Abstract
Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of the basic equations describing the transient pipe flow. In this paper, the RS is calculated with the use of convolution integral of the local derivative of pressure and creep function that describes the viscoelastic behavior of the pipe-wall material. The main equations of a discrete bubble cavity model (DBCM) are based on a momentum equation of two-phase vaporous cavitating flow and continuity equations written initially separately for the gas and liquid phase. In transient flows, another important source of pressure damping is skin friction. Accordingly, the wall shear stress model also required necessary modifications. The final partial derivative set of equations was solved with the use of the method of characteristics (MOC), which transforms the original set of partial differential equations (PDE) into a set of ordinary differential equations (ODE). The developed numerical solutions along with the appropriate boundary conditions formed a basis to write a computer program that was used in comparison analysis. The comparisons between computed and measured results showed that the novel modified DBCM predicts pressure and velocity waveforms including cavitation and retarded strain effects with an acceptable accuracy. It was noticed that the influence of unsteady friction on damping of pressure waves was much smaller than the influence of retarded strain.
Highlights
If we look at plastic pipes, which are starting to displace metal pipes, the researchers have mostly used the two basic cavitation models, i.e., the discrete vapor cavity models (DVCM) and the discrete gas cavity models (DGCM). Apart from these two models, alternative models have been developed, including a revised version of the DVCM model proposed by Adamkowski [6,7] as well as a model based on two-phase flow equations that can be called a discrete bubble cavity model (DBCM), which was developed by Shu [8]
The new model takes into account three very important phenomena: unsteady wall shear stress, vaporous cavitation, and pipe-wall retarded strain
The conducted comparative studies have shown that with the help of the presented model, it is possible to simulate pressure and velocity waveforms in which vapor areas appear as a result of the cavitation phenomenon in plastic pipes
Summary
Cavitation is one of the natural phenomena whose thorough understanding should be a scientific priority. During water hammer, such cavitation areas, due to the large time necessary for desorption and absorption, are beneficial Their presence causes a faster damping of dynamic waveforms, as the “air bags” emitted by their action resemble local air–liquid shock absorbers. If we look at plastic pipes, which are starting to displace metal pipes (especially in water supply systems), the researchers have mostly used the two basic cavitation models, i.e., the DVCM and the DGCM Apart from these two models, alternative models have been developed, including a revised version of the DVCM model proposed by Adamkowski [6,7] as well as a model based on two-phase flow equations that can be called a discrete bubble cavity model (DBCM), which was developed by Shu [8]. The main objective of this paper is to present a novel DBCM that will enable the simulation of transient cavitating flows in plastic pipes
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