Louver Length and Fin Array Geometry

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Chapter 3 – Comparison of Baseline Heat Transfer and Friction Factor

The first focus of this study was to find how changes in louver length affected heat transfer on the tube wall and the friction factor of the louvered array. Experimental heat transfer measurements were made at 20 streamwise locations with the use of thermocouples imbedded in the heated wall. These measurements were made at Re = 230, 615, and 1016 for Ll/Fh = 100% baseline tests. For Ll/Fh = 70% and 82%, tests were run at Re = 1001, 606, and 227 which were only 1.4% below the Reynolds numbers for Ll/Fh = 100%, so accurate comparisons can still be made between louver lengths. Nusselt numbers based on Lp were used to compare the tube wall heat transfer for all Re and louver lengths. Pressure drop measurements were made from pressure taps placed upstream of the entrance louver and downstream of the exit louver, as was mentioned in Chapter 2. The pressure drops measured were converted to Fanning friction factors for comparison purposes. The definitions for Reynolds number, streamwise Nusselt number, and Fanning friction factor related to this study were also given in Chapter 2.
Ebeling and Thole (2004) reported experimental and computational tube wall heat transfer results for the Ll/Fh = 100%. Since changes were made to the calculation of the radiation losses from the tube wall and the Ll/Fh = 100% baseline tests were rerun in this study, only the results from this study will be shown for comparison to the short louver lengths.

Tube Wall Heat Transfer Coefficients

Figures 3.1 through 3.3 show experimental Nusselt numbers with respect to non-dimensional fin depth (X) for the three louver lengths and Reynolds numbers. The Nusselt numbers shown were calculated only with the center channel thermocouples mentioned in Chapter 2 as the thermocouples located above and below the center channel thermocouples were used solely to determine periodicity. Figure 3.1 shows the heat transfer results for the Ll/Fh = 100% baseline tests at all three Reynolds numbers along with a diagram of a single full louver row for reference. In the entrance region (X = 0.025) the Nusselt numbers are high for all Reynolds numbers because of the small temperature difference between the inlet air and the temperature at the X = 0.025 thermocouple. At X = 0.075, the flow reacts to the angled portion of the turnover louver and causes an increase in heat transfer. From X = 0.075 to X = 0.225, the flow is transitioning between duct directed flow to louver directed flow. Flow from X = 0.225 to 0.475 is totally louver directed. The results in this louver directed region look similar to the results one might see for flow over a flat plate, because louver directed flow is essentially flat plate flow with interruptions in the boundary layer from the leading edges of the louvers. The Nusselt numbers start to rise from X = 0.475 and spike at X = 0.575. This spike is caused by the 54˚ turn the flow makes as it goes past the turnover louver. Following the spike, the Nusselt numbers decrease once again until the flow reaches the exit louver. At the exit louver, the flow makes its final turn, and the tube wall heat transfer increases again. These increases in heat transfer at the entrance, turnover, and exit louvers occur because the redirections thin the thermal boundary layer. As the Reynolds number decreases, the response of the flow to these turns diminishes. At Re = 230, there is no increase in heat transfer at the turnover louver, showing that the momentum of the fluid is too low to be strongly redirected.
Figures 3.2 and 3.3 show the tube wall heat transfer results for the Ll/Fh = 82% and 70% louver lengths respectively. Both figures have nearly identical trends and values so only Figure 3.2 will be discussed. Looking at Figure 3.2, the trends are much different than those for the Ll/Fh = 100% louver length. The first noticeable trend is that there are no spikes in the Nusselt numbers at the entrance and turnover louver. The flow is less sensitive to the redirection at these points because the louvers are farther away from the wall. The Nusselt numbers from X = 0.075 to 0.325 resemble the results for the louver directed flow region shown in Figure 3.1. There is a sudden change in the slope of the results from X = 0.325 to 0.375 and then the Nusselt numbers stay fairly constant until X = 0.925 with the exception of the slight dip at 0.625. At X = 0.925, the Nusselt number starts to rise again. However, due to the lack of response at the turnover louver which has twice the redirection angle of the exit louver, we believe that the increase in Nusselt number is caused by conduction losses out the end of the instrumented wall. A thermocouple was placed downstream of the heated portion of the wall in an attempt to make a conduction loss correction, but the loss was two-dimensional in nature and could not be accounted for with a one-dimensional calculation. These conduction losses did not occur in the Ll/Fh = 100% tests because the instrumented Lexan wall used in those tests only extended to the end of the heater.
With the exception of the sudden decreases in Nusselt number at X = 0.375 and the small dip at X = 0.625, the results look similar to results for a channel flow which inherently reaches a steady value for the heat transfer coefficient after becoming thermally fully developed. However, as the lines for the different Reynolds numbers show augmented constant values, it seems as if there is still some component of flat plate flow which is Reynolds dependent. The difference in results for the 100% louver length and those for the shorter louver lengths can be explained by the differences in geometry between the two. Figure 3.4 shows a comparison of the 100% and 82% louver length geometries and how the geometry for the short louver lengths allows for channel flow results in tube wall heat transfer. Notice for Ll/Fh = 82%, it can be seen that the flow region near the tube wall is bounded by the wall and the flat landings of the top and bottom fin surface (outlined in red). The louver directed flow (outlined in blue), moving at 27˚ relative to the flow over the flat landing acts as the fourth boundary. It was seen with smoke visualization that there are two mostly distinct flow regions for the short louver lengths. This is far different than the flow through the 100% louvers which is all louver directed. With this being said, the flow over the flat landings of the 82% louver length seem to be coming to some thermally fully developed state at X = 0.375 at each of the Reynolds numbers.
No explanation can be given for why the Nusselt numbers drop at X = 0.375 and 0.625. These points coincide with two louver positions upstream and two louver positions downstream of the turnover louver, so possibly the turnover louver is having some extended influence over the flow. As will be shown in Chapter 5, the Nusselt numbers for the 70% louver length winglet tests also show amplified Nusselt number reductions at these same points.
Comparisons of the tube wall Nusselt numbers for the 100%, 82%, and 70% louver lengths are given for all Re in Figures 3.5 through 3.7 so the effect of changing louver length can be seen directly. Also shown in these plots are results for thermally fully developed channel flow for a constant heat flux condition on one wall (Kakaç et al. 1987) and results for a flow over a flat plate with a constant heat flux condition (Incropera and DeWitt 2002). Figure 3.5 shows this comparison for Re = 1016/1001. Notice that all the results are the same at X = 0.025 and 0.075. Following the turnover louver, the 100% louver length results show an increase while the results for the short louver lengths continue downward. The 100% results then drop below the short louver length results from X = 0.325 to 0.475 but go well above them near the turnover louver. Finally they drop below the short louver length results at X = 0.775 and continue downward while the short louver length results remain fairly steady. Another point to mention is that the results for the 70% and 82% louver lengths are nearly identical. Finally, notice how the experimental results do not match either the fully developed channel flow or the flat plate flow. Ebeling and Thole (2004) showed that 100% louver length tube wall performance is higher than that of a flat plate because of boundary layer thinning from the leading edge of each louver.
Because the realistic louver lengths do not match either flow type, we believe this is further evidence that some complex combination of channel and flat plate flow is occurring near the tube wall. Looking at Figures 3.6 and 3.7, as the Reynolds number is reduced, the short louver length results become increasingly higher than those for the 100% louver length. At the lower Reynolds numbers, the short louver length results match each other very well, just as they did for Re = 1016.
Given in Figure 3.8 are the average Nusselt numbers of the baseline tests for each louver length and Re as well as results for the fully developed channel flow and flat plate flow mentioned above. Figure 3.8 shows a linear relationship between Re and average Nusselt number for each louver length, but the slope for the Ll/Fh = 100% is lower than that of the short louver lengths. Results at Re = 1016 are the same for all louver lengths, however, the short louver lengths show much higher average heat transfer at the lower two Reynolds numbers. All louver lengths achieved higher tube wall Nusselt numbers than the developed channel flow and flat plate flow. As expected from the results seen in the Nusselt plots, the tube wall heat transfer for the short louver lengths was essentially the same over the Reynolds number range. Although the Ll/Fh = 100% baselines showed large spikes due to boundary layer thinning at the entrance turnover, and exit louvers, the constant heat transfer caused by the channel flow with the short louver lengths produced higher heat transfer over the Re range.
Tafti and Cui (2003) also showed that tube wall heat transfer was higher for their short louver length case than their 100% louver case, however, they reported that the results for each louver length had the same slope over the Reynolds number range. We believe that the reason why we showed a slope change while they did not lies in the fact that they only modeled a single periodic louver for simulation, losing the effect of the spikes in the 100% louver data at the entrance, turnover, and exit louvers. Since the magnitude of these spikes increases with Re, the slope is expected to be higher than that of the short louver length results where no effects are amplified by increasing Re.
One trend we cannot match with Tafti and Cui (2003) is why the 70% and 82% louver lengths showed nearly identical heat transfer results. Their intermediate louver length was such that the fin had no flat landing and therefore no channel flow. Although no tests were run to determine why our results matched for the short louver lengths, our hypothesis is that results would differ if the louver length decreased significantly and/or the test section was fully heated. Consider the extreme case where louver length is zero and there are only plates aligned with the flow. Since there is no longer a fourth bounding surface, (that was created by the louver directed flow) channel flow would not be possible. It is also possible that if the fins were heated, different temperature profiles on the fins caused by the different louver lengths would yield dissimilar boundary conditions for the 70% and 82% channel flows. Different boundary conditions could easily increase or decrease the length required to become fully developed and therefore the overall heat transfer on the tube wall.

Friction Factor Measurements

Figure 3.9 shows friction factor results at several Reynolds numbers for all three fin lengths compared to friction factor data for an actual heat exchanger with Ll/Fh = 82%. Results are also shown for fully developed channel flow and flat plate flow. Extra Reynolds numbers were run for the friction factor tests that were not run for the heat transfer tests so that better trends could be seen. Looking at Figure 3.9, friction factor increases with increasing louver length. This trend is consistent with the friction factor results shown by Tafti and Cui (2003) in their studies of different louver lengths. They were able to report drag due to both shear and pressure forces on the fins as a function of fin height. They showed that the Ll/Fh = 100% louvers have a much higher drag near the tube wall than the short louver lengths, making the overall friction factor higher for the 100% louver case. In a direct comparison of our Ll/Fh = 82% case to Modine’s, the trends match well but our friction factors are lower than Modine’s for all Re. When compared to Modine’s 82% louver length data, our 82% louver length results were 17.03%, 11.03%, and 19.04% lower at Re = 227, 606, and 1001 respectively. We believe that this discrepancy is due to the fact that our tube wall has zero thickness while Modine’s tubes are of finite thickness. This extra tube thickness would cause an increase in friction factor. Once again, friction factor data for fully developed channel flow and flat plate flow do not match those of the different louver lengths.
Through baseline heat transfer and friction factor tests, it was found that the short louver lengths provided better performance than the 100% louver length. Average tube wall Nusselt numbers for Ll/Fh = 82% and Ll/Fh = 70% were equal but both were higher than those for Ll/Fh = 100%. This was attributed to the steady Nusselt number over most of the fin depth. Friction factors were also reduced with the short louver lengths because there is less blockage to the flow over the flat landings than there is for a fully angled louver.

Delta Winglet Studies for Ll/Fh = 100% Louver Length

The first focus of this study was to complete baseline testing to determine the effect of the fins on tube wall heat transfer. The second focus was to design and test a method for augmenting tube wall heat transfer. Although the fins in a heat exchanger account for most of the surface area, the tube wall is the primary heat transfer surface where greater temperature differences provide more potential for convective heat transfer.
Several possible methods for heat transfer augmentation were researched, but not all were practical for incorporation in a louvered fin exchanger. The biggest limitations were the small areas available for application of an augmenting feature and feature manufacturability. Delta winglets were ultimately chosen as the best method for augmentation due to their small size and ability to provide a favorable combination of high heat transfer and low pressure drop. They are also manufacturable using the same stamping technique that cuts and shapes the louvers. Delta winglets work by producing longitudinal vortices that thin the thermal boundary layer of a surface and cause bulk mixing of the fluid downstream of the winglet. It has also been shown in past studies, that placed in series, each successive winglet increases the vortex strength of the upstream winglet and increases surface heat transfer (Chen et al. 1998, Tiwari et al. 2003). This trend lends itself perfectly to the louvered fin exchanger, where a winglet placed on each louver could act as a booster to the winglet on the upstream louver.
In this chapter the results for all of the tests run in the Ll/Fh = 100% winglet studies will be shown and discussed. Heat transfer measurements will be given for all tests. Friction factor measurements were added in the middle of this project, so results will only be shown when available.

Winglet Testing Overview

As discussed in Chapter 2, there were several winglet parameters that were tested during this segment of the project. Winglet test parameters can be split into three categories: individual winglet parameters, overall winglet setup parameters, and flow parameters. The individual winglet parameters tested were AOA, DFW, AR, shape, orientation, direction, and thickness. The definitions for these parameters were given in section three of Chapter 2. Overall winglet setup parameters involved how winglet direction and orientation varied through the test section. Examples would be directing all of the winglets towards the tube wall, directing every other winglet away from the tube wall, turning half of the winglets backwards, etc. The specifics of these cases as well as naming conventions and diagrams will be given later in this chapter. The flow parameters were the three Reynolds numbers tested. Testing at the various Reynolds numbers gave comparisons of heat transfer and friction factor augmentations at various driving speeds.
With this many parameters, a full test matrix would have been too large and time consuming. For this reason, a flexible testing scheme was employed so several different avenues could be explored to obtain maximum tube wall heat transfer augmentation. Therefore, the direction of the project as well as the specific parameters being tested may be hard to follow without an overview. All of the tests conducted along with the results of each test can be seen in Table 4.1. In the table, the tests have been divided into main section seen in orange and subsections seen in blue. In most cases, one to three trial repeats were done, but only the average results of the trials are given.
Throughout winglet testing, AOA, DFW, AR, and Re were not changed, however, some were discontinued due to poor performance. Other parameters related to winglet shape, winglet orientation, winglet direction, and overall winglet setup were changed throughout the course of testing based on results that were available at the time. The original testing scheme had winglets on every louver aimed towards the heated wall in the VG-F orientation. Figure 4.1 shows the side, top, and bottom views of this configuration. Winglets were placed on the underside of the louvers downstream of the turnover louver because the air makes contact with the bottom surface in this region. All tests were completed with the winglets in the rear half of the test section on the underside of the louvers. Later testing used an alternating winglet orientation and direction setup. Not including the entrance, turnover, and exit louvers, winglets on the odd louvers had winglets aimed at the wall in the VG-F orientation. The even numbered louvers had winglets aimed away from the wall in the VG-B orientation. Views of this setup can be seen in Figure 4.2. This configuration was changed once more to one with an alternating winglet direction but with all winglets in the VG-B orientation (Figure 4.3).
Different winglet shapes and thicknesses were also used later in testing. Rectangular winglets were added to regular testing, always alternating in direction. Finally, tests with winglets of louver thickness were run to simulate winglets produced from a stamping process.
Only a few thick winglets tests were run, always with alternating direction.
The individual winglet parameters used in experiments can be seen in Table 4.2. All parameter levels, with the exception of DFW, were chosen based on the intermediate levels used in past winglet studies. Since DFW was a new parameter, values were chosen based on geometrical constraints and an educated guess of the expected effect of DFW on tube wall heat transfer. The smallest DFW chosen was the shortest allowable distance due to the size of the louver bracket. Also, we felt that moving the winglet too far from the wall would produce poor heat transfer augmentation, so a relatively small maximum value of DFW = 0.29Lp was chosen. The height of the delta winglet (b/2) was kept constant at 0.295 in (7.5 mm, 0.27Lp) while length (c) was altered to vary the AR. The height was chosen so that the tip of the winglet would be close to half of the fin pitch minus the louver thickness but would not result in a winglet length that was too close to the louver pitch.
Now that an overview of the tests and winglet parameters has been completed, specific details of the test conditions and methods used to reduce the test matrix size will be given.

Taguchi Trials

To test every combination of the parameters and levels shown in Table 4.2, 81 tests would have had to be run. We felt that a design of experiments was the best approach to obtain useful information on trends while only doing a fraction of the tests. The Taguchi method was chosen as the design of experiments used in this study (Roy 2001).
The Taguchi method was developed by Dr. Genechi Taguchi as a method of improving quality of manufactured products. However, his methods can easily be applied to academic research. The root of his method lies in determining contributions of a single variable to the result of a multi-variable problem by using a predetermined orthogonal test array based on the number of parameters and levels to be tested. In this study, the parameters refer to AOA, DFW, AR, and Re while the levels are the specific values of the parameters (i.e. AOA = 20˚, DFW = 0.15Lp, etc.). There were four parameters studied and three levels of each parameter. This combination of parameters and levels fit into a Taguchi L-9 array which only required that nine tests be completed to obtain trend information. The L-9 array used in this study can be seen in Table 4.3.
The results of the Taguchi method are given in parameter level importance plots that give two useful pieces of information. They show the trend of influence over the range of parameter levels and also the sensitivity of the results to the parameters. A statistical analysis is also done that gives an indication of which parameters are the most important to the result and also an idea of what result one might expect from the optimized parameter levels.
Forwards Vortex Generator Testing
Winglet testing began by applying the Taguchi approach to winglets placed on every louver in the VG-F orientation, all aimed towards the wall. Each winglet was aimed towards the wall because it was thought that directing the vortices towards the wall would give the best heat transfer augmentation. Once again, this configuration can be seen in Figure 4.1.
With the Taguchi test matrix set, delta winglet trials began. However, poor initial results stopped the testing within the Taguchi test matrix after only two tests. These two tests, Taguchi test 6 and Taguchi test 1, can be seen in Figures 4.4 and 4.5. In the legend of the streamwise Nusselt plots that will be shown, the percentage of heat transfer augmentations for each test is given. Neither figure shows good positive augmentation with results of 3.76% and -2.58% respectively. Figure 4.4 shows some augmentation from X = 0.125 to X = 0.625, but results after X = 0.625 are less than or equal to the baseline results. In Figure 4.5, the winglet results match the baseline data until X = 0.625 where they are also lower than or equal to the baseline data. As stated earlier, these initial results led to the first stray from the planned test matrix. The next test run consisted of our hypothesized best case parameters. These parameters were the closest DFW (0.15Lp), AOA = 40˚, AR = 1.5, and Re = 1016. Seen in Figure 4.6, this configuration only led to an average augmentation of 2.60%. Once again, at X = 0.625, the winglet results fell below the baseline results, meaning that the tube wall temperatures were actually higher in the winglet tests than in the baseline tests. The hot air near the wall was not getting swirled to the center of the channel with the vortices as expected. We decided that circulating the air towards and away from the wall by changing the winglet direction might remedy the hot wall temperatures.

Table of Contents
Abstract
Acknowledgements
Nomenclature
List of Figures
List of Tables
1. Introduction
1.1 Literature Review
1.2 Necessity and Objectives of Current Study
2. Experimental Facility and Instrumentation
2.1 Louver Length and Fin Array Geometry
2.2 Experimental Facility
2.3 Winglets setup
2.4 Instrumentation
2.5 Data Acquisition Hardware and Data Collection Techniques
2.6 Data Reduction
2.7 Uncertainty Estimates
2.8 Benchmarking the Test Sections
3. Comparison of Baseline Heat Transfer and Friction Factor
3.1 Tube Wall Heat Transfer Coefficients
3.2 Friction Factor Measurements
4. Delta Winglet Studies for Ll/Fh = 100% Louver Length
4.1 Winglet Testing Overview
4.2 Taguchi Trials
4.3 Backwards Vortex Generator and Rectangular Winglets Testing
4.4 Summary of Findings
5. Delta Winglet Studies for the Ll/Fh = 70% Louver Length
5.1 Winglets Testing Overview
5.2 Heat Transfer, Friction Factor, and Efficiency Index Results
5.3 Summary of Results and Optimization
6. Conclusion and Recommendations for Future Work
6.1 Louver Length Conclusions
6.2 Winglet Conclusions
6.3 Future Recommendations
References
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