rather than ordered cones or hemispheres, the calculation of Af, Sf, and A, was adapted accordingly. To do so, each cell of the 3D surface height matrix was evaluated independently to determine its windward frontal area and windward wetted area. These were then summed to obtain Af and As for the entire surface. Since there are no discrete roughness elements, Af = Sf following this procedure. Performing the calculation cell by cell in this manner removed any subjectivity that might have been introduced by selecting only conically shaped peaks above some critical height in the surface height matrix. The values of Ls were then used to estimate ks for each surface using a curve fit to data assembled by Sigal and Danberg and repeated in [20].

This same cell-by-cell computation yielded yet another area ratio found to be of some importance in this study. This is the total wetted surface area (both windward and leeward) to smooth surface area ratio (S^/S).

Of the 25 3D maps reported in [1], six were selected for this study. These include one pitted surface, two coated/spalled surfaces, one fuel deposit surface, and two erosion/deposit surfaces. The statistics for the scaled models of each of the six surfaces are contained in Table 1. Representative 2D traces from each surface are shown in Figure 1. [Note: the vertical dimension has been magnified to show roughness features.] The first is a surface that exhibited severe pitting. It is pockmarked with 40-80m m deep craters, each with a width-to-depth ratio of 10 to 20. The second surface is a TBC coated surface that exhibited intermittent debond without spallation. This created an undulating surface with a regular pattern of peaks and valleys not unlike closely-packed spherical segments. Surface #3 is a TBC surface which experienced extensive spallation. Surface #4 is an example of fuel deposits that are elliptical in shape and aligned with the streamwise flow direction. The last two surfaces are representative of combined erosion and deposits with smaller, more jagged roughness elements than surface #4.

To properly scale these six surfaces for wind tunnel testing, two parameters were monitored: the roughness height to boundary layer momentum thickness ratio (Rz/9) and the roughness regime as defined by k+ (Rek in some texts). To properly compute these two parameters for the turbine hardware used in this study would have required a detailed knowledge of the operating environment (pressures, temperatures, etc...) for each of the measured blades. Using this operational data, a boundary layer calculation could be performed to compute 9 (for Rz/9) and u (for k+). Since operational data was not supplied by the manufacturers, estimates of these parameters were made as follows. For all cases, the blade Reynolds number, Rec, was approximated at 2x106. This is in the range of values cons idered typical for high pressure turbine vanes/blades as reported by other researchers [4,13]. The local momentum thickness at the given 3D map's chordwise location was then estimated using a zero pressure gradient, incompressible, turbulent boundary layer correlation from the leading edge to that point on the blade [5 /x = 0.16Rex-1/7 or 5 /c = 0.16(x/c)6/7Rec-1/7 and 9 @ 0.0975 from a power-law boundary layer profile]. Admittedly, this estimate is an oversimplification. Turbine blade boundary layers are not turbulent from the leading edge and they are subject to pressure gradients, transonic Mach numbers, freestream turbulence, and (of course) roughness. Yet, the range of Rz/ 9 estimates obtained by this method (0.5 to 3) are comparable to those obtained by more sophisticated means [20,21] (see Table 1). Moreover, even a more rigorous, fully-scaled computational estimate on a smooth blade geometry would not account for the boundary layer altering effects of the surface roughness and may not be more accurate. Finally, the goal of this study is not to assess engine-specific roughness effects but rather to use realistic turbine roughness to develop an improved physical understanding that will benefit the entire turbine industry. So, the simple estimates were deemed appropriate and adequate.

From this estimate for 9, the ratio Rz/ 9 was computed and the necessary scaling was determined for each 3D map. At the nominal Rex of 9x105 used in this study, the boundary layer momentum thickness in the wind tunnel is approximately 2mm (Re 9 @ 1500). This mandated scalings between 25 and 63 depending on the model (Table 1).

Because of the inherent difficulty with trying to match 2 parameters simultaneously for a wide variety of surfaces, the k+ roughness scaling was monitored to insure operation in the same roughness regime for the actual part and the scaled model. Nikuradse [24] classified roughness into three regimes: aerodynamically smooth (k+<5), transitionally rough (5 < k+ < 70), and completely rough (k+>70). In the smooth regime, roughness is not a factor and cf is only a function of Re. In the completely rough regime, roughness dominates cf which becomes essentially independent of Re. Finally, in the transitionally rough regime cf is a function of both roughness and Re. Again, for the present study a standard, zero-pressure gradient boundary layer correlation for cf (cf = 0.026Re-17) was used to estimate k+ (k+ = Rec (k/c)^cfj2 ) for each surface. Use of the

Sigal-Danberg ks correlation (Eqn. 7) insured that ks scaled directly with k (Rz), the result being that k+ was in the same regime for each surface and its scaled model.

Once properly scaled, plastic roughness models were fabricated using a StrataSys Inc. GeniSys Xi 3D printer. The printer has a maximum part fabrication size of 200x300x200mm and creates models by extruding plastic in 0.3mm thick layers to slowly build up the part. The typical wind tunnel roughness model was composed of six individual roughness panels (140mm x 120mm each) with a mean thickness of 6mm. Arranged three abreast, the panels nearly fill the wind tunnel test section width of 380mm. If after scaling the 3D roughness map there was insufficient area to fill the entire wind tunnel test section (280mm x 360mm), the roughness data were mirrored until the minimum area requirements were exceeded.

Description of Experimental Facility

Wind Tunnel Facility:

The research facility used for the experiments is shown in Figure 2. The open loop wind tunnel uses a main flow blower to provide a nominal mass flow of 1.2kg/s to the test section. A heat exchanger at the main flow blower discharge can be used to vary the flow temperature from 18 to 54° C. The main flow enters a conditioning plenum of 0.6m diameter before reaching the rectangular test section. This conditioning plenum has one layer of perforated aluminum plate followed by 7.6cm of honeycomb straightener, and three layers of fine screen. A circular-to-rectangular foam nozzle conducts the flow from the plenum cross-section to the 0.24m by 0.38m test section. With this conditioning, 2D flow uniformity of ±3% in velocity is obtained over the center 0.32m of the test section span. Without employing turbulence generation devices, the freestream turbulence level at the test section was 1%.

At 1.22m from the plenum exit a knife-edge boundary layer bleed with suction removes the bottom 1.27cm of the growing boundary layer, making the aspect ratio (span/height) of the final test section approximately 1.7. The top wall of this final section pivots about its forward end in order to adjust the pressure gradient in the tunnel. For the tests presented here, the wall was adjusted to produce zero freestream acceleration over the roughness test panels. At 2.54cm from the boundary layer suction point, a 1.6mm diameter cylinder spans the test section to trip the boundary layer to turbulent. The leading edge of the roughness panel sections are located 1.04m from the boundary layer suction point. The roughness panels (generally six panels make a single set) are installed in a 0.28m streamwise gap in the lower wall. The tunnel then continues 0.62m beyond the trailing edge of the roughness panels.

Freestream turbulence is generated using two distinct methods. For high turbulence generation, a "Tee" located upstream of the conditioning plenum inlet leads to a bypass blower, which generates a bypass flow in parallel with the main flow. This bypass flow is re-injected from two opposing rows of holes located on the top and bottom of the test section, 1.02m upstream of the boundary layer bleed. A heat exchanger in the bypass line is used to remove the heat of compression from the bypass flow. This jet-injection turbulence generation device produces a turbulence level of 11% at the roughness panels. A standard square-bar grid was used to obtain a lower turbulence level of 5%. The grid is composed of 1.34cm square bars spaced 6cm apart and is located 0.2m upstream of the boundary layer bleed.

Flow velocity is measured using a single-element hot-wire anemometer. A co-located flow thermocouple with 0.3mm bead diameter is used for flow temperature measurement. The two instruments are mounted on a 3-axis traverse system located atop the wind tunnel. A magnetically encoded linear position indicator affixed to the traverse was used to determine the probe position to within 2.5mm. Uncertainty in the velocity measurement stems primarily from the calibration fit accuracy. When compared to a co-located Kiel probe velocity measurement, the error is within ±1.5% at flow rates of interest.

cf Measurement:

A number of researchers have struggled with the complexities of making drag measurements over rough surfaces. Two common methods relying solely on velocity measurements are a boundary layer momentum balance and log-region curve fitting. For a zero streamwise pressure gradient flow, the change in boundary layer momentum thickness (9) can be related directly to cf by cf = 2d9/dx. This is the momentum balance method. It requires a minimum of two velocity profiles separated by a streamwise distance (dx) over the rough surface. The second method assumes the presence of a loglinear region in the rough wall turbulent boundary layer velocity profile (when plotted in wall units). This "log-law" region has been shown to be present in rough wall data, though the log-region constant (B) is typically adjusted as a function of ks. Both of these methods require assumptions to be made about the y=0 wall elevation, which is problematic for rough surfaces. Considering this and other drawbacks of velocity-based cf measurements, Acharya et al. [2] concluded that, "an accurate independent measurement of cf is thus of central importance to any experiment on rough-wall boundary layers." Based on this conclusion, Acharya et al. employed a force-balance to measure the actual skin friction force on a roughness coupon in their flowfield.

Following this reasoning, the present work uses a hanging element balance to obtain cf. The balance configuration is shown in Figure 3. Four 0.25mm diameter, 0.7m long Nichrome wires attached to an apparatus atop the tunnel allow the roughness panels to be freely suspended in the floor of the wind tunnel. The wires are located outside the wind tunnel and are affixed to the four corners of a metal support plate upon which the six plastic roughness panels are mounted. When air is flowing in the tunnel, the plate moves downstream under the applied shear force. This motion was a maximum of 1.9mm for the roughest panel tested (with turbulence). This horizontal plate motion is accompanied by a slight vertical plate motion (2.6mm for the maximum case) of the heavy support plate which produces the necessary restoring force. For small-angle motions such as this, the restoring force is approximately linear with streamwise plate deflection. Using a string-pulley apparatus with fractional gram weights, this restoring force was calibrated over the full range of deflections observed in practice. The plate deflection was measured using a Capacitec Model #4100-S capacitance meter mounted to the side of the test plate, outside the tunnel walls. The meter is stationary, while a parallel metal bracket is mounted to the moving panel. The air gap between the stationary meter face and the parallel bracket face is the capacitor thickness. The required ground loop from the moving bracket to the power supply and meter is formed using the metal suspension wires. In this way, no friction is added to the plate motion due to the meter. The wire-pulley calibration is remarkably linear and repeatable with least squares correlation coefficients of 0.9999 and repeatable slopes within ±1.5%.

The test plate is suspended with a 0.5mm gap at the leading edge and a trailing edge gap which is 0.5mm greater than the maximum expected excursion. These gaps allow unrestrained motion of the plate under the applied shear force. The gaps also permit differential pressure forces to affect the net displacement of the test plate. To mitigate these pressure forces, the leading edge gap was covered with a 0.05mm thick stainless steel sheet with 7mm overlap with the roughness panels. The initial 10mm of each panel was smooth to accommodate this overlap without interference. Despite this precaution, differential pressures still accounted for 5-15% of the net plate motion. To calculate this component of the force, three pressure taps were installed at mid-plate thickness on the adjoining stationary plexiglass pieces, both upstream and downstream of the suspended aluminum support plate with the roughness panels. The three pressure taps were ganged together to produce mean pressures for both the leading and trailing edge of the free-floating test section. A Druck LPM-5481 low pressure transducer was used to monitor this differential pressure and deduct it from the total displacement (force) measured by the Capacitec meter. With these precautionary measures, smooth plate cf values were found to be within 5% of standard correlations. Repeatability was within ±2% and bias uncertainty was estimated at ±0.0002 for the smooth plate measurement of cf = 0.00354 at Rex = 900,000. The operation of the Druck transducer and Capacitec meter were found to be very sensitive to temperature, greatly affecting the quoted uncertainty. As such, the main flow heat exchanger was employed to maintain constant room temperature to within ±0.5° C during testing.

St Measurement:

For the heat transfer measurements, a FLIR Thermacam SC 3000 infrared camera system is mounted with the lens fit into a hole in the plexiglass ceiling of the tunnel. The camera has a sensitivity of 0.03° C (at 30° C) and allows framing rates of approximately one Hz. At the focal distance of 37 cm, the camera field of view is roughly 70 x 90 mm. This limited field of view is centered at a distance of 1.20m from the leading edge of the tunnel floor. This puts the mean streamwise position of the heat transfer measurement roughly 2cm downstream of the center of the roughness panels (x = 1.18m). The 320 x 240 pixels of the FLIR camera allowed excellent resolution of the roughness features during the transient experiments. For the measurements reported in this study however, the surface temperatures were simply area-averaged to obtain the representative surface temperature history required for St determination.

The Stanton number was determined from this surface temperature history using the method of Schultz and Jones [25]. This technique uses Duhamel's superposition method to calculate the surface heat flux given the surface temperature history. It assumes the panels are a semi-infinite solid at constant temperature at time t = 0. To accomplish this, the entire test section was soaked at room temperature for several hours before testing. Using the main flow heat exchanger, a hot-gas air flow was then initiated instantaneously while monitoring the freestream velocity and temperature as well as the average surface temperature (with the IR camera). The heat transfer coefficient (h) at the ith time step was then calculated using the expression from Schultz and Jones.

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