Laminar fluid flow in concentric annular ducts of non-conventional cross-section applying GBI method

Abstract

Fluid flow in concentric or eccentric annular ducts have been studied for decades due to large application in medical sciences and engineering areas. This paper aims to study fully developed fluid flow in straight ducts of concentric annular geometries (circular with circular core, elliptical with circular core, elliptical with elliptical core, and circular with elliptical core) using the Galerkin-based Integral method (GBI method). The choice of method was due to the fact that in the literature it is not applied in ducts of cross-sections of the annular shape with variations between circular and elliptical. Results of different hydrodynamics parameters such as velocity distribution, Hagenbach factor, Poiseuille number, and hydrodynamic entrance length, are presented and analyzed. In different cases, the predicted hydrodynamic parameters are compared with results reported in the literature and a good concordance was obtained.

Irregularly-bounded cross sections’ shape factors from high-order piecewise-polynomials

“…Detailed information on this procedure can be found in earlier papers by the authors [15,34,35,37] and in a broad literature timeframe [38][39][40][41]. This time, we put special emphasis on the construction of the basis functions Bi , which have a direct dependence on the local approximants.…”

“…The authors discussed the implications of incorrect aperture shape factors and the limited provision of models in the literature to compute them in a previous paper [15] with dense literature background under the perspective of KC models. Specifically, the inability to capture the correct dependence of permeability on porosity [16], limited comprehension of the linear and nonlinear effects [17], and insufficiency of geometrical parameters to [18,19] were a few hindrances pointed out.…”

“…This paper aims to present a model to compute shape factors for apertures with arbitrary boundaries, besides enabling hydrodynamic characterization and flow profiling for generic cross-sections. Our method is based on the GBI formulation proposed in [15,34,35], which relies on two underlying pillars: accurate shape reconstruction by high-order piecewise polynomials, and factor recovery by Poiseuille number. The GBI technique treats the fluid flow as fully developed under the laminar regime, thus allowing a reasonable comprehension of cross-sectional motion.…”

Heat Transfer and Fluid Flow in Concentric Annular Ducts Using the Galerkin-Based Integral Method: A Numerical Study

“…Solution approximation methods have been developed, over the years, to present information about parameters that characterize flow in ducts with arbitrary geometries and particular annular [9][10][11].…”

“…In the same study area, Lee and Lee [10] apply the same method used by Lee and Kuo [9] to obtain values for Nusselt number and friction factor in an elliptical duct with and without a circular core. Dos Santos Júnior et al [11] present a study for fluid flow (fully developed) in straight ducts with concentric annular geometries (circular with circular core, elliptical with elliptical core, elliptical with elliptical core and circular with elliptical core) using the Galerkin-based integral method (GBI method) Results of different hydrodynamic parameters, such as velocity distribution, Hagenbach factor, Poiseuille number and hydrodynamic input length, are presented and analyzed.…”