Effects of large-scale free stream turbulence on a turbulent boundary layer
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1 Effects of large-scale free stream turbulence on a turbulent boundary layer Nicole S. Sharp Cornell University Presented in partial completion of the requirements for the degree of Master of Science in Aerospace Engineering 6 February 9
2 N. S. Sharp 6 February 9 M.S. Defense Introduction The turbulent boundary layer
3 N. S. Sharp 6 February 9 M.S. Defense Introduction L/δ = ratio of free stream lengthscale to boundary layer depth FSTI = free stream turbulence intensity = (<u > / /U)
4 Introduction N. S. Sharp 6 February 9 M.S. Defense
5 Previous Work Hancock and Bradshaw (983, 989) Intensities < 6% Re θ >, Studied Mean flow characteristics Variances Conditional averaging Correlated some variables using an empirically determined parameter, β u u L e U / 3/ u L u e U d u dx P. E. Hancock and P. Bradshaw, The effect of free-stream turbulence on turbulent boundary layers, J. Fluids Engi. 5, 983. P. E. Hancock and P. Bradshaw, Turbulence structure of a boundary layer beneath a turbulent free stream, JFM, 5, 989. N. S. Sharp 6 February 8 M.S. Defense
6 N. S. Sharp 6 February 8 M.S. Defense Previous Work Thole and Bogard (996) Intensities < % Re θ ~ 6 Studied Mean flow characteristics Variances Cross-correlation Length scales Spectra Found integral length scales at free stream values until y/δ ~.3 K. A. Thole and D. G. Bogard, High free stream turbulence effects on turbulent boundary layers, J. Fluids Engi., 8, 996.
7 N. S. Sharp 6 February 8 M.S. Defense Experimental Set-Up Active grid introduces large-scale turbulent eddies higher Re λ Plate is 3M downstream to allow development of FST
8 Results Law of the Wall 5 8 Cases Re = < Re λ < 55 u + 5 Re = 6 Re = 6 Re = 6.5% < FSTI <.5% Re = 45 Re = 5 Re = < Re θ < 84 Re = 55 DeGraaff & Eaton () N. S. Sharp 6 February 8 M.S. Defense
9 N. S. Sharp 6 February 8 M.S. Defense Results 5 Law of the Wall u + 5 Re λ 6 55 U (m/s) FSTI.5% 8.%.% Re θ Re = Re = 6 Re = 55 DeGraaff & Eaton () Re τ Grid none active, off active, on 5 4
10 N. S. Sharp 6 February 8 M.S. Defense Velocity Variances Normalized <u > Profiles Normalized <v > Profiles Normalized <uv> Profiles Re = Re = Re = Re = 6 3 Re = 6. Re = 6 8 Re = 55 Re = 55 Re = 55 DeGraaff & Eaton ().5 DeGraaff & Eaton () DeGraaf & Eaton () <u > / u 6 4 <v > / u.5.5 <uv> / u Velocity variances and covariance show trends in agreement with previous investigations. D. B. DeGraaff and J. K. Eaton, Reynolds-number scaling of the flat-plate turbulent boundary layer, J. Fluid Mech. 4,.
11 N. S. Sharp 6 February 8 M.S. Defense Cross-Correlation.4 Correlation Coefficient Profiles <uv> / <u > / <v > /. -. Re = Re = 6 Re = 55 DeGraaff & Eaton () Penetration of uncorrelated u- and v-components of FST decreases the crosscorrelation coefficient throughout the boundary layer D. B. DeGraaff and J. K. Eaton, Reynolds-number scaling of the flat-plate turbulent boundary layer, J. Fluid Mech. 4,.
12 <u > / <v > N. S. Sharp 6 February 8 M.S. Defense <(du/dx) > / <(dv/dx) > Anisotropy Large-Scale Anisotropy Profiles Small-Scale Anisotropy Profiles 6.8 Re = Re = Re = Re = 6 Re = 55 Re = FST increases levels of anisotropy throughout the boundary layer at both the large- and small- (derivative) scales.
13 N. S. Sharp 6 February 8 M.S. Defense Skewness Large-Scale U-Direction Skewness Profiles Large-Scale V-Direction Skewness Profiles.5 <u 3 > / <u > 3/ <v 3 > / <v > 3/.5 Re = Re = 6 Re = 6 Re = Re = Re = 6 Re = 6 Re = FST smears out the statistical effects of transition between a boundary layer and the free stream.
14 N. S. Sharp 6 February 8 M.S. Defense Kurtosis Large-Scale U-Direction Kurtosis Profiles Large-Scale V-Direction Kurtosis Profiles 5 Re = Re = 5 Re = 6 Re = 6 Re = 55 Re = 6 Re = 6 Re = 55 5 <u 4 > / <u > <v 4 > / <v > Boundary layers with FST have u- and v-direction kurtosis values very near 3, indicating essentially Gaussian behavior at the largescale.
15 Derivative Skewness U-Direction Derivative Skewness Profiles V-Direction Derivative Skewness Profiles Re = Re = Re = 6 Re = 6.8 Re = 6.5 Re = 6 Re = 55 Re = 55 <(du/dx) 3 > / <(du/dx) > 3/.6 <(dv/dx) 3 > / <(dv/dx) > 3/ FST smears out the statistical effects of transition between a boundary layer and the free stream. N. S. Sharp 6 February 8 M.S. Defense
16 N. S. Sharp 6 February 8 M.S. Defense Derivative Kurtosis <(du/dx) 4 > / <(du/dx) > 4 U-Direction Derivative Kurtosis Profiles V-Direction Derivative Kurtosis Profiles 8 3 Re = Re = 6 Re = 6 Re = 6 5 Re = 6 Re = 6 4 Re = 55 Re = 55 <(dv/dx) 4 > / <(dv/dx) > Unlike at the large-scale, the derivative kurtosis in the u- and v- directions show strongly non-gaussian behavior.
17 E ( ) / u N. S. Sharp 6 February 8 M.S. Defense Power Spectra Spectral Evolution for Re = 6 Spectral Evolution for Re = 55 Spectral Evolution for Re = 7 = 7 = 534-5/3 5 = 75 = -5/3 5 = 3 = -5/3. = 67 = 5 E ( ) / u E ( ) / u = 5. = 5. = = 4 = = 5 = = 5 =
18 N. S. Sharp 6 February 8 M.S. Defense Energy Spectra: Canonical Canonical boundary layer shows two peaks in the energy spectra u x Inner peak: λ x + ~ Outer peak: λ x ~ 6δ x Hutchins N, and Marusic I. Largescale influences in near-wall turbulence. Phil. Trans. R. Soc. A. v. 365, 7.
19 N. S. Sharp 6 February 8 M.S. Defense Energy Spectra: Non-Canonical Re λ = Re λ = 6 Re λ = 55 Normalized Spectrum for R =, Re = 45 y/ ~.6 Normalized Spectra for R = 6, Re = 95 y/ ~.5.4 Normalized Spectra for R = 55, Re = y/ ~ E / u E / u E / u.6 + ~ ~ ~ ~ ~ 9 ~ 9... /.. /... / Inner peak: λ x + ~ Inner peak: λ x + ~ Inner peak: λ x + ~ 9 Outer peak: λ x ~ 6δ Outer peak: λ x ~ 5δ Outer peak: λ x ~ 9δ
20 N. S. Sharp 6 February 8 M.S. Defense Evolution of Spectra Inner peak fades further from the wall, indicating the presence of a scale native to the boundary layer. E ( ) / u = 75 = 5 = 375 = 75 Evolution of Energy Spectra Increasing Re λ = 6.. /
21 Evolution of Spectra, Re λ = λ / δ κ E /u τ 3D View from Side λ / δ. Contour View from Top N. S. Sharp 6 February 8 M.S. Defense.
22 Evolution of Spectra, Re λ = 6 λ / δ κ E /u τ 3D View from Side λ / δ.4 Contour View from Top N. S. Sharp 6 February 8 M.S. Defense.
23 Evolution of Spectra, Re λ = 55 λ / δ κ E /u τ 3D View from Side λ / δ.6 Contour View from Top N. S. Sharp 6 February 8 M.S. Defense.
24 λ / δ Evolution of Spectra. Re λ =..4 κ E /u τ Re λ = 6..6 Re λ = 55 λ / δ. N. S. Sharp 6 February 8 M.S. Defense
25 N. S. Sharp 6 February 8 M.S. Defense Conclusions Observed effects of free stream turbulence on structure throughout the boundary layer Found that FST affected higher-order moments at the large- and the small-scale throughout the boundary layer. Matched findings of Hutchins and Marusic for near-canonical boundary layer case Observed two broadened peaks rather than three distinct peaks in energy spectra of boundary layers with free stream turbulence Noted complex interactions between free stream and boundary layer structure extending even below =
26 N. S. Sharp 6 February 8 M.S. Defense Image Credits Some images used in this presentation are not under the author s copyright. The sources for these are acknowledged below: Slide Large eddies in a turbulent boundary layer, M. Gad-el-Hak, Virginia Commonwealth University, Slide 4 Turbomechanical figure from Wu, Jacobs, Hunt, and Durbin. JFM, v. 398, 999. Turbomachinery visualization, Mitsubishi, Boundary layers in atmosphere, Caroline Bain, University of Leeds, Wind turbines, Rochester Solar Technologies, Slide 6 K. A. Thole and D. G. Bogard, High free stream turbulence effects on turbulent boundary layers, J. Fluids Engi., 8, 996.
27 N. S. Sharp 6 February 8 M.S. Defense Acknowledgements The author would like to thank the following individuals for their assistance and support: Stephanie Neuscamman Joseph Shoer Juan Isaza Erika Johnson Doug Kutz Sergiy Gerashchenko My Special Committee My Family This work was funded by the National Science Foundation.
28 Unforeseen Delays N. S. Sharp 6 February 8 M.S. Defense
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