Holistic Unsteady-Friction Model for Laminar Transient Flow in Pipeline Systems

Abstract

This paper proposes a holistic unsteady-friction model for the transient simulation of the condition of laminar initial flow. The effect of wall shear stress is considered through the introduction of radial-velocity distribution with kinematic viscosity from a simplified two-dimensional Navier-Stokes equation. The model simultaneously addressed the frequency-dependent friction and the unsteady friction associated with local and convective acceleration on the platform of the impulse-response method. A widely used hypothetical example demonstrated that the proposed model appropriately and simultaneously expressed the effect of pressure damping from both the radial-velocity variation with viscosity and acceleration terms. The nonlinear mutual effects were examined between two distinct energy-dissipation mechanisms by comparing the behavior of the pressure head between the proposed and existing models. Comparisons of the experimental results illustrated that the combined model exhibited predictive and fitting capabilities for the pressure-head oscillation and shape for both the end and middle positions of a reservoir-pipeline-valve system. The proposed model showed significantly improved predictability over the frequency-dependent friction model for the early pressure associated with a water hammer. The comparison of the performance between the developed model and the traditional method of characteristics approach demonstrated the robustness of the proposed method in both its computational efficiency and its representation of a real-life system.