12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

LARGE-SCALE FLOW ORGANIZATION OF WALL-BOUNDEDTURBULENCE OVER FLUSH-MOUNTED ROTATING DISCS

Kushal U. Kempaiah
Faculty of Aerospace Engineering
Delft University of Technology
2629 HS Delft, The Netherlands
k.ujjainikempaiah@tudelft.nl

Jacopo Sem
Faculty of Aerospace Engineering
Delft University of Technology
2629 HS Delft, The Netherlands

Woutijn J. Baars
Faculty of Aerospace Engineering
Delft University of Technology
2629 HS Delft, The Netherlands

ABSTRACTextensively for over 30 years (Leschziner, 2020). In a
DNS study of Quadrio & Ricco (2004), a reduction in
friction drag of up to 45% was reported, albeit this study
was limited to a friction Reynolds number of Reτ = 200(note that Reτ ≡ δuτ /ν or δ + is the ratio of the channel
half-width or boundary layer thickness δ, to the viscous
length scale ν/uτ ). Recently, Kempaiah et al. (2020)
conducted experiments on a transverse oscillating walland explored an oscillating time-scale down to t+ = 94
at a Reynolds number of Reτ = 570; their results werein line with the earlier DNS studies of Quadrio & Ricco(2004) in terms of friction drag being higher when approaching the temporal scale of near-wall turbulence.
Since the working mechanism of this global actuation
method relies on a motion that scales with the viscoustime-scale, an experimental implementation of this actuation method is practically challenging when moving
towards higher Reynolds numbers, primarily due to highinertial and vibrational forces required to sustain thehigh-frequency oscillation.
Recently, Marusic et al. (2021) postulated that amore effective drag reduction at high Reynolds number conditions can be achieved with wall-oscillation frequencies on the order of large, outer-scaled flow features.
Still, the current work focuses on relatively low Reynolds
number conditions and follows the control concept of
Keefe (1997). He proposed a wall-normal vorticityforcing through an array of flush-mounted discs within
the wall, each rotating at a constant angular velocity(top view in fig. 1c). That is, each disc belonging toa spanwise row in a streamwise–spanwise array, rotateswith the same orientation, but alternates from row-torow. In this way the convective flow encounters a degree of spanwise wall-oscillation. The wave motion isperpendicular to the flow and maximum in amplitude
when considering the spanwise centre of a streamwise
line of discs. Note that a practical implementation ofthis actuation method is relatively easy: it does not require any oscillatory, linear motion, but is only based on
rotational motion. This control concept was examinedusing DNS of channel flow by Ricco & Hahn (2013), who

Rotating discs, flush-mounted within the wall beneath a turbulent boundary layer, affect the large-scale
flow dynamics. An organized array of rotating discs is asurrogate for the transverse-oscillating wall concept thatis known to reduce turbulent friction drag, since the convecting flow encounters a travelling wave, particularly inthe spanwise centre of the discs. This work experimentally assesses the flow manipulation of this wall-based
actuation method using planar and stereoscopic particle
image velocimetry (PIV). Experiments were conductedin a developing turbulent boundary layer, at Reτ ≈ 910,
and with an optimized viscous-scaled sizing and layoutof the discs following the direct numerical simulation(DNS) study of Ricco & Hahn (2013). Planar PIV in thestreamwise–wall-normal plane over the spanwise centreof the discs revealed a reduction of the in-plane Reynolds
stresses, suggesting a suppression of the near-wall turbulence auto-generation process. Wall-parallel planes ofvelocity data at a height of 70 viscous units above thewall revealed two distinct types of streamwise-oriented
regions, comprising low- and high-momentum pathways.
These spanwise alternating regions were also captured
using the stereo-PIV measurements downstream of the
disc-array. It was observed that the mean boundary
layer flow is pulled closer to the wall in the disc center, resulting in a higher mean velocity and a less intense streamwise Reynolds stress for a given wall-normalheight. With this effect being maximum in the disc center, while being absent between the discs, this type offlow manipulation could be optimized in terms of turbulence suppression (and potentially in terms of friction
drag reduction at high Reynolds numbers), by considering larger discs.

INTRODUCTION
An active flow control method for turbulent friction
drag reduction, relying on transverse wall-oscillation attime-scales matching the most energetic temporal scalesof the near-wall turbulence (t+ ≈ 100) has been studied

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
(a) Top view(c) Detailed top view of disc-array

1.80 mSuspended flat plate

1

xs

ys

x

zs

xs = 1.34 m

P5Tripping condition(b) Side view

zs

P1
P2

ys

U∞

1.2D

0.60 m

U∞

4

3

2

4

3

P4

Row number:
1

2

Angular velocity Ω

1.5D

D = 0.055 m

P3

δ99

xs

Disc-motor assembly

Figure 1: Schematic of the experimental TBL flow setup, with the array of rotating discs flush-mounted in aflat plate. Acquisition planes of PIV measurements and camera placements are also indicated (not to scale).
Table 1: TBL parameters at xs = 1.535 m.

inferred maps of friction drag reduction as a functionof the viscous-scaled disc diameter (D+ ≡ Duτ /ν) andedge velocity (W + ≡ W/uτ with W = 0.5DΩ, in whichΩ is the angular rate-of-rotation); a maximum wall-dragreduction of 23% was found at a friction Reynolds number of Reτ = 180.
Our current work explores the wall-based actuation method of turbulent boundary layer (TBL) flow at
Reynolds numbers higher than the ones available in theliterature, and using an experimental implementation of
the technique (Sem, 2021). To the authors’ knowledge,
this is the first practical realization of this type of flow
control method and a description of the hardware, as
well as the PIV-based velocity measurements for assessment of the large-scale flow organization, are covered
next.

Reτ

Reθ

δ

θ

uτ

H

910

1950

87 mm

8.8 mm0.15 m/s

2.03

targets the near-wall cycle turbulence and should therefore adhere to a viscous scaling. With the current
boundary layer parameters of table 1, the disc diameter
became D = 0.055 m. The array was constructed withstreamwise and spanwise spacings of 0.083 m (1.5D) and
0.065 m (1.2D), respectively, to allow mounting of the
DC electric motors to the bottom side of the plate. Eachmotor contained a double ball-bearing shaft to which thediscs were directly mounted. All motors were poweredwith a single power supply and their angular velocities,Ω, were measured using a tachometer. Variations in Ωof each individual disc were less than 3% of the mean Ω.
This work includes results corresponding to two different
edge velocities, W + = 10 and W + = 25. So the former
corresponds to the largest friction drag reduction, while
the latter should result in an increase of friction drag(see fig. 4b of Ricco & Hahn, 2013).

EXPERIMENTAL CAMPAIGNWind tunnel and array of rotating discs
Experiments were conducted in an open-return lowspeed wind tunnel at the Faculty of Aerospace Engineering of the Delft University of Technology. A boundary
layer with a slight favorable pressure gradient was generated using a flat plate comprising a width of 0.60 m
and a length of 1.80 m (fig. 1a). The boundary layer
was tripped using distributed roughness elements of
1.0 cm in height, following the work of Kempaiah et al.
(2020). Throughout this paper, coordinates x, y and z
denote the streamwise, wall-normal and spanwise directions of the flow, and lower-case u, v and w represent
the Reynolds decomposed fluctuations of velocity, respectively. TBL parameters are listed in table 1 andwere determined from the measured velocity profile ofthe uncontrolled flow (fig. 2a, described later).
An array of 4 × 3 flush-mounted rotating discs was
designed per the optimal case in terms of the largest
drag reduction identified by Ricco & Hahn (2013): a
disc diameter of D+ = 550 and a disc-edge velocity of
W + = 10. Even though their Reynolds number was relatively low (Reτ = 180), this type of actuation method

Particle image velocimetry
Planar-PIV measurements were performed in two
configurations, being (1) a streamwise–wall-normal(x, y)–plane, and (2) a wall-parallel (x, z)–plane. The(x, y)–plane measurements were conducted over the centreline of the most downstream disc, and were imaged
using a single camera, labelled as ‘P1’ in fig. 1a. The(x, z)–plane measurements were performed using two
cameras (‘P2’ and ‘P3’ in fig. 1b) and the total fieldof-view (FOV) covered the entire disc-array. The exact height of the wall-parallel plane (y + = 70) was determined a-posteriori by comparing the mean velocity in the plane to the mean velocity profile extracted
from the (x, y)–plane measurements. Finally, stereoPIV measurements were performed in a wall-normal–
spanwise (y, z)–plane, downstream of the aft-centre disc2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
Table 2: Summary of PIV measurements (note: different configurations were not acquired simultaneously).

Config.

Type

Plane

# of cameras

Field-of-view

Image res.

Interog. window

Vector pitch

1

Planar(x, y)

1 (P1)

75 × 63 mm234 px/mm

32 × 8 px2

0.12 mm2

Planar(x, z)

2 (P2 & P3)

250 × 210 mm2

10 px/mm

24 × 24 px2

0.25 mm3

Stereo(y, z)

2 (P4 & P5)

55 × 55 mm230 px/mm

64 × 64 px2

0.50 mm(a) Mean streamwise velocity profile(b) Budget of the in-plane Reynolds stresses

8

25

6

20

DNS

hu′ u′ i+

W+ = 0W + = 10u+

hu′ u′ i+

15
10

4
2
hv ′ v ′ i+

DNS
W+ = 0

5

W

0
100

101

y+

102

+

0

= 10

hu′ v ′ i+

-2
100

103

101

y+

102

103

Figure 2: (a) Streamwise mean velocity profile for the uncontrolled (W + = 0) and controlled (W + = 10) cases,and (b) the corresponding profiles of all Reynolds stresses in the (x, y)–plane. Only every 2nd PIV data pointis shown for clarity of the graphs, and DNS profiles are taken from Schlatter & Örlü (2010).

good agreement with the DNS data in the inner region.
Discrepancies in the outer-region are described to the favorable pressure gradient of the experimental flow (constant cross-sectional area wind tunnel in which the flat
plate is suspended).

at xs = 1.67 m (roughly 0.45D behind the disc-array).
Two cameras were employed (‘P4’ and ‘P5’ in fig. 1a)and were situated outside of the flow, placed at a stereoscopic angle of 55◦ .
For PIV acquisition, the flow was seeded with fog
droplets of 1 µm diameter, produced with a SAFEX
fog generator. Illumination was provided by a Quantel
Evergreen 200 laser (Nd:YAG, 2×200 mJ, 15 Hz) andthe laser sheet thickness was on the order of 1 mm.
Images were captured using LaVision Imager sCMOS
cameras (2560 × 2160 px2 , 16 bits and 6.5 µm pixel size)
equipped with Nikon lenses of 105 mm focal length.
Post-processing employed an image interrogation using the multi-pass cross-correlation (including windowrefinement and deformation, Scarano & Riethmuller,
2000); non-isotropic windows were used for the (x, y)–plane measurements to increase the wall-normal resolution. Further details of the PIV processing and resolutions of the velocity fields are provided in table 2.

For the case of optimal control (W + = 10), velocity data is available only for y + < 100. That is, theFOV was decreased in size to achieve a higher near-wallresolution. When inspecting the mean velocity profile(scaled by the uτ of the uncontrolled case), it is evident that the velocity decreases below y + ≈ 10. This
indicates a reduction of the average friction drag at thecentre-spanwise location where the measurement was
taken. Moreover, a peak-to-peak reduction of 30% in
hu′ u′ i+ occurs, together with significant reductions in
the magnitudes of hu′ v ′ i+ and hv ′ v ′ i+ below y + ≈ 100.
A reduction of the mean velocity and turbulence intensities is associated with a reduction in turbulent friction
drag generation (Baron & Quadrio, 1995). Note that
our study is the first demonstration-experiment, butthat a direct determination of the reduction in friction
drag was not reliable, due to wall-reflections of the rotating discs and minor vibrations in the setup (requiring
an adaptation of the structure). As a consequence of the
non-uniform actuation in the span, the wall-drag modification also depends strongly on the z location (and x),
as detailed in the work of Ricco & Hahn (2013). Nevertheless, we here continue with a description of how therotating disc-array affects the large-scale flow organization. For this we inspect the other two PIV measurement configurations, described next.

BOUNDARY LAYER PROFILES
Figures 2a and 2b present profiles of the mean velocity and the Reynolds stresses, respectively. Profiles
are generated by streamwise averaging the (x, z)–plane
PIV data over the streamwise extent of the aft disc.
First, the profiles of the uncontrolled case (W + = 0)
are compared to profiles of DNS data of TBL flows, extracted from Schlatter & Örlü (2010). The wall-normal
trends from the experimental data, of both the mean
velocity u and the Reynolds stresses hu′i u′j i+ , show a3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(a) W + = 0(d) W + = 0(u − u)/u

hu′ u′ i+

0.1

0

0

-1

-0.1

-1

0

1

2

(b) W + = 10

3
4
x/D

5

6

1

z/D

z/D

8

1

6

0
4

-1
-1

7

0

1

2

4

5

6

7

x/D

(e) W + = 10

(u − u)/u3

hu′ u′ i+

0.1

0

0

-1

-0.1

-1

0

1

2

3

4

5

6

1

z/D

z/D

8

1

4

-1
-1

7

x/D

(c) W + = 25

6

0

0

1

2

4

5

6

7

x/D

(f ) W + = 25

(u − u)/u3

hu′ u′ i+

0.1

0

0

-1

-0.1

-1

0

1

2

3

4

5

6

1

z/D

z/D

8

1

6

0
4

-1
-1

7

0

1

2

3

4

5

6

7

x/D

x/D

Figure 3: (a-c) Contours of the in-plane streamwise velocity, where u is the mean velocity of the entire wallparallel plane of the uncontrolled case, W + = 0. (d-f) Contours of the streamwise Reynolds stress, all normalizedwith the uτ in table 1. Edges of the discs, and their rotation direction, are drawn in black; small white regions
mask spurious vectors, which were a consequence of laser reflections on the discs.

LARGE-SCALE FLOW ORGANIZATION

nounced in the regions between the discs (Wise et al.,2014). Wall-parallel planes of velocity at lower heights
are challenging to acquire, due to laser wall-reflections
and alignment issues and the current planes are therefore a surrogate of the trends very near-the wall, wheninterchanging the low- and high-momentum pathways.
In order to make a qualitative comparison of how themean flow is organized in the spanwise direction, thewall-parallel planes are streamwise-averaged in the region downstream of the aft row of discs, in the range
5.5 ≤ x/D ≤ 7. The spanwise profiles for all cases of
W + are shown in fig. 4. Notably, the regions of a velocity deficit in the case of control is narrower than theregion of velocity surplus, but is more intense. Averaging the spanwise velocity over one periodic-unit of
the flow (−0.6 ≤ z/D ≤ 0.6) yields the three verticallines in fig. 4, indicating a monotonic trend towards ahigher mean velocity when W + increases. Only when
the wall-normal profiles (varying along the span) collapse in outer-scaling (adhering to a so-called ‘outerlayer similarity’), at this wall-normal height, the spanwise trend and thus the average can be a surrogate forthe spanwise variation in friction drag, An interpretation of fig. 4 in this context is too speculative, giventhat the outer-layer similarity has not been confirmed,
because of the relatively low acquisition location of theWall-parallel plane
The normalised streamwise velocity in the wallparallel plane at a height of y + = 70 (fig. 3a-c) shows
low- and high-momentum pathways, in streamwisealigned regions over the centre of the discs and in between them, respectively. For the case of optimal control(W + = 10), the flow over the spanwise-centred disc most
aft in the array has a higher velocity, being consistent
with fig. 2a. It is evident that the increase and decrease of the velocity in these low- and high-momentum
pathways is strengthened when moving towards the caseof W + = 25 (fig. 3c). For all cases, the mean velocity
slightly decreases towards the end of the measurement
region (x/D → 7) because of the streamwise development of the TBL flow. The effect of control also increases significantly with downstream distance, due tothe relatively short extent of the array in x.
Recall that a relatively high-speed region at y + = 70
corresponds to a relatively low-speed region lower in theboundary layer. In this context, the occurrence of lowmomentum pathways very close to the wall, over the
spanwise centre of the discs, was attributed to a viscous sub-layer being produced by a radial flow fromthe von Kármán pumping effect that is highly pro-4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
the same observations that were made in fig. 4 (the wallnormal height of the wall-parallel plane is shown withthe horizontal dashed line in all sub-plots of fig. 5): for agiven height above the viscous sublayer, a higher mean
velocity occurs in the disc centre, while the flow velocity
is lower at the edges of the disc. Thus, the flow over thecentre of the disc exhibits less momentum-deficit. From
the topology of hu′ u′ i+ it is evident that for approximately −0.25 ≤ z/D ≤ 0.25, the streamwise Reynolds
stress is constant in span and suppressed in comparison
to the uncontrolled case.
At this stage it is worth mentioning that the largescale flow organization over the disc array is strongly
reminiscent of the one found over other wall-bounded
turbulent flows with spanwise varying surface conditions. Specifically, wall-bounded turbulence convecting over walls with streamwise-aligned patches of (various degrees of) roughness, with a spanwise periodicity,
are known to include large-scale secondary flows andthe low- and high-momentum pathways discussed earlier with the aid of fig. 3. Details of such flows canbe found elsewhere (Nugroho et al., 2013; Barros &Christensen, 2014; Vanderwel & Ganapathisubramani,
2015, among others). A main difference between thoseflows and the one currently studied is that our actuation method achieves the spanwise varying friction dragwith hydrodynamically-smooth rotating discs (having
no pressure drag). To the contrary, the aforementioned
studies in the literature comprise walls with pressuredrag (e.g., streamwise-aligned roughness-patches of acertain width). The actuation method with the rotating disc does come however with a non-negligible
power requirement for rotating the discs (Ricco & Hahn,
2013). All in all, having demonstrated that this actuation method is capable of establishing large-scale flow(re)organization, the variation in control ‘authority’ interms of disc sizing, layout, and rate-of-rotation makes
this actuation method an attractive candidate when exploring control of high Reynolds number flows. Thoseconditions remain unexplored with DNS and the current
experimental work is a step towards this.

1.5

W + = 0,

10,

25

1

z/D

0.5

0

-0.5

-1

-1.5
-0.2

-0.1

0

0.1

(u − u) /uFigure 4:

Spanwise profiles of the streamwiseaveraged u-velocity component of figs. 3a-c, in therange 5.5 ≤ x/D ≤ 7. Spanwise averages of these
profiles, for one periodic-unit, are shown with thevertical lines for the range −0.6 ≤ z/D ≤ 0.6.

wall-parallel plane (below the onset of the logarithmic
layer at y + = 100), and because of the streamwise development still taking place at the aft end of the array.
Regardless, the current results show that the actuation
method using rotating discs can establish low- and highmomentum pathways; the implications of this for futurestudies of this control technique are further discussed in
the next section considering the cross-planes of velocity.
A final remark about the data in the wall-parallel
plane is concerned with the regions of high and low
Reynolds stress hu′ u′ i+ , in comparison to the uncontrolled case. When focusing on the intense (red) patchesof hu′ u′ i+ in figs. 3e,f, it is observed that these arelocated just downstream of each row of discs. When
accepting that coherent turbulent structures are inclined by roughly 20◦ relatively to the wall, the observations at y + = 70 originated from the wall at a
distance of ∆x+ = 70/ tan (20◦ ) upstream, equating to∆x/D ≈ 0.36. This upstream shift would align the red
patches of intense hu′ u′ i+ with the ‘narrow passages‘ inbetween the discs. Their spanwise location depends on
the rotation-direction of each row of discs.

CONCLUDING REMARKS
An experimental investigation of the large-scale floworganization over an array of flush-mounted rotating
discs under a turbulent boundary layer was conducted.
Different configurations of PIV measurements were employed to reveal (and confirm in relation to the available
literature on the topic) that low- and high-momentum
pathways are established in the flow, due to the spanwise
varying friction drag. It was recently found in a study
with a fixed spanwise varying surface treatment thatthe spanwise wavelength (or disc size) governs the sizeand strength of the secondary flows (Wangsawijaya &Hutchins, 2022). In that study, the authors interpreted
the secondary flows as spanwise-locked large-scale turbulent structures that are present even in smooth-wall
turbulent boundary layers (but without preferred spanwise positioning). It is postulated that the actuation
method using flush-mounted rotating discs will have alarge control authority for the organization of large-scale
flow features; this can be beneficial in terms of friction
drag reduction technologies at high Reynolds number
conditions. Particularly due to the total absence of pres-

Cross-plane downstream of array
Figure 5 displays data of the cross-plane stereo-PIV
field, located just aft of the array. For both the uncontrolled (W + = 0) and optimal control case, the fieldsof the mean streamwise velocity u and Reynolds stresshu′ u′ i+ are shown. Note that the spanwise range covers
the span of the disc located at z = 0. In comparison
to the spanwise-invariant mean flow of the uncontrolled
case, a clear spanwise modulation of the velocity isocontours appears in the case of W + = 10. This reflects

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022(a) W + = 0(c) W + = 0

u/u∞
1

1
0.7

hu′ u′ i+

1
0.7

8
7

0.4

0.4

0.8

6

y/δ

y/δ

0.2
0.6

0.1
0.07

0.2
5

0.1
0.07

4

0.04

3

0.4

0.04
0.02

0.02

0.2

-0.5

-0.25

(b) W + = 10

0
z/D

0.25

0.5

2

-0.5

-0.25

1
0.7

1

1
0.7

0.4

0.8

0.4

0.25

0.5

z/D

(d) W + = 10

u/u∞

0

hu′ u′ i+
8
7

y/δ

y/δ

6

0.2
0.6

0.1
0.07

0.2
5

0.1
0.07

4

0.04

3

0.4

0.04
0.02

0.02

0.2

-0.5

-0.25

0

0.25

0.5

2

-0.5

-0.25

0

0.25

0.5

z/D

z/D

Figure 5: Contours of (a,b) the streamwise velocity and (c,d) the streamwise Reynolds stress for both W + = 0

and W + = 10. Note that the ordinate has a logarithmic scale. For clarity, the set of red-shaded lines on (a,b)
are iso-contours at u/u∞ = 0.2 : 0.1 : 0.7 and the lines on (c,d) are iso-contours at hu′ u′ i+ = 2 : 1 : 7.
Nugroho, B., Hutchins, N. & Monty, J. P. 2013 Largescale spanwise periodicity in a turbulent boundary
layer induced by highly ordered and directional surface roughness. J. Fluid Mech. 41, 90–102.
Quadrio, M. & Ricco, P. 2004 Critical assessment of
turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 512, 251–271.
Ricco, P. & Hahn, S. 2013 Turbulent drag reduction
through rotating discs. J. Fluid Mech. 722, 267–290.
Scarano, F. & Riethmuller, M. L. 2000 Advances in iterative multigrid PIV image processing. Exp. Fluids
29 (1), S051–S060.
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers.
J. Fluid Mech. 659, 116–126.
Sem, J. 2021 Rotating discs for turbulent drag reduction: an experimental study. Master’s thesis, Delft
University of Technology, Delft, The Netherlands.
Vanderwel, C. & Ganapathisubramani, B. 2015 Effectsof spanwise spacing on large-scale secondary flows inrough-wall turbulent boundary layers. J. Fluid Mech.
774, R2.
Wangsawijaya, D. D. & Hutchins, N. 2022 Investigationof unsteady secondary flows and large-scale turbulence in heterogeneous turbulent boundary layers. J.
Fluid Mech. 934, A40.
Wise, D.J., Alvarenga, C. & Ricco, P. 2014 Spinning outof control: Wall turbulence over rotating discs. Phys.
Fluids 26 (12), 125107.

sure drag with this control system (but, the power for
spinning the discs should be accounted for). In the future, it will be interesting to examine if discs can besized/laid out to increase the benefit of the reduced flowinduced friction in the centre area of the discs, so thatit leads to a global friction drag reduction.

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Marusic, I., Chandran, D., Roughi, A., Fu, M. K., Wine,D., Holloway, B., Chung, D. & Smits, A. J. 2021 An
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