Numerical Simulation of Unsteady Friction in Transient Two-Phase Flow with Godunov Method

Abstract

Most numerical transient flow models that consider dynamic friction employ a finite differences approach or the method of characteristics. These models assume a single fluid (water only) with constant density and pressure wave velocity. But when transient flow modeling attempts to integrate the presence of air, which produces a variable density and pressure-wave velocity, the resolution scheme becomes increasingly complex. Techniques such as finite volumes are often used to improve the quality of results because of their conservative form. This paper focuses on a resolution technique for unsteady friction using the Godunov approach in a finite volume method employing single-equivalent twophase flow equations. The unsteady friction component is determined by taking into account local and convective instantaneous accelerations and the sign of both convective acceleration and velocity values. The approach is used to reproduce a set of transient flow experiments reported in the literature, and good agreement between simulated and experimental results is found.

Additional Friction Factor Optimized for Modeling Transient Flows Following Air-Pocket Entrapment in Stormwater Systems

“…However, Bousso and Fuamba did not study the air-pocket entrapment problem, but they integrated the presence of a low volume of air distributed in the water. In addition, the variable friction factor of Bousso and Fuamba (2013) is more difficult to calculate than the one presented in the present study, which has a similar form to the Darcy-Weisbach friction factor.…”

“…In addition to the steadystate friction factor, the supplementary friction function improves the approximation of the pressure attenuation of the water hammer wave. Bousso and Fuamba (2013), using the Godunov finitevolume method, numerically simulated transient flows caused by valve closing. They applied an unsteady friction factor, which was decomposed into static friction and unsteady friction components.…”