A Study of the Flow in an S-shaped Duct

Abstract

Flows in S-shaped ducts find applications in aircraft air intakes. The flow in four square cross-sectioned, S-shaped ducts of different curvatures is investigated at moderate Reynolds numbers. A non-dimensional parameter, defined as the ratio of radial pressure gradient to centrifugal force, is proposed and its relation to other well-known non-dimensional numbers (e.g. Pressure coefficient, Reynolds number and Dean number) is stated. The variation of the said parameter with the normalized curved duct?s axial distance is shown to collapse onto a single curve for circular and square cross sectioned, 90 deg curved ducts and S-shaped ducts. Data scatter in the parameter's variation is noted and subsequent detailed measurements in S-shaped ducts show that it is due to firstly, flow separation at the inner wall of the first bend and secondly, the formation of stream-wise vortices on the outer-wall of the second bend. These stream-wise vortices can either be, depending on duct curvature, a pair of counter-rotating vortex or a single vortex. The formation mechanism of these stream-wise vortices is explained qualitatively with the well-known Squire and Winter formula and this formula is used to predict the vortex configuration based upon sign changes in vertical velocity gradients along the outer-wall of the second bend. Quantitatively, the different vortex configuration of these stream-wise vortices was shown to depend strongly on the inlet boundary layer thickness. When boundary layer thickness increases, a corresponding increase in bulk swirl magnitude is noted in the first bend of the S-shaped duct. The increase in bulk swirl altered the vertical velocity gradients along the wall of the S-duct which led to the growth of the said stream-wise vortices in the second bend of the S-duct. The vorticity growth rate of these stream-wise vortices is larger for a thick inlet boundary layer. Lastly, to improve the flow in S-ducts, vortex generators, tangential blowing and vortex generator jets as flow control methods are implemented. The three methods suppress flow separation and reduce total pressure loss. However, they increase the swirl (or cross flow) magnitude and the flow is non-uniform (or skewed) at the S-duct exit.