«Automation and Informatization of the fuel and energy complex»

On the convergence of the "estimated flow rate" method for hydraulic network flow rate distribution analysis

UDC: 519.61:621.644
DOI: 10.33285/2782-604X-2023-12(605)-44-52

Authors:

¹ Piping Systems Research & Engineering Co (NTP Truboprovod), Moscow, Russia

Keywords: hydraulic network, edge flow rates, node pressures, classical flow rate distribution task, "estimation flow rates" algorithm, optimization problem, uniform convergence, modified "estimation flow rates" algorithm

Annotation:

The article contains the mathematical prove of uniform convergence from any initial point of "estimation flow rates" algorithm (EFR) for classical flow rate distribution problem (CFRDP), for some class of networks with odd head loss vs flow rate edge functions. EFR algorithm (one of variants of "chord algorithms") was earlier described and successfully used during several decades. The result clarifies the nature of EFR stability. It is found out that for CFRDP in the form of optimization problem for node pressures, each step of EFR algorithm is continuous mapping which strictly decreases the value of minimized function for all points expect the only fixed point (which is CFRDP unique solution). In this way the uniform convergence of EFR follows from general topological theorem which is formulated and proved in the article. Also, a more universal modification of EFR (MERP) is proposed for more general class of network (without demand of odd edge head loss vs flow rate function), which keeps the same uniform convergence property for most hydraulic networks in engineering practice.

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