Turbulent flows generated/designed in multiscale/fractal ... - Ercoftac

1 ST UK-JAPAN BILATERAL WORKSHOP
28-29 March 2011
Department of Aeronautics | Imperial College London
S. Laizet, Y. Sakai, J.C. Vassilicos
Turbulent flows
generated/designed in
multiscale/fractal ways:
fundamentals and
applications
FINAL PROGRAMME
Nagoya University

1ST UK-JAPAN BILATERAL WORKSHOP
1ST UK-JAPAN BILATERAL WORKSHOP
Programme
MONDAY 28 MARCH 2011
8.30-9.00: Arrival and Registration (free entrance)
9.00-9.15: Introduction by J.C. Vassilicos (Imperial College London, UK)
First session: Fundamentals
9.15-9.50: W.K. George (Imperial College London, UK) Freeing turbulence from the tyranny of the past
9.50-10.25: M. Oberlack (TU Darmstadt, Germany) Beyond mean flow scaling laws - how to obtain higher order moment
scaling from new statistical symmetries
10.25-11.00: S. Goto (Okayama University, Japan) Multiscale self-similar coherent structures in developed turbulence
11.00-11.30: COFFEE BREAK
Second session: Different ways of generating turbulence
11.30-12.05: N. Sekishita (Toyohashi University of Technology, Japan) Successful attempts of large scale-turbulence
realization by a Makita-type turbulence gen- erator and a buoyancy jet in a cross wind
12.05-12.40: T. Ushijima (Nagoya Institute of Technology, Japan) Mean flow development of wake behind the Sierpinski
tetrahedron
12.40-14.15: LUNCH
14.15-14.50: K. Nagata (Nagoya University, Japan) Reexamination of fractal-generated turbulence using a smaller
wind tunnel
14.50-15.25: P. Valente (Imperial College London, UK) Decay of homogeneous turbulence generated by a fractal
square grid: wind tunnel experiments
15.25-16.00: P. Lindstedt (Imperial College London, UK) Fractal generated turbulence in isothermal and reacting opposed
jet flows
16.00-16.30: TEA BREAK
Third session: Multi-points statistics and intermittency
16.30-17.05: J. Peinke (University of Oldenburg, Germany) A new class of turbulence - insights from the perspective
of n-point statistics
17.05-17.40: C. Keylock (Sheffield University, UK) The wake structure, energy decay and intermittency behind a fractal
fence
TUESDAY 29 MARCH 2011
Fourth session: Flow design for applications
9.15-9.50: Y. Sakai (Nagoya University, Japan) Mixing of high-Schmidt number scalar in regular/fractal grid turbulence:
Experiments by PIV and PLIF
9.50-10.25: J. Nedic (Imperial College London, UK) Aero-acoustic performance of fractal spoilers
10.25-11.00: COFFEE BREAK
11.00-11.35: N. Soulopoulos (Imperial College London, UK) A turbulent premixed flame in fractal-grid generated turbulence
11.35-12.10: T. Sponfeldner (Imperial College London, UK) A parametric study of the effect of fractal-grid generated
turbulence on the structure of premixed flames
12.10-13.30: LUNCH
Fifth session: Simulations
13.30-14.05: B. Geurts (Twente University, Holland) Turbulence modulation through broad-band forcing
14.05-14.40: S. Laizet (Imperial College London, UK) Direct Numerical Simulation of multiscale generated turbulence
14.40-15.00: TEA BREAK
15.00-15.35: M. Pettit (Imperial College London, UK) LES/DNS of Opposed Jet Flows Employing Fractal Turbulence-
Generating Plates
15.35-16.10: H. Suzuki (Nagoya University, Japan) DNS on spatially developing fractal generated turbulence with heat
transfer
16.10-16.30: Discussion/Conclusion
Introduction
After more than a century of exhaustive research on the aerodynamics and hydrodynamics
of geometrically simple shapes, whether streamlined as in wings or bluff as in spheres and
cylinders, it is blindingly natural to expect much of the future in fluid mechanics to lie in the
aerodynamics and hydrodynamics of geometrically complex, and thereby multiscale, shapes.
The simplest cases of multiscale shapes are fractal shapes, which is why they have been a good start.
These are multiscale shapes with a complex appearance which can nevertheless be defined with only a
small number of scaling parameters.
To my knowledge, the study of turbulent flows generated/designed in multiscale/fractal ways started
in the UK with an experimental publication in 2001. These multiscale/fractal ways include multiscale/
broadband forcings as well as multiscale/fractal boundary and/or initial conditions. The first computational
model of turbulence subjected to fractal/broadband forcing which was neither motivated by nor limited to
intricacies of Renormalisation Group theory appeared in 2002, also from the UK.
The idea was to interfere with the multiscale dynamics, inner geometry and topography of the turbulence
itself and find out whether qualitatively different types of turbulence can be created. Whilst this idea is
perhaps easy to accept for multiscale/broadband forcings it is less easy to accept for multiscale/fractal
initial/boundary conditions.
This is where the work of William K. George over the past quarter century fits in and gives meaning
to the endeavour, in particular his work on the importance and imprint of initial/boundary conditions
on turbulent flows. If turbulent flows keep a degree of memory of the conditions which generate them,
then the possibility exists of designing bespoke turbulent flows taylor-made for particular applications.
This is far better than turbulent flow control if it can be achieved. Multiscale/fractal generation/design
is about using multiscale/fractal objects (such as grids, fences, profilers etc) to shape the nature of the
resulting turbulent flow over a broad range of scales for a broad range of applications. Below is a list of
applications touched upon in this 1st Japan-UK meeting. More applications will be discussed in the 2nd
Japan-UK meeting one year from now.
1. Fractal mixers: fractal grids can be used to design turbulent flows with low power losses and high
turbulence intensities for intense yet economic mixing over a region of designed length and location.
2. Fractal combustors: the fractal design of a long region of high turbulence intensity and its location are
of great interest for premixed combustion and may pave the way for future fractal combustors particularly
adept at operating at the lean premixed combustion regime where NOx emissions are the lowest. In fact
results recently obtained at Imperial’s Mechanical Engineering Department suggest that fractal design
seems to generate turbulent flame speeds which increase by even more than the increase in turbulence
intensities!
3. Fractal spoilers and airbrakes can have significantly reduced sound pressure levels without degrading
the lift and drag characteristics of the wing system.
4. Fractal wind breakers and fractal fences: a fractal fence, for example, can have increased resistance
because of all its empty areas, yet be an effective fence by modifying the momentum profiles in its lee
and thereby forcing deposition of particulates, snow etc where desired.
A lot of the driving force taking this new subject forward now comes from outside the UK and from
Japan in particular. This very meeting would not have happened without the success of our Japanese
colleagues in Nagoya who developed an entire research programme on the topic, secured a very
substantial Japanese research grant to support it and also obtained a travel grant to allow interactions
with us in Europe. This meeting also shows that activity is growing in continental Europe too, beyond the
fog in the English channel. Indeed, beyond this fog, a substantial German research grant was given to
Oldenburg last year for research on fractal-generated turbulence; and it is only because of the initiative
and help of Jean-Paul Bonnet and his colleagues in Poitiers that we were able to participate in the EU’s
OPENAIR programme, without which we would not have been able to demonstrate the acoustic and
aerodynamic performance of fractal spoilers.
J.C. Vassilicos
Department of Aeronautics, Imperial College London, UK
2 Turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
Turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 3

first session | Fundamentals
Fundamentals | first sessioN
monday 28 MARCH 2011 | 9.50-10.25
MONDAY 28 MARCH 2011 | 9.15-9.50
Freeing turbulence
from the tyranny of
the past
W.K. George
Department of Aeronautics, Imperial College London, UK
There have been numerous studies over the past few decades about how
scientists do research on difficult and intractable problems, both how we function
as individuals and collectively. While we would like to think that as individuals we
are purely objective, all evidence suggests that we are not, and our judgements are
strongly influenced by intuition and past prejudices. In groups we tend to cluster
around ‘group-think’, substituting consensus for critical analysis. Moreover there is
a ‘herd’ instinct, meaning there is a tendency to flock to a new idea, often without a
good reason for doing so.
Of course none of this behaviour has ever happened in turbulence. Nonetheless,
by examining the problems those in other fields have had, we can learn how to
guard against them in the future. Therefore the first part of this presentation will
focus on the phenomena of how we function as turbulence researchers. And the
second will try to identify potential problem areas where if we are not careful ideas
we have long assumed to be true might be adopted as religious principles, even if
they are false or only partially true.
Also in this talk we will try to distinguish between the mathematics of turbulence
and the physics of turbulence. In mathematics, equations are precisely determined,
and the laws of mathematics which must be applied to find solutions are welldefined
Physicists, on the other hand, build mathematical models of the universe
as we find it. Once we have built the model and defined the boundary conditions,
however, there is nothing that is arbitrary: the laws of mathematics take over. The
problem in turbulence (and other fields as well) is that often the consequences
of the mathematics for our solutions are not consistent with what we observe in
nature. So is the problem with our model, or is it with the boundary conditions
we have assumed to be true? Since often we have had to assume these to be
applied at infinity, we cannot be sure. Nonetheless, there are usually some criteria
for evaluation we can agree upon. For example if our model is the Navier-Stokes
equations, it should not generally be our first assumption that they are wrong,
especially for the constant density flow of a Newtonian fluid. Nor should we throw
away so quickly a theory developed for an infinite domain if our experiment is
performed in a box. In fact it will probably be more productive to examine what
the consequences are of the finite domain or our attempts to realize the solution in
nature. Numerous examples will be used to illustrate these points [1,2,3,4,5].
Beyond mean flow scaling
laws - how to obtain higher
order moment scaling from
new statistical symmetries
1 st UK-JAPAN BILATERAL WORKSHOP, IC LONDON, UNITED KINGDOM, 28./29.3.2011
BEYOND MEAN FLOW SCALING LAWS - HOW TO OBTAIN HIGHER ORDER MOMENT
M. Oberlack 1,2,3 , A. Rosteck 1 UK-JAPAN 3 BILATERAL SCALING FROM WORKSHOP, NEW STATISTICAL IC LONDON, SYMMETRIES
UNITED KINGDOM, 28./29.3.2011
1 1
Chair of Fluid st UK-JAPAN BILATERAL WORKSHOP, IC LONDON, UNITED KINGDOM, 28./29.3.2011
Dynamics, BEYOND MEAN Technische FLOW SCALING Universität Darmstadt, GERMANY
Martin Oberlack LAWS 1,2,3 - HOW & Andreas TO OBTAIN Rosteck 1 HIGHER ORDER MOMENT
2
Center of BEYOND Smart MEAN Interfaces, 1 Chair FLOW of Fluid SCALING TU Dynamics SCALING
Darmstadt, LAWS , Technische FROM - HOW NEW Universität Germany
TO STATISTICAL OBTAIN Darmstadt, HIGHER SYMMETRIES
64289 Darmstadt, ORDER MOMENT Germany,
1 st UK-JAPAN
3
GS Computational Engineering, 2 BILATERAL WORKSHOP, IC LONDON, UNITED
SCALING CenterFROM of Smart NEW Interfaces, STATISTICAL TU Darmstadt, SYMMETRIES
KINGDOM, 28./29.3.2011
64287 Darmstadt, Germany
TU Darmstadt, Germany
3 GS Computational
Martin
Engineering,
Oberlack
TU 1,2,3 Darmstadt,
& Andreas
64293
Rosteck
Darmstadt, 1
BEYOND 1 MEAN FLOW SCALING LAWS - HOW TO OBTAIN HIGHER ORDER GermanyMOMENT
Chair of Fluid Dynamics , Technische Universität Darmstadt, 64289 Darmstadt, Germany,
We investigate the symmetry We investigate and the symmetry 2 Martin SCALING Oberlack FROM
invariance Center and of Smart invariance structure 1,2,3 NEW & Andreas STATISTICAL RosteckSYMMETRIES
Interfaces, structure TUof Darmstadt, of the infinite 1
1 64287 set of set Darmstadt, multi-point of multi-point Germany correlation correlation (MPC) equations
for the fluctuations velocity 3 , Technische Universität Darmstadt, 64289 Darmstadt, Germany,
2 GS and Computational pressure u(x, t) fluctuations and
(MPC) equations for
Chair of Fluid Dynamics
the velocity and pressure
Engineering,
p(x, u(x, t) t) TUand Darmstadt, p(x, t) 64293 Darmstadt, Germany
Center of Smart Interfaces, Martin TUOberlack Darmstadt, 1,2,3 & 64287 Andreas Darmstadt, Rosteck 1 Germany
3 GS 1 Computational Chair of Fluid Dynamics Engineering,
, Technische TU Darmstadt, Universität64293 Darmstadt, Darmstadt, 64289 Darmstadt, Germany Germany,
We investigate the
S i{n+1} = ∂R symmetry and
i {n+1}
n invariance structure
+ Ū k(l) (x
∂t
(l) ) ∂R of the infinite
i {n+1}
− ν ∂2 R i{n+1}
set of multi-point correlation (MPC) equations
for the velocity 2 Center of Smart Interfaces, TU Darmstadt, 64287 Darmstadt, + R Germany
3 and pressure fluctuations u(x,
∂Ūi (l)
∂x
t) and p(x,
k(l) ∂x
t)
k(l) ∂x
i{n+1} [i (l) →k (l) ]
GS Computational k(l) ∂x k(l)
l=1
Engineering, TU Darmstadt, 64293 Darmstadt, Germany
We investigate the symmetry and invariance structure
∂u i(l) u k(l) (x (l) )
− R i{n} [i (l) →0]
+ ∂P i {n} [l]
+ ∂R (1)
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]
S i{n+1} = ∂R of the infinite set of multi-point correlation (MPC) equations
for the + Ū k(l) (x ,
i {n+1}
n
∂t
(l) ) ∂R i {n+1}
− ν ∂2 R i{n+1}
∂Ūi (l)
We
velocity
investigate
and pressure
the symmetry
fluctuations
and invariance
u(x, t)
structure
and p(x,
of
t)
the infinite set of multi-point + R
∂x k(l)
∂x ∂x k(l) i(l)
∂x k(l) ∂x
i{n+1} correlation [i
∂x
(l) →k (l) ] (MPC) equations
for the velocity and pressurel=1
fluctuations u(x, t) and p(x, t)
k(l) k(l)
∂x k(l)
∂u i(l) u k(l) (x (l) )
where n =1...∞. − RIn i{n} (1)[i the (l) →0] MPC tensor is defined + ∂P i {n} [l]
as R i{n+1} + ∂R (1)
S i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]
= u i(0) (x (0) ) · ...· u i(n) (x (n) ) , and with , the
four variations S i{n+1} of = ∂R
i{n+1} = ∂R
i {n+1}
n
+ Ū k(l) (x
∂t i {n+1}
n (l) ) ∂R i {n+1}
it we have + a complete Ū k(l)
∂x
statistical k(l) (x ∂x
description i(l) ∂x
of turbulence. k(l)
∂t
(l) ) ∂R − ν ∂2 R i{n+1}
∂Ūi (l)
+ R
∂x i {n+1}
− ν ∂2 k(l) ∂x k(l) ∂x R i{n+1} [i i{n+1}
(l) →k (l) ]
k(l) ∂x
+ R k(l)
∂Ūi (l)
l=1
∂x k(l) ∂x k(l) ∂x
i{n+1} [i (l) →k (l) ]
k(l) ∂x k(l)
Equation (1) admits∂u l=1
all i(l) symmetries u k(l) (x (l) of ) the Navier-Stokes equations where they originally emerged from at the
where n =1...∞. In (1) the
first place. Nevertheless equation ∂uMPC i(l) (1) upossesses k(l)
tensor (x (l) ) is defined as R
additional symmetries i{n+1} = u
(see i(0) (x
Oberlack, (0) ) · ...· u
Rosteck i(n) (x
2010 (n) ) , and with the
& Rosteck
four variations− of Rit Oberlack 2011)
i{n} we[i (l) have →0] a complete statistical + ∂P i {n} [l]
description + ∂R (1)
− R i{n} [i (l) →0]
+ ∂P i {n} [l]
+ ∂R (1)
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ]
i {n+2} [i (n+1) →k (l) ][x (n+1) → x (l) ],
∂x k(l) ∂x i(l) of turbulence. ∂x k(l)
,
∂x k(l) ∂x i(l) ∂x k(l)
Equation (1) admits all symmetries of the Navier-Stokes equations
G sh : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = e asŪ i, ˜R ij (x, y) =e where they originally emerged as (1 − e as )Ūi(x)Ūj(y) − R ij (x, y) from at the
where n =1...∞. first place. In (1) Nevertheless MPC equation tensor is(1) defined possesses as Radditional symmetries (see Oberlack, Rosteck 2010 , ··· & Rosteck
where n =1...∞. In (1) the MPC tensor is defined i{n+1} = u
as R i(0) (x
i{n+1} = u (0) ) · ...· u
i(0) (x
Oberlack 2011)
(0) ) · ...· i(n) (x
u (n) ) , and with the
i(n) (x (n) ) , and with the
four variations
four
of
variations
it we have
G L(a) : ˜x of= it
a complete
x, we˜r have
i(l) = arcomplete statistical
i(l) , ˜Ū i = statistical
description Ūi + L (i) , description
of turbulence.
of turbulence.
Equation (1) Equation admits all (2)
G
(1) symmetries admits
sh : ˜R ij
˜x (x, =
all
x,
symmetries of the Navier-Stokes
y) ˜r =R i(l) = ij (x, r i(l) y) ,
of
− ˜Ū the i L =
Navier-Stokes
e (i) Ū asŪ equations
j (y) i, − ˜R ij L (x, (j) Ūy) equations where
i (x) =e − as L (1
where they originally
(i) L − e (j) , as they
··· )Ūi(x)Ūj(y)
originally emerged
−
emerged from
R ij (x, y)
from at
, ···
at the the
first place. Nevertheless first place. Nevertheless equation (1) equation possesses (1)
G L(ab)
G : ˜x = x, ˜r i(l) = r i(l) , ˜Ū L(a) : ˜x = x, ˜r i = Ūi, ˜R i(l) = r i(l) , ˜Ū
possesses additional additional symmetries symmetries (see Oberlack, (see Oberlack, Rosteck Rosteck 2010 2010 & & Rosteck
Oberlack 2011) Oberlack 2011)
i = + ij
L (x, (i) , y) =R ij (x, y)+L (ij) , ···
(2)
˜R ij (x, y) =R ij (x, y) − L (i) Ū j (y) − L (j) Ū i (x) − L (i) L (j) , ···
G The latter G sh are : ˜x purely x, statistical ˜r i(l) = r i(l) properties , ˜Ū i of the equations (1), while G sh can be identified as a statistical scaling
group G(SSG) L(ab) and : ˜x G= L(a)
x, ˜r , i(l) G L(ab)
= r i(l) as, statistical ˜Ū
= e asŪ i, ˜R
i = Ūi, translation ˜R
ij (x, y) =e as (1 − e as − R ij (x, y) sh : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = e asŪ i, ˜R ij (x, y) =e as − e as )Ūi(x)Ūj(y) − R ij (x, y) , ··· , ···
ij (x, y) =R groups ij (x, (STG). y)+L (ij) , ···
G G
Assuming L(a) : ˜x x, ˜r i(l) r i(l) , ˜Ū i =
a plane parallel turbulent shear Ūi + L
flow, (i) ,
L(a) : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = the infinite set of equations (1) and the corresponding symmetries
provide the
The latter are purely statistical Ūi + L (i) ,
properties of the equations (1), while G ˜R ij invariant (x, y) =Rsurface ij (x, y) condition − L sh can be identified as a statistical scaling
(i) Ū j (y) − L (j) Ū i (x) − L (i) L (j) , ···
(2)
(2)
˜R group ij (x,(SSG) y) =Rand ij (x, G L(a)
y) , −G L L(ab) (i) Ūas statistical translation groups (STG).
Assuming
G L(ab) :
a
˜x
plane x,
parallel
˜r i(l) = r
dx 2 turbulent i(l) , ˜Ū
j (y) − L (j) Ū i (x) − L (i) L (j) , ···
i
= dr =
shear Ūi,
(k) flow, ˜R ij (x,
the
y)
infinite
=R ij (x,
dŪ1 set
y)+L
of equations
=
= dR (ij) , ···
G (11)(x, (1) y) and the corresponding symmetries
provide the invariant
L(ab) : ˜x = x, ˜r i(l) = r i(l) , ˜Ū i = = ··· (3)
k 1 x 2
surface Ūi, ˜R ij (x, y) =R ij (x, y)+L (ij) , ···
+ k x kcondition
The latter are purely statistical properties 1 r (k) of the (kequations 1 − k 2 + k(1), a )Ū1 while + l 1 G sh can I(x, bey)
identified as a statistical scaling
The latter aregroup purely (SSG) statistical and G
with the group parameters L(a)
properties , G
k L(ab)
of
dx asthe statistical equations
1 , k 2 2 , k
= x , k dr translation (1), while groups G sh (STG). can be
a ,(k)
l 1 and
=
l 11 descending dŪ1 from the
= dR identified
groups (11)(x,
(2) y) as a statistical scaling
and
= ···
the classical symmetry
group (SSG) Assuming and G (3)
groups here L(a) a , plane G
written L(ab) parallel as statistical
in infinitesimal k turbulent 1 x 2 + k shear translation
x forms. k 1 r flow,
(k) (k
the groups
1 −
infinite(STG).
k 2 + k
set of a )Ū1 +
equations
l 1 I(x, (1) and y) the corresponding symmetries
provide parallel theturbulent invariant surface shear flow, condition the infinite set of equations (1) and the corresponding symme-
Assuming a plane
tries provide the with invariant the group surface parameters condition k 1 , k 2 , k x , k a , l 1 and l 11 descending The abbreviation from the groups I(x, y) (2) isandefined the classical I(x, symmetry y) =
groups here written in infinitesimal dx 2
= dr forms. (k)
dŪ1
=
[2k 1 − 2k= 2 + dR k a
(11)(x, y)
]R (11) (x, = y)+l ··· 11 − k a Ū i (x)Ūj(y) (3) −
dx k 1 x 2 + k x k 1 r (k) (k 1 − k 2 + k a l)Ū1 1 (Ūi(x)+Ūj(y)) + l 1 I(x, and y)
2
the indices in brackets denote
= dr (k)
dŪ1
=
no
The = dR (11)(x, y)
summation
abbreviation
but instead = I(x, ··· y)
each
is defined
component
as I(x,
is (3) to
y)
be
=
with the group k 1 xparameters 2 + k x k 11 r , (k) k 2 , k x
(k , k 1a −, l 1
k 2 and + lk 11 a )Ū1 descending + l 1
taken
[2k 1
from
separately.
−
I(x,
2kthe 2 +
y) groups k a ]R (11)
(2)(x, and y)+l the classical 11 − k a Ū i
symmetry (x)Ūj(y) −
groups here written in infinitesimal forms.
From
l 1 (Ūi(x)+Ūj(y))
(3) we may derive
and
various
the indices
new
in
scaling
brackets
laws
denote
with the group parameters k 1 , k 2 , k x , k a , l 1 and l 11 descending from the groups (2) and the classical symmetryfor
the
no
MPC
summation
tensor. Presently,
but instead
we
each
invoke
component
symmetries
is to
in
be
groups here written in infinitesimal forms.
The abbreviation I(x, y) is defined as I(x, y) =
the
taken
range
separately.
[2k of the validity of the logarithmic law of the
wall
From 1 − 2k
i.e.
(3) 2 + k
k 1 −
we a ]R
k
may (11) (x, y)+l
2 + k
derive
a =0and
various 11 − k
compute
new a Ū
scaling i (x)Ūj(y) −
the Reynolds
laws for
The abbreviation l 1 (Ūi(x)+Ūj(y)) I(x, y) andisthedefined indices in asbrackets I(x, y) denote =
stresses
the MPC
in
tensor.
the range
Presently,
or the logarithmic
we invoke symmetries
law of the
in
[2k 1 −no 2ksummation - but -instead each- component - is to be
wall.
the 2 + range k a ]R
The parameters
of (11) the(x, validity y)+l
of the
of 11
new
the − k
equations
logarithmic a Ū i (x)Ūj(y)
describing
law−of the
l 1 (Ūi(x)+Ūj(y)) taken separately.
the
wall
Reynolds
i.e. k 1 −and stresses
k 2
the + kindices have a =0and in
been determined
compute bracketsthe denote
from
Reynolds
From (3) we may derive various new scaling laws for the
no summation
DNS-data
stressesbut in
of
the instead
a boundary
rangeeach or
layer
the component logarithmicis flow at Re
law to be
Θ = 2003
of the
separately. the MPC tensor. Presently, we invoke symmetries in
Figure 1. Comparison of the DNS data (dotted lines) with taken separately.
by
wall.
Hoyas
The
and
parameters
Jimenez
of
(2006).
the new
In
equations
figure 1
describing
the range of the validity of the logarithmic lawone of the can
the scaling laws resulting from the new symmetries (solid From (3) see
the we that
Reynolds may thisderive provides
stresses various have
excellent new beenscaling determined
matchlaws in the
from for log
the
wall i.e. k
lines)
region.
DNS-data 1 − k
of 2 + k
a boundary a =0and compute the Reynolds
the MPC layer flow at Re Θ = 2003
stresses tensor. in the Presently, range or wethe invoke logarithmic symmetries law ofinthe
Figure 1. Comparison of the DNS data (dotted lines) the with rangeby Hoyas and Jimenez (2006). In figure 1 one can
wall. ofThe theparameters validity of of the thelogarithmic new equations lawdescribing
of the
the scaling laws resulting from the new symmetries (solid see that this provides an excellent match in the log
wall i.e. the k 1 Reynolds − k 2 + kstresses a =0and havecompute been determined the Reynolds from the
lines)
region.
stressesDNS-data in the range of a boundary or the logarithmic layer flow at law Re Θ of = the 2003
Figure 1. Comparison of the DNS data (dotted lines) with wall. The by Hoyas parameters and Jimenez of the new (2006). equations In figure describing 1 one can
the scaling laws resulting from the new symmetries (solid the Reynolds see thatstresses this provides have been an excellent determined matchfrom in the the log
lines)
DNS-data region. of a boundary layer flow at Re Θ = 2003
Figure 1. Comparison of the DNS data (dotted lines) with by Hoyas and Jimenez (2006). In figure 1 one can
the scaling laws resulting from the new symmetries (solid see that this provides an excellent match in the log
lines)
region.
where n=1...∞. In (1) the MPC tensor is defined as
have a complete statistical description of turbulence.
and with the four variations of it we
Equation (1) admits all symmetries of the Navier-Stokes equations where they originally emerged from in the first place.
Nevertheless equation (1) possesses additional symmetries (see [6,7])
The latter are purely statistical properties of the equations (1), while G sh
can be identified as a statistical scaling group
(SSG) and G L(a)
, G L(ab)
as statistical translation groups (STG).
Assuming a plane parallel turbulent shear flow, the infinite set of equations (1) and the corresponding symmetries provide
the invariant surface condition
with the group parameters k 1
, k 2
, k x
, k a
, l 1
and l 11
descending from the groups (2) and the classical symmetry groups here
written in infinitesimal forms.
The abbreviation I(x, y) is defined as: I(x, y) = [2k 1
- 2k 2
+ k a
]R (11)
(x,y) + l 11
- k a
U i
(x)U j
(y) - l 1
(U i
(x) + U j
(y)) and the indices in brackets
denote no summation but instead each component is to be taken
From (3) we may derive various new scaling laws for the MPC
tensor. Presently, we invoke symmetries in the range of the validity
of the logarithmic law of the wall i.e. k 1
− k 2
+ k a
= 0 and compute
the Reynolds stresses in the range or the logarithmic law
of the wall. The parameters of the new equations describing the
Reynolds stresses have been determined from the DNS-data of
a boundary layer flow at Re τ
= 2003 by Hoyas and Jimenez [8].
In figure 1, one can see that this provides an excellent match in
the log region.
4 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 5

first session | Fundamentals
Multi-scale Self-similar Coherent Structures in Developed Turbulence
Susumu Goto
Department of Mechanical Engineering, Okayama University, Okayama, 700-8530, Japan
E-mail: goto@mech.okayama-u.ac.jp
In order to reveal the coherent structures in fully developed turbulence and to understand their
roles in the dynamics and statistics of turbulence, direct numerical simulations (DNS) of homogeneous
isotropic turbulence in a periodic cube are conducted. By the DNS employing the Fourier spectral
method with 2048 3 grid points, turbulence at the Taylor-length based Reynolds number equal to 580
is simulated.
The multi-scale coherent structures are, then, visualised by the iso-surfaces of the coarse-grained
enstrophy, which is estimated by the low-pass filtering of the Fourier components of the vorticity field.
Results are shown in the figure below. It is clearly observed that thus visualised coherent vortical
structures have mainly tubular shapes with radii of the order of the coarse-graining scale, whereas
MONDAY
their28 length
MARCH
is as long
2011
as the integral
| 10.25-11.00
length.
This multi-scale self-similar coherent structures play roles in the turbulence dynamics. For example,
the fractal structure of preferentially concentrated heavy small particles in turbulence is well described
in term of these multi-scale coherent structures.
It is also important to describe, based on these coherent structures, one of the most important
dynamics of turbulence, i.e. the energy cascade. To investigate this process in detail, we introduce
(Goto 2008, JFM) scale-dependent energy and its transfer. It is, then, numerically verified that the
Multiscale self-similar
coherent structures in
developed turbulence
energy at a scale (l, say) is confined in the coherent vortex tubes at l, whereas the energy at scale l
transfers (probably to smaller scales) the regions surrounding the vortex tubes at l, where the strain
rate at the scale l is high. This result implies that the energy cascade is caused by the creation of the
thinner vortex tubes by the vortex stretching in larger-scale strain field around fatter vortex tubes.
Indeed, we can easily find the invents which support this scenario of the energy cascade.
Two problems arise from this conclusion, however. First one is on the universality of turbulence
statistics, since the above mechanism of the energy cascade implies that coherent structures at the
Taylor micro scale can be directly created by the large-scale structures at the integral length. Secondly,
to my knowledge, the relation between the Kolmogorov energy spectrum and this mechanics
S. Goto
of turbulent energy cascade is still open; where is the spiral structure, for example?
Department of Mechanical Engineering, Okayama University, JAPAN
Different ways of generating turbulence | SECOND session
MONDAY 28 MARCH 2011 | 11.30-12.05
Successful attempts of large
scale-turbulence realization
by a Makita-Type turbulence
generator and a buoyant jet
Successful Attempts of Large Scale-Turbulence Realization
in a cross by a Makita-Type wind Turbulence Generator
and a Bouyance Jet in a Cross Wind
N. Sekishta and H. Makita
Toyohashi University of Technology, JAPAN
Nobumasa SEKISHITA 1 and Hideharu MAKITA 2
1,2 Toyohashi University of Technology
(a) (b) (c) (d)
FIG 1: Iso-surfaces of the enstrophy of the coarse-grained enstrophy at (a) coarse-grained 680η, (b) 340η (c) 170η and at (d)(a) 84η; 680η, where η is(b) the 340η (c)
170η and
Kolmogorov
(d) 84η;
length
where
scale. All
η
ofis these
the
scales
Kolmogorov
are in the inertial range.
length
The sidescale. of the shown
All
cube
of
is 5400η
these scales
in (a,b,c), and 1700η in (d).
are in the inertial range. The side of the shown cube is 5400η in (a,b,c), and
1700η in (d).
In order to reveal the coherent structures in fully developed turbulence and to
understand their roles in the dynamics and statistics of turbulence, direct numerical
simulations (DNS) of homogeneous isotropic turbulence in a periodic cube are
conducted. By the DNS employing the Fourier spectral method with 2048 3 grid
points, turbulence at the Taylor-length based Reynolds number equal to 580 is
simulated. The multiscale coherent structures are then visualised by the isosurfaces
of the coarse-grained enstrophy, which is estimated by the low-pass
filtering of the Fourier components of the vorticity field. Results are shown in the
figure. It is clearly observed that thus visualised coherent vortical structures have
mainly tubular shapes with radii of the order of the coarse-graining scale, whereas
their length is as long as the integral length. This multiscale self-similar coherent
structures play roles in the turbulence dynamics. For example, the fractal structure
of preferentially concentrated heavy small particles in turbulence is well described
in term of these multiscale coherent structures.
It is also important to describe, based on these coherent structures, one of the
most important dynamics of turbulence, i.e. the energy cascade. To investigate
this process in detail, we introduce [9] scale-dependent energy and its transfer.
It is then numerically verified that the energy at a scale (l, say) is confined in the
coherent vortex tubes at l, whereas the energy at scale l transfers (probably to
smaller scales) the regions surrounding the vortex tubes at l, where the strain rate
at the scale l is high. This result implies that the energy cascade is caused by the
creation of the thinner vortex tubes by the vortex stretching in larger-scale strain
field around fatter vortex tubes. Indeed, we can easily find the invents which support
this scenario of the energy cascade.
Two problems arise from this conclusion, however. First one is on the universality
of turbulence statistics, since the above mechanism of the energy cascade implies
that coherent structures at the Taylor microscale can be directly created by the
large-scale structures at the integral length. Secondly, to my knowledge, the relation
between the Kolmogorov energy spectrum and this mechanics of turbulent energy
cascade is still open; where is the spiral structure, for example?
Hibarigaoka 1-1, Tenpaku, Toyohashi, Aichi 441-8580, Japan
Atmospheric boundary layers were seki@me.tut.ac.jp simulated in a laboratory wind tunnel by
regulating parameters of a turbulent shear flow generator. The generator has a
shear Atmospheric flow device boundary and layers an were active simulated grid in with a laboratory agitator wind wings tunnel driven by regulating by 40 parameters stepping of a
motors. The generator could control turbulence characteristics; mean velocity
turbulent shear flow generator. The generator has a shear flow device and an active grid with agitator wings
U=0~8m/s, turbulence intensity u’/U ∞
=1~13% and integral scale L ux
=0.02~1.9m.
driven by 40 stepping motors. The generator could control turbulence characteristics; mean velocity
Reynolds stress distributions were also intensified throughout the thick boundary
U=0~8m/s, layer by the turbulence present intensity setup. The u'/Umaximum =1~13% and turbulence integral scale Reynolds L ux =0.02~1.9m. number, Reynolds R λ
, reached stress
distributions about 650 were at Ualso ∞
=8m/s intensified and throughout the spectrum the thick had boundary a wide layer inertial by the sub present range setup. comparable
The maximum
turbulence to those Reynolds in natural number, atmospheric R , reached boundary about 650 layers. at U =8m/s and the spectrum had a wide inertial
subrange Coherent comparable structures to those were in natural investigated atmospheric in boundary a round layers. jet of heated air with temperature
difference, Coherent structures 0, 20, were 40 and investigated 60K. The in a round present jet of heated jet was air with vertically temperature ejected difference, in a 0, cross 20, 40
flow field. Three kinds of flow pattern in the jet with smoke were observed by flow
and 60K. The present jet was vertically ejected in a cross flow field. Three kinds of flow pattern in the jet
visualization in the cross flow generated with or without a turbulence grid. In the
with smoke were observed by flow visualization in the cross flow generated with without a turbulence
case of mode I, hairpin-type vortices occurred in the jet. Two vortex tubes with and
grid. without In the strong case of mutual mode I, hairpin-type interaction vortices (bifurcation) occurred in were the jet. generated Two vortex for tubes mode with II and and without III,
strong respectively. mutual interaction Vortex (bifurcation) behaviour, were the generated convection for mode velocity II and III, of the respectively. coherent Vortex vortices, behavior, the
convection Strouhal velocity number, of the etc., coherent was vortices, investigated the Strohal from number, the results etc., was of investigated motion pictures from the results taken of
motion by a high pictures speed taken camera by a high (1000frame/s). speed camera (1000frame/s). The convection The convection velocity velocity of the of the coherent
structures structures decreased decreased with increasing with increasing the temperature the difference. temperature These vortex difference. shedding frequencies These vortex and the
shedding frequencies and the Strouhal numbers decreased with increasing the
Strohal numbers decreased with increasing the temperature difference.
temperature difference.
vortex formation region vortex region
Y/D
20
10
0
flow
0 20 40 60 80 100
X/D
Fig. 1. Turbulent Shear flow generator. Fig. 2 Vortex formation region and vortex region.
6
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
7

SECOND session | Different ways of generating turbulence
Different ways of generating turbulence | SECOND session
MONDAY 28 MARCH 2011 | 12.05-12.40
Mean flow
development of wake
behind the Sierpinski
tetrahedron
T. Ushijima
Department of Engineering Physics, Electronics and Mechanics,
Graduate School of Engineering, Nagoya Institute of Technology,
JAPAN
MONDAY 28 MARCH 2011 | 14.15-14.50
Re-examination of
fractal-generated
turbulence using a
smaller wind tunnel
K. Nagata, Y. Sakai, H. Suzuki and H. Suzuki
Department of Mechanical Science and Engineering, Nagoya University,
Furoh-cho, Chikusa-ku, Nagoya 464-8603 JAPAN
This work is motivated by two physical facts: firstly fractal dimension of foliage
distribution of crown tree is in the range between 2 and 2.4. Secondly, wind drag
exerted on the tree is proportional to wind speed despite large Reynolds number
based on the wind speed and square root of the projected area of trees. The latter
suggests that the crown tree structure is optimal to the wind resistance and this
feature can be relevant to the fractal geometry of the tree. Direct application can be
artificial windbreakers during the development of forestation.
The Sierpinski tetrahedron has the fractal dimension of 2, which is the same as
that of foliage distribution, and can cover the projected area efficiently. We used this
three dimensional fractal structure as a model of tree to understand the turbulence
generated in the natural environment.
In this preliminary report, the mean flow development of the wake behind the
Sierpinski tetrahedron was investigated. The Sierpinski tetrahedron is installed at
the upstream end of a small scale wind tunnel, which has 130mm by 130mm cross
section and 2000mm in length. Development of the mean and r.m.s. velocities in
the streamwise direction is measured at single experimental condition (4.9 ms -1 at
the bulk velocity) by both Pitot tube and hot wire anemometry.
The mean velocity distribution in the cross section is quite inhomogeneous. Near
the Sierpinski object, the local mean velocity varies by ±40 percent of the mean
velocity over the cross section of the section and it remains strongly inhomogeneous
far downstream. Inhomogeneity is a source of turbulence energy and produces
relatively large fluctuations. Turbulence intensities decrease from 20 to 10 percent
during the test section. Turbulence energy obeys the linear decay law. Reynolds
number based on Taylor micro scale is around 150.
Our findings suggest that use of fractal objects can reduce the size of turbulent
mixers, which is practical in the situation where a turbulent jet is not suitable for
mixing.
We reexamined the multiscale/fractal generated turbulence by Hurst & Vassilicos
[4], Seoud & Vassilicos [5] and Mazellier & Vassilicos [10] using a smaller wind
tunnel. The test section of the wind tunnel is 0.3x0.3x4.0m 3 . The square-type
fractal grid (blockage ratio σ = 0.25, thickness ratio t r
= 13.0, fractal dimension
D f
= 2, L 0
= 163.8 mm, L 1
= 78.9 mm, L 2
= 38.1 mm, L 3
= 18.3 mm, t 0
= 11.7 mm,
t 1
= 4.9 mm, t 2
= 2.1 mm, t 3
= 0.9 mm, where L i
are the successive bar length
and ti are the successive bar thickness: see [4] and [5] for detail) was installed at
0.15m downstream of the entrance of the test section. The Reynolds numbers Re 0
based on t 0
and mean flow velocity upstream of the grid are 6,000 and 11,400. The
instantaneous streamwise velocities are measured using the hot-wire anemometry
with a self-made I-probe. The diameter and length of the sensor are d = 5 μm and
l = 1 mm, respectively. The results are compared with those by [10] who used the
larger wind tunnel. Figure 1 shows the normalised profiles of rms velocities. Here,
x is the streamwise distance from the grid, x* is the wake-interaction length scale
(see [10]), x peak
is the streamwise location where turbulence intensities exhibit the
peak value and subscript c denotes the value on the centre line. Our results using
a smaller wind tunnel agree well with that by [10]. Other statistics, for example
skewness and flatness factors, also agree well with those of [10].
Figure 1 Streamwise evolution of turbulence intensities normalized by their
values at x = x peak
8 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 9

SECOND session | Different ways of generating turbulence
Different ways of generating turbulence | SECOND session
monday 28 MARCH 2011 | 14.50-15.25 MONDAY 28 MARCH 2011 | 15.25-16.00
The decay of
homogeneous
turbulence generated
by multiscale grids
Fractal generated
turbulence in
isothermal and reacting
opposed jet flows
P.C. Valente, J.C. Vassilicos
Department of Aeronautics, Imperial College London, UK
R.P. Lindstedt, P. Geipel and K.H.H. Goh
Department of Mechanical Engineering, Imperial College London, UK
A new experimental investigation of freely decaying homogeneous, quasi-isotropic
turbulence generated by a low-blockage space-filling fractal square grid is
presented. We find good agreement with previous works by Seoud & Vassilicos [5]
and Mazellier & Vassilicos [10] but also extend the length of the assessed decay
region and consolidate the results by repeating the experiments with different
anemometry systems and probes of increased spatial resolution. It is confirmed
that this moderately high Reynolds number Re λ
turbulence does not follow the
classical high Reynolds number scaling of the dissipation rate ε ~ u′3/L which is
in fact a direct reflection of the proportionality between the Taylor-based Reynolds
number, Re λ
, and the ratio of integral scale L and the Taylor micro-scale λ. Instead
we observe a proportionality between, L, and, λ, during decay. Alternative reasons
for this non-classical behaviour are discussed, including various ways in which the
turbulence may fall into a self-preserving, single-length-scale state induced by the
initial conditions of this particular flow.
It is shown that the measured 1D spectra can be reasonably collapsed using a
single length-scale over the entire decay region even though the Reynolds number
is high enough for conventional decaying turbulence to display 1D spectra with twoscale
(inner and outer) Kolmogorov scaling. We propose a correction for the weak
anisotropy of the flow by computing the 3D spectrum function from two component
velocity signals leading to further improved single-scale non-Kolmogorov collapse.
Detailed checks on homogeneity and isotropy are also presented indicating that
the single-length scale behaviour can not be an artifice of the hardly present
inhomogeneity.
The opposed jet configuration presents a canonical geometry suitable for the
evaluation of calculation methods seeking to reproduce the impact of strain and
re-distribution on turbulent transport in reacting and non-reacting flows. The
geometry has the advantage of good optical access and, in principle, an absence
of complex boundary conditions. Disadvantages include low frequency flow motion
at high nozzle separations and comparatively low turbulence levels causing bulk
strain to exceed the turbulent contribution at small nozzle separations. In the
current work, fractal generated turbulence has been used to increase the turbulent
strain and velocity measurements for isothermal and reacting flows are reported
with an emphasis on the axis, stagnation plane and the distribution of mean and
instantaneous strain rates. Energy spectra were also determined and it showed
that fractal grids increase the turbulent Reynolds number range from 48–125 to
109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated
plate turbulence generators. The applied instrumentation comprised hotwire
anemometry, particle image velocimetry and a multi-step adaptive algorithm was
developed and used to determine conditional statistics for reacting cases. Examples
are given with respect to velocity and scalar statistics, the motion of the stagnation
plane and with probability density functions for the instantaneous inclination of the
flame sheet also determined. Finally, a proper orthogonal decomposition technique
was adopted in order to examine the eigenmodes resulting from an analysis of the
instantaneous vector fields and the dominant structures identified. The work shows
that the application of fractal-generated turbulence holds significant advantages in
the context of the opposed jet geometry.
10 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 11

THIRD session | Multi-point statistics and intermittency
Multi-point statistics and intermittency | THIRD sessioN
monday 28 MARCH 2011 | 16.30-17.05
A new class of
turbulence - insights
from the perspective of
n-point statistics
R. Stresing, J. Peinke
Institute of Physics, University of Oldenburg, GERMANY
monday 28 MARCH 2011 | 17.05-17.40
The wake structure,
energy decay and
intermittency behind a
fractal fence
C.J. Keylock
Department of Civil Engineering, University of Sheffield, UK
R.E. Seoud, J.C. Vassilicos
Department of Aeronautics, Imperial College London, UK
We apply a method based on the theory of Markov processes to fractal-generated
turbulence and obtain joint probabilities of velocity increments at several scales.
From experimental data we extract a Fokker-Planck equation which describes
the interscale dynamics of the turbulence. In stark contrast to all documented
boundary-free turbulent flows, the multiscale statistics of velocity increments, the
coefficients of the Fokker-Planck equation, and dissipation-range intermittency are
all independent of Reynolds number. These properties define a qualitatively new
class of turbulence. Furthermore we use the multiscale statistics of homogeneous
isotropic turbulence which can described by a stochastic “cascade” process of the
velocity increment from scale to scale by a Fokker-Planck equation. We show how
this description can be extended to obtain the complete multi-point statistics of the
velocity field, i.e. we achieve an explicit expression for the joint probability p(u(x 1
),
u(x 2
), ..., u(x n
)), where u(x i
) is the velocity at the spatial point x i
(spatial point are
obtained along one line using Taylor’s hypothesis of frozen turbulence). We extend
the stochastic cascade description by conditioning on the velocity value itself and
find that the corresponding process is also governed by a Fokker-Planck equation,
which contains as a leading term a simple additional velocity-dependent coefficient
in the drift function. Taking into account the velocity dependence of the Fokker-
Planck equation, the multi-point statistics in real space can be expressed by the
two-scale statistics of velocity increments, which are equivalent to the three-point
statistics of the velocity field. Thus, we propose a stochastic three-point closure for
the velocity field of homogeneous isotropic turbulence.
This paper reports the results of experiments on the structure of the wake behind
fences inserted in a boundary layer flow in a wind tunnel, which was undertaken in
the Shinjo wind tunnel in Japan, with Kouichi Nishimura (University of Nagoya) and
colleagues at the Nagaoka Institute for Snow and Ice Studies. The fences varied in
their porosity and the spacing of struts but, in addition, two fences were deployed
where the struts were organised in a fractal pattern. Hence, this study marks a
departure from previous work that has focussed on the flow structure behind fractal
fences away from boundaries.
In general our results indicate that the nature of the fence, such as its porosity, has
a larger control on wake structure than the Reynolds number of the flow (flows had
mean input velocities of either 6 ms -1 or 8 ms -1 ). However, we also find cases where
the multiscale nature of the forcing with the fractal fences results in differences in
wake structure that are greater than those due to porosity or Reynolds number. In
particular, we show that the proportion of dissipation taking place over the range of
forced scales is greater for the fractal fences and given the slope of the spectrum in
this region, the implication is that the scale-to-scale transfer over this region is not
inertial in a strict sense. This result parallels that from other studies on multiscale
forcing in recent years by Vassilicos and coworkers.
In order to study this effect in more detail, we also examine the properties of
synthetic turbulence generated from the experimental time series and by a
comparison to the forcings at individual scales, attempt to identify the manner in
which the unique properties of the fractal-forced flows become manifest.
12 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 13

FOURTH session | Flow design for applications
Flow design for applications | FOURTH session
TUESDAY 29 MARCH 2011 | 9.15-9.50
Mixing of high-Schmidt
number scalar in regular/
fractal grid turbulence:
Experiments by PIV and PLIF
Y. Sakai, K. Nagata, H. Suzuki, and R. Ukai
Department of Mechanical Science and Engineering, Nagoya
University, Japan
Turbulent mixing of high-Schmidt-number passive scalar in the regular and fractal
grid turbulence is experimentally investigated using a water channel. A turbulence
generating grid is installed at the entrance to the test section, which is 1.5 m in
length and 0.1 m x 0.1 m in the cross section. Two types of grids are used: one
is a regular grid of the square-mesh and biplane construction, and another is a
square type fractal grid, which was first investigated by Hurst & Vassilicos [4] and
Seoud & Vassilicos [5]. Both grids have the same solidity of 0.36. The Reynolds
number based on the mesh size, Re M
= U 0
M eff
/ν is 2,500 in both flows, where U 0
is the cross-sectionally averaged mean velocity, M eff
is the effective mesh size and
ν is the kinematic viscosity. A fluorescent dye (Rhodamine B) is homogeneously
premixed only in the lower half stream, and therefore, the scalar mixing layers with
an initial step profile develop downstream of the grids. The Schmidt number of
the dye is O(10 3 ). The time-series particle image velocimetry (PIV) and the planar
laser induced fluorescence (PLIF) technique are used to measure the velocity and
concentration field. The results show that the turbulence intensity in the fractal
grid turbulence is much larger than the one in the regular grid turbulence (See
Fig.1), and the turbulent mixing in the fractal grid turbulence is strongly enhanced
compared with in the regular grid turbulence at the same Re M
(See Fig.2). It is also
found that the scalar dissipation takes place locally even in the far downstream
region at M eff
= 120 in the fractal grid turbulence.
TUESDAY 29 MARCH 2011 | 9.50-10.25
Aero-acoustic
performance of
fractal spoilers
J. Nedic, B. Ganapathisubramani, J.C. Vassilicos
Department of Aeronautics, Imperial College London, UK
J. Boree, L.E. Brizzi, A. Spohn
Institut P’, CNRS • ENSMA • Universite de Poitiers, FRANCE
One of the major environmental problems facing the aviation industry is that of
aircraft noise. The work presented here, done as part of the EU’s OPENAIR Project,
looks at reducing spoiler noise whilst maintaining lift and drag characteristics
through means of large-scale fractal porosity. It is hypothesised that the highly
turbulent flow generated by fractal grids, which have multiple-length-scales, would
reduce the impact of the re-circulation region and with it, the low frequency noise
it generates. In its place, a higher frequency noise is introduced which is more
susceptible to atmospheric attenuation and could be deemed less offensive to
the human ear. A total of nine laboratory scaled spoilers were looked at, seven
of which had a fractal design, one with a regular grid design and one solid for
reference. The spoilers were inclined at an angle of 30 o . Force, acoustic and flow
visualisation experiments on a flat plate were carried out, where it was found that
the present fractal spoilers reduce the low frequency noise by 2.5dB. Results show
that it is possible to improve the acoustic performance by modifying a number of
parameters defining the fractal spoiler, some of them very sensitively. From these
experiments, two fractal spoilers were chosen for a detailed aero-acoustic study on
a three-element wing system, where it was found that the fractal spoilers had a 1dB
reduction in the sound pressure level and were also able to maintain the amount of
lift and drag generated by the wing system.
Figure 1 The streamwise evolutions of
streamwise velocity fluctuation intensity
normalized by
Figure 2 Instantaneous fluctuating concentration field at
around x/M eff = 80 by the regular grid (left side) and the fractal
square grid (right side). Red: c = 0.3, Blue: c = -0.3.
Note: M eff = 10 mm for the regular grid (left side),
M eff = 5.68 mm for the fractal grid (right side)
14 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 15

FOURTH session | Flow design for applications
Flow design for applications | FOURTH session
TUESDAY 29 MARCH 2011 | 11.00-11.35
Turbulent premixed
flames in fractal-gridgenerated
turbulence
N. Soulopoulos 1 , J. Kerl 1 , F. Beyrau 1 , Y. Hardalupas 1 , A.M.K.P.
Taylor 1 and J.C. Vassilicos 2
1
Department of Mechanical Engineering, Imperial College London, UK
2
Department of Aeronautics, Imperial College London, UK
TUESDAY 29 MARCH 2011 | 11.35-12.10
A parametric study about
the effect of fractal-grid
generated turbulence on the
structure of premixed flames
T. Sponfeldner 1 , S. Henkel 1 , N. Soulopoulos 1 , F. Beyrau 1 ,
Y. Hardalupas 1 , A.M.K.P. Taylor 1 , J.C. Vassilicos 2
1
Department of Mechanical Engineering, Imperial College London, UK
2
Department of Aeronautics, Imperial College London, UK
Reactions between fuel and oxidiser take place at the molecular level, so turbulent
motion at the smallest scales has an immediate effect on the process. We are
concerned here with premixed combustion, where the fuel and the oxidiser are
homogeneously mixed before reacting; spark-ignition internal combustion engines
are a notable example of premixed combustion in applications. In the flamelet
description of turbulent premixed combustion, the thickness of a laminar flame with
the same fuel-to-air ratio remains relatively unaffected by the turbulence. A main
effect of turbulence is, through the stretch rate, to increase the surface area of the
flamelets and, thus, increase the reaction rate.
The parameters used to describe a premixed flame are the normalised turbulent
fluctuations u’/s L
where u’ is the rms of the turbulent fluctuations and s L
is the laminar
flame speed, and the ratio l/l F
where l is the integral length scale and l F
is the laminar
flame thickness.
Turbulent premixed flames are established in a square burner, where a regular
square mesh grid and a space-filling fractal square grid are used to generate
turbulence at various distances upstream of the flame stabilisation position, so
different values of u’/s L
and l/l F
are obtained; 0.76 < u’/s L
< 1.79 and 7.1 < l/l F
< 11.8.
The measurement techniques include OH* chemiluminescence and OH Planar
Laser Induced Fluorescence (PLIF) which are used to measure the turbulent flame
speed, the flame width, the instantaneous flame front, the flame curvature and the
flame surface density.
The main result of the present measurements is that, at the same level of
normalised turbulent fluctuations and similar integral length scales, the flames
show larger turbulent flame speeds when using the fractal grid than when using the
square grid. An attempt to explain this difference relates to the different turbulence
decay between normal- and fractal grid-generated turbulence.
‘Fractal’ or multiscale turbulence-generating grids produce bespoke turbulent flows
designed for the particular application at hand [4]. They allow more design and
optimisation flexibility than conventional turbulence generators like perforated
plates, for example, and generate high turbulence intensity at some distance away
from the grid and over a long region downstream at a low pressure drop cost. This
extended region of high turbulence intensity and the fact that it is possible to design
where this region starts and its overall extent are of great interest for premixed
combustion and may pave the way for future fractal combustors particularly adept
at operating at the lean premixed combustion regime where NOx-emissions are
the lowest. The high turbulence intensity, in particular, increases turbulent burning
speed and leads to higher power densities of the flame. In previous work we
observed a significant increase of turbulent flame speed when using a fractal
instead of a regular grid [12].
In this work we further investigate the influence of fractal-grid generated turbulence
on the structure of a premixed V-shaped methane-air flame. For a parametric
study, a set of different space-filling fractal square grids is designed and several
design parameters such as the blockage ratio and the ratio between the sizes of
the largest and the smallest structures of the fractal grids are varied independently
from each other. A regular square mesh grid with the same blockage ratio as two
of the fractal grids acts as reference case. The velocity fields for the different grids
are characterized based on hot wire measurements. The structure of the generated
flames is investigated using the conditioned particle image velocimetry technique
[13]. Quantities like the flame brush thickness, flame surface density and the
turbulent burning velocity as well as the flow field characteristics are compared.
Preliminary results show significantly higher corrugation of the flames and larger
flame brush thicknesses for all fractal grids.
16 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 17

FIFTH session | Simulations
Simulations | FIFTH sessioN
TUESDAY 29 MARCH 2011 | 13.30-14.05
Turbulence
modulation through
broad-band forcing
B. Geurts
Twente University, HOLLAND
TUESDAY 29 MARCH 2011 | 14.05-14.40
Direct Numerical
Simulation of
multiscale generated
turbulence
S. Laizet, J. C. Vassilicos
Department of Aeronautics, Imperial College London, UK
E. Lamballais, V. Fortuné
Institut P’, CNRS • ENSMA • Universite de Poitiers, FRANCE
The response of turbulent flow to forcing that is simultaneously imposed at a variety
of length- scales is investigated numerically. This is a prime example of “modulated
turbulence” in which a pre-specified departure from Kolmogorov turbulence is the
target, e.g. to control mixing-rates or emphasize certain length-scales to stimulate
embedded small scale chemical processes. We review the direct forcing approach
and discuss the response to time-modulated forcing. Comparison is made with
theoretical predictions. The occurrence of response maxima is presented and
interpreted in terms of experimental observations reported in literature. A central
remaining issue is the rigorous connection between the “modulating mechanism”
and the associated broadband forcing. In case the modulation is derived from flow
through complex gasket-structures, the possibility offered by immersed boundary
methods to represent the flow and the geometry in all their details, is discussed.
Some simulation results for turbulent pipe flow, tripped by flanges derived from
fractal geometries, are presented.
Multiscale (fractal) geometry is a concept in which a given pattern is repeated and
split into parts, each of which being a reduced-copy of the whole. Multiscale (fractal)
objects can be designed to be immersed in any fluid flow where there is a need to
control the turbulence generated by the object. Experiments carried out at Imperial
College London have shown that such objects can be used to control and manage
the transition from laminar to turbulent flows. It was found that, unlike a regular
object (where the turbulence is generated by only one scale), a slight modification of
one of the object’s parameters can deeply modify the turbulence generated by the
fluid’s impact on the object. Multiscale objects offer the opportunity to discover new
complex flow effects/interactions that can help understand how to control and/or
manage complex fluid flows. Furthermore, such multiscale objects can be designed
as energy-efficient mixers, be designed to have a high sound transmission loss,
be used around and/or inside buildings in order to reduce the cost of heating and/
or cooling and therefore save energy (opening vents, louvres, etc.) or be used to
force drifting of snow or sand to occur in a predictable place, rather than randomly.
The experiments from Imperial College were performed without time for
optimisation and adaptation. Hence, possibilities for improvement are considerable
with the potential to set new industrial standards. However, the development of
such new flow solutions cannot be bring to fruition without a clear understanding
of the unique properties of multiscale-generated flows. It is clear that carrying out
experiments will help to tackle this ambitious task but will not be enough, even
with advanced visualisation tools. It is absolutely necessary to undertake numerical
simulations of such complex flows. In this work, these multiscale-generated flows
will be investigated using High Performance Computing (HPC) resources [14,15]. It
provides an opportunity to understand their highly unusual properties and it will be
very useful to propose high-quality standards of new technologies.
18 turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: fundamentals and applications 19

FIFTH session | Simulations
Simulations | FIFTH sessioN
TUESDAY 29 MARCH 2011 | 15.00-15.35
LES of opposed jet
flows employing
fractal turbulencegenerating
plates
M. Pettit, S. Wysocki, P. Geipel, A. M. Kempf
Department of Mechanical Engineering, Imperial College London, UK
TUESDAY 29 MARCH 2011 | 15.35-16.10
DNS on spatially
developing fractal
generated turbulence
with heat transfer
H. Suzuki 1 , K. Nagata 1 , Y. Sakai 1 , T. Hayase 2
1
Department of Mechanical Science and Engineering, Nagoya
University, JAPAN
2
Institute of Fluid Science, Tohoku University, Sendai, JAPAN
Generation of fully developed, isotropic turbulence is essential for the entire
range of industrial combustors, as it promotes the mixing of reacting species and
therefore improves efficiency in burning and reduces the emission of harmful waste
products. However, such turbulence must typically be generated actively, which is
often achieved by incorporating a swirl design. In laboratory experiments, blocking
plates, grids or meshes, which are designed to encourage the transition from
laminar to turbulent Large Eddy flow, Simulation are also of Opposed used. Jet Flows Employing Fractal Turbulence-
Opposed jet configurations are widely Generating used Plates for the investigation of laminar and
turbulent premixed [16], partially-premixed
M. Pettit, S. Wysocki, P.
[17]
Geipel,
and
A. M.
non-premixed
Kempf
flames [18]. The
compactness of the flow domain is of benefit to experimental and numerical studies
Imperial College, Exhibition Road, London SW7 2AZ, UK, e-mail: a.kempf@imperial.ac.uk
alike, while good optical access to the stagnation plane and flame is permitted
Generation of fully developed, isotropic turbulence is essential for the entire range of industrial
for the laser-based measurement techniques used to obtain two-dimensional
combustors, as it promotes the mixing of reacting species and therefore improves efficiency in
velocity and burning scalar and reduces data. the Through emission of the harmful use waste of products. a fractal However, turbulence-generating such must plate
typically be generated actively, which is often achieved by incorporating a swirl design. In
(Fig. 1) positioned
laboratory experiments,
downstream
blocking
of
plates,
the
grids
conventional
or meshes, which
perforated
are designed to
plate,
encourage
Geipel
the
et al.
[19] report transition a significant from laminar increase to turbulent flow, in are turbulent also used. Reynolds numbers achieved for the
configuration, Opposed while jet configurations avoiding are extinction widely used for of the the investigation flame of due laminar to and excessive turbulent premixed strain rates
at the stagnation [1], partially-premixed plane. [2] The and non-premixed generated [3] flames. turbulence The compactness has of been the flow shown domain is of to be fully
benefit to experimental and numerical studies alike, while good optical access to the stagnation plane
developed and flame isotropic permitted near for the to laser-based the nozzle measurement exit techniques planes. used to obtain two-dimensional
In the present
velocity and
work,
scalar
LES
data. Through
is used
the use
to
of a
acquire
fractal turbulence-generating
a more complete
plate (Fig. 1)
understanding
positioned
of
downstream of the conventional perforated plate, Geipel et al. [4] report a significant increase in
the mechanisms turbulent Reynolds that provide numbers achieved this level for the of configuration, turbulence, while avoiding by allowing extinction of inspection the flame of the
due to excessive strain rates at the stagnation plane. The generated turbulence has been shown to be
flow field development within nozzles of the opposed jets (Fig. 2). Statistical
fully developed and isotropic near to the nozzle exit planes.
measures of first and second moments of flow velocity are obtained from simulations
In the present work, Large Eddy Simulation is used to acquire a more complete understanding of the
and compared
mechanisms
to in-nozzle
that provide
measurements.
this level of turbulence,
Entirely
by allowing
accurate
inspection of
representation
the flow field
of the
complex plate development geometry within the nozzles requires of the opposed grid resolutions jets (Fig. 2). Statistical typical measures of of first a Direct and second Numerical
moments of flow velocity are obtained from simulations and compared to in-nozzle measurements.
Simulation. Entirely The accurate study representation also aims of the to complex provide plate geometry a deeper requires insight grid resolutions into typical the of application
a
of the theory Direct upon Numerical which Simulation. the The study fractal also aims plate to provide was a deeper designed, insight into the and application may of potentially
the theory upon which the fractal plate was designed, and may potentially suggest modifications or
suggest modifications improvements that may or improvements be made to further improve that the may characteristics be made of the flow to within further region improve the
characteristics
of the flame.
of the flow within the region of the flame.
In recent years, fundamental characteristics of fractal generated turbulence (FGT)
[4] are investigated experimentally. The most noteworthy characteristic of FGT is a
constancy of the integral length scale in the streamwise direction [5]. In this work,
we focus on the heat transfer generated by the constant mean temperature gradient
[20, 21] in the FGT by means of direct numerical simulation. It is known that the
temperature variance DNS on Spatially generated Developing by the mean Fractal temperature Generated Turbulence gradient exponentially
with Heat Transfer
increases in the streamwise direction [20]. This streamwise evolution corresponds
to an exponential increase H. Suzuki of the 1 , K. Nagata large 1 , Y. scale Sakai 1 ,[20]. and T. Thus, Hayase 2
it is worth investigating
the streamwise evolution of the temperature fluctuation generated by the constant
1 Department of Mechanical Science and Engineering, Nagoya University, Nagoya, Japan
mean temperature gradient 2 Institute in of Fluid the Science, spatially Tohoku developing University, Sendai, FGT. Japan
hsuzuki@nagoya-u.jp
Direct numerical simulations based on the finite difference method is used for
A BST R A C T
analysis of the heat transfer phenomena generated by constant mean temperature
In recent years, fundamental characteristics of fractal generated turbulence (FGT) 1 are investigated
gradient experimentally. in the spatially The most noteworthy developing characteristic FGT. of FGT Our is a numerical constancy of the techniques integral length scale are in based
streamwise direction
on the numerical scheme 2 . In this work, we focus on the heat transfer generated by the constant mean temperature
gradient 3,4 in the FGT by means developed of the direct numerical by Morinishi simulation. It et is known al. [22], that the which temperature enables variance us to
generated by the mean temperature gradient exponentially increases in streamwise direction
perform DNS with analytically-expanded conservation of velocity 3 . This streamwise
and temperature
evolution corresponds to exponential increase of the large scale 3 . Thus, it is worth investigating the streamwise
fluctuations. evolution In of addition, temperature fluctuation higher generated order terms, by the constant i.e, mean viscous temperature and gradient diffusion in the spatially terms, were
developing FGT.
discretized Direct by numerical the higher-order simulation based on central the finite difference compact method schemes is used for analysis [23] of and the heat Fourier transfer series
expansion. phenomena Figure generated 1 by shows constant mean the temperature streamwise gradient in evolutions the spatially developing of temperature FGT. Our numerical variance
techniques are based on the numerical scheme developed by Morinishi et al. 5 , which enables us to perform DNS
in the fractal with analytically-expanded and classical conservation grid turbulence. of velocity and temperature The fluctuations. temperature In addition, variance higher order terms, in classical
i.e, viscous and diffusion terms, were discretized by the higher-order central compact schemes
grid turbulence increases exponentially. In contrast, that in FGT 6 and Fourier series
expansion. Figure 1 shows the streamwise evolutions of temperature variance in the fractal and classical
monotonically
grid
decreases turbulence. in downstream The temperature variance region, in classical where grid turbulence increases is exponentially. decaying. In contrast, that in FGT
monotonically decreases in downstream region, where turbulence is decaying.
Figure 1: The fractal cross
grid used in the present work.!
Figure 2: The resulting instantaneous axial velocity field within a single
nozzle, corresponding to section ‘A-A’ in Fig. 1. Blue dashed lines
indicate positions of the perforated TGP and fractal cross grid.
Figure 1 The streamwise evolutions of temperature variance in fractal (FGT) and classical (CGT) grid turbulence
References
1 D. Hurst and J. C. Vassilicos, Phys. Fluids 19, 035103 (2007).
2 R. E. Seoud and J. C. Vassilicos, Phys. Fluids 19, 105108 (2007).
20 turbulent flows generated/designed ! in multiscale/fractal ways: fundamentals and applications
turbulent flows generated/designed in multiscale/fractal ways: 3 A. Sirivat and Z. Warhaft, J. Fluid Mech. 128, 323-346 (1983).
fundamentals and applications 21
References
4 M. R. Overholt and S. B. Pope, Phys. Fluids 8, 3128 (1996).
[1] Jones, W.P., Prasetyo, Y., Symp. (Int.) Combust. (1996) 26:275-282
5 Y Morinishi, J. Comput. Phys. 143, 90-124 (1998).

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