Conceptual analogy for modelling entrapped air action in hydraulic systems

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.