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- Mathematical modeling of pressurized system behaviour with entrapped airPublication . Martins, Sandra Carvalho; de Sousa Ramos, Helena Maria; Almeida, António B.The presence of entrapped air in pressurized hydraulic systems is considered a critical condition for the infrastructure security, due to the transient pressure enhancement related with its dynamic behaviour, similar to non-linear spring action. A mathematical model for the assessment of hydraulic transients resulting from rapid pressurizations, under referred condition is presented. Water movement was modeled through the elastic column theory considering a moving liquid boundary and the entrapped air pocket as lumped gas mass, where the acoustic effects are negligible. The method of characteristics was used to obtain the numerical solution of the liquid flow. The resulting model is applied to an experimental set-up having entrapped air in the top of a vertical pipe section and the numerical results are analyzed.
- Conceptual analogy for modelling entrapped air action in hydraulic systemsPublication . Martins, Sandra Carvalho; de Sousa Ramos, Helena Maria; Almeida, António B.Hydraulic systems are dynamically susceptible in the presence of entrapped air pockets, leading to amplified transient reactions. In order to model the dynamic action of an entrapped air pocket in a confined system, a heuristic mathematical formulation based on a conceptual analogy to a mechanical spring-damper system is proposed. The formulation is based on the polytropic relationship of an ideal gas and includes an additional term, which encompasses the combined damping effects associated with the thermodynamic deviations from the theoretical transformation, as well as those arising from the transient vorticity developed in both fluid domains (air and water). These effects represent the key factors that account for flow energy dissipation and pressure damping. Model validation was completed via numerical simulation of experimental measurements.