Hydraulic networks with pressure-dependent closure relations, under restrictions on the value of nodal pressures. Maxwell matrix properties and monotonicity of flow distribution problem solution

Abstract

In the article, which continues the research of article [1], the results of previous article are generalized to “abstract” hydraulic networks. Additional existence theorems are proved for classical flow distribution problem (CFDP) for hydraulic networks with pressure-dependent closure relations, under restriction on nodal pressures. Hydraulic network Maxwell matrix properties are establish, related to monotonicity of CFDP solution.

On the Convergence of “Estimated Flow Rate” Method for Hydraulic Network Flow Rate Distribution Analysis

“…Note also that on each iteration original network is replaced by linear one with similar edge properties -passive edges remain passive, and active edges have the same head at zero flow rate -so for solutions on each iteration the same theorems (proven in [25]) for network solutions in restricted node pressure space is applied, as for original network problem, and already after the first iteration node pressure values are usually close enough to the solution, and this minimizes risk of occasional «blowout» of node pressures during iterations into zone where the model is not adequate (fluid is boiling or condensing, or choked flow occurs). This is one of the reasons of EFR is so stable to initial point selection.…”