Effects of boundary roughness and inertia on the fluid flow through a corrugated pipe and the formula for the Darcy–Weisbach friction coefficient

• Published in: International journal of engineering science Vol. 152; p. 103293
• Main Authors: Marušić-Paloka, Eduard, Pažanin, Igor
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2020; Elsevier BV
• Subjects: Boundary conditions; Boundary layers; Boundary-layer correctors; Coefficient of friction; Computational fluid dynamics; Darcy–Weisbach law; Fluid dynamics; Fluid flow; Higher-order asymptotic approximation; Incompressible flow; Inertia; Inertia effects; Navier-Stokes equations; Periodic rugosities; Periodic variations; Pipe flow; Pipes; Pressure drop; Roughness; Viscous fluids; Boundary-layer correctors; Inertia effects; Pipe flow; Periodic rugosities; Darcy–Weisbach law; Higher-order asymptotic approximation
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2020.103293

We consider an incompressible viscous fluid flowing through a cylindrical pipe with rough wall. Motivated by the applications, we assume the periodicity of the roughness in the longitudinal direction and that the flow is governed by the prescribed pressure drop between pipe’s ends. The goal of the paper is to investigate the effects of the corrugated boundary on the fluid flow by taking into account the effects of inertia as well. Starting from the Navier–Stokes system and employing the average boundary roughness as the small parameter, we propose a higher-order correction of the standard Hagen–Poiseuille velocity via boundary layer analysis. Using the obtained result we propose the new formula for the Darcy–Weisbach friction coefficient.