New 1D Unsteady Friction Model for Turbulent Rough Pipe Flows Undergoing Slow to Intermediate Acceleration–Deceleration: Closely Packed Uniform Hemispheres

A new unsteady friction model suitable for one-dimensional (1D) pipe network modeling of turbulent rough pipe flows is proposed. The new model has been developed based on an original set of water flow experiments in a reservoir-pipe-reservoir setup with uniform hemispherical roughness. Whereas previous studies have focused on rapidly accelerated–decelerated flows, this study investigates mildly accelerated–decelerated flows that are common in practice. In terms of flow physics, our experiments revealed the following: (1) the effect of roughness is implicit in the initial wall shear stress such that the wall-generated turbulence diffuse out quicker than a smooth pipe flow counterpart, (2) all established flow transition regimes for smooth pipe flows are also valid in rough pipe flows, and (3) mild transitions are characterized by frozen turbulence behavior at the beginning and pseudosteady behavior toward the end of the transient event. Based on these observations and on a recent model valid for rapid transitions, we have developed a new model for the total wall shear stress that is valid for slow to rapid transitions and for rough pipes. Comparison with experimental data show good agreement.