Experimental Results And Discussion

Baseline Nusselt numbers. Baseline Nusselt numbers Nuo, used to normalize the ribbed channel values, are measured in a smooth rectangular test section with smooth walls replacing the two ribbed test surfaces. Except for the absence of the ribs, all geometric characteristics of the channel are the same as when the ribbed test surfaces are installed. These measurements are made in the downstream portions of the test section where the channel flow is hydraulically and thermally fully developed. All Nuo baseline values are obtained using a toJtw temperature ratio of 0.93 to 0.95. In addition, baseline measurements are conducted with all four surfaces wrapped with etched foil heaters to provide a heat flux boundary condition around the entire test section. The variation of baseline Nusselt numbers with Reynolds number ReDh is shown in Fig. 2.3. Here, values determined from an average of measurements made on the top and bottom walls, are presented. These values are in agreement with the McAdams smooth circular tube correlation [2] for ReDh<60,000, with values which are slightly lower than the correlation at higher ReDh.

Spatially-resolved distributions of local Nusselt numbers. Figure 2.4 presents spatially-resolved Nusselt number ratios, measured over about two periods of ribbed pattern, on the bottom test surface. The results are shown for ReH=10,000 and Toi /Tw =0.95. In the figure, flow is directed from bottom to top in the increasing x / Dh direction. The red diagonal regions show Nu / Nuo values measured on the tops of the ribs. The data presented are time-averaged, determined from 25 instantaneous data sets acquired over a period of 25 seconds.

As indicated in Fig. 2.4, Nu / Nuo ratios are relatively very high along the tops of the ribs.

When compared along the rib tops, values are then highest near the upstream and downstream edges. As one moves from the rib in the streamwise or + x / Dh direction, local Nu / Nuo values initially decrease, and then are low relative to other locations on the test surface. This is due to a re-circulating flow region just downstream of the rib, where flow direction next to the surface is opposite to the bulk flow direction. Note that a shear layer forms between this re-circulating flow region and the bulk flow located just above the rib. A region with relatively higher values of Nu/Nuo values then follows at slightly higher X/Dh (where Nu/Nuo>3.2), which is due to reattachment of the shear layer which is initially formed above the re-circulating flow region. With an additional increase in streamwise development, Nu / Nuo values decrease slightly once again (and then sometimes increase locally) as a second 45 ° rib is approached. These are due to a smaller region of re-circulating flow which forms just upstream of each rib turbulator. This pattern of flow and surface Nusselt number variations then repeats itself as additional ribs are encountered along the test surface. Other factors which affect the heat transfer augmenations are the skewing and three-dimensional nature of the boundary layer which develops due to the angled orientations of the ribs. Increased levels of three-dimensional turbulence production, turbulence transport, and the large-scale vortex pairs, which form in the channel, also make contributions.

The effects of Reynolds number on spatially-resolved Nusselt number ratios are apparent if the data in Fig. 2.5 for ReH=90,000 are compared to the data in Fig. 2.4 for Re^=10,000. The data presented in both figures are measured on the same part of the test surface for Toi /Tw of 0.92 to 0.95. The results shown in Fig. 2.5 are also time-averaged using 25 instantaneous data sets. As before, the red diagonal regions with relatively high Nu / Nuo ratios are also present on the tops of the ribs in Fig. 2.5. Over this region, again, as before, the highest Nusselt number ratio values are again present near the edges of the rib tops. Comparison at the two different ReH then shows that Nu / Nuo values on rib tops are higher as ReH increases, a conclusion also supported by measurements made at ReH of 18,300, 25,000, and 60,800. On the flat region just downstream of the ribs at slightly larger x / Dh, local Nu / Nuo values at ReH=90,00 are then lower than values measured at the same X / Dh and z / Dh at ReH=10,000. Nu / Nuo values for ReH=90,000 then increase continually as X / Dh increases, and the next rib is approached (Fig. 2.5). As mentioned, this is different from the results presented in Fig. 2.4 for ReH=10,000, where the initial increase due to shear layer re-attachment is followed by a decrease of local Nu / Nuo values. These differences with Reynolds number are thus due to re-circulation zones downstream of the ribs, which appear to become larger and stronger as the Reynolds number increases. Thus, the effects of Reynolds number on Nu /Nuo distributions are most prominent on the ribs, and on regions just downstream and parallel to ribs.

The effects of Reynolds number on local Nu / Nuo distributions are further illustrated by the results presented in Figs. 2.6 and 2.7. In the first of these figures, local Nu / Nuo data are given as they vary with X /Dh for constant Z/Dh =0. In the second of these figures, Nu / Nuo data are given as they vary with Z / Dh for constant X / Dh =6.90. These data are obtained from survey results (such as the ones shown in Figs. 2.4 and 2.5) at ReH ranging from 10,000 to 90,000, and about constant temperature ratio Toi /Tw of 0.92- 0.95. In Fig. 2.6, local Nu /Nuo values at X / Dh =6.53 to X / Dh =6.67 correspond to locations upstream of the central rib. X / Dh =6.67 to X / Dh =6.75 are then located on the rib, and X / Dh =6.75 to X / Dh =7.14 correspond to the flat surface downstream of the rib. In Fig. 2.7, Z / Dh =-0.20 to Z / Dh =0.16 and Z / Dh =0.27 to Z / Dh =0.39 correspond to spanwise locations on the flat portions of the surface between ribs, and

Z/Dh =0.16 to Z/Dh =0.27 correspond to locations on the central rib. Figures 2.6 and 2.7 both show that Nu / Nuo ratios generally increase somewhat on the rib tops as ReH increases. In contrast, Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as ReH increases. Because of the normalization employed, this means that the observed Nusselt number Nu increases with Reynolds number are slower than baseline Nuo increases with ReH on flat regions, and more rapid on the ribs themselves. Such changes are partially due to increases in the size and strength of the flow re-circulation region, and the shear layer associated with it, as the Reynolds number increases. In both cases, Nu / Nuo values are generally much higher than 1.0 on most of the test surface, including the flat regions between the ribs, irrespective of the value of Reynolds number employed.

Local instantaneous and time-averaged flow structure. A time-sequence of flow visualization images are presented in Fig. 2.8 for ReH=480, which are illuminated downstream of the rib turbulator test section at X =1462 mm. These data are obtained at this low Reynolds number because diffusion and increased unsteadiness at higher Reynolds numbers result in smeared and unrecognizable flow patterns. Each image in Fig. 2.8 extends in the vertical direction from the bottom to the top of the channel, and in the horizontal direction over a distance of about 2.0 channel heights. The spanwise center of each image is then located at the spanwise center of the test section at Z / Dh =0. The most important features in each image are two large vortex pairs (indicated by mushroom-shaped smoke patterns), which emanate from the bottom and top channel surfaces. These vortex pairs are formed by the effects of the ribs, which are arranged perpendicular to each other on the top and bottom surfaces, as they force air to and from both of these test surfaces. As a result of this motion, viscous effects, and continuity, pairs of counter-rotating streamwise vortices form. The secondary flows within and around these vortices are especially intense because of the blockage effects produced by the ribs. Figure 2.8 shows that these vortex pairs change substantially with time, as indicated by different convolutions and distortions of smoke patterns in different images. Each pattern is produced by complex, unsteady secondary flows, which also rearrange distributions of streamwise velocity. As a result, shear gradients are spread over the entire channel cross section.

Figure 2.9 then shows that two dominant vortex pairs, with opposite orientations, are present at Reynolds numbers ReH from 270 to 800. At some ReH , these primary vortex pairs are more convoluted and distorted than at others. The two vortex pairs are sometimes located on opposite sides of the channel, with upwash regions directed in opposite directions (i.e. at ReH=310), or with the vortex pairs oriented diagonally with respect to each other (i.e. at ReH=430 and ReH=480). The vortices aid convective processes for heat transfer augmentation by: (i) increasing secondary advection of fluid between the central parts of the channel and regions near the wall, and (ii) producing regions with high, three-dimensional shear and high magnitudes of turbulence production over much of the channel cross section, thereby substantially increasing turbulence transport levels in all three coordinate directions.

Time-averaged data also provide evidence of significant mixing and pairs of counter-rotating vortices in the rib turbulated channel. These data are presented in Figs. 2.10a-d, and are measured at ReH=10,500 and X =1235 mm, which is located just downstream of the test section. The surveys are made over a spanwise-normal plane, which extends about one channel height in each direction.

Evidence of the primary vortex pairs is provided by regions of positive and negative vorticity, which are adjacent to each other, in the survey of streamwise vorticity in Fig. 2.10d. One of these primary pairs is positioned near the top surface just to the right of Z / H =0, and one is positioned near the bottom surface also at Z / h values slightly larger than zero. In each case, an upwash region is located between the two vortices in each pair. These upwash regions are evident in the surveys of local streamwise velocity and local total pressure in Figs. 2.10a and 2.10b, respectively. In each case, the upwash region, which is present near each wall, is indicated by a deficit of each quantity because of advection of fluid with low total pressure and low velocity away from the walls by secondary flows contained within the vortices. The static pressure survey in Fig. 2.10c also shows important variations in the upwash regions, however, in this case, local upwash magnitudes are not necessarily lower than surrounding values.

The nature of these distributions, as well as the vorticity distribution in Fig. 2.10d, are consistent with the flow visualization results in Figs. 2.8 and 2.9. In both cases, complicated, spatially-varying distributions are present. For the data in Fig. 2.10d, this is because the results are a time-average of a flow field with highly distorted and convoluted vortices and secondary flows. The complexity of the flow field is also illustrated by the smaller vorticity signatures from other secondary vortices and vortex pairs in Fig. 2.10d (which are located away from the vorticity signatures associated with the primary vortex pairs).

Spatially-averaged Nusselt numbers. Spatially-averaged Nusselt number ratios Nu /Nuo, determined from local data (such as that shown in Figs. 2.4 and 2.5), are determined for the diagonal directions shown in Fig. 2.11. These diagonal directions are oriented parallel to and perpendicular to the direction of the ribs located along the bottom test surface. As shown in Figure 2.11, w /Dh is then the diagonal directed normal to the ribs, and l/ Dh is the diagonal directed parallel to the ribs. The origin of the l/Dh and W /Dh axes is positioned at X /Dh =6.53.

(W / Dh )max then equals the spacing between adjacent ribs, or the rib pitch in the direction normal to the ribs.

The resulting data, for Reh from 10,000 to 90,000 at constant Toi / Tw of 0.93-0.95, are shown in Figs. 2.12 and 2.13. Nu /Nuo in the first of these figures are averaged in the W /Dh direction, and shown as they vary with L / Dh. The data are approximately constant with L / Dh at each Reynolds number, ReH. This is important because it means that the flow at each Reynolds number considered is thermally fully developed.

The Nu /Nuo distributions at each ReH in Fig. 2.13 (averaged in the l/ Dh direction and shown as they vary with W /Dh), then show important variations with W /Dh/(W/Dh )max because this coordinate is oriented perpendicular to the direction of the ribs. These include Nu /Nuo increases with ReH at the top of the central rib. At larger W /Dh >0.55, which correspond to locations downstream of the central rib, Nu /Nuo values then decrease substantially as ReH increases. This is mostly due to increases in the strength and size of the flow re-circulation region downstream of the rib, which occurs as the Reynolds number ReH becomes larger.

The Nu /Nuo data presented in Figs. 2.14 and 2.15 are obtained for ReH of about 60,000, and the same surface layout given in Fig. 2.11, except these data are obtained at a location farther upstream where the thermal boundary layers are still developing. In this case, the origin of the L/Dh and W /Dh coordinates is located at X /Dh =0.15. In Fig. 2.14, the Nu /Nuo data measured upstream show significant variations with L / Dh, which confirms that the thermal boundary layers at this measurement location are not fully developed.

A similar conclusion is reached if the Nu /Nuo data, given in Fig. 2.15 as dependent upon w /Dh/(W /Dh )max, are examined. For regions upstream of the rib ( w /Dh/(W /Dh )max<0.42), on the rib (0.42< W /Dh/ (W/Dh)max<0.52), and downstream of the rib (w /Dh/(W/Dh )max>0.52), the Nu /Nuo values measured at the upstream locations are often higher than values measured at the downstream locations, when compared at the same W /Dh/(W / Dh )max. This is because of thinner, less-than-fully developed thermal boundary layers at the upstream location, which also cause Nu /Nuo to decrease continually with streamwise development over each segment of the test surface.

Globally-averaged Nusselt numbers and friction factors. Figures 2.16, 2.18, and 2.19 present globally-averaged Nusselt number ratios for fully-developed flow conditions, which are determined by averaging all the local data in the rectangular area enclosed by the lengths (L /Dh )max and (W /Dh )max shown in Fig. 2.11. Globally-averaged Nusselt number ratios are thus determined from the results in Figs. 2.12 and 2.13. The data in Figs. 2.16-2.19 are given for Reynolds numbers ReH from 10,000 to 90,000 and Toi /Tw of 0.93-0.95. Results from Han and

Park [2], Han et al. [4], and Taslim et al. [5] are included for comparison.

Recall that the present 45 ° square ribs are arranged so that they are perpendicular on opposite channel walls. They are installed in a channel with aspect ratio of 4, ratio of rib height to hydraulic diameter e / Dh of .078, and rib pitch-to-height ratio p / e of 10. The Han and Park [2]

data used for comparison are obtained in a channel with the same aspect ratio, same e / Dh, and same p / e. The continuous ribs on two opposite walls are arranged so that they are parallel to each other at angles of 30 °, 45 °, 60 °, and 90 ° relative to the bulk flow direction. The data used for comparison from Han et al. [4] are for square channels with 90 ° continuous ribs, 60 ° continuous ribs, and 60 ° broken ribs. In all cases, the ribs are parallel on opposite channel walls, e / Dh is .063, and p / e is 10. The Taslim et al. [5] data used for comparison are also obtained in a square channel with p/e =10. For these data, e/Dh=.083. In addition, the 45 ° oriented ribs are arranged in the same direction on opposite channel walls, and placed at streamwise locations so that they are staggered with respect to each other. Figure 2.16 shows that globally-averaged Nusselt number ratios generally decrease somewhat as ReH increases for all of the configurations. For the present rib-turbulator arrangement, globally-averaged ratios vary from 3.36 to 2.82 as ReH increases from 10,000 to 90,000. At Reynolds numbers lower than 20,000, these data are also in approximate agreement with results from Taslim et al. [5]. At higher ReH, the present results lie between the 60 ° broken rib data, and the 60 ° continuous rib data from Han et al. [4]. The present data are slightly higher than the Han and Park [2] Nusselt number ratios in Fig. 2.16. These data are given for ReH=30,000, and increase continually as the rib angle increases from 30 ° to 90 °.

Measured friction factor ratios in the rib-turbulator channel for ReH of 10,000 to 90,000 at Toi / Tw of 0.93-0.95 are shown as they depend upon ReH in Fig. 2.17. These f / fo data are also compared with results from Han and Park [2], Han et al. [4], and Taslim et al. [5]. Here, the Han and Park [2] f / fo data again increase continually with rib angle for ReH=30,000. The present data are then in rough agreement with the Han and Park 45 ° oriented rib results. The present friction factor data are then higher than the other data presented in Fig. 2.17, except for ReH>40,000, where the present results show approximate agreement with the 60 ° continuous rib data from Han et al. [4].

Globally-averaged Nusselt number ratios and friction factor ratios from Figs. 2.16 and 2.17 are plotted together in Fig. 2.18 for Rbh from 10,000 to 90,000 and To/Tw of 0.93- 0.95. Here, globally-averaged Nusselt number ratios generally decrease as f / fo increases in almost all cases as channel and rib geometry are held constant. This is consistent with the Han and Park [2] data in Fig. 2.18, since each data point from this source represents a different rib angle with respect to the oncoming flow direction. The four associated data points are located from left to right in this figure as rib angle increases from 30° to 45 ° to 60 ° to 90 °. Overall, the best performance in the coordinates of Fig. 2.18 (as characterized by the highest Nusselt number ratios at the lowest f / fo values) is produced by the 45 ° oriented ribs from Taslim et al. [5], followed by the 60° broken ribs from Han et al. [4], and then by the present 45 ° rib turbulators. The differences between the present data and the Taslim et al. [4] results are partially due to the different channel aspect ratios employed.

Performance parameters. These comparisons are further illustrated by the plot of performance parameters Nu / Nuo /(f / fo )13 as dependent upon ReH in Fig. 2.19. This performance parameter is employed because it gives the ratio of heat transfer augmentation to friction augmentation in a form in which the pumping power is the same for both [44].

Performance parameter magnitudes for the present study are determined from the data in Figs. 2.16-2.18, and decrease from 1.66 to 1.42 as ReH increases from 10,000 to 90,000 in Fig. 2.19. Here, as in the previous figure, the best overall performance is provided by the Taslim 45 ° ribs at ReH<12,000, and by Han 60 ° broken ribs at higher ReH greater than 12,000. Our performance parameters are then lower than these two data sets when compared at the same Reynolds number (in part, because of the different channel aspect ratios used). Performance parameter magnitudes from the present study are then in approximate agreement with the 60 ° continuous rib data from Han et al. [4] for ReH<40,000. The present data then lie between the 60 ° continuous rib data and the 60 ° broken rib data at higher Reynolds numbers.

Overall, these rib turbulator channel performance parameters are a result of vortex induced secondary flows and shear layer re-attachments, which result in augmented three-dimensional turbulence transport, and increased secondary flow advection. Also important are the relatively high pressure losses and friction factors produced by the form drag which develops around the rib turbulators.

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