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

EFFECT OF INCOMING BOUNDARY LAYER CHARACTERISTICS ON AN
AIR LAYER WITHIN A LIQUID TURBULENT BOUNDARY LAYER

Lina Nikolaidou
Angeliki Laskari
Department of Process and Energy
Department of Process and Energy
Delft University of Technology
Delft University of Technology
Mekelweg 2, 2628 CD Delft. Netherlands Mekelweg 2, 2628 CD Delft, Netherlands
M.Nikolaidou@tudelft.nl
A.Laskari@tudelft.nl

Christian Poelma
Tom van Terwisga
Department of Process and Energy
Department of Maritime and Transport Technology
Delft University of Technology
Delft University of Technology/
Mekelweg 2, 2628 CD Delft, Netherlands Maritime Research Institute of the Netherlands (MARIN)
C.Poelma@tudelft.nl
Mekelweg 2, 2628 CD Delft, Netherlands
T.v.Terwisga@marin.nl

ABSTRACT

varied via changing the air injection position. Only marginal
differences in the resulting air layer thickness and length wereobserved, although the interface was shown to be more energetic for larger development lengths; however, no detailed
study of the liquid flow field around the layer was performed.
In the same study, the effect freestream velocity was also investigated. An increase in the air layer length with increasing freestream velocities was observed, with the maximum airlayer length (for a specific freestream velocity) occurring at approximately a half gravity wave length (Zverkhovskyi, 2014).
In the study of Pearce et al. (2015), the incoming liquid TBL
thickness was varied by artificial thickening (or thinning) at
the water tunnel inlet, and the effect of different freestream
velocities was also examined. In contrast to the results from
Zverkhovskyi (2014), an increase in the freestream velocity
led to a shorter air cavity while the opposite was true for a decrease of the boundary layer thickness. The authors attributed
the latter to the lower kinetic energy at the air-water interface,although no turbulence profile measurements were performed
to further support this assumption.
Much fewer studies are available on the effect of incoming boundary layer characteristics on the air layer thickness.
This is possibly due to the difficulties that such a measurement
entails. Instead of measuring the air layer thickness directly,
Qair
with
many studies define a nominal air thickness tair = BU∞
Qair the air flow rate, B the injector span and U∞ the liquid
freestream velocity (Elbing et al. (2008, 2013); Peifer et al.
(2020)). However it is still unclear how this relates to the physical air layer thickness.
In the above studies, a cavitator or a backward facing step(BFS) was used upstream of the air injection. In the absenceof such inserts (which is the desirable configuration for fullscale applications), the effect of the upstream conditions on
the characteristics of the resulting air layer is expected to bestronger. Nonetheless, experiments in such a geometry for a
bubble drag reduction regime (BDR) showed that a doublingof the boundary layer thickness at the injection position had anegligible effect on the resulting drag (Elbing et al., 2008); thiseffect was not investigated in the case of an air layer however.

An air layer within a liquid turbulent boundary layer(TBL) is formed by controlled air injection underneath a flat
plate. The incoming boundary layer as well as the flow aroundthe air layer were measured with planar particle image velocimetry (PIV). The effect of different incoming liquid flow
characteristics on the air layer geometry is investigated byvarying both the freestream velocity and the streamwise development length of the TBL. The latter was realized throughchanging the position of the air injection along the length of
the water tunnel facility. Increasing the freestream velocity resulted in an increase of the air layer length, while its maximum
thickness remained relatively unaltered. An increase in the
TBL development length, had a similarly marginal effect on
the resulting maximum air layer thickness but led to a shorter
air layer length. The latter could be attributed to a decrease inlocal mean velocity due to the TBL growth, reflected in a decrease of the air layer to boundary layer thickness ratio (from0.27 to 0.17). The results of this study are expected to provide
insight on the design conditions of an air layer drag reduction
system installed in the hull of a ship.

MOTIVATION
Friction drag accounts on average for approximately 70%of the overall resistance of a ship (Larsson & Raven, 2010),
and thus a large part of a typical ship’s propulsive power isrequired to overcome it. To reduce this drag air layer lubrication techniques have been proposed and investigated overthe past years, among other methods. These techniques could
lead to fuel cost savings and a lower environmental impact.
While drag reduction measurements using a variety of injectors and flow conditions have been performed by different research groups to date, few scaling laws able to collapse thedata are available. Past studies, depending on the capabilitiesof the experimental facilities used, investigated the effect of thefreestream velocity and/or the incoming liquid boundary layer
thickness on the air layer flow in different ways. In the study of
Zverkhovskyi (2014), the incoming liquid TBL thickness was

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

Figure 1: Schematic representation of the setup. The two different injection positions are indicated in red. FOV1 is the field of viewfor the incoming boundary layer and FOV2 for the flow around the air layer. The measuring system is shown for position x = 1.45 m.
In the case of the measurement in position x = 3.95 m the entire measurement system moves downstream. Flow is from right to left.

Table 1: Summary of the incoming boundary layer prop-

in a stable air layer for all cases tested here (see also Nikolaidou et al., 2021). The flow was tripped with a 0.5 mm thickzig-zag trip located 8 cm downstream of the start of the flat
plate. The corresponding Reθ at the tripping location varied
from 150 to 190 based on the Blasius’s solution for a laminarboundary layer.

erties for two different injection positions.

Pos.

x
(m)

U∞
(m/s)

Rex

Reθ

Reτ

θ
(mm)

1

1.45

0.68

993250

2970

1532

4.13

1

1.45

0.77

1118530

3677

1688

4.41

1

1.45

0.86

1261500

3614

1409

4.02

1

1.45

0.92

1363000

4781

2098

4.93

2

3.95

0.71

2808450

5343

3481

7.43

2

3.95

0.80

3161580

7462

4495

8.9

2

3.95

0.89

3436500

7254

3352

7.76

2

3.95

0.96

3713000

8025

3636

7.97

The incoming boundary layer upstream of the air injection, as well as its development around the air cavity, were
measured simultaneously with planar (2D-2C) PIV using two
high-resolution LaVision LX pro (16 MegaPixel), 12-bit cameras. The acquisition frequency was 0.7 Hz and 1600 statistically independent images were recorded for each dataset. The
laser sheet was introduced from the bottom creating a thinsheet (∼ 1 mm) in a streamwise–wall-normal (x-y) plane at
the tunnel’s mid-span. The optical magnification was approximately 12 px/mm for the larger (downstream) FoV and 27
px/mm for the smaller (upstream) one, resulting in a spatial
resolution of the velocity field (based on the final interrogation window size) of 2 mm and 0.88 mm respectively. Finally, a LaVision’s Imager sCMOS CLHS camera was used
to image the air layers in a streamwise-spanwise plane. The
image acquisition rate was 2 Hz, allowing independent snapshots. The field of view was approximately 700 x 600 mm2
and the magnification approximately 3.6 px/mm in both directions. A sketch of the experimental setup can be seen in figure
1.

In the current study, we aim to revisit some of these questions, specifically targeting the effect of the incoming boundary layer characteristics on the geometry of the air layer developed downstream of the air injection, without the use of a cavitator or a BFS. This is achieved by varying both the freestream
velocity and the streamwise development length of the liquidboundary layer, resulting in a large range of Reynolds numbers for the incoming flow. The effect of those changes in the
resulting air layer geometry are subsequently evaluated.

The experimental campaign included both a variationof the air injector position (in x, with x=0 at the origin of
the boundary layer) and the freestream velocity. The tested
freestream velocities ranged from 0.68 m/s to 0.96 m/s with a
Reynolds number based on the water depth, Red ranging from3.94 × 105 to 5.45 × 105 . The air injector was positioned
0.45 m and 1.95 m from the start of the test section. However, as indicated by previous measurements at the water tunnel (Harleman et al. (2011)), the boundary layer developmentment starts in the contraction region prior to the test section(approximately 1 m upstream). This is also considered in thecurrent measurements. In each position, apart from measurements with an air layer present, single phase flow measurements (without the air layer) were performed as well to serve
as a reference case. In the current paper, the incoming TBL
results are presented for the one phase flow case only. These
are summarized in table 1. It must be noted that the incoming boundary layer experiences the presence of the air layer
and results of the two phase flow case are expected to show adifference as seen in Anand (2021).

EXPERIMENTAL SETUP
Experiments were performed in the water tunnel of theLaboratory for Aero & Hydrodynamics of the Delft University of Technology. The test section of the tunnel has a crosssectional area of 60 × 60 cm2 and a length of 5 m. The open
surface of the water tunnel was covered with two identical flat
plates, each 2.485 m long, tightly placed one after the other.
The water depth was d = 58 cm. One of the plates was fitted with a slot type air injector, spanning the central 58 cm
of the plate width. The length of the slot was 4 mm. Bothplates were equipped with side fences to prevent the air fromescaping through the sides. Compressed air was injected fromthe top side of the plate through two manifolds and dispersed
over the width of the slot. The air flow rate, Qair , was manually controlled with a valve and measured with a rotameter.
A constant air flow rate of 42 l/min was used which resulted

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

(a)

(e)

(b)

(f)

(c)

(d)

Air layer length

Air layer length

(g)

(h)

Figure 2: Characteristic air layer images for different air injection positions and freestream velocities. For the shorter development
length of x = 1.45 m (a)-(d) and the larger development length of x = 3.95 m (e)-(h). Flow is from down up.

Figure 4: Side view of the air layer. Flow is from right to left.
Figure 3: Double mean streamise velocity profiles of the incoming boundary layer for the two different air injection positions compared with LDA data from De Graaff & Eaton(2000).

The boundary layer thickness was defined as the wall normal distance where the velocity is 99% of the freestream velocity U∞ . The freestream velocity U∞ and δ99 were then determined iteratively with U∞ defined as the mean of all data
points with y > δ99 . The friction velocity was determinedwith the Clauser chart method (Clauser (1956)). The computed freestream velocities indicated a increase of 4% fromthe shorter to the longer development length in the absence ofa slopping bed in the bottom of the tunnel (see also table 1).
The incoming boundary layer thickness for the larger development length (δ99 = 96 mm) was approximately double in size
compared to the smaller development length (δ99 = 53 mm).
Next the air layer characteristics (length Lair and thickness tair ) were computed. In this case tair is the actually measured one. The air layer length was determined from the images of the down-up camera (see camera in figure 1). An edge
detection algorithm was employed to locate the closure line of
the air layer in each image (figure 2). This included a medianfiltering of the image, background normalization, increase of
the contract. The grayscale image was then binarized based on

RESULTSFirst a characterization of the incoming TBL was performed for the two different air injection positions (x = 3.95
m and x = 1.45 m). Mean velocity profiles and mean normal
and shear stresses were computed but only the mean velocities are discussed in this paper. The mean velocity profiles
were spatially averaged over the length of the field of view
(FOV1 in figure 1) in the absence of strong streamwise gradients. The double average profiles in the case of the higher
freestream velocity considered can be seen in figure 3. It must
be noted that FOV1 was considerably larger than the boundary
layer thickness (larger than 1.5δ99 ). Due to imperfections of
the setup and the water tunnel itself, the freestream region was
more noisy than expected and a large extent of FOV1 & FOV2
in the wall-normal direction provided a clearer picture of thefreestream region.

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

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5: Mean correlation map for the shorter streamwise development length (a),(c),(e). The black dotted line indicates the edge ofthe air layer. Contours of the mean streamwise velocity in the same position (b),(d),(f). The air layer is in black.

(a)

(b)

Figure 6: Air layer length (a) and maximum air layer thickness (b) in different freestream velocities and two streamwise development
lengths.

a threshold and the air closure line was detected (blue lines infigure 2). At each instantaneous image, Lair was estimated as
the shortest streamwise distance of the identified closure linefrom the injector. This was done to ensure that only the spanwise homogeneous part of the air layer is considered (indicatedas “length” in figure 4). At higher velocities and for the larger
development length, air leakage was observed in the form of
three elongated air stripes creating an inhomogeneous distribution in the spanwise direction (see also figures 2g and 2h).
The length of these air strips is not considered in the aforementioned definition since it is still unclear if these regions
contribute to drag reduction. Furthermore, they could not be
quantified with the present set-up.

the determination of the mean air water interface and its maximum thickness (at the apex of the concave interface) for all
conditions. Another way of determining the air layer thickness from PIV images was proposed by Anand (2021), where
the air-water interface is estimated at each time instance, using the instantaneous instead of the mean correlation maps. It
must be noted that an estimate of the Lair could be also obtained by the mean correlation map in a similar manner as tair
was determined. However, difficulties pertaining to the unsteady character of the closure region of the air layer made thedetection of Lair through the PIV images challenging, especially for the higher freestream velocities. As a result the airlayer length Lair was determined solely based on the imaging
camera.

The thickness tair was determined from the mean correlation value R of the particle image pairs (figure 5). Morespecifically, a noticeable decrease of the correlation value wasobserved inside the air layer because of the absence of seeding
particles in the air phase. Subsequent appropriate thresholding
and image processing of the mean correlation maps allowed

Once the air layer geometry is determined, it is possible
to get an idea of the mean flow around the air layer (figures
5d,5e,5f). As the boundary layer approaches the air layer it experiences consecutively an adverse, a favorable and then again
an adverse pressure gradient. The boundary layer is thinnest

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

Figure 7: Mean streamwise velocity profile in the case of the higher velocity for the shorter (x = 1.45 m) and the longer (x = 3.95 m)
streamwise developing length.

approximately at the apex of the air layer. Similar observations were also documented in Anand (2021). In the case ofincreasing freestream velocity, the magnitude of the alternating pressure gradients is qualitatively smaller. Further analysisof the liquid flow around the air layer is ongoing.
The effect of the different freestream velocities and air injection positions on the air layer characteristics can be seen in
figure 6. Increasing U∞ resulted in a marked increase of Lair ,a trend qualitatively matched for the two different TBL development lengths; an increase in the latter led to a consistently
shorter Lair for all velocities although that effect was much
weaker (figure 6a). The variation of tair in response to changes
in both U∞ and development length was within the experimental uncertainty of 2 mm (owing to the sensitivity of the detection method and the PIV resolution) and thus no measurable
effect of either parameter could be identified (figure 6b).

ation was significantly large and as a result the local velocity
at the air thickness height tair in this case would be closer tothe freestream velocity in comparison to our case here. Apartfrom the effect of the local velocity to the air layer, potential
effects due to the different structuring of the TBL as it develops downstream are much more difficult to identify in the current campaign but they are expected to exert a larger influenceon the instantaneous rather than average characteristics of the
air liquid interface (such as the different topology observed infigure 2).
In conclusion, increasing the freestream velocity resulted
in an increase of the air layer length, while its maximum thickness remained relatively unaltered. An increase in the TBL
development length, had a similarly marginal effect on the resulting maximum air layer thickness but led to a shorter air
layer length. Consideration of the thickness ratio between the
air layer and the TBL reveals that the liquid velocity in thevicinity of the air layer has the bigger effect on the air layer
length. In the real case scenario of an air layer beneath the hullof a ship, the air layer thickness would be a small fraction of
the the incoming boundary layer (∼ 1) and thus considerationsin this study could help in the air injection position along thehull.

DISCUSSION AND CONCLUSIONS
The aforementioned observations indicate that both theincoming boundary layer characteristics and the freestream velocity affect the air layer geometry. Larger air layer lengths
were found for larger freestream velocities. This effect of thefreestream velocity on the air layer length is intuitively easierto grasp; in order to better understand the effect of the TBL
development length however, it is instructive to consider the
thickness ratio between the air layer and the TBL δtair . For
99
both injector locations, the air layer is significantly thinnerthan the TBL - its maximum reaching just the end of the log( δtair ≈ 0.17) and the lower wake region ( δtair ≈ 0.27) for the99
99
larger development length (x = 3.95 m) and the shorter one (x= 1.45 m), respectively. It then follows that the local mean
velocity of the TBL at the height of the air layer would decrease as the TBL develops downstream (from 0.76 m/s to 0.75
m/s approximately for the higher U∞ shown in figure 7). The
resulting decrease in the air layer length is then in line withthe observed speed dependency discussed above. This indicates that, as far as the mean characteristics of the air layer
are concerned - and for the range of conditions tested here the liquid velocity in the vicinity of the air layer is the mostprominent influence. In the study of Zverkhovskyi (2014), thefreestream velocity rather than the local one was identified tohave the bigger effect on the air cavity length. However in the
aforementioned study the thickness ratio δtair under consider-

ACKNOWLEDGEMENTS
This work is part of the public-private research program“Water Quality in Maritime Hydrodynamics” (AQUA) project
P17-07. The support by the Netherlands Organisation for
Scientific Research (NWO) Domain Applied and Engineering
Sciences, and project partners is gratefully acknowledged.

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512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
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