## X

Height (m)

Figure 12. Temperature Profile of Erosion Cone Element from General Pin Expression Requested Experimental Action

As mentioned earlier, the experimental skin friction results for the Erosion 2 surface are surprising. The experimental results suggest that that the skin friction coefficient decreases 11.58% from an Rex of 5.5x10s to an Rex of 7.0x 105, while the code prediction decreases negligibly from an Rex of 5.5x105 to an Rex of 7.0x105. The code predictions suggest that the flow has reached completely rough flow. Since the two experimental data points were acquired using two different velocity measurement devices, the experimental measurements should be repeated using the hot wire anemome ter.

For many of the surfaces, there are heat transfer and skin friction results for only two or three average Reynolds numbers. To validate the model, the surfaces need to be evaluated over a greater Reynolds number range. The annual report for 1 March 2000 to 28 February 2001 reports that the maximum Reynolds number for the wind tunnel is 4x106. Six or seven measurements of skin friction coefficient and Stanton Number are needed for each surface over the Reynolds number range of 5.5x105 to 4x106. Future Computational Action

While some of the questions posed at the beginning of the report have been answered, some questions have not been answered, and some questions have been added. Adding the ellipsoidal blockage model to the BLACOMP predictions of the Deposit surface and the Deposit Layered surface lowered the skin friction predictions. The predicted skin friction coefficients are 21% and 12% higher than the measured coefficients for the Deposit surface and the Deposit Layered surface, respectively. The cause(s) of this over predictions will be investigated.

Several mechanisms are present in causing the over predicitons of the Stanton numbers of each of the surfaces. The increased surface area caused by elliptical blockages as compared to circular blockages will be added to the discrete element code. The "fin effect" of temperature change along the height of the roughness elements will also be further investigated. A subroutine could be added to BLACOMP to integrate the fin equation at every x location for the cone surfaces, but creating this subroutine would require considerable effort. Adapting the subroutine for a randomly-rough surface, will require even more time because of the range of shapes, spacings, and heights of random blockage elements. An average element diameter and spacing technique needs to be developed for randomly-rough surfaces.

### Conclusions

The modified discrete-element model for predicting skin friction and heat transfer over randomly-rough surfaces involves placing a reference surface at the mean hydraulic elevation of the rough surface. Drag and heat transfer are calculated on the roughness elements depending on the local flow velocity and the equivalent ellipsoidal dimensions of the roughness.

The friction coefficient predictions using the model are higher than the experimental measurements for most of the surfaces. While the predictions are higher than the experimental measurements, the model does predict trends that are similar to trends in the experimental data. For example, the model predicts that the Deposit Cone surface will have a higher friction coefficient than the Deposit surface, which will have a higher friction coefficient than the Deposit Layered surface. The experimental data show the same trend with the deposit surfaces. The Erosion Layered surface is most like the circular-blockage, discrete-element model in that it has sparse roughness with circular blockages and flat surface below the mean elevation. For the Erosion Layered surface, the discrete-element prediction is within 2% of the experimentally measured friction coefficient.

The discrete-element model did fail to predict one trend shown in the experimental results. For an increase in Reynolds number over the Erosion 2 surface, the experimentally measured friction coefficient decreased over 10%. The discrete-element predictions showed a negligible decrease over the same increase in Reynolds number.

The Stanton number predictions using the new model are considerably higher than the experimentally measured values for all of the surfaces. The Stanton number predictions agree much better with the raw experimental measurements, but after the experimental measurements are corrected for roughness material properties, the predictions are higher. The "fin" effect, by which the temperature of the roughness elements changes along the height of the blockage into the flow, was investigated as a possible cause for the over predictions of Stanton number. The Erosion Cone surface was found to exhibit some "fin" effect, but the total "fin" effect cannot be evaluated without the solution of the full conjugate heat transfer problem.

More experimental data are needed to refine the model for both skin friction and heat transfer predictions. At least four more Reynolds numbers over the region of 9x 105 to 4x106 are needed for each rough surface. This should help validate the trend in measured friction coefficient exhibited by the Erosion 2 surface. A better estimate of the experimental uncertainty is also needed to help refine and validate the model. References

Delany, N. K., and N. E. Sorensen. "Low-Speed Drag of Cylinders of Various Shapes." NACA TN 3038, 1953.

Gatlin, B. and B. K. Hodge. An Instructional Computer Program for Computing the

Steady, Compressible Turbulent Flow of an Arbitrary Fluid Near a Smooth Wall. Department of Mechanical Engineering, Mississippi State University, Second printing, 1990.

Hodge, B. K., J. Bons, R. Sondergaard, and R. Rivir. "Real Surface Effects on Turbine Heat Transfer and Aerodynamic Performance: Annual Report, 1 March 2000 to 28 February 2001."

Janna, W. S. Introduction to Fluid Mechanics. Boston: PWS Kent. Second edition. 1994.

Lindsey, W. F. "Drag of Cylinders of Simple Shapes." NACA TR 619, 1938.

Morris, H. M. Applied Hydraulics in Engineering. New York: The Ronald Press Company. Second edition. 1972.

Nikuradse, J. "Laws for Flows in Rough Pipes." VDI-Forchungsheft 361, Series B, Vol. 4, 1933. NACA TM 1292, 1950.

Pinson, M. W., and T. Wang, "Effect of Two-Scale Roughness on Boundary Layer Transition Over a Heated Flat Plate: Part 1—Surface Heat Transfer." ASME Journal of Turbomachinery. Vol. 122, pp. 301-307.

Schlichting, H. "Experimental Investigation of the Problem of Surface Roughness." Ingenieur-Archiv, Vol. VII, No. 1, 1936. NACA TM 823, 1937.

Taylor, R. P. "A Discrete Element Prediction Approach for Turbulent Flow over Rough Surfaces." Ph.D Dissertation. Mississippi State University. 1983.

Submitted for: IGTI 2002.

St and cf Augmentation for Real Turbine Roughness with Elevated Freestream

Turbulence

J. Bons Associate Professor Air Force Institute of Technology

### Abstract

Experimental measurements of skin friction (cf) and heat transfer (St) augmentation are reported for low speed flow over scaled turbine roughness models. The models were scaled from surface measurements taken on actual, in-service land-based turbine hardware. Model scaling factors ranged from 25 to 63, preserving the roughness height to boundary layer momentum thickness ratio for each case. The roughness models include samples of deposits, TBC spallation, erosion, and pitting. Measurements were made in a zero pressure gradient turbulent boundary layer at two Reynolds numbers (Rex = 500,000 and 900,000) and three freestream turbulence levels (Tu = 1%, 5%, and 11%). Measurements at low freestream turbulence indicate augmentation factors ranging from 1.1-1.5 for St/Sto and from 1.3-3.0 for cf/cfo (Sto and cfo are smooth plate values). For the range of roughness studied (average roughness height, k, less than 1/3rd the boundary layer thickness) the level of cf augmentation agrees well with accepted equivalent sandgrain (ks) correlations when ks is determined from a roughness shape/density parameter. This finding is not repeated with heat transfer, in which case the ks-based St correlations overpredict the measurements. Both cf and St correlations severely underpredict the effect of roughness for k+ < 70 (when ks, as determined by the roughness shape/density parameter, is small). A new ks correlation based on the rms surface slope angle overcomes this limitation. Comparison of data from real roughness and simulated (ordered cones or hemispheres) roughness suggests that simulated roughness is fundamentally different from real roughness. Specifically, ks values that correlate cf for both simulated and real roughness are found to correlate St for simulated roughness but overpredict St for real roughness. These findings expose limitations in the traditional equivalent sandgrain roughness model and the common use of ordered arrays of roughness elements to simulate real roughness surfaces. The elevated freestream turbulence levels produce augmentation ratios of 1.2 & 1.5 (St/Sto) and 1.2 & 1.3 (cf/cfo) compared to the Tu=1% flow over the smooth reference plate. The combined effects of roughness and elevated freestream turbulence are greater than their added effects suggesting that some synergy occurs between the two mechanisms. Specifically, skin friction augmentation for combined turbulence and roughness is 20% greater than that estimated by adding their separate effects and 9% greater than compounding (multiplying) their separate effects. For heat transfer augmentation, the combined effect of turbulence and roughness is 6% higher than that estimated by compounding their separate effects at high freestream turbulence (Tu = 11%). At low turbulence (Tu = 5%), there is a negative synergy between the two augmentation mechanisms as the combined effect is now 12% lower than that estimated by compounding their separate effects.

Nomenclature

Af - windward frontal surface area of roughness elements on sample

As - windward wetted surface area of roughness elements on sample cf - skin friction coefficient, t w/(0.5p Uoo2)

c - blade/vane chord cp - specific heat at constant pressure h - convective heat transfer coefficient k - average roughness height (» Rz)

(also thermal conductivity). ks - equivalent sandgrain roughness k+ = ksut/v ° Rek

Ku - kurtosis of height distribution (Eqn 5)

N - number of points in profile record

Prt - turbulent Prandtl number (@ 0.9)

Ra - centerline average roughness (Eqn 1)

Rec - Reynolds number based on blade chord and exit conditions

Rt - maximum peak to valley roughness

Rz - average peak to valley roughness S - surface area of sample without roughness

Sf - total frontal surface area of sample Sw - total wetted surface area of sample Sk - skewness of height distribution (Eqn

St - Stanton Number, h/(pcpU¥) T - temperature [° C] t - time [s]

Tu - freestream turbulence, u'/U¥ [%] U¥ - freestream velocity u' - fluctuating velocity (rms) ut - friction or shear velocity ^¡tw/p x - streamwise distance from tunnel floor leading edge y - surface height coordinate after removal of polynomial fit to surface curvature a - thermal diffusivity (k/pcp)

a rms - rms deviation of surface slope angles

Ô - boundary layer thickness h - efficiency factor (St/Sto)/(cf/cfo)

1c - correlation length

Ls - roughness shape/density parameter

v - kinematic viscosity 9 - boundary layer momentum thickness p - density tw - wall shear subscripts adj - adjusted ks value required to match Schlichting cf correlation to data max - maximum height in profile record min - minimum height in profile record o - smooth plate reference at low freestream turbulence s - surface value ¥ - freestream value

Introduction/Background

Modern land-based turbine airfoils operate in severe environments with high temperatures and near critical stresses. Highly turbulent combustor exit flows spew hot combustion products and other airborne particulates at the turbine surfaces for more than 20,000 hours before regularly scheduled maintenance. Due to this harsh operating environment, turbine surfaces experience significant degradation with service. Measurements reported previously by this author [1] and others [2,3,4] indicate an order of magnitude or greater increase in rms roughness is typical for a first stage high pressure turbine vane or blade.

For over twenty years, the effects of these elevated levels of surface roughness on turbomachinery performance have been studied at all practical levels; from fundamental flat-plate wind tunnel research, to multi-blade cascade facilities, to full-up system level tests. These studies all support the expected result that roughness increases surface drag and heat transfer (though to varying degrees). For turbomachinery, this translates to higher heat loads, accelerated part degradation, and lower stage efficiencies.

At the system level, Blair [5] was perhaps the first to report roughness-related increases in St on a rotating turbine facility. In his study, premature boundary layer transition combined with other roughness-induced effects to produce a nearly 100% increase in St for some cases. Guo et al. [6] also reported a two-fold increase in heat transfer for a factor of 25 increase in roughness height (Rz) on their fully scaled nozzle guide vane facility. In their studies with compressors and pumps, Boynton et al. [7], Suder et al. [8], and Ghenaiet et al. [9] all observed 3-5 points loss in efficiency with roughened blades. With the exception of Ghenaiet et al., who actually simulated metal erosion due to sand ingestion, all of these system-level tests have been conducted using uniformly distributed roughness (e.g. sand or painted-on particulates).

Sand and powders have also been used to simulate rough surfaces in turbine cascades, where more detailed blade surface measurements can be made [10,11,12]. These studies have each documented effects similar to those of their system-level counterparts; accelerated boundary layer transition, increased heat transfer, and increased blade losses. A fourth cascade study by Abuaf et al. [13] explored the benefits of metal polishing processes and found that a factor of three reduction in centerline-averaged roughness produced up to a 15% reduction in blade surface integrated heat transfer at some Reynolds numbers.

Unlike system and cascade level tests, flat-plate wind tunnel testing has explored a broader spectrum of surface roughness characterizations. In addition to sand roughness experiments [2,14], researchers have used distributed cylinders [15,16], spherical segments [17,18], cones [19,20], and pedestals [21]. In each case, the roughness element size and spacing was selected to match a predetermined set of roughness statistical parameters. This set could include traditional parameters such as Ra or Rz (Rz » k, the mean roughness height) or more sophisticated characterizations such as correlation length [17], rms deviation of surface slope angles [2], or a roughness shape/density parameter [20] in combination with other parameters. The majority of these researchers have also correlated their findings in terms of the equivalent sandgrain roughness, ks, in an effort to translate their characterizations of turbine roughness into the much wider array of roughness encountered in pipe flows and external aerodynamics. A notable exception to this is the work of Taylor et al. [17] which has pursued a discrete-element model (DEM) to evaluate distributed roughness elements. Both methods (ks and DEM) have met with varying degrees of success when brought to bear at the cascade and system level. Consequently, designers and operators continue to make significant allowances (safety margins) for uncertainty when calculating heat transfer or losses in operating rough turbines.

It is possible that part of this difficulty in modeling lies with the fact that different roughness-producing mechanisms (deposits, erosion, pitting, and coating spallation) have unique surface features. For example, as shown in [1], pitting and spallation have large roughness recesses below the surface mean line while deposits are characterized by peaks above the mean line. Fundamental fluid dynamics research (most recently by Kithcart and Klett [22]) has shown that recesses have a more marked effect on St than on cf when compared with hills of equivalent dimensions. This is attributed to the reduced form drag and enhanced three-dimensional flows (vortices) associated with recesses vs. peaks. Nuances such as this can easily be lost when 1 or 2 roughness parameters are used to characterize a wide variety of rough surfaces with discrete, uniform elements. This then creates biases in the final roughness correlation which accentuate one type of roughness while de-emphasizing another.

One way to avoid this bias generated by distributed roughness characterizations of "real" roughness is to employ scaled replicas of actual turbine surfaces in fundamental wind tunnel testing. Results can then be evaluated without bias to a particular dominant shape or spacing. The objective of the present study is to begin building such a database. Accordingly, a diverse (though certainly not comprehensive) collection of six actual surface roughness samples (from [1]) were scaled and tested in a flat plate wind tunnel. Both cf and St were measured and comparisons were made with contemporary roughness correlations found in the open literature. Correlations were also attempted with a number of the roughness parameters cited in previous studies and the most promising candidates were identified.

In addition, it is natural for the turbine designer to be suspicious of data taken in the often pristine laboratory environment. Thus, the relevance of laboratory findings to the actual turbine operating environment is of critical importance. One of the significant features of turbine flowfields that could have a synergistic effect with roughness is freestream turbulence. There have been very few studies which have considered the coupled effects of freestream turbulence and surface roughness. Turner et al. [11] found the effect of grid-generated (~7%) turbulence to be similar to a two order of magnitude increase in Ra (as determined by the blade mean heat transfer coefficient). The combined effect of turbulence and roughness was approximately additive. A similar finding was reported by Bogard et al. [20] for turbulence levels up to 17%. Finally, the results reported by Hoffs et al. [12] using 5% and 10% turbulence in a cascade facility with rough blades lack sufficient detail to determine whether roughness and turbulence effects are complementary. However, the effects of the two different mechanisms on heat transfer are clearly shown to be distinct and significant. The present study expands the existing database to include both St and cf measurement at 5% and 11% freestream turbulence. Again, these measurements are taken using scaled "real" roughness models versus the simulated roughness characterizations (e.g. sand or cones) employed in previous studies.

### Surface Roughness Measurement and Fabrication

In preparation for the current study, nearly 100 land-based turbine components were assembled from four manufacturers: General Electric, Solar Turbines, Siemens-Westinghouse, and Honeywell (formerly Allied-Signal) Corporation. The articles were selected by each manufacturer to be representative of surface conditions generally found in the land-based gas turbine inventory. Chord dimensions on the assembled blades and vanes ranged from 2 to 20cm and included samples with thermal barrier coatings (TBC).

In order to respect proprietary concerns of the manufacturers, strict source anonymity has been maintained for all data presented in this publication.

Extensive 2-D and 3-D surface measurements were made on the assembled hardware [1] using a Taylor-Hobson Form Talysurf Series 2 contact stylus measurement system. This device uses a 1.5 mm radius diamond-tipped conical stylus to follow the surface features for a given part. The instrument has a maximum horizontal stroke of 50mm and can measure a total vertical range of 2mm with a precision of 32nm. 3D measurements were made by indexing the part by specified increments in the horizontal direction perpendicular to the stroke of the contact stylus. Increments from 5 to 40 microns were used to map out regions from 1x1mm square to 40x40mm square for various components. Once a 3D map was taken, the Talymap™ software was used to remove the part's form with a polynomial least squares surface fit. With the form removed, the relevant statistics could be extracted from the roughness data. Evaluations were conducted to compute the centerline averaged roughness, Ra, the rms roughness, Rq, the maximum peak-to-valley roughness, Rt, the skewness, Sk, and the Kurtosis, Ku, as defined below (ymean = 0):

Each 3D map was also evaluated in smaller subsets (or cutoffs) to estimate Rz, the average of the local Rt values over the entire map. Rz is commonly used as an estimate of the average roughness height, k. The 3D maps were then evaluated using 2D auto-correlations in both the streamwise and cross-stream directions. The correlation lengths, 1c, were calculated as the distance at which the autocorrelation functions fell to a value of 0.1. In addition, by dissecting the 3D surface map into its 200 to 1000 individual 2D traces, the local surface slope angles between each measurement point could be calculated. The sum of these angles over the entire 3D surface was then used to compute the rms deviation of surface slope angles, a rms, considered by some [2,20] to be an important roughness parameter. a rms was calculated for both the streamwise and cross-stream directions.

One final measurement made from the 3D surface maps was the roughness shape/density parameter, Ls. This parameter was developed by Sigal and Danberg [23] to correlate the ks estimation process to both the spacing and shape of roughness elements. The parameter was derived for use with two and three dimensional roughness elements (e.g. ribs or cones) mounted to a smooth surface. It is defined as, l .=—r A

where S is the reference area of the sample surface (without roughness), Sf is the total frontal surface area of the roughness elements on the sample, As is the windward wetted surface area of a roughness element, and Af is the frontal surface area of a roughness element. Since the surfaces being evaluated in this study were real roughness surfaces

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