Analytical solution to the viscous flows in curved duct with inlet swirl

This paper describes the approximate viscous solution to the analytical approach, based on the conservation of angular momentum flux, formulated previously by Kitoh (J. Fluid Mech, Vol. 175 p. 429, (1987)) to predict the decay of the swirling motion along a curved duct. Only the inviscid approximate solution was presented by Kitoh (1987). The present approximate solution takes into account the frictional forces on the pipe wall and, includes an additional factor to compensate for the absence of the radial velocity components in the original formulation, when the inlet streamwise swirl intensity is low. As a consequence of the frictional effects, different decay patterns for the swirl intensities along a curved duct are observed. Measurements in 180-degree bends with different levels of inlet swirl intensities by Hawthorne (Proc. R. Soc. Lond. A, Vol. 206, p. 374, (1951)) Shimizu & Sugino (Bulletin JSME, Vol. 23, p. 1443, (1980)) were used to compare with the present approximate solution. Good agreement can be obtained in both cases.