Relevance of Unsteady Friction to Pipe Size and Length in Pipe Fluid Transients

This paper investigates the importance of pipe system scale-specifically pipe length and diameter-on unsteady friction in pipe transients. A dimensionless analysis is conducted for the one-dimensional (1D) water-hammer model in this study and the analytical expression for the relative importance of unsteady friction damping to the total friction damping is obtained in the frequency domain. In addition, a two-dimensional (2D) waterhammer model coupled with a 2D turbulence model is applied to a reservoir-pipe-valve system. A parametric study covering a number of pipe diameters, pipe lengths, and initial Reynolds numbers is conducted. The investigation spans a range of water-hammer travel time and turbulent radial diffusion timescales. In each case, the transient is generated by a sudden and complete valve closure. The analytical solution for the importance of unsteady friction is verified by the numerical simulations and the results show that unsteady friction damping has less effect on the damping rate of the transient envelope as (1) the ratio of the wave travel timescale to the radial diffusion timescale increases and (2) the product of the initial friction factor and Reynolds number increases. Furthermore, the findings of this study are validated by both laboratory and field experiments from literature. The implication of the findings is that the role of unsteady friction on the damping rate of the transient envelope diminishes with the scale ratio of pipe length and pipe diameter and that laboratory experiments, which are usually limited to relatively small scale ratios of pipe lengths and diameters, have lead researchers to overestimate the importance of unsteady friction on the damping of the transient envelope in real large pipe-scale systems.