T T

In this expression, the summation is made over all steps prior to the ith time step. A typical h history calculation using this method is shown in Figure 4. As shown, after some initial instability due to random temperature fluctuations over the initial time steps, the h history settles down to a near constant value. The figure also shows the transient flow and surface temperatures over the same time history. The thermophysical properties, thermal conductivity (k) and thermal diffusivity (a=k/pcp), for the plastic panels were determined using a National Standards conductivity meter and calorimeter. The measurements yielded the following values: k = 0.226 W/mK ±5% and cp = 1913 J/kgK ±3%. The plastic density is 1207 kg/m3 ±2%.

For heat transfer measurements, the hanging cf balance was removed and the six roughness panels were mounted on a 12-mm thick plexiglass sheet. This plexiglass sheet has approximately the same thermophysical properties as the plastic panels to avoid thermal wave reflections at the contact surface. A thermocouple sandwiched between the panels and the plexiglass sheet indicated a slight rise in temperature after approximately 30 seconds for the typical test case. Thermocouples mounted to the underside of the plexiglass support sheet showed no significant change within the total test time of approximately 90 seconds. This confirmed the use of the semi-infinite conduction assumption in the data processing. Uncertainties due to surface radiation were eliminated by performing an in-place calibration with the panels soaked at various temperatures over the range of tunnel operation. Thermocouples mounted in the test panel assured uniform temperatures to within ±0.5° C during this calibration. The average of these thermocouple readings was then correlated to the average surface temperature as recorded by the infrared camera. This measured difference between the actual temperature and the recorded infrared temperature was used to adjust the recorded temperature histories during transient testing. In this way, radiation heat transfer losses are accounted for in the final temperature history. The infrared measurement was also sensitive to the ambient temperature of the air between the roughness panels and the receiving optics. This too was accounted for in the data processing.

By meticulously accounting for various losses as outlined above, smooth plate St values were found to be within 2% of a standard correlation. Repeatability was within ±5% and bias uncertainty was estimated at ±0.00015 for the smooth plate measurement of St = 0.00216 at Rex = 900,000.

Results and Discussion

The results are presented in order of increasing complexity. First, the smooth plate data are presented to verify that the wind tunnel facility meets the accepted standards for a zero-pressure gradient, turbulent boundary layer. Following this, the rough plate data are presented in detail. A smaller subset of this data is contained in [26] with limited discussion. Finally, the elevated turbulence data are presented for the smooth and rough panels in that order.

Smooth Baseline:

The smooth plate St and cf data are presented in Figures 5 & 6 for two Reynolds numbers. Standard flat plate correlations for cf and St [27] are also indicated on the plots as follows:

0.026 0.5cf cf =-¡7- and St =-, r-—---- (Eqns 8 & 9)

The smooth plate data show agreement to within 5% and 2% of the cf and St correlations respectively.

Effect of "Real" Roughness:

The same figures also show the cf and St values obtained for the six rough panels at the same two Rex values. St augmentation ratios (St/Sto) vary from 1.1-1.5 and cf/cfo varies from 1.3-3.0 (a factor of 3-4 times greater augmentation). As indicated previously, empirical correlations for cf and St of rough surfaces have universally been developed based on experimental data with either sand roughness or uniform arrays of roughness elements. Even the uniform roughness array data are generally converted to equivalent sandgrain roughness, ks, before correlation. So, in order to assess how well these correlations apply to the "real" roughness in this study, the ks from each roughness type must be determined. These values were computed based on Ls (Eqn. 7) and are tabulated in Table 1.

A comparison with four cf roughness correlations is shown in Figure 7 for the data at Rex = 900,000. These correlations are respectively:

Cf = [1.4 + 3.7 log(x/ks)]"2 from White [28] Cf = 0.168 [ln(845/ks)]"2 from Kays and Crawford [29] cf = [2.87 + 1.58 log(x/ks)]"25 from Schlichting [30]

Cf = [3.476 + 0.707 log(x/ks)]"2'46 from Mills [27]

The smooth cf value is indicated as a dashed line in Figure 7 for reference. As shown, the correlations bound the data for all but the first three surfaces. It should be noted that these correlations were all developed using data in the fully rough regime (k+ > 70). Referencing the data in Table 1, it is clear that the first 3 surfaces in the plot do not meet this criterion. Hence, the correlations significantly underpredict cf for these panels (even falling below the smooth reference at very low k+). The fact that the cf correlations nicely bracket the experimental data in the fully rough regime suggests that ks (as estimated using Ls in Eqn. 7) might be an appropriate parameter for cf prediction of "real" rough surfaces in this regime. In the other roughness regimes, however, the ks values obtained using Eqn. 7 are clearly inappropriate. Most notable are the two "aerodynamically smooth" plates (k+ < 5) which are clearly not smooth. In this regime, an equivalent roughness parameter directly related to the characteristic roughness height, (e.g. ks = k/2), is perhaps more appropriate. If this simple relation is substituted for the Eqn. 7 ks formulation in cases where it yields ks < k/2, the results are closer to reality. Predictions with each of the four correlations using this minimum threshold for ks are also included in the figure with dashed lines. Similar results are found for the cf data at Rex = 500,000, where the Rz/ 9 ratios are slightly smaller and the k+ values are about half of their level at Rex = 900,000.

The St data are presented in the same manner in Figure 8. In this case, three correlations are used for comparison:

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