## Info

Cfo Cfo

The subscripts "R", "Tu", and "RTu" represent cf measurements with roughness only, turbulence only, and the two effects combined respectively. Identical expressions can be written for St as well. Figures 16a-d contain these measures (for cf and St) for all 6 samples in Table 1 at the two elevated Tu levels.

In all four figures, the additive predicted effects are less than the synergistic (or actual combined) effects. The average discrepancy is 2% for the 5% Tu ASt/St results (Figure 16c) and roughly 20% for the other three figures. Even when the compound prediction is used, the results are on average 6% low for ASt/St, (at 11% Tu) and 9% low for Acf/cfo (at both 5% and 11% Tu). This suggests that there is indeed some physical coupling mechanism between the two effects that is responsible for the added enhancement when they are combined.

In the case of skin friction, freestream turbulence and roughness have opposing effects on the near wall momentum distribution. When plotted in wall units, the log region of the smooth-wall, low turbulence velocity plot is suppressed by roughness and enhanced by turbulence. As such, it would be unlikely that a synergy could be occurring in the near wall shear itself. The likely candidate for coupling is the form drag associated with the roughness elements themselves. For the panels in this study, all roughness peaks are smaller than 1/3rd of the boundary layer thickness. The majority of the peaks are situated around the momentum thickness, approximately 1/10th of the boundary layer thickness. In this region of a rough-wall turbulent boundary layer, the momentum is relatively depressed. Accordingly, peaks in this region of the boundary layer have a reduced drag signature due to the lower dynamic pressure available. Since freestream turbulence has a tendency to enhance the near-wall momentum (Figure 13), the drag on roughness elements would increase synergistically. Since this form drag is such a large component of the overall c augmentation due to roughness, this is a probable explanation for the observed synergy.

The results with heat transfer are less tractable. At 5% Tu, the additive effect is slightly less than the synergistic effect on St (2% less on average). This is consistent with results reported by Turner et al. [11] when 7-8% Tu was added to their rough-surfaced cascade facility. They found the combined effect to be approximately additive, though boundary layer transition was a complicating factor that could not be isolated and removed from the results. At the higher turbulence level of 11% in this study, however, the additive result undershoots the synergistic effect by an average of 21%. This does not follow the stated conclusion of Bogard et al. [20] that at high turbulence levels the effects are essentially additive as well. In their flat-plate roughness study, Bogard et al. reported average turbulence levels of 13% and the individual effects on heat transfer were ASt/Sto @ 30% for turbulence and ASt/Sto @ 60% for roughness. The additive effect from these two is 90% while the compound effect is 108%. Their reported synergistic effect was 100%, essentially midway between the two computations. So, their data may show some synergy after all. Perhaps there is some threshold turbulence level at which synergy begins to be apparent.

This conjecture is supported by the ASt/Sto results for the compound predictions in figures 16 c&d. In this case, there is actually a negative synergy (average of -12%) between roughness and turbulence at 5%Tu. This means that if the net effect of the two individual augmentation mechanisms is compounded, the result is greater than the effect in "real life". Since secondary (vortical) flows have been identified as a critical feature of St augmentation in roughness, it may be that low freestream turbulence levels disrupt the natural formation of shed vorticity from roughness peaks and valleys. Whatever the explanation, the effect is clearly limited since at the higher turbulence level of 11%, synergy is once again positive (average +6%, as noted above).

This non-linear behavior in St augmentation between 1%, 5%, and 11% freestream turbulence is evidenced when comparing efficiency factors as well. As mentioned in the introduction, previous work with regular arrays of dimples and hemispheres by Kithcart and Klett [22] showed that h increases as roughness elements become more recessed below the mean surface height. In their study, dimple arrays measured an h of 0.75 or greater whereas hemispheres with identical spacing and radius measured h @ 0.5. For a "real" rough surface the statistical skewness (Sk) provides a quantitative measure of the relative concentration and size of peaks and valleys. As reported in [1], a large positive skewness denotes large protrusions above the mean and is typical of surfaces with deposits or erosion A large negative skewness denotes recesses or cavities typical of pitting or spallation.

Figure 17 shows the efficiency factors vs. skewness for all 6 roughness panels in this study. Data for each of the three levels of Tu (1%, 5%, and 11%) is presented. Polynomial curve fits to each set of data are superposed on the plot. These fits exclude the data points near h ยป 0.9 with Sk @ 0 as these correspond to surface #2. This surface was identified earlier as having an augmented heat transfer more typical of simulated roughness rather than "real" roughness. The curves highlight a noticeable trend to higher h with decreasing Sk, as expected based on the Kithcart and Klett results. As anticipated, surface #2 does not follow this trend. The curves also underscore a distinct difference between the two levels of freestream turbulence. 5% Tu has virtually no effect on h while 11% Tu results in an across the board increase of 0.1 in h. Clearly, between the grid-generated low turbulence and jet-generated high turbulence, some mechanism comes to bear to alter the energy and momentum exchange in this turbulent boundary layer. More work is needed to determine if the observed behavior is a function of turbulence level, roughness type, turbulence lengthscale, or some combination of these parameters.

### Summary and Conclusions

Heat transfer and skin friction measurements have been made on roughness panels in a low-speed, zero pressure gradient wind tunnel. The roughness panels are scaled models of actual turbine surfaces rather than the traditional simulated roughness using sand or ordered arrays of cones or spherical segments. Results indicate that this "real roughness" is distinctly different from simulated roughness. Standard roughness correlations for both St and cf have been evaluated and new correlations are proposed in some cases. The combined effect of freestream turbulence and roughness is also evaluated in detail for these "real roughness" models. Based on the findings, the following conclusions are made:

1) Roughness effects on skin friction are 2-4 times as significant as those on heat transfer.

2) Standard correlations (e.g. from Schlichting) provide a good estimate for cf augmentation due to roughness when the roughness is in the fully rough regime (k+ > 70). This conclusion is based on the use of the Sigal and Danberg correlation for ks as a function of k and Ls (a shape/density roughness parameter).

3) Standard correlations (e.g. from Dipprey and Sabersky) overpredict rough surface St by 10% when the roughness is in the fully rough regime (k+ > 70). Again, ks is calculated as a function of k and Ls.

4) Existing St and cf correlations severely underpredict the effect of roughness when k+ < 70. This discrepancy is related to the dependency of ks on k. An alternative formulation for ks as an exclusive function of the rms surface slope angle (a rms) is proposed to replace the Sigal Danberg formulation over the range of roughness included in this study (0.5 < k/9 < 3).

5) Even when ks is adjusted to match the Schlichting cf correlation with the experimentally measured values, St correlations based on this ks are still too large by 10%. This observation is true for the "real" roughness models but not for "simulated" (cone) roughness models, in which case this ks gives an excellent St match between data and correlations. This observation highlights a distinct difference between "real" and "simulated" roughness. If shown to be more generally true, it would suggest that simulated rough surfaces with ordered roughness elements can be used to model either the heat transfer behavior or the skin friction behavior of "real" turbine roughness, but not both simultaneously.

6) Freestream turbulence effects on heat transfer are 2-3 times as significant as those on skin friction, the opposite of roughness effects.

7) When turbulence and roughness are both present, synergies are generated which create larger effects on cf and St than those obtained by adding (or compounding) their individual effects. This difference can reach 20% when compared to a simply additive approach to account for both effects. An exception to this is the combined effect on St at low turbulence levels. In this case, negative synergies appear to be present when both roughness and turbulence are present.

### Acknowledgements

The author is indebted to numerous personnel at the four industrial partners for providing the turbine hardware. Primary among these are: Dr. Boris Glezer formerly of Solar Turbines, Dr. Ron Bunker and Mr. Paul Suttmann at General Electric, Mr. Mohan Hebbar at Siemens-Westinghouse, and Dr. William Troha and Mr. Shawn Pollock of Honeywell Corporation. The author would also like to acknowledge those who assisted in the collection of this data: Captain Jess Drab and 2Lt Christine Ellering at the Air Force Institute of Technology and Cadets Nathan Loucks and Dick Janssen of the United States Air Force Academy. In addition, collaborations with Dr. Keith Hodge and Mr. Steve McClain at Mississippi State University and Drs. Richard Rivir and Rolf Sondergaard of the Air Force Research Lab are appreciated. The testing was conducted at the Air Force Research Lab Aero-thermal research laboratory with technical support from Mr. William Nilson, Mr. Jay Anderson, and Mr. Andy Pitts. The assistance of Ms. Nikki Widmor at the University of Dayton Research Institute in determining the plastic properties is gratefully acknowledged. This work was sponsored by the US Department of Energy -National Energy Technology Laboratory through a cooperative agreement with the South Carolina Institute for Energy Studies at Clemson University. The views expressed in this article are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or U.S. Government.

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