Experimental and Computational Investigation of a Fractal Grid Wake A. Fuchs W. Medjroubi H. Hochstein G. G ulker and J. Peinke Institute of Physics and ForWind University of Oldenburg K upkersweg 70 26129 Oldenburg Germany

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Experimental and Computational Investigation of a Fractal Grid Wake

A. Fuchs, W. Medjroubi, H. Hochstein, G. G¨ulker, and J. Peinke

Institute of Physics and ForWind, University of Oldenburg, K¨upkersweg 70, 26129 Oldenburg, Germany

(Dated: October 13, 2022)

Fractal grids generate turbulence by exciting many length scales of diﬀerent sizes simultaneously

rather than using the nonlinear cascade mechanism to obtain multi-scale structures, as it is the

case for regular grids. The interest in these grids has been further building up since the surprising

ﬁndings stemming from the experimental and computational studies conducted on these grids. This

work presents experimental wind tunnel and computational ﬂuid dynamics (CFD) studies of the

turbulent ﬂow generated by a space-ﬁlling fractal square grid. The experimental work includes

Particle Image Velocimetry (PIV) and hot-wire measurements. In addition, Delayed Detached Eddy

Simulations (DDES) with a Spalart-Allmaras background turbulence model are conducted using

the open-source package OpenFOAM. This is the ﬁrst time DDES simulations are used to simulate

and characterize the turbulent ﬂow generated by a fractal grid. Finally, this article reports on the

extensive statistical study and the direct comparison between the experimentally and numerically

acquired time series to investigate and compare one-point- and two-point statistics. Our goal is to

validate our computational results and provide enhanced insight into the complexity of the multi-scale

generation of turbulence using a fractal grid with a low number of fractal iterations. In particular,

we investigate the diﬀerent turbulent structures and their complex interaction in the near-grid region

or the production regime of the fractal grid ﬂow.

I. INTRODUCTION

Grid-generated turbulence has been investigated for

more than 70 years, being the most common method to

create turbulence in wind tunnels under controlled condi-

tions. The turbulence generated by the so-called regular

grids is nearly homogeneous and isotropic downstream

from the grid [

]. Nevertheless, the Reynolds numbers

and the turbulent length scales obtained are quite low

(

Reλ

u0λ/ν <

100, where

Reλ

is the Reynolds number

based on the Taylor microscale

, the root mean square

of the velocity ﬂuctuations

pheu2i

and the kinematic

viscosity

). This constitutes a handicap when it is

desired to investigate features of high Reynolds number

turbulence. Several other grids were proposed to overcome

this problem, including the use of mechanically moving

parts called active grids [

–

]. In [

], the use of an active

grid resulted in turbulence with higher Reynolds number

(

Reλ

= 390), higher turbulence intensities, and larger

integral length scales. Moreover, the resulting energy

spectrum had a wider inertial subrange, about two orders

of magnitude in wavenumber, compared to a regular grid.

Hurst and Vassilicos [

] proposed another method to

generate higher Reynolds numbers and high turbulence

intensities, which does not involve mechanically moving

grid components and is easier to use and construct. In

[

], the authors characterized the turbulence generated

by three types of fractal grids (cross, I and square shaped

grids), using 21 diﬀerent grids in wind tunnel experiments.

The main idea behind fractal grids is to use grids that con-

sist of a multi-scale collection of obstacles and openings

based on a speciﬁc pattern, which is repeated in increas-

ingly numerous copies at smaller scales. Fractal therefore

emphasizes that these grids have multiple scales that are

self-similar. This property helps reduce the parameters

necessary to specify the design of these multi-scale grids.

Besides the easy way to generate high Re-number turbu-

lence, the topic of fractal grid turbulence has attracted

considerable attention due to the speciﬁc features of the

wake ﬂow.

The concept behind fractal grids is to generate turbu-

lence by directly exciting a wide range of length scales at

once, rather than using the nonlinear cascade mechanism

to obtain multi-scale structures, as it is the case for regular

grids. These ﬂow structures of diﬀerent scales inﬂuence

each other and show very diﬀerent properties compared

to all previously documented turbulent ﬂows. Interesting

results were obtained using Fractal Square Grids (FSG)

with low blockage ratios (around 25%). These results

include obtaining higher Reynolds numbers, even in small

and conventional-size wind tunnels, compared to regular

grids. In addition, it was shown that there exists an ex-

tended region between the fractal grid and a downstream

distance, where the turbulence intensity increases progres-

sively to reach a maximum value at a distance

xpeak

[

]. This region is called the production region. The

turbulence intensity then decays downstream from

xpeak

following what was thought ﬁrst to be an exponential

law [

] but was shown later on to be a fast power law

[

]. These ﬁndings contradict what is typically reported

for regular grid turbulence, namely that the turbulence

decays directly at the lee of the grid following a power-law

[

]. Another interesting characteristic of fractal grid tur-

bulence is that longitudinal and lateral turbulent integral

length scales and Taylor microscales were reported to vary

slowly downstream of the grid [7].

A more detailed study of the decay region mentioned

in [

] was conducted by Seoud and Vassilicos [

], which

conﬁrmed the ﬁndings in terms of turbulent length scale

behavior and turbulence intensity decay law. Moreover, it

was shown that the ratio of the longitudinal length scale

and Taylor microscale remains approximatively constant

arXiv:2210.06208v1 [physics.flu-dyn] 12 Oct 2022

in the decay region. In [

] this striking be-

havior was set into the context of a non constant energy

dissipation rate

Cε

. Contrary to what is predicted by

the Richardson-Kolmogorov phenomenology, the authors

could collapse one-dimensional energy spectra at diﬀer-

ent wake positions using only one length scale and

They also presented assessments of the homogeneity and

isotropy of the turbulence produced by FSG [7].

Vassilicos and Mazelier [

] related

xpeak

to the wake-

interaction length scale

x∗

, which is the ratio of the length

of the biggest square bar and its thickness.

x∗

is found to

be the appropriate length scale to characterize ﬁrst and

second-order statistics of the turbulent ﬂow generated

by FSG. The authors also showed that the turbulence

statistics are non-homogeneous and non-Gaussian in the

production region but become homogeneous and Gaussian

in the decay region. They suggested that the FSG can

be used for ﬂow control and to enhance turbulent mixing

properties by understanding and determination of how

xpeak

and the generated turbulence intensities depend on

fractal grid geometry.

Several Direct Numerical Simulations (DNS) were con-

ducted to investigate the ﬂow generated by fractal grids

[

–

]. Although these simulations qualitatively repro-

duced some of the underlying characteristics of fractal grid

turbulence, quantitative comparisons with experimental

data was not possible for mainly three reasons. First,

the simulations were conducted at very small Reynolds

numbers compared to the experiments. As an example,

in [

] the Reynolds number based on the eﬀective mesh

size (see Section II) is

ReMef f

= 4430 for the simula-

tions and

ReMef f

= 20800 for the experiments, which

is a reduction with a factor of 5. Second, fractal grids

with a smaller iteration number were simulated, mainly 3

iterations, compared to the available experimental studies

where the iterations vary from 4 to 6. Finally, the extent

of the computational domain in the streamwise direction

was limited due to the high computational cost associated

with DNS. As all the ﬂow details have to be resolved, the

meshes used in the diﬀerent DNS simulations are huge

in terms of the number of nodes. Therefore, substantial

computational power is needed to keep the computational

time realistic. In the following, we summarize two impor-

tant DNS reference papers.

Laizet and Vassilicos [

] conducted DNS simulations

using the numerical code Incompact3d based on sixth-

order compact schemes for spatial discretization and

second-order Adams-Bashforth schemes for temporal dis-

cretization. They modeled a regular and a fractal grid

(with the same eﬀective mesh size) using Immersed Bound-

ary Method (IBM) and their total numerical mesh of 765

million points. They could recover the production and

decay regions as well as the decay behavior of the turbu-

lence intensity, although they did not test the simulation

results to determine the nature of the decay law. More-

over, the turbulence recovered in the wake of the fractal

grid was found to be not homogeneous, which contradicts

the ﬁndings in the experiments [

]. They related this

observation to the small iteration number of their fractal

grid (

= 3) and the domain size chosen to be insuﬃcient

for reaching homogeneity.

In a more recent paper, Laizet and Vassilicos [

] used

a new version of Incompact3d, which scales better when

used with large numbers of computational cores. They

simulated one regular and three square fractal grids (with

diﬀerent aspect ratios). The simulations required the

use of 3456 computational cores. The DNS results show

that the turbulence produced by the fractal grids is more

intermittent than the one produced by regular ones. Nev-

ertheless, the extent of the computational domain and

number of fractal iterations (

= 3) were still insuﬃcient

to obtain homogeneous turbulence in the decay region.

Therefore, they emphasize the need for more simulations

with extended computational domain and bigger itera-

tions (

N >

3) and experiments with

= 3 to be able to

compare the results with DNS. The authors also showed

that the value of

xpeak

introduced in [

] does not apply

for their grids, which have a smaller N, and introduced a

new xpeak formula based on N and the blockage ratio σ.

IIn the present paper, the wake of the ﬂow through an

= 3 fractal square grid is investigated numerically and

experimentally. The experimental data was acquired from

PIV and hot-wire anemometry. Our main purpose is to

validate our numerical simulations against the experimen-

tal results and to characterize the turbulence generated

by fractal grids in terms of turbulent kinetic energy decay

law and one-point statistical quantities such as turbulence

intensity, third and fourth central moment and probability

density functions of the velocity ﬂuctuations. Further-

more, the characterization of such turbulent ﬁelds will

assess the capabilities of DDES in reproducing the ex-

perimental results. A further goal of this investigation

is to compare experimental and numerical data of the

wake of a fractal grid with the experimental examination

of a regular grid with the same mesh size and blockage

ratio. Our simulations and experiments also involve an ex-

tended domain to obtain more homogeneous and isotropic

turbulence than DNS obtained so far.

This paper is organized as follows. Section 2 introduces

the geometrical aspects of the fractal square grid and of

a regular grid having the same mesh size and blockage

ratio. The regular grid has been investigated only experi-

mentally and is used here for comparison purposes. The

experimental setup and details of the PIV and hot-wire

anemometry used are presented in Section 3. Section

4 is dedicated to the numerical setup, including a brief

overview of the turbulence modeling and the numerical

solver. Section 5 discusses the low-order and higher-order

statistics results. Finally, in Section 6 the conclusions are

presented with an outlook for further investigations.

II. GRID GEOMETRICAL PARAMETER

Figure 1shows the grids used in the present work. They

are placed at the inlet of the test section of a wind tunnel

in the experiments and considered when implementing

the corresponding numerical simulations (see also Figure

2b).

(a) (b)

FIG. 1. Illustration of (a) the used

= 3 space-ﬁlling square

fractal grid (FSG) geometry and (b) the regular grid used for

comparison.

In general, fractal grids are constructed from a multi-

scale collection of obstacles based on a single pattern

repeated in increasingly numerous copies with diﬀerent

scales. As presented in [

], fractal grids can be constructed

using diﬀerent geometrical patterns (see Figure 1 in [

]).

We selected a frequently used pattern for our fractal grid

[

], to be able to set our results in the context of

other research activities. The pattern of our fractal grid

is based on a square shape with

= 3 fractal iterations.

The fractal iteration parameter is the number the square

shape that is repeated at diﬀerent scales. At each iteration

(

= 0

, ..., N −

1), the number of squares is four times

higher than in the iteration

j−

1. Each scale iteration

is deﬁned by a length

and a thickness

of the

square bars constituting the grid. The thickness of the

square bars in the streamwise direction is kept constant.

The dimensions of the square patterns are related by the

ratio of the length of subsequent iterations

Lj−1

and by the ratio of the thickness of subsequent iterations

tj−1

; respectively. The geometry of the fractal

grid used in this paper is completely characterized by

two further parameters, namely the ratio of the length

of the ﬁrst iteration to the last one

LN−1

and the

ratio of the thickness of the ﬁrst iteration to the last one

tN−1

. Moreover, a fractal grid is said to be space-

ﬁlling, when its fractal dimension

= 2 (see [

], for

the deﬁnition of Df), which is the case when RL= 0.5.

Contrary to regular grids, fractal grids, especially frac-

tal square grids, do not have a well-deﬁned mesh size.

However, an equivalent eﬀective mesh size was deﬁned in

[7] as

Meff =4T2

P√1−σ, (1)

where

is the cross-section of the wind tun-

nel/simulation domain,

is the perimeter of the fractal

grid and

is the blockage ratio, which can be determined

by a calculation using the following formula

σ=A

T2=

L0t0

N−1

j=0

4j+1Rj

LRj

t−t2

N−1

j=1

22j+1R2j−1

T2.

(2)

is the sum of the areas

covered by each fractal

iteration

and corrected by the areas covered by two

iterations.

is therefore, the fractal grid’s total area.

It should be noted that the local blockage ratio varies

strongly for diﬀerent parts of the grids. A complete

quantitative description of the fractal grid we used in this

study is shown in table I.

Another important length, which seems to collapse

several turbulent statistical quantities of the streamwise

ﬂuctuating velocity, is the position of maximum turbu-

lence intensity

xpeak

, which also deﬁnes the production

(

x < xpeak

) and decay regions (

x > xpeak

). It was intro-

duced by Mazellier and Vassilicos [

] and deﬁned using

the empirical formula

xpeak ≈0.45L2

,(3)

which relies upon

xpeak

to the geometrical properties of

the fractal grid. This means that the turbulence generated

by fractal grids can be “manufactured”.

To account for the distance at which the diﬀerent wakes

generated by the fractal grid bars interact, [

] introduced

the wake-interaction length scale

x∗

. It is deﬁned with

the formula

x∗

and is in our case

x∗

= 953 mm

(see deﬁnitions of

and

in table I). The deﬁnitions

of the fractal grid eﬀective mesh size eq.

(1)

and the

blockage ratio eq.

(2)

has the advantage of returning the

eﬀective mesh size when applied to a fractal grid so that

a comparison can be made between regular and fractal

grids based on

Meff

. In this respect, we experimentally

investigated a regular grid (shown in Figure 1b) with the

same mesh size (

Meff

) and blockage ratio as the

used fractal grid for comparison.

III. EXPERIMENTAL SETUP

The experiments were conducted in a closed loop wind

tunnel with test section dimensions of 200 cm x 25 cm

x 25 cm (length x width x height) at the University of

Oldenburg. The wind tunnel has a background turbu-

lence intensity along the centerline of the complete test

section of approximately 2% for

U∞≤

10 m/s. The inlet

velocity was set to 10 m/s, corresponding to a Reynolds

TABLE I. Geometrical properties of the fractal grid used in this study.

Nσ/% L0/mm t0/mm RLRtLrtrMeff /mm T/mm

3 38.2 138.4 20.1 0.52 0.36 3.7 7.7 24 250

number related to the biggest grid bar length

of about

ReL0=U∞L0/ν = 83800,

where

is the kinematic vis-

cosity. Optical access is provided through the wind tunnel

side walls. The experimental data were acquired from hot-

wire anemometry and Particle Image Velocimetry (PIV)

measurements.

Constant temperature anemometry measurements

of the velocity were performed using (Dantec 55P01

platinum-plated tungsten wire) single-hot-wire with a

wire sensing length of about

= 2

1 mm and a

diameter of

= 5

µm

which corresponds to a length-

to-diameter ratio of

lw/dw≈

400. A StreamLine mea-

surement system by Dantec in combination with CTA

Modules 90C10 and the StreamWare version 3.50.0.9 was

used for the measurements. The hot-wire was calibrated

with Dantec Dynamics Hot-Wire Calibrator. The over-

heat ratio was set to 0.8. In the streamwise direction,

measurements were performed on the centerline between

5 cm

≤x≤

176 cm distance to the grid. The data was

sampled with the frequency

= 60 kHz with a NI PXI

1042 AD-converter and a total of 3.6 million samples were

collected per measurement point, representing 60 seconds

of measurement data. To satisfy the Nyquist condition,

the data was low-pass ﬁltered at frequency fl= 30 kHz.

In addition to the hot-wire measurements, the ﬂow

velocity is measured with two-component (2C) two-

dimensional (2D) Particle Image Velocimetry (PIV). A

double-pulsed Nd:YAG laser system illuminates the ﬂow

with a maximum energy output of 2x380 mJ pulse

−1

(

= 532 nm, Quantel Brilliant B Twin). The laser system

is set at a sampling frequency of 10 Hz and a laser pulse

delay of 63

µs

(time between two image frames) in order

to record statistically independent images. To illuminate

the desired ﬁeld of view, a laser light sheet is formed with

an optical arrangement (spherical lens

(f=−100 mm)

and cylindrical lens (

= 200 mm)) to converge the sheet

into a minimum thickness of around 2 mm. The light

sheet plane is in the vertical mid-plane of the wind tun-

nel. The ﬂow was seeded with Di-Ethyl-Hexyl-Sebacat

(DEHS) droplet aerosols generated by a Palas AGF 5

aerosol generator for atomizing liquids. The diameter of

the mist of DEHS droplets used in the present study is

about 0,3

µm

to 1

µm

. At each measuring station (there

are 15 stations in total) 3000 double images are recorded

by a cooled digital 14 bit CCD Camera (PCO1600) with

1600x1200 pixel resolution. The camera looks perpendic-

ular to the light sheet from the side and is synchronized

with the laser sheet pulse at 10 Hz. The camera is ﬁt-

ted with a Nikon mikro Nikkor 55 mm objective lens

set with an aperture setting of f/8. A minimal eﬀect of

peak locking was found for these experimental conditions.

The PIV analysis is done using commercial PIV software

(

PIV View

version 3.5.7) using an interrogation window

of 2 mm

. The vector ﬁelds are obtained by processing

the PIV images using a recursive cross-correlation engine

with a ﬁnal interrogation window of size 16 x 16 pixels

with 75% overlap.

IV. NUMERICAL SETUP

A. Turbulence modelling

The three-dimensional, incompressible Navier-Stokes

equations describe the ﬂow generated by a fractal grid.

The equations are discretized and solved using a turbu-

lence model. In this investigation, the Delayed Detached

Eddy Simulation (DDES) [

] with a Spalart-Allmaras

background turbulence model [

], commonly referred to

as SA-DDES is used. DDES is a hybrid method stem-

ming from the Detached Eddy Simulation method (DES)

[

], which involves the use of Reynolds Averaged Navier-

Stokes Simulation (RANS) at the wall and Large Eddy

Simulation (LES) away from it. This method combines

the simplicity of the RANS formulation and the accuracy

of LES, with the advantage of being less expensive in

terms of computational time when compared with pure

LES. DDES is an improvement of the original DES for-

mulation, where the so-called ”modeled stress depletion”

(or MSD), is treated [

]. MSD occurs when the LES

mode of the DES method is operating in the boundary-

layer [

]. In DDES, a shield function is derived, which

guarantees that the boundary layer is solved by the RANS

mode of the DES model. In the following, a brief descrip-

tion of SA-DDES is given. For more information refer to

[20,24].

In the framework of eddy viscosity models, the Reynolds

stresses are expressed in terms of the eddy viscosity

νt

and the strain-rate tensor

Sij

given by the formulation

−huiuji

= 2

νtSij

. We consider the Spalart-Allmaras

model, which is a RANS model based on the eddy viscosity

approach [

], where a transport equation is deﬁned for

the modiﬁed turbulent viscosity ˜νas follows

∂˜ν

∂t +uj

∂˜ν

∂xj

=cb1(1 −ft2)˜

S˜ν−hcw1fw−cb1

κ2ft2i˜ν

d2

σ∂

∂xj(ν+ ˜ν)∂˜ν

∂xj+cb2

∂˜ν

∂xi

∂˜ν

∂xi.

(4)

˜ν

is related to the turbulent eddy viscosity by the equation

νt= ˜νfν1,(5)

and the function fν1is deﬁned as

fν1=χ3

χ3+c3

ν1

,(6)

where

˜ν

being the kinematic viscosity.

is deﬁned

S=fν3S+˜ν

κ2+d2fν2,(7)

where

is the magnitude of the vorticity, and the func-

tions fν2and fν3are deﬁned as follows

fν2=1

(1 + χ/cν2)3,

fν3=(1 + χfν1)(1 −fν2)

χ,

(8)

where,

is the distance to the closest wall. Finally,

fω

is a function, which also contains the distance

and is

deﬁned as

fω=g1 + c6

ω3

g6+c6

ω31

,(9)

where

and

are deﬁned as

cω2

(

r6−r

) and

˜ν

Sκ2d2

. The remaining model constants are deﬁned in

[21].

The DES model used in this contribution was obtained

by replacing the distance variable

with the distance

deﬁned by the expression

d=min(lRAN S , lLES ) = min (d, CDES ∆) ,(10)

where,

CDES

= 0

65 is a constant and

∆ = max(∆x,∆y,∆z)

represents the grid size (the

ﬁlter size). One of the well-known shortcomings of DES

is the so-called Grid Induced Separation (GIS) which can

lead to the reduction of the RANS Reynolds stresses.

This problem occurs when the model operates in LES

mode in the boundary-layer [

], which results in the

separation point moving upstream (thus the name GIS).

This results from the fact that in reﬁned regions of the

mesh,

lLES

becomes smaller and the switch from RANS

to LES occurs prematurely. To overcome this problem,

the ”detached” version of the DES method was proposed

in [

]. In DDES, the switching from RANS to LES

mode is performed in a more complex manner, where an

empirical shielding function

is introduced. This results

in the following expression for the DDES length scale

lDDES =lRANS −fdmax(0, lRANS −lLES ),(11)

where

tends towards 0 inside the boundary-layer region

and towards 1 away from the boundary-layer. Moreover,

is a continuous function that enables a smooth transi-

tion between the RANS and the LES regions.

B. Mesh and Numerical Method

The numerical simulation was set up analogous to the

experiments in order to compare the results consistently.

The open source code OpenFOAM [

] was used to solve

the incompressible Navier-Stokes equations. OpenFOAM

is based on a collocated formulation of the ﬁnite volume

method, and it consists of a collection of libraries writ-

ten in C++, which can be used to simulate a large class

of ﬂow problems. For more information, see the oﬃcial

documentation [

]. The solver used in this investigation

is the transient solver pimpleFoam, which is a merging

between the PISO (Pressure implicit with splitting of op-

erator) and SIMPLE (Semi-Implicit Method for Pressure

Linked Equation) algorithms. A second-order central-

diﬀerencing scheme is used for spatial discretization, and

a backward, second-order time-advancing schemes were

used. The solver is parallelized using the Message-Passing

Interface (MPI), which is necessary for problems of this

size. The SA-DDES model used in this work is already

implemented in the oﬃcial release of OpenFOAM.

The numerical mesh was generated using the built-

in OpenFOAM meshing tools blockMesh and snappy-

HexMesh [

]. First, a background mesh constituted of

hexahedral cells ﬁlling the entire computational domain

is generated using blockMesh. The snappyHexMesh tool

is then applied on the generated hexahedral mesh, which

includes the fractal mesh. As a result, an unstructured

mesh is obtained, where regions of interest in the wake

are reﬁned, as shown in Fig. 2a. Locally reﬁning the

mesh required the use of the parallel option of the snap-

pyHexMesh tool. The mesh obtained is composed of a

total of 24 million cells.

The fractal grid is simulated in a domain with similar

dimensions as the real wind tunnel. The domain begins 2

m upstream of the fractal grid and covers a distance of 2

m downstream (see Fig. 2b). The ﬂow-parallel boundaries

are treated as frictionless walls, where the slip boundary

condition was applied for all ﬂow variables. At the inﬂow

boundary, Neumann boundary condition was used for the

pressure and Dirichlet condition for the velocity. At the

outﬂow boundary, the pressure was set to be equal to the

static pressure and a Neumann boundary condition was

used for the velocity. On the fractal grid, a wall function

is used for the modiﬁed viscosity

˜ν

, with the size of the

ﬁrst cell of the mesh in terms of the dimensionless wall

distance is y+∼200 [26].

For each simulation, 480 processors were used, and for

each time step 4.5

of data was collected for post-

processing. The data sampling frequency was 60

kHz

chosen to match the experimental one. It took approx-

imately 72 hours to simulate one second of data and a

total of 16 seconds of numerical data was collected. The

data was collected in the same positions as for the experi-

mental study. The numerical simulations were conducted

on the computer cluster of the ForWind Group [27].

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ExperimentalandComputationalInvestigationofaFractalGridWakeA.Fuchs,W.Medjroubi,H.Hochstein,G.Gulker,andJ.PeinkeInstituteofPhysicsandForWind,UniversityofOldenburg,Kupkersweg70,26129Oldenburg,Germany(Dated:October13,2022)Fractalgridsgenerateturbulencebyexcitingmanylengthscalesofdierentsizessimultan...

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Experimental and Computational Investigation of a Fractal Grid Wake A. Fuchs W. Medjroubi H. Hochstein G. G ulker and J. Peinke Institute of Physics and ForWind University of Oldenburg K upkersweg 70 26129 Oldenburg Germany.pdf

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Experimental and Computational Investigation of a Fractal Grid Wake A. Fuchs W. Medjroubi H. Hochstein G. G ulker and J. Peinke Institute of Physics and ForWind University of Oldenburg K upkersweg 70 26129 Oldenburg Germany

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