Session HB: Turbulent Boundary Layers V

Investigation of Turbulent Wall Pressure Fluctuations over a wide Reynolds Number Range of Turbulent Pipe Flows

The flow noise induced by turbulent wall pressure fluctuations under a moderate to high Reynolds number turbulent boundary layer constitutes a primary limitation on acoustic array performance. The widest and highest ranges of the Reynolds numbers of interest are most easily achieved in pipe flow configurations. It is therefore of interest to investigate the turbulent boundary layers which are generated on a pipe wall to assess if this class of flows can sufficiently replicate the turbulent boundary layers to which an acoustic array is exposed. Turbulent wall pressure fluctuations were measured under the aqueous turbulent boundary layer in a 3.5-inch diameter circular pipe. A linear array of small diameter wall pressure sensors flush mounted in the pipe wall recorded wall pressure fluctuations for a range of centerline flow velocities. These data were used to perform spectral analysis of the turbulent energy in the flow. Reynolds number effects were explored and comparisons were made with wall pressure fluctuations under flat plate turbulent boundary layers.   

Mean profile of a high-Reynolds-number smooth-flat-plate turbulent boundary layer

Although smooth-flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century, measurements at Reynolds numbers typical of marine \& aerospace transportation systems are scarce. Experimental results at momentum-thickness Reynolds numbers (Re) up to 150,000 from the US Navy W.B. Morgan Large Cavitation Channel using a polished 12.9-m-long flat-plate test model at water flow speeds up to 20 m/s are presented. Mean velocity profiles were measured 10.7 m from the leading edge of the model over a wall-normal range from less than one wall unit to more than twice the nominal boundary layer thickness using particle-tracking and laser-Doppler velocimetry. Static pressure and average skin-friction were measured independently. A mild favorable pressure gradient led to a flow speed increase of 2.5\% over the test surface. The measurements span a factor of three in Re and were fitted to within experimental uncertainty using one set of constants and modern empirical inner- and outer-profile forms based on traditional TBL asymptotics. The fitted profiles satisfy the von-Karman momentum integral to within 1\%, and show distinct differences from equivalent zero pressure gradient results. [Supported by DARPA \& ONR]   

Turbulence in Favorable pressure gradient (FPG) boundary layers

Our objective is to study the effect of favorable pressure gradient on near wall structures in a sink flow turbulent boundary layer over a smooth wall. 2D PIV measurements have been performed upstream of and within the region of constant acceleration parameter, $K$=\textit{$\nu $dU}/\textit{dx/U}$^{2}$, of 0.575X10$^{-6}$. In the initial range, where $K$ increases to its asymptotic value, all the Reynolds stresses and skin friction coefficient, $c_{f}$, decay. In the region of constant $K$, the stresses continue to decay in the outer layer, but $c_{f}$ and all the Reynolds stress components increase close to the wall ($y$/\textit{$\delta $}$<$0.2). The stresses collapse when scaled with the local freestream velocity, $U_{0}$(x). TKE production and wall normal transport of turbulence also scale with $U_{0}$(x)$^{3}$/\textit{$\delta $}(x) close to the wall. PIV data obtained in wall-parallel planes show the expected low speed streaks (LSS) bounded by large structures in the zero pressure gradient range. Narrower LSS persist also in the constant K area, but the signatures of large structures diminish. In both regions, small-scale structures, with signatures suggesting inclined quasi-streamwise vortex pairs, appear predominantly in the LSS areas, suggesting that they are preferred sites of turbulence production.   

Roughness Signature in the Outer Layer of a Turbulent Boundary Layer

Roughness signature, consisting of bumps (slope flattening) in energy spectra at roughness scale wavenumbers, have been observed in the outer-layer high resolution PIV data obtained in a turbulent channel flow over 3D rough surfaces. The measurements cover the entire well-characterized channel flow with $\delta $/$k$=50 ( $k$ is roughness height) and $k_{s}^{+}$=90-150. For the present Reynolds numbers, \textit{Re}$_{\tau}$=3520-5360, these spectral bumps fall in 10-30 times the local Kolmogorov scale. Instantaneous realizations, swirling strength based linear stochastic estimation, and bandpass-filtered velocity maps indicate that this phenomenon is a result of rapid entrainment of eddies generated near the wall by large scale, outer-layer structures. This process floods the boundary layers with eddies of 1-3 times the roughness height, in addition to those generated by local production. Consequently, the energy and shear spectra show an excessive amount roughness-scale energy in the outer-layer. On going time-resolved measurement focus in this interaction between inner and outer layer structures. Thus, although the means flow and second order moment statistics satisfy Townsend's hypothesis, the small scale turbulence maintains the roughness signature.   

Turbulence Structure in Oscillating Channel Flow

The structure of turbulence in an oscillating channel flow with near-sinusoidal fluctuations in bulk velocity is investigated. Phase-locked particle-image velocimetry data in the streamwise/wall-normal plane are interrogated to reveal the phase-modulation of two-point velocity correlation functions and of linear stochastic estimates of the velocity fluctuation field given the presence of a vortex in the logarithmic region of the boundary layer. The results reveal the periodic modulation of turbulence structure between large-scale residual disturbances, relaminarization during periods of strong acceleration, and a quasi-steady flow with evidence of hairpin vortices which is established late in the acceleration phase and persists through much of the deceleration period.   

Analysis of Velocity Measurements on a Towed, Flexible Cylinder

High resolution stereo-PIV measurements were made on a long, flexible cylinder towed in the David Taylor Model Basin. The experiments were performed from 12 to 30 kts to generate Reynolds numbers based on momentum thickness greater than one million. The cylinders (130 m long, 38 mm diameter) were approximately neutrally buoyant and towed through a stationary laser sheet oriented perpendicular to the tow direction to obtain 3D velocity fields. The objective of the study was to quantify the mean and fluctuating velocity fields in the turbulent boundary layer on an experimental towed array (flexible cylinder) where boundary layer thickness is much greater than the cylinder radius. Algorithms for image pre-processing and filtering were applied to enhance the instantaneous images and mask the cylinder and its shadow as they move in the 80 cm x 85 cm field of view. Relevant boundary layer parameters were determined as a function of streamwise position and Reynolds number. Initial results indicate that the velocity defect law provides the best collapse of the data in the outer region of the boundary layer, while the log law relation is effective very close to the surface of the cylinder.   

Effect of wall-mounted cylinders on a turbulent boundary layer: hot wire measurements

Wall-mounted cylinders with height-to-diameter ratio H/D = 2 and large enough to protrude into the logarithmic region, H$^{+}$= 200, are used to alter a turbulent boundary layer with Re$_{\tau }$=1150 in an attempt to affect the organization of the coherent vortical structures. Hot-wire measurements, including velocity profiles and frequency spectra, were acquired downstream of a single cylinder and spanwise arrays of cylinders. The single cylinder yielded a momentum deficit that extended from z$^{+}$=20 to 200, and a redistribution of the streamwise rms velocity towards the half cylinder height with a corresponding increase in the power spectral density over a broad frequency range. Cylinder arrays with 3D spanwise spacing yielded significant wake interactions. The largest mean streamwise velocity deficits and rms values occurred in the log region at mid-span between cylinders. More detail on the effect of cylinder spacing will be provided in the talk. The results suggest that turbulence within the boundary layer leads to broader spanwise interactions than those occurring in wakes of cylinder arrays in uniform cross flow.   

Effect of wall-mounted cylinders on a turbulent boundary layer: V3V measurements

Volumetric 3-Component Velocimetry (V3V) was used to examine the flow structure downstream of arrays of wall mounted-cylinders in a turbulent boundary layer with Re$_{\tau }$=2460. The cylinders, which had height-to-diameter ratio H/D = 4 and H$^{+}$= 455, extended through the logarithmic region. Measurements were acquired in fields that extended over a range 16 to 34 cylinder-diameters downstream of spanwise arrays of cylinders with a spacing of four and eight cylinder diameters (0.2$\delta $ and 0.4$\delta )$. The cylinder array with 4D spacing yielded significant wake interactions: the streamwise velocity deficit was greater at the mid-spacing than directly behind a cylinder; the distinction between the downwash regions (behind a cylinder) and the upwash regions (at the mid-spacing) diminishes with increasing downstream distance; and the rms velocity in all components is highest at the half-cylinder-height. These effects occur to a much lesser degree in the case of the array with 8D spacing. Details on parametric effects as well as the instantaneous three-dimensional structure will be provided in the talk.   

The Drag of 2D Single-Roughness Elements Immersed in Turbulent Boundary Layers

Most of drag studies on flow behind single protuberances in laminar boundary layers focusing mainly with transition, with few studies as regards to turbulent boundary layers. The primary aim of this work was to determine the drag of these protuberances since they exist in practical flows. The experiment was conducted in the turbulence water tunnel research facility at Cambridge University Engineering Department. Measurements were taken using 2D-PIV on 3 types of rough wall configuration involving 2D rough bar with the triangular, circular and semi-circular shapes. The total drag for these 3 types of single protuberances was calculated by considering the undisturbed boundary layer upstream and downstream of the boundary layer. The result reveals that the drag is dependent on the area facing the flow with the triangular shape creating the most drag and the semi-circular the least drag.   

Turbulence characteristics around a staggered wind farm configuration: A wind tunnel study

Turbulent flow around a wind farm is characterized by the coexistence and superposition of multiple wind turbine wakes. The understanding of the momentum transport and velocity fluctuations at different locations in the wind farm is essential to improve energy production and the structural stability of the different turbines. In this study, a staggered model wind farm was placed in the boundary layer wind tunnel of the Saint Anthony Falls Laboratory at the University of Minnesota. The staggered wind farm consisted on 10 rows in the streamwise direction by 2--3 columns. A cross-wire anemometer was used to obtain high-resolution measurements of 2 velocity components (streamwise and vertical) inside and above the model staggered wind farm. Full characterization of the turbulent flow was obtained at a vertical plane parallel to the flow direction through the entire wind farm and at 4 spanwise vertical planes (located at 5 rotor diameter behind the 4th, 6th, 8th and the 10th row). Special emphasis is placed on the description of the enhancement of the turbulence levels in the wind farm as a function the number of rows of the wind farm as well as the growth of the internal boundary layer induced by the wind farm. The results are being used to develop new parameterizations of wind turbines for high-resolution and large-scale numerical models.