Session R19: Boundary Layers VIII: Experimental

Large field of view multi-resolution experimental measurement of the spatial structure of a high Reynolds number turbulent boundary layer

A multiple camera, multiple resolution PIV system consisting of nine highe resolution cameras and two dual cavity lasers is used to instantaneously measure a large streamwise, wall-normal field of view (2$\delta \times 1.5\delta$), while simultaneously resolving the near-wall flow down to a height of y $+ \approx$ 3 at Reynolds numbers of Re$\tau \approx $ 8, 000 to 30, 000. The high spatial resolution in the near-wall vicinity enables direct estimation of the wall shear stress and allows for subsequent and conditional analysis of both the near-wall and larger outer flow structures and fluctuations. The quality of this measurement is assessed via statistical comparison with previous measurements made using hot-wire anemometry and compared with the highest available Reynolds number DNS. Conditional two-point correlations, and conditional mean structures will be presented.   

Turbulence measurements in high Reynolds number boundary layers

Measurements are conducted in zero pressure gradient turbulent boundary layers for Reynolds numbers from Re$_{\theta} =$ 9,000 to 225,000. The experiments were performed in the High Reynolds number Test Facility (HRTF) at Princeton University, which uses compressed air as the working fluid. Nano-Scale Thermal Anemometry Probes (NSTAPs) are used to acquire data with very high spatial and temporal precision. These new data are used to study the scaling behavior of the streamwise velocity fluctuations in the boundary layer and make comparisons with the scaling of other wall-bounded turbulent flows.   

Effect of pressure gradient fluctuations on boundary layer turbulence

The present study focuses on the effect of large-scale pressure gradient fluctuations on turbulence in both, zero pressure gradient (ZPG) and mean favorable pressure gradient (FPG) boundary layers. Time-resolved, two-dimensional PIV data in the streamwise-wall-normal plane enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the material acceleration of the fluid. In both boundary layers, sweeps (u$^{\prime} $\textgreater\ 0, v$^{\prime} $\textless\ 0) mostly occur during periods of adverse pressure gradient fluctuations ($\partial $p$^{\prime} $/$\partial $x \textgreater\ 0), while favorable pressure gradient fluctuations ($\partial $p$^{\prime} $/$\partial $ x \textless\ 0) accompany ejections (u$^{\prime} $\textless\ 0, v$^{\prime} $\textgreater\ 0). Conditional averaging indicates that in the ZPG boundary layer, large-scale $\partial $p$^{\prime} $/$\partial $x \textgreater\ 0 events accompanying sweeps lead to the formation of a growing region of ejection downstream, in a phenomenon resembling adverse-pressure induced flow separation. This phenomenon is much less pronounced in the FPG boundary layer, as the large-scale $\partial $p$^{\prime} $/$\partial $ x \textgreater\ 0 events are for the most part significantly weaker than the mean FPG. Conditional sampling and instantaneous data in the ZPG boundary layer also confirm that although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps, others are not. In the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. The mechanisms initiating these structures presumably occur far upstream of the peak in favorable pressure gradient fluctuations.   

Boundary layer response to periodic spanwise perturbation by an array of obstacles

Hot-wire and stereoscopic particle image velocimetry (SPIV) measurements were performed on zero pressure gradient turbulent boundary layers perturbed by a single array of cylinders extending into the log region. The array spacing had a strong effect on the resulting vortex packet organization. With $0.6\delta $ array spacing, incoming vortex packets are frequently enhanced and remain stable over a downstream distance of $7\delta $. On the other hand, a $0.2\delta $ spacing strongly disturbed incoming packets initially, but the incoming organization frequently reappeared by $2\delta $ downstream. Measurements indicate that the effect of the perturbation is strongest in the mid-span location between array elements. Furthermore, hot-wire measurements suggest that the strongest velocity perturbations migrate upwards with increasing downstream distance. SPIV results in streamwise-spanwise planes at different heights will be compared to show how structural aspects of the perturbation vary with downstream distance.   

Latest Developments on Obtaining Accurate Measurements with Pitot Tubes in ZPG Turbulent Boundary Layers

Ability of available Pitot tube corrections to provide accurate mean velocity profiles in ZPG boundary layers is re-examined following the recent work by Bailey {\it et al}. Measurements by Bailey {\it et al.}, carried out with probes of diameters ranging from 0.2 to 1.89 mm, together with new data taken with larger diameters up to 12.82 mm, show deviations with respect to available high-quality datasets and hot-wire measurements in the same Reynolds number range. These deviations are significant in the buffer region around $y^{+}=30-40$, and lead to disagreement in the von K\'arm\'an coefficient $\kappa$ extracted from profiles. New forms for shear, near-wall and turbulence corrections are proposed, highlighting the importance of the latest one. Improved agreement in mean velocity profiles is obtained with new forms, where shear and near-wall corrections contribute with around 85\%, and remaining 15\% of the total correction comes from turbulence correction. Finally, available algorithms to correct wall position in profile measurements of wall-bounded flows are tested, using as benchmark the corrected Pitot measurements with artificially simulated probe shifts and blockage effects. We develop a new scheme, $\kappa B-$Musker, which is able to accurately locate wall position.   

Direct measurement of the velocity joint probability density function and higher order moments in turbulent boundary layer flows

This work shows how the joint probability density function (JPDF) of the streamwise and wall normal velocity components of a zero-pressure gradient turbulent boundary layer (ZPG-TBL) can be directly measured using the methodology and theoretical framework proposed by Soria \& Willert (2012) MST 23, 065301. Higher order moments including Reynolds stresses can be computed directly from two-component (2C) JPDFs of the streamwise and wall normal velocity components by taking moments of the 2C-JPDF. The base data for the direct measurement of the 2C-JPDF are single-exposed image pairs typically used to determine instantaneous 2C-2D particle image velocimetry (PIV) fields. However, in the new direct measurement method, the instantaneous velocity samples necessary to build up the JPDF never need to be determined, which avoids the problems in PIV due to large velocity gradients that are typically encountered in turbulent wall-bounded flows. This new method has been applied to single-exposed image pairs acquired over a range of Reynolds numbers ranging up to $Re_{\tau} = 19500$ in ZPG-TBL experiments. This paper presents directly measured 2C-JPDFs across the ZPG-TBL as well as higher moment distributions determined from these 2C-JPDFs.   

Measurement of entropy generation within bypass transitional flow

A flat plate made from quartz was submersed in the Idaho National Laboratory's Matched Index of Refraction flow facility. Particle Image Velocimetry and Particle Tracking Velocimetry were utilized to capture spatial vector maps at near wall locations \textit{within a transitional boundary layer}. Entropy generation was then calculated directly from measured velocity vector fields using an integral approach. Two flows were studied: a Zero Pressure Gradient (ZPG) and an Adverse Pressure Gradient (APG), with $\beta $ $\approx$ -0.039. Near the leading edge of the plate, the free stream turbulence intensity (FSTI) to drive bypass transition was 7.5\% and 4.25\% for the ZPG and APG, respectively. Towards the downstream side of the plate, the FSTI was 2.5\% and 3\% for ZPG and APG, respectively. The integral approach for entropy generation rate, within the transitional region of flow, will be utilized as a design parameter to systematically reduce losses. As a second observation, the entropy generation can be shown to predict the onset of transitional flow.   

Logarithmic Boundary Layers in Strong Taylor-Couette Turbulence

We provide direct measurements of boundary layer profiles in highly turbulent Taylor-Couette flow up to $Re = 2 \times 10^6$ using high-resolution particle image velocimetry and particle tracking velocimetry, complemented by DNS data on the same system up to $Re = 10^5$. We find that the mean azimuthal velocity profile at the inner and outer cylinder can be fitted by the von K\'arm\'an log law, but with corrections due to the curvature of the cylinder, which we theoretically account for, based on the Navier-Stokes equation and a closure assumption for the turbulent diffusivity. In particular, we study how these corrections depend on the cylinder radius ratio and show that they are different for the boundary layers at the inner and at the outer cylinder.   

Logarithmic region of turbulent boundary layer from low to high Reynolds numbers

Recent high Reynolds number experiments indicate that von Karman constant ($\kappa )$ is close to 0.38. In the classical moderate Reynolds number experiments, however, show the value of $\kappa =$0.41. In this study we would like to discuss the discrepancy between these two values. Analyzing the data in the range of 1500\textless Re$_{\mathrm{\theta }}$\textless 27300, we suggest the idea of Quasi Logarithmic Region (QLR) in which the log law is approximately satisfied and discuss the above issue. Using the QLR, we report the Reynolds number dependence of $\kappa $, and recommend the appropriate log-law region.