Well resolved instantaneous proﬁles in high Reynolds

17th International Symposium on Applications of Laser Techniques to Fluid Mechanics

Lisbon, Portugal, 07-10 July, 2014

Well resolved instantaneous profiles in high Reynolds numberrough-wall flows

Dougal T. Squire∗1, Caleb Morrill-Winter1, Charitha M. de Silva1, Nicholas Hutchins1 and IvanMarusic1

1: Department of Mechanical Engineering, University of Melbourne, Victoria 3010, AUSTRALIA.∗ correspondent author: [email protected]

Abstract A unique particle image velocimetry experiment is detailed which provides high resolution, instantaneous velocity fields in

a zero pressure gradient rough-wall turbulent boundary layer at friction Reynolds number, Reτ ≈ 11, 600. The imaging system consists

of eight highly magnified cameras which are arranged to capture a horizontally narrow streamwise/wall-normal plane that spans the

entire wall-normal extent of the boundary layer. Flow statistics from this measurement agree well with multi-sensor hot-wire anemom-

etry measurements taken at matching Reynolds number. A visual investigation of the instantaneous velocity fields and velocity profiles

reveals large regions of uniform streamwise momentum, similar to those previously observed in smooth wall boundary layers. The

energy spectra and co-spectrum reveal that the current measurement is contaminated by high wavenumber measurement noise, but that

the contribution from the noise to the total energy is small.

1. Introduction

In the vast majority of engineering applications, the region of fluid flow in close proximity to a wall occurs athigh Reynolds number and is turbulent. In cases of flows over streamlined bodies at realistically large Reynoldsnumbers (such as ships and aircraft), this region - called the boundary layer - can account for up to 50% ofthe total drag (Marusic et al., 2010a). With increasing Reynolds number, the separation between the largest(O (δ)) and smallest (O (ν/Uτ)) scales in turbulent boundary layers increases, where δ is the boundary layerthickness, Uτ is the wall friction velocity and ν is the kinematic velocity. An important aspect of increasingReynolds number is that the largest length scale becomes increasingly large in comparison to the smallestlength scale (Klewicki (2010); Marusic et al. (2010b)). Recent DNS studies (for example, Hoyas and Jimenez(2006), Pirozzoli and Bernardini (2013) and Schlatter and Orlu (2010)) provide flow information across the fullrange of scales present, but these studies are limited to Reynolds numbers well below those of most practicalengineering applications. To adequately understand the flow physics of turbulent boundary layers, well resolvedexperiments at high Reynolds numbers are essential.

The exact nature of the range of turbulent motions present in smooth-wall turbulent wall flows, and theirrelationship to the skin friction drag, has been the subject of investigations for several decades (Robinson,1991). Perhaps the most significant result of these studies is the observation of certain recurrent, quantifiablefeatures - coherent structures - that populate the turbulent boundary layer. A large range of structures havebeen observed, which have scales that span from O (ν/Uτ) to O (δ). For recent reviews of the full range ofboundary layer coherent motions, readers are referred to Panton (2001), Marusic et al. (2010b) and Adrian(2007). Meinhart and Adrian (1995) noted the existence of large, time-varying, irregularly shaped zones ofnear-uniform streamwise momentum in the turbulent boundary layer, termed ‘momentum zones’, separated bythin shear layers. Priyadarshana et al. (2007) showed that the streamwise-velocity/spanwise-vorticity co-spectrahas a high- and low-wavenumber peak, which correlate with maxima and minima in the spanwise vorticityspectrum, respectively. The authors relate the former observation to spatially concentrated patches of advectingvorticity, and conjecture that the latter is the spectral signature of a passing momentum zone. Adrian et al.(2000b) suggested that the momentum zones are generated beneath packets of hairpin-shaped vortices, whichoccur in a hierarchy of scales across most of the boundary layer. Such vortical structures have been observedto exist and persist in turbulent flows (Adrian and Moin, 1988; Zhou et al., 1999, 1996), and the notion these

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structures have properties that scale with distance from the wall was suggested by Townsend (1980) and hasbeen explored by Perry and Chong (1982), Perry et al. (1986), Perry and Marusic (1995) and Marusic andPerry (1995). In the case of a rough-wall turbulent boundary layer, there is experimental evidence of outer-layer similarity (Raupach et al., 1991); that turbulent motions outside of the roughness sublayer are (at leastin a time-averaged or statistical sense) independent of roughness geometry and viscosity at sufficiently highReynolds number (Townsend, 1980). However, there is little experimental evidence for outer-layer similarity ofinstantaneous features (Volino et al., 2007). The experiments detailed in this paper are a part of a broader study,targeted at investigating the wall-normal structure of the smooth- and rough-wall turbulent boundary layer (withparticular emphasis on momentum zones and the regions of high intensity vorticity that exist between them),and how it pertains to the corresponding velocity profile in an instantaneous sense. Here, a set of rough-wallmeasurements are detailed and validated, and preliminary results are presented.

Kulandaivelu (2012) used hot-wire anemometry (HWA) to obtain well resolved streamwise velocity datasetsat Reynolds numbers ranging between Reτ = 2, 740 and Reτ = 22, 880, where Reτ = δUτ/ν is the frictionReynolds number. Similarly, well resolved spanwise and wall-normal velocity datasets have also been obtainedusing hot-wire anemometry (Baidya et al., 2012; Osterlund, 1999) and laser-Doppler anemometry (De Graaff

and Eaton, 2000). However, unless multiple probes and complex arrangements are employed, such single pointmeasurements are not capable of providing quantitative information on the spatial structure of the instantaneousvelocity field. The particle image velocimetry (PIV) technique is commonly used in the investigation of spatialphenomena in turbulent flows. However, in high Reynolds number boundary layers it is typically difficult toobtain a resolution close to the smallest scales present in the flow while still retaining a large enough field ofview. The pairing of long-distance imaging techniques with particle image velocimetry to obtain high resolutioninstantaneous velocity information, especially near the wall, has become increasingly popular in recent years.Kahler et al. (2006) used an Infinity K2 long-distance microscope to image a 2.82 mm × 4.32 mm regionof a turbulent boundary layer at an observation distance of 387 mm. More recently, Cierpka et al. (2013)constructed the mean velocity profile of the turbulent boundary layer using four, independently captured, field-of-views (FOVs), each at a different magnification level. The smallest FOV (10.90 mm × 8.84mm at a workingdistance of 1 m) was located closest to the wall in order to resolve the small length scales present in this region,and to allow for data to be obtained very close to the wall. Following from Cierpka et al. (2013), de Silva et al.(2014) employed eight cameras simultaneously at two magnifications to generate a FOV extending several δ inthe streamwise direction. An additional camera was used to image a region very close to the wall at a resolutionof the same order as the smallest length scales present in this region. The present experiment employs an arrayof 8 cameras, aligned in the wall-normal direction, which are used to investigate a region that spans the fullextent of the boundary layer height. The resulting spatial resolution is sufficient to resolve scales in the orderof the Kolmogorov microscale of turbulence, η, at a friction Reynolds number of approximately 11,600.

Velocity fields obtained using PIV typically contain appreciable noise. The CCD and CMOS sensors com-monly used in this technique have an inherent noise floor (Hain et al., 2007). Additionally, and usually moreimportantly, noise can be introduced into the measurement by factors including aberrations in the imagingoptics, out-of-plane motion, inhomogeneous illumination and out of focus particles (Meinhart et al., 1999;Westerweel et al., 1997). For a detailed discussion of the contributors to noisy velocity fields in PIV, readersare directed to Adrian and Westerweel (2010) and Raffel (2007). Investigation of the power spectra of veloc-ity have shown that PIV measurement noise occurs across a range of wavenumbers, and can infect the scaleswhich contain significant turbulent energy (Atkinson et al., 2014). Foucaut et al. (2004) showed that the noise iswhite, and that its level depends strongly on the recording set-up. The presence of such noise in PIV amplifiesmeasurements of turbulent fluctuations. If physical conclusions are to be drawn from PIV measurements, it istherefore critical to understand the nature, range and affect of any measurement noise present.

This paper details the experimental arrangement used to obtain highly resolved instantaneous snapshotsof the rough-wall turbulent boundary layer at Reτ ≈ 11, 600. The resulting flow statistics are compared withmulti-sensor hot-wire measurements taken in the same facility at approximately matched Reynolds number.Coordinates x, y and z are used throughout this paper to denote the streamwise, spanwise and wall-normaldirections, respectively. U and W are the instantaneous streamwise and wall-normal velocities, U and W arethe corresponding mean velocities, and u and v are the fluctuations. The superscript + refers to variables

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normalised by viscous variables.

𝑥 𝑦 𝑥 𝑦

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Figure 1: Schematic of the experimental arrangement. (a) shows the full experiment arrangement, (b) shows the indi-vidual field of view of each of the eight cameras (−−) and the combined total field of view (−), (c) presents the opticalarrangement on each of cameras one to seven. Note that camera eight has only a single 180 mm lens.

2. Experiment description

Experimental facilityThe experiments are performed in the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT) atthe University of Melbourne. In this open-return blower wind tunnel, the turbulent boundary layer is developedon the floor of the 1 m × 1.89 m × 27 m (z × y × x) working section. The long streamwise developmentlength enables a high Reynolds number boundary layer to be generated at relatively low free-stream velocities,resulting in larger viscous length scales, and allowing for high spatial resolution measurements with the currentequipment at high Reynolds numbers. A detailed description of the facility is provided by Nickels et al. (2007).In this experiment, the entire working section floor is covered with a single sheet of 36 grit sandpaper. PIVmeasurements in the streamwise/wall-normal plane are carried out 22m downstream of the beginning of the

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sandpaper. Experiments are conducted at free-stream velocities of 12.4 m/s and 20 m/s, with correspondingfriction Reynolds numbers of approximately 11,600 and 19,800, respectively. In this paper, however, onlyresults obtained at Reτ ≈ 11, 600 are discussed.

InstrumentationThe experimental arrangement, presented in Figure 1, consists of eight, 14-bit PCO 4000 PIV cameras, eachwith a CCD sensor resolution of 4008×2672 pixels. The cameras are orientated with the larger sensor dimensionin the wall normal direction of the measurement plane, and are staggered vertically such that the combinedfield of view is a single, narrow, vertical column that spans the entire boundary layer (37mm × 543 mm - seeFigure1(b)). Due to the size constraints of the cameras, every second camera in the imaging array is located onthe opposite side of the wind tunnel working section.

Each of the lower seven cameras is equipped with a Tamron SP AF 180mm macro photography lens, aSigma APO EX DG 2× teleconverter, and a 109 mm bellows. The arrangement generates a resolution of 14µm/pixel at an imaging distance of ≈ 1m, which results in a field of view of 37 mm × 56 mm. At Reτ ≈ 11, 600,a 32 × 32 pixel interrogation window corresponds to approximately 15 × 15 viscous units. A long-rangemicroscope, such as the Infinity-K2 (Kahler et al., 2012), does not utilise the full extent of the large formatPCO 4000 sensors, and is therefore not well suited for these measurement. In order to ensure that the fullwall-normal extent of the boundary layer is observed, the eight camera is equipped with a Tamron SP AF180mm macro lens to generate a field of view of 129 mm × 194 mm. Note that for this camera, only theregion of the image that overlaps horizontally with the field of view from the bottom cameras is consideredduring processing, as illustrated in Figure 1(b). Table 1 summarises the physical parameters associated with theReynolds numbers investigated in this study.

Table 1: Summary of physical and processing parameters. Note that l is the extent of one side of the interrogation window

PIV cameras 1 - 7 PIV camera 8U∞ Reτ Reθ δ99 ν/Uτ (µm) pixels l+(= luτ/ν) pixels l+(= luτ/ν)12.4 11,600 35,930 382 mm 31 32 × 32 15×15 64 × 64 100×10020.0 19,800 59,440 386 mm 19 32 × 32 25×25 64 × 64 163×163

The flow is seeded with tracer particles delivered by a Rosco aqueous-glycol-solution smoke generator.The mean particle size is approximately 1− 2 µm. A Spectra Physics ‘Quanta-Ray’ PIV 400mJ/pulse Nd:YAGdouble-pulse laser is used to generate a streamwise/wall-normal plane of the boundary layer. The light sheetis introduced from the top of the tunnel. Two plano-convex cylindrical lens’ reduce the spanwise thicknessof the coincident beams to approximately 0.6 mm. The narrow beams are subsequently spread into a sheetusing a plano-concave cylindrical lens of focal length -25 mm. While significant light is lost through theoptical configuration, it is nonetheless possible to obtain well illuminated PIV image pairs due to the narrowstreamwise extent of the laser sheet. Because of the significant difference between the magnification of the topcamera and that of the other cameras, it is infeasible to optimise the particle displacement for all cameras usinga single laser. Here, the separation in time between releasing each energised laser cavity is chosen to obtaina maximum in-plane displacement of the particles across cameras one to seven of approximately 18 pixels.The corresponding maximum particle displacement in camera eight is equal to approximately five pixels. Theexperimental parameters of the present study are summarised in Table 2.

To complement the PIV measurement, a constant temperature multi-sensor hot-wire anemometry (HWA)measurement is performed at Reτ ≈ 11, 600. The probe employed is a miniature version of the Mitchelland Foss spanwise vorticity probe (Foss and Haw, 1990). The probe consists of a vertical ×-array (orientedorthogonal to the wall, with each wire angled at 45◦ and -45◦, respectively), accompanied by two single wirespositioned parallel to the wall and perpendicular to the mean flow. All four wires are contained within a volumewith dimensions 0.5 mm × 0.5 mm × 0.5 mm. At Reτ ≈ 11, 600, each dimension associated with the hot-wireprobe has a viscous length scale of approximately 15 wall units. Note that although this value is the same asthe width and height in wall units of a 32 × 32 pixel PIV interrogation window at matched a Reynolds number,

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Table 2: Summary of experimental parameters

General parametersTotal field of view 37mm × 543mmNumber of velocity vectors per image 2.9×105

Laser sheet thickness ≈ 0.6mmParticle size ≈ 1 µmSeeding Polyamide particlesFlow medium Air

PIV cameras 1 - 7Total wall normal extent 3.2mm - 373.5mmField of view (per camera) 37mm × 56mmf-number 5.6Depth of focus ≈ 0.6mmOptical magnification 14 µm/pixel

PIV camera 8Total wall normal extent 356.2mm - 550.2 mmField of view (per camera) 129mm × 194mmf-number 16Depth of focus ≈ 1.8mmOptical magnification 49 µm/pixel

the spatial filtering effect of the hot-wire probe configuration is not the same as the box-filtering effect of thePIV processing scheme.

CalibrationTypically, the accuracy of PIV measurements is influenced by perspective errors, and by distortions caused byoptical components. This is particularly true in high resolution measurements, where a large number of lensesare required in series to provide the desired magnification. Because of this, the use of a de-warping pixel-to-realconversion process, rather than the application of a single scaling factor, is crucial. Here, a calibration processsimilar to that given by de Silva et al. (2014) is employed. A glass calibration target, with a grid spacing of 2.5mm, is employed to allow imaging from both sides of the tunnel.

To reduce the intensity of the reflection of the laser sheet from the wall, the tunnel floor was coated withultra-flat black spray paint. Additionally, the lowest camera in the imaging array is positioned such that thelowest wall normal position of this camera is approximately 3mm from the crest of the local roughness height.Thus, the wall location cannot be determined using the reflection of the calibration grid in the wall [de Silvaet al. (2014)]. Instead, the location of the field of view relative to the wall is determined directly from the gridlocations on the calibration target.

Vector EvaluationThe PIV images are processed using a PIV package developed at the University of Melbourne. Prior to dis-placement evaluation, each raw PIV image is histogram filtered to between 0.1% and 3% of the total raw imageintensity, and the average image for each camera is subtracted. The cross-correlation for cameras one to sevenis performed using a fast-Fourier-transform based cross-correlation algorithm with multigrid (Willert, 1997)and window deformation (Huang et al., 1993a,b; Jambunathan et al., 1995; Scarano, 2002). Window deforma-tion is not utilised when processing the images from camera 8, since camera 8 mostly images the free-stream.The final interrogation window size for each camera is presented in Table 1. Two multigrid passes were usedin all cases, with each dimension of the initial interrogation window corresponding to twice that of the finalpass. For cameras one to seven, a 50% overlap of the final interrogation window was employed. To maintaina uniform vector spacing across all of the cameras, the vector spacing of camera 8 is matched to that of the

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lower cameras. Note that the particle diameter in the image plane of camera 8 ranges from one to two pixels,less than that recommended by Prasad et al. (1992). Thus, the measured displacement for a particular windowis biased towards integer pixel values (Westerweel, 1997). In the images obtained from cameras one to seven,the particle diameter is significantly larger (≈ 3 − 6 pixels) so the effect of pixel-locking in these regions issignificantly less.

Due to the optical aberrations and lack of light caused by the lens configuration associated with each cam-era, the extreme edges of the processed fields are observed to contain large numbers of spurious vectors. Tominimise the effect of spurious vectors on the resulting flow statistics, the velocity fields from each camera arestitched such that the overlap region of the stitched field for each camera pair is equal to the overlap regionfrom the camera in the pair which contains the lowest number of spurious vectors in that region. The exceptionis in the overlap region between cameras seven and eight, where the higher resolution vectors of camera sevenare utilised to the camera’s full wall-normal extent.

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Figure 2: Comparison of flow statistics U/U∞, u2, w2 and −uw obtained from planar PIV, and multi-sensorhot-wire anemometry experiments. The green ◦ symbols represent the hot-wire data, the solid blue line (−)indicates the present PIV study. The vertical dashed line represents the demarcation between camera seven andcamera eight of the current study

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3. Results

Flow statisticsThe validation of the current measurement is carried out through an analysis of single point statistics, and thecomparison of these statistics with those from multi-sensor hot-wire anemometry. The streamwise mean flowcharacteristics, streamwise and wall-normal variances, and Reynolds shear stress are compared. In the case ofthe PIV measurement, these quantities are obtained from an ensemble average of 2880 instantaneous fields,which are also averaged along the streamwise direction of the measurement plane (considered approximatelyhomogeneous for these measurements). The PIV and HWA data are at matched Reynolds numbers. Becauseof this, and due to the large error associated in determining Uτ above the rough-wall, the first and second ordermoments are normalised by U∞ and U2

∞, respectively rather than by the friction velocity. The boundary layerthickness, δ, used to normalise the wall-normal location, is defined here as the location at which the meanvelocity is 99% of the freestream velocity.

The mean streamwise velocity profile is shown in Figure 2(a). For comparison, the velocity profile obtainedfrom HWA is also presented. There is good agreement between the two measurements. As outlined in §2, itis not possible to obtain PIV vectors closer than approximately 3 mm from the tallest local roughness peak,

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Figure 3: An example instantaneous: (a); velocity profile (solid blue line, −), (b); velocity field, and (c); wall-normalstreamwise velocity gradient field. The mean velocity profile is also shown as a dashed blue line −−) in (b). Note that in(b) and (c) one unit on the abscissa corresponds to three units on the ordinate.

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Figure 4: Example instantaneous velocity profiles: (a); where the boundary layer interface is instantaneously very low(solid blue line, −), (b); where there are very clear regions of relatively uniform streamwise momentum (solid blue line,−), and (c) where the boundary layer interface is instantaneously very high (solid blue line, −). The mean velocity profileis included in all figures (dashed blue line, −−).

due to the reflection of the laser sheet from the wall, and hence the HWA data extends closer to the wall thanthe PIV data. Inspection of the PIV profile, reveals small steps at each of the camera overlap locations. Themaximum step occurs at the overlap between cameras seven and eight and has a magnitude of 0.005U∞, whichis considered to be within the experimental error of the measurement. The vertical dashed line shows themaximum wall normal location of camera seven; the position at which there is a step increase in the resolutionof the statistics.

Figures 2(b), 2(c) and 2(d) present the streamwise and wall-normal variance profiles, and the u−w velocitycovariance (Reynolds stress) respectively. Again, good agreement is observed between the PIV and HWA data,especially in the outer region of the flow. A discussion of the effects of noise and spatial attenuation on thepresented statistics is given below. To demonstrate the value of the PIV measurement in obtaining well-resolvedinstantaneous velocity profiles, Figure 3 presents an example instantaneous velocity profile (3a), velocity field(3b) and wall-normal streamwise velocity gradient field (3c). Note that every second velocity vector is used tocalculate, ∂U/∂z and the resulting field has been median filtered using a 5× 5 window. Visual inspection of theinstantaneous field shows three regions of relatively uniform momentum. Bounding these regions are thin shearlayers that coincide with apparent step increases in the instantaneous velocity profile. These layers are mosteasily observed in the wall-normal gradient of the streamwise velocity. Additionally, there is a terminatingshear layer observed at the outer instantaneous edge of the boundary layer where the velocity reverts to thefreestream value. This is consistent with the concept of the viscous super-layer and the accompanying velocityjump observed by Chauhan et al. (2012). The authors note that similar velocity characteristics are observed inall of the instantaneous fields so far examined. The observations agree with those first made by Meinhart andAdrian (1995) and Priyadarshana et al. (2007). Figure 4 shows example instantaneous velocity profiles wherethe boundary layer thickness is instantaneously very low (4a), and very high (4c).

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Determination of the wall shear velocityThe friction velocity, Uτ, is a key parameter in rough and smooth wall boundary layers. For smooth walls,this quantity is proportional to the shear stress at the wall, and scales the inner layer of the turbulent boundarylayer velocity profile. Historically, the accurate determination of Uτ, particularly by indirect means, is difficult.This is especially true above rough walls, where the virtual origin of the wall, ε, and the roughness function,∆U+, are additional unknown parameters. Perry and Li (1990), Krogstad et al. (1992) and Choi (1989) suggestmethods for the determination of Uτ above a rough wall from the mean velocity profile. In this study, amodified Clauser chart method is used to calculate estimates of the friction velocity for both the PIV and HWAdata. Such methods traditionally require the calculation of the wall offset, ε (either as an initial step or from themodified Clauser fit). Here, ε is assumed to be equal to 0.6mm; approximately half of the maximum peak-to-trough roughness height (this value has been confirmed from detailed single-sensor HWA profiles). The methodemployed minimises the error between the inner normalised velocity data, and the rough wall-boundary layerequation in the logarithmic region of the boundary layer using:

UUτ

=1κ

log[(z + ε)Uτ

ν

]+ A − ∆U+ (1)

where κ = 0.39, A = 4.3 (Marusic et al., 2013), and Uτ and ∆U+ are chosen to minimise the least-squared errorbetween the left- and right-hand sides of equation (1) across the log region. Here, upper and lower log regionbounds of z+ = 100 and z/δ = 0.125 are used (Schultz and Flack, 2007).

Uτ is also estimated independently from the total shear stress at the plateau of the Reynolds shear stressprofile using

Uτ =

√−uvpeak (2)

where ν∂U/∂y is not included inside the square-root due to its negligible effect. Table 3 compares the wallshear velocity obtained using the modified Clauser method with that from the total shear stress method. Theresults from both the PIV and the HWA measurement are presented. The height of the peak in the Reynoldsstress is taken as the mean of the data over the region 7 . z . 50 mm (230 . z+ . 1, 610). Because of the errorassociated with this approach, the range in Uτ associated with considering the highest and lowest Reynoldsstress across this region is also included in Table 3. Figure 5 illustrates the results from each of the methodsused to find Uτ. The largest discrepancy in Uτ across the two independent measurement techniques, and the

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Figure 5: The two independent methods used to find Uτ: (a); the results of the modified Clauser fit for the PIV (−) andthe HWA data (◦), the red dashed line (−−) is the smooth-wall log law profile with κ = 0.39 and A = 4.3, (b); a close upview of the Reynolds shear stress obtained from the PIV measurement (−) and from HWA (◦), the peak of the Reynoldsshear stress is taken as the average of the data between z = 7 mm and z = 50 mm, shown for the PIV data (−−) and HWAdata (−−)

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Table 3: The wall shear velocity, Uτ, as determined from a modified Clauser method and the total shear stress method

Modified Clauser method Total shear stress methodPIV 0.467 0.486+0.009

−0.012HWA 0.456 0.492+0.008

−0.006

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Figure 6: Inner normalised Kolmogorov length scale as a function of wall-normal position as determined from themulti-sensor hotwire experiment data (◦). The solid blue line (−) shows the ratio of the interrogation window size to thekolmogorov length scale. The vertical dashed line represents the demarcation between camera seven and camera eight ofthe current study, at which there is a step increase in spatial resolution

two independent methods is 9.5%. Throughout this paper, values of friction velocity obtained using the totalshear stress are used.

Spatial resolutionThe novelty of the current measurements is that eight cameras are utilised simultaneously to provide a highspatial resolution throughout most of the boundary layer. Figure 6 presents the inner normalised Kolmogorovlength scale, η+, as a function of wall normal-position, estimated from the HWA dataset. η is estimated assum-ing local isotropy, such that the turbulent dissipation rate, ε ≈ 15ν(∂u/∂x)2. Additionally plotted is the ratio ofthe PIV interrogation window size to the Kolmogorov micro-scale, l/η. This quantity provides an indication ofthe number of energy containing Kolmogorov length scales being averaged by the PIV measurement at eachwall-normal location. It is apparent that the present measurement is capable of resolving scales on the order ofη across the full extent of the boundary layer.

The box-filtering influence of the processing in the current PIV measurement spans approximately 15 ×15 × 19 wall units. Each of the four hot-wire elements on the multi-sensor probe employed have a length ofapproximately 15 wall units, and the spacing between the cross-wire elements in the array is also close to 15wall units. It is therefore expected, though not known for certain, that the spatial averaging effect of the HWAand PIV in this study are similar. Both ×-wire anemometry and PIV are subject to errors which act to increasethe variance of the measurement. In PIV this is due to measurement noise (Atkinson et al., 2014), while in×-wires the error results from the spacing between the wires in the spanwise direction (Philip et al., 2013). InFigure 2(c), the wall-normal variance obtained using PIV is observed to deviate below that from HWA. Thisis likely to be a result of attenuation and amplification differences between the two measurement techniques.However, the collapse of the low order statistics between the HWA and PIV observed in Figure 2 is withinmeasurement error.

It is important to note that spatial attenuation and measurement noise have conflicting effects on the PIVmeasured variances. It is possible to obtain estimates of the turbulent fluctuations that look ‘good’, whenin reality the flow may be spatially under-resolved and contaminated by measurement noise (Atkinson et al.,2014). To qualitatively investigate the severity and affect of measurement noise in the present measurement,

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Figure 7: The one-dimensional pre-multiplied streamwise energy spectrum, kxφuu, as a function of the streamwisewavenumber (k+

x ) at: (a); z+ ≈ 127, and (c); z+ ≈ 2, 245. The solid green lines (−) show the results from the HWAmeasurement. The solid blue lines (−) are obtained using the PIV data. (b) shows a close-up of the region where the PIVenergy spectrum is observed to deviate from the HWA energy spectrum. The vertical dashed black (−−) line representsthe largest wavenumber (determined by observation) at which deviation begins to occur. The vertical dashed red (−−)shows the wavenumber of the PIV window.

the one-dimensional pre-multiplied streamwise energy spectrum, kxΦuu, is presented in Figure 7 as a functionof the streamwise wavenumber (k+

x ) at selected wall positions. The energy spectra obtained from the PIVand HWA measurements are compared. Pre-multiplying the energy spectrum provides a representation of theenergy contribution to the total energy spectrum of a particular wavenumber (or scale of motion). Because ofthe small window size employed to calculate the energy spectrum from the PIV data (equal to the number ofvectors in the streamwise direction of a single field), there are non-periodic end effects, which infect the entirerange of measurable wavenumbers. Hence, a Hamming window was applied. The three smallest wavenumbersare removed from the PIV energy spectrum, as the energy here is influenced by the scale of the Hammingwindow.

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10

z/δ

ξ%

Figure 8: Estimation of the percentage contribution of the noise to the streamwise variance, u2 (�), wall-normal variancev2 (◦), and Reynolds shear stress uv (4) with wall-normal location.

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The deviation of the PIV pre-multiplied energy spectrum from that of the HWA observed in Figure 7(a)at wavenumbers greater than k+

x ≈ 0.047 is due to high wavenumber noise that is not present in the hot-wiredata. The contribution from noisy energy to the total energy spectrum decreases with increasing wall-normalposition, suggesting that the noise is flow dependent. Figure 7(c) shows that by z+ = 2, 245 there is a negligiblecontribution to the total energy due to noise. The difference in the area between the PIV and HWA energyspectra is estimated by the noise contribution to the streamwise variance at each wall normal location withinthe region 0.0466 ≤ k+

x ≤ 0.4205. Estimates of the affect of measurement noise on w2 and uw can also beobtained from the wall-normal energy spectrum and the streamwise/wall-normal co-spectrum, respectively. Itis noted that measurement noise appears to influence the same range of wavenumbers in all three spectrum. Theestimated percentage increase in the error relative to the hotwire, ξ, of u2, w2 and uw due to measurement noiseat each wall-normal location are presented in Figure 8. The largest five wall-normal positions are not shown asthese locations are in the free-stream where the variance is very low, resulting in unrealistically large estimatesof ξ. One interesting observation is that the estimated percentage error of the Reynolds shear stress is less thanthat of the velocity variances for all wall-normal locations. This is due to the fact that the measurement noiseon u is most likely uncorrelated with the measurement noise on w.

4. Conclusion

The present contribution is a description of a novel PIV experiment, which is capable of obtaining well-resolvedinstantaneous velocity snapshots of a high Reynolds number rough-wall turbulent boundary layer. The arrange-ment consists of eight high-resolution cameras, staggered vertically in the wall normal direction, such that thecombined field of view extends the full height of the boundary layer in the streamwise/wall-normal plane. Theflow statistics obtained from this arrangement compare well with those from multi-sensor hot-wire anemom-etry at an approximately matched Reynolds number, providing some validation of the accuracy of the currentarrangement.

Well resolved instantaneous velocity fields are obtained, which provide information on the instantaneousstructure of the outer region of the rough-wall turbulent boundary layer. Initial observations reveal regionsof relatively uniform streamwise momentum that exist throughout the outer region of the boundary layer, vi-sually similar to those previously observed by Meinhart and Adrian (1995); Adrian et al. (2000b,a) abovesmooth-walls. The present experiment is part of a broader study, aimed at investigating the instantaneousspatial structure of the turbulent boundary layer above rough- and smooth-walls.

Acknowledgements

The authors gratefully acknowledge support from the Australian Research Council

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Well resolved instantaneous proﬁles in high Reynolds