Supercritical Froude Number Flow through Ducts with Statistically Roughened Walls

Abstract

High-speed fluid flows over roughened surfaces occur in many engineering applications; one important application involves high velocity water flows in pipelines with roughened interior walls where the wall roughness affects head loss estimates necessary for engineering design purposes. The present analysis provides an analytical solution of the fluid physics underlying the induced static pressure profile resulting from high Froude number supercritical velocity through duct with random wall roughness. The analytic solution of the hyperbolic governing small perturbation velocity potential equation subject to high Froude number flows brings forward characteristic wave solutions that determine the static pressure profile in a duct with random height wall roughness. While current engineering practice utilizes semi-empirical engineering equations employing test data to determine the friction factor, velocity and static pressure profiles and head loss for different roughness types in different sized ducts as a function of Reynolds number (as summarized in a later section of the paper), the present analysis provides a new analytical method to determine the fluid physics involved in the static pressure change induced by wall random roughness in ducts subject to high Froude number supercritical flows.