La solution exprimée sous forme de fonctions de transfert, comme pour les deux précédentes approches, met en évidence explicitement la présence de modes de résonance/anti-résonance. Finalement, nous illustrons les résultats vis à vis de simulations non-linéaires et de données réelles et proposons une régulation de niveau basée sur cette dernière approche. / New challenges arise from energy transition toward a more sustainable energy mix. Hydropower is already the main source of renewable electricity. In order to integrate a massive increase in generation of renewable intermitent energies, improving the flexibility of run-of-the-river hydropower plants becomes essential. In this thesis, we focus on run-of-the river power plants facing water level constraints. Safety issues, partly due to the multiple uses of water, and the opportunity to modulate turbined flow rates have led us to adress the problem of flow modelisation in open channels that connect run-of-the rivers facilities with each others. An accurate model is provided by the Saint-Venant equations. From these latters, we have proposed different approaches to characterize analytically the flow dynamics in response to turbined flow variations. The system dynamics have been considered around a subcritical stationary non-uniform regime typical of hydroelectric configuration. The first approach is based on a low frequency approximation. The second approach is based on a parametric model reduction technique. By seeking explicitly an approximate solution to the linearized Saint-Venant equations around an hydroelectric configuration, we have proposed a third approach. A space-frequency criterion is introduced, which shows a bias in low frequency. Results of the first approach are then used to propose a reduced order model asymptotically exact in low frequency. As for the two other approaches, the solution takes the shape of parametric transfer functions. Resonance/anti-resonance modes explicitly appear. Finally, comparisons with non-linear simulations taking into account actual real data are discussed and a water level controller is developed based on the last approach.
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Flow modelling in compound channels : momentum transfer between main channel and prismatic or non-prismatic floodplainsBousmar, Didier 12 February 2002 (has links)
Flow modelling in a compound channel is a complex matter. Indeed, due to the smaller
velocities in the floodplains than in the main channel, shear layers develop at the
interfaces between these subsections, and the channel conveyance is affected by a
momentum transfer corresponding to this shear layer, but also to possible geometrical
changes in a non-prismatic reach.
In this work, a one-dimensional approach, the Exchange Discharge Model (EDM), is
proposed for such flows. The EDM accounts for the momentum transfer between
channel subsections, estimated as proportional to the velocity gradient and to the
discharges exchanged through the interface; where two main processes are identified :
(1) the turbulent exchange, due to the shear-layer development; and (2) the geometrical
transfer, due to cross-sectional changes. The EDM is successfully validated for
discharge prediction, but also for water-profile computation, through comparison with
existing laboratory and field measurements.
The momentum transfer due to turbulent exchanges is then studied experimentally,
theoretically and numerically. At first, new experimental data, obtained by using
Particle Tracking Velocimetry techniques, are presented : the periodical vortex
structures that develop in the shear layer are clearly identified and characterised.
Secondly, a hydrodynamic linear stability analysis enables to predict quite successfully
the wave length of some observed vortices. Lastly, an Unsteady-RANS numerical
method is used to simulate the perturbation development. The estimated vortex wave
lengths agree again with the measurements and the theoretical predictions, although
vortices merging occurs in the simulation results, which was actually not observed
experimentally. The velocity-profile prediction is found improved when the effect of
vortices is considered, thanks to the corresponding additional shearing.
The geometrical transfer is also investigated experimentally and numerically. Novel
experiments are designed, with the measurements of the flow in a compound channel
with symmetrically narrowing floodplains. The mass transfer and the evolution of the
flow distribution along the channel length are clearly observed. A significant additional
head loss due to this transfer is measured, in accordance with the EDM hypothesis.
Measured water profiles are finally compared successfully with the EDM predictions.
In addition to the EDM development and validation, the so-called Lateral Distribution
Method (LDM) is also investigated and the significance of the secondary-currents
models proposed by previous authors for this method is discussed. When considering
the velocity-profile prediction, the effect of these helical secondary currents is again
clearly highlighted, by using dispersion terms in the Saint-Venant equations. However,
the actual physical meaning of the related dispersion coefficients remains uncertain. In
addition, an extended LDM is also proposed and discussed for non-prismatic flow
modelling, using the new narrowing-channel data set./La modélisation des écoulements dans les rivières à plaines inondables est
particulièrement complexe. En effet, la vitesse de l'eau étant plus faible sur la plaine
d'inondation que dans le lit mineur, une couche de cisaillement se développe à
l'interface entre ces sous-sections. La débitance totale de la rivière est dés lors réduite, à
cause du transfert de quantité de mouvement qu'occasionne la présence de la couche de
cisaillement, mais aussi de part les changements de géométrie qui peuvent se produire
dans un lit non-prismatique.
La présente thèse propose, pour la représentation de tels écoulements, une nouvelle
approche uni-dimensionnelle dénommée Modèle des Débits d'Echange ("Exchange
Discharge Model" – EDM). Le transfert de quantité de mouvement entre les soussections
de la rivière est pris en compte par l'EDM comme étant proportionnel au
gradient de vitesse entre celles-ci et aux débits échangés à travers leur interface. A cette
interface, deux phénomènes sont essentiellement présents : (1) un échange turbulent, dû
au développement de la couche de cisaillement; et (2) un transfert géométrique,
correspondant aux changements de section. L'EDM est validé avec succès pour la
prédiction du débit et pour le calcul de lignes d'eau, par comparaison avec des données
existantes de laboratoire et de terrain.
Le transfert de quantité de mouvement dû à l'échange turbulent est ensuite étudié
expérimentalement, théoriquement et numériquement. De nouvelles mesures sont
obtenues, au moyen d'une technique de vélocimétrie par suivi de particules. Les
structures périodiques qui se développent dans la couche de cisaillement sont clairement
identifiées et caractérisées. Deuxièmement, une analyse linéaire de stabilité
hydrodynamique permet de prédire théoriquement les longueurs d'onde de quelques
tourbillons qui ont été observés expérimentalement, et ce avec succès. Enfin, un modèle
numérique, de type "Unsteady-RANS", est utilisé pour simuler la croissance des
tourbillons dans la couche de cisaillement. Encore une fois, les longueurs d'onde obtenues correspondent relativement bien avec les valeurs mesurées et prédites
théoriquement; bien que les coalescences de tourbillons qui se produisent
numériquement n'aient pas été observées expérimentalement. La prédiction des profils
de vitesse est améliorée, lorsque l'effet des tourbillons est considéré, grâce à la
contrainte de cisaillement additionnelle que ceux-ci génèrent.
Les transferts géométriques sont également explorés expérimentalement et
numériquement. Une nouvelle campagne expérimentale a été réalisée, en considérant
l'écoulement dans un lit composé symétrique, dont les plaines d'inondation se
rétrécissent progressivement. Le transfert de masse entre sous-sections et la
redistribution des débits qui lui est associée sont clairement observés au long du canal.
Une importante perte de charge additionnelle due à ce transfert est mesurée, en
concordance avec les hypothèses de l'EDM. Finalement, les lignes d'eau mesurées sont
reproduites avec succès par un calcul utilisant l'EDM.
En complément au développement et à la validation de l'EDM, la "Lateral Distribution
Method" (LDM) est également utilisée, avec pour objectif la clarification du rôle des
termes de courants secondaires proposés par différents auteurs. Par rapport à la
prédiction du profil de vitesse, l'effet de ces courants secondaires est très marqué. Il est
ici reproduit en utilisant des termes de dispersion dans les équations de Saint-Venant.
Cependant, le sens physique des valeurs des coefficients de dispersion qui doivent être
utilisés est discutable. Par ailleurs, une LDM étendue, pour les écoulement en lits nonprismatiques,
est proposée et commentée, en utilisant le nouveau jeu de données pour le
canal convergent.
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