Hydraulic Network Analysis Research Articles

Modeling and simulation of water distribution systems using timed hybrid Petri nets

This paper deals with modeling and simulation of water distribution systems using Hybrid Petri Nets. A methodology for building a Timed Hybrid Petri Net (THPN) model is proposed; the model is derived from a set of equations describing conservation of mass and energy that specify the behaviour of a water distribution network. A simulation technique for the execution of a THPN in which the transitions firing velocities are established from the linearised conservation of energy equations is presented; it shows both transient and steady state for the analysis of hydraulic networks. Based on this technique, a simulator in Matlab has been developed.

Optimization model for water distribution network considering minimization of total replacement cost and stabilization of flow velocity in pipelines

This study proposes a method using genetic algorithms (GA) to optimize selection of appropriate pipe diameter during pipeline replacement planning for water distribution networks. Mathematical programming problems were first formulated to minimize cost of replacement while considering hydraulic constraints such as flow velocity for each pipe and water pressure at each node. In addition to the economic perspective, stability of flow velocity in pipes was considered as another objective function of the multipurpose programming problem. After this, a GA model combined with hydraulic pipe network analysis was created: the HGA model. Finally, a case study was conducted to show the validity of the proposed model. Results reveal that this multipurpose HGA model is useful for optimization of pipeline replacement planning.

Pressure Control for Leakage Minimisation in Water Distribution Systems Management

A model to support decision systems regarding the quantification, location and opening adjustment of control valves in a network system, with the main objective to minimise pressures and consequently leakage levels is developed. This research work aims at a solution that allows simultaneously optimising the number of valves and its location, as well as valves opening adjustments for simulation in an extended period, dependently of the system characteristics. EPANET model is used for hydraulic network analysis and two operational models are developed based on the Genetic Algorithm optimisation method for pressure control, and consequently leakage reduction, since a leak is a pressure dependent function. In these two modules, this method has guaranteed an adequate technique performance, which demands a global evaluation of the system for different scenarios. A case study is presented to show the efficiency of the system by pressure control through valves management.

Modelling of polymer electrolyte membrane fuel cell stacks based on a hydraulic network approach

Polymer electrolyte membrane (PEM) fuel cells convert the chemical energy of hydrogen and oxygen directly into electrical energy. Waste heat and water are the reaction by-products, making PEM fuel cells a promising zero-emission power source for transportation and stationary co-generation applications. In this study, a mathematical model of a PEM fuel cell stack is formulated. The distributions of the pressure and mass flow rate for the fuel and oxidant streams in the stack are determined with a hydraulic network analysis. Using these distributions as operating conditions, the performance of each cell in the stack is determined with a mathematical, single cell model that has been developed previously. The stack model has been applied to PEM fuel cell stacks with two common stack configurations: the U and Z stack design. The former is designed such that the reactant streams enter and exit the stack on the same end, while the latter has reactant streams entering and exiting on opposite ends. The stack analysed consists of 50 individual active cells with fully humidified H2 or reformate as fuel and humidified O2 or air as the oxidant. It is found that the average voltage of the cells in the stack is lower than the voltage of the cell operating individually, and this difference in the cell performance is significantly larger for reformate/air reactants when compared to the H2/O2 reactants. It is observed that the performance degradation for cells operating within a stack results from the unequal distribution of reactant mass flow among the cells in the stack. It is shown that strategies for performance improvement rely on obtaining a uniform reactant distribution within the stack, and include increasing stack manifold size, decreasing the number of gas flow channels per bipolar plate, and judicially varying the resistance to mass flow in the gas flow channels from cell to cell. Copyright © 2004 John Wiley & Sons, Ltd.

Flower, a model for the analysis of hydraulic networks and processes

We have developed in the past years a model that describes hydraulic networks that are typical of the cryogenic interconnection of superconducting magnets. The original model, called Flower, was used mostly to provide consistent boundary conditions for the operation of a magnet. The main limitations were associated with the number and nature of modelling elements available, and to the maximum size of the model that could be solved. Here we present an improvement of the model largely relaxing the above limitations by the addition of new modelling elements, such as parallel flow heat exchangers, and by a significant improvement in the numerics of the solver, using sparse matrix storage and solution techniques. We finally show a typical application to the case of a magnet quench in the LHC string.

Hydraulic networks in nature

The analysis of natural hydraulic networks over a wide range of scales, allowed by modern digital mapping technology, reveals extraordinary diversity of natural forms, and yet deep regularity and symmetry, regardless of geology, climate, vegetation or exposed lithology. River networks are indeed a paradigm of scale-invariant, or fractal, forms ubiquitous in nature, whereas tidal networks bear the both the signatures of scaling processes and of different dynamic origin and susceptibility to environmental factors. Here I review a subjective choice of linked results, suggesting that the dynamic origin of the recurrence of similar network forms in nature relates to a common mechanism of growth and stabilization of open, dissipative systems with many degrees of freedom.

Simulation of Water Networks Containing Controlling Elements

Theoretical models for hydraulic network analysis often assume idealized pipe networks. Practical network packages, however, allow for a variety of necessary controlling elements. Sometimes these are introduced as generalized pipe elements, thus hiding the inherent discontinuous operation of nonreturn valves and pressure reduction valves. It is well known that the inclusion of such elements may cause numerical difficulties because of singularities. This paper presents an algorithm based on loop equations. It features a dynamic loop structure that is updated automatically according to the state of the controlling elements. It is shown that this provides a logical solution to the discontinuous operation of the controlling elements and also results in a highly efficient network simulation algorithm.

An artificial neural network for non-iterative calculation of the friction factor in pipeline flow

Abstract A non-iterative procedure was developed, using an artificial neural network (ANN), for calculating the friction factor, f, in the Darcy-Weisbach equation when estimating head losses due to friction in closed pipes. The Regula-Falsi method was used as an implicit solution procedure to estimate the f values for a range of Reynolds numbers, Re, and relative roughness e/D values (where e is the pipe roughness and D is the pipe diameter). In developing the ANN model, three configurations were evaluated: (i) the input parameters Re and e/D were taken initially on a linear scale; (ii) the first input parameter Re was transformed to a logarithmic scale; and (iii) both input parameters (Re and e/D) were transformed to a logarithmic scale. Configuration (iii) yielded an optimal ANN model with 14 neurons in each of three hidden layers. This configuration was capable of predicting the values of f in the Darcy-Weisbach equation for any given Re in the range of 2×103–1×108 and e/D in the range of 1×10−6–5×10−2. These values were in close agreement with those obtained using the numerical technique. The developed ANN model may offer significant advantages when dealing with flow problems that involve repetitive calculations of the friction factor such as those encountered in the hydraulic analysis of pipe networks and pressurized irrigation systems.

CATHENA: A thermalhydraulic code for CANDU analysis

This paper describes the Canadian algorithm for thermal hydraulic network analysis (CATHENA) transient, thermalhydraulics code developed for the analysis of postulated upset conditions in CANDU® 1 CANDU® is a registered trademark of Atomic Energy of Canada Limited (AECL). 1 reactors. The core of a CANDU reactor consists of a large number of horizontal pressure tubes containing fuel bundles. As a result of the unique design of the CANDU reactor, the CATHENA thermalhydraulic code has been developed with a number of unique modelling capabilities. The code uses a one-dimensional, two-fluid, nonequilibrium representation of two-phase flow. Some of the unique features of the CATHENA code are the one-step semi-implicit numerical method used and the solid heat transfer modelling capability that allows horizontal fuel bundles to be represented in detail. The code has been used in the design and analysis of CANDU-3, CANDU-6 and CANDU-9 reactors. The code has also been used for the design and analysis of the multiple applied lattice experimental (MAPLE) class of reactors and for the analysis of thermalhydraulic experimental programs conducted by Atomic Energy of Canada Limited (AECL).

Network Linear Programming as Pipe Network Hydraulic Analysis Tool

An accurate network linear programming (NLP) algorithm for the hydraulic analysis of water pipe networks is developed and compared with direct equation solving techniques. Accuracy is achieved by the use of a novel iterative scheme in which successive linear approximations to the nonlinear head loss equations are refined for each pipe in the region of the emerging solution. The use of primal-dual and simplex method NLP solvers in the iterative strategy is investigated, with a hybrid scheme being shown to reduce execution times by an order of magnitude. Nevertheless, the direct equation solving algorithm of Todini and Pilati remains much more efficient than the best NLP algorithm. A new algorithm for the analysis of locally controlled feedback devices is developed for inclusion in the NLP strategy. The uniqueness of pipe network hydraulic solutions is also investigated. Although some doubt has been expressed regarding uniqueness of solutions to networks that contain locally controlled feedback devices, evidence of nonuniqueness has not been forthcoming. Arguments in support of unique solutions for such networks are presented.

Finite element analysis of blood flow through biological tissue

Quantitative analysis of blood perfusion has been performed with a hierarchical mixture model of blood perfused biological tissue, for low Reynolds steady state Poiseuillian flow through two-dimensional, computer generated, rigid, arterial vascular trees. The mixture model describes blood flow through the vasculature by spatial and hierarchical flow components, both related to the blood pressure gradient via an extended Darcy equation. The Darcy-permeability tensor is derived from the geometry of the vascular tree, the fluid viscosity, and the vascular hierarchy which is quantified by a dimensionless parameter xo. Finite element results of fluid pressure and flow on certain levels of the hierarchy are compared to correspondingly volume averaged pressures and flows calculated by hydraulic network analysis. The correspondence between the finite element results and the network results strongly depends on the quantification of the hierarchy, which should be closely related to the hierarchical fluid pressure. Two methods for hierarchical quantification have been used, one of which is based on the network fluid pressure and the other on the segment diameters. With the first method a good correlation between x0 and fluid pressure, and consequently a good correspondence between finite element and network results, are found. The second method yields a poor correlation between xo and fluid pressure. However, still satisfying correspondence between finite element and network results is found.

96/06035 Inhour equation and kinetic distortion in a two-point reactor kinetic model

This paper describes the Canadian algorithm for thermal hydraulic network analysis (CATHENA) transient, thermalhydraulics code developed for the analysis of postulated upset conditions in CANDU®1 reactors. The core of a CANDU reactor consists of a large number of horizontal pressure tubes containing fuel bundles. As a result of the unique design of the CANDU reactor, the CATHENA thermalhydraulic code has been developed with a number of unique modelling capabilities. The code uses a one-dimensional, two-fluid, nonequilibrium representation of two-phase flow. Some of the unique features of the CATHENA code are the one-step semi-implicit numerical method used and the solid heat transfer modelling capability that allows horizontal fuel bundles to be represented in detail. The code has been used in the design and analysis of CANDU-3, CANDU-6 and CANDU-9 reactors. The code has also been used for the design and analysis of the multiple applied lattice experimental (MAPLE) class of reactors and for the analysis of thermalhydraulic experimental programs conducted by Atomic Energy of Canada Limited (AECL).

Integration of a Model for Hydraulic Analysis of Water Distribution Networks with an Evolution Program for Pressure Regulation

Abstract: This paper describes a computational model for hydraulic analysis of water distribution networks specifically developed to be used with an evolution program (EP) for optimal pressure regulation. The hydraulic solver uses a method based on loop equations, namely, the linear theory method (LTM). Network topology analysis is performed using depth‐first‐search and breadth‐first‐search algorithms that are devised to ensure the connectedness of a network and to enable easy identification of loops. The model developed enables rapid evaluation of a network for different topologic conditions (i.e., the connectivity of the nodes caused by different valve settings) as required by the EP. A variable number of LTM iterations throughout the evolution process is used to speed up the search. A sample network problem is used to illustrate the efficiency of both the model for hydraulic analysis and the EP.

An Improved Method for Incorporating Pipe Components into the Analysis of Hydraulic Networks

The design of pipe networks can be a tedious and time-consuming process. Numerical solutions that implement the finite element (FE) method have been widely used for the hydraulic analysis of these networks. Existing FE procedures allow for the inclusion of network components such as tees, bends, contractions, expansions, diffusers, and valves into the hydraulic analysis. There are instances, however, when the application of this technique can become problematic due to the prohibitive number of network components. Current FE approaches for incorporating network components into the hydraulic analysis treat system components as separate elements. The associated increase in the number of nodes in the network results in more unknowns and subsequently more equations to be solved simultaneously. The method proposed in this article for the hydraulic analysis of pipe networks handles components by adding their contribution to nodal equations rather than treating them as separate elements. This minimizes the total number of nodes in the network. The proposed method requires less computer time and memory requirements for analyzing a given network while preserving the accuracy of the analysis by incorporating the hydraulic effects of network components. Computer memory requirements for storing and analyzing hydraulic networks with components using the proposed method are comparable to existing FE procedures that ignore these components altogether.

Steady‐State Fluid Network Analysis

The node method for steady state hydraulic network analysis has been studied by several researchers with different ways of handling the non‐linearities that are present in the head‐loss equations but convergence problems were continuously observed. The hybrid element formulation presented in this paper is a definite way of overcoming this problem. It should be incorporated in the governing equations when an element with very low resistance is present on the network. This formulation assures that the nodal heads and the element flows are calculated to the desired degree of accuracy.

Modeling Expansion/Contraction, Valve and Booster Pump in Hydraulic Pipe Network Analysis: A Finite Element Approach

ABSTRACT Anew model and efficient formulation for the in-corporation of various essential network components such as contractions and expansions, diffusers, valves, and booster pumps into the analysis of irrigation and distribution pipe networks is presented. The solution technique is based on the linear theory method, nodal head equations and the application of the finite element method. The finite element model results were compared with the results of a linear theory model. The correlation in terms of values of junction pressures and element flow rates was high. The advantages of the technique include reduced computer space requirement, implementation through existing finite element codes, simplicity of application to large networks, the ability to model and incorporate all essential network components into the analysis, and ease of use with large capacity and small computers. The technique has potential applications to municipal water supplies, irrigation pipe networks, food and material handling and transportation, fuel distribution networks, and engine cooling systems.

Finite Element Formulation of Tee and Bend Components in Hydraulic Pipe Network Analysis

ABSTRACT Anew model and efficient formulation for the incorporation of bend and tee components into the analysis of irrigation and distribution pipe networks is presented. The solution technique is based on the linear theory method, nodal head equations and the application of the finite element method. The finite element model results were compared with the results of a linear theory model. The correlation in terms of values of junction pressures and link flow rates was high. The advantages of the technique include reduced computer space requirement, implementation through existing finite element codes, simiplicity of application to large networks, the potential of modeling and incorporating other essential network components such as expansions, contractions, diffusers, valves, and pumps, into the analysis, and ease of use with large capacity and small computers. The technique has potential applications to municipal water supplies, irrigation pipe networks, food and material handling and transportation, fuel distribution networks, and engine cooling systems.

A common network flow formulation for several civil engineering problems

Abstract This paper discusses a common network flow problem that arises in four areas of civil engineering. The problem is one of identifying arc flows that simultaneously satisfy the circuit and node law constraints for a given network. Applications and computational procedures in the areas of elastic structural analysis, hydraulic network analysis, traffic equilibrium and construction task scheduling are described. The interpretation of decision variables and mathematical functions will vary depending on the application, but the general priblem formulation and solution technique for each application remains essentially unchanged. Analogies between the different applications may enhance the conceptual understanding and intuition of engineers working in each area.

Optimal Selection of Pumps in an Hydraulic Network

The selection of pumps in an hydraulic network (such as those found in plant firewater systems or hydraulic control systems) is formulated as a mixed integer nonlinear program. The design objective is to minimize the total relative pump first cost. The piping network is assumed to exist and hence is not modified during the optimization process. A method is given for the transformation of the mixed integer nonlinear program into a mixed integer separable program. This formulation allows the use of efficient algorithms for the design of hydraulic networks. It also offers an alternative for the analysis of hydraulic networks. This technique may also be used for the analysis and design of general networks with nonlinear elements subject to convexity conditions. Two examples are given which consider an analysis problem and a design problem.

SOME PROBLEMS OF CIVIL ENGINEERING ANALYSIS AND THE THEORY OF (GENERALIZED) GEOMETRIC PROGRAMMING

Abstract We consider problems of analysis in three major areas of Civil Engineering, namely: i) Hydraulic Network analysis, specifically, the determination of flow rates and junction pressures in hydraulic networks, when inlet and outlet flow rates or inlet and outlet pressure heads are known. ii) Elastic analysis of pinpointed trusses, specifically, the determination of stresses and strains in the members of pinjointed trusses when deformations or external loads at the joints are known. iii) Traffic network analysis, specifically, the determination of equilibrium traffic flows and link travel costs in highway networks when the origin to destination input flows or origin to destination travel costs are fixed. In this paper we show that each of these problems may be viewed as a (generalized) geometric programming problem. This illustrates the common structure of these problems in a very simple and unified manner and it also provides a mechanism through which the modern theory of mathematical programming ca...