Computational Fluid Dynamics to Study the Origin of Secondary Flows in Square Ducts With Straightened Elbow Concept Governed by Artificial Body Force

The 90° pipe bend is perhaps the most frequently used fitting in piping systems. The secondary flow and associated losses occurring in such bends are therefore of considerable engineering importance. However, although many investigators have studied the problem, it is still unclear how secondary flows develop, and get triggered. The curvature of the 90-degree elbow induces centrifugal force, causing the development of such secondary flow. The intensity of the secondary flow is dependent on the radius of the bend curvature (R) and Reynolds number (Re). The objective of this study is to gain an understanding of how of the triggering mechanism and development of this flow which should depend on R and Re. A commercial tool, COMSOL Multiphysics, is used to model the flow in a fully straight duct under the action of a “centrifugal” body force was studied. The domain of study was divided in three duct sections, the inlet duct, the “elbow” duct (where the “centrifugal” body force was applied), and the outlet duct. Special attention was paid to the secondary flows in the “elbow” duct near the elbow inlet. The study is conducted for different laminar Reynolds numbers (Re = 10 and 100), and different radius of curvatures (R/D = 2 and 5). It was found both the pressure gradient in the flow transversal direction and the flow “radial” advection appear to be responsible for the initiation of secondary flow phenomena and its propagation. When using slip wall conditions, the secondary flow gets weaker, or even its swirling motion disappears. It also appears to be that the full formation of the secondary flow of the vortex type occurs at the same “arc length” distance, regardless of the representative “radius of curvature.”