Modelling water hammer in viscoelastic pipelines: short brief

Analytical expressions for effective weighting functions used during simulations of water hammer

“…Proper modelling of flows of liquids under pressure in such systems remains a significant challenge. Among the key issues widely discussed in new publications on the subject, special emphasis is placed on the correct modelling: of the time-varying hydraulic resistance (Vardy and Brown, 2003;Zarzycki et al, 2011;Reddy et al, 2012), cavitation (Zarzycki and Urbanowicz, 2006;Lewandowski, 2009, 2012;Bergant et al, 2006;Karadžić et al, 2014;Soares et al, 2015), the interaction between the liquid and walls of the conduit Henclik, 2015;Zanganeh et al, 2015), the viscoelastic phenomenon that occurs during the flow in a piping made of engineering polymers (Weinerowska-Bords, 2015; Soares et al, 2012; Keramat et al, 2013;Pezzinga et al, 2014;Urbanowicz et al, 2016). Taking into account all of the above phenomena while simulating unsteady flows has seemed impossible until recently.…”

Transient Liquid Flow in Plastic Pipes

“…Among the different numerical methods enabling resolving the system of above equations, particular attention should be paid to the MOC scheme, which perfectly interprets the essence of physical phenomena of transient flow, and at the same time is characterized by fast convergence, ease of incorporating various boundary conditions, together with the high accuracy of calculation results. The detailed numerical solution may be found in recent papers [30], [32] and [33].…”

“…These two factors described by convolutional integrals require effective solutions to accelerate the calculation process. The integral describing unsteady friction was effectively solved by Urbanowicz [28], using the suggestions of Vardy and Brown [29]; in contrast, the integral for the viscoelastic nature of retarded strain has been previously solved in a complicated manner [14] and [30]. In this study, it will be solved in a much simpler way, using Schohl's effective solution [31], to further improve its effectiveness.…”

Parameters affecting water hammer in metal pipelines

“…exceeds at least three times the increase that would occur in an analogue plastic conduit. In addition, the deformation of the pipe walls is elastic, and not as in the case of plastic pipes, viscoelastic [1], the maximum possible pressures may even double the value calculated from formula (1). Such an increase may be the result of the superposition of pressure waves (primary and secondary) during the flows in which liquid column separation occur commonly known as cavitation [2,3].…”