Modeling slack flow in hydraulic pipelines by means of a consistent thermodynamic theory

This work presents a consistent thermodynamic model to describe cavitating flows in hydraulic pipelines. Although the model is capable to describe the vaporous cavitation phenomenon in unsteady as well as steady regimes, the application presented herein is restricted to slack flow condition, which takes place under steady state. The flow is assumed to be homogeneous and isothermal and the fluid is regarded as a pseudo-mixture, comprising the liquid, its vapor and an inert gas. The constituents are assumed to be compressible and to coexist at every material point and time instant. The balance equations of mass for each constituent are considered in the model, along with one balance equation of momentum for the mixture as a whole, all of them within the one-dimensional context. The existence of a small amount of inert gas along with the vapor ensures the necessary thermodynamic condition to describe the opening and closing of the cavity. It also allows the description of the vaporous cavitation phenomenon in any region of the fluid flow domain by means of a same set of equations. The phase change transformation is properly accounted for as an irreversible process. The obtained results by means of simple numerical simulations in steady state show that model is capable to coherently describe the continuous opening and closure of the cavities as long as the flow does not become sonic.