The Hydraulics of Open Channel Flow : An Introduction

The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.arnoldpublishers.com/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est"

Environmental Hydraulics of Open Channel Flows

The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals to the reader (e.g. Fig. P-1). The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.bh.com/companions/0340740671/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est

The Hydraulics of Open Channel Flow

English Preface The book is an introduction to the hydraulics of open channel flows. The material is designed for undergraduate students in Civil, Environmental and Hydraulic Engineering. It will be assumed that the students have had an introductory course in fluid mechanics and that they are familiar with the basic principles of fluid mechanics : continuity, momentum, energy and Bernoulli principles. The book will first develop the basic principles of fluid mechanics with applications to open channels. Open channel flow calculations are more complicated than pipe flow calculations because the location of the free-surface is often unknown 'a priori' (i.e. beforehand). Later the students are introduced to the basic concepts of sediment transport and hydraulic modelling (physical and numerical models). At the end of the course, the design of hydraulic structures is introduced. The book is designed to bring a basic understanding of the hydraulics of rivers, waterways and man-made canals (e.g. Plates a-1 to a-13) to the reader. The lecture material is divided into four parts of increasing complexity : - Part I : Introduction to the basic principles. Application of the fundamental fluid mechanics principles to open channels. Emphasis on the application of the Bernoulli principle and Momentum equation to open channel flows. - Part II : Introduction to sediment transport in open channels. Basic definitions followed by simple applications. Occurrence of sediment motion in open channels. Calculations of sediment transport rate. Interactions between the sediment motion and the fluid motion. - Part III : Modelling open channel flows. Physical modelling of open channel flows. Numerical modelling of open channel flows. Physical modelling : application of the basic principles of similitude and dimensional analysis to open channels. Numerical modelling : numerical integration of the energy equation; one-dimensional flow modelling. - Part IV : Introduction to the design of hydraulic structures for the storage and conveyance of water. Hydraulic design of dams, weirs and spillways. Design of drops and cascades. Hydraulic design of culverts : standard box culverts and minimum energy loss culvert. Basic introduction to professional design of hydraulic structures. Application of the basic principles to real design situations. Analysis of complete systems. Applications, tutorials and exercises are grouped into four categories : applications within the main text to illustrate the basic lecture material, exercises for each chapter within each section, revision exercises using knowledge gained in several chapters within one section, and major assignments (i.e. problems) involving expertise gained in several sections : e.g., typically section I and one or two other sections. In the lecture material, complete and detailed solutions of the applications are given. Numerical solutions of some exercises, revision exercises and problems are available on the Internet (Publisher's site : http://www.arnoldpublishers.com/). A suggestion/correction form is placed at the end of the book. Comments, suggestions and critic are welcome and they will be helpful to improve the quality of the book. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. "Errare Humanum Est" ( )

Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed

On the relevance of the dam break problem in the context of nonlinear shallow water equations

The classical dam break problem has become the de facto standard in validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration. The main purpose of this study is to check the pertinence of the NSWE for flooding processes. From the mathematical point of view, the answer is not obvious since all derivation procedures assumes the total water depth positivity. We performed a comparison between the two-fluid Navier-Stokes simulations and the NSWE solved analytically and numerically. Several conclusions are drawn out and perspectives for future research are outlined.Comment: 20 pages, 15 figures. Accepted to Discrete and Continuous Dynamical Systems. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutyk

A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available

A hybrid stabilization technique for simulating water wave - Structure interaction by incompressible Smoothed Particle Hydrodynamics (ISPH) method

The Smoothed Particle Hydrodynamics (SPH) method is emerging as a potential tool for studying water wave related problems, especially for violent free surface flow and large deformation problems. The incompressible SPH (ISPH) computations have been found not to be able to maintain the stability in certain situations and there exist some spurious oscillations in the pressure time history, which is similar to the weakly compressible SPH (WCSPH). One main cause of this problem is related to the non-uniform and clustered distribution of the moving particles. In order to improve the model performance, the paper proposed an efficient hybrid numerical technique aiming to correct the ill particle distributions. The correction approach is realized through the combination of particle shifting and pressure gradient improvement. The advantages of the proposed hybrid technique in improving ISPH calculations are demonstrated through several applications that include solitary wave impact on a slope or overtopping a seawall, and regular wave slamming on the subface of open-piled structure

Single and multiphase CFD approaches for modelling partially baffled stirred vessels: comparison of experimental data with numerical predictions

Whilst the use of CFD to study mixing vessels is now common-place, there are still many specialised applications that are yet to be addressed. Here we present CFD and PIV results for a hydrodynamic study of a partially baffled vessel with a free surface. The standard k.ε and SSG Reynolds Stress turbulence models are used and the numerical predictions of the mean flow field are compared with experimental data for single phase modelling. At low rotation rates a flat free surface is observed and the flow is simulated using a single phase model, whilst at high rotation rates an Eulerian–Eulerian multiphase model is used to capture the free surface location, even under conditions when gas is drawn down to the impeller. It is shown that there are significant transient effects that mean many of the “rules of thumb” that have been developed for fully baffled vessels must be revisited. In particular such flows have central vortices that are unsteady and complex, transient flow-induced vortical structures generated by the impeller–baffle interactions and require a significant number of simulated agitator rotations before meaningful statistical analysis can be performed. Surprisingly, better agreement between CFD and experimental data was obtained using the k.ε than the SSG Reynolds stress model. The multiphase inhomogeneous approach used here with simplified physics assumptions gives good agreement for power consumption, and with PIV measurements with flat and deformed free surfaces, making this affordable method practical to avoid the erroneous modelling assumption of a flat free surface often made in such cases

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic