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

DRAG REDUCTION BY MEANS OF AN ARRAY OF STAGGEREDCIRCULAR CAVITIESFrancesco Scarano
Dep. of Aerodynamics and Propulsion
ISAE - SUPAERO
10 Av. Belin, 31400 Toulouse France
francesco.scarano@isae-supaero.fr

Erwin R. Gowree
Dep. of Aerodynamics and Propulsion
ISAE - SUPAERO
10 Av. Belin, 31400 Toulouse France

Marc C. Jacob
Lab. de Mécanique des Fluides etd’Acoustique, UMR 5509 CNRS, Université deLyon, Ecole Centrale de Lyon, INSA Lyon,
Université Claude Bernard Lyon I, 36 Av. Guy
de Collongue, 69130 Ecully, France

ABSTRACTand height) which is between 10 and 20 viscous units (ν/Uτ ,where Uτ is the friction velocity). The spanwise wall oscillations technique consists in imposing a spanwise modulationof the flow with a wavelength which is between 200 and 8000
wall units; the consequence is an attenuation of the turbulent
activity thus a skin friction reduction. The practical implementation of the spanwise oscillations, in both real and laboratory
conditions, is limited by the high complexity of the setup andthe need of using an active forcing (Auteri et al., 2010; Marusic et al., 2021).

Further insight into the physics of boundary layer developing over perforated plates at moderate Reynolds numbers isgained from a combined experimental and numerical investigation. The findings are consistent with literature as to the possibility of reducing drag with circular perforations. Indeed, experimental results evidence a modification of the mean velocity profile, a reduction of the burst intensity and a thickening of
the viscous sublayer. In contrast to other studies, the skin friction reduction is more pronounced when increasing the open
area ratio, which is achieved by increasing the cavity diameter or equivalently by decreasing the inter-cavity spacing. The
numerical investigations reveal spanwise patterns promoted by
the perforations, which resemble those generated by spanwise
wall oscillations and could explain the reduction in turbulent
activity observed experimentally.

Skin friction drag reduction can be achieved either by reducing the Reynolds shear stress or by enhancing the wallnormal convection term (see the FIK equation (Fukagata et al.,2002)). The enhancement of the wall-normal convection term
explains the skin friction drag reduction in presence of wallnormal blowing (Kametani et al., 2015) despite the increase in
Reynolds shear stress.

INTRODUCTION
The control of turbulent skin friction drag is a crucial taskthat can have a significant importance both in aeronauticalcontext, where minimising the skin friction drag would havean impact on greenhouse gas emissions (Ricco et al., 2021;
Leschziner, 2020), as well as in the design of thermal insulators and heat exchangers.
Skin friction drag reduction mechanisms started to gaininterest in the 80’s, the majority of the techniques are basedon the modification or disruption of the near wall turbulent
cycle; this usually manifests in the attenuation of the turbulent
activity (namely sweep (u > 0, v < 0) and ejections (u < 0, v >0) altogether known as bursts) and the consequent reduction of
the Reynolds shear stress.
Techniques such as riblets (Garcı́a-Mayoral & Jiménez,2011), and spanwise wall oscillation (Marusic et al., 2021)
have proven to be effective in reducing skin friction. The riblets hinder the spanwise movement of the coherent structuresinside the boundary layer and have a charateristic size (spacing

Recent studies conducted on large dimples (van Nesselrooij et al., 2016) (diameters up to four times the boundary
layer thickness) and cavities (Bhat et al., 2021; Silvestri et al.,2017; Gowree et al., 2019) (diameter in wall units 20 < d + <145) demonstrated the possibility of obtaining a significant
drag or turbulent activity reduction at certain Reynolds numbers. The mechanism involved is not completely clear and it issometimes associated with a passive jetting phenomenon (especially when the cavities are connected to a backing cavity)that dampens the wall normal velocity fluctuations reducing
the Reynolds shear stress (Bhat et al., 2021), or the propertyof an array of orifices to absorb turbulent activity (bursts) in asimilar manner as they absorb acoustic fluctuations (Silvestri
et al., 2017). Another explanation (van Nesselrooij et al.,2016) is that the cavities or dimples create what is sometimes
called ”meandering motion” that disrupts the near wall turbulent cycle.

112th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
(a)
1
2
3
4
5
6
7
8
9

flat plate
test model
optical alignment
probe holder
adjustment screw
hot wire
traversing systempitottripping

7

8

4
3
10

6

10 flap

U∞

Y
2

9

X

5

1

(b)
l

Z+
Z0
Z−

δ
L
2

L

U∞

Figure 1.

Table 1.

Experimental setup a) and test models b).

CASE

d+

L+

d3L11

85

115

150

305

425

540

0.1168

d4L11

110

155

200

305

425

540

0.2077

d5L11

140

190

245

305

425

540

0.3245

d6L11

165

230

295

305

425

540

0.4673

d3L07

85

115

150

195

270

345

0.2885

d3L11

85

115

150

305

425

540

0.1168

d3L16

85

115

150

445

615

790

0.0552

d3L22

85

115

150

610

850

1080

0.0292

d5L22

140

190

245

610

850

1080

0.0811OAR

Flow and geometrical parameters for the three different test conditions, downstream measurement location.

OBJECTIVES AND SETUP

at which the Reynolds number based on the momentum thickness for the smooth case is respectively Reθ = 1830, 2710 and
3380. The values in wall units of the diameter d + and thecavity spacing L+ calculated with the smooth friction velocity are reported in Table 1 together with the open area ratio(OAR). They have been chosen in agreement with previous
studies Gowree et al. (2019); Silvestri et al. (2017).

With the aim to further prove the application of staggered cavities as a skin friction drag reduction technique,accurate boundary layer surveys are conducted in the low
Reynolds number wind tunnel of ISAE-SUPAERO on a flat
plate equipped with a square insert panel (l = 400 mm) which
varies from a smooth baseline surface to models with arraysof circular cavities (Fig. 1). A zero pressure gradient is ensured by the deflection of a flap at the trailing edge of theflat plate (acceleration parameter smaller than 10−7 ). Opticalmonitoring ensured precise measurements of the probe-to-wall
distance (Gowree et al. (2015)). The perforated model is composed of a staggered array of cavities that have a fixed depthof 4 mm, a diameter between 3 and 6 mm, a stagger angle of
45o and a cavity spacing ranging between 7 and 22 mm. The
measurements have been performed one boundary layer thickness (δ ) downstream of the last row of cavities in the direct
wake of a cavity (Z0 ) and in the two spanwise locations (Z+and Z− ). Three flow conditions were tested 10, 15 and 20 m/s

In order to better understand the three-dimensional mean
flow topology, a large eddy simulation (LES) of a portionof the experimental domain is conducted with the code IC3(Grébert et al., 2017) using the experimental mean velocity
profile as inlet condition. The lack of synthetic turbulence at
the inlet limited this study to the mean flow quantities. The
numerical domain keeps the same geometrical parameters but
it is limited to three rows of cavities. The numerical simulation
has been carried on one configuration only, the d5L22 (5 mmdiameter, 22 mm spacing).

2

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

(a)
30.0

(b)
30.0

Schlatter Re✓ = 3273
smooth Re✓ = 3380

20.0

20.0

L+

U+

U+

d+

10.0

10.0

0.0 0
10

Schlatter Re✓ = 3273
smooth Re✓ = 3380

101

102
Y

0.0 0
10

103

101

+

102
Y

103

+

Figure 2. Mean streamwise velocity in wall units at the trailing edge of the model for the Z0 location at 20 m/s, actual friction velocity
is used, size of markers represents the increase in d + /L+ , a) effect of d + for fixed L+ , b) effect of L+ for fixed d + , the in creasing
values of d + , and L+ respectively are indicated by the arrows.

RESULTS AND DISCUSSION

multiplied by a constant k a burst is detected (Sullivan & Pollard (1996)). The short-term RMS is computed considering
a time window which has to be of the order of magnitude of
the characteristic time of the passage of a structure (T + ∼= 20),
Tu2
where T + = ν τ . Given a fluctuating quantity Q(xi ,t) the shortterm average of the variable in the interval time T can be defined as

The mean velocity profiles in wall units at the measurement location Z0 are reported in Fig. 2 for a 20 m/s free stream
velocity. The friction velocity Uτ is obtained with the Clauser
chart technique by a fit of the mean profiles with the Spalding equation (Kendall & Koochesfahani, 2008) with k = 1
and B = 5.5. The actual friction velocity is used to nondimensionalise in inner units all the statistics as well as all
the geometrical parameters reported from now on. The profile
in red represents the smooth baseline and shows a good matchwith the numerical results by Schlatter & Orlu (2010). The
profiles for the perforated cases are plotted in black using different dimensions for the markers, bigger markers represents
larger values of d + or L+ . The mean velocity profiles exhibita mild deviation from the smooth baseline, which is more evident in the wake region. The effect is more pronounced forlarger values of d + and for smaller values of L+ . For thelargest values of L+ (cavities furthest) the smooth conditionis almost retrieved.
The friction coefficient C f is computed from C f = 2Uτ
2 U∞ . In Fig. 3 a) the variation of the local friction coefficient with respect to the smooth baseline case is plottedagainst the d + . A local skin friction reduction is found for all
the flow conditions; the skin friction reduction increases withd + . An opposite trend is present when plotting the variationof skin friction coefficient against L+ (not shown). In Fig. 3 b)
the local skin friction reduction is plot against the OAR. The
data show an overall decreasing trend which confirms that having a more dense array of cavities (increasing the OAR) has abeneficial effect on the skin friction drag. When increasing the
OAR the boundary layer thickens and the momentum thickness increases with respect to the smooth case, Fig. 3 c). A
similar trend is documented for the shape factor H, suggestingthat the profiles are fuller. The plots against OAR appear more
scattered with respect to the ones against d + or L+ , one reason could be that the OAR has been varied by changing two
different parameters (diameter and spacing).
The Variable Interval Time Averaging (VITA) technique
has been applied to the profiles (Blackwelder & Kaplan, 1976).
This technique allows to detect shear events in a turbulent
boundary layer which can be associated to bursts. The shortterm RMS is compared to the long-term RMS of the entire signal. If the short-term RMS is larger than the long-term RMS

b i ,t, T ) =Q(xZ t+ T2

t− T2

Q(xi , s)ds

(1)

and the short term variance is
c2 (x ,t, T ) − [U(xb i ,t, T )]2 .
c i ,t, T ) = U
var(x
i

(2)

The detection is then based on a Heaviside function
D(t) = 1

c i ,t, T ) > k · σu2 ;if var(x0otherwise(3)

where σu2 is the variance of the entire signal. For each value of
Y + it is possible to obtain the conditional streamwise velocity
namely the average burst. The burst intensity can be definedas the peak-to-peak value of the conditional streamwise velocity (Silvestri et al., 2017). In Fig. 4 the intensity profiles arereported for 10 m/s when varying a) the d + , b) L+ . As forthe mean velocity profiles, the effect is more pronounced forlarge values of d + and small values of L+ which correspond tohigher OAR. For the small d + as well as large L+ the smoothintensity profile is almost retrieved.
The root mean square of the streamwise velocity in wall
units σu+ is reported in Fig. 7 for the case d5L11 at 10 m/s
and compared with the smooth baseline case. The inner peak
appears unchanged both in position and in magnitude when theactual friction velocity is employed, although not shown here,
the peak is lower with respect to the smooth case when thefriction velocity of the smooth case is used. The presence ofa second peak around Y + = 100, again this behaviour is more
pronounced when increasing the d + (not shown here).
Similar considerations can be made when looking at thetwo dimensional (2D) premultiplied power-spectra, shown in3

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

(b)

0.0

−10.0

−20.0
100

150

200

(c)
15.0

10 m/s
15 m/s
20 m/s(θcav − θsm )/θsm [%]10 m/s
15 m/s
20 m/s(Cfcav − Cfsm )/Cfsm [%](Cfcav − Cfsm )/Cfsm [%]

(a)
0.0

10.0

−10.0

5.0

−20.0

250

10 m/s
15 m/s
20 m/s

0.0
0

0.1

0.2

d+

0.3

0.4

0

0.5

0.1

0.2

0.3

0.4

0.5

OAR

OAR

Figure 3. Skin friction coefficient percentage variation, a) effect of d + at the three flow conditions, b) effect of the OAR, c) momentum
thickness percentage variation between perforated and smooth, effect of OAR.

(a)
103

(b)
103

smooth102smooth

102

Y+

Y+

d+

L+

101

101

0

1
intensity201
intensity

2

Figure 4. VITA intensity profile at 10 m/s, increasing size of the circles (and following the arrows) represents the increase in d + andL+ , a) effect of d + , b) effect of L+ .
(a)

(b)

Figure 5. 2D premultiplied turbulence spectra of the streamwise velocity fluctuation non-dimensionalised by the actual friction velocity at 10 m/s a) smooth baseline, b) d5L11 case.

Fig. 5. The energy distribution is affected by the cavities withthe presence of a second peak around Y + = 100. This suggeststhat the cavities act to increase the energy of the outer-layer
structures.

The effect of the measurement locations Z+ and Z− withrespect to Z0 is addressed in Fig. 6 only for the case d6L11(where the most significant skin friction variation is found)but similar considerations can be made for all the cases tested.

4

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

(a)
103

25.0

smooth Re✓ = 1830

Schlatter Re✓ = 2000

Z0
Z

smooth Re✓ = 1830

Z+

Z0
Z
Z+

20.0
U+

102

15.0

Y+

10.0
101

5.0
0.0 0
10

101

102
Y

Figure 6.

103

+

σu+

2

The numerical results, limited to the case d5L22, reveal
the generation of a counter-rotating vortex pair and a recirculating flow inside each cavity, as shown in Fig. 8. These
structures bend the streamlines in the vicinity of the perforations thus generating a steady streamwise and spanwise velocity pattern in the near wall region (Fig. 9.a).
The streamwise evolution along the yellow dotted line of
the spanwise mean velocity is plotted in Fig. 9.b: it shows aremarkable similarity with the evolution resulting from a nearwall spanwise forcing as reported by Marusic et al. (2021).
According to these authors, drag reduction can be obtained by
imposing an upstream travelling wave at the wall:

2.0
1.5
1.0

0.0 0
10

1
intensity

Effect of spanwise measurement location on a) mean streamwise velocity profile, b) VITA intensity profile.

2.5

0.5

0

smooth
d5l11
101

102



103

W (x,t) = A cos

Y+
Figure 7. Root mean square of the streamwise velocity inwall units at the trailing edge of the model at 10 m/s, comparison between smooth baseline and d5L11, actual friction
velocity is used.

2π
2π
t
x−
λx
T


(4)

where A is the amplitude of the oscillation, λx is the wavelength and T is the period of the oscillation. A steady versionof the technique, introduced by Viotti et al. (2009), has provento be effective and leads to a drag reduction (up to 52%) bygenerating a spatial Stokes layer that disrupts the near wall
turbulent cycle.
The main differences with respect to the results reported
by Viotti et al. (2009) are the smaller amplitude of the oscillations and the different spanwise profiles (Fig. 9.c), coupledwith the fact that here the flow is at rest at the wall due tothe no-slip condition, but it was not zero in the case of Viotti
et al. (2009) due to the oscillating wall condition. The current
numerical results show that the wavelength λx+ is imposed by
the streamwise spacing of the cavities and that it lies in therange of the wavelengths for which drag reduction is reported
by Viotti et al. (200 < λx+ < 8000).
The results however evidence several similarities withuniform blowing (Kametani et al., 2015): the shape of themean velocity profile, the increase of the thickness and theshape factor. In addition, the presence of a second peak in
the premultiplied power spectrum at Y + = 100 and the increase in the root mean square of the freestream velocity forthe same location suggest an increase in the energy content of
the outer structures. The mechanism for skin friction reduction
by means of blowing is completely different with respect to the
spanwise wall oscillations. In fact, as mentioned in the introduction, the skin friction reduction is achieved by the reductionof the mean wall-normal convection term which overcomes theBoth in the mean velocity profiles and the intensity profiles thethree measurements (Z0 , Z+ , Z− ) are indistinguishable. This
result confirms that the skin friction reduction is not just a local artefact but that it is uniform along the span.

Y
X
Z

Figure 8. Iso-surface of the Q-criterion d5L22 at 10 m/s,
coloured by the contour of V /U∞ × 100 from -5% (blue) to
5% (red).

5

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

(a)

(b)

(c)

x

2000

250

z

1800

200

1600
1400

150
Y+

X+

1200
1000
800

λx

100

600

50

400
200
0

0
5

0

5

W + ·10 2

L

1

0.5

0

0.5

1

W + /A

Figure 9. Spanwise mean flow from the numerical simulation at 10 m/s for d5L22, slice at y+ = 5 parallel to the wall, contour of
W /Uinf between -1.5 and 1.5 % a), spanwise flow evolution along the dashed line b), spanwise profiles at discrete streamwise locations
c).

increase of the turbulent (Reynolds shear stress) term. The suction acts in the opposite way, it dampens the Reynolds shear
stress contribution but increases the mean wall-normal convection leading to a skin friction increase (Kametani et al., 2015).
However, despite the similarities in the results, it is rather difficult to link the topology inside the cavity with uniform blowing. The recirculation inside the cavity, in fact, does not affectthe total wall-normal mass flow rate. For this reason if thecavities create a blowing they should create an equal amountof suction, if this is the case therefore it is unlikely that the reduction due to the blowing will overcome the increase due tothe suction.

is decreased. The overall behaviour appears to be governed by
the concentration of cavities namely by the OAR parameter. In
the current investigation, the drag reduction benefit persisted
for all the conditions tested.

SUMMARY
The current results confirm the possibility of using a staggered array of cavities as a skin friction reduction technique. A
modification of the mean velocity profiles and an intensity reduction of the burst is evidenced. The skin friction reduction ismore pronounced when increasing the d + and when decreasing L+ , namely when the Open Area Ratio is increased. Another effect of the cavities is to thicken the boundary layer andto increase the shape factor. This effect is more pronounced
for larger OAR. The premultiplied spectra evidence an effectof the cavities in the outer layer with the presence of a second
peak around Y + = 100. The current results shows similarities
with uniform blowing however this link cannot be fully supported by the flow topology. However, the 3D flow topology
arising from the numerical simulation shows that the cavities
are equivalent to a generator of steady spanwise flow oscillations in the streamwise direction. The measurements at different spanwise locations (Z0 , Z+ , Z− ) provide some confidence
that the skin friction reduction is not just a local artefact in thewake of the cavities but can be considered uniform along thespan.

A possible explanation is that the blowing phenomenon is
not created by the recirculating vortex but by some sort of resonance which acts in certain conditions (particular diameterto-height ratio or a certain value of the impinging boundary
layer). This could potentially generate an unsteady and nonuniform blowing. Similar results have been recently documented by Bhat et al. (2021) for small cavities backed by another cavity. Despite the mean velocity flux through all holes
being negligible, instantaneous upward and downward components through the holes are reported. The direction of the flow
is influenced by the structures immediately above the cavities,
resulting in a dampening of the Reynolds shear stress and aconsequent skin friction reduction.
What has to be underlined is the difference between thecurrent results and the findings of Silvestri et al. (2017) and
Gowree et al. (2019). In the work of Silvestri et al. (2017)
the cavities are not staggered, they are designed to match thedimensions of the coherent structures in a boundary layer (thespacing is 100 viscous units in the spanwise direction and 1000in the streamwise direction). A decrease of burst intensity is
documented up to a certain value of the cavity diameter in wall
units (d + = 145). The explanation given by the authors is thatthe cavities ingest the sweeps thus reducing the skin friction.
If the cavities are too big the shear layer above the cavities
breaks , which reduces drag benefit. Gowree et al. (2019) evidenced a pefrormance loss when increasing the Reynolds number based on the cavity diameter. In the current study changing
the Reynolds number (obtained by changing the velocity) has
only a weak effect on the performances. What has to be underlined are the completely different trends with respect to thestudy of Silvestri et al. (2017). The current results evidence
an increase of the performance when d + is increased and L+

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Osaka, Japan, July 19–22, 2022
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