Smooth Channel Results

Figures 1.6-1.8 contain the smooth duct data for three different channel configurations:

stationary, rotation with 3 =90° and rotation with ¡=135°. Each case is subdivided into four experiments: (a) Re=5000, (b) Re=10000, (c) Re=20000, and (d) Re=40000. The corresponding rotation numbers for these cases are 0.305, 0.151, 0.075 and 0.038 respectively. Please reference Figure 1.3 for the data legend and surface locations within the channel. Figure 1.6 contains data for the stationary cases. The initial decrease in the normalized Nusselt number plots is attributable to the entrance effect in thermally developing flow. The plots all approach a horizontal asymptote as the flow approached the thermally fully developed state.

Figure 1.7 shows the results for the rotation cases where the duct is oriented at ¡=90°, that is, orthogonal to the plane of rotation. As was expected, the trailing surfaces exhibit higher heat transfer enhancement than the leading surfaces due to the migration of the colder core fluid toward the trailing surface caused by the Coriolis rotational forces. At a duct angle of ¡=90°, the channel can be assumed to hold symmetry about the plane of rotation. This means that both of the leading surfaces (leading-outer and leading-inner) should have identical Nu plots, the trailing surfaces should exhibit identical behavior, and the two side surfaces should be equal. This is validated relatively well as seen in the figures, with a slight bias between the two trailing surfaces. An increase in the Reynolds number tends to suppress the effect of rotation. All six surfaces show very little streamwise variation in the Nu number plots. Both of the side surfaces (inner and outer) have a heat transfer enhancement nearly equal to the value of the two trailing surfaces.

Figure 1.8 presents the results of the smooth rotation case with the channel oriented at b=135° with respect to the plane of rotation. Figure 1.8a shows that at a low Reynolds number (high rotation number), there are distinguishable differences in the heat transfer trends among the various surfaces. It can be seen that the trailing-outer and outer surfaces exhibit the highest heat transfer enhancement of all of the surfaces in the duct. This is attributed to the fact that these two surfaces are the primary recipients of the shifting of the cooler core flow under rotation. This phenomenon is illustrated in Figure 1.5 of the preceding section. After the flow impinges on the trailing-outer and outer surfaces, it passes along the leading and trailing surfaces to the inner surface, where the heat transfer coefficient is the lowest, and the secondary flow slows down dramatically. Then the flow cycles again, passing from the leading most corner diagonally across the channel toward the trailing most corner. At a high rotation number, the inner surface heat transfer follows a trend quite similar to the stationary cases. It appears that this inner surface is barely affected by rotation. Both of the trailing surfaces have higher heat transfer coefficients than the leading surfaces. A new and interesting finding is the substantial difference in the heat transfer coefficient between the two trailing surfaces. Furthermore, this span-wise difference does not come into effect until nearly half-way through the channel for high rotation numbers (Ro=0.305). It is also shown that the leading surface heat transfer increased when compared to the orthogonal channel. The overall increase in heat transfer from nearly all surfaces can be attributed to the fact that twisting the channel greatly increased the linear distance along which the main Coriolis force is directed (from leading most to trailing most corner) and provides an overall better mixing than the b=90° case. In the b=90° case, the principal Coriolis vector in the core region of the flow acts across only a short distance (the short width of the channel) and does not serve to mix the flow as well as the twisted channel.

One evident contrast of the results of the b=135° case (Figure 1.8) compared to the b=90° (Figure 1.7) case is apparent in the side surfaces. For the twisted channel, the trend of the outer surface increases while the inner surface trend decreases with X/D. Furthermore, the inner surface decreases in a similar way as seen in the stationary case. The outer surface, which trails after the inner surface, experiences a heat transfer enhancement of as much as three times that of the inner surface for the b=135° case. This is due to the shift of the primary Coriolis induced flow vector from the center of the trailing surface in the b=90° case to the trailing most corner in the b=135° case. This trailing most corner is adjacent to the outer surface, and therefore the outer surface benefits greatly in heat transfer enhancement due to the twisting of the duct. This is desirable since the outer surface of the b=135° case is closer to the trailing edge of the turbine blade, and thus is likely to experience a higher external heat flux than the inner surface. The inner surface interfaces with the side surface of the adjacent cooling passage, and therefore is less likely to be considered a critical surface.

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