Increasing interest in the role of wetlands in pollutant removal, flood plain management, and sedimentation in recent years has prompted research into hydraulic processes inherent to these systems. The research described in this thesis focuses on flow processes within ecosystems known as riparian wetlands. An attempt has been made to summarize existing research in this field to ensure that a contribution will be made to the field of hydraulics. Included in this thesis are results from laboratory models investigating flow through vegetation in riparian wetlands. Particular emphasis in this research has been placed on velocity profile measurement of flow within vegetation. Measurements were taken within various density configuration of rigid simulated vegetation for emergent and submerged cases. In addition, many of the experiments tested the effect on the velocity profile when two distinct layers of vegetation are present. The results described herein should aid in visualization of flow processes within riparian wetlands. / Master of Science

No / The determination of velocity profiles in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that drives the Prandtl’s second kind of secondary flow in the cross section. Due to these currents the maximum velocity appears below the free surface. This is called the dip phenomenon. The classical log law describes the velocity distribution in the inner region of the turbulent boundary layer. The Coles law and its wake function are not able to predict the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier-Stokes equations and yields a new formulation of the vertical velocity profile in the outer region of the boundary layer in the central cross section area of steady, fully developed turbulent flows in open channels. This formulation is able to predict primary velocity profiles for both narrow and wide open channels. This new law is a modification of the classical one, it involves an additional parameter CAr that is a function of the position of the maximum velocity ξdip and roughness height (kS).ξdip may be derived either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channel has been used for validating the new law. The agreement between the experimental data and the profile given by the law is very good, despite the simplification used.

The purpose of this work is to develop a continuum theory that may be used to predict the effects of anisotropic boundary vibrations on loose granular assemblies. In order to do so, we extend statistical averaging techniques employed in the kinetic theory to derive an anisotropic flow theory for rapid, dense flows of identical, inelastic spheres. The theory is anisotropic in the sense that it treats the full second moment of velocity fluctuations, rather than only its isotropic piece, as a mean field to be determined. In this manner, the theory can, for example, predict granular temperatures that are different in different directions. The flow theory consists of balance equations for mass, momentum, and full second moment of velocity fluctuations, as well as constitutive relations for the pressure tensor, the flux of second moment, and the source of second moment. The averaging procedure employed in deriving the constitutive relations is based on a Maxwellian that is perturbed due to the presence of a deviatoric second and full third moment of velocity fluctuations. Because the theory is anisotropic, it can predict the normal stress differences observed in granular shear flows, as well as the evolution to isotropy in an assembly with granular temperatures that are initially highly anisotropic. In order to complement the theory, we employ similar statistical techniques to derive boundary conditions that ensure that the flux of momentum as well as the flux of second moment are balanced at the vibrating boundary. The bumps are hemispheres arranged in regular arrays, and the fluctuating boundary motion is described by an anisotropic Maxwellian distribution function. The bumpiness of the surface may be adjusted by changing the size of the hemispheres, the spacing between the hemispheres in two separate array-directions, and the angle between the two directions. Statistical averaging consistent with the constitutive theory yields the rates at which momentum and full second moment are transferred to the flow. In order to present results in a form that is easy to interpret physically, the statistical parameters that describe the boundary fluctuations are related in a plausible manner to amplitudes and frequencies of sinusoidal vibrations that may differ in three mutually perpendicular directions, and to phase angles that may be adjusted between the three directions of vibration. The focus of the results presented here is on the steady response of unconfined granular assemblies that are thermalized and driven by horizontal bumpy vibrating boundaries. In a first detailed study of the effects of the boundary geometry and boundary motion on the overall response of the assemblies, the anisotropic theory is reduced to a more familiar isotropic form. The resulting theory predicts the manner in which the profiles of isotropic granular temperature and solid volume fraction as well as the uniform velocity and corresponding flow rate vary with spacings between the bumps, angle of the bump-array, energy of vibration, direction of vibration, and phase angles of the vibration. In a second study, we solve the corresponding, but more elaborate, boundary value problem for anisotropic flows induced by anisotropic boundary vibrations. The main focus in presenting these results is on the differences between granular temperatures in three perpendicular directions normal and tangential to the vibrating surface, and how each is affected by the bumpiness of the boundary and the direction of the vibration. In each case, we calculate the corresponding nonuniform velocity profile, solid volume fraction profile, and mass flow rate.

Shear velocity is a critical variable used in many hydrodynamic and aeolian applications. The Law of the Wall is commonly used to derive shear velocity as the product of the slope of a measured velocity profile and the von Kármán constant, κ = 0.4. However, a number of hydrodynamic experiments show that there is a substantial apparent decrease of κ in sediment-laden flow, which was explained by: 1) The energy loss to support the sediment particle suspension in the fluid and 2) The buoyancy effect due to stratification. The energy loss is associated with sediment concentration and grain size, and the stratification can be characterized by sedimentological flux Richardson number or gradient Richardson number. Since there is an apparent change of κ, the term “apparent von Kármán parameter”, or κa, was adopted from Wright and Parker to replace κ in sediment-laden flow. There has been no study to attempt to detect and to evaluate the variability of κa during aeolian saltation, which is the purpose of this dissertation research. Two “clear air” runs and fifteen “sediment-laden” runs were conducted at the northeast coast of Brazil. Wind profile data were collected by a stack of cup anemometers; “true” shear velocity was estimated by an ultrasonic anemometer; and sediment mass flux profile and grain size were estimated from the sand samples collected in a stack of vertical hose-style traps. With these estimates, κa, sediment concentration and sedimentlogical Richardson numbers were derived. Regression analysis indicates that there is a statistically insignificant relationship between κa and grain size, which may be caused by small range of grain size in the study site. However, there is strong statistical relationship between κa and bulk, volumetric concentration below 25 mm, S25, and between κa and sediment transport rate Q (kg/m/s) as: ka = -2088.4S25 0.3964 and ka = -3.134Q 0.4011 A strong relationship was also found between κa and sedimentological Richardson numbers in the lower saltation layer, which can be well explained by the stratification theory.

The purpose of this research was to assess the effects of local turbulence and velocity profiles on electromagnetic (magnetic) flow meters. According to the American Water Works Association, “No tool available to water utilities has played a greater part in the conservation of water than the water meter (AWWA 2002).” Consequently, it is imperative to understand what variables may influence magnetic flow meter accuracy. Even though other researchers have explored the effects of turbulence profile development on orifice plates, the literature is not clear how magnetic flow meters respond to the effect of local turbulence. Accordingly, this study investigated the effects of local turbulence and velocity profiles on magnetic flow meter accuracy. Using five magnetic flow meters from five different manufacturers, laboratory tests were conducted with a CPA 65E flow conditioner located at different distances upstream of the meter. Numerical modeling using commercially available computational fluid dynamics software indicated that the deviations in flow meter accuracy were not proportional to the levels of local turbulence. It appears that magnetic flow meters may only be influenced by local turbulence to the degree that the upstream disturbance that distorts the velocity profile also increases local turbulence.

<p> Forced convection mass transfer rates from single gas bubbles, with accompanying chemical reaction, were determined experimentally in the intermediate Reynolds number range. The reacting system carbon dioxide-monoethanolaminc was chosen for this study. </p> <p> A mathematical model, describing forced convection mass transfer from a single sphere with accompanying first or second order reaction, was developed and solved using finite-difference techniques. Hydrodynamic conditions in the intermediate Reynolds number region were described using Kawaguti-type velocity profiles. </p> <p> The numerical solutions of the model have been compared with the experimental results of this study as well as with previous theoretical and experimental results. </p> / Thesis / Doctor of Philosophy (PhD)

Abstract Methods are proposed to take account of the effect of emergent vegetation (which covers only part of the channel bed) on conveyance and depth-averaged velocity in open channels. For emergent vegetation strips parallel to the flow direction, discharge can be predicted separately for each vegetated or non-vegetated zone. The equations of Kaiser (1985) and Nuding (1991, 1994) can predict the influence of the vegetation on conveyance within the non-vegetated zone via the composite roughness formula of Pavlovski (1931). In order to predict the lateral distribution of depth-averaged velocity within the non-vegetated zone, the equations of Nuding (1991, 1994) have been modified to take account of the relation between non-vegetated zone width, apparent shear stress on the vegetation interface and the maximum velocity which will occur. For more complex geometries, two-dimensional numerical hydraulic models using existing software and existing relations for the prediction of eddy viscosity are recommended.

This study aims to better understand the characteristics of the tidal- current profiles and the near-bed boundary layer structures off the southwestern coast of Taiwan. The velocity profile is measured by a bottom-mounted ADCP. Six experiments were conducted, each lasted 10~20 days and the water depth ranging 12~18 m. Twenty-minute averaged velocity profiles have been fitted to a logarithmic form with 4% accuracy. The friction velocity (u*) and roughness length (z0) are then derived from the slope and intercept of the best-fitted straight lines. Our results show that the profile shape and friction velocity vary tidally, the latter reaches O(0.06)ms-1 during peak current flow. The magnitude of z0 is large and scattered, but it shows a general trend of decrease with increasing flow speed. The observed log-layer height increases, and the bottom drag coefficient (CD) decrease, respectively with increasing flow speed. Measurements also show that water turbidity increases with rainfall, as a result the z0 and CD also increase. Finally, harmonic analysis of the tidal currents indicate significant changes between winter (homogeneous) and summer (stratified) conditions. In winter the vertical variation of orientation and phase is small, whereas in summer there was a 150 orientation and 250 phase difference (the bottom currents lead the surface currents) between the near surface and near bed regions.

Abstract : The industrial partner of this project uses a slurry bubble reactor for the production of biogenic methanol. In the latter syngas is dispersed into the slurry continuous phase containing both liquid and solid phases. The rising bubbles containing a wide spectrum of the bubbles sizes, interact with the continuous phase due to the interface momentum transfer. The latter includes the drag, lift, wall lubrication and turbulent dispersion terms that require average bubble size, which needs to be calculated. One way to predict this average bubble size is by using population balance model (PBM), which can be coupled with the Eulerian framework. PBM also needs closure kernels for the bubble coalescence and bubble breakup. In this study, the influence of bubble coalescence and bubble breakup kernels have been studied in two- and three-phase system using eulerian approach, which solves momentum equation for each phase. The influence of the mesh sizes, number of bubble classes, numerical schemes, wall lubrication force and turbulent dispersion force are also included. In the two-phase system, results show that the Luo coalescence model needs to be tuned when used in combination with the Luo breakup kernel. The combination of the Luo coalescence and the Lehr breakup kernels (Luo-Lehr) show promising time-averaged radial profiles of gas holdup and axial liquid velocity as compared to empirical values. In the three-phase system, the combination of the Luo coalescence and the Lehr breakup kernels (Luo-Lehr) and the Luo coalescence and the Luo breakup kernels (Luo-Luo) predict convincing time-averaged radial profile of axial solid velocity as compared to experiments. However, at an elevated superficial gas velocity, a non-realistic behavior was predicted when compared to empirical observations. The sensitivity analysis results show that the 3 mm mesh size depicts a trend similar to the empirical values of the radial profiles of the gas holdup, axial liquid velocity, and solid axial velocity. The number of bubble classes influence the predicted bubble size distribution in the three-phase system while the numerical discretizing schemes have no influence on the results. The bench simulation results show that the inclusion of the turbulent dispersion term using a single porous tubular sparger influences the hydrodynamic behavior of the bubble column. / Le partenaire industriel de ce projet utilise un réacteur à suspension à trois phases pour la production de méthanol biogénique. Dans celui-ci, le gaz de synthèse est diffusé par barbotement dans la phase à suspension qui contient à la fois les phases liquide et solide. Les bulles en ascension présentent un large spectre de tailles et interagissent avec la phase à suspension en échangeant de la quantité de mouvement via leurs surfaces. Cet échange comprend les forces de trainé, de portance, de lubrification en proche parois et de dispersion par turbulence; lesquelles requièrent notamment le calcul de la taille moyenne des bulles. Une façon de prédire numériquement cette taille moyenne est de recourir à un modèle de bilan de population (PBM, de l’anglais Population Balance Model), qui peut être couplé avec un model multiphasique eulérien. Un tel PBM a requière des modèles de fermetures pour la coalescence et la rupture des bulles. Dans la présente étude, l'influence des modèles noyaux de coalescence et de rupture des bulles a été étudiée pour des systèmes à deux et à trois phases en utilisant l’approche eulérienne. L'influence de la taille du maillage, du nombre de classes de bulles, du schéma numérique, de la force de lubrification en proche parois et de la force de dispersion par turbulence sont également incluses. Dans un système bi-phasique, les résultats montrent que le modèle de coalescence Luo doit être ajusté lorsqu'il est utilisé en combinaison avec le noyau de rupture Luo. La combinaison des noyaux de coalescence Luo et de rupture Lehr (Luo-Lehr) montrent des profils radiaux moyennés dans le temps qui sont valides pour la concentration de gaz et la vitesse axiale du liquide par rapport aux mesures expérimentales. Dans le système triphasé, la combinaison des modèles noyaux de coalescence de Luo et de rupture de Lehr (Luo-Lehr) et de la coalescence de Luo et de rupture de Luo (Luo-Luo) prédisent des profils radiaux moyennés dans le temps qui sont valides pour la vitesse axiale moyenné dans le temps par rapport aux expériences. Cependant, à une vitesse de gaz superficielle élevée, ces profils prédisent un comportement non réaliste par rapport aux observations empiriques. Les résultats de l'analyse de sensibilité du maillage montrent qu’avec des cellules de 3 mm, le model prédit une tendance similaire aux valeurs empiriques pour les profils radiaux de concentration du gaz, de vitesse axiale du liquide et de vitesse axiale solide. Le nombre de classes de bulles influe sur les distributions prédites de taille de bulle dans le système triphasé alors que les schémas de discrétisation numériques n'ont aucune influence sur les résultats. Les résultats des simulations d’un banc d’essai avec diffuseur à bulles poreux montrent que tenir compte du terme de dispersion influence le comportement hydrodynamique de la colonne à bulles.

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