Streamwise Averaged Nusselt Number Ratio

Averaging the streamwise data for each surface provides a method of comparing the surfaces and the effect of rotation. Figures 1.12 and 1.13 presents the streamwise averaged data vs. Rotation number for the orthogonal and twisted channel. The solid line plots are for the dimpled channel and the dotted line plots are for the smooth channel.

Figure 1.12 presents the data for the orthogonal (3=90°) dimpled and smooth channel. From this plot, it can be seen that the dimpled trailing surfaces show greater dependence on rotation number than all other surfaces, with nearly 100% improvement in enhancement from the stationary to the highest rotation number case. The dimpled leading surfaces show very little dependence on rotation number due to the stable, thick boundary layer on the leading surface. The slight non-symmetry between the two leading surfaces is due to experimental uncertainty. A most interesting issue arises when comparing the side surfaces (inner and outer) of the dimpled channel to those of the smooth channel. It can be shown that while the side surfaces of the dimpled channel initially experience a higher enhancement without rotation, the smooth channel side surfaces show greater dependence on rotation than the dimpled channel side surfaces. This is possibly attributable to the disruption of the Coriolis vortices by the dimples. For the smooth surface, the Coriolis vortex passes from the center of the channel toward the side surfaces (see Figure 1.5), where it enhances the heat transfer from the side surfaces. The secondary flow generated by the dimple has no single principal direction, and likely serves to reduce the intensity of the Coriolis vortices. Because of this, the effect of rotation is reduced for the side walls of the dimpled channel.

Figure 1.13 shows the streamwise averaged data vs. Rotation number for the twisted (b=135°) dimpled and smooth channel. The dimpled trailing-outer surface shows the strongest dependence on rotation number and is clearly the primary recipient of enhancement for the twisted channel under rotation. In addition, the dimpled leading-outer and trailing-inner surfaces now show a moderate to high dependence on rotation number. This was also explained in the discussion of figure 1.11 where it was noted that the smaller scale vortices shed by the dimple are able to capture some of the lower enthalpy fluid, which is better distributed by the Coriolis vortices for the twisted channel. Again, it is noticed that the side surfaces of the twisted channel are enhanced less by rotation than those of the smooth duct due to the disruption of the Coriolis vortices by the vortices shed by the dimple.

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