Near wall turbulence: An experimental view

The present paper draws upon the experience of the author to illustrate the potential of advanced optical metrology for understanding near-wall-turbulence physics. First the canonical flat plate boundary layer problem is addressed, initially very near to the wall and then in the outer region when the Reynolds number is high enough to generate an outer turbulence peak. The coherent structure organization is examined in detail with the help of stereoscopic particle image velocimetry (PIV). Then the case of a turbulent boundary layer subjected to a mild adverse pressure gradient is considered. The results obtained show the great potential of a joint experimental-numerical approach. The conclusion is that the insight provided by today's optical metrology opens the way for significant improvements in turbulence modeling in upcoming years.

This article appears in the following collection:

Figure 1

Instantaneous visualization of a turbulent boundary layer at high Reynolds number using smoke and a YAG laser light sheet.

Figure 2

Turbulence intensity components in a flat plate turbulent boundary layer, obtained from HWA. $\blacksquare {\text{Re}}_{\theta }=20800,$ Carlier and Stanislas [5]; + Klebanof [6], × Erm and Joubert [7], and DNS Spalart [8].

Figure 3

Horseshoe vortex model of Theodorsen reproduced from Ref. [9].

Figure 4

Near wall streaks visualization using the bubble wire technique by Kline et al., reproduced from Ref. [10].

Figure 5

Model of near wall organization by Blackwelder and Kaplan, reproduced from Ref. [15].

Figure 6

Model of hairpin packets of Adrian, reproduced from Ref. [17].

Figure 7

Premultiplied spectra as a function of wavelength and wall distance at two Reynolds numbers showing the development of the outer turbulence peak when the Reynolds number increases, reproduced from Ref. [21].

Figure 8

Sketch of the flow over an airfoil at low angle of attack emphasizing the TBL in the APG region on the suction side.

Figure 9

Instantaneous map of the streamwise velocity fluctuations in a high-Reynolds-number turbulent boundary layer [25].

Figure 10

Photo of the boundary layer wind tunnel at Laboratoire de Mécanique de Lille (LML).

Figure 11

Correlation in a plane parallel to the wall between the low-speed streaks and the ejections (left) or sweeps (right), reproduced from Ref. [35].

Figure 12

Correlation in a plane parallel to the wall between the high-speed streaks and the ejections (left) or sweeps (right), reproduced from Ref. [35].

Figure 13

Correlation at different wall distances between the low-speed streaks and the negative vortices (left) and between the high-speed streaks and the same negative vortices (right), reproduced from Ref. [35].

Figure 14

Correlation at different wall distances between the ejections and the negative vortices (left) and between the sweeps and the same negative vortices (right), reproduced from Ref. [35].

Figure 15

Model of very near wall organization in a plane parallel to the wall below $y^{+}=50$.

Figure 16

Model of Schoppa and Hussain, reproduced from Ref. [39].

Figure 17

Visualisation of streaks (yellow), vortices below $y+=50$ (blue), and vortices above $y+=50$ (red) in a DNS of channel flow at Re = 600 from [65] (2009).

Figure 18

Model of near wall organization.

Figure 19

Spatial organization of coherent structures obtained by Dekou et al., reproduced from Ref. [49]. Positive and negative vortices are highlighted in red and blue respectively while low- and high-momentum regions are highlighted in green and yellow respectively.

Figure 20

Spanwise correlation of the positive vortical motions and the low-momentum regions (left), the high-momentum regions (right) plotted at different wall-normal positions at Re = 9830, reproduced from Ref. [49]. Black, $0.037\delta$; blue, $0.14\delta$; green, $0.27\delta$; and red, $0.55\delta$.

Figure 21

Model of outer organization of Dekou et al., reproduced from Ref. [49].

Figure 22

Cuts of the wall pressure and streamwise velocity fluctuation correlation $Rpu$ in the $\mathrm{\Delta }ty$ plane at $z/\delta =0$ and at ${\text{Re}}_{\theta }=10000$ with (a) $p>0$ and (b) $p<0$. Reproduced from Ref. [52].

Figure 23

Cuts of the $Rpu,Rpv,Rpw$ wall pressure and velocity fluctuations correlations in the $zy$ plane at (a) $\mathrm{\Delta }t/Ue=-1.46$, (b) $\mathrm{\Delta }t/Ue=-0.46$, (c) $\mathrm{\Delta }t/Ue=0.00$, (d) $\mathrm{\Delta }t/Ue=0.16$, (e) $\mathrm{\Delta }t/Ue=0.36$, and (f) $\mathrm{\Delta }t/Ue=0.96$ and at ${\text{Re}}_{\theta }$ =10 000 with $p>0$. Reproduced from Ref. [52].

Figure 24

Cuts of the field pressure and streamwise velocity fluctuation correlation $Rpu$ in the $\mathrm{\Delta }ty$ plane at $z/\delta =0$ and at (a) ${\text{Re}}_{\theta }=7300,{y_p}^{+}=28$, (b) ${\text{Re}}_{\theta }=10000,{y_p}^{+}=48$, and (c) ${\text{Re}}_{\theta }=18000,{y_p}^{+}=85$. Reproduced from Ref. [52].

Figure 25

Model of spectra including an extra range of large scales between $1/{\delta }_{\infty }$ and $1/{\delta }_{*}$, reproduced from Ref. [53].

Figure 26

Set of high-Reynolds-number facilities used in Ref. [55] to validate the model developed by Vassilicos et al., reproduced from Ref. [53].

Figure 27

Streamwise turbulence intensities as a function of wall distance and for different Reynolds numbers. Comparison between the model (symbols) and the experimental data (lines) from the facilities of Fig. 26. Reproduced from Ref. [55].

Figure 28

Streamwise evolution of the streamwise turbulence intensity profile in a turbulent boundary layer under adverse pressure gradient from different experiments and DNS, collected by Shah et al. The reference velocity $Uo$ is the external velocity at the beginning of the APG region. The wall-normal coordinate is scaled with the kinematic viscosity and the friction velocity at the beginning of the APG region. Reproduced from Ref. [61].

Figure 29

Prediction of the turbulence intensity profiles in the diverging part of a converging-diverging turbulent channel flow using an EB-RSM turbulence mode [62]. Lines, model; symbols, DNS data from Marquillie et al., reproduced from Ref. [63].

Figure 30

Sketch of a simplified model simulating the flow on the suction side of an airfoil.

Figure 31

$Q$-criterion visualization of the vortical structures generated near the wall in a DNS of converging-diverging plane channel flow, reproduced from Ref. [65].

Figure 32

Visualization of the low-speed streak generated near the wall in a DNS of converging-diverging plane channel flow, reproduced from Ref. [66]. The black frame gives the typical size of the window on which averaging of the streaks is performed.

Figure 33

Visualization of the vortical structures generated at the origin of the outer turbulence plume in a DNS of converging-diverging plane channel flow, reproduced from Ref. [66]. Left, vorticity; right, $Q$ criterion.

Figure 34

APG ramp model of the EUHIT experiment, reproduced from Ref. [69].

Figure 35

Streamwise pressure gradient distribution along the EUHIT APG ramp model, reproduced from Ref. [69].

Figure 36

Instantaneous plot of the streamwise component of the velocity fluctuations in the APG field of view of the EUHIT experiment.

Figure 37

Turbulence intensity profiles in the diverging part of the EUHIT experiment, measured by 2D2C PIV by Cuvier et al., reproduced from Ref. [69]. (a) Streamwise turbulence intensity, (b) wall normal turbulence intensity, (c) turbulent shear stress, (d) same measurements near the wall at station $s=5.6$ m using high-magnification time-resolved PIV [69]. Wall scaling of panel (c) is based on the local skin friction at $s=5.6$ m, ${\delta }_0$ is the boundary layer thickness at s = 1.36 m, and $U_{\infty }$ the free stream velocity upstream of the ramp.

Figure 38

Scaling of the mean velocity profile in the EUHIT experiment based on Ref. [23]. $U_e$, external velocity; ${\delta }^{*}$, displacement thickness; and ${\delta }_{90}$, boundary layer thick ness at 90% of $U_e$.

Figure 39

Scaling of the pressure gradient in the EUHIT experiment. Following Ref. [22], the slope of the curve is the parameter $\mathrm{\Lambda }$ defined by Eq. (5).