225

1 INTRODUCTION

Friction is a critical factor when it comes to fuel

consumption of ships. The lower the friction the lower

the energy demand. Therefore, the EU project

AIRCOAT

aims at reducing hull friction to a

minimum. In water ferns, the Salvinia effect of a

micro-and nanostructured surface with hydrophobic

and hydrophilic characteristics allows for air retention

under water [1] and while the air spring effect

contributes to the air layer stability [6]. Inspired by the

Salvinia effect, the AIRCOAT project intends to

develop a biomimetic passive air layer technology.

The AIRCOAT project has received funding from the European

Union’s Horizon 2020 research and innovation programme under

grant agreement N°764553.

With a passive air layer covering the hull, the contact

area between water and ship is decreased significantly

which reduces fuel consumption, carbon dioxide

emission as well as acoustic emissions [11, 12]. Water

flowing along a solid wall is subject to the no-slip

condition with a boundary layer where the fluid

velocity increases normal to the surface from zero

velocity to freestream velocity [17]. But if the fluid

flows along an otherwise liquid or gaseous interface

the conditions is expected to differ, which results in

friction reduction [10]. To better understand the

underlying mechanism of the friction reduction over

the hydrophobic AIRCOAT surface, Fraunhofer CML

(CML) built a flow channel that creates a stationary

turbulent flow driven by hydrostatic pressure. Water

is send in a circuit and the test section is a square duct

of 40 mm edge length. Made from acrylic glass it

allows for noninvasive measurement by a laser

Validation of a Flow Channel to Investigate Velocity

Profiles of Friction-Reducing Ship Coatings

J. Weisheit, V.E. Schneider, J.M. Serr, N. Hagemeister & J. Oeffner

Fraunhofer Centre for Maritime Logistics and Services CML, Hamburg, Germany

ABSTRACT: Reducing friction with specialised hull coatings or air lubrication technologies has a potential

reducing energy consumption and emissions in shipping. The EU project AIRCOAT combines both by

developing a passive air lubrication technology inspired by nature that is implemented on a self-adhesive foil

system. Besides validating the friction reduction it is of high interest to understand the underlying mechanism

that causes the reduction. Therefore, a flow channel was designed, that creates a stationary turbulent flow

within a square duct allowing for non-invasive measurements by laser doppler velocimetry. The high spatial

resolution of the laser device makes recording velocity profiles within the boundary layer down to the viscous

sublayer possible. Determination of the wall shear stress τ enables direct comparison of different friction

reduction experiments. In this paper we validate the methodology by determining the velocity profile of the flat

channel wall (without coatings). We further use the results to validate a CFD model in created in OpenFOAM.

We find that velocities along the longitudinal axis are generally in good agreement between numerical and

experimental investigations.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 1

March 2021

DOI: 10.12716/1001.15.01.24

226

doppler velocimeter (LDV). The device allows to

resolve the boundary layer and the evaluation of the

wall shear stress in the boundary layer which is

important when it comes to the assessment of wall

friction [4]. This study will explain the design and

methodology of the flow channel built to perform

measurements in a fully developed turbulent flow, the

experimental setup and measurements, performed

with a non-intrusive LDV device. To further validate

the experimental data a comparison with literature is

presented. This validation of flow conditions in the

test section and measurement technique acts as a

prerequisite to perform future measurements with the

novel air retaining surface to measure the slip

velocities over a hydrophobic wall. In order to better

understand the underlying principle of drag

reduction, the study further presents a validation of a

Computational Fluid Dynamics (CFD) model of the

channel. The motivation behind the numerical

investigations is crosschecking of the experiments as

well as creating a reference for modelling and

analysing novel coatings through separate developed

wall functions in a Reynolds Averaged Navier Stokes

(RANS) simulation.

Figure 1. Cross-section of the flow channel duct with

removable cap

2 METHODOLOGY

2.1 Channel Setup

The designed flow channel follows a simple and low-

cost but effective approach of achieving a fully

turbulent flow as well as a fully developed flow

profile over the channel height and width. The flow

channel setup resembles the setup of [15] and is of a

widely adapted setup for this kind of measurement.

The three main features to achieve a fully

developed and undisturbed (as much as possible)

flow for the presented setup are: 1) a flow induced by

hydrostatic pressure with an inflow tank based on an

overflow principle to minimise any influence of the

pump, which fills the inflow tank, 2) a nozzle in front

of the test section specifically designed to minimise

flow separation and 3) a test section with a length of

3000 mm and a square cross section of 40.00 mm

height and width resulting in the length to height

ratio of 75. The flow is driven by a constant water

column, which is depicted in the general flow tank

setup as vertical pipe in Fig. 2. A constant water

column is guaranteed by the design of the inflow tank,

separated into three compartments, with the vertical

pipe attached to the centre compartment. Water is

pumped into the left compartment, which will spill

any excess water into the centre compartment. When

the centre compartment is filled, excess water flows

into the right compartment. This last compartment is

connected to the basin from which the pump is

circulating the water back to the inflow tank, i.e. the

first compartment. As long as more water is pumped

into the elevated inflow tank than is flowing out of the

pipes connecting duct and inflow tank, the water

column is constant and producing a stationary flow

within the test section.

With the flow established, the water is directed

into the test section, which is accomplished by using a

specifically designed nozzle. Studies have shown that

specific geometries reduce the flow separation in

nozzles with the best results originating from

applying a polynomial of fifth order [18]. This

approach has been adapted for the cross-section

changing from a circular inflow into the nozzle to a

square shaped outflow from the nozzle into the test

section. By using additive manufacturing the complex

nozzle geometry, depicted in Fig. 2, has been printed

and adapted in several iterations to satisfy criteria

such as mechanical stability and water tightness. From

the nozzle, the flow enters the 3 m long test section

where according to [16] fully developed turbulent

flow can be expected after passing 70D. The test

section is made of acrylic glass and features a

removable cover, see Fig. 1. This removable cover

allows access over the whole length of the test section.

With this key feature it is possible to apply different

materials within the duct. In that manner different

materials, e.g. the aforementioned foil with

hydrophobic properties that can be utilised as ship

coating, will be tested regarding friction reduction.

The flat and transparent channel walls enable LDV

measurements, which is also the main reason for the

square cross section. A circular pipe would provide a

more preferable environment from a hydrodynamic

point of view but would interfere with the laser and

cause unwanted refraction and reflections, which

again leads to erroneous measurements. Being

transparent over the full length there are no

limitations to locating the LDV along the flow

channel.

2.2 LDV Measurements

With a LDV device it is possible to measure velocity

without intruding the flow. The device is mounted

perpendicular to the flow channel and the main flow

direction and the measurement volume (MV) is

oriented normal to the channel wall. The details of

LDV principle are well known and described in detail,

e.g. in [4]. Within this study the principle is only

summarised to explain the basics and why it is a

preferable technique for boundary layer assessment

based on [2].

227

Figure 2. Schematic overview of the flow channel with its main components: inflow tank, vertical pipe to build hydrostatic

pressure, L-pipe to direct the flow towards the duct, nozzle with changing cross-section as proposed by [18], test section,

small nozzle and valve for flow speed control, outflow tank to regulate water column behind the test section, basin with

excess water to feed pump and collect excess water from inflow tank.

u df=

(1)

Applying the two Doppler frequencies fD,1 and fD,2,

the velocity of the crossing particle can be determined

by Eq. 2. The utilised device has laser beams of

wavelength λ1 = 532 nm and λ2 = 561 nm meeting

under an angle of 16 degrees.

( )

2sin / 2





(2)

Other than measurements with a conventional

LDV, which obtains velocity values for the entire MV,

a Profile Sensor allows a higher spatial resolution and

the velocity as well as the position of a particle

crossing the MV can be obtained. The position, z, of

the tracer particle can be determined by the frequency

quotient and the calibration function,



, which is

provided by the manufacturer [7]. With a known z-

position the actual fringe spacing and velocity can be

derived [3]. For measurements close to wall - as it is

intended in our work to analyse the boundary layer

flow - the Profile Sensor is of advantage. The LDV

Profile Sensor by ILA R& D [8] offers a spatial

resolution up to 1% of the measurement volume

length. With a determination of particle positions

within the MV the boundary layer, with its linear

velocity gradient, can be observed.



(3)

An LDV device allows only for a quasi-point

measurement of flow velocity. Therefore, to record a

velocity pattern across the channel height or width

multiple measurements need to be performed. After a

quasi-point measurement is completed the MV is

moved to different location by mechanical traversing

and new measurement is started. Afterwards the

recorded data from one MV is stitched together to

present a flow pattern or near-wall velocity profile.

Figure 3. Fringe System of two crossing laser beams. By the

combination of two different wave lengths (green areas: λ1

and λ2), the known fringe distances d along with a

calibration function the velocity and the position of a

crossing particle can be calculated. At a particle crossing the

MV causes a change in fringe distance and two Doppler

frequencies.

3 CFD SIMULATIONS

Table 1. Physical constants for CFD simulation

_______________________________________________

Quantity Unit Value

_______________________________________________

Density kg/m

998.00

Viscosity kg/ms 0.001005

_______________________________________________

In order to quickly transfer experimental results to

technical implementation and estimate the

performance of surface or hull coatings, e.g. the

aforementioned passive air layer, in real world

applications, the use of CFD simulations is envisaged.

However, to be able to use these tools with

confidence, they have to be validated by experimental

results. Furthermore, CFD simulations can be used for

sanity checks of experimental results. If numerical and

experimental results are sufficiently similar it is easier

to exclude methodical flaws or systematic measuring

errors. Consequently, the internal features of the flow

channel described above have been replicated in a

Computer Aided Design (CAD) environment to feed

into the simulation pipeline.

228

3.1 Numerical setup

In this study a finite-volume approach is used which

utilises the OpenFOAM v1806 package [13]. Only one

half of the channel is modelled taking advantage of

the symmetry in order to reduce the computational

effort. The computational domain is depicted in Fig. 4.

The setup at hand utilises the Reynolds-Averaged-

NavierStokes-Equations with k-ω-SST turbulence

model according to [9] to simulate the effects of

turbulent flow while limiting the computational

effort. Since the flow is gravity driven and assumed to

be steady, the buoyantBoussinesqSimpleFoam [14] solver

and second-order accuracy schemes have been

selected. Physical constants were defined according to

Table 1.

Due to unknown turbulence properties of the flow

at the inlet, initial turbulence parameters were

estimated based on the preliminary study and the

assumption of fully developed flow with isotropic

turbulence at the inlet as given in Table 2. A

turbulence parameter study was not conducted as not

to distort the validation through false optimisation of

input quantities.

Table 2. Initial turbulence parameters

_______________________________________________

Quantity Units Value

_______________________________________________

κ m/s

1.0070 10

−6

ω s

−1

0.20356

ν m

/s 0.01059

_______________________________________________

3.2 Preliminary study

A preliminary study has been performed to estimate

the flow velocities in different parts of the flow

channel, namely the vertical pipe, the L-pipe, the

nozzle, the test section, the small nozzle and the

outflow tank. For this purpose a simple base grid was

developed as follows. The maximum cell size was set

to 0.011 m. The cell size was halved at the nozzle,

which leads into the test section and then halved

again for the section stretching from the beginning of

the second nozzle through the outflow pipe into the

outflow basin. To capture the boundary layer prism

cells were applied on the walls. Since the actual local

flow velocities were only known for the test section at

this stage from the experiments, the thickness of the

wall layer was kept constant throughout the domain,

which resulted in a variation of y+ values throughout

the domain. However, for estimation of the local

velocities this seemed to be sufficient. Fig. 4 shows the

magnitude of the velocity in the channel’s symmetry

plane for the base grid configuration.

Figure 4. Velocity magnitude in channel symmetry plane,

with water flowing from the inlet at the top left into the

vertical pipe and onwards into the L-pipe, accelerating

inside the nozzle before entering the test section with a

maximum velocity of approx. 0.3 m/s, exiting the test

section into the second nozzle and finally reaching the

outflow tank.

The water enters the inlet at a velocity of about

0.01 m/s and on close inspection flow separation can

be spotted on the inside of the sharp 90 degree angle

turn inside the L-pipe. The velocity stays

approximately constant until it reaches the nozzle

before the test section. Moving through the nozzle

into the test section, the flow accelerates to close to 0.3

m/s in the centre of the duct. After passing the test

section the flow accelerates further in the small nozzle

due to the reduction in cross section and exits the

outlet pipe into the outlet tank as a distinctive jet.

3.3 Grid study

Based on the results of a preliminary study, a grid

study has been performed to study the sensitivity of

the results regarding the spatial resolution of the

geometry. For this study the maximum cell size was

systematically varied by factor of 1.5 to derive one

more coarse and two finer grids. The target y

was set

to ≤ 1 to accurately model the boundary layer which is

of prime importance for the planned application of

the channel. This means that the number of boundary

layer cells varies between the grids. There were no

significant differences found between the different

grids with volume fluxes, mean and maximum

velocities as well as velocity profiles at the 70D

position in the experiment found to be in good

agreement. The data presented in the following

belongs to the grid with a base size of 0.0103 m, which

corresponds to the preliminary mesh (base size = 0.011

m) with a minor adjustment to increase the mesh

quality to allow for the changes in the boundary layer

mesh.

4 RESULTS

4.1 Velocity Patterns of Experiments and Numerical

Simulation

Velocity patterns are presented for one longitudinal

location along the flow channel at 70D, in which D is

the hydraulic diameter of the duct. With the current

setup and under given circumstances of chosen

equipment the Reynolds number is Re = 11.400 in

reference to D. The measurements were conducted at

one Reynolds number and under the assumption of

stationary flow. The normal axis for each pattern is in

the centre of the duct for the smallest influence

possible by the walls. Presented are velocity patterns

across the duct’s height, z-pattern, as well as width, y-

pattern, in Fig. 5.

The experimental results are 1D measurements and

presented are mean values from four measurements.

The different markers indicate the z-pattern and y-

pattern, respectively. Moreover, an error bar

represents the standard deviation for experimental

results. The LDV device allows for two parallel

measurements at the same time since the two laser

beams can record velocities independent from each

other, although a measurement event is only valid if

the two laser beams detect the same particle. A

repetition of that process is performed afterwards.

CFD results are presented by dashed and dotted lines,

respectively.

229

From Fig. 5 can be seen that the velocity is

symmetric at the respective centre line over the height

as well as width, which implies a full turbulent flow.

Furthermore, a good agreement with CFD results is

clearly visible. Especially the centre line flow shows

good agreement for z-pattern as well as y-pattern.

Mean velocities are similar to CFD results and the

standard deviation for the mean values is small. The

measurements closer to the respective channel wall

show that turbulence increases and uncertainties of

the measurement increase as well. This becomes also

visible from the comparison of selected values in

experimental data close to the wall. With the different

velocities for the points closest to the wall for z-

pattern and y-pattern it becomes visible that the

experimental data is highly depending on a thorough

set-up and fussy alignment of laser device and flow

channel.

Figure 6. Velocity profile close to the wall with a linear fit

(blue line) to determine wall shear stress. The fit curve is

forced through zero to imply zero velocity at the wall.

Contrary to CFD results, experimental results do

not show zero velocity, since a measurement close to

the wall is time consuming and requires high effort.

Still, to get an idea of flow conditions a rather coarse

measuring grid is sufficient. The comparison shows

that the flow at 70D is fully turbulent and the

respective pattern is nearly symmetric. Furthermore,

the y-pattern differs from the z-pattern due to the

orientation of the MV that hasn’t been changed during

the experiments. A measurement to assess the

velocities close to the wall, that allow the

determination of wall shear stress, is presented in 4.2.

4.2 Near Wall Measurements

A near wall measurement is performed to estimate the

possibilities of boundary layer investigations and

determination of wall shear stress, τ, within the

current channel construction and setup. The MV is

located so close to the wall that half the MV is inside

the channel and the other half disappearing in the

channel wall. After the successful measurement of

10000 particles crossing the MV, the MV is moved

step wise away from the wall. Subsequently all

recorded MVs are stitched together to build a near-

wall flow profile over half the duct (δ = 20 mm). Fig. 6

depicts the near linear increase of velocity between

200 and 800 micrometre wall distance. A linear fit

curve is added to distinguish the intended area. For

velocity values further away from the wall, a non-

linear gradient becomes visible. Also, clearly visible

are the limits of the LDV device, which allows no

detection of particles slower than 0.025 m/s (see Sec. 5

for further discussion). Therefore, the linear fit curve

is forced to go through zero, since a point directly at

the solid wall has zero velocity. The slope of the

straight line, or the gradient of the velocity profile

near the wall, is assumed to represent the near wall

shear stresses from the channel wall [17]. From the

relation in Eq. (4), τ can be calculated and can serve as

a variable for further boundary layer evaluations with

η being the dynamic viscosity of water and ∂u/∂y the

local shear velocity [16]. The determination of τ is

highly depending on water carefully recorded

velocity and a constant temperature, since small

deviations have a strong impact on the result. Fig. 6

indicates room for improvement. Ideally all grey dots

would match the blue line.

Figure 5. Velocity patterns at 70D. y pattern is the velocity

pattern across the channel width, whereas z pattern is the

velocity across the channel height. Horizontal error bars

denote the standard deviation of the respective point

measurement.





(4)

The velocity profile across half the channel duct

recorded with a spatial resolution in the near-wall

area is presented in Fig. 7, in a semi-logarithmic plot

with dimensionless values u

over y

(with u

= u/uτ

and y

= (y ∙ uτ )/ν).

From this depiction the non-zero velocity from

experimental data becomes visible as well. The blue

line represents the area of the linear increase and the

green line the log law based on u

= 1/κ

∗

ln(y

) + C

with κ ≈ 0.41 and C

≈ 5.2. The logarithmic part of the

profile is represented better than the linear portion.

This again points out the need for high profoundness

in terms of near-wall experiments. Other than that a

general agreement between experimental data,

theoretical values and literature data, approves the

measurement concept and the procedure to determine

τ. Although, leaps and irregular values for

experimental data implies partly erroneous

230

measurements. This can be ascribed to the stitching

process of the MVs and the recording on different

days. Moreover, the determination of wall shear

stresses is prone to changes in temperature. This is not

considered sufficiently within the selected approach.

Nonetheless, the linear part is distinguishable from

logarithmic area and therefore determination of slip

velocity seems realisable. Results from own numerical

calculations are not presented due to the fact that the

selected RANS approach uses wall functions. These

wall functions are boundary conditions which

presume predefined turbulence parameter and

velocity profiles normal to the walls, which are

derived from the law of the wall. Hence, the

compliance to the law of the wall is inherent.

Figure 7. Velocity profile across half the channel duct in

comparison with theoretical values and CFD data from [19].

The green line crosses exp. data in the logarithmic layer,

whereas the blue line crosses exp. data in the viscous

sublayer.

5 CONCLUSION AND OUTLOOK

The general methodology and the proof-of-concept of

how to assess the friction reducing capabilities of an

air retaining surface were presented. The fundamental

principle of the passive air lubrication AIRCOAT

surface is to mimic the air retaining properties of the

Salvinia fern on a foil system, which has both

hydrophilic as well as hydrophobic characteristics.

One goal of the AIRCOAT project is to prove the

friction reducing properties of such an artificial foil in

order to validate its potential as a sustainable future

ship hull coating. This study serves as the prerequisite

for the long term goal to identify and investigate the

slip velocity active over a passive air layer. Here, the

methodology was validated in a controlled steady

environment by investigating a flat surface.

The construction of a flow channel driven by a

constant water column, the measurement with a LDV

Profile Sensor and the implementation of

corresponding CFD simulations were reported. The

flow channel follows a low-coast approach with the

goal of a fully turbulent flow. One Re number was

chosen to compare physical experimental results to a

CFD simulation. A comparison of experimental data

and CFD results of vertical and horizontal flow

patterns showed close resemblance across the square

cross-section.

Measurements close to the wall showed the

advantage of the LDV Profile Sensor that yielded high

resolution measurements within the boundary layer

and the near-wall area. The linear increase in velocity,

i.e. the local shear velocity, was identified and the

mean wall shear stress τ determined.

The performed experiments concluded that well

controlled flow conditions and a thorough

experimental setup are utterly important to use the

full capability of the high spatial resolution achievable

with a Profile Sensor, e.g. sturdy construction or

temperature monitored fluids.

For future measurements a Profile Sensor with

carrier-frequency technique to better identify particles

with a near zero velocity is preferable [5]. Such a

sensor has the advantage of enabling the

determination of flow speeds close to the wall reliably

and thus leads to an improved the determination of

wall shear stresses.

In future experiments the presented methodology -

and validated for flat surface with no air layer - will be

used to assess turbulent flow above a structured

surface with air layer - to identify the velocity profile

and the slip velocity. Furthermore, comparing the

measured wall shear stress, τ, of flat and structured

surface can give a drag reducing capabilities of

passive air retaining surfaces.

Introducing air into the system will bring new

challenges. The phase flow regime with the air layer

under water will introduce reflection of the laser

beam due to different refraction indices of water and

air. A reflecting surface is detrimental in achieving a

strong LDV measurement signal. Nonetheless, a

comparison of these future measurements with the

herein presented methodology and reference

measurements allow to achieve a valuable

contribution in assessing and validating biologically

inspired friction reducing ship coatings or surfaces.

The flow channel will further enable the

development and validation of custom wall functions

for RANS CFD simulations that can subsequently be

used to extrapolate the effect of novel coatings such as

AIRCOAT to large scales such as ships or the inner

walls of pipes and tubes.

ACKNOWLEDGEMENT

The study was performed as part of the AIRCOAT project.

The AIRCOAT project has received funding from the

European Union’s Horizon 2020 research and innovation

programme under grant agreement N° 764553. Special

thanks goes to Prof. Dr.-Ing. Michael Schlüter and his team

from the Institute of Multiphase Flows of the Hamburg

University of Technology for giving advise during flow

channel design and for lending the LDA Profile Sensor.

Furthermore, we thank Prof.(i.R.) Dr. Wolfgang Mackens

and his team from the "DLR School Lab" of the Hamburg

University of Technology for laboratory access.

231

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