Efficient Code for Steady-State Flows in Networks

Epp, Robert; Fowler, Ann

doi:10.1061/jyceaj.0002316

Cited by 125 publications

(45 citation statements)

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“…• Loop or simultaneous path methods, which are based on loop energy balances and describe the system state with loop flow rate variables, e.g. (Carpentier et al, 1985;Epp and Fowler 1970).…”

Section: Code De Champ Modifiémentioning

confidence: 99%

Modeling Control Valves in Water Distribution Systems Using a Continuous State Formulation

Piller

Zyl

2014

J. Hydraul. Eng.

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Control valves are commonly used for the operation of water distribution systems. Modeling these devices typically requires that their operating states are known, or that a computationally expensive search is undertaken over all possible operating states. This paper presents a novel method of modeling control valves (including flow control, pressure sustaining, pressure reducing and check valves) in extended-period simulations of water distribution systems. Instead of the normal discrete control problem formulation, it is approached with the Karush-Kuhn-Tucker equations for an optimization problem with constraints.The proposed method does not pre-require the operating state (open, closed, active) of each valve to be determined, as this is done implicitly. Pipe and valve flow rates and nodal heads are determined by (1) minimizing deviations from targets at control valves and (2) satisfy the state equations (conservation of mass and energy) by solving a constrained least-square problem.

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Section: Code De Champ Modifiémentioning

confidence: 99%

Modeling Control Valves in Water Distribution Systems Using a Continuous State Formulation

Piller

Zyl

2014

J. Hydraul. Eng.

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“…First of all, as an intermediate step in calculations, it determines a correction of flow for each loop independently and then applies these corrections to compute the new flow in each conduit. It is not as efficient as the improved Hardy Cross method [2,3] that considers the entire system simultaneously. The improved Hardy Cross method [2], as an intermediate step determines corrections for each loop but treats the whole network system simultaneously, and then applies this correction to compute the new flow in each conduit, as in the original version [1].…”

Section: Introductionmentioning

confidence: 99%

“…It is not as efficient as the improved Hardy Cross method [2,3] that considers the entire system simultaneously. The improved Hardy Cross method [2], as an intermediate step determines corrections for each loop but treats the whole network system simultaneously, and then applies this correction to compute the new flow in each conduit, as in the original version [1]. It is more efficient, but the intermediate step in calculations is not eliminated.…”

Section: Introductionmentioning

confidence: 99%

“…The Hardy Cross method [1], introduced in 1936, is the first useful procedure for the calculation of flow distribution in looped networks of pipes. A further step was made with the introduction of the modification to the original Hardy Cross method in 1970 by Epp and Fowler [2]. The original Hardy Cross method [1] is a single adjustment method.…”

Section: Introductionmentioning

confidence: 99%

“…It is more efficient, but the intermediate step in calculations is not eliminated. While using the matrix form in the original Hardy Cross method is not mandatory [1], for the improved version it is [2]. In the original paper of Hardy Cross from 1936 [1], the problem is not solved using any kind of matrix calculations.…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Iterative Method for Looped Pipe Network Hydraulics Free of Flow-Corrections

Brkić¹,

Praks

2019

Fluids

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The original and improved versions of the Hardy Cross iterative method with related modifications are today widely used for the calculation of fluid flow through conduits in loop-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in municipalities, water in waterworks or hot water in district heating systems, air in ventilation systems in buildings and mines, etc. Since the resistances in these networks depend on flow, the problem is not linear like in electrical circuits, and an iterative procedure must be used. In both versions of the Hardy Cross method, in the original and in the improved one, the initial result of calculations in the iteration procedure is not flow, but rather a correction of flow. Unfortunately, these corrections should be added to or subtracted from flow calculated in the previous iteration according to complicated algebraic rules. Unlike the Hardy Cross method, which requires complicated formulas for flow corrections, the new Node-loop method does not need these corrections, as flow is computed directly. This is the main advantage of the new Node-loop method, as the number of iterations is the same as in the modified Hardy Cross method. Consequently, a complex algebraic scheme for the sign of the flow correction is avoided, while the final results remain accurate.

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2024

Hydraulics and Pneumatics in Environmental Engineering

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Efficient Code for Steady-State Flows in Networks

Cited by 125 publications

References 0 publications

Modeling Control Valves in Water Distribution Systems Using a Continuous State Formulation

Modeling Control Valves in Water Distribution Systems Using a Continuous State Formulation

An Efficient Iterative Method for Looped Pipe Network Hydraulics Free of Flow-Corrections

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