Great Mysteries of Engineering Fluid Dynamics
The Corner Attraction
by G.D. Stubley
Synopsis
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Figure 3.1: Wireframe model of a square duct illustrating the development of the velocity profile on the y = 0 centre-plane. |
The above figure, Figure 3.1, shows a wireframe model of a long square duct. The x axis, aligned with the duct centre-line, is in the axial direction. If fluid enters the duct with a uniform axial velocity, u , there will be a region of developing flow in which the shape of the axial velocity profile over the duct cross-sectional area changes with axial distance. Sufficiently far downstream, the flow becomes fully developed. The axial velocity profile no longer varies with axial distance once the flow is fully developed. The fully developed axial velocity profile, u(y, z), varies, over the duct cross-section, from zero at the walls to a maximum at the duct centreline, (y = 0, z = 0).
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Figure 3.2: Fringe plot of the fully-developed velocity profile of laminar flow through a square duct. The flow direction is out of the page. |
Figure 3.2 shows the fully-developed velocity profile for incompressible laminar flow through the square duct. Notice how the isovel contours quickly become rounded in the corners. In the vicinity of the upper right corner, the wall shear stresses on the right and top walls act to create a region of relatively slow moving fluid in the corner. For a given distance off the right wall, the axial speed is greater near the y = 0 centre-plane than near the corner.
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Figure 3.3: Fringe plot of the fully developed velocity profile of turbulent flow through a square duct. |
Figure 3.3 shows the fully-developed velocity profile for turbulent flow in the square duct. A difference between the laminar and turbulent profiles is that the rounding of the iso-vel contours in the corners is considerably reduced. Indeed, for a given distance off the right wall, the axial speed increases slightly as the corner is approached from the y = 0 centre-plane.
It appears that high speed fluid in the core of the duct is being pushed into the corners. Why?
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