Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
Theoretical analysis of free-surface flows in rectangular annular cross-section
Submission Author:
L. Enrique Ortiz-Vidal , SP
Co-Authors:
L. Enrique Ortiz-Vidal, Guilherme Henrique Fiorot
Presenter: L. Enrique Ortiz-Vidal
doi://10.26678/ABCM.ENCIT2022.CIT22-0625
Abstract
One of the main properties of free-surface flows, as for most industrial flows, is the mean flow velocity. Its estimation can be used to design machines, predict head loss in hydraulic installation, and detect equipment failures in many industrial processes. More specifically, for open-channel flows with rectangular cross-sections, this estimation is straightforward. If one establishes the geometry, the fluid thermophysical properties, and the flow rate, the flow depth and the mean flow velocity can be obtained through analytical and semi-empirical formulae from Fluids Mechanics principles. However, any study reporting the same procedure has been not reported for free-surface flows within channels with annular cross-sections, according to the authors' knowledge. In the present paper, we explore the conservation equations solution for a free-surface flow of a Newtonian fluid in a closed channel with a rectangular-annular cross-section, in steady-state and uniform regimes. The Darcy-Weisbach friction factor in combination with the Churchill equation, and hydraulic-diameter approach are used. Expressions for the flow cross-section area and the wetted perimeter of the partially full annular channel flow, both terms of hydraulic-diameter definition, are derived from trigonometric rules as a function of the flow depth. The effect of the inner-duct eccentricity on the geometrical expressions is also considered. The MATLAB(R) software is used for calculation. We found that multiple mathematical solutions for flow depth can be found for a fixed set of entry parameters. The influence of inclination angle, flow rate, fluid viscosity, inner and outer diameters of the annular-channel, and eccentricity is discussed. The values for those parameters range according to published studies; for example, flow rates between 5 and 350 liters per minute, and inclination angles until 30 degrees. As the ultimate result, the variation on the flow velocity estimation is presented. The subject brought in the present work poses a problem for engineers and should be taken into account when estimating flow parameters in this scenario
Keywords
Free-surface flow, annular-channel flow, Friction Factor, hydraulic diameter
