Abstract
The draining operation involves the presence of entrapped air pockets, which are expanded during the phenomenon occurrence generating drops of sub-atmospheric pressure pulses. Vacuum air valves should inject enough air to prevent sub-atmospheric pressure conditions. Recently, this phenomenon has been studied by the authors with an inertial model, obtaining a complex formulation based on a system composed by algebraic-differential equations. This research simplifies this complex formulation by neglecting the inertial term, thus the Bernoulli’s equation can be used. Results show how the inertial model and the simplified mathematical model provide similar results of the evolution of main hydraulic and thermodynamic variables. The simplified mathematical model is also verified using experimental tests of air pocket pressure, water velocity, and position of the water column.
Highlights
Draining processes are periodically repeated for cleaning and maintenance purposes in hydraulic installations [1,2]
A semi-empirical flow model was proposed for studying this operation in a long-scale pipeline without air valves, which is a type of rigid column flow model (RCFM) [13]
Despite the RCFM predicting accurately the main hydraulic and thermodynamic draining maneuvers in water pipelines [16], the numerical resolution is still complex since the utilizing of specialized math software suitable for solving a complex system composed of algebraic-differential equations [2,13,17,18,19,20] is necessary
Summary
Draining processes are periodically repeated for cleaning and maintenance purposes in hydraulic installations [1,2]. Despite the RCFM predicting accurately the main hydraulic and thermodynamic draining maneuvers in water pipelines [16], the numerical resolution is still complex since the utilizing of specialized math software suitable for solving a complex system composed of algebraic-differential equations [2,13,17,18,19,20] is necessary In this sense, when the inertial term of the water movement equation is neglected, the resolution of the system is easier compared to the RCFM since water columns can be modeled using algebraic equations (Bernoulli’s equation) [21,22,23]. The comparison between computed and measured main hydraulic and thermodynamic variables and the analysis of results between the simplified mathematical model and the RCFM indicate the adequacy of the proposed model
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