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.
Highlights
Where k f is the Brunone coefficient, D is the pipe diameter, V is the water velocity, a is the pressure wave celerity, t is the time and x is the abscissa
This paper focuses on the resolution of unsteady friction using the Godunov approach in a finite volume method with single-equivalent two-phase flow equations
The differences between simulated results with a dynamic friction component and those with a static friction component are more important in the case of a closed upstream valve than a closed downstream valve
Summary
Where k f is the Brunone coefficient, D is the pipe diameter, V is the water velocity, a is the pressure wave celerity, t is the time and x is the abscissa. The first approach involves calculating the local and convective acceleration in the source term S (see Equation (4)) as treated by Bergant et al [10], Brunone et al [14] and Bughazem and Anderson [15]. The first approach uses finite differences, while the second employs the method of characteristics that is a graphical procedure for the integration of partial differential equations (PDEs) [18]. [6] used the second type of resolution with the characteristic equations developed by Vitkovsky et al [11] to calculate the dynamic friction component. The formulation of the dynamic friction component in the instantaneous accelerations-based model has been tested with finite difference techniques and the method of characteristics. There is a lack of literature on the use of the finite volume technique in instantaneous accelerationsbased models
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