Spatial characteristics of a zero-pressure-gradient turbulent boundary layer in the presence of free-stream turbulence

Particle image velocimetry (PIV) measurements are performed to examine the structural organization inside a turbulent boundary layer under the influence of free-stream turbulence (FST). In particular, streamwise-wall-normal plane PIV measurements are presented for two cases at two different turbulent intensity levels (about 13% and 8%). The free-stream turbulence is generated using an active grid in a wind tunnel. The statistical information of the flow regarding the wall-normal velocity and Reynolds shear stress are presented. The effect of increasing the turbulence level in the free stream for these flows has been found to have similarities with increasing Reynolds number for high-Reynolds-number canonical flows. Quadrant analysis is performed to determine the contributions of different Reynolds-stress-producing events. In this regard, the distribution of momentum transport events shows some similarity with channel flows, which can be justified by comparison of similar intermittency characteristics of both flows. In addition, the coherent structures found inside the boundary layer have inclined features that are consistent with the previous studies for canonical flows. The fact that the external disturbance, such as FST in this study, does not alter the organization of the structures inside the boundary layer supports the growing evidence for a universal structure for wall-bounded flows.

Figure 1

Schematic of the test section with illuminated field of view (not to scale).

Figure 2

(a) Mean and (b) variance profiles of the streamwise velocity component in inner scaling from the present PIV measurements and hot-wire measurements from Dogan et al. [5]. Canonical cases from the literature are included for comparison. Dashed line in panel (a) is the log law with coefficients $\kappa =0.384$ and $B=4.4$. Markers on the PIV data curve are undersampled for clarity.

Figure 3

Mean wall-normal velocity profile in (a) inner scaling, (b) outer scaling as proposed by Wei and Klewicki [23]. Markers on the PIV data curve are undersampled for clarity. Case B: filled diamond, case D: filled square.

Figure 4

Variance profiles of the wall-normal velocity fluctuations. The ordinates show the profiles as (left) normalized by inner scaling and (right) normalized by the variance of the free-stream streamwise velocity fluctuations (blue outlined). Markers on the PIV data curve are interpolated data points for clear representation. Case B: filled diamond, case D: filled square.

Figure 5

(a) Shear stress correlation coefficient and (b) inner-normalized Reynolds shear stress profiles. Markers on the PIV data curve are interpolated data points for clear representation. Case B: filled diamond, case D: filled square.

Figure 6

Contour plot of two snapshots of instantaneous inner-normalized Reynolds shear stress ($-u{v}^{+}$) for case B. The enclosed region shows the data from the field of view. Flow is from left to right as indicated by the arrow on top left.

Figure 7

Contour maps of the normalized PDF of $uv$. The ordinates show the wall-normal location in inner (left) and outer (right) scaling. (a) Case B, (b) case D.

Figure 8

Comparison of the PDFs of the two FST cases at two wall-normal locations (a) $y^{+}\approx 100$ (b) $y/\delta \approx 0.2$. Case B: filled diamond, case D: filled square.

Figure 9

Comparison of the PDFs of the normal Reynolds stresses for the two FST cases at two wall-normal locations, $y^{+}\approx 100$ and $y/\delta \approx 0.2$. Case B: filled diamond, case D: filled square.

Figure 10

Covariance integrands of $u$ and $v$ fluctuations for case B (orange) and case D (black) at various wall-normal locations: (a) $y^{+}\approx 32$, (b) $y^{+}\approx 100$, (c) $y/\delta \approx 0.1$, and (d) $y/\delta \approx 0.42$. Negative contours are shown with dashed lines. The outermost contour level and the increment are 0.01 and 0.01 for positive contours, respectively, and $-0.01$ and $-0.01$ for negative contours, respectively. Zero contours are not shown.

Figure 11

(a) Schematic illustrating quadrant splitting of the $u\text{−}v$ plane with shaded hole region. (b) Fractional contributions to the Reynolds shear stress by each quadrant at $y^{+}\approx 40$ for various hole sizes, $h$, for both FST cases. Symbols are explained in the legend.

Figure 12

Distribution of quadrant contributions based on the hole size of $h=2$ for both FST cases. Symbols are explained in the legend.

Figure 13

(a) Figure 12 replotted showing only Q2 and Q4 events for cases B and D, separately. (b) Distribution of the ratio Q2/Q4. Symbols are explained in the legend.

Figure 14

$R_{uu}$ correlation computed at different wall-normal locations. (a) $y^{+}\approx 55$ ($y/\delta \approx 0.01$), (b) $y^{+}\approx 100$ ($y/\delta \approx 0.02$), (c) $y^{+}\approx 320$ ($y/\delta \approx 0.065$), (d) $y^{+}\approx 500$ ($y/\delta \approx 0.1$), (e) $y/\delta \approx 0.4$. Orange line: case B, black line: Case D. Negative contours are shown with dashed lines. The outermost contour level and the increment are 0.1 and 0.05 for positive contours, respectively, and $-0.1$ and $-0.05$ for negative contours, respectively. Zero contours are not shown.

Figure 15

$R_{uu}$ correlation comparison for FST cases at different wall-normal locations as indicated on the plots. Representative contour level is 0.25. Canonical cases from the literature are included (where data are available) for comparison. Dashed line: ${\text{Re}}_{\tau }=4000$ from Gomit et al. [41], dot-dashed line: ${\text{Re}}_{\tau }=1100$ from the present study case without FST.

Figure 16

Comparison of the inclination angle, ${\theta }_L$, obtained through hot-wire and PIV measurements. Symbols are explained in the legend.

Figure 17

(Top) $R_{uu}$, (middle) $R_{vv}$, and (bottom) $R_{uv}$ correlations at (left) $y/\delta \approx 0.06$ and (right) $y/\delta \approx 0.4$ for both FST cases in comparison with the canonical cases from the literature. Dashed line: ${\text{Re}}_{\tau }=4000$ from Gomit et al. [41], dot-dashed line: ${\text{Re}}_{\tau }=1100$ from the present study case without FST.

Figure 18

Wall-normal variation of (a), (c) streamwise and (b), (d) wall-normal length scales based on $R_{uu}=0.5$ and $R_{vv}=0.5$ for both FST cases. Case B: filled diamond, case D: filled square.

Figure 19

Wall-normal variation of Taylor microscale for both FST cases. Case B: filled diamond, case D: filled square.