[american institute of aeronautics and astronautics 24th aiaa aerodynamic measurement technology and...

24th AIAA Aerodynamic Measurement Technology . AIAA -2004-2392 and Ground Testing Conference Portland, OR 28 June – 1 July, 2004

American Institute of Aeronautics and Astronautics

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Can We Ever Rely on Results from Wall-Bounded Turbulent Flows without Direct Measurements

of Wall Shear Stress?

Hassan Nagib* and Chris Christophorou.† Illinois Institute of Technology, Chicago, IL, 60616

Jean-Daniel Reudi‡ SLF, Davos Dorf, 7260, Switzerland

Peter Monkewitz§ Swiss Federal Institute of Technology (EPFL), Lausanne,1015, Switzerland

Jens Österlund** Swedish Defense Research Agency(FOI), Stockholm, Sweden

and

Steve Gravante†† International Truck and Engine Corporation, Melrose Park, IL 60160

Recent improvements in three techniques for measuring skin friction in two- and three-dimensional turbulent wall-bounded shear flows are presented. The techniques are: oil-film interferometry, hot wires mounted near the wall, and surface hot-film sensors based on MEMS technology. First, we demonstrate that the oil-film interferometry technique can be used to measure the skin friction magnitude and its direction in two- and three-dimensional wall-bounded shear flows. The results also demonstrate that accurate measurements of the mean skin friction with MEMS sensors are possible. Second, fluctuating skin friction is measured in two- and three-dimensional turbulent boundary layers using a MEMS sensor and a wall-wire as reference. Statistics like skewness, flatness and spectra of the turbulent skin friction are presented to demonstrate the potential and limitations of the MEMS sensor. Finally, the skin friction is measured using the oil film technique with an accuracy of about 1.5%, over the range of Reynolds numbers 10,000 < Reθ < 70,000, in a zero pressure-gradient boundary layer. The results are very well represented by the log-law with κ = 0.38, C = 4.1.

I. Introduction and Our Preferred Techniques HE contribution of skin friction represents a significant part of the drag in almost all transportation systems. Designers of all kinds of vehicles strive for the most efficient configuration, which requires the understanding

and prediction of skin friction and its contribution to the drag. Depending on the application, various skin-friction measurement techniques have been employed in the past1-35. However, all of these techniques suffer to different degrees from limitations. The accurate measurement of skin friction is of great importance for the characterization of wall-bounded shear flows. For instance, the fluctuating skin friction, in particular, provides indications of local turbulent heat and/or mass transfer. * Professor, Associate Fellow AIAA. † Research Associate, Mechanical, Materials and Aerospace Engineering. ‡ Research Scientist, Swiss Avalanche Research Institute. § Professor, Laboratory for Fluid Mechanics. ** Senior Research Scientist, Aeronautics Division, FFA. †† Product Manager, CFD, Engine Simulation, Dept. 580.

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24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference 28 June - 1 July 2004, Portland, Oregon

AIAA 2004-2392

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.



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Many friction measurement techniques have been developed over the years and their potential and limitations have been explored. The most comprehensive reviews of such methods are those by Hanratty and Campbell9, by Haritonidis10, and by Fernholz et al.6. Here, we will only present some recent improvements achieved with three of these techniques applied in two- and three-dimensional wall-bounded shear flows. The techniques are: oil-film interferometry, hot wires mounted close to the wall, and surface hot-film sensors based on MEMS technology. Oil-film interferometry is one of the few methods available for the direct and absolute measurement of skin friction. The technique consists of measuring the thinning rate of an oil film as it is being acted upon by the wall shear. This method allows very accurate measurements of the mean skin friction and does not require specific and expensive equipment. A simple camera and a monochromatic light source are the only devices needed to perform oil-film interferometry measurements. The utilization of this technique in two-dimensional flows was demonstrated in a number of studies (Fernholz et al.6; Janke15; Seto and Hornung33; Nishizawa et al.26; Tanner and Blows34). Our recent work8, 31 focused on some improvements of this method for measurements in three-dimensional wall-shear flows, including the measurement of the direction of the wall shear. For a reliable measurement of turbulent skin friction over a large range of Reynolds numbers two main conditions need to be satisfied. The first requirement, concerning protruding sensors, is that the result must not depend on the type of boundary layer; in other words, the method must not use non-universal models for specific boundary layer regions, such as the log law where the constants depend on the pressure gradient, for instance. Most techniques that utilize protruding sensors rely on the linear mean velocity profile in the viscous sublayer, i.e. U+= y+ in nondimensional wall variables U+ ≡ U / Uτ and y+ ≡ y Uτ / ν, where Uτ = (τw / ρ)1/2 is the friction velocity, y the wall-normal coordinate, ν the kinematic viscosity, τw the wall-shear stress, and ρ the fluid density. The viscous sublayer extends from the wall to the commonly accepted limit of y+ ≈ 5. The probe has to be positioned close enough to the wall in order to be within the viscous sublayer, but high enough to avoid heat conduction and manufacturing difficulties. As a consequence, measurements with wall hot-wire sensors, for instance, are often limited to relatively low wall-shear stresses and Reynolds numbers. To overcome the above limitations, a simplified approach (Ősterlund27) is sometimes used for the measurement of skin friction with a wall hot wire mounted at a fixed (dimensional) height h above the wall, where h+ may be larger than 5, but should be less than 20 to avoid the overlap (or log) region. This is possible because, within a class of similar boundary layers, the velocity profile in wall units U+ = f (y+) remains sufficiently universal beyond the viscous sublayer (of course, only U+ = y+ near the wall is truly universal by definition). Hence, the wall hot wire at fixed values of h does not require an in situ calibration, but can be calibrated in any similar reference boundary layer using a simple calibration like τw = f ( E2). Note that this technique also eliminates the need for a delicate traversing mechanism. The second requirement is that the sensor must be small enough to avoid spatial averaging, which leads to an under-estimation of the fluctuating shear stress (Johansson and Alfredsson1; Ligrani and Bradshaw21; Khoo et al.19). Manufacturing techniques and mechanical constraints limit the size of traditional hot-wire sensors, but recent developments in micro machining (the MEMS technology) has made the manufacture of micron size wall sensors which do not protrude into the flow possible (Huang et al.13; Jiang et al.16). Because of their small size, MEMS-based skin-friction or heat-transfer sensors (micro wall hot-films) allow the measurement of the local turbulent wall-shear stress at higher Reynolds numbers than with other techniques, as demonstrated by Jiang et al.16, 17, Kimura et al.20 and Miyagi et al.23. Nevertheless, the use of MEMS sensors for skin friction measurements has been widely questioned, since a number of authors (for instance Hites et al.11) have reported significant inconsistencies in the results. A recent systematic study by Ruedi et al.31 has demonstrated that consistent and accurate mean skin friction values can be obtained with MEMS-based hot films if an adequate overheat is used. The same authors extended the study to the measurement of the fluctuating skin friction32.

Recent developments in micro-machining technology (MEMS) have finally made it possible to manufacture sensors with very small sizes. Skin-friction or heat transfer sensors are some of the potential applications of MEMS technology that can be used for steady or unsteady measurements. Several studies (Ősterlund27) have shown that the unsteady or turbulent skin friction can be satisfactorily measured with MEMS sensors. However, significant scatter has often been reported in the measurement of the mean wall shear. Poor calibration repeatability of various MEMS sensors has been encountered by a number of experimentalists, but no clear explanation of the source of these discrepancies has been proposed. MEMS sensors have a much higher resistance than common hot films, hence with most standard anemometers they cannot be operated at a high overheat ratio. As a result, in most studies, MEMS sensors have been operated with overheat ratios below 1.1, resulting in low sensitivity and high dependence on ambient temperature variations and substrate conduction effects. The idea was therefore to use an appropriate anemometer to overcome the overheat ratio limitation in order to improve repeatability and accuracy.

In our recent work32 a simple method is outlined to measure the skin friction with a wall wire located outside of the viscous sublayer. A systematic study of the parameters influencing wall friction measurements with MEMS



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sensors is resented. Measurements by the three techniques are compared to each other and to past measurements in the same facility. The measured turbulence intensities of the order of 0.4 are in general agreement with a number of experimental and DNS studies. However, the fluctuating quantities measured with this MEMS sensor, operated at an over-heat ratio of 1.3, are shown to depend on the Reynolds number or mean skin friction. Therefore, such a high over-heat ratio, which was proven to dramatically increase the accuracy of mean skin friction measurements in a previous study by the authors, may not be appropriate for the measurement of fluctuating wall-shear with MEMS sensors, particularly at low mean shear values.

An experiment in non-equilibrium and three-dimensional turbulent boundary layers will be used to illustrate the paramount importance of independent measurement of the wall shear stress. Measurements of the magnitude and direction of the wall-shear stress were made using oil film interferometry utilizing the techniques described by Reudi et al.31 and highlighted in Figure 1. A pressure-driven, three-dimensional, layer, shown schematically in Figure 2 was experimentally documented and computed using a standard RANS code. The experiments utilized several measurement techniques including SPIV and oil-film interferometry. With the independent and accurate measurement of the magnitude and direction of the wall-shear stress, as displayed in Figure 3, and the careful representation of limited boundary conditions, the good agreement of Figure 4 between computation and experiment, suggests that the capabilities of current Reynolds stress model computations may be better than we expected. A three-dimensional turbulent boundary layer over a flat plate is studied recently by Gravante8. At the first measurement station, the boundary layer is nearly two-dimensional, and the secondary flow is generated via the removal of mass through the side wall of the high speed test section of the Mark V. Morkovin wind tunnel. The 3DTBL is subject to an adverse pressure gradient as a result of the turning streamwise flow. This flow field is the three-dimensional equivalent to a two-dimensional flat plate turbulent boundary layer subject to an adverse pressure gradient. The mean flow is measured with a seven-hole probe and the turbulence quantities are measured using a stereo particle image velocimeter. The wall shear stress vector and its direction are measured directly using oil film interferometry. Measurements indicate that the TKE increases slightly due to the three-dimensional mean flow mainly through changes in <u’2>. The Reynolds stresses are all affected by the mean flow three-dimensionality with turbulence production and the pressure-rate-of-strain tensor playing the major role in the dynamics of the Reynolds stresses. Measurements of Townsend’s structure parameter indicate that it is significantly altered by the mean flow three-dimensionality, especially near wall. Values are typically below the 0.15 value reported in 2DTBL’s. Reduction in a1 is mainly attributed to reduction <u’v’> near the wall. The eddy viscosity is highly anisotropic. In addition, the shear stress vector in the plane of the wall both leads and lags the gradient vector. The lag of the shear stress vector is mainly due to the residual history of the upstream two-dimensional turbulent boundary layer still present in the developing 3DTBL. No explanation of the lead is forwarded. The longitudinal and transverse integral length scales are changed by the mean flow three-dimensionality. In most cases, the size of the energy containing eddies decreases with increasing mean flow three-dimensionality except for those responsible for <w’2> which increase in size. It is hypothesized that the structure responsible for the u’ motions is turned by the cross flow and now produces w’ motions. Analysis of the joint PDF’s of the Reynolds stresses <u’v’>, <v’w’> and <u’w’> indicate that the ability of the turbulent motions to produce u’v’ sweeps is reduced. In addition, the frequency of quadrant I and quadrant III v’w’ motions as well as the frequency of quadrant III u’w’ motions are also increased. Conditional averaging produces turbulent motions consistent with the horseshoe/hairpin vortices observed in two-dimensional turbulent boundary layers with the following exception: the angle of inclination relative to the wall can be as large as 90◦.

Finally, we will return to the most classical zero pressure-gradient boundary layer but with an emphasis on high Reynolds numbers to illustrate the importance of independent and accurate measurement of the skin friction. Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number (Reθ) were recently completed28. The experiments were performed in two facilities, the MTL wind tunnel at KTH and the NDF wind tunnel at IIT. While the KTH experiments were carried out on a flat plate, the model used in the NDF was a long cylinder with its axis aligned in the flow direction. Both experiments were conducted in a zero-pressure gradient, covered the range of Reynolds numbers based on the momentum thickness from 2,500 to 27,000, and utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. Contrary to the conclusions of some earlier publications, careful analysis of the data revealed no significant Reynolds number dependence for the parameters describing the overlap region using the classical logarithmic relation. The parameters of the logarithmic overlap region were found to be constant and were estimated to be: κ = 0.38, B = 4.1. These two experiments have been recently extended to Reynolds numbers based on momentum thickness exceeding 70,000. The current experiments were also carried out in the National Diagnostic Facility (NDF) at IIT on a 10 m long and 1.5 m wide flat plate using free-stream velocities ranging from 30 to 85 m/s. Again, hot-wire anemometry and oil-film interferometry was used to measure the velocity profiles and the wall-shear stress, respectively.



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II. Highlights of Our Recent Results Our recent and ongoing research in high Reynolds number included the measurements of mean velocity

distributions in the overlap region, over the range of Reynolds numbers 10,000 < Reθ < 70,000, under five different pressure-gradient. The pressure-gradient conditions include adverse, zero, favorable, strongly favorable and complex gradients. Again, the wall-shear stress was measured using oil-film interferometry, and hot-wire sensors were used to measure velocity profiles. Parameters of the logarithmic overlap region developed from these higher Reynolds number boundary layers continue to be consistent with our recent findings and to remain independent of Reynolds number. The best estimate of the log-law parameters from the zero-pressure gradient boundary layers is � = 0.38, B = 4.1. However, the Kármán “coefficient” (κ) is found to vary considerably for the non-equilibrium boundary layers under the various pressure gradients. The results highlight the variation with pressure gradient not only in the outer region of the boundary layer but also within the inner region. The results will be presented later this summer at an IUTAM 2004 conference celebrating one hundred years of boundary layer research24. Recently, we also presented highlights of the zero-pressure gradient (ZPG) cases at a meeting in memory of Tony Perry25. Figure 5 through 9 compare our recent ZPG measurements with the recent two sets of measurements of Hites and Österlund29. The value of the Kármán constant extracted using the correlation proposed by Fernholz4 (in effect the same relation can be extracted from the work of Don Coles for the 1968 Stanford Meeting on turbulent boundary layers; see volume II) and all three sets of data is approximately 0.38.

We find that, a slightly modified version of the nearly a century old Prandtl-Kármán skin friction relation provides an exceptional agreement with zero pressure-gradient boundary (ZPG) layer data; if the FLAT PLATE data of Nikuradse were initially used in the relation we could have known the relation very well for many decades. In fact many of the commonly used skin friction relations for ZPG layers provide correct predictions for all practically encountered Reynolds numbers if they are underpinned by the same accurate measurements. The differences between the various commonly used skin-friction relations, including those based on the log law or a power law velocity profile can only be resolved by theoretical arguments or the detailed measurements of velocity profiles over a wide range of Reynolds numbers. In the equilibrium ZPG layers, the resulting skin friction is independent of whether the momentum thickness Reynolds number is varied by changing the free-stream velocity or the downstream distance; i.e., no effects for initial conditions.

The Prandtl-Kármán relation is based on integral boundary layer theory and an empirical coefficient. It is quite ironic that the version most commonly used for zero-pressure gradient boundary layers:

(Cf)-0.5 = 4 (log ((Cf)-0.5 Rex ) - 0.4

contains the constant 0.4 which is based on Nikuradse’s pipe data. The only modification we make to this relation to fully agree with our data is changing this constant to a value of 2.12. This modification also renders the relation compatible with Nikuradse’s flat plate boundary layer data which have been the subject of frequent controversy and questions. One of the difficulties of utilizing this relation is its implicit form. A much simpler explicit relation has been in the literature for nearly four and a half decades and is based on the logarithmic velocity profile. We will designate it as the Coles-Fernholz relation:

Cf = 2( (1/κ ) ln (Reθ) + C)-2

As demonstrated by Figures 5 through 9 the data of Österlund, Hites and Christophorou for ZPG boundary layers

leads to the values κ = 0.38 and C = 4.1. Since the late 1960’s and primarily based on the extensive detailed work of Don Coles, the most commonly used version of this relation utilized κ = 0.41 and C = 5. For convenience in using this relation we also found based on the results of Österlund, and Christophorou the correlation:

Reθ = 0.018 Rex 0.85.

In Figures 8 and 9 we demonstrate the behavior of the above two relations, and other commonly used ones,

based on our experimental results. In particular, in Figure 9, the relations are displayed up to Reynolds numbers higher than any encountered in practical engineering applications. The agreement between the relations when they are based on the same accurate empirical results is quite clear and surprising. Therefore, it appears that the differences between the various commonly used skin-friction relations, including those based on the log-law or a power-law velocity profile, can only be resolved by theoretical arguments or the detailed measurements of velocity profiles over a wide range of Reynolds numbers.



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III. Conclusion One of the cornerstones of our approach to measurements of turbulent wall-bounded flows is the independent

and accurate measurement of the wall shear stress with oil-film interferometry. We believe the only wall-bounded flow that may not require such measurements is the fully developed pipe flow, where the careful measurement of pressure gradient can lead to an accurate determination of the friction velocity.

Accurate measurements of turbulent wall-bounded flows require the independent or direct measurement of the wall shear stress. Oil film interferometry is the most reliable method for accurate and direct measurement of mean skin friction (~ 1.5%) and it can also measure its direction. The key to achieving such accuracy are the independent determination of the oil viscosity as a function of temperature, the steady and monitored temperature of the oil and the surface during the experiment, and the processing of the images using advanced digital acquisition and processing31. Until another even more reliable technique is developed it should be accepted as the standard for such measurements. Wall-wire type probes, fabricated by micro fabrication techniques or possibly based on MEMS technology, provide the best potential for unsteady wall-shear stress measurements32. It is now clear to us that the accurate measurement of wall-shear stress requires different techniques for the mean and the unsteady components.

The only wall-bounded flow that may not require an independent measurement of the mean shear stress is the fully-developed pipe flow, where the careful measurement of pressure gradient can lead to an accurate determination of the friction velocity. For non-equilibrium boundary layers under various pressure-gradient conditions and three-dimensionalities, one can be dramatically misled by other indirect techniques for the determination of wall-shear stress. A great deal of our confusion regarding the data and the perceived disagreement between computations and measurements in wall-bounded turbulent flows may be traceable to the lack of direct wall-shear measurements.

Acknowledgments The results presented here are based on work funded by the Air Force Office of Scientific Research, USAF,

under grant number F49620–01–1-0445, by the Swiss Federal Office for Education and Science (OFES) under contract BBWN2.97.0294, by the European project AEROMEMS, contract BRPR-CT97–0573, to investigate the feasibility of using MEMS technology for boundary layer control on aircraft, and by ERCOFTAC. We wish to especially thank Prof. H. H. Fernholz of TU Berlin, Prof. Y. C. Tai of Caltech, Prof. C. M. Ho of UCLA, and Prof A. Johansson of KTH in Stockholm for providing various sensors that were used in the various studies leading to this work.

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velocity field in the viscous sublayer. Physics of Fluid 31 (5) 1026-1033. 2 J. M. Bruns, H. H. Fernholz, P. A. Monkewitz. 1999. An experimental investigation of a three-dimensional turbulent

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34 L. H. Tanner and L. G. Blows. 1976. A study of the motion of oil films on surfaces in air flow, with application to the measurement of skin friction. Journal of Physics E: Scientific Instruments 9, 194 –202.

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Figure 1. Scheme for processing of images from oil film interferometry.



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Figure 2. Setup of Gravante’s8 experiment.

Figure 3. Highlights of two-component measurements of skin friction in a three-dimensional turbulent boundary layer.



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Figure 4. Comparison of skin friction results in three-dimensional boundary layer with RSM computations.

Figure 5. Variation of skin friction with momentum-thickness Reynolds number for recent oil-film measurements from three experiments in zero-pressure gradient boundary layers compared with commonly used relations.



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Figure 6. Variation of skin friction with momentum-thickness Reynolds number for recent oil-film measurements in zero-pressure gradient boundary layers compared with modified versions of commonly used relations and one classical relation.

Figure 7. Variation of skin friction with momentum-thickness Reynolds number for recent oil-film measurements in zero-pressure gradient boundary layers compared with modified versions of commonly used relations and selected earlier

measurements.



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Figure 8. Variation of skin friction with momentum-thickness Reynolds number for recent oil-film measurements in zero-

pressure gradient boundary layers compared with modified versions of commonly used relations.

Figure 9. High Reynolds number extrapolations of skin friction based on modified versions of commonly used relations

derived with the aid of recent oil-film measurements in zero-pressure gradient boundary layers.

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