Student Number : 0100281N - MSc(Eng) Research Report - School of Civil and Environmental Engineering - Faculty of Engineering and the Built Environment / Many environmental and engineering projects require prediction of the velocity of flow in river channels, in terms of those channel properties and flow characteristics which induce resisting forces or an energy loss to the flow. Relationships such as the Manning, Chézy and Darcy-Weisbach equations have been in use for a century or more. All of them account for resistance with a single coefficient of resistance, and the central problem is evaluation of this coefficient. Experimental results by different researchers have shown that Manning’s n varies strongly with the ratio of flow depth to roughness height. It is constant for values of this ratio above about 4, but increases significantly for lower values. This suggests that the equation is not suitable in its original form for the case of intermediate-scale roughness. The roughness is intermediate-scale if the relative submergence ratio of flow depth to roughness elements height lies between 1 and 4. The influence of the roughness elements on flow resistance in this regime is caused by a combination of both element drag and boundary shear, or friction. The results of an experimental study with hemispherical roughness elements are presented, showing how the roughness element size, spacing and pattern influence flow resistance. For the range of conditions tested, Manning’s n appears to depend on roughness element size, spacing and pattern.

Thesis submitted in fulfilment of the requirements for the degree Doctor of Technology: Mechanical Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology 2014 / Open channels, flumes or launders are used in the mining industry to transport slurries during processing and to disposal sites. Water plays a major part in the makeup of these slurries, its usage and availability is critical in countries where there are strict water usage management programs. The optimisation of flume design involves the maximisation of solids transport efficiency whilst, at the same time reduces water usage. The design of open channels is complex as it is dependent on both the slurry rheology and the channel shape. Very little has been reported in the literature for predicting non-Newtonian laminar flow in open channels of arbitrary cross-section. The only method available was that proposed by Kozicki and Tiu (1967, 1986). The shape factors they used were those evaluated from analytical solutions for flow of Newtonian fluids in open channels of the same cross-section. However, they carried out no experimental work to validate their model. Few experimental studies have been made on the effect of shape on non-Newtonian flow in open channels. Naik (1983) tested kaolin in water suspensions in a rectangular channel. Coussot (1994) provided some data for the flow of a Herschel-Bulkley fluid in rectangular and trapezoidal channels. Fitton (2007; 2008) obtained data for flow of three different non-Newtonian fluids (carboxymethylcellulose, carbopol and thickened tailings) in a semi-circular channel. A large experimental database for non-Newtonian flow in rectangular open channels was published by Haldenwang (2003) at the Flow Process Research Centre, Cape Peninsula University of Technology. Guang et al. (2011) performed Direct Numerical Simulations of turbulent flow of a yield- pseudoplastic fluid in a semi-circular channel. They compared their simulations with actual field measurements and found them to over-predict the flow velocity by approximately 40%. The source for this discrepancy was difficult to ascertain. A comprehensive database was compiled during this research of the flow of three non–Newtonian fluids in rectangular, trapezoidal, semi-circular and triangular channels. The flow of carboxymethylcellulose solutions and aqueous kaolin and bentonite suspensions was investigated in a 10 meter long flume at angles ranging from 1° to 5° from the horizontal plane. The effect of channel shape on the friction factor-Reynolds number relationship for laminar and turbulent open channel flow of these three fluids was investigated. New models for the prediction of laminar and turbulent flow of non-Newtonian fluids in open channels of different cross-sectional shapes are proposed. The new laminar and turbulent velocity models are compared with three previously-published velocity models for laminar flow and five previously-published velocity models for turbulent flow using average velocity as comparison criteria. For each channel shape, the laminar flow data can be described by a general relationship, f = K/Re where f is the Fanning friction factor and Re is the appropriate Haldenwang et al. (2002) Reynolds number. The K values were found to be 14.6 for triangular channels with a vertex angle of 90°, 16.2 for semi-circular channels, 16.4 for rectangular channels and 17.6 for trapezoidal channels with 60 degree sides. These K values were found to be in line with those reported by Straub et al. (1958) and Chow (1969) for open channel laminar flow of Newtonian fluids as opposed to the assumption made by Haldenwang et al. (2002; 2004) of using a constant value of 16 based on the pipe flow paradigm for all channel shapes. This new laminar model gave a closer fit to the laminar flow data than those from the three previously-published models. However, the presence of the yield stress still presents a problem, which makes the flow prediction in laminar flow for such fluids not very accurate. The investigation on non-Newtonian turbulent flow of the three fluids in the four different shaped open channels revealed that the data was described by the modified Blasius equation f = a Re b where a and b are constant values determined for each channel shape and Re is the Haldenwang et al. (2002) Reynolds number. Values of a and b for a rectangular channel were found to be 0.12 and -0.330, for a semi- circular channel 0.048 and -0.205, for a trapezoidal channel with 60° sides, 0.085 and -0.266 and for a triangular channel with vertex angle of 90°, 0.042 and -0.202. New laminar and turbulent velocity models were derived from using the new laminar f = K/Re and turbulent f = a Re b, friction factor-Reynolds number relationship. The laminar velocity model did not always give the best result, but the majority of the time it did, compared to the three previously published models. The new turbulent velocity model yielded the best results when compared to the five previously published models using average velocity as comparison criteria. The composite power law modelling procedure of Garcia et al. (2003) used for pipe flow predictions was extended to the present work on non-Newtonian flow in open channels of various cross-sections. The results show that the modelling technique used by Garcia et al. (2003) for pipe flow can be used to adequately predict flow in an open channel of a given cross-sectional shape provided that an appropriate Reynolds number is used to take into account the non-Newtonian behaviour of the test fluid. It was found that the results using the Haldenwang et al. (2002) Reynolds number yielded better results than those based on the adapted Metzner-Reed Reynolds number. The correlations and models developed and experimentally validated during this research can be used to further improve the design of rectangular, semi-circular, trapezoidal and triangular open channels to transport non-Newtonian fluids.

<p> Flows in channels or estuaries may exhibit variations in density arising· from differences in temperature, salinity or suspended solids. In the absence of significant vertical mixing, stable, discrete layers may form with distinct density interfaces. </p> <p> This thesis presents a computational approach for the analysis of two-layer, vertically stratified, one-dimensional horizontal flows in open channels. A variety of such problems are identified and a critical survey of the existing literature is presented. A framework is defined against which these problems are classified and decomposed into analytical problems of the simplest possible scope. Based on the conditions that lead to changes in flow characteristics, four research areas are examined. These are energy balance, interfacial hydraulic jump, lock exchange flows, and long transitions. Although restricted to essentially one-dimensional flows, the analytical study of these four areas is extended to allow for non-uniform velocity distribution the introduction of boundary-layer displacement thicknesses and correction factors for kinetic energy and momentum. Also, a significant feature of the study is the ability to handle channels of arbitrary cross-sectional geometry. </p> <p> The basic philosophy of the approach followed in this study is to develop a relatively simple and computationally econaoical procedure which is applicable to a wide variety of problems involving channels systems of arbitrary geometry and boundary conditions. A library of computer subroutines provides a convenient means of developing an open-ended system of computational techniques for the solution of a wide range of problems. Such a library of computational algorithms may also promote. cooperation and collaboration among researchers and engineers concerned with stratified flow hydraulics. Such algorithms should provide solutions for frequently recurring problems, should be mutually compatible and allow the construction of relatively complex analytical models in a modular fashion. A comprehensive library of routines is developed which consists of fourty-four subroutines and functions. This evolves as a well-defined hierarchy of algorithms in which the most basic algorithms are nested within the more sophisticated ones to the sixth or seventh level. </p> <p> The computational algorithms are tested for theoretical and computational performance. Numerical predictions are compared with available experimental and field data. Moreover, an experimental program is described which is designed and carried ·out to verify the numerical predictions obtained for the first of the above-mentioned four topics. </p> <p> An important aspect of the study is the illustration of the application of the routines in the solution of typical practical problems such as selective withdrawal from stratified water bodies and recirculation of cooling water from power plants. In addition, to facilitate utilization of the programs by others, complete documentation and listings are provided. </p> / Thesis / Doctor of Philosophy (PhD)

Το θέμα της παρούσας εργασίας είναι η μελέτη της ροής ύδατος εντός ανοιχτού αγωγού ορθογωνικής διατομής κατά την περίπτωση όπου έχουμε υπερχειλιστή λεπτής στέψης και ανάντη αυτού παρουσιάζεται ανισοκατανεμημένη παροχή. / Flow study in the downstream of one spillway with thin top, inside an rectangular open channel, in cases of uneven supply upstream of spillway.

The original ARID (Algae Raceway Integrated Design) raceway was an effective method to increase temperature toward the optimal growth range. However, the energy input was high and flow mixing was poor. Thus, the ARID-HV (High Velocity Algae Raceway Integrated Design) raceway was developed to reduce energy input requirements and improve flow mixing. This was accomplished by improving pumping efficiency and using a serpentine flow pattern in which the water flows through channels instead of over barriers. A prototype ARID-HV system was installed in Tucson, Arizona, and the constructability, reliability of components, drainage of channels, and flow and energy requirements of the ARID-HV raceway were evaluated. Each of the electrical energy inputs to the raceway (air sparger, air tube blower, canal lift pump, and channel recirculation pump) was quantified, some by direct measurement and others by simulation. An algae growth model was used to determine the algae production rate vs. flow depth and time of year. Then the electrical energy requirement of the most effective flow depth was calculated. Channel hydraulics was evaluated with Manning's equation and the corner head loss equation. In this way, the maximum length of channels for several raceway slopes and mixing velocities were determined. Algae production in the ARID-HV raceway was simulated with a temperature and light growth model. An energy efficient design for the ARID-HV raceway was developed.

L'installation de systèmes de mesure est d'une utilisation cruciale pour la gestion des réseaux d'assainissement ou des canaux d 'irrigation. La plupart des structures gouvernementales ou privées ainsi que les agglomérations s'équipent de systèmes de mesure de débit afin de se conformer avec la législation européenne. La plupart des débitmètres fournissent des données en temps réel i.e. l'information est transmise en permanence. aux centrales d'acquisition pour une gestion de l'architecture du système de canaux. La mesure en canaux ouverts est souvent ultrasonore. L'objectif de cette thèse est de proposer une méthode en temps réel afin de corréler les vitesses locales en une vitesse moyenne dans les conditions observables par les utilisateurs en canaux ouverts. Les thématiques impliquées à cette étude sont multiples: les techniques de mesure, l'hydrodynamique en canaux ouverts représentée par la turbulence (ici plus particulièrement les courants secondaires), les lois de paroi, le nombre de Froude ... l'ensemble de ces thématiques doit être investi en canaux pleinement développés où les conditions sont stables dans l'espace mais aussi pour des conditions perturbées telles que les structures hétérogènes ou transitoires.La technique de mesure est un point clé: quelle est la technique la plus applicable aux conditions de mesure i.e. les canaux étroits? Les canaux étroits varient très rapidement en tem1es de taux de remplissage : la technique la plus adaptée est le profileur ultrasonique.La compréhension des effets hydrodynamiques est essentielle afin de développer un modèle de conversion. Les canaux droits sont influencés par l'hydrodynamique des écoulements, la géométrie mais aussi et principalement par leurs interactions. En canaux droits, les courants secondaires sont primordiaux même s'ils se traduisent par un effet le plus observable : le dip-phénomène, i.e. la présence d'un maximum de vitesse non pas à la surface d'eau mais en dessous pour les canaux étroits. Ces courants secondaires sont fortement sensibles au rapport d'aspect, la géométrie et la variabilité de la rugosité le long de la paroi, passablement sensible à la rugosité et indépendant du nombre de Froude .Les perturbations, à l'aval desquelles sont installés les débitmètres ultrasonores, sont majoritairement représentées par les coudes et les jonctions. Dans les coudes, les tourbillons sont liés aux forces centrifuges (gros tourbillon) et la turbulence (petit tourbillon). Pour les jonctions, les tourbillons diffèrent des deux précédentes configurations avec la présence à l'aval de la jonction de 3 tourbillons (due à un étirement des tourbillons par l'arrivée latérale). Les capteurs ne sont pas installés directement au niveau de la perturbation mais à l'aval. Dans la littérature, les distances requises pour retrouver des conditions proches de l'écoulement pleinement développé devraient excéder environ 50 hauteurs d'eau. En pratique, ces distances sont plus proches de5-10 fois la largeur du canal ou du tirant d'eau. L'application de modèle basée sur l'écoulement pleinement développé corrélé à un capteur n'est pas recommandable... / The installation of flow rate measurement systems is an important factor in regard to the management of sewer and irrigation networks. Most cities and infrastructure succeed in obtaining sufficient flow measurements to satisfy European Regulation rules. Most flow meters comprise real time systems; this means that the information is permanently transferred to a data base for the management and optimization of the particular network. The measurement technology deployed is typically ultrasound based. Within the number of measurement points a high percentage are often deficient and create specific difficulties (>75% of Venturi flumes are inaccurate according to Anglian Water, a UK water and wastewater company). The study presented here focuses on flow meters which calculate discharge using measurement of level, cross sectional area and the correlation of local velocity to generate a mean value. The aim of this thesis is to propose a real time method to enable determination of this “conversion” under realistic configurations which Users find in open channels. The synthesis of measurement points through an understanding of hydraulic conditions (Bonakdari, 2006) provides a method to create flow data allowing local point velocities to be converted into an overall mean value. The approach has limitations and may fail in industrial situations but can be used for very complex configurations. It also requires specialists with knowledge of the technique who are rarely available to Users. What is proposed here is an alternative method to Bonakdari for simpler configurations. The aim is to evaluate the flow rate with acceptable accuracy using these technics and to establish a relationship between local velocities and the mean velocity according to Regulatory requirements (8% are required in UK, 5 to 8% in Germany depending on area). The individual components are here: the measurement techniques; the hydrodynamics represented with the turbulence (secondary currents in open channels); the wall / roughness effects; the Froude number … for fully developed conditions where conditions become stable in space but for disturbed conditions, as well such as heterogeneous structures or transition conditions.

This thesis aims to develop control algorithms for irrigation canals in an experimental framework.These water transport systems are difficult to manage and present low efficiencies in practice. As a result, an important percentage of water is lost, maintenance costs increase and water users follow a rigid irrigation schedule.All these problems can be reduced by automating the operation of irrigation canals.In order to fulfil the objectives, a laboratory canal, called Canal PAC-UPC, was equipped and instrumented in parallel with the development of this thesis. In general, the methods and solutions proposed herein were extensively tested in this canal.In a broader context, three main contributions in different irrigation canal control areas are presented.Focusing on gate-discharge measurements, many submerged-discharge calculation methods are tested and compared using Canal PAC-UPC measurement data. It has been found that most of them present errors around ±10%, but there are notable exceptions. Specifically, using classical formulas with a constant 0.611 contraction value give very good results (error<±6%), but when data is available, a very simple calibration formula recently proposed in the literature significantly outperform the rest (error<±3%). As a consequence, the latter is encouragingly proposed as the basis of any gate discharge controller.With respect to irrigation canal modeling, a detailed procedure to obtain data-driven linear irrigation canal models is successfully developed. These models do not use physical parameters of the system, but are constructed from measurement data. In this case, these models are thought to be used in irrigation canal control issues like controller tuning, internal controller model in predictive controllers or simply as fast and simple simulation platforms. Much effort is employed in obtaining an adequate model structure from the linearized Saint-Venant equations, yielding to a mathematical procedure that verifies the existence of an integrator pole in any type of canal working under any hydraulic condition. Time-domain and frequency-domain results demonstrate the accuracy of the resulting models approximating a canal working around a particular operation condition both in simulation and experiment.Regarding to irrigation canal control, two research lines are exploited. First, a new water level control scheme is proposed as an alternative between decentralized and centralized control. It is called Semi-decentralized scheme and aims to resemble the centralized control performance while maintaining an almost decentralized structure. Second, different water level control schemes based on PI control and Predictive control are studied and compared. The simulation and laboratory results show that the response and performance of this new strategy against offtake discharge changes, are almost identical to the ones of the centralized control, outperforming the other tested schemes based on PI control and on Predictive control. In addition, it is verified that schemes based on Predictive control with good controller models can counteract offtake discharge variations with less level deviations and in almost half the time than PI-based schemes.In addition to these three main contributions, many other smaller developments, minor results and practical recommendations for irrigation canal automation are presented throughout this thesis.

The dynamic wave model (the complete form of the saint-Venant equations), as applied to flow routing in irrigation canals or flood routing in natural channels, is associated with parameter and model uncertainties. The parameter uncertainty arises due to imprecision in the estimation of Manning’s n used for calculating the friction slope (sf) in the momentum equation of the dynamic wave model. Accurate estimation of n is difficult due to its dependence on several channel and flow characteristics. The model uncertainty of the dynamic wave model arises due to difficulty in applying the momentum equation to curved channels, as it is a vector equation. The one-dimensional form of the momentum equation is derived assuming that the longitudinal axis of the channel is a straight line, so that the net force vector is equal to the algebraic sum of the forces involved. Curved channel reaches have to be discretized into small straight sub-reaches while applying the momentum equation. Otherwise, two- or three-dimensional forms of the momentum equation need to be adopted. A main objective of the study presented in the thesis is to develop a fuzzy dynamic wave model (FDWM), which is capable of overcoming the parameter and model uncertainties of the dynamic wave model mentioned above, specifically for problems of flow routing in irrigation canals and flood routing in natural channels. It has been demonstrated earlier in literature that the problem of parameter uncertainty in infiltration models can be addressed by replacing the momentum equation by a fuzzy rule based model while retaining the continuity equation in its complete form. The FDWM is developed by adopting the same methodology: i.e. By replacing the momentum equation of the dynamic wave model by a fuzzy rule based model while retaining the continuity equation in its complete form. The fuzzy rule based model is developed based on fuzzification of a new equation for wave velocity, to account for the model uncertainty and backwater effects. A fuzzy dynamic wave routing model (FDWRM) is developed based on application of the FDWM to flow routing in irrigation canals. The fuzzy rule based model is developed based on the observation that inertia dominated gravity wave predominates in irrigation canal flows. Development of the FDWRM and the method of computation are explained. The FDWRM is tested by applying it to cases of hypothetical flow routing in a wide rectangular channel and also to a real case of flow routing in a field canal. For the cases of hypothetical flow routing in the wide rectangular channel, the FDWRM results match well with those of an implicit numerical model (INM), which solves the dynamic wave model; but the accuracy of the results reduces with increase in backwater effects. For the case of flow routing in the field canal, the FDWRM outputs match well with measured data and also are much better than those of the INM. A fuzzy dynamic flood routing model (FDFRM) is developed based on application of the FDWM to flood routing in natural channels. The fuzzy rule based model is developed based on the observation that monoclinal waves prevail during floods in natural channels. The natural channel reach is discredited into a number of approximately uniform sub-reaches and the fuzzy rule based model for each sub-reach is obtained using the discharge (q)–area (a) relationship at its mean section, based on the kleitz-seddon principle. Development of the FDFRM and the method of computation are explained. The FDFRM is tested by applying it to cases of flood routing in fictitious channels and to flood routing in a natural channel, which is described in the HEC-RAS (hydrologic engineering center – river analysis system) application guide. For the cases of flood routing in the fictitious channels, the FDFRM outputs match well with the INM results. For the case of flood routing in the natural channel, optimized fuzzy rule based models are derived using a neuro-fuzzy algorithm, to take the heterogeneity of the channel sub-reaches into account. The resulting FDFRM outputs are found to be comparable to the HEC-RAS outputs. Also, in literature, the dynamic wave model has been applied in the inverse direction for the development of centralized control algorithms for irrigation canals. In the present study, a centralized control algorithm based on inversion of the fuzzy dynamic wave model (FDWM) is developed to overcome the drawbacks of the existing centralized control algorithms. A fuzzy logic based dynamic wave model inversion algorithm (FDWMIA) is developed for this purpose, based on the inversion of the FDWM. The FDWMIA is tested by applying it to two canal control problems reported in literature: the first problem deals with water level control in a fictitious canal with a single pool and the second, with water level control in a real canal with a series of pools (ASCE Test Canal 2). In both cases, the FDWMIA results are comparable to those of the existing centralized control algorithms.