Open Channel Networks Research Articles

Stability of Boundary Feedback Control Based on Weighted Lyapunov Function in Networks of Open Channels

A Lyapunov function is constructed based on the weighted sum of entropies for the case of two open channels in cascade, which is described by the Saint-Venant equations. A class of boundary feedback controllers is presented to guarantee the local closed-loop asymptotic stability in a neighborhood of the equilibrium point by means of the Lyapunov design approach.

Data reconciliation of an open channel flow network using modal decomposition

This article presents a method to estimate flow variables for an open channel network governed by the linearized Saint-Venant equations and subject to periodic forcing. The discharge at the upstream end of the system and the stage at the downstream end of the system are defined as the model inputs; the flow properties at selected internal locations, as well as the other external boundary conditions, are defined as the outputs. Both inputs and outputs are affected by noise and we use the model to improve the data quality. A spatially dependent transfer matrix in the frequency domain is constructed to relate the model input and output using modal decomposition. A data reconciliation technique is used to incorporate the error in the measured data and results in a set of reconciliated external boundary conditions; subsequently, the flow properties at any location in the system can be accurately estimated from the input measurements. The applicability and effectiveness of the method is demonstrated with a case study of the river flow subject to tidal forcing in the Sacramento-San Joaquin Delta, in California. We used existing USGS sensors in place in the Delta as measurement points, and deployed our own sensors at selected locations to produce data used for the validation. The proposed method gives an accurate estimation of the flow properties at intermediate locations within the channel network.

Effect of Channel Shape on Time of Travel and Equilibrium Detention Storage in Channel

For a catchment comprising a network of open channels and overland planes, the time of travel and the equilibrium detention storage in the channels have profound effects on the runoff characteristics of the catchment. For channels with long time of travel and large detention storage, they produce smaller catchment outflow, and the converse is true. Intuitively, the shape of the channels must have an effect on both the time of travel and the detention storage. Hence, the channel shape can be used as a means to manage the runoff from a catchment. In this technical note, the effect of channel shape on the time of travel and the equilibrium detention storage has been compared for seven channel shapes. The channels are subject to a uniform lateral inflow and a constant upstream inflow. The seven channel shapes are (1) square; (2) wide rectangular; (3) deep rectangular; (4) triangular; (5) vertical curb; (6) parabolic; and (7) circular. The comparison shows that channels with long time of travel also have large...

オブジェクト指向プログラミングによる再帰的開水路網モデルの構築とXML による記述

オブジェクト指向プログラミングによる再帰的開水路網モデルの構築とXML による記述

On a 2D ‘zoom’ for the 1D shallow water model: Coupling and data assimilation

In the context of river hydraulics we elaborate the idea of a ‘zoom’ model locally superposed on an open-channel network global model. The zoom model (2D shallow water equations) describes additional physical phenomena, which are not represented by the global model (1D shallow water equations with storage areas). Both models are coupled using the optimal control approach when the zoom model is used to assimilate local observations into the global model (variational data assimilation) by playing the part of a mapping operator. The global model benefits from using zooms, while no substantial modification to it is required. Numerical results on a toy test case show the feasibility of the suggested method.

Three Guest-Including Coordination Solids from a Single Crystallization: A Discrete Cage and Open-Channel Networks from 1-D Ladders and 1-D Ribbons

A study of the coordination assemblies that result from the complexation of 1,3,5-tri(4-sulfophenyl)benzene, L3-, with copper(II) in the presence of pyridine is presented. The present results offer some insights into the subtleties of designing coordination polymers and open-channel solids. From an initial crystallization, three different single crystalline solids, 1-3, are obtained. Compounds 1 and 2 are Cu pyridyl complexes of the trianionic form of the ligand whereas compound 3 is a Cu pyridyl complex of the monoprotonated form, HL2-. Compound 1 is a discrete cage complex. Compound 2 is a 1-D ladder structure that has open channels, and compound 3 is a 1-D ribbon structure that assembles into open channels. All three complexes form from the same crystallization in a ratio of 90:9:1, and all three have the same Cu coordination sphere. The exact ratio of products can be altered by varying the Cu counterion or by the addition of methanol. Addition of hexamethylenetetramine results in the exclusive formation of a different network, 4, which is structurally almost identical to the minor product 3. Single-crystal structures of all four solids are presented along with thermal analysis and IR data for the major products. A number of insights into formation of coordination assemblies are obtained. Compound 3 is discussed as an intermediate to 2, and compounds 3 and 4 offer a design paradigm for the formation of open-channel solids from 1-D building blocks.

Comparison of Gradually Varied Flow Computation Algorithms for Open-Channel Network

This paper presents a comparison of two algorithms—the forward-elimination and branch-segment transformation equations— for separating out end-node variables for each branch to model both steady and unsteady flows in branched and looped canal networks. In addition, the performance of the recursive forward-elimination method is compared with the standard forward-elimination method. The Saint-Venant equations are discretized using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved using the Newton-Raphson method. The algorithm using branch-segment transformation equations is found to be at least five times faster than the algorithm using the forward-elimination method. Further, the algorithm using branch-segment transformation equations requires less computer storage than the algorithm using the forward-elimination method, particularly when only nonzero elements of the global matrix are stored. Comparison between the Gauss-elimination method and the sparse matrix solution technique for the solution of the global matrix revealed that the sparse matrix solution technique takes less computational time than the Gauss- elimination method.

Dual Multilevel Urban Drainage Model

In urban areas, when heavy rains occur, the discharge capacity of sewers is usually unable to transport the effective rainfall reaching the streets. When the runoff flow rate exceeds the capacity of the storm sewer system, the excess flow is conveyed through the street network as overland flow. A dual model is proposed for modeling the system as a double network, formed by an upper network of open channels (street gutters) and a lower network of closed conduits (sewer pipes). What is new in this model is its capacity to take into account the hydrodynamic relationship between the flows in the upper and lower networks. The model is applied to computing the response of a real monitored basin; the historical flow rates measured during a first rainfall event are used to calibrate the model, which is then validated using the simulation of two other measured events.

オブジェクト指向プログラミングによる開水路網のモデル化と不定流の再帰的計算

Computation system of unsteady flow in open channel network with implicit method was established with Object Oriented Programming in Java language. The system has some objects;“River Channel Object” calculates the unsteady flow, “River Node Object” represents the boundary condition (upstream end, confluence, and so on), and “River Object” contains these two kinds of objects.“River Object” can also contain another “River Object”, that is, the open channel network can have recursive structure. This means high re-usability of objects, which was created formerly. Navigating the recursive structure, the system computes the “River Channel” flow and operates some output routines. The program code is easy to understand and reuse, then, effective programming of open channel network was enabled

Gradually Varied Flow Computation in Cyclic Looped Channel Networks

A novel and computationally efficient algorithm is presented to compute the water surface profiles in steady, gradually varied flows of open channel networks. This algorithm allows calculation of flow depths and discharges at all sections of a cyclic looped open channel network. The algorithm is based on the principles of (1) classifying the computations in an individual channel as an initial value problem or a boundary value problem; (2) determining the path for linking the solutions from individual channels; and (3) an iterative Newton–Raphson technique for obtaining the network solution, starting from initial assumptions for discharges in as few channels as possible. The proposed algorithm is computationally more efficient than the presently available direct method by orders of magnitude because it does not involve costly inversions of large matrices in its formulation. The application of this algorithm is illustrated through an example network.

Solute Transport in Open-Channel Networks in Unsteady Flow Regime

In this paper we propose a robust algorithm to evaluate solute transport in open-channel networks with transient storage under an unsteady flow regime. In the proposed approach, through the integration of junction equations into the model and solving them explicitly, the analysis of solute transport problems in open-channel networks is simplified significantly. Furthermore, when coupled with a transient hydrodynamic open-channel network model for flow simulation, the proposed model can be utilized in the solution of solute transport problems under unsteady flow regimes. In the proposed model, the governing equations are written in a conservative form and are solved using a fractional-step algorithm, which is based on a relaxation and central difference scheme. The proposed algorithm is robust and accurate even for advection dominant cases. A pure advection with discontinuities, a field application and solute transport in an open-channel network in an unsteady flow regime are included, to demonstrate the performance of the proposed algorithm.

Characterization and evaluation of potential reuse options for wastewater sludge and combined sewer system sediments in Mexico

Combined sewer systems generate sediments that have characteristics similar to those of primary sludge. Mexico City has such a system composed of a network of pipes, regulation structures (dams, basins) and open channels. The annual generation of sediments is estimated at 2.8 Mm3, which includes 0.41 Mm3 of sludge. As a result, the total capacity for transporting water is reduced considerably, making it necessary to extract yearly an approximate 0.85 Mm3 of those materials and to send them to a final disposal site with a capacity that is being exhausted. As part of the local Governmental effort, this project evaluates the quality of sediments from 6 dams, 4 regulation basins, 2 open channels, and 3 transfer stations. Also, sludge from 20 wastewater treatment plants was sampled. The results showed an important presence of lead and hydrocarbons in some sediments, and some sludge samples contained arsenic and nickel above the limits. Moreover, microbial levels exceeded the limits in all the sediments and sludge samples. Erosion was linked to the generation of an important amount of sediments based on lead concentration. A classification was established to determine the degree of contamination of the sediments as well as the required treatment to allow their potential reuse.

Global controllability between steady supercritical flows in channel networks

AbstractWe consider a tree‐like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of C1‐functions, so no shocks occur. Copyright 2004 John Wiley & Sons, Ltd.

Parameter Estimation for Flow in Open-Channel Networks

Two mathematical models for parameter estimation in closed-loop, open-channel flow networks are presented. The parameter estimation models seek to determine the parameter values that would reproduce an observed flow profile in the channel network. The governing equations for gradually varied flow in channel networks are the optimization models' constraints. The projected augmented Lagrangian method is used to solve the optimization models. Performance of these two optimization models is evaluated for a given closed-loop network configuration. Results establish the potential of the developed models for use in real-life flow scenarios.

Simulation of open channel network flows using finite element approach

This paper presents a finite element method (FEM) for simulating open channel network flows. Using a recursive formula derived from element equations, a relationship for channel junctions is established and a system equation is obtained. The system equation is much smaller in size in comparison with the simultaneous solution approach and its solution provides boundary conditions for single channels. The FEM is applied to solve individual channels, and a double sweep method is employed to save computation time. To demonstrate the potential of the approach, two channel networks were computed. It is shown that the results obtained with the proposed FEM are very close to those given by the widely used Preissmann scheme, indicating that it is an effective method to model flows in open channels.

Method to solve the non‐linear systems of equations for steady gradually varied flow in open channel network

AbstractThe paper concerns the solution of non‐linear system of equations arising while solving a steady gradually varied flow in an open channel network. To reduce the dimensions of final system the depths at each cross‐section and the discharge at each branch are considered as unknowns. Newton and Picard iteration can suffer from non‐convergent saw‐tooth errors. An approach to improve and consequently to ensure the convergence of the Picard method is proposed. Using the average from two successive iterations suppresses the saw‐teeth and gives a robust convergent iteration method to solve a steady gradually varied flow in any type of open channel network. The improvement in performance is confirmed by numerical tests. Copyright © 2004 John Wiley & Sons, Ltd.

Boundary feedback control in networks of open channels

This article deals with the regulation of water flow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies. A control law design based on this condition is illustrated with a simple case study: two reaches in cascade. The proof of the main stability theorem is based on a previous result from Li Ta-tsien concerning the existence and decay of classical solutions of hyperbolic systems.

OPTIMIZATION OF TRANSPORTATION NETWORKS DURING URBAN FLOODING1

ABSTRACT: In this paper a numerical model for flood propagation in urban areas is proposed. It has been applied to evaluate flooding hydraulic characteristics in terms of potential flood elevations, depths, and inundated areas. Furthermore, the algorithm efficiency and the consequent reduced computation time allow the use of the hydraulic model as a part of a more complex system for civil protection actions, planning, and management. During flood events, the transportation network plays a main role both in rescuing people when they are more vulnerable and in moving people and materials from and toward affected areas. The reduced efficiency of this transportation network is evaluated based on a least‐flood‐risk path‐finding algorithm. The results of a case study concerning the northern part of the city of Rome, show that the numerical model for unsteady flow in open channel networks achieves the proposed aims. It has proven to be able to describe the flood hydraulic characteristics and to be suitable for real‐time flood emergency management in urban areas.

Discussion of “Application of Relaxation Scheme to Wave-Propagation Simulation in Open-Channel Networks” by Mustafa M. Aral, Yi Zhang, and Shi Jin

Discussion of “Application of Relaxation Scheme to Wave-Propagation Simulation in Open-Channel Networks” by Mustafa M. Aral, Yi Zhang, and Shi Jin

Closure to “Application of Relaxation Scheme to Wave-Propagation Simulation in Open-Channel Networks” by Mustafa M. Aral, Yi Zhang, and Shi Jin

Closure to “Application of Relaxation Scheme to Wave-Propagation Simulation in Open-Channel Networks” by Mustafa M. Aral, Yi Zhang, and Shi Jin