Turbulent flow in square ducts after an expansion

Abstract

Turbulent flow in a square duct after the expansion was investigated in detail. It was seen that the developing behavior of this flow is very different from that of the flow in straight square ducts. Especially, the secondary flow in a square duct remains very weak and does not develop far downstream, at least through x/Dh = 40, unlike that in a straight square duct. This can be explained by the fact that many streamwise vortices, rather than a vortex pair in the corner region, develop from the distorted vortex loop caused by the free shear of the jet-like flow at the expansion. The results also indicate that the turbulent intensities u', v', and w' do not almost change from x/Dh = 20, at least to x/Dh = 40 (where Dh is the hydraulic diameter). HE flow in square ducts with an expansion, as in a diffuser, has been investigated in detail by fluid engineers such as by Miller.1 After an expansion, a flow separates, has large turbulent eddies, and is regulated through the mixing zone, at which point the flow has a flat and uniform velocity profile. But the studies thus far have concentrated on the flow at and just after the expansion, because the purpose was to develop a practical guide to the energy loss caused by the expansion. As a result, there have been few studies investigating such a flow far downstream. The preliminary experiments reported here investigated the flow in a square duct after expansion and showed that the flat velocity profile rapidly formed after expansion is retained far downstream. This suggests that this flow (including the formation of the secondary flow) has different developing features from those in straight square ducts. This is the motivation of the present study. It is considered that the flow in square ducts after the expansion is, at first, a bounded jet-like flow at the expansion and then becomes a three-dimensio nal duct flow. The bounded rectangular jet was investigated by Foss and Jones2 and Holdeman and Foss.3 They discussed the secondary flow observed in this flowfield and explained the mechanism whereby the secondary flow is produced in such a flowfield. That is to say, a closed vortex loop is formed from the jet free shear at the exit of the jet. This vortex loop (stretched by the velocity gradient in the boundary layer) develops to streamwise vortices and then decays into the free boundary far downstream. There are many studies about turbulent flow in square ducts, especially about the secondary flow generated there. The fully developed flow in square ducts was investigated in detail by Brundrett and Baines,4 Gessner and Jones,5 and others. Melling and Whitelaw,6 as well as Ahmed and Brundrett,7 investigated the developing turbulent flow in square ducts. The most complete description about the turbulent flow in square ducts was obtained in these studies. But, a clear explanation about the formation of the secondary flow has not yet been made, although there have been many studies discussing the mechanism of how the secondary flow is formed in ducts, i.e., by Perkins 8 and Gessner.9 One idea is that some instability is produced with the growth of the boundary layer and then develops streamwise vortices. The secondary flow produced by these streamwise vortices, the magnitude of which is only about 1% of the mean velocity even in fully developed flow, strongly influences both the