An Efficient Iterative Method for Looped Pipe Network Hydraulics

Abstract

Original and improved version of the Hardy Cross iterative method with related modifications are today widely used for calculation of fluid flow through conduits in loops-like distribution networks of pipes with known node fluid consumptions. Fluid in these networks is usually natural gas for distribution in the municipalities, water in waterworks or hot water in district heating system, air in the case of ventilation systems in buildings or mines, etc. Since, the resistances in these networks depend of flow, problem is not linear like in electrical circuits, and iterative procedure must be used. In both version of the Hardy Cross method, in original and in the improved one, initial results of calculation in iteration procedure is not flow, but rather the correction of flow. Unfortunately, these corrections should be added to or subtracted from a flow calculated in previous iteration according to complicate algebraic rules. After the here presented node-loop method, final results in each of the iterations is flow directly rather than flow correction. In that way complex algebraic scheme for sign of flow correction is avoided, while the final results still remain unchanged. Numbers of required iterations for the same results are comparable with the improved Hardy Cross method.All methods from this paper assume equilibrium between pressure and friction forces in steady and incompressible flow. As a result, they cannot be successfully used in unsteady and compressible flow calculations with large pressure drop where inertia force is important. Gas flow in a municipal distribution network [5], air flow in a ventilation system in buildings and mines [6], and of course water flow in waterworks [7] or district heating systems [8] and cooling systems [8] can be treated as incompressible flow since the pressure drop in these kinds of networks are minor even to compress significantly natural gas or air. The same applies to pipelines for distribution of mixed natural gas and hydrogen [9]. Overview of existing methods for calculation of flow distribution in a looped network of pipes Loop-oriented methods; Original and improved Hardy Cross methodThe Hardy Cross method [1] introduced in 1936 is the first useful procedure for the calculation of flow distribution in looped networks of pipes. Further step was made by introduction of the modification in the original Hardy Cross method in 1970 by Epp and Fowler [2]. The original Hardy Cross method [1] as a sort of single adjustment method, first of all, as an intermediate step in calculation, determines correction of flow for each loop independently and then applies this corrections to compute new flow in each conduit. It is not efficient as the improved Hardy Cross method [2,3] that considers entire system simultaneously. The improved Hardy Cross method [2], still firstly as an intermediate step, determines corrections for each loop but treated all network system simultaneously, and then applies this correction to compute new flow in each conduit such as in the original version [1...

Multi Energy System With an Associated Energy Hub: A Review

“…This paper considered the pressure drop in the gas system just as the voltage drop in the power system. In [60] the gas flow was calculated and analyzed using node and loop equations, with the analysis based on the method used in the power system analysis. This method considers the diameter and length of the pipeline, the absolute roughness, gas velocity, dynamic water viscosity, friction factor, and pressure drop.…”