Can the Dean number Alone Characterize Flow Similarity in Differently Bent Tubes?

Abstract

Although flows of fluids in curved channels belong to a classical problem of fluid dynamics, most publications are restricted to investigations of flows in tube coils, or in single bends. This paper presents experimental and numerical (CFD) results concerning Newtonian flows in a set of multiple S-type bends of various orientations. Investigations were conducted for a wide range of Re values (0–3500) and for a significant curvature ratio lying between 0.05 and 0.29, which corresponds to De value falling within the range 0.02–1200. A coiled tube was also examined and treated as the reference geometry. It was shown, that despite a completely different velocity pattern, the nonlinear dependence of normalized flow resistance of wavy tubes and coiled tube of the same curvature ratio overlap within a significant range of De. A novel, close phenomenological formula to estimate the nonlinear flow resistance of tortuous tube in a wide range of De was proposed and compared with those in the literature. The conditions were also determined in which the De might be the only dimensionless group that characterizes such flows.