Figure 223a provides a sketch of the approximate flow behavior as the syrup

Figure 223a provides a sketch of the approximate flow

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refrigerator only moments before the start of our experiment. Figure 2.23(a) provides a sketch of the approximate flow behavior as the syrup oozes along the top of the step and then encounters the corner. As the flow reaches the corner its momentum is very low due to its low speed, and it dividing streamline reattachment point (a) typical fluid parcel trajectory separated region (b) primary recirculation secondary recirculation Figure 2.23: (a) unseparated flow, (b) separated flow. exhibits no tendency to “overshoot” the corner; thus, it oozes around the corner, flows down the vertical face of the step and continues on its way. Fluid initially in the vicinity of the solid surface remains close to it, even when making a 90 degree turn— i.e. , the flow remains “attached” to the surface. Now consider the same experiment but with a less viscous fluid and/or a higher-speed flow. Figure 2.23(b) presents this case. Now the flow momentum is high, and it is difficult for the fluid to turn the sharp corner without part of it overshooting. This high-speed fluid then shears the fluid immediately beneath it at the same time the lower portions of this region begin to move toward the step to fill the void caused, in the first place, by the overshooting fluid coming off the step. The immediate consequence of this combination of physical events is the primary recirculation region indicated in Fig. 2.23(b). (This is just alternative terminology for the vortex shown previously in
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2.5. FLOW VISUALIZATION 41 Fig. 2.16.) Such vortices, or recirculation zones, are common features of essentially all separated flows. We have also indicated several other features found in separated flows. The dividing streamline is shown in red. This is a flow path such that the flow on one side does not mix with flow on the other side (except in turbulent flows). In some flow situations, such as the present one, the flow is quite different in nature, qualitatively, on opposite sides of the dividing streamline, but in other situations we will encounter later, the flow behavior is identical on both sides. Also shown in the figure is the location of the reattachment point . This is the point where the dividing streamline again attaches to the solid surface. Finally, in the lower corner of the step we have pictured a “secondary” recirculation region. This is caused when the reversed flow of the primary vortex is unable to follow the abrupt turn at the lower corner. It then separates from the lower surface, leading to the secondary recirculation shown in part (b) of Fig. 2.23(b). This can occur in very high-speed flows for which the speed in the primary recirculation zone, itself, is large. It should further be noted that an abrupt change in direction induced by geometry (like the corner of the step) is not the only manner in which a flow can be caused to separate. We will see in our later studies that flow may be impeded by increases in pressure in the flow direction.
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