LASER-DOPPLER ANEMOMETRY IN TURBULENT BOUNDARY LAYERS INDUCED BY DIFFERENT TRIPPING DEVICES COMPARED WITH RECENT THEORIES

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1 Fachtagung Lasermethoden in der Strömungsmesstechnik. 7. September 26, Braunschweig LASER-DOPPLER ANEMOMETRY IN TRBLENT BONDARY LAYERS INDCED BY DIFFERENT TRIPPING DEVICES COMPARED WITH RECENT THEORIES M. Kito, E. S. Zanoun, L. Jehring, C. Egbers Department of Aerodynamics and Fluid Mechanics (LAS), Brandenburg niversity of Technology (BT Cottbus), Siemens-Halske-Ring 1, D-36 Cottbus, Germany Abstract The boundary layer characteristics are affected by factors such as freestream turbulence intensity, pressure gradient, tripping device, surface roughness, etc. In the present study, to ensure having turbulent boundary layer, tripping devices were installed close to the leading edge of the flat plate to induce turbulence under different pressure gradients. The effects of the different tripping devices and pressure gradients on the boundary layer characteristics were studied experimentally using the laser-doppler anemometry (LDA) for flow Reynolds number Re θ 1 3 where Re θ is based on the momentum thickness and the free stream velocity. Three different tripping devices [DYMO brand embossing tape letter X (.7 mm, height width) and sand stripes of different heights (A:.17 1 mm and B: mm, height width)] were fixed, separately, 1 mm from the leading edge of the plate in the spanwise direction. The wall skin friction data were obtained utilizing the Clauser chart and then used to normalize the mean velocity profiles. Tripping effects were found to be remarkable at higher Re θ, while the differences are negligible at lower Re θ. The normalized mean velocity profiles were found to be well represented by the power law proposed by Barenblatt (1997) and poorly representing the power law of Zagarola and Smits (1998). The power law coefficients in the overlap region and in the region adjacent to the external flow were observed to depend on both the roughness height and the pressure gradient as well as the Re θ. Introduction nderstanding flow characteristics and scaling laws in turbulent boundary layers is essential for the performance and design aspects of a variety of engineering apparatus in aerodynamics, hydrodynamics, and wind engineering. Most applications of the engineering interests are high Reynolds number flows, and therefore it is a common way to use tripping devices in the laboratory scale to induce the turbulent boundary layers at lower speeds. Good research work in triggered turbulent boundary layers has been reported for cases of wall-bounded shear flows and interesting results have become available that provide new and useful information on the time-averaged and turbulent flow properties in free streams and close to walls. In addition, some efforts have been given to study the effect of the upstream conditions on the mean velocity distribution in the turbulent boundary layers, see e.g. Castillo et al. (2) and Gibbings and El-Shukri (1999). Despite of that noticable effort, a little attention has been paid to the tripping device effect over the mean velocity profile as well as the turbulence

2 characteristics. Therefore, some open questions remain unsolved, suggesting further research for the triggering effect on the mean velocity profile, particularly, in the wake region. Barenblatt et al. (2) suggested that the region between the viscous sublayer and the external flow consists of two separated self-similar structures. They applied their model to 9 zero pressure gradient data sets obtained by different authors during the last 2 years, founding that all the experimental results were described properly when their model was utilized. In this paper, experiments for different tripping devices performed at LAS BT Cottbus were then analyzed with respect to Barenblatt et al. (2) theory. Also the mean velocity profiles in the overlap region were compared with a recent power law proposed by Zagarola and Smits (1998). Therefore, the primary purpose of the present work is to report the effect of different tripping devices on the streamwise mean velocity distribution in flat-plate turbulent boundary layer flows. Of particular interests are the measurements within the so-called overlap region and the wake region as well to explore some issues with scaling the mean flow field in both regions. Hence, measurements in turbulent boundary layers to complete information on the behavior of the mean velocity distribution were conduced in turbulent boundary layers using laser-doppler anemometry. The experiments were carried out in a low speed wind tunnel test facility at LAS BT Cottbus for Re θ 1 3. Experimental conditions and techniques The boundary layer was generated in a closed loop wind tunnel along an aluminum flat plate and utilizing different tripping devices. The wind tunnel, Göttingen type, was designed for good performance up to m/s with a background turbulence intensity.% of the incident flow. The test section has dimensions of 1 6 mm (length width height). All measurements were conducted at 83 mm downstream from the leading edge (see Fig. 1) in a direction perpendicular to the plate using the laser-doppler anemometry (Flowlite-Dantec) working in a back-scattering mode. The dimensions of the LDA control volume are.2.2 mm (dx dy dz). A two-dimensional traversing mechanism (ISEL) having step size from.2 mm to mm was used to traverse the LDA control volume in both x and y directions. The mounted plate was made from an eloxide aluminum to avoid the unnecessary light scattering from the wall and to increase the resultant signal-to-noise ratio and it has dimensions of mm (length width height). A particle generator (Atomizer Aerosol Generator, AMT 23) was used to produce liquid particles with.3 µm diameter needed for seeding the LDA system. Depending on the mean flow velocity, data rates of 1-3 Hz were typically obtained. For computing the mean velocity of the local flow measurements, -2 samples were acquired at every measuring station. Three different tripping devices [DYMO brand embossing tape letter X (.7 mm, height width) and sandpapers of different heights (A:.17 1 mm and B: mm, height width)] were used to trigger the turbulent boundary layer. The first row was fixed across the plate in the spanwise direction 1 mm from the leading edge of the plate, see Fig. 1, and the second at 1 mm, however the third row was fixed directly in front of the first row. For each tripping device, measurements were performed at 9 flow velocities within the range 6-33m/s providing data for Re θ. It is worth noting that the working temperature was kept constant within ±1 C during all the measurements.

3 y 8.3 cm cm 1 cm x Leading edge Flow Laser tube, sending & receiving optics Tripping devices Fig. 1: Sketch showing the positions of the tripping devices and the measuring station. Results and analysis Apparently the objective of the present paper is to clarify the effects of different tripping devices and pressure gradients on the turbulent boundary layer characteristics using the laser- Doppler anemometry (LDA) for Re θ < 1 3. The laser-doppler anemometer was used first in a laminar boundary layer in conjunction with the Blasius (198) velocity distribution in order to make sure that the laser-doppler system gives the right velocity distribution. In the authors sense it was clear that the LDA data for zero pressure gradient boundary layer lie on the Blasius curve proving that the LDA system gives accurate results in fields with velocity gradients, at least, as far as the mean velocities are concerned. Hence, the laser-doppler system can be taken in all kinds of flows even where the Blasius curve does not exist. Thereafter, the boundary layer was tripped and turbulent boundary layer measurements were carried out for zero and slightly negative, i.e. favourable, pressure gradients. The wall friction velocity, u τ, needed for normalizing the wall distance, y =yu τ /ν, and the local velocity, =/u τ, was obtained by utilizing Clauser (196) chart with the logarithmic law constants κ =., B=.1 suggested by Fernholz and Finley (1996) since accurate near-wall data were hard to obtain. Then the measured velocity profiles for the turbulent boundary layer were analyzed with respect to the question of whether the velocity profile in the overlap region behaves in a logarithmic or in a power form. To provide a clear answer for this question and to see the effect of the Re θ on the mean velocity profile, the following diagnostic functions Ξ = y [ d dy ] & Γ = ( y )[ d dy ] (1) proposed by [Wosnik et al. (2) & Österlund (1999)] were utilized, representing the slope of the mean velocity profile described either by the log law or the power law. From Fig. 2, a constant behavior of Γ was observed for the wall distances y <.2δ, assuming that the power law is better for representing the mean velocity distribution in the overlap region. On the other hand, the log-law diagnostic function did not show a constant behavior in the overlap region, and therefore the log law is far from being optimum to represent the

4 mean velocity profile in the overlap region for the current range of Re θ. Moreover, the effect of the tripping device sand stripes B is clearer in Fig. 2b, by producing a highly turbulent boundary layer, and therefore a wider overlap region. It is also clear from Fig. 2b that the log law diagnostic function, Ξ, shows a quasi-constant behavior, proposing that the log law might be a proper selection for the overlap region at lower values of the, i.e. Re θ =33, when the boundary layer is well triggered. 8 (a) Re θ = 2 8 (b) Re θ = Ξ Ξ 2 2 Γ DYMO Brand Sand stripe A Sand stripe B Γ DYMO Brand Sand stripe A Sand stripe B y Fig. 2 Slope of the mean velocity profile versus the normalized wall distance for two different Re θ. Further processing of the data was carried out based on claim made by Barenblatt et al. [1997] that the von Kármán-Prandtl log law, =1/κ ln(y )B, is not appropriate for the mean velocity profile in the overlap region, and therefore they developed an algebraic scaling (power) law velocity profile using the inner wall scaling variables as follows: = C y γ (2) and based on the smooth pipe data of Nikuradse (1932), they estimated both constants, i.e. C and γ, to read as 1 C = ln Re and γ = 3 (2ln Re) (3) 3 2 as can be seen from equation (3), the power exponent (γ) and the multiplication constant (C) are Re-dependent. Hence, the present measurements were evaluated with respect to equation (2), which can be re-written as follows: = C y γ 1 ln γ C = ln y [ y ] = Ψ ()

5 sing the power law coefficients suggested by Barenblatt et al. (1997) and Zagarola & Smits (1998), the data are presented in Fig. 3a & b, respectively. In the (ln y, Ψ) plane, the experimental points, starting from y for various Re θ (Fig. 3a) lie on the solid line Ψ = ln(y ) when Barenblatt et al. (1997) constants, i.e. equation (3), were utilized. Therefore the scaling law proposed by them seems to be appropriate for representing the present boundary layer data for the current Re θ range. On the other hand, the data did not show agreement with the solid line Ψ = ln(y ) when the coefficients C=8.7 and γ=.137 recommended by Zagarola and Smits (1998) were used, see Fig. 3b. It is worth mentioning that both models from Barenblatt et al. (1997) and Zagarola and Smits (1998) were originally developed for the mean velocity profile in the turbulent pipe flow, however they seem to be applicable for use in a turbulent boundary layer with modified constants. Therefore, utilizing the present sets of data both constants, i.e. C & γ, for the power law were re-evaluated, resulting in better representation of the experimental data in the (Ψ, ln y ) plane as can be seen from Fig. 3c. 6. (a) Barenblatt et el. (1997) C = (1/ 3)lnRe / 2 γ = 3/ (2lnRe). (b) Zagarola et el. (1998) C = 8.7 γ =.137 ψ ψ = ln y ψ. ψ = ln y... 6 ln y ln y. (c) Present C = 8.7 γ =.1 Ψ. ψ = ln y ln y Fig. 3: The recalculated data in (ln y, Ψ) plane for Re θ 1 3 based on (a) Barenblatt et al. (1997), (b) Zagarola and Smits (1998) and (c) Present.

6 Figure a and b shows selected samples of the normalized mean velocity profiles for different tripping devices at the same Re θ. It is worth noting that is shifted up by for conven- ience of explanation. The effect of the different tripping devices was observed in the outer region of the mean velocity profile, particularly, for higher values of the Re θ. The data were fitted to the power law, =Cy γ, showing slight change in the power law constants with the way of triggering the turbulence for the lower range of Re θ. The change in the power law coefficients for y >2 were found to be more influenced by the tripping devices at the higher values of Re θ. It might be concluded that the power coefficients of the velocity profiles are lower with sand stripes B than those of others at higher Re θ. This change in power law constants with the tripping device might be interpreted as an effect of the size of vortices generated by the tripping devices. The effective height of the sand stripes B is almost 1 times the sand stripes A, producing larger vortices, which are not easy to disperse. Larger vortices might prevent the velocity growth near to the outer edge of the boundary layer. 3 3 (a) is shifted by (b) 3 3 is shifted by γ = C (y ) DYMO Brand C=8.29, γ=.12 1 C=6.7, γ=.196 Sand stripe A 1 C=8.338, γ=.1 C=6.662, γ=.19 Sandpaper B C=8.187, γ=.1 C=6.62, γ= y 2 γ = C (y ) DYMO Brand C=8., γ=.1 1 C=.289, γ=.227 Sand stripe A 1 C=8.337, γ=.18 C=.1, γ=.23 Sand stripe B C=8.69, γ=.1 C=6.1, γ= Fig. : The mean velocity profiles for different tripping devices at Re θ = 2 (a) and Re θ = 33 (b) y The effect of the pressure gradients is presented in Fig. a and b, while using the tripping device sand stripes B. The plate was mounted with three different angles of attack, namely,, 2, and. (a) 3 3 is shifted by 3 3 (b) is shifted by γ = C (y ) degree 1 C=8.13, γ=.13 C=6.369, γ= degrees 1 C=8.113, γ=.16 C=6.636, γ=.19 degrees C=8.1, γ= C=7.237, γ= y γ 2 = C (y ) degree C=8.22, γ=.17 1 C=6.8, γ=.18 2 degrees 1 C=8.68, γ=.11 C=7.2, γ=.168 degrees C=8.761, γ=.138 C=8.81, γ= Fig. : The mean velocity profiles for different pressure gradients at Re θ =1 (a) and 2 Re θ = (b) with sand stripes B. y

7 To assure the zero pressure gradient, the laminar velocity profile without tripping was checked against the Blasius analytical solution of the laminar boundary layer. The power law coefficients for y >2 were observed to slightly increase when the angle of attack increases. Barenblatt et al. (22) claimed that the power law exponent is close to.2 in the case of the zero pressure gradient turbulent boundary layer and less than.2 for the favorable (slightly negative) pressure gradient. This turns out to be in good agreement with the present experimental observation as can be seen from Fig. a and b. sing the inner-scaling variables, the data of the normalized velocity profiles were compared with both the power scaling law utilizing constants proposed by Zagarola & Smits (1998) (Fig. 6a) and with constants obtained by the present authors (Fig. 6b). Less agreement was observed when comparison was made against Zagarola & Smits (1998). On the hand, better agreement was obtained when the exponent of the power law was changed. 3 (a) 3 (b) = 8.7ln(y ).137 Re θ = = 8.7ln(y ).1 Re θ = Re θ = 27 1 Re θ = 27 Re θ = 2796 Re θ = 323 Re θ = 2796 Re θ = 323 = 8.7ln(y ).137 = 8.7ln(y ) y y Fig. 6: The normalized mean velocity profiles compared with the power scaling law (a) Zagarola and Smits (1998), and (b) Present. Conclusions and Final Remarks The effect of different tripping devices and pressure gradients on boundary layer characteristics were studied experimentally using the LDA. The normalized mean velocity profiles were found to fit the power law in the overlap region and the region adjacent to the outer edge of the boundary layer. The results indicated a dependence of the power-law coefficients upon the way of tripping the boundary layer. In addition, the effects of the tripping devices were found to be prominent at higher Re θ. The power law coefficients were observed to be lower as the angle of attach increased. The mean velocity profiles in the overlap region were compared as well with the power law using coefficients recommended by Barenblatt et al. (1997) and Zagarola & Smits (1998), showing good agreements with the earlier. Hence, the Reynolds number dependent coefficients suggested by Barenblatt et al. (1997) were found to be more appropriate for the measurements presented in this paper. The present results suggest also that the influence of the tripping devices should be taken into account while formulating a model for a turbulent boundary layer investigation. It should be noted also that all measurements will be in good agreement with the logarithmic law coefficients κ =., B=.1 in the overlap region for high enough Re θ since the friction velocity was obtained utilizing the Clauser chart with those coefficients. This raises the necessity of using a different method to

8 obtain the wall friction velocity, and therefore the oil film interferometry as a direct measuring technique for the wall shear stress will be used in the next phase to provide the wall friction velocity. This might offer new a prospective for investigating the mean flow scaling laws in the turbulent boundary layers under different flow regimes. Acknowledgments The present work has been supported by the German Academic Exchange Service (DAAD) for which the authors wish to express their sincere gratitude. References Blasius, 198: "Über Flüssigkeitsbewegung bei sehr kliner Reibung", Proc. Third Int. Math. Congr., Heidelberg, pp Barenblatt, G. I., Chorin, A. J., Prostokishin, V. M., 1997: "Scaling Laws for Fully Developed Turbulent Flow in Pipes: Discussion of Experimental Data", Proc. Natl. Acad. Sci. Vol. 9, Applied Mathematics, pp Barenblatt, G.I., Chorin, A.J., Prostokishin, V.M., 2: "Characteristic length scale of the intermediate structure in zero-pressure-gradient boundary layer flow", Proc. Nat. Acad. Sci. SA, 97, pp Barenblatt, G.I., Chorin, A.J., Prostokishin, V.M., 22: "A model of a turbulent boundary layer with a non-zero pressure gradient", Proc. Nat. Acad. Sci. SA, 99, pp Clauser, F.H., 196: "The turbulent boundary layer", Advances in Applied Mechanics,, pp.1 1. Fernholz, H.H., Finley, P.J., 1996: "The incompressible zero-pressure-gradient turbulent boundary layer: An assessment of the data", Prog. Aerospace Sci, 32, pp Gibbings, J.C., El-Shukri, A.M., 1999: "Effects of sandpaper roughness and stream turbulence on the turbulent boundary layer", Proc Inst. Mech Engrs., 213, part C, pp Nikuradsa, J., 1932: "Gesetzmssigkeiten der Turbulenten Strömung in glatten Rohren, Forschungsh", Ver deutsch. Ing., 36. Österlund, J.M., 1999: "Experimental studies of zero pressure-gradient turbulent boundary layer flow", Ph.D. Theses, Royal Inst. Of Technology, Stockholm, Sweden. Wosnik, M., Castillo, L., and George, W., 2: "A Theory for Turbulent Pipe and Channel Flows", J. Fluid Mech, 21, 11. Zagarola, M. V., and Smits, A. J., 1998: "Mean-Flow Scaling of Turbulent Pipe Flow", J. Fluid Mech, 373, pp

Log laws or power laws: The scaling in the overlap region

Log laws or power laws: The scaling in the overlap region M.V. Zagarola Creare Inc., P.O. Box 71, Hanover, NH 03755 A.E. Perry Department of Mechanical and Manufacturing Engineering Melbourne University,