Session PA: Turbulent Boundary Layers: Complex

Mean Flow and Wall Shear Measurements in Turbulent Boundary Layers with Various Imposed Complex Pressure Gradients

Mean flow velocity profiles with miniature Pitot probes, and wall-shear stress measurements with oil film interferometry, are used to document the development of high Reynolds number turbulent boundary layers on a flat plate under the influence of four different complex pressure gradients. The National Diagnostic Facility (NDF) is uniquely suited for establishing and documenting such flow conditions to serve as grounds for testing various turbulence models in well-known, two-dimensional boundary layers. Each of the four conditions starts with a zero pressure gradient and returns to it again along the test section. Two of the conditions include an adverse gradient region followed by a favorable one, and the other two cases experience the same two effects in the opposite sequence but to comparable magnitudes of free-stream velocity variations. The mean velocity profiles are measured and used to determine parameters such as the shape factor, the logarithmic overlap-region parameters, and the wake or outer flow parameters. The effect of the initial boundary layer conditions on the development of such complex flows is also examined by changing the position of the pressure gradient ``hump'' between two sets of two opposite gradients conditions. The results will be briefly compared to computations at IIT of nearly the same flow conditions.   

Computations of Turbulent Boundary Layers Subjected to Various Localized Pressure Gradients

Four different localized pressure gradient configurations were computed using a commercially available code by means of four RANS turbulence models (SA, $k-\epsilon$, SST and RSM), and compared with experimental measurements of the mean flow quantities and the wall shear stress. The pressure gradients were imposed on high Reynolds number, 2-D turbulent boundary layer developing on a flat plate by changing the ceiling geometry. Two converging humps (at $x=2m$ and $x=5.5m$ from the leading edge of the plate) and two diverging humps at the same locations were considered. The SST model produced the best agreement with experiments. A complimentary study about how the models deal with numerical transition was done by solving a zero pressure gradient (ZPG) configuration. We find that the major differences between the results from the models when predicting mean flow quantities are essentially produced by the numerical transition process. This process does not belong to the models themselves, and it is a procedure by which the software transforms the simple laminar boundary conditions at the inlet into inflow conditions which characterize the turbulent flow when turbulence has already been developed. Therefore, models requiring the simplest inflow conditions lead to better results and consequently models such as the RSM suffer the most and ultimately lead to inferior results.   

Two-point correlations of adverse pressure gradient turbulent boundary layer at high Reynolds number

Two-point correlations are analyzed to investigate structure of adverse pressure gradient turbulent boundary layer at high Reynolds number. The experiment was carried out in the large wind tunnel of Laboratoire de M\'{e}canique de Lille (LML) using synchronized PIV systems and a hot-wire rake of 143 single probes. A specially designed, 30 cm thick, bump was used to obtain the decelerating flow within the test section of the wind tunnel. The thickness of the boundary layer was about 30 cm and Reynolds number based on momentum thickness, Re$_{\theta}$, was 30 000 for 10 m/s external free stream velocity. Simultaneously measured hot-wire data show that extent of the two-point correlations on streamwise -- spanwise plane in this flow is similar to that computed for flat plate turbulent boundary layers case(J. Turbulence, Vol 10, No 21, pp 1-23, 2009). Two-point correlations are also studied on streamwise -- wall-normal plane. Shape of the correlations in this plane, especially in the outer layer, is found to be different than those for flat plate turbulent boundary layer.   

Structures of turbulent boundary layers with adverse pressure gradients

Turbulent structures in spanwise/wall-normal plane of the turbulent boundary layers (TBLs) subjected to adverse pressure gradients (APGs) were investigated by analyzing the DNS database of Lee {\&} Sung (2009). Probability density functions of the strength of the vortex cores normalized by their r.m.s. values displayed that strong swirling motions are frequently observed on the APG TBLs than zero pressure gradient TBLs. Influence of APGs on the population trends of spanwise vortex cores showed that those have a local maximum at the outer region for APG TBLs which might be due to the maximum Reynolds shear stress. Moreover, two-point correlations and linear stochastic estimations were scrutinized to provide statistical evidence for hairpin packet motions in the vertical plane of the TBLs with APGs. We found that wall-normal extent of the contours is elongated vertically owing to the strong swirling motion of the individual vortex located in the wake region or wake-type detached structures.   

Experimental investigation of turbulent sink flow boundary layers

Our objective is to study near wall structures in turbulent boundary layers on smooth walls under favorable pressure gradient. A sink flow is generated in a refractive index matched facility by means of an inclined upper wall. 2D-PIV measurements have been performed, initially at a coarse resolution of 320 $\mu $m, to characterize the mean flow and Reynolds stresses, for a constant acceleration parameter, \textit{K=$\nu $dU/dx/U}$^{2}$, of 0.5 X10$^{-6}$. \textit{Re}$_{\theta }$ drops from 5300 to 2600 over the 260 mm long accelerating range. Consistent with prior studies, acceleration thins the boundary layer. Trends of Reynolds stress vary in the literature. In our data, acceleration increases the magnitude of Reynolds stresses in outer parts of the boundary layer and decreases it in inner parts. An upsurge in all stresses occurs below 200 wall units in later stages of acceleration. When non-dimensionalized with local free-stream or friction velocity, the Reynolds stresses drop everywhere, except for an increase in $<$v'v'$>$ and -$<$u'v'$>$ below 200 wall units. We are following with higher resolution near wall measurements, and plan to acquire 3D data using holography in the near future.   

Interaction between a rough boundary layer and multiple cylinders wakes: application to ecological restoration

Among many ecologically important aspects of fish locomotion, turbulence is thought to create large stability challenges for fishes. Turbulence is a ubiquitous, highly variable feature of aquatic habitats (Denny, 1988). Species that are more prevalent in ``energetic water'' have more effective control systems and greater ability to generate propulsive power to maneuver. Understanding fish responses and interactions with turbulence is an important biological issue pertinent to evolution of swimming mechanisms and capabilities, and ecological roles and distributions of fishes. There is a current lack of quantitative evaluation of such systems. In most natural systems, sediments and various factors in streambed topography create a rough turbulent boundary layer along the bottom. This work used complimentary laboratory experimental studies and previous field observations (Cotel et al. 2005) to determine how a rough turbulent boundary layer interacts with flow structures created by obstacles in a channel using PIV. Preliminary analysis shows a strong interaction between the turbulent boundary layer created by roughness elements and the wakes behind cylinder arrays.   

Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer

Wind-tunnel measurements are performed in order to quantify the vertical transport of momentum and kinetic energy across a boundary layer that includes a three-by-three array of model wind turbines. The data are obtained using stereo-PIV, on 18 planes surrounding a wind turbine. The data are used to compute mean velocity and turbulence properties averaged on horizontal planes. We compare the effects of turbulence stresses with those arising from the averaging of spatially varying mean flow distributions (``canopy stresses''). Results are compared with simple momentum theory and with models for effective roughness length scales that are often used to model wind turbine arrays in computer models for the large scales of the atmosphere. The impact of vertical transport of kinetic energy due to turbulence and mean flow correlations is quantified. It is found that the fluxes of kinetic energy associated with the Reynolds shear stresses are of the same order of magnitude as the power extracted by the wind turbines, highlighting the importance of vertical transport.   

Turbulent properties of a wind-turbine wake developed in a boundary layer flow

Wind turbine wake characteristics are expected to depend on the incoming atmospheric boundary layer flow statistics (e.g., mean velocity distribution, turbulent stresses and turbulent fluxes). Atmospheric stability is also expected to affect the structure of a turbine wake. In this study, results are presented from wind tunnel experiments carried out at the St. Anthony Falls Laboratory atmospheric boundary layer wind tunnel using a model wind turbine placed inside the boundary layer developed over a smooth and rough surface. The structure and behavior of the wind turbine wake are studied also under different conditions of thermal stratification. Thermal stratification levels in the boundary layer were achieved by controlling the temperature of both the tunnel floor and the air flow. A triple-wire (x-wire and cold wire) anemometer and Particle Image Velocimetry (PIV) were used to characterize the turbulent wake downwind of the turbine at different locations. This study provides valuable information about the spatial characteristics of the structure of wind-turbine wakes. This information is being used to test and guide the development of improved parameterizations of wind turbines in high-resolution numerical models, such as large-eddy simulations (LES).   

Statistical and quadrant-hole analysis of the turbulence characteristics in a 3 x 3 wind turbine array boundary layer

Data from a wind-tunnel experiment on the flow within a 3 x 3 array of lightly loaded wind turbine models operating inside a turbulent boundary layer over a rough surface are analyzed. The data are acquired using X hot-wire anemometry and the focus of the analysis is on the possible differences of the flow structures above and below the canopy of wind turbines. Here this question is addressed using quadrant analysis. Conditional averages of turbulent dissipation (a 1-D surrogate) at various heights at 5 diameters downstream is performed for each of the 4 quadrants as well as different ``hole-sizes.'' The results imply significantly less inter-scale correlations in the low-shear region at the bottom of the wind turbine wake than at other wake locations. Inter-scale correlations above and below the wake are also significantly greater than at that low-shear region. Spectral analysis is performed to determine which scales are mostly responsible for the various levels of Reynolds stresses as functions of position in the wind turbine wake.