応用水文 = Applied hydrology

Hydraulic transients in closed conduits have been a subject of both theoretical stud intense practical interest for more than one hundred years. While straightforward in te of the one-dimensional nature of pipe networks, the full description of transient fluid fl pose interesting problems in fluid dynamics. For example, the response of the turbu structure and strength to transient waves in pipes and the loss of flow axisymme pipes due to hydrodynamic instabilities are currently not understood. Yet, such u standing is important for modeling energy dissipation and water quality in transient flows. This paper presents an overview of both historic developments and presen research and practice in the field of hydraulic transients. In particular, the paper cusses mass and momentum equations for one-dimensional Flows, wavespeed, nu solutions for one-dimensional problems, wall shear stress models; two-dimensional and momentum equations, turbulence models, numerical solutions for two-dimen problems, boundary conditions, transient analysis software, and future practical an search needs in water hammer. The presentation emphasizes the assumptions and tions involved in various governing equations so as to illuminate the range of applic ity as well as the limitations of these equations. Understanding the limitations of cu models is essential for (i) interpreting their results, (ii) judging the reliability of the da obtained from them, (iii) minimizing misuse of water-hammer models in both research practice, and (iv) delineating the contribution of physical processes from the contribu of numerical artifacts to the results of waterhammer models. There are 134 refrences in this review article.@DOI: 10.1115/1.1828050 #

A Review of Water Hammer Theory and Practice

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices.
The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control.
Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Stability and Boundary Stabilization of 1-D Hyperbolic Systems

https://www.win.tue.nl/~atijssel/pdf_files/Bergant-Simpson-Tijsseling_2006.pdf

Water hammer with column separation: A historical review

Two-phase flow instabilities: A review

Extended irreversible thermodynamics (EIT) provides a framework for deriving extensions to phenomenological equations (e.g., Newton's law of viscosity, Fick's law of mass transport, and Darcy's law for porous media flow) for problems involving high frequencies (i.e., rapid transients). In this paper, a phenomenological equation is derived for energy loss in 1D unsteady pipe flow using an EIT formalism. The resulting wall shear stress is equal to the sum of (1) the steady-state shear stress; (2) a term that is proportional to the local (i.e., temporal) acceleration; and (3) a term that is proportional to the product of the velocity and the convective (i.e., spatial) acceleration. The form of this EIT-based wall shear stress formula shows that EIT provides a physical basis for instantaneous acceleration based unsteady friction formulas. It also illustrates the limitations and underlying assumptions of these models. For example, instantaneous acceleration based unsteady friction formulas are limited to fast transients (i.e., transients in which the water hammer timescale is significantly smaller than the diffusion timescale). A characteristics solution for unsteady pipe flow is proposed in which the phenomenological equation is used to model energy dissipation. Comparison of numerical test results with measured data from upstream and downstream valve closure laboratory experiments shows excellent agreement.

Extended thermodynamics derivation of energy dissipation in unsteady pipe flow

Under most circumstances, dispersive processes can be neglected in water distribution systems due to high velocities and low dispersion coefficients that ensure that advective transport dominates constituent spreading. However, during periods of low flow, dispersive effects may become important if the velocities are significantly decreased (e.g., during the night). Thus, the question that arises during a 24-h simulation is whether dispersive processes may dominate the transport of chlorine in a water distribution system. Given that advective transport models (e.g., EPANET, PICCOLO, NET, and DWQM) cannot account for dispersive transport, it is likely that these models would underpredict the required concentration of chlorine at locations behind the advective front and overpredict the required concentration at locations in advance of the advective front. There­ fore, when is a purely advective transport model an appropriate solution for contaminant transport in a water distribution system? Two constraining equations are presented to aid the user in assessing the applicability of an advective transport model.

Modeling Low Velocity/High Dispersion Flow in Water Distribution Systems

Discussion of "Extended Thermodynamics Derivation of Energy Dissipation in Unsteady Pipe Flow"

This work formulates a unified set of boundary conditions to efficiently represent the majority of valve and orifice devices found in water supply, transmission, and distribution systems. A particularly useful combination of mathematical components results when a lumped inertia model is linked with a throttling device. This combination of elements, termed a pipe replacement element/valve-in-line (PREVIL), has been constructed to permit a wide range of control-valve/short-pipe combinations to be conveniently modeled with the method of characteristics. The solution is quadratic in form and explicit, regardless of the number of pipes that are connected to the boundary condition. A variety of on-off and modulating valves can be accurately handled within this framework. An additional feature developed in this treatment of pressure-reducing an pressure-sustaining values, flow controllers, and other similar devices permits a more realistic representation of these important control devices. The response time of the regulating valve on opening or closing can be readily approximated so that a greater range of control behavior can be simulated. Application of the combined boundary condition is illustrated in a pipe network.

David H. Axworthy

Papers

A Review of Water Hammer Theory and Practice

Extended thermodynamics derivation of energy dissipation in unsteady pipe flow

Modeling Low Velocity/High Dispersion Flow in Water Distribution Systems

Discussion of "Extended Thermodynamics Derivation of Energy Dissipation in Unsteady Pipe Flow"

Efficient Valve Representation in Fixed-Grid Characteristics Method