Numerical solutions of hyperbolic systems of conservation laws combining unsteady friction and viscoelastic pipes

Abstract

The main contribution of the paper is to incorporate pipe-wall viscoelastic and unsteady friction in the derivation of the water-hammer solutions of non-conservative hyperbolic systems with conserved quantities as variables. The system is solved using the Godunov finite volume scheme to obtain numerical solutions. This results in the appearance of a new term in the mass conservation equation of the classical governing system. This new numerical algorithm implements the Godunov approach to one-dimensional hyperbolic systems of conservation laws on a finite volume stencil. The viscoelastic pipe-wall response in the mass conservation part of the source term has been modeled using generalized Kelvin–Voigt theory. For the momentum part of the source term a fast, robust and accurate numerical scheme linked to the Lambert W-function for calculating the friction factor has been used. A case study has been used to illustrate the influence of the various formulations; a comparison between the classical solution, the numerical solution including quasi-steady friction, the numerical solution incorporating the viscoelastic effects, and measurements are presented. The inclusion of viscoelastic effects results in better agreement between the measured and solved values.

Fluid transients in viscoelastic pipes via an internal variable constitutive theory

“…Such a result contributes to one of the main challenges of the field, as Covas et al [49] stated: "The major challenge of the current and the future work is the distinction between frictional and mechanical dampening." In Covas et al [49] and other subsequent works, as in Duan et al [12] and Seck [59] , the strategy to observe the impact of the fluid transient friction and viscoelastic in the fluid transient is based on computing the model's responses by taking into account only one of these two effects and observe a local pressure response close to the valve. Even though the effect of the viscoelasticity seems to be more significant as it achieved close results to experimental data, in both cases, the pressure signals are attenuated and dispersed similarly.…”

Numerical Analysis of Transient Pressure Damping in Viscoelastic Pipes at Different Water Temperatures

“…The numerical results showed that a higher scale ratio between the pipe length and pipe diameter resulted in an increase in the role of unsteady friction on the peak pressure damping of transient flows in elastic pipes. Based on the experimental data reported by Covas et al [ 14 ], Seck et al [ 20 ] modified the unsteady friction correlation coefficient to improve the accuracy of the unsteady friction model. The results showed that the inclusion of viscoelasticity and unsteady friction generated dramatic peak pressure damping.…”